Campbell Scientific EasyFlux DL CR6OP Owner Manual

Campbell Scientific EasyFlux  DL CR6OP Owner Manual
Product Manual
EASYFLUX DL CR6OP
For CR6 and Open-Path
Eddy-Covariance System
Revision: 02/2020
Copyright © 2017 – 2020
Campbell Scientific, Inc.
Limited Warranty
“Products manufactured by CSI are warranted by CSI to be free from defects in
materials and workmanship under normal use and service for twelve months
from the date of shipment unless otherwise specified in the corresponding
product manual. (Product manuals are available for review online at
www.campbellsci.com.) Products not manufactured by CSI, but that are resold
by CSI, are warranted only to the limits extended by the original manufacturer.
Batteries, fine-wire thermocouples, desiccant, and other consumables have no
warranty. CSI’s obligation under this warranty is limited to repairing or
replacing (at CSI’s option) defective Products, which shall be the sole and
exclusive remedy under this warranty. The Customer assumes all costs of
removing, reinstalling, and shipping defective Products to CSI. CSI will return
such Products by surface carrier prepaid within the continental United States of
America. To all other locations, CSI will return such Products best way CIP
(port of entry) per Incoterms® 2010. This warranty shall not apply to any
Products which have been subjected to modification, misuse, neglect, improper
service, accidents of nature, or shipping damage. This warranty is in lieu of all
other warranties, expressed or implied. The warranty for installation services
performed by CSI such as programming to customer specifications, electrical
connections to Products manufactured by CSI, and Product specific training, is
part of CSI's product warranty. CSI EXPRESSLY DISCLAIMS AND
EXCLUDES ANY IMPLIED WARRANTIES OF MERCHANTABILITY
OR FITNESS FOR A PARTICULAR PURPOSE. CSI hereby disclaims,
to the fullest extent allowed by applicable law, any and all warranties and
conditions with respect to the Products, whether express, implied or
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Assistance
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contact information is for US and international customers residing in countries
served by Campbell Scientific, Inc. directly. Affiliate companies handle repairs
for customers within their territories. Please visit www.campbellsci.com to
determine which Campbell Scientific company serves your country.
To obtain a Returned Materials Authorization (RMA) number, contact
CAMPBELL SCIENTIFIC, INC., phone (435) 227-9000. Please write the
issued RMA number clearly on the outside of the shipping container. Campbell
Scientific’s shipping address is:
CAMPBELL SCIENTIFIC, INC.
RMA#_____
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For all returns, the customer must fill out a “Statement of Product Cleanliness
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concerns for our employees.
Safety
DANGER — MANY HAZARDS ARE ASSOCIATED WITH INSTALLING, USING, MAINTAINING, AND WORKING ON OR AROUND
TRIPODS, TOWERS, AND ANY ATTACHMENTS TO TRIPODS AND TOWERS SUCH AS SENSORS, CROSSARMS, ENCLOSURES,
ANTENNAS, ETC. FAILURE TO PROPERLY AND COMPLETELY ASSEMBLE, INSTALL, OPERATE, USE, AND MAINTAIN TRIPODS,
TOWERS, AND ATTACHMENTS, AND FAILURE TO HEED WARNINGS, INCREASES THE RISK OF DEATH, ACCIDENT, SERIOUS
INJURY, PROPERTY DAMAGE, AND PRODUCT FAILURE. TAKE ALL REASONABLE PRECAUTIONS TO AVOID THESE HAZARDS.
CHECK WITH YOUR ORGANIZATION'S SAFETY COORDINATOR (OR POLICY) FOR PROCEDURES AND REQUIRED PROTECTIVE
EQUIPMENT PRIOR TO PERFORMING ANY WORK.
Use tripods, towers, and attachments to tripods and towers only for purposes for which they are designed. Do not exceed design limits.
Be familiar and comply with all instructions provided in product manuals. Manuals are available at www.campbellsci.com or by
telephoning (435) 227-9000 (USA). You are responsible for conformance with governing codes and regulations, including safety
regulations, and the integrity and location of structures or land to which towers, tripods, and any attachments are attached. Installation
sites should be evaluated and approved by a qualified engineer. If questions or concerns arise regarding installation, use, or
maintenance of tripods, towers, attachments, or electrical connections, consult with a licensed and qualified engineer or electrician.
General
• Prior to performing site or installation work, obtain required approvals and permits. Comply
with all governing structure-height regulations, such as those of the FAA in the USA.
• Use only qualified personnel for installation, use, and maintenance of tripods and towers, and
any attachments to tripods and towers. The use of licensed and qualified contractors is highly
recommended.
• Read all applicable instructions carefully and understand procedures thoroughly before
beginning work.
• Wear a hardhat and eye protection, and take other appropriate safety precautions while
working on or around tripods and towers.
• Do not climb tripods or towers at any time, and prohibit climbing by other persons. Take
reasonable precautions to secure tripod and tower sites from trespassers.
• Use only manufacturer recommended parts, materials, and tools.
Utility and Electrical
• You can be killed or sustain serious bodily injury if the tripod, tower, or attachments you are
installing, constructing, using, or maintaining, or a tool, stake, or anchor, come in contact with
overhead or underground utility lines.
• Maintain a distance of at least one-and-one-half times structure height, 20 feet, or the distance
required by applicable law, whichever is greater, between overhead utility lines and the
structure (tripod, tower, attachments, or tools).
• Prior to performing site or installation work, inform all utility companies and have all
underground utilities marked.
• Comply with all electrical codes. Electrical equipment and related grounding devices should be
installed by a licensed and qualified electrician.
Elevated Work and Weather
• Exercise extreme caution when performing elevated work.
• Use appropriate equipment and safety practices.
• During installation and maintenance, keep tower and tripod sites clear of un-trained or nonessential personnel. Take precautions to prevent elevated tools and objects from dropping.
• Do not perform any work in inclement weather, including wind, rain, snow, lightning, etc.
Maintenance
• Periodically (at least yearly) check for wear and damage, including corrosion, stress cracks,
frayed cables, loose cable clamps, cable tightness, etc. and take necessary corrective actions.
• Periodically (at least yearly) check electrical ground connections.
WHILE EVERY ATTEMPT IS MADE TO EMBODY THE HIGHEST DEGREE OF SAFETY IN ALL CAMPBELL SCIENTIFIC PRODUCTS,
THE CUSTOMER ASSUMES ALL RISK FROM ANY INJURY RESULTING FROM IMPROPER INSTALLATION, USE, OR
MAINTENANCE OF TRIPODS, TOWERS, OR ATTACHMENTS TO TRIPODS AND TOWERS SUCH AS SENSORS, CROSSARMS,
ENCLOSURES, ANTENNAS, ETC.
Table of Contents
PDF viewers: These page numbers refer to the printed version of this document. Use the
PDF reader bookmarks tab for links to specific sections.
1. Introduction................................................................ 1
2. Precautions ................................................................ 2
3. Installation ................................................................. 2
3.1
Wiring ..................................................................................................2
3.1.1 IRGA and Sonic Anemometer ......................................................3
3.1.2 CDM-A116 or VOLT 116 Module ...............................................3
3.1.3 GPS Receiver ................................................................................3
3.1.4 Fine-Wire Thermocouple ..............................................................4
3.1.5 Temperature and Relative Humidity Probe ...................................4
3.1.6 Radiation Measurements Option 1 ................................................5
3.1.7 Radiation Measurements Option 2 ................................................6
3.1.8 Precipitation Gage .........................................................................8
3.1.9 Soil Temperature ...........................................................................8
3.1.10 Soil Water Content ........................................................................9
3.1.11 Soil Heat Flux Plates ...................................................................10
3.1.12 Self-Calibrating Soil Heat Flux Plates ........................................11
4. Operation ................................................................. 12
4.1
4.2
4.3
4.4
4.5
Set Constants in CRBasic Editor and Load Program .........................12
Enter Site-Specific Variables with Data Logger Keypad or
LoggerNet .......................................................................................14
Data Retrieval ....................................................................................24
Output Tables .....................................................................................24
Program Sequence of Measurement and Corrections.........................45
5. References ............................................................... 46
Appendices
A. Vapor Pressure and Dewpoint Temperature ....... A-1
A.1
A.2
A.3
A.4
A.5
Equations to Calculate Dewpoint Temperature from Water
Vapor Density .............................................................................. A-1
Approach to Approximation of Td for the Enhancement Factor ..... A-2
Dewpoint Temperature Equation .................................................... A-3
Online Flux Program ....................................................................... A-3
Reference ........................................................................................ A-4
B. Coordinate Rotations: Double Rotation Method . B-1
B.1
B.2
Matrix Transformation of Instrument to Flow Coordinate
System ..........................................................................................B-1
Natural Wind Coordinated System...................................................B-2
i
Table of Contents
B.2.1 Covariance of Momentum Variables after Coordinate
Rotation .................................................................................B-3
B.2.2 Covariance of a Scalar Variable and Momentum Variable
After Second Coordinate Rotation.........................................B-4
B.3
Extended Equations ..........................................................................B-5
B.4
References ........................................................................................B-6
C. Coordinate Rotations: Planar Fit Method ............ C-1
C.1
C.2
Planar Fit ..........................................................................................C-1
Algorithm .........................................................................................C-3
C.2.1 Variables and Model .................................................................C-3
C.2.2 Covariance of Momentum Variables After Two Coordinate
Rotations ................................................................................C-3
C.2.3 Covariance of a Scalar Variable with Momentum Variable
After Planar Fit Coordinate Rotation .....................................C-4
C.3
Extended Equations ..........................................................................C-6
C.4
References ........................................................................................C-7
D. Frequency Corrections ......................................... D-1
D.1
D.2
Introduction ..................................................................................... D-1
Frequency Loss ............................................................................... D-1
D.2.1 High Frequency Loss ............................................................... D-1
D.2.2 Low Frequency Loss ................................................................ D-2
D.3 Model for Frequency Loss Corrections ........................................... D-2
D.4 Covariance Variables Requiring Frequency Corrections ................ D-3
D.4.1 Momentum Covariance ............................................................ D-3
D.4.2 Sonic Temperature Related Covariance ................................... D-3
D.4.3 Air Temperature Related Covariance ....................................... D-4
D.4.4 CO2 and H2O Related Covariance ............................................ D-4
D.5 Sensor Configuration and Separation Variables.............................. D-4
D.5.1 Path Length Variables .............................................................. D-4
D.5.2 Separation Variables ................................................................ D-5
D.5.3 Fine-Wire Thermocouple ......................................................... D-7
D.6 Surface Layer Atmospheric Stability .............................................. D-8
D.6.1 Aerodynamic Height ................................................................ D-8
D.6.2 Monin-Obukhov Length (L) .................................................... D-9
D.7 Cospectra ....................................................................................... D-10
D.7.1 Cospectra for z/L > 0 (stable surface layer) ........................... D-10
D.7.2 Cospectra for z/L ≤ 0 (neutral to unstable)............................. D-11
D.8 Sub-Transfer Functions ................................................................. D-12
D.8.1 Finite Time Block Averaging................................................. D-12
D.8.2 Line Averaging ...................................................................... D-13
D.8.3 Volume Averaging ................................................................. D-15
D.8.4 FIR Filtering........................................................................... D-16
D.8.5 Time Constant ........................................................................ D-16
D.8.6 Spatial Separation .................................................................. D-17
D.8.7 Total Transfer Function ......................................................... D-18
D.9 Working Model ............................................................................. D-19
D.10 Programmatic Approach to Computations for Correction
Factors ....................................................................................... D-19
D.11 References ..................................................................................... D-21
ii
Table of Contents
E. WPL Corrections .................................................... E-1
E.1
E.2
E.3
Basic Considerations ........................................................................ E-1
Governing Constraint and Mean Vertical Velocity .......................... E-3
Eddy Covariance Measurements ...................................................... E-4
E.3.1 CO2............................................................................................ E-4
E.3.2 H2O ........................................................................................... E-4
E.4
References ........................................................................................ E-5
F. Data Quality Grading .............................................. F-1
F.1
F.2
F.3
F.4
F.5
F.6
Relative Non-stationarity (RNcov) for Steady State ........................ F-1
Turbulent Conditions ....................................................................... F-2
Wind Direction in the Sonic Instrument Coordinate System
(wnd_dir_sonic) ............................................................................ F-5
Overall Quality Grade System ......................................................... F-5
Programmatic Approach .................................................................. F-6
References ........................................................................................ F-7
G. Footprint G-1
G.1
Kljun, et. al. (2004) Analytical Footprint Equations ....................... G-2
G.1.1 Models and Parameters ............................................................ G-2
G.1.2 Application of Analytical Footprint ......................................... G-4
G.1.3 Programmatic Approach .......................................................... G-7
G.2 Derivation of Equations for Upwind Locations at Inflection
Points of Footprint in Kljun et al. (2004) ................................... G-10
G.2.1 Footprint Model ..................................................................... G-10
G.2.2 Upwind location of maximum footprint................................. G-11
G.2.3 Upwind locations of inflection points .................................... G-11
G.3 Kormann and Meixner (2001) Analytical Footprint Equations ..... G-13
G.3.1 Footprint................................................................................. G-13
G.3.2 Programmatic Approach ........................................................ G-14
G.3.3 Application of analytical footprint ......................................... G-15
G.3.4 Programmatic Approach ........................................................ G-17
G.4 Derivation of Analytical Footprint in Kormann and Meixner
(2001)......................................................................................... G-19
G.4.1 Model Derivation ................................................................... G-19
G.4.2 Analytical expression: Vertical profile of eddy diffusivity .... G-20
G.4.3 Analytical expression: Crosswind integrated scalar
concentration distribution ................................................... G-21
G.5 Upwind Locations at Inflection Points of Footprint in
Kormann and Meixner (2001) ................................................... G-28
G.5.1 Footprint Model ..................................................................... G-29
G.5.2 Upwind Location of Maximum Footprint .............................. G-29
G.5.3 Upwind Location of Inflection Points in Footprint Curve ..... G-30
G.6 References ..................................................................................... G-31
H. Surface Energy Flux .............................................. H-1
I.
EasyFlux DL CR6OP Process Flow Diagram ......... I-1
iii
Table of Contents
Figures
4-1.
4-2.
B-1.
C-1.
D-1.
D-2.
Example screen from CRBasic Editor showing user-defined
configuration constants ...................................................................14
Custom keypad menu; arrows indicate submenus ..............................15
As viewed down the zm and z axes and assuming the vertical wind
component is zero, horizontal wind components vm and um are
measured in the instrument coordinate system and then rotated
by angle γ, yielding the streamwise wind velocity vector, u.
The u and v axes of the flow coordinate system are also
shown. ...........................................................................................B-2
Wind direction sectors for which planar fit angles are found by
the user and entered into the program. ..........................................C-2
The sonic coordinate system is shown with positive x, y, and z
axes. Note that the origin of the coordinate system should be
exactly in the center of the sonic volume; as shown, the origin
has been moved slightly downwards for convenience in
displaying the positive z-axis. ...................................................... D-6
The x and y spatial separations between a CSAT3A and EC150. ... D-7
Tables
3-1.
3-2.
3-3.
3-4.
3-5.
3-6.
3-7.
3-8.
3-9.
3-10.
3-11.
3-12.
3-13.
4-1.
4-2.
4-3.
4-4.
4-5.
4-6.
4-7.
4-8.
4-9.
4-10.
4-11.
D-1.
F-1.
F-2.
Default Wiring for IRGA and Sonic Anemometer ...............................3
Default Wiring for GPS Receiver ........................................................4
Default Wiring for Fine-Wire Thermocouple ......................................4
Default Wiring for Temperature and Relative Humidity Probe ...........5
Default Wiring for Radiation Measurement Option 1 ..........................5
Default Wiring for Radiation Measurements Option 2 ........................6
A21REL-12 Wiring (Used with CNF4) ...............................................8
Default Wiring for a CNF4 ..................................................................8
Default Wiring for Precipitation Gage .................................................8
Default Wiring for Soil Thermocouple Probes ....................................9
Default Wiring for Soil Water Content Probes ..................................10
Default Wiring for Non-Calibrating Soil Heat Flux Plates ................11
Default Wiring for Soil Heat Flux Plates (Self Calibrating) ..............11
Station Variables with Descriptions ...................................................16
Instrument Settings with Descriptions ...............................................21
Onsite Zero and Span Variables .........................................................23
microSD Flash Card Fill Times .........................................................24
Data Output Tables ............................................................................25
Data Fields in the Time_Series Data Output Table ............................26
Data Fields in the Diagnostic Output Table .......................................27
Data Fields in the Config_Setting_Notes Output Table .....................28
Data Fields in the Flux_AmeriFluxFormat Output Table ..................28
Data Fields in the Flux_CSFormat Data Output Table ......................31
Data fields in the Flux_Notes Output Table .......................................37
Numerical form (transfer function values versus normalize
frequencies) of sub-transfer function of buoyancy flux
measured by a CSAT3 ............................................................... D-15
Grades of relative non-stationarity, relative integral turbulence
characteristics, and wind direction in the sonic instrument
coordinate system. ........................................................................ F-2
Parameters in the model of integral turbulence characteristics
(ITC).1/ .......................................................................................... F-4
iv
Table of Contents
F-3.
G-1.
G-2.
Overall grades for each flux variable by the grades of relative
non-stationary, relative integral turbulence characteristic, and
wind direction in sonic instrument coordinate system.1/ ............... F-6
Estimated parameters in dimensionless footprint model (F3) ......... G-3
Relationship of Monin-Obukhov length (L) to planetary
boundary-layer height (h) ............................................................ G-8
v
EasyFlux® DL CR6OP
1.
Introduction
EasyFlux® DL CR6OP is a CRBasic program that enables a CR6 data logger to
collect fully corrected fluxes of CO2, latent heat (H2O), sensible heat, ground
surface heat flux (optional), and momentum from a Campbell Scientific openpath eddy-covariance (EC) system with optional GPS and energy balance
sensors. The program processes the EC data using commonly used corrections
in the scientific literature. Because the number of analog channels on the CR6
is limited, the program also supports the addition of a CDM-A116 or
VOLT 116 analog channel expansion module, which allows a full suite of
energy balance sensors, thus enabling the program to calculate the ground
surface heat flux and energy closure. Specifically, the program supports data
collection and processing from the following sensors.
Gas analyzer and sonic anemometer (qty 1)
Supports one combination of gas analyzer and sonic anemometer.
• EC150 with CSAT3A
• IRGASON
GPS Receiver (optional, qty 0 to 1)
• GPS16X-HVS
Fine-wire thermocouple (optional, qty 0 to 1)
• FW05
• FW1
• FW3
Biometeorology (biomet) and energy balance sensors (optional)
• Temperature/Relativity Humidity (RH) Probe (qty 0 to 1)
o HMP155A
o HMP155A:EE181
• Radiation measurements
o Option 1
− NR-LITE2 Net Radiometer (qty 0 to 1)
− CS301 or CS320 Pyranometer (qty 0 to 1)
− CS310 Quantum Sensor (qty 0 to 1)
− SI-111 Infrared Radiometer (qty 0 to 1)
o Option 2
− SN500SS or NR01 or CNR4, 4-Way Radiometer
(qty 0 to 1; if using the CN4, the CNF4 Ventilation
and Heating Unit is also supported)
• TE525MM Rain Gage (qty 0 to 1)
• TCAV Soil Thermocouple Probe (qty 0 to 3)
• Soil Water Content Reflectometer (qty 0 to 3)
o CS616
o CS650
o CS655
• Soil Heat Flux Plates
o Option 1: HFP01 plates (qty 0 to 3)
o Option 2: HFP01SC self-calibrating plates (qty 0 to 3)
EasyFlux is a registered trademark of Campbell Scientific, Inc.
1
EasyFlux® DL CR6OP
2.
3.
NOTE
It may be possible to customize the program for other sensors or
quantities in configurations not described here. Contact Campbell
Scientific for more information.
NOTE
In this manual, “IRGA” refers to either the EC150 or the
IRGASON infrared gas analyzer, “sonic anemometer” refers to
either the CSAT3A or IRGASON sonic anemometer, and “FW”
refers to a FW05, FW1, or FW3 fine-wire thermocouple.
Precautions
•
EasyFlux DL CR6OP requires the CR6 to have operating system (OS)
version 06.08 or newer, the EC100 to have OS version 07.05 or newer. If
using a CDM-A116, it must have OS 2.10 or newer; if using a VOLT 116,
it must have OS 1.0 or newer.
•
The program applies the most common open-path EC corrections to
fluxes. However, the user should determine the appropriateness of the
corrections for their site.
•
Campbell Scientific always recommends saving time-series data in the
event reprocessing of raw data is warranted. Further, the user should
determine the quality and fitness of all data for publication, regardless of
whether said data were processed by EasyFlux DL CR6OP or another tool.
•
As EasyFlux DL CR6OP is not encrypted, users have the ability to view
and edit the code. However, Campbell Scientific does not guarantee the
function of an altered program.
Installation
3.1
Wiring
Install of sensors and system components according to the respective product
manuals. When wiring the sensors to the data logger or to a CDM-A116 or
VOLT 116, the default wiring schemes, along with the number of instruments
EasyFlux DL CR6OP supports, should be followed if the standard version of
the program is being used. TABLE 3-1 through TABLE 3-13 present the
wiring schemes.
An IRGA with an associated sonic anemometer are the only required sensors
for the program. The additional sensors described in the following tables are
optional. Many of the optional sensors are wired to a CDM-A116 or
VOLT 116 module, which effectively increases the CR6 analog channels since
the CR6 itself does not contain enough channels for a full energy balance
sensor suite. If one or more of the optional sensors are not used, the data logger
terminals assigned to those sensor wires should be left unwired.
NOTE
If the standard data-logger program is modified, the wiring
presented in TABLE 3-1 may no longer apply. In these cases, refer
directly to the program code to determine proper wiring.
2
EasyFlux® DL CR6OP
3.1.1 IRGA and Sonic Anemometer
An open-path IRGA and sonic anemometer must be connected to the EC100
electronics, and the EC100 must be wired to a CR6 data logger for
EasyFlux DL CR6OP to be functional. TABLE 3-1 shows the default wiring
for these sensors.
TABLE 3-1. Default Wiring for IRGA and Sonic Anemometer
Sensor
IRGASON or
EC150/CSAT3A
(from EC100)
Quantity
1
Wire Description
Color
CR6 Terminal
SDM Data
Green
C1
SDM Clock
White
C2
SDM Enable
Red/Brown
C3
Signal Ground
Black
G (power ground)
Shield
Clear
AG ⏚ (analog ground)
3.1.2 CDM-A116 or VOLT 116 Module
Due to the limitations on channel count of the CR6, a CDM-A116 or
VOLT 116 module is required when using a fine-wire thermocouple, any of the
radiation sensors except the NR-Lite2, or any of the soil sensors. If using a
CDM-A116 or VOLT 116 prepare the instrument as follows:
1.
Connect the module to a 10-32 VDC power source.
2.
Launch Campbell Scientific’s Device Configuration Utility software
(v2.12 or newer) and select CDM-A100 Series among the list of
Peripheral devices. If this is the first time connecting, follow the
instruction on the main screen to download the USB driver to the PC.
3.
Select the appropriate COM port and click on the Connect button.
4.
Once connected, a list of settings is shown. Navigate to the bottom setting,
CPI Address. Change this value to 1. Click the Apply button at the
bottom of the page and exit the software.
5.
Use a Cat5e or Cat6 Ethernet Cable (included with the CDM-A116 or
VOLT 116) to connect the CPI port on the module to the CR6 CPI port.
3.1.3 GPS Receiver
A GPS receiver such as the GPS16X-HVS is optional, but will keep the datalogger clock synchronized to GPS time. If the CR6 clock differs by one
millisecond or more, EasyFlux DL CR6OP will resynchronize the data-logger
clock to match the GPS. The GPS receiver also calculates solar position.
TABLE 3-2 shows the default wiring for the GPS16X-HVS.
3
EasyFlux® DL CR6OP
TABLE 3-2. Default Wiring for GPS Receiver
Sensor
Quantity
GPS16X-HVS
Wire Description
Color
CR6 Terminal
PPS
Grey
U1
TXD
White
U2
Power Enable Ground
Yellow
G
Rx Data
Blue
G
Shield
Clear
12V
Red
Power Ground
Black
0 or 1
AG ⏚
12V
G
3.1.4 Fine-Wire Thermocouple
Several models of fine-wire thermocouple sensors are available that can be
integrated with the IRGA and sonic anemometer for direct measurements of
sensible heat flux. The EasyFlux DL CR6OP can support from zero to one
fine-wire thermocouple along with the IRGA and sonic anemometer. Shown in
TABLE 3-3 are the available types and default wiring for adding a fine-wire
thermocouple.
TABLE 3-3. Default Wiring for Fine-Wire Thermocouple
Sensor
Quantity
FW05, FW1, or
FW3
0 or 1
Wire Description
Color
CDM-A116 or VOLT 116 Terminal
Signal
Purple
Diff 15H
Signal Reference
Red
Diff 15L
Shield
Clear
AG ⏚
3.1.5 Temperature and Relative Humidity Probe
The EasyFlux DL CR6OP can support from zero to one temperature and
relative humidity probe with the IRGA and sonic anemometer. The default
wiring for the HMP155A or EE181 is shown in TABLE 3-4.
NOTE
There are two options for a temperature and relative humidity
probe, the HMP155A and the EE181. For details and
specifications of these probes, visit www.campbellsci.com. The
physical wiring to the CR6 data logger is the same for each sensor.
The colors of the wires, however, are different. The wire colors
for the EE181 sensor are noted by italic text in TABLE 3-4.
4
EasyFlux® DL CR6OP
TABLE 3-4. Default Wiring for Temperature and Relative Humidity Probe
Sensor
HMP155A/
EE181
Quantity
0 or 1
Wire Description
Color
CR6
Terminal
Temp Signal
Yellow/Yellow
U7
RH Signal
Blue/Blue
U8
Temp/RH Signal
Reference
White/Black
G1/
Shield
Clear/Clear
Power
Red/Red
AG ⏚
+12 V
Power Ground
Black/Black
G
1/Due
to terminal constraints, the temp/RH Probe is a single-ended (SE) voltage measurement. As an SE
measurement from a sensor that is powered continuously, the signal reference and power ground leads should
both be wired to ground (G).
3.1.6 Radiation Measurements Option 1
There are two options for making radiation measurements with
EasyFlux DL CR6OP. The program can support any combination of the four
sensors described in TABLE 3-5. Alternatively, it can support one of the three
types of four-way radiometers described in TABLE 3-6. TABLE 3-5 gives the
default wiring for Option 1. TABLE 3-6 shows the details of the default wiring
for Option 2.
TABLE 3-5. Default Wiring for Radiation Measurement Option 1
Sensor
NR-LITE2 Net
Radiometer
CS301
Pyranometer
CS320 Digital
Heated
Pyranometer
CS310
Quantum Sensor
Quantity
0 or 1
0 or 1
0 or 1
0 or 1
Wire Description
Color
CDM-A116 or VOLT 116
Terminal
(unless indicated as CR6)
Radiation Signal
Red
CR6 U11
Signal Reference
Blue
CR6 U121/
Shield
Black
Signal
White
Signal Reference
Black
Shield
Clear
SDI-12 Signal
White
Signal Reference
Blue
Shield
Clear
Power
Red
Power Ground
Black
CR6 G
Signal
White
Diff 10H
Signal Reference
Black
Diff 10L1/
Shield
Clear
CR6 AG ⏚
Diff 9H
Diff 9L2/
AG ⏚
CR6 U9
CR6 AG ⏚
CR6 AG ⏚
CR6 12V
AG ⏚
5
EasyFlux® DL CR6OP
TABLE 3-5. Default Wiring for Radiation Measurement Option 1
Sensor
SI-111 Infrared
Radiometer
Quantity
0 or 1
Wire Description
Color
CDM-A116 or VOLT 116
Terminal
(unless indicated as CR6)
Target Temp Signal
Red
Diff 11H
Target Temp Reference
Black
Diff 11L
Shield
Clear
Sensor Temp Signal
Green
Sensor Temp Reference
Blue
Voltage Excitation
White
AG ⏚
Diff 12H
AG ⏚
X3
to ⏚ with user-supplied wire
CS301 requires a jumper wire to connect CDM Diff 9L to CDM AG (analog ground)
1/Jumper
2/The
3.1.7 Radiation Measurements Option 2
Three models of four-way radiometers are compatible with the program
EasyFlux DL CR6OP: the SN500SS, NR01, and CNR4. However, only one
model at a time can be used due to channel limitations. The default wiring for
each of the four-way radiometers is shown in TABLE 3-6. TABLE 3-9 and
TABLE 3-10 give information on adding an optional CNF4 ventilation and
heater unit to the CNR4 4-way radiometer.
A CNF4 ventilation and heater unit may also be used with the CNR4 4-way
radiometer for more accurate radiation measurements. The CNF4 requires a
solid-state relay to control the ventilator and heater. An A21REL-12 4-channel
relay driver must be ordered (sold separately) and installed in the system
enclosure just below the CDM-A116 module. TABLE 3-7 lists the wiring
connections needed to power and control the A21REL-12. TABLE 3-8 lists the
wiring for the CNF4.
A CABLE3CBL-1, or similar 3-conductor 22 AWG cable, is recommended for
connections from the A21REL-12 to the CDM-A116, and a CABLEPCBL-1, or
similar 16 AWG 2-conductor power cable, is recommended for power
connections from the A21REL-12 to the DIN rail terminal block.
TABLE 3-6. Default Wiring for Radiation Measurements Option 2
Sensor
SN500SS 4Way
Radiometer
Quantity
0 or 1
Wire Description
Color
CDM-A116 or VOLT 116
Terminal
(unless indicated as CR6)
SDI-12
White
CR6 U9
Shield
Clear
Power
Red
Power Ground
Black
CR6 AG ⏚
CR6 12V
CR6 G
6
EasyFlux® DL CR6OP
TABLE 3-6. Default Wiring for Radiation Measurements Option 2
Sensor
NR01 4-Way
Radiometer
CNR4 4-Way
Radiometer
1/Jumper
Quantity
0 or 1
Wire Description
Color
CDM-A116 or VOLT 116
Terminal
(unless indicated as CR6)
Pyranometer Up Signal
Red (cbl 1)
Diff 9H
Pyranometer Up
Reference
Blue1/ (cbl 1)
Diff 9L1/
Pyranometer Down
Signal
White (cbl 1)
Diff 10H
Pyranometer Down
Reference
Green1/ (cbl 1)
Diff 10L1/
Pyrgeometer Up Signal
Brown (cbl 1)
Diff 11H
Pyrgeometer Up
Reference
Yellow1/ (cbl 1)
Diff 11L1/
Pyrgeometer Down
Signal
Purple (cbl 1)
Diff 12H
Pyrgeometer Down
Reference
Grey1/ (cbl 1)
Diff 12L1/
PT100 Signal2/
White (cbl 2)
Diff 4H
PT100 Reference
Green (cbl 2)
Diff 4L
Current Excite
Red (cbl 2)
X1
Current Return
Blue (cbl 2)
Shields
Clear
Pyranometer Up Signal
Red
Diff 9H
Pyranometer Up
Reference
Blue1/
Diff 9L1/
Pyranometer Down
Signal
White
Diff 10H
Pyranometer Down
Reference
Black1/
Diff 10L1/
Pyrgeometer Up Signal
Grey
Diff 11H
Pyrgeometer Up
Reference
Yellow1/
Diff 11L1/
Pyrgeometer Down
Signal
Brown
Diff 12H
Pyrgeometer Down
Reference
Green1/
Diff 12L1/
Thermistor Signal
White
Diff 4H
Thermistor V Excite
Red
X1
Thermistor Reference
Black
Shields
Clear
0 or 1
to ⏚ with user-supplied wire
AG ⏚
AG ⏚
AG ⏚
AG ⏚
The solid yellow, brown, and purple/pink wires on cable 2 are not used in this code, and may all be connected to G
2/
7
EasyFlux® DL CR6OP
TABLE 3-7. A21REL-12 Wiring (Used with CNF4)
A21REL-12 Terminal
Connecting Terminal
Cable/Wire
+12V
DIN rail terminal block: 12V
CABLEPCBL-1,
red wire
Ground
DIN rail terminal block: GND
CABLEPCBL-1,
black wire
CTRL 1
CDM-A116 SW5V #1
CABLE3CBL-1,
red wire
CTRL 2
CDM-A116 SW5V #2
CABLE3CBL-1,
black wire
CTRL 3
CDM-A116 SW5V #3
CABLE3CBL-1,
white wire
TABLE 3-8. Default Wiring for a CNF4
Sensor
CNF4
Quantity
0 or 1,
only use
if using a
CNR4
Wire Description
Color
CPEC306 Wiring
Tachometer Output
Green
CR6 U7
Tachometer
Reference
Grey
CR6 AG ⏚
Ventilator Power
Yellow
A21REL-12 REL 1 NO
Ventilator Ground
Brown
A21REL-12 REL G
Heater #1 Power
White
A21REL-12 REL 2 NO
Heater #1 Ground
Red
A21REL-12 REL G
Heater #2 Power
Black
A21REL-12 REL 3 NO
Heater #2 Ground
Blue
A21REL-12 REL G
3.1.8 Precipitation Gage
EasyFlux DL CR6OP can support a single TE525MM tipping rain gage, or a
precipitation gage can be omitted. The default wiring for the precipitation gage
is shown in TABLE 3-9.
TABLE 3-9. Default Wiring for Precipitation Gage
Sensor
TE525MM
Tipping Rain
Gage
Quantity
Wire Description
Color
CR6 Terminal
Pulse Output
Black
U6
Signal Ground
White
Shield
Clear
0 or 1
AG ⏚
AG ⏚
3.1.9 Soil Temperature
The TCAV is an averaging soil thermocouple probe used for measuring soil
temperature. EasyFlux DL CR6OP can support up to two TCAV probes. The
8
EasyFlux® DL CR6OP
order of wiring, however, is important. If only one TCAV sensor is used, it
must be wired as described for TCAV #1 in TABLE 3-10. An additional
TCAV sensor would be wired according to TCAV #2 in TABLE 3-10.
CAUTION
If only one TCAV is being used and it is wired to terminals
2H and 2L (leaving terminals 1H and 1L empty), the data
logger will not record any TCAV measurements.
TABLE 3-10. Default Wiring for Soil Thermocouple Probes
Sensor
TCAV #1
TCAV #2
TCAV #3
Quantity
0 or 1
0 or 1
0 or 1
NOTE
Wire Description
Color
CDM-A116 or VOLT 116
Terminal
Signal
Purple
Diff 1H
Signal Reference
Red
Diff 1L
Shield
Clear
Signal
Purple
Diff 2H
Signal Reference
Red
Diff 2L
Shield
Clear
Signal
Purple
Diff 3H
Signal Reference
Red
Diff 3L
Shield
Clear
AG ⏚
AG ⏚
AG ⏚
The CS650 or CS655 sensors also measure soil temperature. If the
CS650 or CS655 sensors are used but no TCAV probes are used,
EasyFlux DL CR6OP will use soil temperature from the CS650 or
CS655 to compute ground-surface heat flux. If available, soil
temperature from the TCAV probe is preferred since it provides a
better spatial average. See wiring details for these sensors in
TABLE 3-11.
3.1.10 Soil Water Content
EasyFlux DL CR6OP supports one of three models of soil water content
sensors: CS616, CS650, or CS655; up to three of one model is supported. A
soil water content sensor can also be omitted without affecting function. The
default wiring for each is shown in TABLE 3-11.
CAUTION
If only one soil water content sensor is being used, wire it
according to the first probe as described in TABLE 3-11. If
only one sensor is being used and it is wired according to
the second or third sensor, EasyFlux DL CR6OP will not
record any measurements from the soil water content
sensor.
9
EasyFlux® DL CR6OP
TABLE 3-11. Default Wiring for Soil Water Content Probes
Sensor
CS616 #1
CS616 #2
CS616 #3
CS650/CS655 #1
CS650/CS655 #2
CS650/CS655 #3
Quantity
0 or 1
0 or 1
0 or 1
0 or 1
0 or 1
0 or 1
Wire Description
Color
CR6 Terminal
Power
Red
+12 V
Signal Output
Green
U3
Enable
Orange
C4
Signal Ground
Black
Power Ground
Clear
Power
Red
+12 V
Signal Output
Green
U4
Enable
Orange
C4
Signal Ground
Black
Power Ground
Clear
Power
Red
+12 V
Signal Output
Green
U10
Enable
Orange
C4
Signal Ground
Black
Power Ground
Clear
SDI-12 Data
Green
U3
SDI-12 Power
Red
+12 V
SDI-12 Reference
Black
G
Shield
Clear
G
Not Used
Orange
SDI-12 Data
Green
SDI-12 Power
Red
+12 V
SDI-12 Reference
Black
G
Shield
Clear
Not Used
Orange
SDI-12 Data
Green
U3
SDI-12 Power
Red
+12 V
SDI-12 Reference
Black
G
Shield
Clear
Not Used
Orange
AG ⏚
G
AG ⏚
G
AG ⏚
G
AG ⏚
U3
AG ⏚
G
AG ⏚
G
3.1.11 Soil Heat Flux Plates
EasyFlux DL CR6OP can support from zero to three standard (non-selfcalibrating) soil heat flux plates. The default wiring for the standard soil heat
flux plates is shown in TABLE 3-12.
10
EasyFlux® DL CR6OP
TABLE 3-12. Default Wiring for Non-Calibrating Soil Heat Flux Plates
Sensor
Quantity
HFP01 #1
HFP01 #2
HFP01 #3
0 or 1
0 or 1
0 or 1
Wire Description
Color
CDM-A116 or VOLT 116
Terminal
Signal
White
Diff 5H
Signal Reference
Green
Diff 5L
Shield
Clear
Signal
White
Diff 6H
Signal Reference
Green
Diff 6L
Shield
Clear
Signal
White
Diff 7H
Signal Reference
Green
Diff 7L
Shield
Clear
AG ⏚
AG ⏚
AG ⏚
3.1.12 Self-Calibrating Soil Heat Flux Plates
EasyFlux DL CR6OP can also support from zero to three of the self-calibrating
soil heat flux plates described in TABLE 3-13. The default wiring for the
self-calibrating soil heat flux plates is shown in TABLE 3-13.
TABLE 3-13. Default Wiring for Soil Heat Flux Plates (Self Calibrating)
Sensor
HFP01SC #1
HFP01SC #2
Quantity
0 or 1
0 or 1
Wire Description
Color
CDM-A116 or VOLT 116
Terminal
Signal
White
Diff 5H
Signal Reference
Green
Diff 5L
Shield
Clear
Heater Signal
Yellow
Diff 13H
Heater Reference
Purple
Diff 13L
Shield
Clear
Heater Power
Red
SW12-11/
Power Reference
Black
G
Signal
White
Diff 6H
Signal Reference
Green
Diff 6L
Shield
Clear
Heater Signal
Yellow
Diff 14H
Heater Reference
Purple
Diff 14L
Shield
Clear
Heater Power
Red
SW12-11/
Power Reference
Black
G
AG ⏚
AG ⏚
AG ⏚
AG ⏚
11
EasyFlux® DL CR6OP
TABLE 3-13. Default Wiring for Soil Heat Flux Plates (Self Calibrating)
Sensor
HFP01SC #3
Quantity
0 or 1
Wire Description
Color
CDM-A116 or VOLT 116
Terminal
Signal
White
7H
Signal Reference
Green
7L
Shield
Clear
Heater Signal
Yellow
Diff 16H
Heater Reference
Purple
Diff 16L
Shield
Clear
Heater Power
Red
SW12-21/
Power Reference
Black
G
AG ⏚
AG ⏚
1/The
SW12 ports on the CDM-A116 are limited to 200mA output. Accordingly, no more than two HFP01SC
sensors may be connected to each port. Connect heater power wires from HFP01SC #1 and #2 to SW12-1, and
connect heater wires from HFP01SC #3 to SW12-2.
4.
Operation
Operating the EasyFlux DL CR6OP requires the user to enter or edit certain
constants and input variables unique to the program or site. Constants are
typically edited only once when first initializing the program. Site-specific
variables are edited upon initial deployment, but also periodically as site
conditions change (e.g., canopy height is a variable that may need to be
adjusted throughout a growing season). Section 4.1, Set Constants in CRBasic
Editor and Load Program (p. 12), gives details on editing constants, and Section
4.2, Enter Site-Specific Variables with Data Logger Keypad or LoggerNet
(p.14), gives details on editing variables.
Typical operation also includes periodic zeroing and spanning of the
IRGASON or EC150 gas analyzer.
4.1
Set Constants in CRBasic Editor and Load Program
Before operating the station, the values for configuration constants should be
verified in the program code.
Once the program is open in CRBasic Editor, find the section titled “USERDEFINED CONFIGURATION CONSTANTS” (see FIGURE 4-1). Review
the constants in this section and modify as needed. If having difficulty locating
the correct lines of code, search the program for the word “unique”. This will
locate all lines of code containing constants that need to be verified. Look for
the text comments on the right side of each line of code for more explanation
of the constant. Generally, the constants fall into four categories:
1.
Program Function Constants
These are constants that determine the timing of code execution,
frequency of writing to output tables, memory allocation, etc. In most
cases, the default constants for these values can be maintained.
One program function constant that should be mentioned specifically
is the ONE_FULL_TABLE constant. If this is set to TRUE, all of
12
EasyFlux® DL CR6OP
the intermediate and auxiliary measurements will be included as data
fields in the main FLUX_CSFormat output table, rather than being
in a separate output table called FLUX_NOTES. For more
information, see Section 4.4, Output Tables (p. 24).
2.
Sensor Selection Constants
All sensor selection constants begin with the prefix SENSOR. The
value is set to -1 as TRUE in the constant table if the system includes
the sensor. For example, if a system has a fine-wire thermocouple, the
constant SENSOR_FW should be set to -1 as TRUE. When set to
TRUE, the wiring in TABLE 3-13 will apply to the sensor and the
data from that sensor will be included in the data output tables.
If a sensor is not used, ensure the constant is set to 0 as FALSE.
NOTE
3.
Sensor Quantity Constants
The value for these constants indicates the number of each type of
sensor in the system. For example, if three soil heat flux (SHF) plates
were being used, the constant NMBR_SHF would be set to 3.
4.
Sensor Calibration Constants
Some sensors have unique parameters for their measurement working
equations (e.g., multipliers and/or offsets for linear working
equations) that are used to convert their raw measurements into the
values applicable in analysis. Typically, these parameter values are
found on the calibration sheet from the sensor’s original
manufacturer. For example, if an NR-LITE2 net radiometer is being
used, a unique multiplier is set in the following line of code:
Constant NRLITE_SENSITIVITY = 16. The comments in the code
explain that the value entered is the sensor sensitivity provided in the
NR-LITE2 calibration sheet.
Constants relating to a particular sensor have been grouped
together and have the sensor selection constant at the beginning,
such that if the sensor selection constant is set to FALSE, the other
constants for that sensor may be ignored. For example, all of the
constants dealing with the temp/RH probe are grouped together
with the SENSOR_TMPR_RH constant at the top. If a temp/RH
probe is not being used, SENSOR_TMPR_RH should be set to
FALSE and the next four constants dealing with multipliers and
offsets will be conditionally excluded in the program.
After all constants are verified, the program should be saved. Save the program
under a new or modified file name to keep track of different program versions.
Finally, send the program to the CR6 using LoggerNet, PC400, or PC200W
user-interface software.
13
EasyFlux® DL CR6OP
FIGURE 4-1. Example screen from CRBasic Editor showing userdefined configuration constants
4.2
Enter Site-Specific Variables with Data Logger Keypad or
LoggerNet
After the eddy-covariance station is installed and the data logger is running the
program, connect a CR1000KD Keyboard Display to the CR6 CS-I/O port to
view a custom menu of station-specific variables (FIGURE 4-2). Use this menu
to enter, view, and modify these variables. Use the up and down arrow buttons
to navigate to different variables. Press Enter to select a variable or to set a
new value after typing it. Press Esc to return to the previous menu.
FIGURE 4-2 depicts the structure of the custom menu. Bypass the custom
menu to interact directly with the data logger through the data logger default
menus. To bypass the custom menus, select < System Menu >. If no
CR1000KD is available, these same variables may be viewed and edited using
LoggerNet connect screen’s numeric display of variables from the Public table.
14
EasyFlux® DL CR6OP
FIGURE 4-2. Custom keypad menu; arrows indicate submenus
15
EasyFlux® DL CR6OP
Before fluxes are processed correctly, the user must go through each of the
station variables and set or confirm the assigned values. TABLE 4-1 gives
short descriptions of each station variable.
TABLE 4-1. Station Variables with Descriptions
Station Variable
Meas Height
Units
m
Default
The height of the center of the
eddy-covariance sensor
measurement volumes above
ground.
height_measurement
Type of surface at the
measurement site. Options are
CROP, GRASS, FOREST,
SHRUB, BARELAND, and
WATER. This is used to
estimate displacement height
(see Appendix D.6.1,
Aerodynamic Height (p. D-8)) and
roughness length (see Appendix
G.1.3, Programmatic Approach
(p. G-7)).
surface_type
1 = CROP
2 = GRASS
3 = FOREST
4 = SHRUBLAND
5 = BARELAND
6 = WATER
7 = ICE
The average height of the
canopy.
height_canopy
0 (Auto)
Displacement height. Set to zero
(0) for program to auto-calculate.
See Appendix D.6.1,
Aerodynamic Height (p. D-8), for
details.
displacement_user
0 (Auto)
Roughness length. Set to zero (0)
for program to auto-calculate.
See Appendix G.1.3,
Programmatic Approach (p. G-7),
for details.
roughness_user
The height of the GPS reciever
above the ground surface. If GPS
is not used, this variable is
omitted.
height_GPS16X
2
Surf Type
adimensional
GRASS
Canopy Height
m
0.5
d
z0
m
m
Description
Name of variable in
Public Table (in
case no CR1000KD
available)
GPS Height
m
1
Bulk Density
kg·m-3
1300
Average bulk density of soil. If
energy balance sensors are not
used, this variable is omitted.
soil_bulk_density
C_dry_soil
J·kg-1 K-1
870
Specific heat of dry mineral soil.
If energy balance sensors are not
used, this variable is omitted.
cds
HFP Depth
m
0.08
Depth of the soil heat flux plates.
If energy balance sensors are not
used, this variable is omitted.
thick_abv_HFP
16
EasyFlux® DL CR6OP
TABLE 4-1. Station Variables with Descriptions
Station Variable
IRGA Coord x
IRGA Coord y
FW Coord x
FW Coord y
Units
m
m
m
m
FW Dim
m
Sonic Azmth
decimal
degrees
Name of variable in
Public Table (in
case no CR1000KD
available)
Default
Description
0 for
IRGASON;
0.04066 for
EC150
Distance along the sonic x-axis
between the sonic sampling
volume and the gas analyzer
sampling volume. If an
IRGASON is used, this should
be set to 0. If an EC150 with
CSAT3A is used, this defaults to
0.04066, which corresponds to
the EC150 mounting position
closest to the CSAT3A sonic
measurement volume.
separation_x_IRGA
0 for
IRGASON;
0.02905 for
EC150
Distance along the sonic y-axis
between the sonic sampling
volume and the gas analyzer
sampling volume. If an
IRGASON is used, this should
be set to 0. If an EC150 with
CSAT3A is used, this defaults to
0.02905, which corresponds to
the EC150 mounting position
closest to the CSAT3A sonic
measurement volume.
separation_y_IRGA
0.005870
Distance along the sonic x-axis
between the sonic sampling
volume and fine-wire
thermocouple. If no fine-wire
thermocouple is being used, this
variable is omitted.
separation_x_FW
0.03259
Distance along the sonic y-axis
between the sonic sampling
volume and the fine-wire
thermocouple. If no fine-wire
thermocouple is being used, this
variable is omitted.
separation_y_FW
FW05_DIA
Identifies which fine-wire
thermocouple is being used and
loads the appropriate diameter.
For FW05_DIA, FW1_DIA and
FW3_DIA, the diameters are
1.27 x 10-5, 2.54 x 10-5, and 7.62
x 10-5 m, respectively. If no finewire thermocouple is being used,
this variable is omitted.
FW_diameter
0
The compass direction in which
the sonic negative x-axis points
(the compass direction in which
the sonic head is pointing).
sonic_azimuth
17
EasyFlux® DL CR6OP
TABLE 4-1. Station Variables with Descriptions
Station Variable
Units
Default
Description
Latitude
decimal
degrees
41.766
The site latitude in degrees North
or South.
Hemisph_NS
adimensional
NORTH
Longitude
decimal
degrees
111.855
The site longitude in degrees
East or West.
Hemisph_EW
adimensional
WEST
The site longitudinal
hemisphere. Options are EAST
or WEST.
Altitude
m
1356
Planar
Fit Alpha
Planar
Fit Alpha
Planar
Fit Alpha
Planar
Fit Alpha
≤ 60
or
≥ 300
> 60
&
≤ 170
> 170
&
< 190
≥ 190
&
< 300
decimal
degrees
decimal
degrees
decimal
degrees
decimal
degrees
The site latitudinal hemisphere.
Options are NORTH or SOUTH.
The site altitude
Name of variable in
Public Table (in
case no CR1000KD
available)
Latitude
hemisphere_NS
1 = North
–1 = South
Longitude
hemisphere_EW
1 = East
–1 = West
altitude
0
Alpha angle used to rotate the
wind when the mean horizontal
wind is blowing from the sector
of 0 to 60 and 300 to 360
degrees in the sonic coordinate
system (wind blowing into sonic
head).1/
alpha_PF_60_300
0
Alpha angle used to rotate the
wind when the mean horizontal
wind is blowing from the sector
of 60 to 170 degrees in the sonic
coordinate system (wind blowing
from the sector left and behind
sonic head).1/
alpha_PF_60_170
0
Alpha angle used to rotate the
wind when the mean horizontal
wind is blowing from the sector
of 170 to 190 degrees in the
sonic coordinate system (wind
blowing from behind sonic
head).1/
alpha_PF_170_190
0
Alpha angle used to rotate the
wind when the mean horizontal
wind is blowing from the sector
of 190 to 300 degrees in the
sonic coordinate system (wind
blowing from the sector right
and behind sonic head).1/
alpha_PF_190_300
18
EasyFlux® DL CR6OP
TABLE 4-1. Station Variables with Descriptions
Station Variable
Planar
Fit Beta
Planar
Fit Beta
Planar
Fit Beta
Planar
Fit Beta
Footprint
Dist of
Interest
≤ 60
or
≥ 300
> 60
&
≤ 170
> 170
&
< 190
≥ 190
&
< 300
≤ 60
or
≥ 300
Units
decimal
degrees
decimal
degrees
decimal
degrees
decimal
degrees
Name of variable in
Public Table (in
case no CR1000KD
available)
Default
Description
0
Beta angle used to rotate the
wind when the mean horizontal
wind is blowing from the sector
of 0 to 60 and 300 to 360
degrees in the sonic coordinate
system (wind blowing into sonic
head).1/
beta_PF_60_300
0
Beta angle used to rotate the
wind when the mean horizontal
wind is blowing from the sector
of 60 to 170 degrees in the sonic
coordinate system (wind blowing
from left and behind sonic
head).1/
beta_PF_60_170
0
Beta angle used to rotate the
wind when the mean horizontal
wind is blowing from the sector
of 170 to 190 degrees in the
sonic coordinate system (wind
blowing from behind sonic
head).1/
beta_PF_170_190
0
Beta angle used to rotate the
wind when the mean horizontal
wind is blowing from the sector
of 190 to 300 degrees in the
sonic coordinate system (wind
blowing from right and behind
sonic head).1/
beta_PF_190_300
The upwind distance of interest
from the station when the mean
horizontal wind is blowing from
the sector of 0 to 60 and 300 to
360 degrees in the sonic
coordinate system (wind blowing
into sonic head).
m
100z
Note: The program will report
the percentage of cumulative
footprint from within this
distance. The default value is
100 times the aerodynamic
height, z. Recall that z is the
difference between the
measurement height and
displacement height.
dist_intrst_60_300
19
EasyFlux® DL CR6OP
TABLE 4-1. Station Variables with Descriptions
Station Variable
Footprint
Dist of
Interest
Footprint
Dist of
Interest
Footprint
Dist of
Interest
1/ Leave
> 60
&
≤ 170
> 170
&
< 190
≥ 190
&
< 300
Units
m
m
m
Name of variable in
Public Table (in
case no CR1000KD
available)
Default
Description
100z
The upwind distance of interest
from the station when the mean
horizontal wind is blowing from
the sector of 60 to 170 degrees in
the sonic coordinate system
(wind blowing from left and
behind sonic head).
dist_intrst_60_170
100z
The upwind distance of interest
from the station when the mean
horizontal wind is blowing from
the sector of 170 to 190 degrees
in the sonic coordinate system
(wind blowing from behind
sonic head).
dist_instrst_170_190
100z
The upwind distance of interest
from the station when the mean
horizontal wind is blowing from
the sector of 190 to 300 degrees
in the sonic coordinate system
(wind blowing from right and
behind sonic head).
dist_intrst_190_300
all planar fit alpha and beta angles set to 0 to use Tanner and Thurtell (1969) method of double coordinate rotations.
20
EasyFlux® DL CR6OP
TABLE 4-2. Instrument Settings with Descriptions
Station Variable
Select
Source
Default
Description
EB
Used to select the barometer to
use for measurements of
ambient pressure. Set to EB for
EC100 enhanced barometer. Set
to BB for the EC100 on-board
basic barometer.
press_source
0 = Basic Barometer
1 = Added by user
2 = Enhanced
Barometer (EB)
FALSE
If the variable Select Source
has been changed, this variable
must be set to TRUE to enable
the change. The program will
return Set Source to FALSE
once the change has been
applied.
set_press_source_flg
–1 = True
0 = False
POWER_ON
Used to power down or power
on the gas analyzer head. The
EC100 electronics and sonic
anemometer will continue to be
powered. Options are
POWER_ON or
POWER_OFF.
IRGA_power
0 = Power On
1 = Power Off
FALSE
If the variable Select IRGA
Power has been changed, this
variable must be set to TRUE
to enable the change. The
program will return Set IRGA
Power to FALSE once the
change has been applied.
set_IRGA_power_flg
–1 = True
0 = False
HEATER_AUTO
Used to enable the automatic
window heater control by
selecting HEATER_AUTO or
to disable the window heaters
by selecting HEATER_OFF.
heater
–1 = off
–2 = auto
FALSE
If the variable Enable Heater
Control has been changed, this
variable must be set to TRUE
to enable the change. The
program will return Set Heater
Control to FALSE once the
change has been applied.
set_heater_flg
–1 = True
0 = False
Change
Pressure
Source
Set
Source
IRGA
Power
Switch
IRGA Power
Set IRGA
Power
Enable
Heater
Control
Heater
Control
Set Heater
Control
Name of variable in
Public Table (in case no
CR1000KD available)
21
EasyFlux® DL CR6OP
TABLE 4-2. Instrument Settings with Descriptions
Station Variable
Spectro_
scopic
correction
Enable the
use of
CO2from
fast air
temperature
Set Use
option for
CO2
Enable
Shadow
Correction
Default
Description
FAST_ON
Used to enable the use of CO2
corrected for spectroscopic
effect from air temperature
measured by fast response
sensors. The use is controled by
selecting FAST_ON or to
disable this use by selecting
FAST_OFF.
select_CO2_fast_tmpr
TRUE = FAST_ON
FALSE = FAST_OFF
FALSE
If the variable CO2 fast T has
been changed, this variable
must be set to TRUE to enable
the change. The program will
return Set CO2 Selected to
FALSE once the change has
been applied.
set_CO2_fast_tmpr_flg
–1 = True
0 = False
CORR_OFF
Used to enable the Kaimal sonic
transducer wind shadowing
correction as described in the
CSAT3B manual. CORR_ON
enables the correction, while
CORR_OFF disables it.
shadow_corr
-1 = CORR_ON
0 = CORR_OFF
FALSE
If the variable Enable Shadow
Correction has been changed,
this variable must be set to
TRUE to enable the change.
The program will return Set
Shadow Correction to FALSE
once the change has been
applied.
set_shadow_corr_flg
–1 = True
0 = False
Shadow
Correction
Set Shadow
Correction
Name of variable in
Public Table (in case no
CR1000KD available)
22
EasyFlux® DL CR6OP
TABLE 4-3. Onsite Zero and Span Variables
Name of variable
in Public Table
(in case no
CR1000KD
available)
On-Site Zero & Span
Variable
Units
Default
Description
Set Zero
adimensional
FALSE
Set this to TRUE after flowing zero
gas through the zero/span shround
and reaching equilibrium.
set_zero_flg
–1 = True
0 = False
0
This is the concentration of span gas
flowing through the zero/span
shroud. It should be on a basis of dry
air.
CO2_span_gas
°C
0
This is the dewpoint temperature of
the H2O span gas generated from a
dewpoint generator. It should match
the dewpoint temperature setting on
the generator.
T_DP_span_gas
Set CO2 Span
adimensional
FALSE
Set this to TRUE after flowing CO2
span gas through the zero/span
shroud and reaching equilibrium.
Set H2O Span
adimensional
FALSE
Set this to TRUE after flowing H2O
span gas through the zero/span
shround and reaching equilibrium.
–
This is a real-time measurement of
CO2 molar mixing ratio (dry basis)
as measured by the gas analyzer.
This can be monitored to know
when equilibrium has been reached.
CO2_mixratio
H2O_mixratio
CO2
ppm
Span
Concentrations
T_DP
CO2_mixratio
ppm
set_CO2_span_flg
–1 = True
0 = False
set_H2O_span_flg
–1 = True
0 = False
H2O_mixratio
ppth
–
This is a real-time measurement of
H2O molar mixing ratio (dry basis)
as measured by the gas analyzer.
This can be monitored to know
when equilibrium has been reached.
Td
deg C
–
This is a real-time measurement of
dewpoint temperature as measured
by the gas analyzer.
T_DP
–
This is a real-time measurement of
dewpoint temperature derived from
measurements by the temp/RH
probe. It is ommitted if there is no
temp/RH probe being used. This
value could potentially be input for
dewpoint temperature, Td above, if a
dewpoint generator is unavailable
and performing a rough H2O span is
helpful (for example, during
troubleshooting).
T_DP_Probe
Td_probe
deg C
23
EasyFlux® DL CR6OP
4.3
Data Retrieval
The program stores a very limited amount of data to the internal CPU of the
data logger, so a microSD Flash card should be used with the CR6. TABLE 4-4
shows the number of days of data a 2 GB, 8 GB, and 16 GB card will typically
hold before the memory is full and data starts to be overwritten. In cases where
real-time remote monitoring is desired, various telemetry options (for example,
cellular, radio, etc.) are available to transmit the processed flux data. Certain
conditions may also allow remote transmittal of time series data. Contact
Campbell Scientific for more details.
TABLE 4-4. microSD Flash Card Fill Times
microSD Flash
card size
Fill time with gas analyzer
and sonic only
Fill time with gas analyzer, sonic, FW,
and biomet/energy balance sensors)1/
2 GB
~29 days
~23 days
8 GB
~121 days
~92 days
16 GB
~242 days
~184 days
1/Biomet
and energy balance sensors used for this fill time estimate include the following: HMP155A, NRLITE2, CS300, LI200X, LI190SB, SI-111, TE525MM, TCAV (qty 2), CS616 (qty 2), and HFP01 (qty 4)
4.4
NOTE
microSD Flash cards from various manufacturers may have
slightly different memory sizes on their 2 GB, 8 GB, and 16 GB
cards, respectively. Also, as a card ages some of its sectors may
become unusable, decreasing the available memory. Fill time
estimates given in TABLE 4-4 are approximations for new cards.
CAUTION
Campbell Scientific recommends and supports only the use of
microSD cards obtained from Campbell Scientific. These cards
are industrial grade and have passed Campbell Scientific hardware
testing. Use of consumer grade cards substantially increases the
risk of data loss.
Output Tables
Besides the standard Public, Status, and TableInfo tables that every data
logger reports, the program has six output tables. TABLE 4-5 gives the names
of these output tables, along with a short description, the frequency at which a
record is written to the table, and the amount of memory allocated from the
CPU and microSD card for each table.
NOTE
The variable naming conventions used by AmeriFlux and other
flux networks have been adopted in the EasyFlux DL CR6OP.
Additionally, an output table called Flux_AmeriFluxFormat
reports the variables in the order and format prescribed
by AmeriFlux (see http://ameriflux.lbl.gov/data/aboutdata/datavariables/).
The Flux_CSFormat and Flux_Notes tables have the same content as they did
in prior versions of EasyFlux DL for CR3000 (v1.0), although variable names
24
EasyFlux® DL CR6OP
have been updated to conform to AmeriFlux convention. If the user would
prefer to have the data fields contained in the Flux_Notes table appended to
the end of the Flux_CSFormat table rather than being placed in a separate
output table, this is possible by changing the constant ONE_FULL_TABLE
from FALSE to TRUE (see Section 4.1, Set Constants in CRBasic Editor and
Load Program (p. 12), on changing constants).
TABLE 4-5. Data Output Tables
Memory on
CR6 CPU
Memory on
microSD Card
SCAN_INTERVAL
(default 100 ms)
Auto-Allocate
(typically less
than 1 hour)
Time_Series is
broken up into
1 day files (see
TABLE 4-4)
Diagnostic
Reports most recent
diagnostic flags
from gas analyzer
and sonic
anemometer
SCAN_INTERVAL
(default 100 ms)
1 record (most
recent scan)
0 records
Config_Setting_Notes
Reports settings for
the gas analyzer and
sonic anemometer
When settings are
changed or system is
power cycled
1 record
300 records
Flux_AmeriFluxFormat
Processed flux and
statistical data
following reporting
conventions and
order of AmeriFlux
NUM_DAY_CPU
(default 7 days)
Broken up into
30-day files;
see TABLE
4-4 for number
of files
NUM_DAY_CPU
(default 7 days)
Broken up into
30-day files;
see TABLE
4-4 for number
of files
NUM_DAY_CPU
(default 7 days)
Broken up into
30-day files;
see TABLE
4-4 for number
of files
Table Name
Description
Recording Interval
Time_Series
Time series data
(aligned to account
for electronic
delays)
Flux_CSFormat
Processed flux and
statistical data
Flux_Notes
Intermediate
variables, station
constants, and
correction variables
used to generate flux
results
OUTPUT_INTERVAL
(default 30 minutes)
OUTPUT_INTERVAL
(default 30 minutes)
OUTPUT_INTERVAL
(default 30 minutes)
TABLE 4-5 through TABLE 4-11 give a description of all data fields found in
each data output table and when each data field is included in the table.
NOTE
Prior to coordinate rotations, the orthogonal wind components
from the sonic anemometer are denoted as Ux, Uy, and Uz.
Following coordinate rotations, the common denotation of u, v,
and w is used, respectively.
25
EasyFlux® DL CR6OP
NOTE
Variables with _R denote that the value was computed after
coordinate rotations were done. Variables with a _F denote that
the value was calculated after frequency corrections were applied.
Similarly, _SND and _WPL refer to variables that have had the
SND correction or the WPL correction applied, respectively.
TABLE 4-6. Data Fields in the Time_Series Data Output Table
Units
Ux
m·s-1
Wind speed along sonic x-axis
Always
Uy
m·s
Wind speed along sonic y-axis
Always
Uz
m·s
Wind speed along sonic z-axis
Always
T_SONIC
deg C
Sonic temperature
Always
diag_sonic
adimensional
Raw sonic diagnostic value (0 indicates no
diagnostic flags set)
Always
CO2_density
mg·m-3
CO2 density
Always
CO2_density_fast_tmpr
mg·m-3
CO2 density whose spectroscopy correction
using fast response temperature
Always
H2O_density
g·m-3
Water vapor density
Always
diag_irga
adimensional
Raw gas analyzer diagnostic value (0
indicates no diagnostic flags set)
Always
T_SONIC_corr
deg C
Air temperature derived from sonic
temperature corrected for humidity and
pressure
If IRGASON is
used
TA_1_1_1
deg C
Air temperature measured by the EC100
temperature probe
Always
PA
kPa
Ambient pressure
Always
CO2_sig_strgth
adimensional
CO2 signal strength
Always
H2O_sig_strgth
adimensional
H2O signal strength
Always
FW
deg C
-1
-1
Description
Data Field
Included
Data Field Name
Air temperature measured by fine-wire
thermocouple
If FW05, FW1, or
FW3 is used
26
EasyFlux® DL CR6OP
TABLE 4-7. Data Fields in the Diagnostic Output Table
Data Field Name
Description
Data Field
Included
sonic_amp_l_f
Amplitude low diagnostic flag
Always
sonic_amp_h_f
Amplitude high diagnostic flag
Always
sonic_sig_lck_f
Signal lock diagnostic flag
Always
sonic_del_T_f_f
Delta Temp diagnostic flag
Always
sonic_aq_sig_f
Acquiring signal diagnostic flag
Always
sonic_cal_err_f
Calibration error diagnostic flag
Always
irga_bad_data_f
Any gas analyzer diagnostic flag is set
Always
irga_gen_fault_f
General system fault diagnostic flag
Always
Startup diagnostic flag
Always
irga_motor_spd_f
Motor speed diagnostic flag
Always
irga_tec_tmpr_f
Thermoelectric cooler (TEC)
temperature diagnostic flag
Always
irga_src_pwr_f
Source power diagnostic flag
Always
irga_src_tmpr_f
Source temperature diagnostic flag
Always
irga_src_curr_f
Source current diagnostic flag
Always
Gas head power down diagnostic flag
Always
Synchronization diagnostic flag
Always
irga_amb_tmpr_f
Ambient temperature probe diagnostic
flag
Always
irga_amb_press_f
Ambient pressure diagnostic flag
Always
irga_CO2_I_f
CO2 I signal diagnostic flag
Always
irga_CO2_Io_f
CO2 Io signal diagnostic flag
Always
irga_H2O_I_f
H2O I signal diagnostic flag
Always
irga_H2O_Io_f
H2O Io signal diagnostic flag
Always
irga_CO2_Io_var_f
CO2 Io variation diagnostic flag
Always
irga_H2O_Io_var_f
H2O Io variation diagnostic flag
Always
irga_CO2_sig_strgth_f
CO2 signal strength diagnostic flag
Always
irga_H2O_sig_strgth_f
H2O signal strength diagnostic flag
Always
Calibration file read error flag
Always
Heater control off diagnostic flag
Always
irga_startup_f
irga_off_f
irga_sync_f
irga_cal_err_f
irga_htr_ctrl_off_f
27
EasyFlux® DL CR6OP
TABLE 4-8. Data Fields in the Config_Setting_Notes Output Table
Data Field
Name
Units
Data Field
Included
bandwidth_freq
Hz
EC100 bandwidth (5, 10, 12, or 20 for 5 Hz, 10 Hz, 12.5
Hz, or 20 Hz respectively)
Always
press_source
adimensional
Sensor used by EC100 for ambient pressure (0 for EC100
Basic Barometer, 1 for user/custom barometer, 2 for
EC100 Enhanced Barometer)
Always
tmpr_source
adimensional
Sensor used by EC100 for ambient temperature (0 for
EC100 Temperature Probe, no other values valid)
Always
CO2_zero_coeff
adimensional
CO2 zero coefficient set from last CO2 zero
Always
CO2_span_coeff
adimensional
CO2 span coefficient set from last CO2 span
Always
H2O_zero_coeff
adimensional
H2O zero coefficient set from last H2O zero
Always
H2O_span_coeff
adimensional
H2O span coefficient set from last H2O span
Always
CO2_span_mixra
ppm
CO2 mixing ratio of span gas
Always
H2O_span_T_DP
deg C
Dew point temperature of span gas
Always
Heat_control
adimensional
Heater Control Setting (–1 for disabled, –2 for auto
control)
Always
IRGA_power
adimensional
Gas head power state (0 for on, 1 for off)
Always
CO2_fast_tmpr
adimensional
If TRUE, CO2 with spectroscopy correction using fast air
temperature is used for flux calculation. If FALSE,
conventional CO2 is used.
Always
Shadow_corr
adimensional
Application of transducer shadowing correction (0 for off,
1 for on)
Always
Description
TABLE 4-9. Data Fields in the Flux_AmeriFluxFormat Output Table
Data Field Name
Units
Description
Data Field Included
TIMESTAMP_START
YYYYMMDDHHMM
Start time of the averaging period
Always
TIMESTAMP_END
YYYYMMDDHHMM
End time of the averaging period
Always
CO2
µmol·mol
CO2 mole fraction
Always
CO2_SIGMA
µmol·mol
Standard deviation of CO2
Always
H2O
mmol·mol-1
Average H2O molar mixing ratio
(dry basis)
Always
H2O_SIGMA
mmol·mol-1
Standard deviation of H2O
Always
FC
µmol·m ·s
CO2 flux after corrections
Always
FC_SSITC_TEST
adimensional
Result of steady state and integral
turbulence characteristics for FC
according to Foken et al. (2004)
Always
LE
W·m-2
Latent heat flux after corrections
Always
LE_SSITC_TEST
adimensional
Result of steady state and integral
turbulence characteristics for LE
according to Foken et al. (2004)
Always
-1
-1
-2
-1
28
EasyFlux® DL CR6OP
TABLE 4-9. Data Fields in the Flux_AmeriFluxFormat Output Table
Data Field Name
Units
Description
ET
mm·hour-1
ET_SSITC_TEST
adimensional
H
W·m-2
H_SSITC_TEST
Data Field Included
Evapotranspiration
Always
Result of steady state and integral
turbulence characteristics for ET
according to Foken et al. (2004)
Always
Sensible heat flux after
corrections
Always
adimensional
Result of steady state and integral
turbulence characteristics for FC
according to Foken et al. (2004)
Always
G
W·m-2
Calculated heat flux at the ground
surface
If energy balance
sensors used
SG
W·m-2
The change in heat storage in the
soil above the soil heat flux plates
during the averaging interval
If energy balance
sensors used
FETCH_MAX
m
Distance upwind where the
maximum contribution to the
footprint is found
Always
FETCH_90
m
Upwind distance that contains
90% of cumulative footprint. If
NAN is returned, integration of
the model never reached 90%
within the allowable distance of
integration. See Appendix G,
Footprint (p. G-1), for more details.
Always
FETCH_55
m
Upwind distance that contains
55% of footprint
Always
FETCH_40
m
Upwind distance that contains
40% of footprint.
Always
WD
decimal degrees
Average wind direction
Always
WS
m·s
Average wind speed
Always
WS_MAX
m·s
Maximum wind speed
Always
USTAR
m·s
Friction velocity
Always
ZL
adimensional
Stability
Always
TAU
kg·m ·s
Momentum Flux
Always
TAU_SSITC_TEST
adimensional
Result of steady state and integral
turbulence characteristics for FC
according to Foken et al. (2004)
Always
MO_LENGTH
m
Monin-Obukhov length
Always
U
m·s
Average streamwise wind
Always
U_SIGMA
m·s-1
Standard deviation of streamwise
wind
Always
V
m·s-1
Average crosswind
Always
V_SIGMA
m·s
Standard deviation of crosswind
Always
-1
-1
-1
-1
-1
-1
-2
29
EasyFlux® DL CR6OP
TABLE 4-9. Data Fields in the Flux_AmeriFluxFormat Output Table
Data Field Name
Units
Description
Data Field Included
W
m·s-1
Average vertical wind
Always
W_SIGMA
m·s-1
Standard deviation of vertical
wind
Always
PA
kPa
Atmospheric Pressure
Always
TA_1_1_1
°C
Air temperature from EC100
temperature probe
Always
RH_1_1_1
%
Relative humidity calculated from
EC100 temperature probe, H2O
(from analyzer), and pressure.
Always
T_DP_1_1_1
deg C
Dewpoint temperature calculated
from EC100 temperature probe,
H2O (from analyzer), and
pressure.
Always
TA_2_1_1
deg C
Air temperature calculated from
sonic temperature, H2O, and
pressure.
Always
RH_2_1_1
%
Relative humidity calculated from
sonic temperature, H2O, and
pressure.
Always
T_DP_2_1_1
deg C
Dewpoint temperature calculated
from sonic temperature, H2O, and
pressure.
Always
TA_3_1_1
deg C
Air temperature from temp/RH
probe
If temp/RH probe
used
RH_3_1_1
%
Relative humidity from temp/RH
probe
If temp/RH probe
used
T_DP_3_1_1
deg C
Dewpoint temperature from
temp/RH probe
If temp/RH probe
used
VPD
hPa
Vapor pressure deficit
If temp/RH probe
used
T_SONIC
deg C
Average sonic temperature
Always
T_SONIC_SIGMA
deg C
Standard deviation of sonic
temperature
Always
PBLH
m
Estimated planetary boundary
layer height
Always
TS_x_1_1
deg C
SWC_x_1_1
%
ALB
adimensional
NETRAD
W·m-2
Soil temperature. x is an index for
the number of soil temperature
measurements made.
If TCAV or CS65X
used (if both, TCAV
temperature is used)
Soil water content. x is an index
for the number of soil sensors.
If CS616 or CS65X
used
Albedo
Net radiation
If SN500SS, NR01, or
CNR4 is used
If SN500SS, NR01,
CNR4 or NRlit2 is
used
30
EasyFlux® DL CR6OP
TABLE 4-9. Data Fields in the Flux_AmeriFluxFormat Output Table
Data Field Name
Units
Description
Data Field Included
PPFD_IN
µmol·m-2·s-1
Photosynthetic photon density
If CS310 is used
SW_IN
W·m-2
Incoming shortwave radiation
If SN500SS, NR01,
CNR4, LI200X, or
CS300 used
SW_OUT
W·m-2
Outgoing shortwave radiation
If SN500SS, NR01,
CNR4, LI200X, or
CS300 used
LW_IN
W·m-2
Incoming longwave radiation
If SN500SS, NR01 or
CNR4 used
LW_OUT
W·m-2
Outgoing longwave radiation
If SN500SS, NR01 or
CNR4 used
P
mm
Precipitation in output interval
If TE525 used
T_CANOPY
deg C
Canopy temperature
If SI111 used
TABLE 4-10. Data Fields in the Flux_CSFormat Data Output Table
Data Field Name
Units
FC_mass
mg·m-2·s-1
FC_QC
Description
Data Field
Included
Final corrected CO2 flux
Always
grade
Overall quality grade for Fc_molar
and Fc_mass following Foken et
al. 2012
Always
FC_samples
count
The total number of time series
samples used in calculation of Fc
Always
LE
W·m-2
Final corrected latent heat flux
Always
LE_QC
grade
Overall quality grade for LE
following Foken et al. 2012
Always
LE_samples
count
The total number of time series
samples used in calculation of LE
Always
H
W·m-2
Final corrected sensible heat flux
derived from sonic sensible heat
flux
Always
H_QC
grade
Overall quality grade for Hs
following Foken et al. 2012
Always
H_samples
count
The total number of time series
samples used in calculation of H
Always
H_FW
W·m-2
Final corrected sensible heat flux
derived from fine-wire
thermocouple measurements
If FW05, FW1,
or FW3 is used
H_FW_samples
count
The total number of time series
samples used in calculation of
H_FW
If FW05, FW1,
or FW3 is used
31
EasyFlux® DL CR6OP
TABLE 4-10. Data Fields in the Flux_CSFormat Data Output Table
Data Field Name
Units
Description
Data Field
Included
If NR-LITE2,
SN500SS,
NR01, or CNR4
is used
NETRAD
W·m-2
Average net radiation (corrected
for wind)
G
W·m-2
Heat flux at the ground surface
If energy
balance sensors
are used
SG
W·m-2
The change in heat storage in the
soil above the soil heat flux plates
during the averaging interval
If energy
balance sensors
used
energy_closure
fraction
The ratio of sensible and latent
heat fluxes over surface heat flux
plus net radiation
If energy
balance sensors
are used
poor_engr_clsur
adimensional
If TRUE, energy closure is poor
likely due to an instrument issue;
check zero and span of analyzyer
If energy
balance sensors
are used
Bowen_ratio
fraction
TAU
kg·m-1·s-2
TAU_QC
The ratio of final sensible heat flux
over final latent heat flux
Always
Final corrected momentum flux
Always
grade
Overall quality grade for tau
following Foken et al. 2012
Always
USTAR
m·s-1
Friction velocity after coordinate
rotations and frequency corrections
Always
TSTAR
deg C
Scaling temperature after
coordinate rotations, frequency
corrections, and SDN correction
Always
TKE
m2·s-2
Specific turbulence kinetic energy
after coordinate rotations
Always
TA_1_1_1
deg C
Average ambient temperature from
EC100 temperature probe
Always
RH_1_1_1
deg C
Relative humidity calculated from
TA_1_1_1 (EC100 temperature
probe), water vapor density, and
pressure.
Always
T_DP_1_1_1
deg C
Average dewpoint temperature
calculated using temperature from
the EC100 temperature probe
Always
amb_e
kPa
Average water vapor pressure
calculated using temperature from
the EC100 temperature probe
Always
kPa
Average saturated water vapor
pressure calculated using
temperature from the EC100
temperature probe
Always
amb_e_sat
32
EasyFlux® DL CR6OP
TABLE 4-10. Data Fields in the Flux_CSFormat Data Output Table
Data Field
Included
Data Field Name
Units
Description
TA_2_1_1
deg C
Average ambient temperature
calculated from sonic temperature,
water vapor density, and pressure
Always
RH_2_1_1
deg C
Average dewpoint temperature
calculated using sonic temperature,
water vapor density, and pressure
Always
T_DP_2_1_1
deg C
Average dewpoint temperature
calculated using sonic temperature,
water vapor density, and pressure
Always
e
kPa
Average water vapor pressure
calculated from sonic temperature
Always
e_sat
kPa
Average saturated water vapor
pressure calculated from sonic
temperature
Always
TA_3_1_1
deg C
Average air temperature from
temp/RH probe
If temp/RH
probe used
RH_3_1_1
%
Average relative humidity from
temp/RH probe
If temp/RH
probe used
T_DP_3_1_1
deg C
Average dewpoint temperature
from temp/RH probe
If temp/RH
probe used
e_probe
kPa
Average saturation vapor pressure
derived from gas analyzer
measurements
If temp/RH
probe used
e_sat_probe
kPa
Average vapor pressure derived
from gas analyzer measurements
If temp/RH
probe used
Average water vapor density
derived from temp/RH probe
measurements
If temp/RH
probe used
H2O_probe
PA
kPa
Average ambient air pressure
Always
VPD
kPa
Vapor pressure deficit
Always
Ux
m·s
Average Ux
Always
Ux_SIGMA
m·s
Standard deviation of Ux
Always
Uy
m·s
Average Uy
Always
Uy_SIGMA
m·s
Standard deviation of Uy
Always
Uz
m·s
Average Uz
Always
Uz_SIGMA
m·s
Standard deviation of Uz
Always
T_SONIC
deg C
Average sonic temperature
Always
T_SONIC_SIGMA
deg C
Standard deviation of sonic
temperature
Always
sonic_azimuth
decimal degrees
Compass direction in which the
sonic negative x-axis points
Always
WS
m·s-1
Average wind speed
Always
-1
-1
-1
-1
-1
-1
33
EasyFlux® DL CR6OP
TABLE 4-10. Data Fields in the Flux_CSFormat Data Output Table
Units
WS_RSLT
m·s-1
Average horizontal wind speed
Always
WD_SONIC
decimal degrees
Average wind direction in the
sonic coordinate system
Always
WD_SIGMA
decimal degrees
Standard deviation of wind
direction
Always
WD
decimal degrees
Average compass wind direction
Always
WS_MAX
m·s
Maximum wind speed
Always
CO2_density
mg·m
Average CO2 mass density
Always
CO2_density_SIGMA
mg·m-3
Standard deviation of CO2 mass
density
Always
H2O_density
mmol·mol-1
Water vapor mass density
Always
H2O_density_SIGMA
mmol·mol-1
Standard deviation of water vapor
mass density
Always
CO2_sig_strgth_Min
adimensional
Minimum CO2 signal strength
Always
H2O_sig_strgth_Min
adimensional
Minimum H2O signal strength
Always
FW
deg C
Average fine-wire thermocouple
temperature
If FW05, FW1,
or FW3 is used
FW_SIGMA
deg C
Standard deviation of fine-wire
thermocouple temperature
If FW05, FW1,
or FW3 is used
P
mm
Total precipitation
If TE525MM is
used
NETRAD_meas
W·m-2
Average net radiation (raw, not
corrected for wind)
If NR-LITE2 is
used
ALB
adimensional
Average albedo
If SN500SS,
CNR4, or NR01
is used
If SN500SS,
CNR4, CS301,
CS320, or NR01
is used
-1
-3
Description
Data Field
Included
Data Field Name
SW_IN
W·m-2
Average incoming short wave
radiation
SW_OUT
W·m-2
Average outgoing short wave
radiation
If SN500SS,
CNR4, or NR01
is used
LW_IN
W·m-2
Average incoming long wave
radiation
If SN500SS,
CNR4, or NR01
is used
LW_OUT
W·m-2
Average outgoing long wave
radiation
If SN500SS,
CNR4, or NR01
is used
T_nr
K
Average sensor body temperature
If SN500SS,
CNR4, or NR01
is used
34
EasyFlux® DL CR6OP
TABLE 4-10. Data Fields in the Flux_CSFormat Data Output Table
Units
R_LW_in_meas
W·m-2
Average raw incoming long wave
radiation
If CNR4 or
NR01
is used
R_LW_out_meas
W·m-2
Average raw outgoing long wave
radiation
If CNR4 or
NR01
is used
PPFD_IN
µmol·s-1·m-2
Average density of photosynthetic
active radiation
If CS310 is used
sun_azimuth
decimal degrees
Solar azimuth
Always
sun_elevation
decimal degrees
Solar elevation
Always
hour_angle
decimal degrees
Solar hour angle
Always
sun_declination
decimal degrees
Solar declination
Always
air_mass_coeff
adimensional
Air mass coefficient: Ratio of the
path length between the current
solar position to the solar noon
Always
daytime
fraction
Day time in fraction of an output
interval
Always
T_CANOPY
deg C
Average temperature of targeted
object
If SI111 is used
T_SI111_body
deg C
Average temperature of sensor
body
If SI111 is used
TS_x_1_1
deg C
Average soil temperature for each
TCAV sensor; x is an index for the
number of TCAV sensors
If TCAV is used
m3·m-3
Average volumetric soil water
content for each CS616, CS650, or
CS655; x is an index for the
number of each sensor model
above
If CS616,
CS650, or
CS655 sensors
are used
SWC_x_1_1
Description
Data Field
Included
Data Field Name
Average water content
reflectometer period for each
CS616; x is an index for the
number of CS616 sensors
CS616_wcr_x_1_1
µs
TS_CS65X_x_1_1
deg C
Average soil temperature for each
CS650 or CS655 sensor; x is an
index for the number of sensors
If CS650 or
CS655
is used
CS65x_ec_x_1_1
dS·m-1
Average electrical conductivity for
each sensor; x is an index for the
number of CS650 or CS655
If CS650 or
CS655
is used
G_plate_x_1_1
W·m-2
Average heat flux through sensor
plate; x is an index for the number
of HFP01 or HFP01SC
If HFP01 or
HFP01SC is
used
If CS616 is used
35
EasyFlux® DL CR6OP
TABLE 4-10. Data Fields in the Flux_CSFormat Data Output Table
Data Field Name
Data Field
Included
Units
Description
W·m-2
Average heat flux across the
ground surface (summation of heat
flux through plate and heat storage
above plate)
If HFP01 or
HFP01SC,
TCAV and/or
CS650/CS655
used
SG_x_1_1
W·m-2
Average heat flux found from heat
storage in soil layer above sensor
plate
If HFP01 or
HFP01SC,
TCAV and/or
CS650/CS655
used
FETCH_MAX
m
Distance upwind where the
maximum contribution to the
footprint is found
Always
FETCH_90
m
Upwind distance that contains 90%
of cumulative footprint
Always
FETCH_55
m
Upwind distance that contains 55%
of footprint
Always
FETCH_40
m
Upwind distance that contains 40%
of footprint. If NAN is returned,
integration of the model never
reached 90% within the allowable
distance of integration. See
Appendix G, Footprint (p. G-1), for
more details.
Always
UPWND_DIST_INTRST
m
Upwind distance of interest for the
average wind direction
Always
FP_DIST_INTRST
%
Percentage of footprint from
within the upwind range of interest
Always
text
Returns either Kljun or
KormannMeixner; the model of
Kljun et al. (2004) is used for
applicable atmospheric conditions,
else the model of Kormann &
Meixner (2001) is used
Always
G_x_1_1
FP_EQUATION
36
EasyFlux® DL CR6OP
TABLE 4-11. Data fields in the Flux_Notes Output Table
Units
UxUy_cov
m2·s-2
Covariance of Ux and Uy
Always
UxUz_cov
m ·s
Covariance of Ux and Uz
Always
UyUz_cov
m ·s
Covariance of Uy and Uz
Always
TsUx_cov
deg C·m·s
Covariance of Ts and Ux
Always
TsUy_cov
deg C·m·s
Covariance of Ts and Uy
Always
TsUz_cov
deg C·m·s
Covariance of Ts and Uz
Always
USTAR_R
m·s-1
Friction velocity after coordinate
rotations
Always
U
m·s-1
Mean streamwise wind speed after
coordinate rotations
Always
U_SIGMA
m·s-1
Standard deviation of streamwise wind
after coordinate rotations
Always
V
m·s-1
Average crosswind speed after
coordinate rotations
Always
V_SIGMA
m·s-1
Standard deviation of crosswind after
coordinate rotations
Always
W
m·s-1
Average vertical wind speed after
coordinate rotations
Always
W_SIGMA
m·s-1
Standard deviation of vertical wind after
coordinate rotations
Always
UV_cov
m·s-1
Covariance of streamwise and
crosswind after coordinate rotations
Always
UW_cov
m·s-1
Covariance of streamwise and
crosswind after coordinate rotations
Always
VW_cov
m·s-1
Covariance of crosswind and vertical
wind after coordinate rotations
Always
UT_SONIC_Cov
m·°C·s-1
Covariance of streamwise wind and
sonic temperature after coordinate
rotations
Always
VT_SONIC_Cov
m·°C·s-1
Covariance of crosswind and sonic
temperature after coordinate rotations
Always
WT_SONIC_Cov
m·°C·s-1
Covariance of vertical wind (after
coordinate rotations) and sonic
temperature
Always
UW_Cov_fc
m2·s-2
Covariance of streamwise and vertical
wind after coordinate rotations and
frequency corrections
Always
VW_Cov_fc
m2·s-2
Covariance of cross and vertical wind
after coordinate rotations and frequency
corrections
Always
WT_SONIC_Cov_fc
m·°C·s-1
Covariance of vertical wind and sonic
temperature after coordinate rotations
and frequency corrections
Always
2
2
Description
Data Field
Included
Data Field Name
-2
-2
-1
-1
-1
37
EasyFlux® DL CR6OP
TABLE 4-11. Data fields in the Flux_Notes Output Table
Data Field Name
Units
Description
Data Field
Included
Covariance of vertical wind and sonic
temperature after coordinate rotations,
frequency corrections, and SND
correction
Always
WT_SONIC_Cov__fc_SND
m·°C·s-1
sonic_samples
count
Number of raw sonic samples in
averaging period without diagnostic
flags
Always
no_sonic_head_Tot
count
Number of sonic samples where no
sonic head was detected
Always
no_new_sonic_data_Tot
count
Number of scans where no sonic data
were received
Always
sonic_amp_l_f_Tot
count
Number of sonic samples with
amplitude low diagnostic flag
Always
sonic_amp_h_f_Tot
count
Number of sonic samples with
amplitude high diagnostic flag
Always
sonic_sig_lck_f_Tot
count
Number of sonic samples with signal
lock diagnostic flag
Always
sonic_del_T_f_Tot
count
Number of sonic samples with delta
temp diagnostic flag
Always
sonic_aq_sig_f_Tot
count
Number of sonic samples with
acquiring signal diagnostic flag
Always
sonic_cal_err_f_Tot
count
Number of sonic samples with
calibration error diagnostic flag
Always
UxCO2_Cov
mg·m-2·s-1
Covariance of Ux and CO2 density
Always
UyCO2_Cov
mg·m ·s
Covariance of Uy and CO2 density
Always
UzCO2_Cov
mg·m ·s
Covariance of Uz and CO2 density
Always
UxH2O_Cov
g·m-2·s-1
Covariance of Ux and water vapor
density
Always
UyH2O_Cov
g·m-2·s-1
Covariance of Uy and water vapor
density
Always
UzH2O_Cov
g·m-2·s-1
Covariance of Uz and water vapor
density
Always
UCO2_Cov
mg·m-2·s-1
Covariance of streamwise wind and
CO2 density after coordinate rotations
Always
VCO2_Cov
mg·m-2·s-1
Covariance of crosswind and CO2
density after coordinate rotations
Always
WCO2_Cov
mg·m-2·s-1
Covariance of vertical wind and CO2
density after coordinate rotations
Always
UH2O_Cov
g·m-2·s-1
Covariance of streamwise wind and
H2O density after coordinate rotations
Always
VH2O_Cov
g·m-2·s-1
Covariance of crosswind and H2O
density after coordinate rotations
Always
-2
-2
-1
-1
38
EasyFlux® DL CR6OP
TABLE 4-11. Data fields in the Flux_Notes Output Table
Units
WH2O_Cov
g·m-2·s-1
Covariance of vertical wind and H2O
density after coordinate rotations
Always
WCO2_Cov_fc
mg·m-2·s-1
Covariance of vertical wind and CO2
density after coordinate rotations and
frequency corrections
Always
WH2O_Cov_fc
g·m-2·s-1
Covariance of vertical wind and H2O
density after coordinate rotations and
frequency corrections
Always
CO2_E_WPL_fc
mg·m-2·s-1
CO2 flux WPL correction term due to
water vapor flux after coordinate
rotations and frequency corrections
Always
CO2_T_WPL_fc
mg·m-2·s-1
CO2 flux WPL correction term due to
sensible heat flux after coordinate
rotations and frequency corrections
Always
H2O_E_WPL_fc
g·m-2·s-1
H2O flux WPL correction term due to
water vapor flux after coordinate
rotations and frequency corrections
Always
H2O_T_WPL_fc
g·m-2·s-1
H2O flux WPL correction term due to
sensible heat flux after coordinate
rotations and frequency corrections
Always
count
Number of CO2 samples without
diagnostic flags and within thresholds
for CO2 signal strength (set in code to
default of 0.6, see Section 4.1, Set
Constants in CRBasic Editor and Load
Program (p. 12)) and the factory
calibrated CO2 measurement range (0 to
1000 µmol/mol)
Always
H2O_samples
count
Number of H2O samples without
diagnostic flags and within thresholds
for H2O signal strength (set in code to
default of 0.7, see Section 4.1, Set
Constants in CRBasic Editor and Load
Program (p. 12)) and the factory
calibrated H2O measurement range (0 to
72 mmol/mol)
Always
no_irga_head_Tot
count
Number of samples where no gas
analyzer head was detected
Always
no_new_irga_data_Tot
count
Number of scans where no gas analyzer
data were received
Always
irga_bad_data_f_Tot
count
Number of IRGA samples with any
IRGA diagnostic flag set high
Always
irga_gen_fault_f_Tot
count
Number of gas analyzer samples with
general system fault diagnostic flag
Always
irga_startup_f_Tot
count
Number of gas analyzer samples with
startup diagnostic flag
Always
CO2_samples
Description
Data Field
Included
Data Field Name
39
EasyFlux® DL CR6OP
TABLE 4-11. Data fields in the Flux_Notes Output Table
Description
Data Field
Included
Data Field Name
Units
irga_motor_spd_f_Tot
count
Number of gas analyzer samples with
motor speed diagnostic flag
Always
irga_tec_tmpr_f_Tot
count
Number of gas analyzer samples with
TEC temperature diagnostic flag
Always
irga_src_pwr_f_Tot
count
Number of gas analyzer samples with
source power diagnostic flag
Always
irga_src_tmpr_f_Tot
count
Number of gas analyzer samples with
source temperature diagnostic flag
Always
irga_src_curr_f_Tot
count
Number of gas analyzer samples with
source current diagnostic flag
Always
irga_off_f_Tot
count
Number of gas analyzer samples with
gas head power down diagnostic flag
Always
irga_sync_f_Tot
count
Number of gas analyzer samples with
synchronization diagnostic flag
Always
irga_amb_tmpr_f_Tot
count
Number of gas analyzer samples with
ambient temperature probe diagnostic
flag
Always
irga_amb_press_f_Tot
count
Number of gas analyzer samples with
ambient pressure diagnostic flag
Always
irga_CO2_l_f_Tot
count
Number of gas analyzer samples with
CO2 1 signal diagnostic flag
Always
irga_CO2_Io_f_Tot
count
Number of gas analyzer samples with
CO2 Io signal diagnostic flag
Always
irga_H2O_I_f_Tot
count
Number of gas analyzer samples with
H2O I signal diagnostic flag
Always
irga_H2O_Io_f_Tot
count
Number of gas analyzer samples with
H2O Io signal diagnostic flag
Always
irga_CO2_Io_var_f_Tot
count
Number of gas analyzer samples with
CO2 Io variation diagnostic flag
Always
irga_H2O_Io_var_f_Tot
count
Number of gas analyzer samples with
H2O Io variation diagnostic flag
Always
irga_CO2_sig_strgth_f_Tot
count
Number of gas analyzer samples with
CO2 signal strength diagnostic flag
Always
irga_H2O_sig_strgth_f_Tot
count
Number of gas analyzer samples with
H2O signal strength diagnostic flag
Always
irga_cal_err_f_Tot
count
Number of gas analyzer samples with
calibration file read error flag
Always
irga_htr_ctrl_off_f_Tot
count
Number of gas analyzer samples with
heater control off diagnostic flag
Always
UxFW_cov
deg C·m·s-1
Covariance of Ux and fine-wire
thermocouple temperature
If FW05,
FW1, or FW3
is used
40
EasyFlux® DL CR6OP
TABLE 4-11. Data fields in the Flux_Notes Output Table
Units
UyFW_cov
deg C·m·s-1
Covariance of Uy and fine-wire
thermocouple temperature
If FW05,
FW1, or FW3
is used
UzFW_cov
deg C·m·s-1
Covariance of Uz and fine-wire
thermocouple temperature
If FW05,
FW1, or FW3
is used
UFW_cov
deg C·m·s-1
Covariance of streamwise wind and
fine-wire thermocouple temperature
after coordinate rotations
If FW05,
FW1, or FW3
is used
VFW_cov
deg C·m·s-1
Covariance of crosswind and fine-wire
thermocouple temperature after
coordinate rotations
If FW05,
FW1, or FW3
is used
WFW_cov
deg C·m·s-1
Covariance of vertical wind and finewire thermocouple temperature after
coordinate rotations
If FW05,
FW1, or FW3
is used
deg C·m·s-1
Covariance of vertical wind and finewire thermocouple temperature after
coordinate rotations and frequency
corrections
If FW05,
FW1, or FW3
is used
The number of valid fine-wire
thermocouple measurements in the
averaging period from which
covariances may be calculated
If FW05,
FW1, or FW3
is used
WFW_cov_fc
Description
Data Field
Included
Data Field Name
FW_samples
count
alpha
decimal
degrees
Alpha angle used for coordinate
rotations (regardless of planar fit or
double rotation method, angle
convention of Wilczak et al. 2001 used)
Always
beta
decimal
degrees
Beta angle used for coordinate rotations
(regardless of planar fit or double
rotation method, angle convention of
Wilczak et al. 2001 used)
Always
gamma
decimal
degrees
Gamma angle used for coordinate
rotations (regardless of planar fit or
double rotation method, angle
convention of Wilczak et al. 2001 used)
Always
height_measurement
m
User entered measurement height of EC
sensors
Always
height_canopy
m
User entered canopy height
Always
surface_type_text
text
User entered surface type
Always
displacement_user
m
User entered displacement height; 0 for
auto calculation
Always
41
EasyFlux® DL CR6OP
TABLE 4-11. Data fields in the Flux_Notes Output Table
Data Field Name
Data Field
Included
Units
Description
d
m
Displacement height used in
calculations; it will equal
displacement_user if user entered a nonzero value; if displacement_user is zero,
program will auto calculate
Always
roughness_user
m
User-entered roughness length. If 0, the
program will autocalculate
Always
z0
m
Roughness length
Always
z
m
Aerodynamic height
Always
MO_LENGTH
m
Monin-Obukhov length
Always
ZL
m·m
Atmospheric surface layer stability
Always
iteration_FreqFactor
count
Number of iterations for recalculating
Monin-Obukhov length and frequency
factors
Always
latitude
decimal
degrees
Latitude; positive for Nothern
hemisphere, negative for Southern
hemisphere
Always
longitude
decimal
degrees
Longitude; positive for Eastern
hemisphere, negative for Western
hemisphere
Always
altitude
m
Number of meters above sea level at the
site
Always
UTC_OFFSET
Hr
The time offset in hours between the
site local standard time and UTC/GMT
Always
separation_x_irga
m
Separation between sonic and gas
analyzer with respect to sonic x-axis
Always
separation_y_irga
m
Separation between sonic and gas
analyzer with respect to sonic y-axis
Always
separation_lat_dist_irga
m
Separation distance between sonic and
gas analyzer along the axis
perpendicular to oncoming wind
Always
separation_lag_dist_irga
m
Separation distance between sonic and
gas analyzer along the axis parallel to
oncoming wind
Always
separation_lag_scan_irga
scans
Number of scans to lag gas analyzer
data relative to sonic data to account for
separation along the axis of oncoming
wind and wind velocity
Always
separation_x_FW
m
Separation between sonic and fine-wire
thermocouple with respect to sonic xaxis
If FW05,
FW1, or FW3
is used
separation_y_FW
m
Separation between sonic and fine-wire
thermocouple with respect to sonic yaxis
If FW05,
FW1, or FW3
is used
-1
42
EasyFlux® DL CR6OP
TABLE 4-11. Data fields in the Flux_Notes Output Table
Description
Data Field
Included
Data Field Name
Units
FW_diameter
m
Effective diameter of fine-wire
thermocouple junction
If FW05,
FW1, or FW3
is used
separation_lat_dist_FW
m
Separation distance between sonic and
fine-wire thermocouple along axis
perpendicular to oncoming wind
If FW05,
FW1, or FW3
is used
separation_lag_dist_FW
m
Separation distance between sonic and
fine-wire thermocouple along axis
parallel to oncoming wind
If FW05,
FW1, or FW3
is used
separation_lag_scan_FW
scans
Number of scans to lag fine-wire
thermocouple data relative to sonic data
to account for separation along axis of
oncoming wind and wind velocity
If FW05,
FW1, or FW3
is used
time_const_FW
m
Calculated time constant of the finewire thermocouple
If FW05,
FW1, or FW3
is used
MAX_LAG
scans
Maximum number of scans to lag gas
analyzer or fine-wire thermocouple data
with respect to sonic data when doing
cross correlation for covariance
maximization. For example, if
MAX_LAG = 2, the program will
consider lags of −2, −1, 0, +1, and +2.
lag_irga
scans
The lag applied to gas analyzer data
with respect to sonic data that
maximizes covariance
Always
lag_FW
scans
The lag applied to fine-wire
thermocouple data with respect to sonic
data that maximizes covariance
Always
FreqFactor_UW_VW
number
Frequency correction factor applied to
momentum fluxes
Always
FreqFactor_WT_SONIC
number
Frequency correction factor applied to
wTs covariance
Always
FreqFactor_WCO2_WH2O
number
Frequency correction factor applied to
wCO2 and wH2O covariance values
Always
FreqFactor_WFW
number
Frequency correction factor applied to
fine-wire thermocouple derived wFW
covariance
Always
amb_rho_d
g·m-3
Average density of dry air using air
temperature from 107 probe
Always
amb_rho_a
kg·m-3
Average density of ambient moist air
using air temperature from 107 probe
Always
rho_d
g·m-3
Average density of dry air using air
temperature from sonic temperature
Always
Always
43
EasyFlux® DL CR6OP
TABLE 4-11. Data fields in the Flux_Notes Output Table
Units
rho_a
kg·m-3
Average density of ambient moist air
using air temperature from sonic
temperature
rho_d_probe
g·m-3
Average density of dry air using air
temperature from a HMP probe
If temp/RH
probe is used
rho_a_probe
kg·m-3
Average density of ambient moist air
using air temperature from a HMP
probe
If temp/RH
probe is used
Cp
J·kg-1·K-1
Specific heat of ambient (moist) air at
constant pressure
Always
Lv
J·g-1
Latent heat of vaporization
Always
T_panel
deg C
Average temperature of the data-logger
wiring panel
Always
batt_volt
volt
Average battery voltage supplying
power to the data logger
Always
Number of slow sequences during the
averaging interval (for example, the
number of times biomet and energy
balance sensors were measured)
Always
slowsequence_Tot
count
nr01_heater_secs
s
cnr4_fan_secs
Description
Data Field
Included
Data Field Name
Always
Number of seconds in the averaging
interval that the NR01 heater was
enabled
If NR01 used
s
Number of seconds in the averaging
interval that the CNR4 fan was enabled
If CNR4 and
CNF4 used
cnr4_heater_1_secs
s
Number of seconds in the averaging
interval that the CNR4 heater #1 was
enabled
If CNR4 and
CNF4 used
cnr4_heater_2_secs
s
Number of seconds in the averaging
interval that the CNR4 heater #2 was
enabled
If CNR4 and
CNF4 used
sn500_heater_secs
S
Number of seconds in the averaging
interval that the SN500SS heater was
enabled
If SN500SS
used
V_CS320
mV
T_CS320
deg C
x_incline
Output voltage from CS320
If CS320 used
Temperature of CS320
If CS320 used
decimal
degrees
Sensor’s incline relative to its x axis
If CS320 used
y_incline
decimal
degrees
Sensor’s incline relative to its y axis
If CS320 used
z_incline
decimal
degrees
Sensor’s incline relative to its z axis
If CS320 used
44
EasyFlux® DL CR6OP
TABLE 4-11. Data fields in the Flux_Notes Output Table
Data Field Name
Data Field
Included
Units
Description
W∙m2∙mV-1
Calibrated multiplier for heat flux plate.
If using HFP01, this value is 1000
divided by the sensitivity as reported in
the calibration sheet. If using HFP01SC,
this is determined from self calibration.
x is an index for the number of sensors.
If HFP01 or
HFP01SC
used
shfp_cal_fail_x_1_1
text
Reads TRUE if any of the readings
from HFP01SC were not valid (NAN)
or if calibrated sensitivity was less than
80% or more than 105% of the nominal
sensitivity reported on the sensor’s
calibration sheet. x is an index for the
number of sensors.
If HFP01SC
used
process_time_Avg
ms
Average processing time for each scan
Always
process_time_Max
ms
Maximum processing time for a scan
Always
buff_depth_Max
number
Maximum number of records stored in
the buffer
Always
shfp_cal_x_1_1
4.5
Program Sequence of Measurement and Corrections
The main correction procedures and algorithms implemented into the program
are listed below. For more information on the sequence of measurements and
corrections, refer to Appendix I, EasyFlux DL CR6OP Process Flow Diagram
(p. I-1). The appendices of this manual will give addition information on each
major correction and its implementation in the program.
1.
Despike and filter 10 Hz data using sonic and gas analyzer diagnostic
codes, and signal strength and measurement output range thresholds.
2.
Coordinate rotations with an option to use the double rotation method
(Tanner and Thurtell 1969), or planar fit method (Wilczak et al.
2001).
3.
Lag CO2 and H2O measurements against sonic wind measurements for
maximization of CO2 and H2O fluxes (Horst and Lenschow 2009,
Foken et al. 2012), with additional constraints to ensure lags are
physically possible.
4.
Frequency corrections using commonly used cospectra (Moore 1986,
van Dijk 2002a, Moncrieff et al. 1997) and transfer functions of block
averaging (Kaimal et al. 1989), line/volume averaging (Moore 1986,
Moncrieff et al. 1997, Foken et al. 2012, van Dijk 2002a), time
constants (Montgomery 1947, Shapland et al. 2014, Geankoplis
1993), and sensor separation (Horst and Lenschow 2009, Foken et al.
2012).
5.
A modified SND correction (Schotanus et al. 1983) to derive sensible
heat flux from sonic sensible heat flux following the implementation
as outlined in van Dijk 2002b. Additionally, fully corrected real
45
EasyFlux® DL CR6OP
sensible heat flux computed from fine-wire thermometry may be
provided.
5.
6.
Correction for air density changes using WPL equations (Webb et al.
1980).
7.
Data quality qualifications based on steady state conditions, surfacelayer turbulence characteristics, and wind directions following Foken
et al. 2012 (or Foken et al. 2004 for the Flux_AmeriFluxFormat
output table).
8.
If energy balance sensors are used, calculation of energy closure based
on energy balance measurements and corrected sensible and latent
heat fluxes.
9.
Footprint characteristics are computed using Kljun et al (2004) and
Kormann and Meixner (2001).
References
Foken et al. (2012) “Eddy Covariance: A Practical Guide to Measurement and
Data Analysis” by Aubinet, Vesala, and Papale from Springer. This book
consists of chapters that are written by specialists in the field. Chapter 4
titled “Corrections and Data Quality Control” is written by Foken et al.
Foken,T,M., Göockede, M., Mauder, L., Mahrt, B., Amiro, W. Munger. 2004.
Post-Field Data Quality Control. Eds: X. Lee, W. Massman, B. Law.
Handbook of Micrometeorology: A Guide for Surface Flux Measurement
and Analysis. Kluwer Academic Publishers. Dordrecht, p. 181-208.
Geankoplis, C.J. 1993. Transportation Processes and Unit Operation. 3rd
Edition. PTR Prentice Hall, New Jersey. pp 114-131 and Appendix.
Horst, T.W., and D.H. Lenschow. 2009. Attenuation of scalar fluxes measured
with spatially-displaced sensors. Boundary-Layer Meteorology 130:275300.
Kaimal, J.C., S.F. Clifford, R.J. Lataitis. 1989. Effect of finite sampling on
atmospheric spectra. Boundary-Layer Meteorology 7:827-837.
Moncrieff, J.B., J.M. Massheder, H. de Bruin, J.A. Elbers, T. Friborg, B.
Heusinkveld, P. Kabat, S. Scott, H. Soegaard, A. Verhoef. 1997. A system
to measure surface fluxes of momentum, sensible heat, water vapour and
carbon dioxide. Journal of Hydrology 188-189:589-611.
Montgomery, R.B. 1947. Viscosity and thermal conductivity of air and
diffusivity of water vapor in air. J. Meteor 4:193–196.
Moore, C.J. 1986. Frequency response corrections for eddy correlation
systems. Boundary-Layer Meteorology 37:17-35.
Schotanus, P.S., F.T.M. Nieuwstadt, H.A.R. Debruin. 1983. Temperature
measurement with a sonic anemometer and its application to heat and
moisture flux. Boundary-Layer Meteorology 26:81-93.
46
EasyFlux® DL CR6OP
Shapland, T.M., R.L. Snyder, K.T. Paw U, A.J. McElrone. 2014.
Thermocouple frequency response compensation leads to convergence of
the surface renewal alpha calibration. Agricultural and Forest Meteorology
189-190:36-47.
Tanner, C.B., and G.W. Thurtell. 1969. “Anemoclinometer measurements of
Reynolds stress and heat transport in the atmospheric surface layer science
lab”, US Army Electronics Command, Atmospheric Sciences Laboratory
TR ECOM 66-G22-F. pp: R1-R10.
van Dijk, A. 2002a. Extension of 3D of “the effect of linear averaging on scalar
flux measurements with a sonic anemometer near the surface” by
Kristensen and Fitzjarrald. Journal of Atmospheric and Ocean Technology
19:80-19.
van Dijk, A. 2002b. The Principle of Surface Flux Physics. Research Group of
the Royal Netherlands Meteorological Institute and Department of
Meteorology and Air Quality with Agricultural University Wageningen.
65p.
Webb, E.K., G.I. Pearman, R. Leuning. 1980. Correction of flux measurements
for density effects due to heat and water transfer. Quart. J. Met. Soc.
106:85-100.
Wilczak, J.M., S.P. Oncley, S.A. Stage. 2001. Sonic anemometer tilt correction
algorithm. Boundary-Layer Meteorology 99:127-150.
47
Appendix A. Vapor Pressure and
Dewpoint Temperature
IRGAs require an occasional span (i.e., field calibration) of water vapor. When
doing a span, the humidity of the span gas must be known and entered using
the On Site Zero & Span menu on the data-logger keypad (or alternatively, it is
entered into ECMon, the IRGA user-interface software). Although this
humidity may be expressed in various units, dewpoint temperature is used
since the H2O span gas is typically generated with a dewpoint generator.
Because dewpoint temperature is used, it is sometimes desirable to convert the
water vapor density measurements of the IRGA to dewpoint temperature,
especially as it provides comparability with the span gas before and after the
span. Accordingly, the program converts water vapor density to dewpoint
temperature using the algorithms described in this appendix.
A.1 Equations to Calculate Dewpoint Temperature
from Water Vapor Density
An EC system measures and reports water vapor density (ρw in g·m-3), air
temperature (T in °C), and total atmospheric pressure (P in kPa). Using the
ideal gas equation, vapor pressure (e in kPa) can be calculated using:
e = ρw Rv (T + 27315
. )
(A-1)
where:
Rv is the gas constant for water vapor (4.61495·10-4 kPa·m3·K-1·g-1))
In this equation, if e were saturation water vapor pressure (es in kPa), T would
be dewpoint temperature (Td). However, since the air is unlikely to be
saturated, other equations are needed to estimate the dewpoint temperature.
Buck (1981) developed equations to relate saturation water vapor pressure to
dewpoint temperature in moist air. The equations were designed to be easily
implemented in a computer program for conversion of saturation water vapor
pressure to dewpoint temperature, or vice versa. The general model of
equations was:
es = f w (Td , P )ews (Td )
(A-2)
where:
es is saturation vapor pressure, and ews(Td) is saturation vapor pressure of pure
water at pressure of the sea level, given by:
 bTd 
ews = a exp

 Td + c 
(A-3)
where: a, b, and c are parameters, and fw(Td, P) is the enhancement factor that
is the ratio of vapor pressure of moist air to that of pure water vapor, given by
A-1
Appendix A. Vapor Pressure and Dewpoint Temperature
f w (Td , P ) =
es
= A + P B + C(Td + D + EP ) 2
ews
[
]
(A-4)
where:
A, B, C, D, and E are parameters. In Buck (1981), Figure 1 and Table 2 show
results for ews(Td) from model (3), and Figure 3 and Table 3 show results for
fw(Td, P) from model (4). Combing the saturation water vapor pressure
equation, which has an error of ± 0.05% in a temperature range of –40 to
+50 °C and within a normal range of surface layer pressures, with the
enhancement factor, which has an equivalent error of ± 0.05% in the same
temperature range, generates the following water vapor pressure equation for
moist air:
17.368Td

0.61121 exp( T + 238.88 ) f w (Td , P )
d

es (Td , P) = 

17.966Td
061121 exp(
) f w (Td , P )

Td + 24715
.
Td ≥ 0
(A-5)
Td < 0
where:
[
+ P 348
.
. × 10 −5 + 7.4 × 10 −9 (Td + 30.6 − 0.38 P)
f w (Td , P ) = 100041
2
]
(A-6)
Given measured water vapor pressure and total pressure from an EC system,
the only unknown variable in equations (A-5) and (A-6) is dewpoint
temperature. However, analytically solving the equations for Td is not feasible
due to complication from the quadratic term in equation (A-6). Fortunately, the
enhancement factor is a very weak function of Td, which is why Buck (1981)
recommended that “a rough approximation of Td will serve nicely in
calculating fw(Td, P)”. A question then emerges concerning what should be
considered reasonable for a rough approximation. In the case that relative
humidity is high, the air temperature measured by an EC system may be close
enough to be a rough estimation of Td, however this may be considered
unreasonable in the sense of a numerical analysis because an error range is
unknown. And in case when relative humidity is low, this approximation could
differ from the true dewpoint temperature by more than 10 °C, making it even
more unreasonable in terms of atmospheric physics. Thus another approach is
proposed by Buck (1981) for calculating a more accurate approximation of Td
as described below.
A.2 Approach to Approximation of Td for the
Enhancement Factor
For general use to calculate dewpoint temperature (Td_gu where subscript gu
indicates general use), Buck (1981) recommended the following equation:
(
)
es Td _ gu , P = 0.61121 exp(
17.502Td _ gu
Td _ gu + 240.97
) f w ( P)
(A-7)
A-2
Appendix A. Vapor Pressure and Dewpoint Temperature
Where:
f w ( P ) = 10007
.
+ 3.46 × 10 −5 P
(A-8)
Unlike fw(Td, P) in equation (A-5), fw(P) in equation (A-7) does not include a
quadratic term of dewpoint temperature, Td_gu can be analytically expressed in
terms of saturation water pressure and total pressure as
Td _ gu =
240.97{ln es − ln[0.61121 f w ( P )]}
(A-9)
17.502 − {ln es − ln[0.61121 f w ( P )]}
Because in equation (A-7) the saturation water vapor equation for pure water
has an error limit of ± 0.2% in a temperature range of −20 to +50 °C and a
normal range of surface-layer pressures [see Figure 1 and Table 1 in Buck
(1981)], and because the enhancement factor also has an error limit of ±0.2% in
a temperature range of −40 to +50 °C [see Figure 3 and Table 3 in Buck
(1981)], the dewpoint temperature for general use (Td_gu) as calculated using
equation (10) has known an error limit and can be considered a relatively
accurate approximation for Td in equation (A-6).
A.3 Dewpoint Temperature Equation
Now that a good approximation for Td is found, Td_gu from equation (A-9)
may be substituted for Td into equation (A-6). The resulting enhancement
factor can then be used along with measured water vapor pressure and total
pressure to give a more accurate dewpoint temperature (Td):
{
{
[
{
[
[
]}
]}
Td _ gu ≥ 0
[
]}
]}
Td _ gu < 0
 238.88 ln es − ln 0.61121 f w (Td _ gu , P )

17.368 − ln es − ln 0.61121 f w (Td _ gu , P )

Td = 

. ln es − ln 0.61121 f w (Td _ gu , P )
 24715

17.966 − ln es − ln 0.61121 f w (Td _ gu , P )
{
(A-10)
Note that in this equation, the variable of Td_gu instead of Td in equation (A-5) is
used to judge the boundary for use of two sub-equations, although using either
variable for the boundary should yield nearly the same result since according to
Buck (1981), Td and Td_gu should be within 0.1 °C of each other as long as the
magnitude of dewpoint temperature is less than 50 °C. Furthermore, the two
sub-equations in equation (5) have the same accuracy around 0 °C dewpoint
temperature for a range of −1 to +1 °C [see Figure 1 in Buck (1981)] and are
effectively interchangeable from −1 to +1 °C. Because the two sub-equations in
equation (A-10) are simply rearrangements of the two sub-equations in
equation (A-5), respectively, the two sub-equations in equation (A-10) also
must be interchangeable from −1 to 1 °C.
A.4 Online Flux Program
The data-logger program calculates Td by first converting measured water
vapor density to water vapor pressure, e (equation A-1). Because dewpoint
A-3
Appendix A. Vapor Pressure and Dewpoint Temperature
temperature is the temperature at which e becomes the saturated vapor
pressure, es, we use the value of e from the IRGA in place of es in equation (A10).
A.5 Reference
Buck, A. L.: 1981, “New equations for computing vapor pressure and
enhancement factor”, J. Applied Meteorol., 20:1527-1532.
A-4
Appendix B. Coordinate Rotations:
Double Rotation Method
The covariance of vertical wind with a scalar (for example, heat, water vapor,
or CO2) yields a scalar flux. The covariance of vertical wind with horizontal
wind along with air density, gives momentum flux. If the measured vertical
wind is not truly normal to the surface of interest, the flux estimates are in error
(Kaimal and Haugen 1969). Flow velocities measured by a three-dimensional
anemometer are defined in an instrument coordinate system. Although the
instrument coordinate system is defined accurately in the manufacturing
process by precision machining, and field mounting may be done carefully to
align the sensor’s vertical axis (zm axis) to be perpendicular to the field surface,
it is almost impossible for the zm axis to be aligned perfectly. Some degree of
leveling errors will be present and surface undulation may occur. Tilts of the
order of a degree could cause errors in excess of 100% for momentum flux
(Kraus 1968). Kaimal and Haugen (1969) further confirmed that large errors
can occur in the measurement of momentum flux unless the sensors are
vertically aligned and horizontally leveled with a great accuracy (at least
± 0.1°). The errors caused by tilt in estimates of flux can be corrected using the
mathematical method of coordinate transforms based on the physical process of
turbulent flows (mean vertical velocity of dry air is zero).
B.1 Matrix Transformation of Instrument to Flow
Coordinate System
Let us define a 3D right-handed orthogonal instrument coordinate system
where um, vm, and wm are the orthogonal components of the 3D wind vector
reported by the sonic anemometer. Now suppose that it is more convenient to
report the same vector but using components on another orthogonal coordinate
system that we will call the flow coordinate system, where the u-axis is parallel
to the mean wind vector over some period of time (i.e., the streamwise vector),
v is the mean crosswind component, and w is the vertical component. This is
possible using the matrix transformation presented in B-1. This transformation
performs the following functions: 1) the instrument coordinate system is
rotated about the wm-axis by a counterclockwise angle γ as viewed against the
wm direction to the 1st rotated coordinate system. If components are reported at
this intermediary stage, u1, v1, w1 are used, where subscript “1” indicates the
value of variable after the 1st rotation; 2) next the coordinate system is rotated
about the v1-axis by a counterclockwise angle α as viewed down the v1 axis.
This results in the 2nd rotated system, where u2, v2, and w2 are the components
of the wind vector after the 2nd rotation; 3) finally the 2nd rotated system is
rotated about the u2-axis by a counterclockwise angle β as viewed against u2
axis, resulting in the final flow coordinate system (u, v, w).
B-1
Appendix B. Coordinate Rotations: Double Rotation Method
NOTE
u
v
=
 
 w
 
The angle rotations from the instrument coordinate system to
natural flow coordinate system are used inconsistently in the
literature. Tanner and Thurtell (1969) used counterclockwise
rotations about vertical and streamwise axes and clockwise
rotation about lateral axis. Wilczak et al (2001) used clockwise
rotations for all of the three axes. The online flux program uses the
rotation convention of Wilzcak et al (2001) regardless of whether
the double rotation or the planar fit method is used.
0
1
 0 cos β

 0 − sin β

 cos α
 0
sin β


cos β  sin α
0
0
1
0
− sin α  cos γ
 − sin γ
0


cos α  0
sin γ
cos γ
 um 
 u1 
 u2 




 
= U ( β ) V=
U=
U ( β ) v2
(α ) W (γ ) vm
( β ) V (α ) v1
 
 
 
w 
w 
w 
 m
 1
 2
0
0  u m



0 vm
 
 
1  wm 
(B-1)
Where U(β), V(α), and W(γ) are the three 3 x 3 matrices shown in the first
equation of (B-1). The rotations are performed sequentially as shown in the
second equation of (B-1). The 2nd and 3rd rotation angles are defined with
respect to the coordinates after the preceding rotation.
B.2 Natural Wind Coordinated System
A 3D right-handed natural wind coordinate system has the u-axis parallel to the
mean or streamwise flow; thus the mean wind components along v-axis (𝑣𝑣̅ ) and
w-axis (𝑤𝑤
�) are zero, as shown in FIGURE B-1.
FIGURE B-1. As viewed down the zm and z axes and assuming the
vertical wind component is zero, horizontal wind components vm
and um are measured in the instrument coordinate system and then
rotated by angle γ, yielding the streamwise wind velocity vector, u.
The u and v axes of the flow coordinate system are also shown.
B-2
Appendix B. Coordinate Rotations: Double Rotation Method
Because velocity in the v direction (orthogonal to u direction) is zero and flow
is horizontally homogenous, the tilt in the v direction causes less error than in
the u direction. Additionally, the calculation of the 3rd rotation angle assumes
the following:
'
'
w2 v2 = 0
which may not necessarily be true in field conditions and introduces more
uncertainties; therefore, the third rotation is not recommended (Wilczak et al.
2001). The algorithm for the first two rotations is given as follows:
angle γ in FIGURE B-1 can be approximated by:
 vm 

 um 
γ = arctan 
(B-2)
This angle is the mean wind direction of 0 to 360° that is output from the
CRBasic instruction of WindVector used in the data logger. The anticlockwise
angle α around the v1-axis is given by:
wm
=
− arctan
u1
um cos γ + vm sin γ
w1
α=
− arctan
(B-3)
The CRBasic function ATN2() is used to calculate (B-3) and return an angle in
the range of ±180°. The result, however, must be further constrained to the
range of ±90° since relative to γ, the range of this angle is narrower and should
be within ±90°.
According to equation (B-1), the first two rotations are expressed as:
 u2  cos α cos γ cos α sin γ − sin α   um 
 um 
v  =
 − sin γ



v =
cos γ
0
R v 
(B-4)
 2 
 m  2  m 
 w2   sin α cos γ sin α sin γ cos α   wm 
 wm 
B.2.1 Covariance of Momentum Variables after Coordinate
Rotation
Using matrix operations, the covariance of the momentum variables can be
reasonably found as follows:
From (B-4), the mean terms can be written as:
 u2 
 um 


v 
=
v
R=
2
 2
 m
 w2 
 wm 
 cos α ( um cos γ + vm sin γ ) − wm sin α 


0


sin α ( um cos γ + vm sin γ ) + wm cos α 
(B-5)
B-3
Appendix B. Coordinate Rotations: Double Rotation Method
And the fluctuation terms can be written as:
 u2′ 
 um′ 
 v′  = R  v′ 
 2 2 m
 w2′ 
 wm′ 
(B-6)
Self-multiplication generates:
 u2′ 
 v′  u '
 2  2
 w2′ 
v2'
 um′ 
w2'  = R2  vm′  um'
 
 wm′ 
vm'
wm'  R2T
(B-7)
Applying Reynolds averaging yields:
 u2' 2

 u2' v2'

u2' w2'

u2' v2'
v2' 2
v2' w2'
u2' w2' 
 um' 2


v2' w2'  = R2  um' vm'


w2' 2 
um' wm'


um' vm'
vm' 2
vm' wm'
um' wm' 

vm' wm'  R2T

wm' 2 

(B-8)
See Appendix B.3, Extended Equations (p. B-5), for the expansion of these
matrix operations for CRBasic coding.
B.2.2 Covariance of a Scalar Variable and Momentum Variable
After Second Coordinate Rotation
The covariance of a scalar variable, Q, and each rotated wind variable is found
by multiplying the fluctuation of the scalar, Q’, to equation B-6, to give
equation B-9:
 u2′ 
 um′ 
Q '  v2′  = R2 Q '  vm′ 
 
 
 w2′ 
 wm′ 
(B-9)
Then by applying Reynolds averaging:
 Q 'u2' 
 Q 'um' 




 Q ' v2'  = R2  Q ' vm'  =
 ' '
 ' '
Q w2 
Q wm 
(
)
 cos α Q 'um' cos γ + Q ' vm' sin γ − Q ' wm' sin α 


' '
' '


−Q um sin γ + Q vm cos γ


sin α Q 'u ' cos γ + Q ' v ' sin γ + Q ' w' cos α 
m
m
m


(
)
(B-10)
B-4
Appendix B. Coordinate Rotations: Double Rotation Method
B.3 Extended Equations
The extended form of Equation (B-8) is given by:
 u '2
 2
 u2' v2'

u2' w2'

u2' w2'   cos α cos γ

'
'

v2 w2 =  − sin γ
 
'2
w2   sin α cos γ

u2' v2'
'2
2
v
v2' w2'
cos α sin γ
cos γ
sin α sin γ
 um'2
− sin α  
' '
0   um vm

cos α  u ' w'
 m m
um' vm'
'2
m
v
vm' wm'
um' wm'   cos α cos γ

'
'

vm wm  cos α sin γ

'2
wm   − sin α

− sin γ
sin α cos γ 
cos γ
sin α sin γ
0
cos α



(B-11)
In Equation (B-11), the extended forms of variance terms in the matrix on the left hand side are, expressed in terms of the
matrices on the right hand side:
(
)
(
u ′2 cos 2 α u ′2 cos 2 γ + v′2 sin 2 γ + w′2 sin 2 α + u ′ v′ cos 2 α sin 2γ − sin 2α u ′ w′ cos γ + v′ w′ sin γ
=
2
m
m
m
m m
m m
m m



2
2
2
2
2
v2′ = um′ sin γ + vm′ cos γ − um′ vm′ sin 2γ


 w′2 sin 2 α u ′2 cos 2 γ + v′2 sin 2 γ + w′2 cos 2 α + u ′ v′ sin 2 α sin 2γ + sin 2α u ′ w′ cos γ + v′ w′ sin γ
=
m
m
m
m m
m m
m m
 2
(
)
(
)
(B-12)
)
In Equation (B-11), the extended forms of covariance terms in the matrix of left hand side are expressed in terms of the
matrices on the right hand side
(
)
1

− um′2 − vm′2 cos α sin 2γ + um′ vm′ cos α cos 2γ + sin α um′ wm′ sin γ − vm′ wm′ cos γ
u2′ v2′ =
2


 ' 1
=
sin 2α  um′2 cos 2 γ + vm′2 sin 2 γ − wm′2 + um′ vm′ sin 2γ  + cos 2α um′ wm′ cos γ + vm′ wm′ sin γ
u2′ w2


2



1

v2′ w2′ =
− sin α  um′2 − vm′2 sin 2γ − um′ vm′ cos 2γ  − cos α um′ wm′ sin γ − vm′ wm′ cos γ

2

(
)
(
(
)
)
(
(
)
(B-13)
)
B-5
Appendix B. Coordinate Rotations: Double Rotation Method
B.4 References
Kaimal, J. C. and Haugen, D. A.: 1969, “Some errors in the measurement of
Reynolds stress”, J. Applied Meteorol., 8:460-462.
Kraus, E. B.: 1968, “What we do not know about the sea-surface wind stress”,
Bull. Amer. Meteorol. Soc., 49:247-253.
Lettau, H. H.: 1968, “Three-dimensional turbulence in unidirectional mean
flow”, In studies of the effects of boundary modification in problems of
small areas meteorology. US Army Electronics Command Technical
Report ECOM66-624-A. pp: 127-156.
Sutton, O. G.: 1948, Atmospheric turbulence. Methuen & Co. Ltd., London.
Tanner, C. B., and Thurtell, G. W.: 1969, “Anemoclinometer measurements of
Reynolds stress and heat transport in the atmospheric surface layer science
lab”, US Army Electronics Command, Atmospheric Sciences Laboratory
TR ECOM 66-G22-F. pp: R1-R10.
Wilczak, J. M., S. P. Oncley, S. A. Stage.: 2001, “Sonic Anemometer tilt
correction algorithm”, Boundary-Layer Meteorol. 99:127-150.
B-6
Appendix C. Coordinate Rotations:
Planar Fit Method
C.1 Planar Fit
The planar fit method of coordinate rotations is based on Wilczak et al. (2001).
The method is used to transform the measured wind velocities in the righthanded measurement coordinate system of a sonic anemometer (um, vm, wm),
where subscript m indicates measurement coordinate system, to the natural
wind coordinate system (u, v, w) if the three rotations are performed.
The first and the second rotations in the planar fit are related to flux; that is,
both rotations transform the measured wind velocities to a coordinate system
with the horizontal coordinate plane parallel to the natural wind plane. The
algorithm used for the planar fit rotations mathematically describes two
counterclockwise coordinate rotations, first about the um-axis by an angle β,
and second about the intermediate v1-axis by an angle α, where the subscript 1
indicates the variable after the 1st rotation. The expression of measured fluxes
in this coordinate system avoids the errors in fluxes due to the tilt of the sonic
anemometer vertical axis away from the vertical axis of the natural wind flow
coordinate system.
The angle α is the angle between the instrument um-axis and the u-v plane of
natural wind (i.e., the tilt angle of the instrument vertical wm-axis away from
the natural wind vertical axis in the instrument um-wm plane), where α increases
clockwise in the 360° domain, which means a clockwise rotation for angle α is
positive and a counterclockwise rotation is negative. The angle β is the angle
between the instrument vm-axis and the u-v plane (i.e., the tilt angle of the wmaxis away from the natural wind vertical axis in the instrument vm-wm plane),
where β increases counterclockwise in the 360° domain, which means a
clockwise rotation for angle β is negative and a counterclockwise rotation is
positive.
Even if the sonic anemometer is well secured and leveled in the field, wind
may force the mounting structure and sonic anemometer to tilt, especially if the
tower is tall (greater than 3 m, for example). The degree of the inclination
depends on the momentum load determined mainly by wind speed.
Furthermore, the natural u-v plain relative to a fixed plain varies if the field
undulates and has a slope that varies from different directions. Therefore, in a
given field station, the two coordinate rotation angles should be defined as a
function of wind direction and wind speed. However, it is not practical to
determine the angles for every possible wind direction and speed, so instead,
the angles are defined for certain sectors of wind direction using data averaged
over a time interval (for example, 30 min), and the dependence on wind speed
is not considered.
For the online planar fit algorithm, four sectors or ranges of wind direction in
the instrument coordinate system are used. The boundaries of sectors match the
boundaries of sectors in “horizontal orientation of the sonic anemometer” for
data quality classification by Foken et al. (2012). Using statistically sufficient
data (see models [37] to [48] in Wilczak et al. [2001]) from the four direction
sectors, a user can calculate the two angles for the four sectors, respectively.
C-1
Appendix C. Coordinate Rotations: Planar Fit Method
The four ranges are given below along with the angle names used in the
program:
Sector 1: [0, 60] and [300, 360]
α_60_300
β_60_300
Sector 2: (60, 170]
α_60_170
β_60_170
Sector 3: (170, 190)
α_170_190
β_170_190
Sector 4: [190, 300)
α_190_300
β_190_300
Sector 1: [0, 60] and [300, 360]
Sector 2: (60, 170]
Sector 3: (170, 190)
Sector 4: [190, 300)
FIGURE C-1. Wind direction sectors for which planar fit angles are
found by the user and entered into the program.
C-2
Appendix C. Coordinate Rotations: Planar Fit Method
C.2 Algorithm
C.2.1 Variables and Model
To use the planar fit method, the user must independently (using postprocessing software and time-series data for an appropriate length of time)
determine the angles for each wind sector and enter these values with the data
logger keypad (see Section 4.2, Enter Site-Specific Variables with Data Logger
Keypad (p. 14)). The online flux program will then select the appropriate angles
based on the mean wind direction during the averaging interval. The CRBasic
code that corresponds to this is as follows:
If (wind direction ≤ 60) OR (wind direction ≥ 300) then:
α = α_60_300
β = β_60_300
If (60 < wind direction ≤ 170) then:
α = α_60_170
β = β_60_170
If (170 < wind direction < 190) then:
α = α_170_190
β = β_170_190
If (190 < wind direction < 300) then:
α = α_190_300
β = β_190_300
Given a pitch angle of α and a roll angle of β, the three orthogonal wind
velocities (u, v, w) after the two rotations can be expressed in terms of the two
angles (α, β) and three directly measured wind velocities (um, vm, wm) as:
0
 u   cos α 0 − sin α  1
v =  0
1
0   0 cos β
  

 w   sin α 0 cos α   0 − sin β
0
  um 
sin β   vm 
 
cos β   wm 
(C-1)
Further:
u 
v
=
 
 w 
 cos α sin α sin β − sin α cos β   um 
 um 
=
 v  R v 
0
cos β
sin β

 m  p  m 
 wm 
 sin α − cos α sin β cos α cos β   wm 
(C-2)
Where Rp is the 3 x 3 matrix in (C-2), and subscript p indicates the planar fit
approach for the rotations.
C.2.2 Covariance of Momentum Variables After Two
Coordinate Rotations
Using matrix operations, the covariance of the momentum variables can be
reasonably found as follows.
C-3
Appendix C. Coordinate Rotations: Planar Fit Method
Using equation (C-2), we can express the mean terms as:
u 
 um 


v 
=
v
R=
  P m
 w 
 wm 
um cos α + sin α ( vm sin β − wm cos β ) 


vm cos β + wm sin β


um sin α − cos α ( vm sin β − wm cos β ) 
(C-3)
and fluctuation terms as:
 u′ 
 um′ 
 v′  = R  v′ 
  p m
 w′
 wm′ 
(C-4)
Self-multiplication generates:
 u′ 
 um′ 
 v′  [u ′ v′ w′] = R  v′  u ' v '
p
 
 m  m m
 w′
 wm′ 
wm'  RpT
(C-5)
Applying Reynolds averaging yields:
 u '2 u ′v′ u ' w' 
 um'2



 u 'v ' v '2 v′w′  = Rp  um' vm'



u ′w′ v′w′ w'2 
um' wm'



um' vm'
vm'2
vm' wm'
um' wm' 

vm' wm'  RpT

wm'2 

(C-6)
These matrix operations can then be expanded to be used in the online flux
program. See Appendix C.3, Extended Equations (p. C-6), for the coding.
C.2.3 Covariance of a Scalar Variable with Momentum Variable
After Planar Fit Coordinate Rotation
The covariance of a scalar variable, Q, and each rotated wind variable is found
by multiplying the fluctuation of the scalar, Q’, to equation (C-4):
 u′ 
 um′ 
' 


Q v′ = RpQ vm′ 
 
 
 w′
 wm′ 
'
(C-7)
C-4
Appendix C. Coordinate Rotations: Planar Fit Method
Applying Reynolds averaging yields:
 Q 'u ′ 
 Q 'um' 




' '
 Q ' v′  R=


Q
v
=
P
m
 ' 
 ' '
Q w′ 
Q wm 
(
Q 'um′ cos α + sin α Q ' vm′ sin β − Q′wm′ cos β

'
'
'

Q vm′ cos β + Q wm sin β

 Q 'u ′ sin α − cos α Q ' v′ sin β − Q ' w' cos β
m
m
 m
(
)
)
 (C-8)



C-5
Appendix C. Coordinate Rotations: Planar Fit Method
C.3 Extended Equations
The extended form of Equation (C-6) is given by:
 u '2 u ′v′ u ′w′

  cos α
 u′v′ v '2 v′w′  =  0

 
u′w′ v′w′ w'2   sin α


sin α sin β
cos β
− cos α sin β
 um'2
− sin α cos β  
  u ' v'
sin β
 m m
cos α cos β  u ' w'
 m m
um' vm'
'2
m
v
vm' wm'
um' wm'   cos α

'
'

vm wm  sin α sin β

wm'2   − sin α cos β

0
cos β
sin β
sin α

− cos α sin β 

cos α cos β 
(C-9)
In equation (C-9), the extended forms of variance terms in the matrix on the left hand side are expressed in terms of the
matrices on the right hand side:
(
)
2
2
2
2
2
2
2
u ′ 2 =
u m′ cos α + sin α vm′ sin β − vm′ wm′ sin 2 β + wm′ cos β + sin 2α ( u m′ vm′ sin β − u m′ wm′ cos β )



2
2
2
2
2
v′ =vm′ cos β + vm′ wm′ sin 2 β + wm′ sin β


 w′2 =u ′2 sin 2 α + cos 2 α v′2 sin 2 β − v′ w′ sin 2 β + w′2 cos 2 β − sin 2α ( u ′ v′ sin β − u ′ w′ cos β )
m
m
m m
m
m m
m m

(
(C-10)
)
In equation (C-9), the extended forms of covariance terms in the matrix of the left hand side are expressed in terms of the
matrices on the right hand side:
(
)
u ′v′ = sin α  1 v′2 − w′2 sin 2 β − v′ w′ cos 2 β  + cos α u ′ v′ cos β + u ′ w′ sin β
(mm
)
m
m m
m m

 2 m




1
2
2
2
2
2
sin 2α u m′ − vm′ sin β − wm′ cos β + vm′ wm′ sin 2 β − cos 2α ( um′ vm′ sin β − um′ wm′ cos β )
u ′w=′
2



 1 v′2 − w′2 sin 2 β − v′ w′ cos 2 β  + sin α u ′ v′ cos β + u ′ w′ sin β
v′w′ =
− cos α
(mm
)
m m
m
m m
 2 m


(
)
(
(C-11)
)
C-6
Appendix C. Coordinate Rotations: Planar Fit Method
C.4 References
Tanner, C. B. and Thurtell, G. W.: 1969, “Anemoclinometer measurements of
Reynolds stress and heat transport in the atmospheric surface layer”,
Research and Development Tech. Report ECOM 66-G22-F.
Wilczak, J.M., S. P. Oncley, S. A. Stage.: 2001, “Sonic Anemometer tilt
correction algorithm”, Boundary-Layer Meteorol. 99:127-150.
Foken et al. (2012) “Eddy Covariance: A Practical Guide to Measurement and
Data Analysis” by Aubinet, Vesala, and Papale from Springer. This book
consists of chapters that are written by specialists in the field. Chapter 4
titled “Corrections and Data Quality Control”.
C-7
Appendix D. Frequency Corrections
D.1 Introduction
The flux of any scalar (e.g., heat, CO2, or H2O) or momentum is a summed
amount of the scalar or momentum through a unit area per unit time (e.g., g m-2
s-1 for H2O), and transported by eddies of various frequencies (i.e., various
sizes and velocities). The relative contribution of flux as a function of eddy
frequency results in a cospectrum for covariance. The total or net flux is found
by integrating over this cospectrum. In order to generate an accurate
cospectrum, a measurement system must be able to measure and process
fluctuations at all frequencies that contribute to the flux. In practice, however,
sensor measurements and digital processing methods cannot fully capture the
instantaneous changes at all frequencies. The uncaptured changes related to
larger eddies results in low frequency losses, and the uncaptured changes
related to smaller eddies results in high frequency losses. Accounting for these
frequency losses requires the corrections described herein.
D.2 Frequency Loss
D.2.1 High Frequency Loss
High frequency loss is caused by sensor response delay, signal averaging over
the measurement path or volume (line/volume averaging), sensor separation,
and low-pass filtering. A brief description of each of these causes is provided
below.
Response delay: A sensor requires a finite amount of time to measure a
stimulus. When fluctuations of a scalar or wind occur faster than this time, high
frequency losses occur. The response delay is described using a time constant
defined as the time the sensor requires to respond to 63.2% of a change in the
input stimulus.
Line/volume averaging: Most sensors measure the change in a variable of
interest over a linear measurement path (CSAT3) or measurement volume
(KH20) and report its spatially averaged value over that path or volume at the
measurement time. Such a sensor cannot accurately report a change in the
variable at a scale of eddies smaller than the dimension of the path or volume,
which attenuates the signal at high frequencies.
Separation: A covariance of wind velocity with CO2 or H2O concentration is
measured using two sensors: a sonic anemometer and an infrared gas analyzer
(IRGA). In most two-sensor combinations, except for the IRGASON which
integrates both sensors into a single head, the wind velocities and gas
concentrations are measured separately in different measurement volumes. This
means that a single eddy may be measured at different times by the two sensors
when the eddy dimension is smaller than the separation, or when a large eddy
boundary moves between the two sensors during measurement. This results in
signal attenuation at high frequencies because the cross correlation of wind
velocities to scalar variable decreases with increases in separation (Kaimal and
Finnigan 1994). Another example of two separated sensors is to use a sonic
anemometer and a fine-wire thermocouple (for example, FW05, FW1, and
FW3) for sensible heat flux to measure covariance of wind velocity with air
temperature.
D-1
Appendix D. Frequency Corrections
Low-pass filtering: A low-pass filter of Finite Impulse Response (FIR)
improves the data quality for spectral analysis by removing the aliasing effect
on the pass-frequency band due to signals at higher frequencies (i.e., frequency
stop-band), but sharply attenuates the signal beyond the user-selected
bandwidth (i.e., frequency pass-band; Campbell Scientific, 2014). This
attenuation helps reduce unwanted aliasing effect on the frequency pass-band,
but it may also result in the loss of high frequency fluxes depending on the
sampling rate and frequency pass-band.
NOTE
The EC100 electronics used with the IRGASON and the
EC150/CSAT3A has five options for bandwidth (i.e., pass-band):
5, 10, 12.5, or 20 Hz. For each option, the filter attenuates the
signals at frequencies beyond the bandwidth.
D.2.2 Low Frequency Loss
Fluxes are typically calculated by taking a block average of the covariance and
other related variables over a 30-minute or longer interval. The bock averaging
is a high-pass filter, which causes low-frequency loss (Kaimal et al., 1989).
D.3 Model for Frequency Loss Corrections
The frequency loss of covariance is determined by the frequency losses of each
variable from which the covariance is calculated. The correction for this loss is
described using a general correction model for covariance of any two variables.
Suppose the measured covariance is given by:
(α w )
'
'
r
Where α can represent T for temperature (oC), ρco2 for partial CO2 density (mg·
m-3), ρh2o for partial H2O density (g·m-3), or u (or v) for horizontal wind speed
(m·s-1); w is vertical wind speed (m·s-1); prime is the departure of variable from
its mean; over-bar denotes the block time average; and subscript r represents a
variable after coordinate rotation correction. Then, the frequency-corrected
covariance is given by:
(α w )
'
'
rf
where subscript f indicates a variable after frequency correction and is defined
as [eq. 1 in Moore (1986)]:
(α w )
'
'
∞

 ∫0 Cα w ( f ) df
= (α w )  ∞
r

 ∫0 Tα w ( f )Cα w ( f ) df
'
rf
'





(D-1)
where other variables are defined as follows:
f – cyclic frequency
Cαw(f) – cospectrum of α with w, which is the distribution of
covariance of α and w as a function of frequency.
D-2
Appendix D. Frequency Corrections
Tαw(f) – transfer function, defined as the relative response to
a measured signal of wind or scalar at f, ranging from 0 for
no response to 1 for full response. The transfer function here
is the total transfer function that is the combined system
response of all sensors and digital processors to report the
signals of covariance of α with w. It is a product of all subtransfer functions (see Appendix D.8, Sub-Transfer
Functions (p. D-12)).
The term in the curly brackets is defined as a frequency correction factor.
Evaluating this factor requires determination of the total transfer function and
the cospectrum within the integration. The total transfer function is a
multiplication of sub-transfer functions (see Appendix D.8, Sub-Transfer
Functions (p. D-12)). A sub-transfer function is covariance-specific, depending on
flow aerodynamics, sensor configuration, and data processing method. The
cospectrum is also covariance-specific, depending on aerodynamic height,
wind speed, and atmospheric stability in the surface layer (see Appendix D.6,
Surface Layer Atmospheric Stability (p. D-8)).
D.4 Covariance Variables Requiring Frequency
Corrections
This section lists the covariance variables that require frequency corrections.
D.4.1 Momentum Covariance
Rotated wind components including u, v, and w are derived from the sonic
anemometer. The covariance of these variables shown below require frequency
correction:
(v w )
'
(
'
and u ' w'
r
)
r
Note that both of these covariances are used for calculating friction velocity (a
scaling parameter in the surface layer).
D.4.2 Sonic Temperature Related Covariance
The following covariances are from measurements from the sonic anemometer
and IRGA and require frequency correction:
(T w )
'
s
'
r
and
(T w )
'
c
'
r
where Ts is sonic temperature and Tc is air temperature calculated from sonic
temperature, water vapor density, and pressure. The data logger program
(
calculates sonic buoyancy flux, Ts ' w'
)
r
, each half hour and then applies the
sonic sensible heat flux (SND) correction to convert the result to buoyancy
flux. The SND correction requires inputs such as the mean water vapor as
measured by the IRGA and air density, which requires mean air temperature.
The mean air temperature may come from the EC100’s temperature probe in
the case of the EC150/CSAT3A, or from Tc in the case of the IRGASON since
the colocated measurements allow for time series calculation of Tc from Ts and
water vapor density.
D-3
Appendix D. Frequency Corrections
NOTE
Tc is considered the most accurate since it does not suffer from
solar heating or radiative cooling. However, Tc can only be
calculated using an IRGASON since the sonic temperature and
water vapor density measurements must be made in the exact same
volume. Pressure in the sample volume is also required, but it is
assumed that there is negligible difference between the pressure in
the sample volume and the pressure measured by the EC100’s
barometer.
D.4.3 Air Temperature Related Covariance
Similar to sonic temperature, covariances from measurements of air
temperature from a fine-wire thermocouple such as the FW05, FW1, and FW3
(hereafter referred as FW), also should be corrected.
(T w )
'
FW
'
r
where TFW is air temperature and subscript FW indicates a fine-wire
thermocouple measurement.
D.4.4 CO2 and H2O Related Covariance
Covariances of CO2 or H2O (measured by the IRGA) with vertical wind
(measured by the sonic anemometer) must be corrected.
′
′
′
′
���������
����������
�𝜌𝜌
𝐶𝐶𝐶𝐶2 𝑤𝑤 �𝑟𝑟 , �𝜌𝜌𝐻𝐻2𝑂𝑂 𝑤𝑤 �𝑟𝑟
where ρCO2 is the mass density of CO2 , and ρH2O is mass density of H2O.
D.5 Sensor Configuration and Separation Variables
Sensor configuration variables, which are required for determining frequency
corrections used in sub-transfer functions that lead to the overall transfer
function in Equation D-1, are described in this section and include descriptors
such as the measurement path dimensions of the sonic anemometer and gas
analyzer, sensor separation between the sonic anemometer and gas analyzer,
and the diameter of the fine-wire thermocouple.
All of these configuration variables are set inside the program. Some of the
variables, such as those dealing with sensor separation, depend on how the
sensors are installed at a site; following installation, the variables should be
measured, recorded, and entered into the program through the data logger
keypad (see Section 4.2, Enter Site-Specific Variables with Data Logger
Keypad (p. 14)).
D.5.1 Path Length Variables
For the CSAT3A or IRGASON sonic anemometer, the path length, lpt_CSAT, is
equal to 0.11547 m. The subscript pt indicates path.
For the EC150 or IRGASON gas analyzer, the path length, lpt_IRGA, is equal to
0.1531 m.
D-4
Appendix D. Frequency Corrections
D.5.2 Separation Variables
In order to find the separation variables, which are entered into the program
through the data logger keypad (see Section 4.2, Enter Site-Specific Variables
with Data Logger Keypad (p. 14)), the center of the gas analyzer measurement
path relative to the sonic coordinate system (see FIGURE D-1 and FIGURE
D-2) must be known. Determine of each of these variables as described below.
IRGA Coord x (reported as the datafield separation_x_irga in the Flux_Notes
output table) is the abscissa (x-coordinate) of the center of the gas analyzer
optical path in the sonic coordinate system. It should be set to 0 m for the
IRGASON and ranges from 0.041 to 0.091 m for the EC150 and CSAT3A,
depending on the EC150’s position in its standard mounting bracket. When an
EC150 and CSAT3A are used, the program assumes a default value of 0.041
m, which corresponds to the furthest forward position of the EC150 in its
standard mounting bracket.
IRGA Coord y (reported as the datafield separation_y_irga in the Flux_Notes
output table) is the ordinate (y-coordinate) of the center of the gas analyzer
optical path in the sonic coordinate system. It should be set to 0 m for the
IRGASON and ranges from 0.029 to 0.033 for the configuration of EC150 and
CSAT3A, depending on the EC150’s position in its standard mounting bracket.
When an EC150 and CSAT3A are used, the program assumes a default value
of 0.029 m, which corresponds to the furthest forward position of the EC150 in
its standard mounting bracket.
D-5
Appendix D. Frequency Corrections
z
x
y
FIGURE D-1. The sonic coordinate system is shown with positive x, y,
and z axes. Note that the origin of the coordinate system should be
exactly in the center of the sonic volume; as shown, the origin has
been moved slightly downwards for convenience in displaying the
positive z-axis.
D-6
Appendix D. Frequency Corrections
FIGURE D-2. The x and y spatial separations between a CSAT3A and
EC150.
D.5.3 Fine-Wire Thermocouple
If a fine wire thermocouple is used, additional configuration and separation
variables must be entered into the program using the data logger keypad (see
Section 4.2, Enter Site-Specific Variables with Data Logger Keypad (p. 14)).
These variables are described below.
Configuration Variable FW Dim
Depending on the fine wire thermocouple model being used, one of the
following constants should be selected as the value for FW Dim, the
configuration variable for dimension or diameter of the fine wire:
FW05_DIA = 1.27×10-5 m for the diameter of the FW05
FW1_DIA = 2.54×10-5 m for the diameter of the FW1
FW3_DIA = 7.62×10-5 m fir the diameter of the FW3
D-7
Appendix D. Frequency Corrections
Separation variables
FW Coord x (reported as the datafield separation_x_FW in the Flux_Notes
output table) is the abscissa (x-coordinate) of fine-wire thermocouple junction
in the sonic coordinate system (see FIGURE D-1 and FIGURE D-2).
FW Coord y (reported as the datafield separation_y_FW in the Flux_Notes
output table) is the ordinate (y-coordinate) of fine-wire thermocouple junction
in the sonic coordinate system.
The values for FW Coord x and FW Coord y are defaulted to 0.006m and
0.03259 m, respectively, for the IRGASON and CSAT3A. These correspond to
the standard mounting and lengths of the FW05, FW1, and FW3. These values
may be easily edited at the site using the data logger keypad (see Section 4.2,
Enter Site-Specific Variables with Data Logger Keypad (p. 14)).
D.6 Surface Layer Atmospheric Stability
The cospectrum in model (D-1) depends on surface layer stability. The stability
is defined as the ratio of aerodynamic height (z) to Monin-Obukhov length (L).
This ratio is greater than 0 if surface layer is stable, 0 if neutral, and less than 0
if unstable. The cospectrum has different model forms for neutral/unstable and
stable conditions (Kaimal et al., 1972). The stability is used as a variable in the
cospectrum model for stable conditions, but not in the models for neutral or
unstable conditions. The sub-sections below describe how the program
calculates values for aerodynamic height and Monin-Obukhov length in order
to determine stability. Stability during each averaging interval is reported in the
Flux_Notes output table as stability_zL.
D.6.1 Aerodynamic Height
Aerodynamic height is the measurement height (zm) minus zero displacement
height, given by:
=
z zm − d
(D-2)
where d is the zero displacement height.
1.
Measurement height is the height of the center of the measurement
volume of the eddy-covariance sensors above the surface of the
ground. It is entered into the program as the variable Meas Height
through the data logger keypad (see Section 4.2, Enter Site-Specific
Variables with Data Logger Keypad (p. 14)) following installation and
whenever the sensor height is adjusted. In the Flux_Notes output
table, the last value to be entered is reported as height_measurement.
2.
Displacement height is the mean height at which the momentum flux
is balanced by the momentum absorption into rough surface elements
such as plants or the ground surface. In the case of flat, bare land, the
height of aerodynamic ground surface is effectively zero. Inside a
canopy, the aerodynamic surface is elevated to some height above the
ground surface. This elevated height is defined as the displacement
height.
D-8
Appendix D. Frequency Corrections
The displacement height can be provided through three options:
a.
Provided by user and input through the data logger keypad
(see Section 4.2, Enter Site-Specific Variables with Data
Logger Keypad (p. 14)) as the variable d. The last value to be
entered is recorded as displacement_user in the Flux_Notes
output table.
b.
If the user leaves the displacement height variable, d, as zero
and the surface type is a crop or grass canopy, the
displacement height is estimated in the program using
equation 4.5 on page 138 in Rosenberg, et al. (1983):
d = 100.979 log
10
hc − 0.154
(D-2a)
where hc is canopy height that is measured periodically by the
user throughout the growing season and entered into the
program with the data logger keypad (see Section 4.2, Enter
Site-Specific Variables with Data Logger Keypad (p. 14)). It
should be set to a constant in the non-growing season.
For surface stypes other than crop, grass, or forest, the ¾ rule, or
d = 3hc/4, is an alternative [p. 71 in Kaimal and Finnigan
(1994)].
c.
If eddy-covariance variables are measured above a forest
canopy, the 2/3 rule (page 116, Oke, 1987) will be used in
the program as:
d = 2hc / 3
(D-2b)
In the program, whenever the canopy height and surface type are re-entered
(see Section 4.2, Enter Site-Specific Variables with Data Logger Keypad (p. 14)),
the zero displacement height is recalculated [Equations (D-2a) and (D-2b)]
unless the user entered a specific value. Aerodynamic height (Equation D-2) is
also recalculated. In the Flux_Notes output table, the value for displacement
height used during each averaging period is reported as d.
D.6.2 Monin-Obukhov Length (L)
Monin-Obukhov length, as given by Rebmann et al. (2012) is an indication of
surface layer depth, in which both shear and buoyancy drive the turbulent
flows, generating turbulence kinetic energy. It is given by:
L= −
where:
u*3
( )
'
'
s
k ⋅ ( g 0 / Ts ) ⋅ wT
(D-3)
rf
k = von Karman constant (0.41)
g0
= acceleration due to gravity at the sea level (9.81 m·s-2)
D-9
Appendix D. Frequency Corrections
Ts
= sonic temperature (K)
u* – friction velocity (m s-1), given by [p. 67 in Stull (1988)
and p. 384 in Wallace and Hobbs (2006)]:
( )
=
u*  u ' w'

NOTE
2
(
'
+ vw
rf
'
)
2
rf
1
4


(D-4)
Recalculation of the Monin-Obukhov length improves accuracy
of the frequency correction factor.
The Monin-Obukhov length is used to determine the form of a cospectrum for
a given covariance and as an independent variable in the cospectrum for stable
conditions (see Appendix D.7, Cospectra (p. D-10), also see Kaimal 1972).
During initial operation of the program and in each calculation interval (for
example, 30 min), the Monin-Obukhov length must be preliminarily estimated
using uncorrected friction velocity and buoyancy flux. Based on this
preliminary Monin-Obukhov length, the appropriate cospectra function, Cαw(f),
[see Equation (D-1)] can be identified and used for the calculation of correction
factors to preliminarily correct these three covariance variables :
( u w ) , ( v w ) , and
'
'
'
r
'
r
( wT )
'
'
r
Thereafter, the Monin-Obukhov length can be recalculated using these
corrected covariance variables, which then requires the frequency correction
factors to be recalculated, which can then be used to further correct the
covariance values. This iterative calculation of Monin-Obukhov length,
frequency correction factors, and covariance values is accomplished in the
program using the While()… Wend() instructions and continues until the
change in frequency correction factors is smaller than 0.0001 (Foken et al.,
2012) or until 10 iterations have completed. The final Monin-Obukhov value is
reported in the Flux_Notes output table as L, and the number of iterations
performed is reported as iteration_FreqFactor.
NOTE
For stable conditions, only the initial calculation of
Monin-Obukhov length is required; recalculation is not needed
because Monin-Obukhov length is not used in the equations for
cospectra under stable conditions and the sign of Monin-Obukhov
does not change after recalculations of correction for covariance
values used to calculate Monin-Obukhov length (see Appendix
D.7, Cospectra (p. D-10)).
D.7 Cospectra
This section contains mathematical descriptions of the cospectra functions used
in Equation (D-1) for various covariance variables in different stabilities.
D.7.1 Cospectra for z/L > 0 (stable surface layer)
D-10
Appendix D. Frequency Corrections
(
For covariances u ' w'
)
(
or v ' w'
r
)
r
:
[from equation 21 in Moore (1986) and eq. 2.80 and Table 2.1 in van Dijk (2002b)]
z
fSuw ( f ) =
u
f
z 
Auw + Buw  f 
u 
2.1
(D-5)


=
Auw 0.124  1 + 7.9
z

L
0.75
z

=
Buw 23.252  1 + 7.9 
L

−0.825
where u is the total mean velocity, or the mean horizontal velocity after
rotation about w-axis.
′
′
′
′
′
′
′ ′
���������
�����������
������������
������������
(𝑇𝑇𝑠𝑠′ 𝑤𝑤 ′ )𝑟𝑟 , (𝑇𝑇
For covariances ���������
𝑐𝑐 𝑤𝑤 )𝑟𝑟 , (𝑇𝑇𝐹𝐹𝐹𝐹 𝑤𝑤 )𝑟𝑟 , (𝜌𝜌𝐶𝐶𝐶𝐶2 𝑤𝑤 )𝑟𝑟 , and (𝜌𝜌𝐻𝐻2𝑂𝑂 𝑤𝑤 )𝑟𝑟 :
[from equation 21 in Moore (1986), equations 12 and 13 in Moncrieff et al.
(1997), and equation 2.80 and Table 2.1 in van Dijk (2002b)]
z
fS sw ( f ) =
u
f
z 
Asw + Bsw  f 
u 
2.1
(D-6)


Asw 0.284  1 + 6.4
=
z

L
0.75
z

Bsw 9.3447  1 + 6.4 
=
L

−0.825
where subscript s is used to represent a scalar variable such as Ts, Tc, Tfw, ρco2,
ρco2_LI, ρh2o, ρh2o_kh, or ρh2o_LI.
D.7.2 Cospectra for z/L ≤ 0 (neutral to unstable)
(
For covariances u ' w'
)
r
(
or v ' w'
)
r
:
[from equation 21 in Moore (1986) and eq. 2.80 and Table 2.1 in van Dijk (2002b)]
D-11
Appendix D. Frequency Corrections
z

 20.78 u f

1.575
  1 + 31 z f 

u 

fSuw ( f ) = 

z
 12.66 f
u

2.4

z 
  1 + 9.6 f 
u 

z
f < 0.24
u
(D-7)
z
f ≥ 0.24
u
′
′
′
′
′
′
′ ′
���������
�����������
������������
������������
(𝑇𝑇𝑠𝑠′ 𝑤𝑤 ′ )𝑟𝑟 , (𝑇𝑇
For covariances ���������
𝑐𝑐 𝑤𝑤 )𝑟𝑟 , (𝑇𝑇𝐹𝐹𝐹𝐹 𝑤𝑤 )𝑟𝑟 , (𝜌𝜌𝐶𝐶𝐶𝐶2 𝑤𝑤 )𝑟𝑟 , and (𝜌𝜌𝐻𝐻2𝑂𝑂 𝑤𝑤 )𝑟𝑟 :
[from equation 25 in Moore (1986), equations 15 and 16 in Moncrieff. et al. (1997)
and eq. 2.84 and Table 2.1 in van Dijk (2002b)]
Similar to stable conditions, the cospectrum of temperature with vertical
velocity in neutral or unstable conditions presented below may be used as the
cospectrum of other individual scalars with vertical velocity.
 12.92 z f

u

1.375
  1 + 26.7 z f 

u 

fS sw ( f ) = 

z

4.378 f
u

2.4

z 
  1 + 3.78 f 
u 

z
u
f < 0.54
(D-8)
z
u
f ≥ 0.54
D.8 Sub-Transfer Functions
The total transfer function found in Equation (D-1) consists of the products of
all sub-transfer functions of each variable used to calculate a covariance. Subtransfer functions account for block averaging, line averaging, sensor volume
averaging (negligible in the cases of the IRGASON and EC150), electronic
data filtering, sensor time response (for example, air temperature measured
using FW sensors), and sensor separation (for example, the x and y separations
of CSAT3A and EC150). These sub-transfer functions are described in the
following sections.
D.8.1 Finite Time Block Averaging
The sub-transfer function for finite time block averaging is derived from
equation 4 in Kaimal et al. (1989) and equation 3 in Massman (2000).
Every covariance is an average covariance over a finite block of time as
defined by the user (e.g., 30 or 60 minutes). Having a finite time block leads to
D-12
Appendix D. Frequency Corrections
attenuation of low frequencies, and therefore, all covariance variables require a
sub-transfer function to account for this. The sub-transfer function [Tsw_BA(f,
Tba)] due to a finite block averaging period (Tba) is given by:
Tsw _ BA ( f , Tba ) = 1 −
sin 2 (π Tba f )
(π Tba f )
(D-9)
2
where subscript BA or ba indicates block averaging and Tba =1800 seconds if a
period of 30 minutes is used.
D.8.2 Line Averaging
Sub-transfer functions for variances of individual variables
The attenuation of variance of vertical velocity (w) from line average is
described using equation 9 in Moore (1986), page 610 in Moncrieff (1997), and
equation 4.10 in Foken et al (2012).
The resulting sub-transfer function applied to vertical wind variance [Tww_LA(f,
lpt_csat, u)] is as follows:
2π l pt _ csat  


2π l pt _ csat
f ) 
f ) 1.5 1 − exp( −
 exp( −
u
4


u
1 +
Tww _ LA ( f , l pt _ csat , u ) =
−

2
( 2π l pt _ csat / u ) f
( 2π l pt _ csat / u ) f 




(D-10)
The sub-transfer function for horizontal velocity variance [Tuu_LA(f, lpt_csat, u)]
has not been well defined for sonic anemometry [page 22 in Moore (1986) and
page 46 in van Dijk (2002b)]. Therefore, the sub-transfer function used by van
Dijk (2002b) for horizontal wind is adopted as an approximation [eq. 2.70 in
van Dijk (2002b)]:
  π l pt _ csat
 sin  u
Tuu _ LA ( f , l pt _ csat , u ) =  
 π l pt _ csat
f

u


f 




2
(D-11)
For the variance of a scalar, s, measured by a gas analyzer, the sub-transfer
function ,
Tss _ LA ( f , l pt _ irga , u ) , is given as follows [eq. 7 in Moore (1986)
and eq. 2.68 in van Dijk (2002b), eq. 4.12 in Foken et al (2012)]:
,u )
Tss _ LA ( f , l=
pt _ irga
1
2π l pt _ irga
u
2π l pt _ irga  


−
−
4
1
exp(
f ) 


2π l pt _ irga
u


 3 + exp( −
f )−
2π l pt _ irga


u
f 
f

u


(D-12)
D-13
Appendix D. Frequency Corrections
Sub-transfer functions for covariance due to line averaging
Sub-transfer functions for covariance of certain scalars with vertical wind are
given below:
u ' w ' or v ' w '
Tuw _ LA ( f , l pt _ csat , u ) = Tuu _ LA ( f , l pt _ csat , u )Tww _ LA ( f , l pt _ csat , u )
(D-13)
s ' w ' (where s is a variable from the IRGA)
Tsw _ LA ( f , l pt _ IRGA , l pt _ csat , u ) = Tss _ LA ( f , l pt _ IRGA , u )Tww _ LA ( f , l pt _ csat , u )
Ts' w'
(D-14)
(from equations 5 to 8 in van Dijk, 2002a)
In cylindrical coordinates, the sub-transfer function for line averaging of
buoyancy flux measured using Campbell sonic anemometer is as follows:
=
TT w _ LA ( f , l pt _ csat , u )
s
91
180π k
2
∞
2π
0
0
∫ ∫
2
K k +K
2
k 2 + K 2 sin 2 θ
2
k +K
2
3
∑ sin c
i =1
k ⋅ li
2
dθ dK
(D-15)
where k is the wave number in the streamwise direction given by
k=
2π f
(D-16)
u
and where k is the wave number vector in cylindrical coordinates given by:
k = [ k K sin θ K cos θ ]
(D-17)
and where li (i = 1, 2, or 3) is a path vector that expresses a path length as three
components in three dimensions, given by:
l1 l pt _ csat
=
 − sin 30o 
l pt _ csat


0 =

 , l2
2
 cos 30o 
 sin 30o 


l pt _ csat
o
l3
=
 3 sin 30  , and
2
 2 cos 300 


 sin 300 


0
 − 3 sin 30 
 2 cos 300 


(D-18)
The integration of equation (D-15) requires much computation, so its
numerical form in Table 1 of van Dijk (2002a) is used (see TABLE D-1).
D-14
Appendix D. Frequency Corrections
TABLE D-1. Numerical form (transfer function values versus normalize frequencies) of sub-transfer
function of buoyancy flux measured by a CSAT3
Normalized
Frequency
< 0.01
0.1
0.2
0.5
1.0
1.2
1.4
1.6
Sub-transfer function
values
1.0000
0.9992
0.9976
0.9900
0.9670
0.9550
0.9417
0.9274
1.8
2.0
2.2
2.4
2.6
2.8
3.0
4.0
0.9122
0.8962
0.8797
0.8626
0.8452
0.8274
0.8096
0.7201
5.0
6.0
7.0
8.0
9.0
10.0
14.0
20.0
0.6353
0.5588
0.4922
0.4355
0.3879
0.3481
0.2445
0.1700
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
0.1134
0.08503
0.06802
0.05668
0.04859
0.04251
0.03779
0.03401
Normalized
frequency
Sub-transfer function
values
Normalized
frequency
Sub-transfer function
values
Normalized
frequency
Sub-transfer function
values
For normalized frequencies between the values listed in the table, the subtransfer function is linearly interpolated between two neighboring independent
normalized frequencies. For normalized frequencies less than or equal to 0.01
Hz, the transfer function value is set to 1. For normalized frequencies greater
than 100 Hz, trends from the first and second order numerical derivatives show
that this sub-transfer function becomes nearly constant beyond 300 Hz at a
value of 1.155511 × 10-4. Therefore, for normalized frequencies from 300 Hz
to 10,000 Hz, the sub-transfer function is set to this value, and for frequencies
falling between 100 Hz and 300 Hz, the sub-transfer function is estimated by
linear interpolation.
D.8.3 Volume Averaging
Volume averaging is considered negligible in the cases of an IRGASON and
EC150 due to the very small diameter to path length ratio, however the subtransfer function for volume averaging is briefly described here for
completeness. A sensor such as a krypton hygrometer (KH20) has a much
higher diameter-path length ratio, so the volume averaging must be taken into
account. Its optical beam diameter is 8 mm, and its path length is 12 to 15 mm
(see the calibration document for the unique path length for a particular KH20).
Andreas (1981) derived an exact transfer function for volume averaging
[equation (18) in Andreas (1981)]. This transfer function includes a first-order
Bessel function of the first kind, which makes the integration of the subtransfer function over the frequency domain in need of significant computation
time.
Later, Moene (2003) used a simpler function to approximate equation (18) of
Andreas (1981) for Krypton hygrometers. His approximation was developed
using the transfer function of Andreas (1981) for a diameter-length ratio
between 0.5 and 1.0 when the ratio of the Kolmogorov microscale (1 mm in
atmosphere) to the path length is 0.1 [Fig. 2 in Andreas (1981)]. The
approximation equation [see page 650 in Moene (2003)] is given by:
D-15
Appendix D. Frequency Corrections

2
 pKH  
f 
 u
 
Th 2 o _ KH _ VA ( f , pKH=
, u ) exp  −2 

(D-19)
where pKH is the path length of KH20.
D.8.4 FIR Filtering
The sub-transfer function for the various data filters available on the EC100
electronics (the EC100 is the electronics module used with the EC150,
CSAT3A, and IRGASON) has not been developed yet. However, it is assumed
to be negligible compared to other sub-transfer functions, assuming the
bandwidth has been appropriately selected for flux measurements.
D.8.5 Time Constant
If a fine wire thermocouple is used, a sub-transfer function describing the
frequency response of the thermocouple should be used and is described by a
simple first order gain function [Square of equation 2 in Moore (1986)]:
TTT _ TC ( f , τ FW ) =
where:
1
1 + ( 2πτ FW f )
2
(D-20)
τFW is the time constant of the FW.
The value of τFW depends on the physical properties of air, physical properties
of the thermocouple, the diameter of the thermocouple wire (D, entered by a
user), and the Nusselt number (Nu). It is given by [equation 3 in Moore (1986)
and equation 4 in Shapland et al. (2014)]:
τ FW = γ
where:
ρ FW CFW 2
D
kaNu
(D-21)
γ is the shape coefficient. It is 0.25 for cylindrical and 0.167
for spherical sensors. For a FW, a cylindrical shape is
assumed since heat can be conducted through two paths
around the junction, each having a cylindrical shape.
ρFW is the material density of the thermocouple
{[8920(constantan) + 8730(chromel)]/2 = 8825 kg /m3,
Omega product literature (undated)}
CFW is the specific heat of the thermocouple materials
{[0.094(constantan) + 0.107 (chromel) ]/2 = 0.1005 cal / (g
°C) =420.7734 J / (kg °C), Omega product literature
(undated)}
ka is the thermal conductivity of air [7.038086×10-5T
+2.42507×10-2 in W/ (m °C), where T is air temperature in
°C, Table 1 in Montgomery (1947)]
D-16
Appendix D. Frequency Corrections
Nu is the Nusselt number. The Nusselt number for a sphere
is used because the aerodynamics around the junction are
influenced by its 3D dimensions [equation 4 in Moore
(1986)]. It is calculated as follows:
=
Nu 2.00 + 0.18Re 0.67
(D-22)
where Re is Reynolds’ number [equation 3.1-2 in Geankoplis
(1993)]
Re =
where:
2 ρ a Du
µ
(D-23)
ρa is air density (calculated online by the data logger),
u
is horizontal wind speed (use sonic data),
µ is viscosity of air [4.9821×10-8T + 1.7168×10-5 in
kg/(m·s), see Table 1 in Montgomery (1947)]
D.8.6 Spatial Separation
For eddy covariance measurements that use two spatially separated sensors for
measurements of wind velocity and a scalar, a passing eddy may be measured
by the two sensors at different times if the sensors are mounted along the mean
wind direction, creating a time lag in the measurements of the downstream
sensor relative to the upstream one. Alternatively, it is possible that the eddy
will be measured by only one of the two sensors if the sensors are mounted
with a separation perpendicular to the mean wind direction (for example, a
lateral separation with sensors mounted in a crosswind orientation) and the
eddy is smaller than the separation distance. This can also happen if the
boundary of the eddy passing through one sensor’s measurement volume does
not reach the measurement volume of the other sensor. Accordingly, the
separation along the wind direction is defined as lag distance and the separation
in crosswind direction as lateral distance.
The magnitude of covariance is decreased due to both the lag distance and the
lateral distance (Horst and Lenschow 2009). In data processing, the loss of
covariance due to the lag distance may be significantly or largely recovered by
realigning the data with various time lags in order to maximize the covariance
(such as, lag maximization), and the loss of covariance due to lateral distance
may be recovered using a frequency correction (Foken et al. 2012). For both of
these corrections, the physical lag and lateral distances are needed.
In the installation of sensors, the horizontal coordinates of the center of the
measurement volume of the scalar sensor relative to the sonic coordinate
system (see FIGURE D-1) should be recorded. The coordinates can be
expressed as a separation vector [x, y].
When wind comes from a direction of zero degrees (i.e., against the direction
in which the sonic anemometer points), the x component of the vector is the lag
distance and the y component of the vector is lateral distance. When the wind
direction is not zero degrees, the separation vector may be projected onto the
wind and crosswind axes by knowing the wind direction (θw) relative to the
D-17
Appendix D. Frequency Corrections
sonic coordinate system and using a coordinate rotation. The resulting
projection along the wind direction is lag distance (dlag) and the projection in
crosswind direction is lateral distance (dlat).
These are given by:
 d lag   cos θ w
 d  =  − sin θ
 lat  
w
sin θ w   x 
(D-24)
cos θ w   y 
The lag distance (dlag) along with wind speed will be used by the data logger
for lag maximization by applying an appropriate lag to the measurement scans
to align the sensors (see lag maximization). The lateral distance is used in a
sub-transfer function of frequency response due to sensor separation,
Tsw _ SP ( f , d lat , u ) , which is given as follows [equation 4.8 in Foken, et. al.
(2012)]:
1.5

 fd lat  
, u ) exp  −9.9 
Tsw _ SP ( f , d lat=
 
 u  

(D-25)
D.8.7 Total Transfer Function
A composite or total transfer function is given by the product of the appropriate
sub-transfer functions for a particular covariance. The total transfer functions
used by the data logger are given in this section (FIR correction currently not
included).
For
u ' w' or v ' w' :
Tuw ( f , l pt _ csat , Tba , u ) = Tuw _ BA ( f , Tba )Tuw _ LA ( f , l pt _ csat , u )
For
(D-26)
Ts ' w' :
TT w ( f , l pt _ csat , Tb , u ) = TT w _ BA ( f , Tba )TT w _ LA ( f , l pt _ csat , u )
s
s
'
s
(D-27)
'
For s w (where s is a variable measured by the IRGA) :
Tsw ( f , l pt _ csat , l pt _ IRGA , dlat , Tba , u ) = Tsw _ BA ( f , Tba )Tsw _ LA ( f , l pt _ csat , l pt _ IRGA , u )Tsw _ SP ( f , dlat , u )
For
TT w ( f , l pt _ csat , d lat , τ FW , Tba , u ) = TT
FW
Fw
w _ BA
(D-28)
'
TFW
w' :
( f , Tba ) Tww _ LA ( f , l pt _ csat , u )TTT _ TC ( f , τ FW )Tsw _ SP ( f , d lat , u )
(D-29)
D-18
Appendix D. Frequency Corrections
D.9 Working Model
Evaluating the correction factor in Equation (D-1) in the data logger program
requires numerical integration. Because the cospectrum changes exponentially
faster at low frequencies than at high frequencies, the interval of integration
can be exponentially increased throughout the integration in order to save
computation time without significantly reducing accuracy. Accordingly, ln f is
used as an integration variable that increases at equal logarithmic intervals of
frequency (f), which effectively increments the frequency interval
exponentially for fast integration over the integration domain. This results in a
working formula that is used to find the covariance:
(α w )
'
'
rf
∞

[ fSα w ( f )] d ( ln f ) 

∫
= α ' w'  ∞ 0

r
 ∫0 Tα w ( f ) [ fSα w ( f ) ] d ( ln f ) 
( )
(D-30)
Recall that even though simple notation for Tαw(f) has been used, this is an
overall transfer function that is comprised of the sub-transfer functions
presented in the sections above and includes independent variables such as
wind speed ( u ), block average period, measurement path length, and/or
sensor time constant and/or lateral separation distance. Accordingly, the
components of the combined transfer function for different variables of vectors
and scalars are unique due to sensor specifications and measurement
installations.
D.10 Programmatic Approach to Computations for
Correction Factors
The correction factor in model (D-30) has a numerator and a denominator. Its
numerator is found from a normalized spectrum, and its denominator is
determined by numerical integration. For both normalized and non-normalized
cospectra, we numerically integrate both the numerator and denominator.
Moore (1986) used the Composite Simpson’s rule to estimate this denominator.
In his estimation, 19 equal integration intervals at a scale of natural logarithm
from 10-5 to 5 Hz were used, which resulted in an integration error smaller than
1%. Currently, this can be further improved due to faster computational speeds
in Campbell data loggers compared to microcomputers at that time. By
increasing the integration range and decreasing the integration intervals, the
data logger can more accurately account for frequency attenuation, particularly
in the lower frequencies of the block averaging sub-transfer function.
Specifically, we extend the integration range from 10-6 to 104 Hz and divide the
range into 100 frequency bins. It is believed that the integration error should be
significantly smaller than Moore (1986) and the accuracy sufficient.
D-19
Appendix D. Frequency Corrections
Because the cospectrum may change exponentially and dramatically in lower
frequencies, the logarithm scale of cyclic frequency may be used for a
numerical integration interval (bin width). For 100 bins from 10-6 to 104 Hz, the
base frequency interval (Δf) is 1.258925 since 10-6×1.258925100 = 10000. The
lower frequency boundary of the jth interval is indexed as the (j-1)th frequency
and the right boundary frequency is indexed as the jth frequency. The interval
of integration (bin width) at natural logarithm scale [Δln(f)] is given by:
(
∆ ln
=
( f ) ln 10−6 ∆f
−6
10 ∆f
= ln
10−6 ∆f
j
) − ln (10
−6
× ∆f
j −1
)
(D-31)
j
= ln ∆f
j −1
The Composite Simpson’s rule writes the integration for the numerator in
model (8.1) as (page 186 in Burden and Faires (1993):
∫ [ fS
∞
0
αw
( f ) ] d ( ln f ) ≈
ln ( ∆f
=
3
+2
49
)
{
∫ [ fS
10000
10
−6
αw
( f ) ] d ( ln f
)
50
10 −6 Sα w (10 −6 )  + 4∑ 10 −6 ∆f 2 k −1 Sα w (10 −6 ∆f 2 k −1 ) 
∑ 10
k =1
−6
k =1
(D-32)
}
∆f Sα w (10 ∆f )  + 10 Sα w (10 ) 
2k
−6
2k
4
4
with an error term as describe on page 186 (Burden and Fares (1993):
104 − 10−6
=
Error
180
≈
20
18
× ( ln ∆f
)
4
2
50
∑ ξ S
100
j
j =1
× ( ln ∆f
50
) ∑ ξ j Sα w (ξ j ) 
4
αw
(ξ j ) 
( 4)
(D-33)
( 4)
j =1
where ζ is a value of frequency that can maximize the value in the square
bracket. The evaluation of this term requires more complicated calculations
because the 4th order derivative of the integrated function is needed. We do not
evaluate this term now, but equation (D-33) can show how the error can be
reduced by adding the number of integration intervals and narrowing the width
of the interval.
Similarly, the denominator with Simpson’s rule applied becomes:
∫
∞
0
Tα w ( f ) [ fSα w ( f ) ] d ( ln f ) ≈
=
ln ( ∆f
3
+2
)
{
10000
10
−6
Tα w ( f ) [ fSα w ( f ) ] d ( ln f
)
50
2 k −1
2 k −1
2 k −1
−6
−6
−6
−6
−6
−6
Tα w (10 )10 Sα w (10 )  + 4∑ Tα w (10 ∆f ) 10 ∆f Sα w (10 ∆f ) 
49
∑T
αw
k =1
∫
k =1
(D-34)
}
(10 ∆f ) 10 ∆f Sα w (10 ∆f )  + Tα w (10 ) 10 Sα w (10 ) 
−6
2k
−6
2k
−6
2k
4
4
4
D-20
Appendix D. Frequency Corrections
The error term of this numerical integration can be calculated using equation
(D-33) if the term
ξ j Sαw (ξ j )
is replaced with Tαw
[ξ ]ξ S
j
j
αw
(ξ j ) .
The code in the program used to calculate the correction factor of one
covariance (Cor_factor) is outlined below:
Cor_factor = 0
for j = 0 to 100
(100 steps)
f = 10-6 × 1.258925J
(Calculation of frequency)
m = 2 + 4 × (j MOD 2) − ABS(j = 0) − ABS(j = 100)
NOTE
M = 1 for j = 0 and j = 100. For all other j, m = 4 if j is odd and
m = 2 if j is even).
[
Numerator
= Numerator + m × fSαβ ( f )
]
[
= Denominator + m × Tαβ ( f ) fSαβ ( f )
Denominator
]
Next j
Cor_factor = Numerator/Denominator
D.11 References
Andreas, E. L.: 1981, “The effects of volume averaging on spectra measured
with Lyman-Alpha hygrometer”, J. Applied Meteorol. 20:467-475.
Burden, R. L. and Faires, J. D.: 1993, Numerical Analysis. PWS Publishing
Company, Boston. pp. 184-189.
Campbell Scientific, Inc. 1998. CSAT3 Three Dimensional Sonic
Anemometer. pp. 25.
Campbell Scientific, Inc. 2006. Type E, Fine Wire Thermocouples: Models
FW05, FW1, and FW3. pp: 2.
Campbell Scientific Inc. 2014. IRGSON Integrated CO2/H2O Open-Path Gas
Analyzer and 3D Sonic Anemometer. Campbell Scientific, Inc. Logan UT.
p. 43.
Geankoplis, C.J. 1993. Transportation Processes and Unit Operation. 3rd
Edition. PTR Prentice Hall, New Jersey. pp 114-131 and Appendix.
Foken, T, R. Leuning, S.R. Onley, M. Mauder, M. Aubinet. 2012. Corrections
and data quality control. In M, Aubient, T. Vesala, D. Papale. (eds). Eddy
Covariance: A Practice Guide to Measurement and Data Analysis.
Springer, New York. p. 85-131.
D-21
Appendix D. Frequency Corrections
Horst, T.W., 1997. A simple formula for attenuation of eddy fluxes measured
with first-order response scalar sensors. Boundary-Layer Meteorology
94:517-520.
Horst, T.W., and D.H. Lenschow, 2009: Attenuation of scalar fluxes measured
with spatially-displaced sensors. Boundary-Layer Meteorology, 130:275300, DOI: 10.1007/s10546-008-9348-0.
Kaimal, J.C., S.F. Clifford, R.J. Lataitis. 1989. Effect of finite sampling on
atmospheric spectra. Boundary-Layer Meteorology 7:827-837.
Kaimal, J. C. and J. J. Finnigan, 1994. Atmospheric Boundary Layer Flows:
Their Structure and Measurement. Oxford University Press, Oxford, 289 p.
Kaimal, J.C., J.C., Wyngaard, Y. Izumi, O.R. Cote. 1972. Deriving power
spectra from a three-component sonic anemometer. J. Appl. Meteorol.
7:827-837.
Leuning, R., K.M. King. 1992. Comparison of eddy-covariance measurements
of CO2 flux by open- and close-path CO2 Analyzers. Boundary-Layer
Meteorology 59:297-311.
Laubach, J., K.G. McNaughton. 1998. A spectrum-independent procedure for
correcting eddy flux measured with separated sensors. Boundary-Layer
Meteorol. 89:445-467.
LI-COR Bioscience. 2001. CO2/H2O Gas Analyzers. pp:19.
Massman, W.J. 2000. A simple method for estimating frequency response
corrections for eddy covariance systems. Agricultural and Forest
Meteorology 104: 185-198.
Moncrieff, J.B., J.M. Massheder, H.de Bruin, J.A. Elbers, T. Friborg, B.
Heusinkveld, P. Kabat, S. Scott, H. Soegaard, A. Verhoef. 1997. A system
to measure surface fluxes of momentum, sensible heat, water vapour and
carbon dioxide. Journal of Hydrology 188-189:589-611.
Moene, A.F. 2003. Effects of water vapor on the structure parameter of the
refractive index for near-infrared radiation. Boundary-Layer Meteorology
107:635-653.
Moore C.J. 1986. Frequency response corrections for eddy correlation systems.
Boundary-Layer Meteorology 37:17-35.
Omega. Undated. Physical Properties of Thermoelement Materials.
Omega.com website.
Rosenberg, N.J., B.L. Blad, S.B. Verma. 1983. Microclimate: The Biology
Environment, 2nd Edition. John Wiley & Sons. pp. 495.
Shapland, T.M., R.L. Snyder, K.T. Paw U, A.J. McElrone. 2014.
Thermocouple frequency response compensation leads to convergence of
the surface renewal alpha calibration. Agricultural and Forest Meteorology
189-190:36-47.
D-22
Appendix D. Frequency Corrections
Stull, R.B. 1988. An introduction to Boundary Layer Meteorology. Kluwer
Academic Publisher, Boston, 666 pp.
van Dijk, A. 2002a. Extension of 3D of “the effect of linear averaging on scalar
flux measurements with a sonic anemometer near the surface” by
Kristensen and Fitzjarrald. Journal of Atmospheric and Ocean
Technology. 19:80-19.
van Dijk, A. 2002b. The Principle of Surface Flux Physics. Research Group of
the Royal Netherlands Meteorological Institute and Department of
Meteorology and Air Quality with Agricultural University Wageningen.
65pp.
Wallace, J. M. and P. V. Hobbs, 2006: Atmospheric Science: An Introductory
Survey. Academic Press, 350 pp.
D-23
Appendix E. WPL Corrections
Due to the vertical gradient of air temperature in the atmospheric surface layer,
rising air parcels have different temperatures and densities than descending
ones. For example, in the case of upward (positive) heat flux when the air
closest to the ground is warmest, rising air parcels on average will be warmer
and less dense than descending ones. In this same case, suppose that the CO2 or
H2O fluxes are zero (rising and descending parcels carry the same amount of
CO2 and H2O), the measurements from an open-path eddy covariance (EC)
system will still report negative (downward) fluxes simply because of the
correlation between rising air parcels and lower air density. This is explained
by mass conservation or air continuity; the decrease in air density due to the
increase in air temperature while the total pressure in surface layer changes
very little, forces air to expand upwards in the atmospheric surface layer. This
expansion generates an upward (positive) flux of air at the measurement point
and leads to a slightly positive mean vertical velocity. Thus, the downward
CO2 or H2O flux measured by open-path EC system may be explained by the
upward flux of air from a net upward vertical velocity.
Depending on whether the temperature profile increases or decreases with
height, the mean vertical velocity may be negative or positive. Typically, it
ranges from −0.75 to 1.5 mm/s when sensible heat flux is between −200 and
600 W/m2 (Fig.1 in Webb et al. [1980]). This change in vertical velocity due to
change in air density is too small to be measured by a 3D sonic anemometer
with sufficient accuracy.
Since typical applications of the open-path EC method do not account for
fluxes associated with non-zero mean flows ( w ≠ 0 ), an appropriate
correction for the vertical velocity due to heat and water vapor transfer is
needed.
E.1 Basic Considerations
Air density (ρa) is a sum of partial densities: dry air density (ρd), water vapor
density (ρv), and CO2 density (ρco2), given by:
ρ a = ρ d + ρv + ρco 2
(E-1)
The contribution of ρCO2 relative to ρd and ρv vapor is very small, and thus can
be considered negligible to the total air density. The equation therefore
becomes:
ρ=a ρ d + ρv
(E-2)
The individual gas laws give the partial pressures of dry air (pd), water vapor
(pv), and (pco2) as follows:
E-1
Appendix E. WPL Corrections
pd =
pv =
R*
md
R*
mv
pCO 2 =
ρd T
ρ vT
R*
mCO 2
(E-3)
ρCO 2T
where subscripts d, v, and CO2 denote dry air, water vapor, and carbon
dioxide, respectively, and are used throughout; m is molecular mass; R* is the
universal gas constant (8.3143 J K-1 mol-1, page 467 of Wallace and Hobbs
[2006]), and T is absolute temperature.
The total air pressure (pa) is given by:
pa = pd + pv + pCO 2
(E-4)
The air pressure, dry-air density, water-vapor density, and CO2 density are
measured and calculated in an EC system. Although the partial pressures of the
different gas components are normally not measured, the other measured
variables may be used to derive the partial pressures. Submitting equation (E-3)
into equation (E-4) yields:
pa
*
RT
=
ρ d ρ v ρCO 2 ρ d ρ v
+
+
≈
+
md mv mCO 2 md mv
(E-5)
Equation (E-5) describes the basic relationship of air and water vapor densities
to temperature and atmospheric pressure. If the term
1
1
= =
T (T + T ' )
1
(E-6)
 T' 
T 1 + 
 T 
'
is expended in a power series of T / T , the partial densities in equation (E-5)
can be written in forms of instantaneous, mean, and fluctuation variables as
follows:
 ρd ρv
+=

 md mv

 ρd ρv
 + =
 md mv
 '
'
v
 ρ d + ρ=
 md mv

'
 T
1 −
*
RT 
 T
2
3
T'  T' 

+   −   + ....
T  T 

 T '2 T '3
pa 

1 + 2 − 3 + ...
*
RT 
T
 T

 T ' T '2 − T '2 T '3 − T '3
pa 

−
+ ....
− +
*
2
3
RT 
T
T

 T
pa
(E7 a )
(E7b )
(E-7)
(E7 c )
E-2
Appendix E. WPL Corrections
Equation (E7b) can further be expressed as:

 ρ d ρ v   T '2 T '3
=
+
+
−
+
1
...




2
R*T  md mv  
T3
 T

pa
−1
(E-8)
Substituting equation (E-8) into equation (E7c) yields:
'2


 ρ d ρ v   T ' T ' 2 − T ' 2 T '3 − T '3
T '3
 T
....
1
...
+ = 
+
−
+
+
−
+


 − +
2
md mv  md mv  
T2
T3
T3
 T
 T


ρ d'
ρ v'
−1
(E-9)
By dropping the second order term (< 10-4) of absolute temperature, the
fluctuation of dry air density can be expressed as:
 m ρ T'
m
− d ρ v' − ρ d  1 + d v 
ρ d' =
mv
 mv ρ d  T
=
− µρ v' − ρ d (1 + µσ )
T'
(E-10)
T
where µ is the molecular weight ratio of dry air to water vapor, and σ is the
mean water vapor mixing ratio.
E.2 Governing Constraint and Mean Vertical
Velocity
The governing constraint that the mean vertical flux of dry air constituent
should be zero is given by:
wρ d = 0
(E-11)
Equation (E-11) is equivalent to:
wρ d =
( w + w )( ρ
'
d
)
+ ρ d' = w ρ d + w ρ d' + w' ρ d + w' ρ d' = w ρ d + w' ρ d'
(E-12)
Equations (E-11) and (E-12) give:
w= −
w' ρ d'
(E-13)
ρd
Submitting equation (E-10) into this equation yields:
=
w µ
w' ρ v'
ρd
+ (1 + µσ )
' '
wT
T
(E-14)
E-3
Appendix E. WPL Corrections
E.3 Eddy Covariance Measurements
E.3.1 CO2
The flux of CO2 can be written as:
'
=
FCO 2 w=
ρCO 2 w' ρCO
+ wρCO 2
2
(E-15)
Replacing the mean vertical velocity ( w ) in the equation with equation (E-14)
yields:
 ρCO 2 ' '

ρ
w ρ v + (1 + µσ ) CO 2 w'T ' 
T
 ρd

'
FCO
=
w' ρ CO
+ µ
2
2
(E-16)
The term in the rectangle bracket is the WPL correction. The first term is due
to water flux and the second is due to heat flux.
ρCO2 is the mean CO2 density measured by an IRGA
ρd is the mean dry air density calculated from air temperature,
pressure, and water vapor density
T is the mean air temperature in Kelvin
µ is 1.60802 (the ratio of dry air molecular weight [md = 28.97
kg·kmol-1] to water molecular weight [mv = 18.016 kg·kmol-1], page
466 in Wallace and Hobbs [2006])
σ is the mean water vapor mixing ratio [ratio of mean water vapor
density ( ρv ) to mean dry air density ( ρd ).
w ' ρv' is the water vapor flux measured using a sonic anemometer and
IRGA.
w ' T ' is the heat flux (after rotations, frequency, and SND
corrections) calculated from a sonic anemometer and optionally with
a fine-wire thermocouple.
E.3.2 H2O
The flux of water vapor is written as:
=
E w=
ρ v w' ρ v' + wρ v
(E-17)
Replacing the mean vertical velocity ( w ) in the equation with equation (E-14)
yields:

ρv

T
E= w' ρ v' +  µσ w' ρ v' + (1 + µσ )

w'T ' 

(E-18)
E-4
Appendix E. WPL Corrections
The term in the rectangle bracket is the WPL correction term. The first term is
due to water flux itself and the second is due to heat flux.
ρv is the mean water vapor density measured by IRGA
w ' ρv' is the water vapor flux (after rotation and frequency
corrections) measured using sonic anemometer and IRGA.
E.4 References
Campbell Scientific, Inc. 2015. CSAT3 Three Dimensional Sonic
Anemometer. Logan, pp: 25.
Schotanus, P.S., F.T.M. Nieuwstadt, H.A.R. Debruin. 1983. Temperature
measurement with a sonic anemometer and its application to heat and
moisture flux. Boundary-Layer Meteorology 26:81-93.
Wallace, J.M., P.V. Hobbs. 2006. Atmospheric Science: An Introductory
Survey, 2nd edition. Elsvier, Amesterdam. pp:483.
Webb, E.K., G.I. Pearman, R. Leuning. 1980. Correction of flux measurements
for density effects due to heat and water transfer. Quart. J. Met. Soc.
106:85-100.
E-5
Appendix F. Data Quality Grading
Data quality assurance (QA) and quality control (QC) are recommended for
eddy covariance (EC) measurements because of complex calculation
procedures (Foken et al. 2012). A number of publications on QA and QC for
EC measurements are available (for example, Foken and Wichura 1996,
Vickers and Mahurt 1997, Shearman 1992, Moncrieff et al. 1997, Aubinet et
al. 2000, Foken et al 2004, 2012).
In the case of this data logger program, QA is accomplished using diagnostic
outputs from the measurement system’s sonic anemometer and infrared gas
analyzer. Specifically, the data logger only uses raw data for flux calculations
when the diagnostic values from both sensors are zero (i.e., sensors work
normally and measurements are in their reasonable ranges), when the
measurements are within the calibrated range of the sensors, and when the
signal strengths are adequate (i.e., when nothing is blocking the optical path).
Even when raw data are not used for flux calculations, they are still stored in
the time series data table. More details on diagnostics are found in the manual
of the respective sensor. Regarding QC, the data logger program follows the
method presented in Foken at al. (2012) to grade the relative quality of CO2,
latent heat, sensible heat, and momentum fluxes. Specifically, the following
three variables are calculated and used to grade the quality of the data:
•
Relative Non-stationarity (RNcov) to describe the steady state
•
relative Integral Turbulence Characteristics (ITC) to define the
developed turbulence condition
•
horizontal wind angle in the sonic anemometer coordinate system
Sections F.1 through F.3 give more information on each of these variables and
how a quality grade for each is assigned. Section F.4 describes how an overall
quality grade is found, and Section F.5 describes how this is implemented into
the data logger program.
NOTE
Due to differences in sonic anemometer models and geometries
used in the AmeriFlux network, AmeriFlux prescribes the usage
of only the steady-state and integral turbulence characteristcs tests
as presented in Foken et al. (2004) for its standard QC results.
Accordingly, the QC outputs in the Flux_AmeriFluxFormat
output table (e.g., FC_SSITC_TEST) ignore the wind direction
and apply the tests as presented in the paper.
See http://ameriflux.lbl.gov/data/aboutdata/data-variables/.
F.1 Relative Non-stationarity (RNcov) for Steady
State
Turbulence flux measurement theory is valid under the steady state conditions
of turbulent flows. In such conditions, the surface layer turbulent flow structure
is independent of time within an averaging interval (e.g., 30 min). The extent to
which conditions conform to a steady state may be described using a variable
F-1
Appendix F. Data Quality Grading
called relative non-stationarity, RNcov, which is defined as the relative
difference between the averaged 5-min and 30-min covariance values, given by
(equations [4.36] to [4.38] in Foken, et al. 2012):
1
100 ×
RN=
cov
∑ ( s′w′ ) − ( s′w′ )
6
6
i =1
ri
( s′w′ )
r
(F-1)
r
where s can be Ts for sonic temperature, Tc for corrected temperature, ρco2 for
CO2 density, ρh2o for H2O density, or u or v for horizontal wind speed; w
represents vertical wind velocity; subscript r indicates the variable after
coordinate rotation; subscript i (for example, 1, 2,…, or 6 if a 30-min averaging
period is used) indicates the covariance of the ith 5 min interval within an
averaging period; and the numerical number of 100 converts the relative nonstationarity into percent. Based on the calculated value of RNcov, the steady
state is classified into nine grades. Grade 1 is most steady and indicates highest
data quality, whereas grade 9 is least steady and indicates relatively lower data
quality (see TABLE F-1).
TABLE F-1. Grades of relative non-stationarity, relative integral turbulence characteristics, and wind
direction in the sonic instrument coordinate system.
RNcov
Relative non-stationarity
[model (2.3) in Foken et al.
(2012)]
Grade
Range (%)
ITCsw and ITCtau
Relative integral
turbulence characteristics
wnd_dir_sonic
Wind direction
[model (2.5) in Foken et al.
(2012)]
Grade
Range (%)
Grade
Range
1 (highest)
[0 , 15)
1 (highest)
[0 , 15)
1 (highest)
[0 – 150°], [210 – 360°]
2
[15 , 30)
2
[15 , 30)
2
[150 – 170°], [190 – 210°]
3
[30 , 50)
3
[30 , 50)
3 (lowest)
[170 – 190°]
4
[50 , 75)
4
[50 , 75)
5
[75 , 100)
5
[75 , 100)
6
[100 , 250)
6
[100 , 250)
7
[250 , 500)
7
[250 , 500)
8
[500 , 1000)
8
[500 , 1000)
9 (lowest)
F.2
≥1,000%
9 (lowest)
> 1,000%
Turbulent Conditions
Turbulence conditions are characterized using a term called integral turbulence
characteristics (ITC), which is defined as a standard deviation of a fluctuating
variable (e.g., momentum variance or temperature variance) normalized by a
scaling factor, for example, friction velocity or scaling temperature (Tilmann
F-2
Appendix F. Data Quality Grading
1972). In a surface layer with fully developed turbulence, a given ITC term is a
constant or at least follows a universal function of the scaling factor.
The most commonly used scaling factor is stability, defined as the ratio of
aerodynamic height (z, sensor sensing height minus zero displacement height)
to the Monin-Obukhov length (L; Stull 1988, Kaimal and Finnigan 1994), or
z/L. The other scaling factor used is (Thomas and Foken 2002):
z+ f
(F-2)
u*
where f is the Coriolis parameter in s-1, u* is friction velocity in m s-1, and z+ is
a constant in m that was introduced and set to “1” to make the scaling factor
dimensionless. For a given site, the Coriolis parameter can be calculated using:
f = 2Ω sin φ
where Ω is angular velocity (7.292 x 10-5·s-1) and ϕ is latitude (positive in the
north hemisphere and negative in the south hemisphere).
ITC values have been accurately simulated using a well-known model (i.e., a
function of the scaling factor) in conditions of fully developed turbulence. ITC
may also be measured and then compared to the modeled ITC to show the
degree to which turbulence has developed at that moment in time. The relative
difference in percentage between the modeled and measured values are noted
by ITCα, where the subscript α indicates the variable of interest. When α is
vertical velocity, w, or horizontal wind speed, u, ITCα is defined as follows:
ITCα _ mod el
100 ×
ITC=
α


−


(α )
'2
u*
r




 measured
ITCα _ mod el
(F-2)
where the ITCα_model term is evaluated using:
𝐼𝐼𝐼𝐼𝐼𝐼 𝛼𝛼_𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
𝑧𝑧 𝑓𝑓
𝑐𝑐𝛼𝛼1 ln 𝑢𝑢+ + 𝑐𝑐𝛼𝛼2
∗
= �
𝑧𝑧 𝑐𝑐𝛼𝛼2
𝑐𝑐𝛼𝛼1 �|𝐿𝐿|�
𝑧𝑧
𝐿𝐿
𝑧𝑧
𝐿𝐿
>0
≤0
(F-3)
where cα1 and cα2 are parameters that depend on surface-layer stability (see
TABLE F-2).
The relative difference in measured and theoretical ITC for temperature (T) is
noted by ITCT and is given by (equation [4.41] in Foken et al. [2012]):
F-3
Appendix F. Data Quality Grading
ITCT _ mod el
ITC=
100 ×
T


−


(T ′ )
2
T*
r




 measured
(F-4)
ITCT _ mod el
where T* is scaling temperature, given by [equation (1.25b) in Kaimal and
Finnigan (1994)]:
T* = −
T ′w′
(F-5)
u*
and the ITCT_model term is evaluated using:
ITCT _ mod el
 z 
= cT 1  
 L
cT 2
(F-6)
where cT1 and cT2 are parameters also depending on surface layer stability (see
TABLE F-2).
TABLE F-2. Parameters in the model of integral turbulence characteristics (ITC).1/
Variable in variance
Vertical velocity
a=W
Horizontal wind speed
a=U
Air temperature
a=T
1/Summarized
cα1
cα2
z/L
0.21
3.1
1.3
0
2.0
1/8
z/L ≤ − 0.032
0.44
6.3
0 < z/L < 0.4
2.7
0
4.15
1/8
z/L ≤ − 0.032
1.4
−1/4
0.02 < z/L < 1
0.5
−1/2
0.02 > z/L > −0.062
1.0
−1/4
−0.062 > z/L > −1
1.0
−1/3
−1 > z/L
0 < z/L < 0.4
− 0.032 < z/L ≤ 0
− 0.032 < z/L ≤ 0
from Tables 4.2 and 4.3 in Foken et al. (2012)
Similarly, ITCsw is used to describe the turbulent conditions when measuring
the covariance of a scalar, s, and vertical wind, w. However, instead of an
explicit equation for ITCsw, its value is conservatively estimated by setting it
equal to ITCT or ITCw, whichever is greater; that is:
ITCsw = max ( ITCT , ITCw )
(F-7)
F-4
Appendix F. Data Quality Grading
ITCsw for fully developed turbulence conditions should be close to zero. The
greater the value of ITCsw becomes, the less developed the turbulence. Foken et
al. (2012) suggested classifying the resulting value into nine grades, where
grade 1 indicates conditions of fully developed turbulence, and grade 9
indicates conditions of undeveloped turbulence (see TABLE F-1).
Similarly, for momentum flux, a conservative approach is used:
max ( ITCu , ITCw ) double rotations used

ITCtau = 
 ITC
planar fit rotations used
 w
(F-8)
It should be noted that the variable u used in calculating ITCu and ITCtau, in the
case of Table 4.2 of Foken et al. (2012), is streamwise wind speed, although
the authors did not explicitly specify this. Accordingly, the raw variable Ux
from a sonic anemometer, which is rarely a streamwise wind speed, must
undergo coordinate rotations. It becomes the streamwise wind speed only after
the first rotation of Tanner and Thurtell (1969) or the third rotation of Wilczak
et al. (2001).
The data logger program uses either method of coordinate rotations, depending
on the selection of the user; however, only the first two rotations of each
method are done in order to reduce unnecessary computation time on the third
rotation. Accordingly, u and subsequently ITCu, are only available to find
ITCtau if the method of Tanner and Thurtell (1969) is selected. If the planar fit
method (Wilczak et al [2001]) is used, ITCtau is simply found from ITCw as an
approximation (see equation F-8).
Similar to the other relative turbulence characteristics, the greater the value of
ITCtau, the less developed the turbulence. The resulting value is classified into
nine grades, where grade 1 indicates fully developed conditions of turbulence,
and grade 9 indicates least developed conditions of turbulence (see TABLE
F-1).
Further, for stable surface-layer conditions beyond the ranges where
parameters are defined in TABLE F-2, the quality grades for ITCα, ITCT, and
ITCtau are conservatively assigned as 9.
F.3 Wind Direction in the Sonic Instrument
Coordinate System (wnd_dir_sonic)
The sonic anemometer has a boom-mount design that may affect the wind flow
when the wind is blowing from behind the boom towards the sonic transducers.
Accordingly, Foken et al. (2012) assigned a poorer data quality grade of 3 to
wind coming from angles 180 ± 10° relative to the sonic coordinate system, a
medium grade of 2 to winds outside of this range but within 29° of 180°, and a
good grade of 1 for all other angles (see TABLE F-1).
F.4
Overall Quality Grade System
Each covariance variable over the averaging period is assigned an overall
quality grade from 1 to 9 based on the individual grades of RNcov, ITCsw, and
F-5
Appendix F. Data Quality Grading
wnd_dir_sonic (see TABLE F-3). Grade 1 is the highest overall quality, and
grade 9 is the poorest.
TABLE F-3. Overall grades for each flux variable by the grades of relative non-stationary, relative
integral turbulence characteristic, and wind direction in sonic instrument coordinate system.1/
wnd_dir_sonic
Overall quality
grade
RNcov
Relative nonstationarity
ITCsw
Relative integral turbulence
characteristic
1 (best)
1
1–2
1
2
2
1–2
1
3
1–2
3–4
1
4
3–4
1–2
1
5
1–4
3–5
1
6
5
7
2
8
6
5
7–8
7–8
9 (worst)
9
9
1/Simplified
F.5
6
Wind direction
2
2
3
Table 4.5 in Foken et al. (2012)
Programmatic Approach
The data logger program determines an overall quality grade using these steps:
1.
Calculate quality variables:
RNcov for
u ' w' , v ' w' , Ts' w' , ρ co' 2 w' ,and ρ h' 2 o w'
ITCtau for momentum flux
ITCTsw for sensible heat, CO2, and H2O fluxes
2.
Use RNcov to grade stationarity, ITCtau and ITCTsw to grade the integral
turbulence characteristics, and wind angle in the sonic coordinate
system to grade wind direction (see TABLE F-2).
3.
Define an array with three elements:
The first element records the best possible quality grade in the overall
grade system for a given grade of relative non-stationarity. For
example, a grade 2 for RNcov can be assigned as grade 2 or 3 in the
overall grade system. In this case, the data logger will store the value
of 2 as the first element in the array.
Similarly, the second element in the array is the best possible quality grade
in the overall grade system for a given grade of the integral turbulence
characteristics.
F-6
Appendix F. Data Quality Grading
The third element in the array is the best possible quality grade in the
overall grade system for a given grade of wind direction.
4.
F.6
The maximum value of the three elements is the overall quality grade
for the variable being evaluated (such as, flux of CO2, H2O, sensible
heat, or momentum).
References
Aubinet M, B. Chermanne, M. Vandenhaute, B. Longdoz, M. Yernaux, E.
Laitat. 2001. Long term carbon dioxide exchange above a mixed forest in
the Belgian Ardennes. Agricultural and Forest Meteorology. 108:293-315.
Foken, T, R. M. Gӧckede, M. Mauder, L. Mahrt, B.D. Amiro, J.W. Munger.
2004. Post-field data quality control. In Lee, X., W. Massman, B. Law
(eds). Handbook of Micrometeorology: A guide for surface flux
measurement and analysis. Kluwer, Dordrecht, pp. 181-208.
Foken, T, R. Leuning, S.R. Onley, M. Mauder, M. Aubinet. 2012. Corrections
and data quality control. In M, Aubient, T. Vesala, D. Papale. (eds). Eddy
Covariance: A Practice Guide to Measurement and Data Analysis.
Springer, New York. pp. 85-131.
Foken, T., B. Wichura. 1996. Tools for quality assessment of surface-based
flux measurements. Agricultural and Forest Meteorology 78:83-105
Kaimal, J. C. and J. J. Finnigan, 1994. Atmospheric Boundary Layer Flows:
Their Structure and Measurement. Oxford University Press, Oxford, 289
pp.
Moncrieff, J.B., J.M. Massheder, H.de Bruin, J.A. Elbers, T. Friborg, B.
Heusinkveld, P. Kabat, S. Scott, H. Soegaard, A. Verhoef. 1997. A system
to measure surface fluxes of momentum, sensible heat, water vapour and
carbon dioxide. Journal of Hydrology 188-189:589-611.
Shearman, R.J. 1992. Quality assurance in the observation area of the
Meteorological Office. Meteorological Magazine 121:212-216.
Stull, R.B. 1988. An introduction to Boundary Layer Meteorology. Kluwer
Academic Publisher, Boston, 666 pp.
Thomas, C., T. Foken. 2002. Re-evaluation of integral turbulence
characteristics and their parameterizations. In 15th Conference on
turbulence and boundary layer, Wageningen, NL, 15-19 July 2002,
American Meteorological Society. Pp. 129-132.
Tillmann, H. 1972. The direct determination of stability, heat and momentum
fluxes in the atmospheric boundary layer from simple scalar variables
during dry unstable conditions. Journal of Applied Meteorology 11:783792.
Vickers, D., L. Mahrt. 1997. Quality control and flux sampling problems for
tower and aircraft data. Journal of Atmospheric Ocean Technology
14:512-526.
F-7
Appendix F. Data Quality Grading
“Data Variables” from AmeriFlux website.
http://ameriflux.lbl.gov/data/aboutdata/data-variables/. Accessed 6 Jan
2017.
F-8
Appendix G. Footprint
The percentage of measured scalar flux from an area of interest is a major
indicator of appropriate site selection and station design. The upwind range
within which the sources/sinks contribute a given percent of total fluxes (for
example, 40, 55, and 90%) is typically desired by an investigator. Additionally,
the location of sources/sinks that contributes most to the measured fluxes is
often of interest (Kljun et al. 2004). These footprint characteristics can be
calculated using a footprint function of the measured scalar flux.
A footprint function of measured scalar flux, given by f(x, y, zm) where x and y
are horizontal spatial variables with positive x-axis pointing into the
streamwise direction and zm is measurement height, is a probability spatial
distribution of the relative contribution to the fluxes measured at the point (0,
0, zm), assuming that surface sources/sinks in the x-y domain as described by
F ( x , y ,0) are horizontally homogenous, or in other words F(x,y,0) is a
constant. The footprint, f(x, y, zm), can be implicitly defined using the measured
flux, F(0,0,zm), and the flux spatial function at the surface, F(x,y,0), given by:
F (0, 0, zm ) =
∞
∫ ∫
−∞
∞
0
F ( x, y , 0 ) f ( x, y , zm ) dxdy
(G-1)
The two functions inside the double integration describe the amount of
contribution to the measured flux from sources/sinks across the integrated area.
Given the two functions, the proportion of the measured flux from a smaller
defined area can also be calculated. For a general case, this equation may be
simplified by the assumption that F(x,y,0) is a constant (in example,
sources/sinks of flux are horizontally homogenous). The CRBasic online
calculations are designed for this general case. Therefore, F(x,y,0) is treated as
a constant and only the footprint [f(x, y, zm)] requires greater characterization.
To calculate the footprint in the CRBasic flux program, an analytical equation,
f(x, y, zm), is needed. Several studies (Gash, 1986; Schuepp, et al., 1990;
Schmid, 1994; Hsieh, et al., 2000; Kormann and Meixner, 2001; Kljun, et al,
2004) provide analytical footprint equations. The equations of Kljun, et al
(2004) were developed more recently than the others, and accordingly are used
in the CRBasic program. Their application, however, is limited to the following
ranges of atmospheric stability, friction velocity, and measurement height:
1.
−200 ≤ ( zm − d ) / L ≤ 1
2.
u* ≥ 0.2
3.
zm − d ≥ 1 m
(G-2)
where d is zero displacement height and L is Monin-Obukhov length. For cases
outside of the ranges above, the analytical footprint equation of Kormann and
Meixner (2001) is used.
G-1
Appendix G. Footprint
G.1 Kljun, et. al. (2004) Analytical Footprint
Equations
G.1.1 Models and Parameters
By applying dimensional analysis (Buckingham П method, see Stull 1988) and
analyzing numerical simulations, Kljun et al (2004) summarized footprints in
field scale for a given roughness length ( z0 ) and ratio of aerodynamic height
to planetary boundary-layer (PBL) height as a dimensionless footprint ( F* ) in
terms of dimensionless length ( X * ) for the range of conditions presented in
(G-2). The summarized footprint is represented by the model:
k2
  X + k 
 X +k 
=
F* ( X * ) k1  * 4  exp  k2  1 − * 4 
k3  
 k3 
 
(G-3)
where ki (subscript i = 1, 2, 3, and 4) is a parameter. If the parameters in the
model are given, the dimensionless footprint can be calculated for different
dimensionless lengths. These parameters can be statistically estimated using
the sampled values of X * and F* . The dimensionless length is a combination
of vertical wind standard deviation (σw), friction velocity ( u* ), measurement
aerodynamic height (z), and streamwise distance to measurement location (x),
given by:
a1
σ  x
X* =  w 
 u*  z
(G-4a)
where a1 is a parameter that was found to be 0.8 by numerical simulations
using the software LPDM-B. To consider the zero displacement height (d) over
different surface types, the variable z should be interpreted as the measurement
aerodynamic height ( z = z m − d ), which was confirmed by Dr. Kljun per
email on November 14, 2014. The dimensionless footprint of F* is a
combination of vertical wind standard deviation, friction velocity, planetary
boundary-layer height (h), measurement aerodynamic height, and streamwise
footprint integrated over cross-wind (i.e., marginal streamwise footprint) at a
field scale [ f y ( x , z ) in m-1], given by:
a2
−1
σw  
z
  1 −  zf y ( x, z )
h
 u*  
F* 
=
(G-4b)
where a2 is a parameter that was found to be -0.8 by simulation using the
software LPDM-B.
For a given case, the values of σw, u* , h, and z are known and the value of
f y ( x , z ) can be numerically simulated (Horst and Weil 1992). Given these
values, X * and F* can be calculated using (G-4a) and (G-4b). Kljun, et al
(2004) then used calculated values of dimensionless footprint and
dimensionless length as samples to statistically estimate the parameters of k1 to
G-2
Appendix G. Footprint
k4 in model (G3) for four roughness lengths and four ratios of aerodynamic
height to PBL height as shown in TABLE G-1.
TABLE G-1. Estimated parameters in dimensionless footprint model (F3)
𝑘𝑘1
𝑘𝑘2
z0 = 0.01 m
𝑘𝑘3
𝑘𝑘4
𝑘𝑘1
z0 = 0.1 m
𝑘𝑘2
𝑘𝑘3
𝑘𝑘4
0.005
0.024
3.84
31.0
18.0
0.028
2.47
22.0
12.0
0.075
0.024
4.11
33.0
15.0
0.027
2.87
24.0
10.0
0.250
0.021
3.61
35.0
12.0
0.026
3.40
27.0
10.0
0.500
0.025
4.23
33.0
9.0
0.028
5.06
32.0
12.0
z/h
z0 = 0.30 m
z0 = 1.0 m
0.075
0.042
4.06
19.0
7.00
0.052
2.40
11.0
5.00
0.250
0.038
4.24
21.0
7.00
0.050
3.19
14.0
4.00
0.500
0.042
6.02
23.0
6.00
0.051
3.93
15.0
3.00
Even without the PBL height, it is possible to use these parameters. From
figure 7 in Kljun et al (2004) it is evident that k1 can be well described using a
function of the natural logarithm of z0, which is independent of z/h. This
function is given by (left-top panel in figure 7, equation 13 in Kljun et al
[2004], and email from Dr. Kljun in Feb 10, 2015).
k1 ≈
0.175
(G-5a)
3.418 − ln z0
Parameters k3 and k4 are both linear functions of ln z0. Parameter k3 is given by
(left bottom panel in figure 7 and equation 15 in Kljun et al [2004]).
k3 ≈ 4.277 × ( 3.418 − ln z0 )
(G-5b)
and parameter k4 is given by (right bottom panel in figure 7 and equation 16 in
Kljun et al [2004]).
k4 ≈ 1.685 × ( 3.418 − ln z0 )
NOTE
(G-5c)
Although the parameters published in Kljun et al. (2004) had
fewer significant digits, email correspondence with Dr. Kljun
dated Feb 10, 2015, led to the adoption of three digits after the
decimal for parameters in Equation G-5a through G-4c.
Parameter k2 is independent of z0 and is a constant. Determining its value
requires taking the integral of F* ( X * ) (the over-hat indicates they are equations
with statistically-estimated parameters) over the entire domain of X and setting
it equal to one, as shown here (see appendix in Kljun et al. [2004]):
*
G-3
Appendix G. Footprint
∫
∞
k4
−k
Fˆ*=
Γ ( k2 ) 1
( Xˆ * )dXˆ * k1k3 exp(k2 )k=
2
2
(G-5d)
Substituting (G-5a) and (G-5b) into (G-5d) leads to:
exp(k2 )k2− k Γ ( k2 ) =
1.336050
2
(G-5e)
A numerical solution then generates k2:
k2 = 3.682540
(G-5f)
G.1.2 Application of Analytical Footprint
The marginal streamwise footprint [ f y ( x , z ) ] in (G-4b) is required to calculate
the needed footprint characteristics. However, for many years its analytical
form and the resulting cumulative footprint were unavailable for a wide range
of stabilities and wind velocity profiles. This motivated several studies to
conduct numerical simulations (Hsieh et al. 2000, Kljun et al 2004), which
could then be used to develop analytical footprint equations (for example
model [G3] and TABLE G-1).
Given an analytical form of f y ( x , z ) , the calculation of footprint characteristics
is straight forward. The sections below present equations for footprint
characteristics such as the percentage of flux from a defined upwind range of
interest and the point of maximum source/sink contribution to the measured
flux. These equations relate f y ( x , z ) , F* ( X * ) , and footprint characteristics.
Percentage of measured scalar flux from the upwind range of interest
Given the marginal streamwise footprint f y ( x , y ) , the percentage of
contribution from the sources/sinks within the upwind range of R, [ PF ( R) ],
can be calculated using:
pF ( R ) = 100 ∫
R
− Rk 4
f y ( x, z )dx
(G-6)
where −Rk4 is the downwind location of starting contribution of sources/sinks
to measured fluxes.
G-4
Appendix G. Footprint
Since:
a2
∫
R
− Rk 4
R
 σw   z 
 u   1 − h  z ∫− R f y ( x, z ) dx
 * 
f y ( x, z ) dx =
a
−1
 σw   z 
−
1
 u   h  z
 * 
−1
k4
2
(G-7)
=
 σw 
u 
 * 
− a2
1
z R
 1 −  ∫− R Fˆ* ( Xˆ * ) dx
z
h
k4
and because F* ( X * ) is defined in the domain of X * > − k 4 , this low limit of
integration is the value of x at X * ( x ) = − k 4 . Thus, Rk4 is given by:
u 
Rk 4 = k4 z  * 
σw 
a1
(G-8)
Submitting (G-7) into (G-6) generates:
σw 

 u* 
pF ( R ) 100 
=
− a2
1
z R
 1 −  ∫− R F* [ X * ( x ) ] dx
z
h
(G-9)
k4
Calculation for this is possible using numerical integration of the dimensionless
footprint F* [ X * ( x )] at discrete, incremental values of x, starting at a low value
given by −Rk4 and increasing until the value for R is reached. Specifically, the
value for dimensionless footprint at each value of x is found by using equations
(G-3) and (G-4a) with measured variables (σw and u*), known variables (z), and
estimated parameters [ki, given by (G-5a), (G-5b), (G-5c), and (G-5f)], as
shown here:
k2
   σ 0.8 x
  σ 0.8 x


w
+ k4 
+ k4  
   w
 
u
z
 exp k 1 −  u*  z

F* [ X * ( x )] k1   * 
=

2




k3
k3









 
 
(G-10)
The values for dimensionless footprint at every interval of x may then be
summed to estimate the value of the integral term in equation (G-9) for
calculation of p F ( R ).
Upwind location of source/sink that contributes most to the measured flux
Differentiating both sides of (G-4b) with respect to x generates:
df y ( x, z )  σ 
=  w
dx
 u* 
− a2
z  −1 dF* dX *

1 −  z
h
dX * dx

(G-11)
G-5
Appendix G. Footprint
The marginal streamwise footprint [ f y ( x , z ) ] is a bell-shape function with
respect to x, with a maximum occurring at xmax, which follows that:
df y ( x, z )
dx
=0
(G-12)
x = xmax
For real-world cases in the field, the terms of measured variables in the righthand-side of (G-11) will never equal zero, therefore, equation (G-12) can only
be true when the last two derivative terms are evaluated as zero at xmax, that is:
dF* dX *
dX * dx
(G-13)
=0
x = xmax
This can be expanded to the following equation:
a1
dF* dX *
k1 k 2  σ w   X * ( xmax ) + k 4 
=
  

dX * dx x = x
k 3 z  u*  
k3

k 2 −1
 
exp  k 2  1 −
 
max
X * ( xmax ) + k 4   X * ( xmax ) + k 4 
=
  1 −
 0
k3
k3
 

This equation is then solved for X * ( x max ) > − k 4 , resulting in the upwind
distance from the measurement station to the location that contributes most to
the measured flux being expressed as:
u 
xmax
= ( k3 − k 4 ) z  * 
σw 
0.8
(G-14)
According to (G-6) and (G-9), the percentage of contribution to the measured
flux within an upwind range of xp, where subscript p indicates percent and can
have a value of 0 to 100 [e.g., PF ( x10 ) = 10 and PF ( x90 ) = 90 ], can be expressed
as:
σw 

 u* 
=
pF ( x p ) 100 
0.8
1
z x
 1 −  ∫− R F* [ X * ( x ) ] dx
z
h
p
(G-15)
k4
This is an increasing monotonic function of xp. Given this, for a value of
p F ( x p ) , only one value of xp can be found. The value of xp may be estimated
by performing a numerical integration of p F ( R) as described in the section
above. Using a subscript i for x indicates the sequential number of numerical
integration steps, the two neighbor values of p F ( x i ) less than the target value
of p (for example, p = 10) and p F ( x i+1 ) greater than the target value can then
be used to interpolate a more precise value of xp where PF(xp) = p.
G-6
Appendix G. Footprint
G.1.3 Programmatic Approach
Roughness length
Applying model (G3) requires knowing the roughness length in order to
calculate the parameters (G-5a) to (G-5c). The roughness length depends on
surface type (for example, bare land, water surface, crops, grasses, trees, and
shrubs) and is approximately 0.13hc for crops and grasses, where hc represents
canopy height (Tanner and Pelton, 1960; Stanhill, 1969), 0.06hc for forests
(Jarvis, et al., 1976; Raupach, et al., 1991), and 0.033hr, where hr represents
roughness element height for bare land (for example, sands) (Raupach, et al.,
1991). A more accurate value of roughness length depends not only on the
surface type but also on surface roughness texture (for a canopy, this texture
can be described using vegetative surface area per unit volume). However, this
texture, the canopy height, and the resulting roughness length may change
quickly during certain periods of the growing season. This makes it impractical
to input a single roughness length that will be valid for a long time periods.
Accordingly, the roughness length should be updated periodically, which is
possible using the well-known equation of a wind profile under neutral
conditions [equation (4.2) in Rosenberg et al. (1983)]:
 k u2 +v2

u*

z0 =
( zm − d ) exp  −




(G-16)
where k is von Karman constant (0.41) and ū and ῡ are the two orthogonal
components of mean horizontal wind speeds, respectively. The roughness
length is automatically updated by the data logger at the end of each averaging
interval as long as the surface layer stability is under neutral conditions, as
defined by the strict criterion of z / L < 0.02 (Hsieh et al. 2000). The updated
roughness length will then be used for the calculation of parameters k1, k3, and
k4 using (G-5a) to (G-5c).
Until an averaging period occurs with neutral stability, an initial value for
roughness length must be estimated and used. Accordingly, our programmatic
approach is to require that the user select, among the options in a menu, the
land type that most closely matches the area around their eddy covariance
station. The program then uses this input to calculate an initial roughness
length as follows:
z0 = 100.997 log
10 hc − 0.883
(G-17)
for crops and grasses (Szeicz et al 1969), 0.06hc for forests and shrubs, and
0.01 m for bare land and water surfaces (i.e., corresponds to the parameters for
lowest roughness length in TABLE G-1). As soon as measured half-hourly data
are available and the stability is under neutral conditions, this initial roughness
length will be updated using (G-16).
G-7
Appendix G. Footprint
Calculation for parameters of k1 to k4
k1 ≈
0.175
3.418 − ln z0
k2 ≈ 3.682540
k3 ≈ 4.277 ( 3.418 − ln z0 )
k4 ≈ 1.685 ( 3.418 − ln z0 )
Calculation of planetary boundary-layer height
TABLE G-2. Relationship of Monin-Obukhov length (L) to planetary boundary-layer height (h)
L (m)
−5
−30
−650
∞
1000
130
84
h (m)
2000
1500
1200
1000
800
250
200
The Monin-Obukhov length is calculated in eddy covariance flux
measurements, and then it is used to find the PBL height using the data points
in TABLE G-2 and linear interpolation.
Upwind location of source/sink that contributes most to the measured flux
(maximum location)
The following equation is used in the data logger:
u 
xmax
= ( k3 − k 4 ) z  * 
σw 
0.8
Upwind inflection points of footprint
The footprint is a bell-shaped function with one maximum point (turning point)
and two inflection points. Because the footprint changes most in the segments
from the left inflection point (xIL) to xmax and from xmax to the right inflection
point (xIR), these inflection points may be used as boundaries for special
numerical integration segments where the integration intervals are smaller to
provide greater accuracy. Outside of these special segments, the integration
intervals may be larger and thereby decrease the computation required.
Specifically, the inflection point located at the left side of xmax (xIL) is given as:
=
xIL

xmax   k2 − 1 
 k3 
 − k4 
k3 − k4  
k2 

and the other is at the right side of xmax (xIR):
=
xIR

xmax   k2 + 1 
 k3 
 − k4 
k3 − k4  
k2 

G-8
Appendix G. Footprint
See the derivation of the inflection points in Appendix G.2, Derivation of
Equations for Upwind Locations at Inflection Points of Footprint in Kljun et al
(2004) (p. G-10).
Percentage of measured scalar flux from the upwind rand of interest to
measurements
As explained previously, the percentage of measured flux coming from an area
of interest may be calculated with the data logger using the following equation:
k2
0.8
σ  1 z  R
pF ( R ) =
100 k1  w 
1 −  ∫
 u*  z  h  − R
k4
  σ w 0.8 x

   σ w 0.8 x

+ k4 
+ k 4 
 
   
  u*  z
 exp k 1 −  u*  z
  dx
2




k3
k3





 



where the integral is evaluated using numerical integration.
Within the first integration segment (from Rk4 to xIL), the trapezoidal rule for
numerical integration is used with the segment divided into q intervals, where q
is an integer selected such that the resolution of the numerical integration
yields reasonable accuracy without a large burden in computation (for example,
q = 20).
Within the second segment (xIL to xmax), the trapezoidal rule is still used with an
integration interval of (xmax - xIL)/q.
The third segment also uses the trapezoidal rule and extends from xmax to xIR +
(xIR - xmax) with an integration interval of (xIR- xmax)/q. The fourth and final
segment begins at the end of the 3rd segment. The fourth segment uses
integration intervals with a size of 4z. Although these intervals may be
significantly larger than the intervals used in the other segments, the integration
accuracy should still be acceptable since Boole’s rule, rather than the
trapezoidal rule, is used within this segment and the slope of the footprint
should be changing very slowly throughout the segment. The fourth segment
initially extends to 200z beyond the segment starting point or until the the
cumulative flux reaches 90%. If the distance of interest is not reached at the
end of the fourth segment but is within another 100z, an additional 25
integration intervals are added to the segment, with the endpoint being the
distance of interest. If the distance of interest is beyond another 100z, it is
assumed that the cumulative footprint would be wholly contained within the
distance of interest, thus 99% is reported as the cumulative flux within the
distance of interest. If the cumulative flux never reaches 90%, which is
possible under certain conditions where the numerical integration is inadequate
or the model does not truly reflect the real footprint distribution, the distance
for 90% flux will be reported as NAN (not a number).
Scaling the integration intervals within each segment provides a way to have
higher integration resolution when the slope of footprint changes more
dramatically while still limiting the size of the integration interval when the
slope is not changing as much. This approach is successful in converging the
percentage flux to a value of one if numerically integrated over the entire
domain. An additional advantage of this approach is that because xmax must be
used as a segment boundary, the peak value of the function is never missed,
which contributes to greater accuracy of the overall numerical integration.
G-9
Appendix G. Footprint
Upwind range within which the sources/sinks contributes a given percent
to measured flux
If this upwind range is denoted using xp where subscript p indicates the given
percent, it can be implicitly expressed in an equation as:
k2
0.8
σ  1 z  x
p=
100 k1  w 
1 −  ∫
 u*  z  h  − R
p
k4
  σ w 0.8 x

   σ w 0.8 x

+
+ k 4 
k
 
   
4 
  u*  z
 exp k 1 −  u*  z
  dx
2



k3
k3
 




 



Among the values of p F ( x p ) that were found in the process of numerical
integration described above, if the value in current iteration is just greater than
the target percentage (for example, p = 40), a more precise value of x40 [for
example, p F ( x 40 ) = 40 ] can be interpolated using this value along with the
value in previous iteration. In this way, x40, x55, and x90 are found.
G.2 Derivation of Equations for Upwind Locations at
Inflection Points of Footprint in Kljun et al.
(2004)
As described above, integration segment boundaries should be determined by
the upwind inflection points of the footprint. Since the footprint is known to be
a bell-shaped function, there is one maximum point (xmax) and two inflection
points (xIL and xIR) on both sides of the maximum, respectively. Accordingly,
xmax may be found by setting the first order derivative of the footprint function
to zero. Similarly, xIL and xIR may be found by setting the second order
derivative to zero. The following section shows this derivation for these points.
G.2.1 Footprint Model
The footprint in Kljun et al. (2004) is given in the form of a dimensionless
footprint [ F* ( X * ) ]:
k2
 
 X + k4 
X * + k4  
=
F* ( X * ) k1  *
 exp  k2  1 −

k3  
 k3 
 
(G-18)
where ki (subscript i = 1, 2, 3, and 4) is a parameter, and X * is the
dimensionless length. It is a combination of vertical wind standard deviation
(σw), friction velocity ( u* ), measurement aerodynamic height ( z = z m − d ),
and the upwind distance (x) from the measurement location given by:
a1
σw  x

 u*  z
X* = 
(G-19)
where a1 is a parameter. The dimensionless footprint of F* is a combination of
vertical wind standard deviation, friction velocity, planetary boundary-layer
height (h), measurement aerodynamic height, and streamwise footprint
G-10
Appendix G. Footprint
integrated over cross-wind (i.e., marginal streamwise footprint) at a field scale
[ f y ( x , z ) in m-1], given by:
a2
−1
σ  
z
=
F*  w   1 −  zf y ( x, z )
h
 u*  
(G-20)
where a2 is a parameter.
G.2.2 Upwind location of maximum footprint
Differentiating both sides of (G-20) with respect to x generates:
df y ( x, z )  σ 
=  w
dx
 u* 
− a2
z  −1 dF* dX *

1 −  z
h
dX * dx

(G-21)
The derivative of dimensionless length with respective to x is greater than zero
and is independent of x; therefore:
df y ( x, z )
dx
= 0 at
dF*
dX *
=0
(G-22)
which indicates f y ( x , z ) and F* reaches the maximum at the same upwind
location (xmax). Therefore, the location of maximum footprint satisfies the
following equation:
dF*
k1k2  X * ( xmax ) + k4 
=


dX * x = x
k3 
k3

k2 −1
 
exp  k2  1 −
 
max
X * ( xmax ) + k4    X * ( xmax ) + k4 
1−
 =
 0
k3
k3
 

(G-23)
Solving this equation for X * ( x max ) > − k 4 generates:
xmax
=
 u* 

σw 
0.8
( k3 − k 4 ) z 
(G-24)
G.2.3 Upwind locations of inflection points
Differentiating both sides of (G-21) with respect to x generates:
d 2 f y ( x, z )  σ w 
=


dx 2
 u* 
− a2
z  −1 d 2 F*  dX * 

1 −  z


h
dX *2  dx 

2
(G-25)
The derivative of dimensionless length with respective to x is greater than zero
and is independent of x; therefore:
d 2 f y ( x, z )
dx 2
= 0 at
d 2 F*
dX *2
=0
(G-26)
G-11
Appendix G. Footprint
which indicates f y ( x , z ) and F* have inflection points at the same upwind
locations, and therefore:
d 2 F*
dX *2
=0
(G-27)
This can be used to find the upwind locations of the inflection points in the
footprint curve.
Referencing (G-23), the first order derivative of dimensionless footprint can be
written as:

dF* k2  X * + k4 
=

 − 1 F*
dX * k3  k3 


−1
(G-28)
Using this equation, the derivative at the second order can be derived as:
d 2 F*
dX *2
 X * + k4  dF* dF* 
k2  1  X * + k4 
=
−
− 

 F* + 

k3  k3  k3 
 k3  dX * dX * 
−2
−1


−2
k  X +k 
k2
=
− 22  * 4  F* + 22
k3  k3 
k3

2
 X + k  −1 
 * 4  − 1 F*
 k3 

2
(G-29)

 X + k 
 
k
 X + k 
=
− 22 F*  * 4  + k2  * 4  − 1 
k3  k3 
 k3 
 

−2
−1
In this equation, the term ahead of the curly bracket is not zero. Therefore, in
order to satisfy (G-27), the term inside the curly bracket must be zero. If
assuming:
 X + k4 
X = *

 k3 
−1
(G-30)
The term inside the curly bracket satisfies (G-27) in the following form:
X 2 + k2 [ X − 1] =
0
2
(G-31)
Solving this equation, substituting (G-19) into X, and referencing (G-24) leads
to an equation for the left inflection point:
G-12
Appendix G. Footprint

xmax   k2 − 1 
 k3 
 − k4 
k3 − k4  
k2 

=
xIL
(G-32)
Similarly, the equation for the right inflection point is obtained by:

xmax   k2 + 1 
 k3 
 − k4 
k3 − k4  
k2 

=
xIR
(G-33)
G.3 Kormann and Meixner (2001) Analytical
Footprint Equations
G.3.1 Footprint
As an alternative to the analytical approach used by Kljun, et al., (2004), which
is limited by the conditions presented in (G-2), the footprint was derived by
Kormann and Meixner (2001) based on Van Ulden (1978) as [(see the detailed
derivations in Appendix G.4, Derivation of Analytical Footprint in Kormann
and Meixner (2001) (p. G-19)]:
1.
Two-dimensional (2D) marginal streamwise footprint
 z m +1 
 zr 
ξ µ  µ +1  exp  −ξ 
x 
Γ(µ)  x 

1
f y ( x, z )
=
(G-34)
where r, μ, and ξ are composites of other variables which have been combined
for succinctness in the expression. Each of these variables is defined below.
r (shape factor):
r =2 + m − n
(G-35)
where m is the exponent in a vertical profile of horizontal wind [see (G74) in Appendix G.4, Derivation of Analytical Footprint in Kormann and
Meixner (2001) (p. G-19)], and n is the exponent in a vertical profile of eddy
diffusivity [see (G-63) in Appendix G.4, Derivation of Analytical
Footprint in Kormann and Meixner (2001) (p. G-19).
μ:
µ=
m +1
r
(G-36)
ξ:
ξ=
U
κr 2
(G-37)
G-13
Appendix G. Footprint
where U is the wind constant in a vertical profile of horizontal wind [see
(G) in74 Appendix G.4, Derivation of Analytical Footprint in Kormann
and Meixner (2001) (p. G-19)], and κ is the constant in power-law profile of
the eddy diffusivity.
κ=
ku* z1− n
ϕc /
( z L)
(G-38)
The calculations for the variables: m, n, U, and κ will be given in the
following sections.
G.3.2 Programmatic Approach
The 3D footprint [ f ( x , y , z ) ] can be expressed in terms of a marginal
streamwise footprint and a down-wind probability distribution of scalar
concentrations from upwind sources in a domain of x and y [c(x, y)] [see model
(9) in Horst and Weil, (1992) and model (8) in Kormann and Meixner, (2001)],
given by:
f ( x, y , z ) = c ( x, y ) f y ( x, z )
(G-39)
where:
=
c ( x, y )
 1  yu ( x )  2 
exp  − 
 
2π xσ y
 2  xσ y  
u ( x)
(G-40)
where the constant σ y is the standard deviation of crosswind scalar
concentration and ū(x) is the effective velocity of the scalar plume. This
equation is derived from model (10) in Horst and Weil (1992) and model (9) in
) in the
Kormann and Meixner (2001) after the simple scalar dispersion (
model is replaced with a detailed descriptive dispersion [ σ y x / u ( x ) ], which
σ
depends on distance from the station (x) and effective velocity of the scalar
plume [ū(x)]. Substituting (G-34) and (G-40) into (G-39) leads to the threedimensional footprint:
=
f ( x, y , z )
u ( x)
 z m +1
ξ  µ +2
2π σ y Γ ( µ )  x
µ
 1

− 2
exp

 x


2

1  yu ( x )   
r
 ξ xz + 
 

2  σ y   


(G-41a)
where:
Γ ( µ )  κr 2
u ( x) = U

1 U
Γ  
r
m
r
x

(G-41b)
See (G-82) to (G-92) in Appendix G.4, Derivation of Analytical Footprint in
Kormann and Meixner (2001) (p. G-19), for associated derivations.
G-14
Appendix G. Footprint
G.3.3 Application of analytical footprint
Unlike the dimensionless footprint in Kljun et al., (2004), the footprint
developed by Kormann and Meixner, (2001) explicitly gives the analytical
marginal (cross-wind integrated) streamwise footprint (G-34) and threedimensional footprint (G-41a and G-41b). Both can be directly used to
calculate the footprint characteristics.
Percentage of measured scalar flux from the upwind range of interest
The percentage of contribution from these sources/sinks, within the upwind
range of interest, to the measured flux [ p F ( R) ] is given by:
R
pF ( R ) = 100 ∫ f y ( x, z ) dx
0
= 100
R
 zr 
ξ µ z m +1
1
lim ∆x →0 ∫
exp
 −ξ  dx
0 +∆x µ +1
x
x 
Γ(µ)

(G-42)
where the Gamma function of μ can be accurately approximated using Memes
(2010):
Γ(µ) ≈
 
2π  1 
1
 µ +
1
µ e 
12 µ −

 
10 µ






µ
(G-43)
Location of source/sink that contributes most to the measured flux
1. Approach using 2D marginal streamwise footprint [fy (x,z)]
Differentiating (G-34) with respect to x generates:
df y ( x, z ) ξ µ z m +1 d  1
 z r 
=
exp
 −ξ x  
 µ +1
Γ ( µ ) dx  x
dx


ξ z
 z   − ( µ + 1) ξ z 
= exp  −ξ
  µ + 2 + x µ +3 
Γ (ξ )
x  x


µ
µ
=
ξ z
m +1
m +1
Γ(µ)
r
r

z   ξ z − x ( µ + 1) 

x 
exp  −ξ
(G-44)
r
r

x
µ +3


The marginal streamwise footprint [ f y ( x , z ) ] is a bell-shape function with
respect to x, with the maximum found at xmax, which follows that:
df y ( x, z )
dx
=0
x = xmax
(G-45)
G-15
Appendix G. Footprint
All terms except for the term in the square bracket in (G-43) are greater
than zero for any real-world case in the field, and therefore setting that
term equal to zero results in the solution for xmax:
ξ zr
=
µ +1
xmax
2.
(G-46)
Approach using 3D footprint [f (x,y,z )]
Differentiating (G-41a) with respect to x at y = 0
df ( x, 0, z )
=
dx
=
 u ( x)
 z r 
exp
 −ξ x  
 µ +2
2π σ y Γ ( µ ) dx  x


ξ z
µ
m +1
µ
m +1
ξ z
d

2π σ y Γ ( µ )
exp  −ξ
  1 du ( x ) ( µ + 2 ) u ( x ) ξ z u ( x ) 
+

  µ + 2 dx −
µ +3
µ +4
x x
x
x

z

(G-47a)
r
r
The footprint [ f ( x ,0, z ) ] is a bell-shape function along x, with the
maximum found at xmax, which follows that:
df ( x, 0, z )
dx
=0
(G-47b)
x = xmax
To satisfy this equation, the term inside curly bracket in (G-47a) must be
zero, or:
 1 du ( x ) ( µ + 2 ) u ( x ) ξ z r u ( x ) 
−
+
 µ +2

dx
x µ +3
xµ +4  x= x
x
0
=
(G-47c)
max
Using (G-41b), the derivative term is expressed as:
du ( x )
dx
m
mΓ ( µ )  κr 2  r mr −1
=U

 x
1 U 
rΓ  
r
(G-47d)
Substituting this equation along with (G-41b) into (G-47c) leads to:
m
m
 mr −1

r r
r
 mx − ( µ + 2 ) x + ξ z x 
0
=
 rx µ + 2
x µ +3
xµ +4 

 x = x
(G-47e)
max
Because x
≠ 0 , it can be simplified as:
G-16
Appendix G. Footprint
 mx − r ( µ + 2 ) x + rξ z r  x = x
0
=
max
(G-47f)
The solution of this equation is the location of source/sink that contributes
most to the measured flux and is given as:
xmax =
rξ z r
(G-48)
2r + 1
For practical purposes of handling the computation required for the numerical
integration, we use xmax from the 2D footprint approach, although, admittedly,
in some cases the solution from the 3D footprint may be preferable since the
3D footprint uses the detailed descriptive dispersion [see page 215 in Kormann
and Meixner (2001)].
Upwind range within which the sources/sinks contribute 10 or 90 percent to
measured flux. According to (G-41), the percentage of contribution to the
measured flux from the upwind range of xp, where subscript p indicates percent
of 0 to 100, and can be expressed as:
pF ( x p ) 100
=
x
 zr 
1
ξ µ z m +1
lim ∆x →0 ∫
exp
 −ξ  dx
0 +∆x µ +1
x
x 
Γ(µ)

p
(G-49)
This is an increasing monotonic function of xp; therefore, for a given value of
p F ( x p ) , there is a unique value of xp that can be found. Similar to the method
described for applying the Kljun et al (2004) model, the value of xp may be
estimated by performing a numerical integration for intervals of x and then
interpolating values of PF(xp) to find the corresponding value of xp for
( )
pF x p = p
where p = 40, 55, or 90.
G.3.4 Programmatic Approach
Calculate the individual variables
Find the exponent of vertical profile of eddy diffusivity [see (G-65) Appendix
G.4, Derivation of Analytical Footprint in Kormann and Meixner (2001) (p. G-19)]:
 1
1 + 5 z / L

n=
1 − 24 z / L

 1 − 16 z / L
z/L>0
(G-50)
z/L≤0
Find the exponent of vertical profile of horizontal wind [see (G-76) Appendix
G.4, Derivation of Analytical Footprint in Kormann and Meixner (2001) (p. G-19)]:
m=
u*
z
φm  
L
k u ( z) + v ( z)
2
2
(G-51)
G-17
Appendix G. Footprint
where φm ( z / L) is wind shear, given by:
1 + 5 z / L
z 
φm   = 
1
−
L 
(1 − 16 z / L ) 4
z/L>0
z / L≤ 0
(G-52)
Find the wind constant [see (G-74) in Appendix G.4, Derivation of Analytical
Footprint in Kormann and Meixner (2001) (p. G-19)]
u 2 ( z) + v 2 ( z)
U =
(G-53)
zm
Composite variables
Calculate the shape factor and other composite variables:
r =2 + m − n
(G-54)
μ:
µ=
m +1
(G-55)
r
ξ:
ξ=
U
(G-56)
κr 2
Calculate the gamma function of μ [see Nemes (2010), verified as accurate]
Γ(µ) ≈
 
2π  1 
1
 µ +
1
µ e 
12 µ −

10 µ
 






µ
(G-57)
Footprint characteristics
Percent of measured scalar flux from upwind range of interest to
measurements:
=
pF ( R ) 100
R
 zr 
ξ µ z m +1
1
lim ∆x →0 ∫
exp
 −ξ  dx
0 +∆x µ +1
Γ(µ)
x
x 

(G-58)
Similar to the description of applying the Kljun et al (2004) model, the integral
is evaluated by the data logger using four integration segments, each containing
scaled integration intervals so as to increase resolution when the slope of the
function is changing more and decrease computation when the slope is
changing less. The segment boundaries and interval sizes are the same as
G-18
Appendix G. Footprint
described previously, except that when applying the Kormann and Mexiner
(2001) model, zero instead of Rk4 is used as the first segment’s lower boundary.
Location of source/sink that contributes most to the measured flux:
xmax
ξ zr
=
µ +1
(G-59)
Upwind inflection location of footprint, where the Kormann and Meixner
(2001) model is a bell-shaped function, there is one maximum point (turning
point) and two inflection points. As described previously, these points should
be used as boundaries for the numerical integration segments. One of the
inflection points (xIL) is located at the left side of the maximum point and given
by:

=
xIL xmax  1 −



µ+2 
1
and the other is at the right side (xIR) and given by:

=
xIL xmax  1 +



µ+2 
1
See the derivation of these inflection points in Appendix G.5, Upwind Locations
at Inflection Points of Footprint in Kormann and Meixner (2001) (p. G-28).
Upwind range within which the sources/sinks contributes a given percent to
measured flux:
p 100
=
x
 zr 
1
ξ µ z m +1
lim ∆x →0 ∫
exp
 −ξ  dx
0 +∆x
x µ +1
x 
Γ(µ)

p
(G-60)
Because an analytical solution for xp is not available, the value of xp can be
interpolated in the process of numerical integration of (G-58) when p is
between two consecutive integrated values. In this way, x40, x55, and x90 are
found.
G.4 Derivation of Analytical Footprint in Kormann
and Meixner (2001)
G.4.1 Model Derivation
Following Horst and Weil (1992), the probability distribution of a scalar
concentration downwind of a sink/source in three dimensions may be described
using a function c( x , y , z ) , where x and y are horizontal spatial variables with
x-axis following mean wind direction, and z is a vertical spatial variable. The
function is approximated using two independent probability distributions of
downwind scalar concentration in two dimensions and the vertical profile of
horizontal wind speed [ u( z ) ], given by:
G-19
Appendix G. Footprint
c ( x, y ) c ( x, z )
c ( x, y ) c ( x, z )
=
∞
u ( x)
∫ u ( z )c ( x, z ) dz
=
c ( x, y , z )
(G-61)
0
where u ( x ) is termed as a plume effective velocity. In probability theory,
integration of c( x , y , z ) over the entire domain of y is the marginal (cross-wind
integrated) probability distribution of the downwind scalar concentration in x
and z [ c y ( x , z ) ]. Applying this integration to both sides of (G-61) generates:
c y ( x, z ) =
c ( x, z )
(G-62)
u ( x)
According to K-theory, the product of the vertical profile of eddy diffusivity [
K ( z ) ] and the vertical scalar concentration gradient is the scalar flux.
Therefore, the cross-wind integrated footprint [ f y ( x , z ) , i.e. the cross-wind
integrated probability distribution of flux] is given as:
f y ( x, z ) = − K ( z )
dc y ( x, z )
(G-63)
dz
To analytically express f y ( x , z ) for real-world applications, K ( z ) and c y ( x , z )
must be analytically expressed in terms of measured variables.
G.4.2 Analytical expression: Vertical profile of eddy diffusivity
The vertical profile of eddy diffusivity can be described as:
K ( z ) = kz n
(G-64)
where k is the von Karman constant (0.41), and n is the power exponent
depending on the surface layer stability, given by (Huang 1979):
1

1 + 5 z / L
z dK ( z ) 
=
n = 
K ( z ) dz
1 − 24 z / L

 1 − 16 z / L
z/L>0
(G-65)
z/L≤0
Equations (G-64) and (G-65) express the vertical profile of eddy diffusivity in
terms of measured variables.
G-20
Appendix G. Footprint
G.4.3 Analytical expression: Crosswind integrated scalar
concentration distribution
The most common analytic expression for the cross-wind integrated scalar
concentration distribution [ c y ( x , z ) ] is a Gaussian plume model (van Ulden
1978, Horst and Weil 1992), given by:
  Bz  r 
exp  − 
=
c y ( x, z )
 
u ( x) z ( x)
  z ( x )  
A
(G-66)
where A, B, and r are parameters. u ( x ) is the effective speed of plume
advection along the streamwise wind vector, implicitly defined in (G-61),
given explicitly by:
∞
∫ u ( z ) c ( x, z ) dz
u ( x) =
∫ c ( x, z ) dz
y
0
(G-67)
∞
0
y
and z ( x ) is the effective height of plume advection along the wind stream,
defined by:
∞
∫
z ( x) =
∫
0
zc y ( x, z ) dz
∞
0
(G-68)
c y ( x, z ) dz
The remaining work is to find parameters of A, B, and r, and analytically
express u ( x ) and z ( x ) in terms of measured variables.
Parameter estimation: A and B
Examination of equation (G-62) reveals that because c( x , z ) is the probability
distribution of scalar concentration in two dimensions, we effectively have:
∫
∞
0
c y ( x, z ) dz =
1
(G-69)
u ( x)
which means:
A
=
z ( x)
=
  Bz  r 
∞
∫0 exp  −  z ( x )   dz




B
B
=
r
  Bz    Bz  1  1 
∞
Γ
exp
∫0  −  z ( x )   d  z ( x )  r  r 





(G-70)

G-21
Appendix G. Footprint
The solution to parameter B is needed. Submitting (G-66) into (G-68)
generates:
  Bz r   Bz 
∫0 z exp  −  z ( x )   d  z ( x ) 
  

 
z ( x) =
r
  Bz    Bz 
∞
exp

∫0  −  z ( x )   d  z ( x ) 
  

 
∞
(G-71)
Multiplying B / z ( x ) to both sides of this equation leads to:
  Bz  r   Bz 
∫0 z ( x ) exp  −  z ( x )   d  z ( x )  Γ  2 
  

 
r
B =
=
r
  Bz    Bz 
1
∞
Γ
 
∫0 exp  −  z ( x )   d  z ( x ) 
r
  

 
∞
Bz
(G-72)
Equations (G-70) and (G-72) give:
A=
rΓ ( 2 / r )
[Γ (1 / r )]
2
(G-73)
B=
Γ (2 / r )
Γ (1 / r )
Parameter estimation: r
This parameter is a shape factor of the plume, given by van Ulden (1978):
r =2 + m − n
(G-74)
where n is the power exponent of the vertical profile of eddy diffusivity [see
(G-64) and (G-65)], and m is the exponent of the vertical profile of horizontal
wind, given by:
u ( z ) = Uz m
(G-75)
which depends on the surface layer stability, given by [page 16, Kaimal and
Finnigan (1994)]:
m
=
u*
z du ( z )
z
=
φm  
u ( z ) dz
ku ( z )  L 
(G-76)
G-22
Appendix G. Footprint
where φm ( z / L) is wind shear and given by:
1 + 5 z / L
z 
φm   = 
1
−
L 
(1 − 16 z / L ) 4
z/L>0
(G-77)
z / L≤ 0
The other parameter U in (G-75) is a wind constant and can be calculated using
measured u ( z ) and calculated m:
=
U
u (z)
=
zm
ux ( z) + u y ( z)
(G-78)
zm
Analytical expression: Effective height of plume advection [ z ( x ) ]
Examining (G-71) reveals that the numerator can be analytically evaluated only
if the term B / z ( x ) is multiplied to both sides of the equation. As a result, it
becomes a Gamma function; therefore, the effective speed of plume advection
cannot be analytically expressed in terms of measured variables using its
definition in (G-68). Alternatively, differentiating both sides of (G-68) with
respect to x generates:
dz ( x )
=
dx
∫
∞
0
z
∂ c y ( x, z )
∞
zc y ( x, z ) dz
∫
∂x
− 0∞
∞
∫ cy ( x, z ) dz ∫ cy ( x, z ) dz
0
0
∫ [ z − z ( x )]
∞
=
dz
∂ c y ( x, z )
∂x
∞
∫ cy ( x, z ) dz
0
∫
∞
∂ c y ( x, z )
dz
∂x
∞
∫ cy ( x, z ) dz
0
0
(G-79)
dz
0
Neglecting the streamwise eddy diffusion, the change in concentration along
the wind direction (derivative term) must cause a change in flux due to the
continuity in air mass (van Ulden 1978, Horst and Weil 1992), given by:
u (z)
∂ c y ( x, z )
∂x
∂ 
=
−
−K ( z)
∂z
∂ c y ( x, z ) 

∂z

(G-80)
Submitting (G-64) and (G-75) into this equation generates:
∂ c y ( x, z )
∂x
=
k
U
z −m
∂  n ∂ c y ( x, z ) 
z

∂z
∂z

(G-81)
G-23
Appendix G. Footprint
Submitting this equation into (G-79) generates:
dz ( x )
dx
U
∞
 ∞ 1− m ∂ n ∂ c y ( x, z )
∂ n ∂ c y ( x, z ) 
dz − z ( x ) ∫ z − m
z
dz 
 ∫0 z ∂ z z
0
∂z
∂z
∂z

c y ( x, z ) dz 
1
k
∫
∞
0
(G-82)
The equation can then be evaluated by substituting (G-66) into the three
integration terms on the right-hand side. Performing these three substitutions at
once becomes overly complex, so substitution and simplification of each
integral term is presented separately here:
Integration term in the denominator
∫
∞
0
A
∞
c y ( x, z ) dz =
z ( x ) u ( x ) ∫0
  Bz r 
A
1
Γ 
exp  − 
 dz =

Bru ( x )  r 
  z ( x)  
(G-83)
The first integration term in the numerator
Assuming that the gradient of scalar concentration at the surface ( z = 0 ) and
beyond the top of boundary-layer ( z → ∞ ) is zero and the concentration
beyond the top of boundary-layer is zero, this integration can be evaluated as
follows:
∫
∞
0
z
1− m
∂
n
∂ c y ( x, z )
=
z
dz z
∂z
∂z
1− m + n
∂ c y ( x, z )
∂z
−
∫

n−m
n−m
rB
A (1 − m ) z
n−m
∂z
0
∫
∞
0
z
n − m −1
n − m −1
n−m
u ( x)
n − m −1
u ( x)
∫
1− m
c y ( x, z ) dz
∞
0
n−m


  Bz  r 
exp  − 
  dz
z ( x) u ( x)
  z ( x )  
( x) 
∫
∞
0
n − m −1
dz
A
u ( x)
A (1 − m )( n − m ) z
B
n
∞
A (1 − m )( n − m ) z
=
z
c y ( x, z ) −
=
(1 − m )( n − m )
=
∞
0
0
=
− (1 − m )  z
B
∂ c y ( x, z )
∞

z x 
 ( )
Bz
n − m −1
  Bz  r   Bz 
exp  − 

 d
  z ( x )    z ( x ) 
( x)  n − m 
Γ


 r 
( x)  2 
Γ
(G-84)
 
r
G-24
Appendix G. Footprint
The second integration term in the numerator
Using the same derivation approach, the second integration terms in the
numerator can be evaluated as:
∫
∞
0
z
−m
∂
n
∂ c y ( x, z )
=
z
dz z
∂z
∂z
− m+n
∂ c y ( x, z )
∂z
= m z

∞
−
∫
∞
0
z
n
∂ c y ( x, z )
∂z
0
n − m −1
c y ( x, z ) −
∞
0
=
− m ( n − m − 1)
∫
∞
0
z
∫
∞
0
dz
−m
c y ( x , z ) dz
n−m−2
n − m −1


  Bz  
exp  − 
  dz
z ( x) u ( x)
  z ( x)  
r
A
  Bz 
Am ( n − m − 1) z
( x ) ∞  Bz 
=
−
 exp  − 

n − m −1
0 
B
u ( x)
 z ( x) 
  z ( x) 
n−m−2
n−m−2
∫
r
  Bz 

d
  z ( x) 
Am ( n − m − 1) z
( x)  n − m −1 
=
−
Γ

n − m −1
 r 
rB
u ( x)
n−m−2
Amz
( x)  1 
BΓ  
=
−
n−m
r
B u ( x)
n−m−2
(G-85)
Amz
( x)  2 
=
−
Γ 
n−m
r
B u ( x)
n−m−2
G-25
Appendix G. Footprint
Substituting the evaluated terms in (G-83), (G-84), and (G-85) into (G-82)
expresses the derivative of the effective height with respective to x as a
fundamental differential equation:
dz ( x )
dx
A
U
=
=
=
=
κ
U
κ
U
κ
U
κ
U
Bru ( x )
Γ
rB
Γ
rB
rB
2
()
()
z
r
rB z
1− r
()
1
z
n−m
( x )  2  
Γ  

 r  
u ( x)
n−m−2
n−m
r
n − m −1
B
( x)
n−m
r
n − m −1
B
2+m−n
Γ
2
r
1
 A (1 − m ) z ( x )  2 
 Amz
Γ   − z ( x) −

 B
r
B u ( x)


n − m −1
1
κ
z
( x)
(G-86)
n−m
1− ( 2 + m − n )
( x)
( x)
This fundamental equation can be written as:
κ
∫ rz ( x ) dz ( x ) = U r
r −1
2
B r ∫ dx
(G-87)
therefore:
 κr 2
z ( x) = B 
 U
1
r
x

(G-88)
Analytical expression: Effective speed of plume advection [ u ( x ) ]
Substituting (G-74) into (G-66) gives:
∞
u ( x) =
U ∫ z m c y ( x, z ) dz
0
∞
∫
0
c y ( x, z ) dz
(G-89)
G-26
Appendix G. Footprint
The denominator was evaluated in (G-83) and the integration term in the
numerator can be evaluated as:
z c y ( x, z )dz
=
∫
∞
0
m
∫
∞
0
=
=
  Bz  r 
z
exp  − 
  dz
z ( x) u ( x)
  z ( x )  
A
m
Az
B
( x )  Bz 

∫
u ( x)  z ( x) 
m
m +1
Az
rB
m
∞
0
  Bz  r   Bz 
exp  − 
 d

  z ( x )    z ( x ) 
(G-90)
( x)  m +1 
Γ

u ( x)  r 
m
n−m
Substituting this equation along with (G-83) into (G-89) generates:
Az m ( x )
 m +1 
 m +1 
Γ

m
rB u ( x )  r 
z ( x )  r 
=
u ( x) = U
A
Bm
1
1
Γ 
Γ 
rBu ( x )  r 
r
U
m +1
Γ
(G-91)
Substituting the analytical expression of effective height of plume advection
[ z ( x ) ] into this equation generates:
 m +1 

2
r   κr
u ( x) = U 

U
1
Γ  
r
Γ
m
r
x

(G-92)
By substituting the solved parameters of A and B (G-73), analytically expressed
effective height of plume advection [ u ( x ) , see (G-88)], and analytical
expressed effective speed of plume advection [ z ( x ) , see (G-92)] into (G-66),
finally, the cross-wind integrated scalar concentration distribution can be
analytically expressed in terms of spatial variables (x and z), the constant in the
power-law profile of the eddy diffusivity ( κ ), and calculated variables from
measurements (m, n, and U).
G-27
Appendix G. Footprint
That is:
r
c y ( x, z )
U
 
 
 
Bz
exp
− 
1
1
   κr 2  r
 κr 2  r
B
x
x
  B
 U 
   U 
Γ (2 / r)
Γ (1 / r )
2
Γ [( m + 1) / r ]  κr
m
r
 U x


Γ (1 / r )
2







r







(G-93)
r
 U 
=
 2 
U Γ [( m + 1) / r ]  κr x 
m +1
r
 Uz r 
exp  − 2 
 κr x 
More succinctly, given that:
ξ=
U
κr 2
(G-94)
µ=
m +1
r
the cross-wind integrated scalar concentration distribution, in an analytical
form, can be presented as:
=
c y ( x, z )
µ
 zr 
 1
exp
ξ


 −ξ x 
UΓ(µ)  x 


r
Examining equation (G-62) reveals that the cross-wind integrated footprint can
be thus derived as:
f y ( x, z ) = − K ( z )
= −κz n
=
dc y ( x, z )
dz
r

ξ
UΓ(µ) 
1

z r 
rz r −1 
x

x 
x 
 exp  −ξ
 −ξ

(G-95)
 z m +1 
 zr 
ξ µ  µ +1  exp  −ξ 
x 
Γ(µ)  x 

1
G.5 Upwind Locations at Inflection Points of
Footprint in Kormann and Meixner (2001)
As described previously, integration segment boundaries should be determined
by the upwind inflection points of the footprint. Since the footprint is known to
G-28
Appendix G. Footprint
be a bell-shaped function, there is one maximum point (xmax) and two inflection
points (xIL and xIR) on both sides of the maximum, respectively. Accordingly,
xmax may be found by setting the first order derivative of the footprint function
to zero. Similarly, xIL and xIR may be found by setting the second order
derivative to zero. The following section shows derivations for these points.
G.5.1 Footprint Model
The cross-wind integrated footprint [fy(x, z)] in Kormann and Meixner (2001) is
given by:
f y ( x, z )
=
 z m +1 
 zr 
ξ µ  µ +1  exp  −ξ 
Γ(µ)  x 
x 

1
(G-96)
where x is the upwind distance to the measurement station; z is measurement
aerodynamic height; m is the exponent of the vertical profile of horizontal wind
velocity; and r, μ, and ξ are composite variables, given by:
Shape factor:
r =2 + m − n
(G-97)
where n the exponent of vertical profile of eddy diffusivity.
μ:
µ=
m +1
r
(G-98)
ξ:
ξ=
U
κr 2
(G-99)
where U is the wind constant.
G.5.2 Upwind Location of Maximum Footprint
Differentiating (G-96) with respect to x generates:
df y ( x, z ) ξ µ z m +1 d  1
 z r 
exp  −ξ 
=

Γ ( µ ) dx  x µ +1
dx
x 

(G-100)
 z r   ξ z r − x ( µ + 1) 
ξ µ z m +1
exp  −ξ  
=

Γ(µ)
x 
x µ +3


G-29
Appendix G. Footprint
The marginal streamwise footprint [ f y ( x , z ) ] is a bell-shape function with
respect to x, with the maximum found at xmax, which follows that:
df y ( x, z )
dx
(G-101)
=0
x = xmax
All terms except for the term in the square bracket in (G-100) are greater than
zero for any real-world case in the field, and therefore setting that term equal to
zero results in the solution for xmax:
xmax =
ξ zr
µ +1
(G-102)
G.5.3 Upwind Location of Inflection Points in Footprint Curve
Differentiating both sides of (G-100) with respect to x generates:
d 2 f y ( x, z ) ξ µ z m +1 d 
 z r   ξ z r − x ( µ + 1)  
exp
=


 −ξ  
dx 2
x 
x µ +3
Γ ( µ ) dx 


(G-103)
=
 z r   z r  ξ z r − x ( µ + 1)  ( µ + 3) ξ z r ( µ + 1)( µ + 2 ) 
ξ µ z m +1
+
exp  −ξ  ξ 2 

−
Γ(µ)
x  x 
x µ +3
xµ +4
x µ +3



Because the footprint is a bell-shaped function, it has two inflection points.
One is to the left of xmax (xIL), and the other is to the right of xmax (xIR. Equation
(G-103) must equal zero at the inflection points. In this equation, the term
ahead of the curly bracket is never zero. Therefore we can simply set the terms
in the curly brackets to zero to find the inflection points:
ξ
r
z r  ξ z − x ( µ + 1) 

x µ +3
x2 
−

( µ + 3) ξ z r ( µ + 1)( µ + 2 )
xµ +4
+
x µ +3
(G-104)
=
0
Rearranging the terms in this equation yields:
ξ 2 z 2 r − 2 ( µ + 2 ) ξ z r x + ( µ + 1)( µ + 2 ) x 2 =
0
(G-105)
Solving the quadratic equation results in:
x=
(
ξ zr µ + 2 ± µ + 2
( µ + 1)( µ + 2 )
)
(G-106)
G-30
Appendix G. Footprint
Substituting xmax [see equation (G-102)] into (G-106) and then taking the point
to the left results in:

=
xIL xmax  1 −



µ+2 
1
(G-107)
and taking the point to the right gives:

=
xIR xmax  1 +



µ+2 
1
(G-108)
G.6 References
Gash J.H.K. 1986. A note on estimating the effect of a limited fetch on
microclimate evaporation measurements. Boundary-Layer Meteorology
35:409-413.
Hsieh, C.I., G. Katul, T.W. Chi. 2000. An approximation analytical model for
footprint estimation of scalar fluxes in the thermal stratified atmospheric
flows. Boundary-Layer Meteorology 35:409-413.
Horst, T.W., J.C. Weil. 1992. Footprint estimation for scalar flux
measurements in the atmospheric surface layer. Boundary-Layer
Meteorology 59:279-296.
Huang, C.H. 1979. A theory of dispersion in turbulent shear flow. Atmospheric
Environment 13:453-463.
Jarvis, P.G. G.B. James, J.J. Landsberg. 1976. Coniferous forest. In vegetation
and the atmosphere, Vol 2, Monteith J.L. ed, Academic, London, pp. 171240.
Kaimal, J.C., J.J. Finnigan. 1994 Atmospheric Boundary Layer Flows: Their
structure and Measurement. Oxford University Press, Oxford, pp. 3-31.
Kljun, N, P. Calanca, M.W. Rotach, H.P. Schmid. 2004. A simple
parameterization for flux footprint predictions. Advances in Water
Resources 23:765-772.
Kormann, R, F.X. Meixner. 2001. Analytical footprint model for non-neutral
stratification. Boundary-Layer Meteorology 99:207-224.
Nemes, G. 2010. New asymptotic expansion for the Gamma function. Archiv
der Mathematik 95:161-169
Raupach, M.R., R.A. Antonia, S. Rajagopalan. 1991. Rough-wall turbulent
boundary layers. Appl Mech Rev. 44:1-25.
Rosenberg, N.J., B.B. Blad, S.B. Verma. 1983. Microclimate: The Biological
Environment, 2nd ed. John Wiley & Son, New York, pp. 135.
Schmid, P.H. 1994. Source areas for scalar and scalar fluxes. Boundary-Layer
Meteorol 67:293-318.
G-31
Appendix G. Footprint
Schuepp, P.H., M.Y. Leclerc, J.I. MacPherson, R.L. Desjardins. 1990.
Footprint prediction of scalar from analytical solution of diffusion
equation. Boundary-Layer Meteorol 50:355-373.
Szeicz, G., G. Endrodi, S. Tajchman. 1969. Aerodynamic and surface factors in
evaporation. Water Resource Research 5:380-394.
Stanhill, G. 1969. A simple instrument for the field measurements of turbulent
diffusion flux. J Appl Meteorol 8:509.
Stull, R.B. 1988. An Introduction to Boundary Layer Meteorology. Kluwer
Academic Publishers, Netherlands, 666 pp.
Tanner, C.B. W.L. Pelton. 1960. Potential evapotranspiration estimates by the
approximate energy balance method of Penman. J Geophys Res 65:3391.
van Ulden A.P. 1978. Simple estimates for vertical diffusion from sources near
the ground. Atmospheric Environment 12:2125-2129.
G-32
Appendix H. Surface Energy Flux
Calculation of the soil surface heat flux is done only if all necessary
measurements are available, which includes soil heat flux, soil temperature,
and soil volumetric water content.
The soil surface heat flux, G, typically reported in units W∙m-2, is found by
summing the average soil heat flux measured at some depth and the change in
heat storage in the layer of soil above that depth over some interval of time:
𝐺𝐺 = 𝐺𝐺𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷ℎ + ∆𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝐺𝐺𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷ℎ in the program is found by averaging the heat flux measurements from
soil heat flux plates over the averaging interval, e.g., 30 minutes. If there are
multiple heat flux plates, an average of the temporal averages of each plate is
used.
In the data logger program, calculation of the change in storage is done as
follows:
∆𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =
where:
�𝑐𝑐𝑠𝑠 𝜌𝜌𝑠𝑠 �𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑓𝑓 − 𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑖𝑖 � + 𝑐𝑐𝑤𝑤 𝜌𝜌𝑤𝑤 �𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑓𝑓 𝑞𝑞𝑣𝑣,𝑓𝑓 − 𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑖𝑖 𝑞𝑞𝑣𝑣,𝑖𝑖 ��𝐷𝐷
∆𝑡𝑡
𝑐𝑐𝑠𝑠 = the specific heat of dry mineral soil at the site in
J∙kg-1∙K-1. This value is among the station configuration
variables (see C_dry_soil in TABLE 4-1) entered by the
user. If no value was entered, a default of 870 is used.
𝜌𝜌𝑠𝑠 = the soil bulk density at the site in kg∙m-3 and is entered
by the user (see Bulk Density in TABLE 4-1). If no value
was entered, a default of 1300 is used.
𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑓𝑓 = the soil temperature averaged over the last minute
of the current flux averaging interval.
𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑖𝑖 = the soil temperature averaged over the last minute of
the previous flux averaging interval.
𝑐𝑐𝑤𝑤 = the specific heat of liquid water in J∙kg-1∙K-1. A value of
4210 is used, which is the specific heat of liquid water at
0 °C.
𝜌𝜌𝑤𝑤 = the density of liquid water in kg∙m-3. A value of 1000 is
used.
𝑞𝑞𝑣𝑣,𝑓𝑓 = the volumetric water content averaged over the last
minute of the current flux averaging interval (e.g., 30
minutes).
𝑞𝑞𝑣𝑣,𝑖𝑖 = the volumetric water content averaged over the last
minute of the previous flux averaging interval.
𝐷𝐷 = the depth in m below the surface at which the soil heat
flux plates are buried and is entered by the user (see HFP
Depth in TABLE 4-1). If no value was entered, a default of
0.08 is used.
H-1
Appendix H. Surface Energy Flux
∆𝑡𝑡 = the length of time of the flux averaging interval (e.g.,
30 minutes.
NOTE
TCAV and CS65X sensors both make soil temperature
measurements. However, if they are both being used, the TCAV
measurements will be used preferentially for 𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑓𝑓 and 𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝑖𝑖 , as
the TCAV provides a greater spatial average.
NOTE
The program supports either CS655s or CS65Xs for
measurements of soil water content. It won’t support both types of
sensors at the same time.
NOTE
If a CS655 is used, outputs for water content are corrected for
temperature as detailed in the CS655 manual. The temperature
measurement from the TCAV sensor assumed to be closest to the
CS655 is used for this correction.
It is assumed that soil sensors are installed in a manner similar to that presented
in the figure below. In many applications, the setup shown in the figure (one
heat flux plate, one TCAV, and one CS655) is replicated for better spatial
averaging at the site. Accordingly, the program supports up to three soil heat
flux plates (HFP01 or HFP01SC), three soil temperature sensors (TCAV or
CS65X), and three water content sensors (CS616 or CS65X).
All soil sensors must be completely inserted into the soil face before the hole is
backfilled.
H-2
Appendix H. Surface Energy Flux
Finally, if a measurement of average net radiation over the flux-averaging
interval is available, energy closure may be calculated as follows:
𝐸𝐸𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 =
𝐿𝐿𝐿𝐿 + 𝐻𝐻
𝑅𝑅𝑛𝑛 − 𝐺𝐺
Where all variables are in W∙m-2 and LE is latent heat flux, H is sensible heat
flux, and Rn is net radiation.
H-3
Appendix I. EasyFlux DL CR6OP
Process Flow Diagram
Sequence of Program Functions
Every SCAN_INTERVAL (default 100 ms)
Collect raw data from gas analyzer, sonic anemometer, FW (if
applicable), and panel temp
⇩
Align data, accounting for electronic delays
⇩
Parse out diagnostic flags from gas analyzer and sonic data
⇩
Calculate various variables (e.g., e, rho_d, rho_a, Td, CO2_mixratio,
H2O_mixratio, RH)
⇩
Store raw data in multiple datasets, each dataset with a different lag
applied to gas analyzer data relative to sonic data (to be used later in
cross correlation; lags from -MAX_LAG to +MAX_LAG are used;
MAX_LAG default is 2)
⇩
If using FW, store raw data in multiple datasets, each dataset with a
different lag applied to FW data relative to sonic data (to be used later
in cross correlation; lags from -MAX_LAG to +MAX_LAG are used;
MAX_LAG default is 2)
⇩
Write a record to ts_data and diagnostic output tables
Every SLOWSEQUENCE_SCAN_INTERVAL (default 5 s)
Measure battery voltage
⇩
Measure biomet and energy balance (slow response) sensors
⇩
I-1
Appendix I. EasyFlux DL CR6OP Process Flow Diagram
If station variables have changed, save new values to memory
Every 5 Minutes
Do coordinate rotations and find the 5-minute covariances for u with w,
v with w, Ts with w, CO2 with w, and H2O with w (used later for steady
state test for quality grading; see Appendix F on Data Quality Grading).
Every AVERAGING_INTERVAL (default 30 minutes)
Filter out data with diagnostic flags or signal strengths or
measurements outside of acceptable ranges, do coordinate rotations
(use double coordinate rotation method unless planar fit angles have
been entered by user), and recalculate all covariances with rotated
wind components. (See Appendix B on Double Coordinate Rotation
and Appendix C on Planar Fit Rotation.)
⇩
Use rotated wind components to find turbulent kinetic energy, friction
velocity, and preliminary values of Monin-Obukhov length and stability
⇩
Calculate frequency correction factors for wTs, wu, and vw to account
for block averaging and line averaging. If conditions are stable,
iteratively calculate Monin-Obukhov length, cospectral equations, and
correction factors until factors change by <0.0001 or until 10 iterations
have completed. (See Appendix D on Frequency Corrections.)
⇩
Calculate value for steady state test using the 30-minute momentum
covariances and the 5-minute momentum covariances. (see Appendix
F on Data Quality Grading.)
⇩
Calculate the overall quality grade for momentum flux. (See Appendix F
on Data Quality Grading.)
⇩
Calculate and use a new roughness length if 1) user didn’t enter a fixed
value, 2) there is neutral stability, and 3) wind speed is >3 m/s. (See
Appendix G on Footprint.)
⇩
Calculate footprint characteristics using the Kljun et al (2004) model if
conditions are appropriate, else use Kormann and Meixner (2001)
model. (See Appendix G on Footprint.)
⇩
I-2
Appendix I. EasyFlux DL CR6OP Process Flow Diagram
Calculate the covariance of CO2 and rotated wind components for
each lagged dataset.
⇩
Find the effective lateral separation distance between gas analyzer and
sonic (to use in frequency correction) and the effective separation scan
lag (used to constrain which lagged datasets are physically possible).
(See Appendix D on Frequency Corrections.)
⇩
Find the dataset with the physically possible lag that maximizes the
covariance of CO2 and vertical wind. Use this dataset for the
FLUX_AMERIFLUXFORMAT and FLUX_CSFORMAT output tables. If
any results are invalid, continue with lag of zero. (See Appendix D on
Frequency Corrections.)
⇩
Assume the same lag found for CO2 will also maximize covariance of
H2O and vertical wind. Calculate covariances of appropriately lagged
H2O and rotated wind components.
⇩
Calculate cospectra functions and frequency correction factors for
covariances of CO2 and rotated wind components, taking into account
attenuation from block averaging, line averaging, and spatial
separation. (See Appendix D on Frequency Corrections.)
⇩
Calculate cospectra functions and frequency correction factors for
covariances of H2O and rotated wind components, taking into account
attenuation from block averaging, line averaging, and spatial
separation. (See Appendix D on Frequency Corrections.)
⇩
Calculate final momentum flux from rotated and frequency corrected
covariances of u with w and v with w.
⇩
Apply SND correction to the rotated and frequency corrected
covariance of w and Ts.
⇩
Calculate specific heat of ambient (moist) air and calculate final
sensible heat flux.
⇩
Calculate scaling temperature (used for data quality grading). (See
Appendix F on Data Quality Grading.)
I-3
Appendix I. EasyFlux DL CR6OP Process Flow Diagram
⇩
Apply WPL correction to rotated and frequency corrected covariance of
CO2 and vertical wind for final CO2 flux. (See Appendix E on WPL
correction.)
⇩
Apply WPL correction to rotated and frequency corrected covariance of
H2O and vertical wind. Then multiply result by calculated latent heat of
vaporization for final latent heat flux. (See Appendix E on WPL
correction.)
⇩
Calculate Bowen Ratio
⇩
Calculate the overall quality grades for fluxes of sensible heat, latent
heat, and CO2. (See Appendix F on Data Quality Grading.)
⇩
Calculate the covariance of FW temperature and rotated wind
components for each lagged dataset.
⇩
Find the effective lateral separation distance between FW and sonic (to
use in frequency correction) and the effective separation scan lag
(used to constrain which lagged datasets are physically possible). (See
Appendix D on Frequency Corrections.)
⇩
Find the dataset with the lag that maximizes the covariance of FW
temperature and vertical wind. Use this dataset for the
FLUX_AMERIFLUXFORMAT and FLUX_CSFORMAT output tables. If
any results are invalid, continue with lag of zero.
If FW05, FW1,
or FW3 is used
⇩
Calculate the time constant for the FW (to be used in frequency
corrections). (See Appendix D on Frequency Corrections.)
⇩
Calculate frequency correction factors for covariances of FW
temperature and rotated wind components, taking into account
attenuation from block averaging, line averaging, spatial separation,
and the FW time constant. (See Appendix D on Frequency
Corrections.)
⇩
Calculate final fine-wire sensible heat flux
I-4
Appendix I. EasyFlux DL CR6OP Process Flow Diagram
⇩
If energy balance
sensors are used
Calculate soil surface energy flux. (See Appendix H on Surface Flux.)
⇩
Calculate energy closure
⇩
Write records to the Flux_AmeriFluxFormat, Flux_CSFormat, and
Flux_Notes output tables
I-5
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