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. 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RMA#_____ 815 West 1800 North Logan, Utah 84321-1784 For all returns, the customer must fill out a “Statement of Product Cleanliness and Decontamination” form and comply with the requirements specified in it. The form is available from our website at www.campbellsci.com/repair. A completed form must be either emailed to repair@campbellsci.com or faxed to (435) 227-9106. Campbell Scientific is unable to process any returns until we receive this form. If the form is not received within three days of product receipt or is incomplete, the product will be returned to the customer at the customer’s expense. Campbell Scientific reserves the right to refuse service on products that were exposed to contaminants that may cause health or safety 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 Australia Location: Phone: Email: Website: France Garbutt, QLD Australia 61.7.4401.7700 info@campbellsci.com.au www.campbellsci.com.au Brazil Location: Phone: Email: Website: São Paulo, SP Brazil 11.3732.3399 vendas@campbellsci.com.br www.campbellsci.com.br Edmonton, AB Canada 780.454.2505 dataloggers@campbellsci.ca www.campbellsci.ca Bremen, Germany 49.0.421.460974.0 info@campbellsci.de www.campbellsci.de Location: Phone: Email: Website: Beijing, P. R. China 86.10.6561.0080 info@campbellsci.com.cn www.campbellsci.com.cn San Pedro, Costa Rica 506.2280.1564 info@campbellsci.cc www.campbellsci.cc Location: Phone: Email: Website: New Delhi, DL India 91.11.46500481.482 info@campbellsci.in www.campbellsci.in Stellenbosch, South Africa 27.21.8809960 sales@campbellsci.co.za www.campbellsci.co.za Spain Location: Phone: Email: Website: Location: Phone: Email: Website: Bangkok, Thailand 66.2.719.3399 info@campbellsci.asia www.campbellsci.asia UK Location: Phone: Email: Website: Shepshed, Loughborough, UK 44.0.1509.601141 sales@campbellsci.co.uk www.campbellsci.co.uk USA South Africa Costa Rica Location: Phone: Email: Website: Location: Phone: Email: Website: India China Location: Phone: Email: Website: Vincennes, France 0033.0.1.56.45.15.20 info@campbellsci.fr www.campbellsci.fr Germany Canada Location: Phone: Email: Website: Location: Phone: Email: Website: Thailand Barcelona, Spain 34.93.2323938 info@campbellsci.es www.campbellsci.es Location: Phone: Email: Website: Logan, UT USA 435.227.9120 info@campbellsci.com www.campbellsci.com

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