LeeSandersDissertation

LeeSandersDissertation
AN ATMOSPHERIC CORRECTION
ALGORITHM FOR
HYPERSPECTRAL IMAGERY
by
Lee C. Sanders
Bachelor of Science Rochester Institute of Technology (1994)
A dissertation submitted in partial fulfillment
of the requirements for the degree of Ph.D.
in the Chester F. Carlson Center for Imaging
Science in the College of Science of the
Rochester Institute of Technology
September 1999
Signature of the Author_________________________________________
Accepted by __________________________________________________
Coordinator, Ph.D. Degree Program
CHESTER F. CARLSON
CENTER FOR IMAGING SCIENCE
COLLEGE OF SCIENCE
ROCHESTER INSTITUTE OF TECHNOLOGY
ROCHESTER, NY
CERTIFICATE OF APPROVAL
Ph.D. DEGREE DISSERTATION
The Ph.D. Degree of Dissertation of Lee C. Sanders
has been examined and approved by the
dissertation committee as satisfactory for the
dissertation requirement for the
Ph.D. degree in Imaging Science
____________________________________
Dr. John Schott, Dissertation Advisor
____________________________________
Dr. Roger Easton
____________________________________
Dr. Zoran Ninkov
____________________________________
Dr. Russell Kraus
1 September 1999
ii
DISSERTATION RELEASE PERMISSION
ROCHESTER INSTITUTE OF TECHNOLOGY
COLLEGE OF SCIENCE
CHESTER F. CARLSON CENTER FOR IMAGING SCIENCE
Title of Thesis: An Atmospheric Correction Technique for
Hyperspectral Imaging
I, Lee C. Sanders, hereby grant permission to the Wallace Memorial Library of R.I.T. to reproduce
my thesis in whole or in part. Any reproduction will not be for commercial use or profit.
Signature:_________________________________________
Date: 1 September 1999
iii
AN ATMOSPHERIC CORRECTION TECHNIQUE
FOR
HYPERSPECTRAL IMAGERY
by Lee C. Sanders
Submitted to the Chester F. Carlson Center for Imaging Science
in the College of Science
in partial fulfillment of the requirements
for the Ph.D. Degree
at the Rochester Institute of Technology
ABSTRACT
Radiometrically calibrated hyperspectral imagery contains information relating to the material
properties of a surface target and the atmospheric layers between the surface target and the
sensor. All atmospheric layers contain well-mixed molecular gases, aerosol particles, and water
vapor, and information about these constituents may be extracted from hyperspectral imagery by
using specially designed algorithms. This research describes a total sensor radiance-to-ground
reflectance inversion program. An equivalent surface-pressure depth can be extracted using the
NLLSSF technique on the 760nm oxygen band. Two different methods (APDA, and NLLSSF) can
be used to derive total columnar water vapor using the radiative transfer model MODTRAN 4.0.
Atmospheric visibility can be derived via the NLLSSF technique from the 400-700nm bands or
using a new approach that uses the upwelled radiance fit from the Regression Intersection Method
from 550nm-700nm. A new numerical approximation technique is also introduced to calculate the
effect of the target surround on the sensor-received radiance. The recovered spectral reflectances
for each technique are compared to reflectance panels with well-characterized ground truth.
iv
Acknowledgements
I wish to thank all of my family, both the Sanders' and the Haywards for their unwavering
support during all these college years. I thank Dr. John Schott for believing in me enough
to take me on as one of his Ph.D. students, for his willingness to share and teach his
extensive technical expertise, and for his sense of humor. A hearty thank you to my
associate Rolando Raqueno who wrote the IDL routines for the MODTRAN 4.0 LUT
generator, with whom I have worked with these last five years on different contracts, and
who has put up with me constantly barging into his office. Thanks to Scott Brown who has
endured my constant questioning on MODTRAN and grills a really mean smoked pork.
Thank you to Tim Gallagher and Bryce Nordgren, my associates in developing the MISI; I
learned a lot from both of you. Thank you to Dr. Robert Green, Dr. Daniel Schläepfer,
and Dr. Chris Borel for sharing your algorithms and your time so I could include them in
this research project. Thank you to Lex Berk and Dr. Steven Adler-Golden for helping me
to understand MODTRAN better and having the patience to return my numerous e-mails.
Thanks to Jim Chetwynd for all the help with MODTRAN and helping me with the Mie
scattering codes. A very special thank you to CIS system administrators Sue Michel and
Bob Krzaczek for keeping my computers available and running optimally and answering all
my stupid Unix questions. Thank you Sue Chan for being such a warm, charming person
and a treasured friend (who always made sure I took care of things like register for
classes). Finally, thank you to all the students, faculty, and staff of the CIS for making it
such a fun and wonderful place.
v
Dedication
I wish to dedicate this research to my loving and patient wife, Vivian, who has sacrificed as much
as I have in order to produce this scientific work.
vi
TABLE OF CONTENTS
1.
INTRODUCTION................................................................................................................................1
2.
BACKGROUND ..................................................................................................................................3
2.1
2.2
2.3
2.3.1
2.3.2
2.4
2.4.1
2.4.2
2.4.3
2.5
2.6
3.
A HISTORY OF HYPERSPECTRAL IMAGING .........................................................................................3
INFORMATION EXTRACTION FROM HYPERSPECTRAL DATA..............................................................11
TECHNIQUES FOR IN-SCENE EXTRACTION OF ATMOSPHERIC PARAMETERS .....................................17
The Atmospheric Pre-Corrected Differential Absorption Technique (APDA).......................17
The NonLinear Least-Squares Spectral Fit Model (NLLSSF) ...............................................24
ATMOSPHERIC AEROSOLS: DESCRIPTION AND EXISTING ALGORITHMS ............................................38
Aerosol Properties .................................................................................................................38
The Fourier Transform Method .............................................................................................40
The Principal Components Method .......................................................................................44
REVIEW OF THE RADIATIVE TRANSFER PROCESS .............................................................................49
THE RADIOMETRY LUT AND THE ATMOSPHERIC CORRECTION ALGORITHM ...................................56
COMPONENTS OF THE ATMOSPHERIC CORRECTION ALGORITHM ...........................59
3.1
3.2
3.3
3.3.1
3.3.2
3.4
3.5
OVERVIEW OF THE COMPLETE ALGORITHM .....................................................................................59
TERRAIN HEIGHT .............................................................................................................................62
AEROSOLS ........................................................................................................................................62
Non-Unique Radiometric Solutions for Aerosols...................................................................63
The Regression Intersection Method for Aerosol Correction (RIMAC) ................................65
COLUMN WATER VAPOR..................................................................................................................69
THE ATMOSPHERIC POINT SPREAD FUNCTION (PSF) .......................................................................70
4. RESULTS AND DISCUSSION OF INVERSION FROM SENSOR RADIANCE TO GROUND
REFLECTANCE UNITS ............................................................................................................................80
4.1
4.2
4.3
4.3.1
4.3.2
4.4
4.4.1
4.4.2
HYDICE RUN 29 ARMS SITE IMAGE ..............................................................................................80
AVIRIS BOREAS IMAGE ..................................................................................................................88
HYDICE WESTERN RAINBOW IMAGE (LOW ALTITUDE) .................................................................92
Cr08m33 Old Panels .............................................................................................................93
Cr08m33 New Panels ............................................................................................................98
HYDICE WESTERN RAINBOW IMAGE (HIGH ALTITUDE)...............................................................103
Cr15m50 Old Panels ...........................................................................................................104
Cr15m50 New Panels ..........................................................................................................110
5.
SUMMARY ......................................................................................................................................116
6.
CONSIDERATIONS FOR FUTURE WORK...............................................................................118
7.
APPENDIX .......................................................................................................................................120
7.1
APPENDIX A: COMPUTATION OF OFF-AXIS SOLID ANGLE OF SENSOR IFOV CROSS-SECTION .......120
7.2
APPENDIX B: ADDITION TO LOOP.F OF MODTRAN 4.0 SOURCE CODE ........................................122
7.3
APPENDIX C: ANALYSIS OF THE HYDICE RUN 29 NLLSSF 2ND PASS REFLECTANCE INVERSION
USING AN ISOTROPIC ATMOSPHERIC PSF. ...................................................................................................124
7.4
APPENDIX D: THE USER'S MANUAL FOR THE ATMOSPHERIC CORRECTION ALGORITHM "TOTAL
INVERSION" ..................................................................................................................................................127
8.
REFERENCES.................................................................................................................................182
Table of Figures
vii
Figure 2.1-1. Internal schematic of the AIS _________________________________________________4
Figure 2.1-2. The AVIRIS instrument with labeled components and attributes (Vane, 1993). ___________5
Figure 2.1-3. An AVIRIS image cube that shows spatial and spectral dimensions. ___________________7
Figure 2.1-4. The HYDICE instrument _____________________________________________________9
Figure 2.1-5. The Modular Imaging Spectrometer Instrument (MISI) ____________________________10
Figure 2.2-1. Aerial spectral sampling of an AVIRIS scene showing the ground field of view, spectral pixel
samples, and sample spectrum.______________________________________________________12
Figure 2.2-2. Laboratory spectrum of kaolinite showing the absorptions at 1.4µm and the doublet at
2.2µm (arrows).__________________________________________________________________13
Figure 2.2-3. Mineral mapping of the Cuprite mining region, Nevada with the Tricorder algorithm
(courtesy of Clark, USGS)__________________________________________________________15
Figure 2.2-4. Various spectra of potato plants with increasing chlorophyll levels top to bottom (spectra
courtesy of USGS). _______________________________________________________________16
Figure 2.2-5. Column water vapor impact on atmospheric transmission spectrum from 0.86-1.017µm __16
Figure 2.3-1. Linear regression across the 940nm water vapor band (courtesy of Daniel Schlaepfer and
Chris Borel). ____________________________________________________________________20
Figure 2.3-2. RMS relative error in % water vapor for 379 reflectance spectra using four different water
vapor retrieval techniques. _________________________________________________________22
Figure 2.3-3. Examples of a calculated water vapor transmittance spectrum and measured reflectance
spectra of vegetation and snow (Gao, 1993). ___________________________________________26
Figure 2.3-4. Simplex changing shape as minimum is sought in two-dimensional space (lower right frame
has simplex contracting around calculated global minimum). ______________________________27
Figure 2.3-5. Flow chart of amoeba curve-fitting technique for columnar water vapor. ______________28
Figure 2.3-6. A MODTRAN 4 NLLSSF spectrum and AVIRIS Boreas measured spectrum for the oxygen
band at 760nm . _________________________________________________________________30
Figure 2.3-7. Surface pressure and elevation over target. _____________________________________32
Figure 2.3-8. NLLSSF for aerosols over the 16% ARM site gray panel . __________________________34
Figure 2.3-9. Water vapor spectral fit for the HYDICE Run29 16% gray panel (6.803 g/cm^2). ________36
Figure 2.3-10. Calculated surface reflectance compared to measured field spectral reflectance for the
ARM site gray panels (from nominal 2% reflectance – 64% reflectance). _____________________37
Figure 2.4-1. Typical particle size distribution curves for a rural aerosol type. _____________________40
Figure 2.4-2. Retrieved directional reflectance shape residuals for various spatial wave numbers
(Martonchik, 1992). ______________________________________________________________43
Figure 2.4-3. Retrieved directional reflectance shape residuals for various spatial wave numbers
(Martonchik, 1992). ______________________________________________________________44
Figure 2.5-1. Direct solar radiance path. __________________________________________________50
Figure 2.5-2. Atmospheric scattered upwelling radiance ______________________________________50
Figure 2.5-3. Scattered solar downwelling radiance. _________________________________________51
Figure 2.5-4. Trapping effect radiance. ___________________________________________________52
Figure 2.5-5. Environmental or adjacency radiance. _________________________________________52
Figure 2.5-6. The sensor ground-projected pixel grids containing the fractional contributions of the
ground reflectance at each atmospheric layer height. These grids are summed over the layers to
eventually generate the spatial weighting for the ground reflectance. ________________________54
Figure 2.6-1. Overview of the atmospheric correction algorithm. _______________________________57
Figure 3.1-1. The components of atmospheric correction and their flow to derive the estimated ground
reflectance (illustration courtesy of Nina Raqueño) ______________________________________61
Figure 3.3.1-1. The regression line shows the non-unique combinations of aerosol standard deviation and
number density that yield equivalent atmospheres at 410nm._______________________________64
Figure 3.3-1 Example of In-Class Distributions in Two Bands
(Barnes, 1997)___________________66
Figure 3.3-2 RIMAC Flow Chart _________________________________________________________67
Figure 3.5-1. Atmospheric path for light scattered into the sensor path from a surround ground-projected
pixel (green) and contributes to the irradiance leaving the target ground-projected pixel (red). ___71
viii
Figure 3.5-2. The geometry for the solid angle of what the source (the surround pixel) sees of the unit
cross-section of the IFOV.__________________________________________________________73
Figure 3.5-3. Fractional scattering contribution kernel in the 402nm AVIRIS band (left) and the 2100nm
band (right) for a rural aerosol. _____________________________________________________75
Figure 3.5-4. Fractional scattering contribution kernel (PSF) in the 400nm HYDICE band (left) and the
2100nm band (right) for a rural aerosol. ______________________________________________76
Figure 3.5-5. Fractional scattering contribution kernel (PSF) for a desert aerosol in all bands. ________76
Figure 3.5-6. The resolved environmental/adjacency radiance vector from HYDICE Run 29. _________77
Figure 3.5-7. The different radiance components from the HYDICE Run 29 scene (the radiance
components shown do not include interaction with the ground target). _______________________78
Figure 4.1-1. HYDICE ARM site gray panels (photo on right courtesy of MTL).____________________81
Figure 4.1-2. Plot of reflectance error for the inversion to reflectance using the truth (default) data from
the time of acquisition . ____________________________________________________________82
Figure 4.1-3. Plot of reflectance error for the inversion to reflectance using the truth (default) surface
elevation, RIMAC for the aerosol visibility, and NLLSSF for the columnar water vapor. _________82
Figure 4.1-4. Same options as 4.1-3 after second pass. _______________________________________83
Figure 4.1-5. Plot of reflectance error for inversion to reflectance using the image-wide average NLLSSF
for surface elevation, RIMAC for the aerosol visibility, and NLLSSF for the columnar water vapor. 83
Figure 4.1-6. Run29 plot of reflectance error using NLLSSF for all options._______________________84
Figure 4.1-7. Run29 plot of reflectance error after second pass with NLLSSF for all options. _________84
Figure 4.1-8. Run29 plot of reflectance error using image-wide average NLLSSF for elevation, RIMAC for
visibility, and NLLSSF for columnar water vapor. _______________________________________85
Figure 4.1-9. Estimated image-wide reflectance error for ground targets of 18% reflectance or less. ___85
Figure 4.1-10. RMS reflectance error comparison for ARM site panels. __________________________86
Table 4.1-10. Estimated atmospheric parameters from using different options in the inversion from sensor
radiance to ground reflectance algorithm. Note: The surface elevation is also coupled to the
pressure profile in the radiosonde and the water vapor amount is the total sun-target-sensor column
value.__________________________________________________________________________86
Figure 4.2-1. Boreas plot of reflectance error using the single scattering radiative transfer model from
Equation (2-36). _________________________________________________________________89
Figure 4.2-2. Boreas inversion error using truth (default) elevation, RIMAC for aerosols, and NLLSSF for
columnar water vapor. ____________________________________________________________89
Figure 4.2-3. Boreas error using image-wide average NLLSSF elevation, RIMAC for aerosols, and
NLLSSF for columnar water vapor. __________________________________________________90
Figure 4.2-4. Boreas inversion error using NLLSSF for all options. _____________________________90
Figure 4.2-5. Boreas inversion error for second pass with all NLLSSF options. ____________________91
Figure 4.2-6. AVIRIS Boreas multiple scattering RMS recovered reflectance errors._________________91
Table 4.2-1. Estimated atmospheric parameters from using different options in the inversion from sensor
radiance to ground reflectance algorithm. Note: The surface elevation is also coupled to the
pressure profile in the radiosonde and the water vapor amount is the total sun-target-sensor column
value.__________________________________________________________________________91
Figure 4.3.1-1. Recovered reflectance error for cr08m33 old panels using all default (truth) for options. 93
Figure 4.3.1-2. Recovered reflectance error for cr08m33 old panels using default (truth) for elevation,
RIMAC for visibility, and NLLSSF for water vapor.______________________________________94
Figure 4.3.1-3. Recovered reflectance error from cr08m33 old panels using image-wide average NLLSSF
elevation, RIMAC for visibility, and NLLSSF for water vapor. _____________________________94
Figure 4.3.1-4. Second pass recovered reflectance error from cr08m33 old panels using image-wide
average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor. _______________95
Figure 4.3.1-5. Recovered reflectance error from cr08m33 old panels using NLLSSF for all options. ___95
Figure 4.3.1-6. Second pass recovered reflectance error from cr08m33 old panels using NLLSSF for all
options. ________________________________________________________________________96
Figure 4.3.1-7. Estimated image-wide reflectance error for ground targets of 18% reflectance or less. __96
Figure 4.3.1-8. Yuma site run cr08m33 RMS recovered reflectance errors for old panels. ____________97
Table 4.3.1-1. Estimated atmospheric parameters from using different options in the inversion from sensor
radiance to ground reflectance algorithm. Note: The surface elevation is also coupled to the
ix
pressure profile in the radiosonde and the water vapor amount is the total sun-target-sensor column
value.__________________________________________________________________________97
Figure 4.3.2-1. Recovered reflectance error for cr08m33 new panels using default (truth) options. _____98
Figure 4.3.2-2. Recovered reflectance error for cr08m33 new panels using default (truth) for elevation,
RIMAC for visibility, and NLLSSF for water vapor.______________________________________98
Figure 4.3.2-3. Recovered reflectance error from cr08m33 new panels using image-wide average NLLSSF
elevation, RIMAC for visibility, and NLLSSF for water vapor. _____________________________99
Figure 4.3.2-4. Second pass recovered reflectance error from cr08m33 new panels using image-wide
average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor. _______________99
Figure 4.3.2-5. Recovered reflectance error from cr08m33 new panels using NLLSSF for all options. __100
Figure 4.3.2-6. Second pass recovered reflectance error from cr08m33 new panels using NLLSSF for all
options. _______________________________________________________________________100
Figure 4.3.2-7. Yuma site run cr08m33 RMS recovered reflectance errors for new panels. ___________101
Table 4.3.2-1. Estimated atmospheric parameters from using different options in the inversion from sensor
radiance to ground reflectance algorithm. Note: The surface elevation is also coupled to the
pressure profile in the radiosonde and the water vapor amount is the total sun-target-sensor column
value._________________________________________________________________________101
Figure 4.4.1-1. Recovered reflectance error for cr15m50 old panels using default (truth) options. _____104
Figure 4.4.1-2. Second pass recovered reflectance error for cr15m50 old panels using default (truth)
options. _______________________________________________________________________105
Figure 4.4.1-3. Recovered reflectance error for cr15m50 old panels using default (truth) for elevation,
RIMAC for visibility, and NLLSSF for water vapor._____________________________________105
Figure 4.4.1-4. Second pass recovered reflectance error for cr15m50 old panels using default (truth) for
elevation, RIMAC for visibility, and NLLSSF for water vapor. ____________________________106
Figure 4.4.1-5. Recovered reflectance error from cr15m50 old panels using image-wide average NLLSSF
elevation, RIMAC for visibility, and NLLSSF for water vapor. ____________________________106
Figure 4.4.1-6. Second pass recovered reflectance error from cr15m50 old panels using image-wide
average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor. ______________107
Figure 4.4.1-7. Recovered reflectance error from cr15m50 old panels using NLLSSF for all options. __107
Figure 4.4.1-8. Second pass recovered reflectance error from cr15m50 old panels using NLLSSF for all
options. _______________________________________________________________________108
Figure 4.4.1-9. Estimated image-wide reflectance error for ground targets of 18% reflectance or less. _108
Figure 4.4.1-10. Yuma site run cr15m50 RMS recovered reflectance errors for old panels. __________109
Table 4.4.1-1. Estimated atmospheric parameters from using different options in the inversion from sensor
radiance to ground reflectance algorithm. Note: The surface elevation is also coupled to the
pressure profile in the radiosonde and the water vapor amount is the total sun-target-sensor column
value._________________________________________________________________________109
Figure 4.4.2-1. Recovered reflectance error for cr15m50 new panels using default (truth) options. ____110
Figure 4.4.2-2. Second pass recovered reflectance error for cr15m50 new panels using default (truth)
options. _______________________________________________________________________110
Figure 4.4.2-3. Recovered reflectance error for cr15m50 new panels using default (truth) for elevation,
RIMAC for visibility, and NLLSSF for water vapor._____________________________________111
Figure 4.4.2-4. Second pass recovered reflectance error for cr15m50 new panels using default (truth) for
elevation, RIMAC for visibility, and NLLSSF for water vapor. ____________________________111
Figure 4.4.2-5. Recovered reflectance error from cr15m50 new panels using image-wide average NLLSSF
elevation, RIMAC for visibility, and NLLSSF for water vapor. ____________________________112
Figure 4.4.2-6. Second pass recovered reflectance error from cr15m50 new panels using image-wide
average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor. ______________112
Figure 4.4.2-7. Recovered reflectance error from cr15m50 new panels using NLLSSF for all options. __113
Figure 4.4.2-8. Second pass recovered reflectance error from cr15m50 new panels using NLLSSF for all
options. _______________________________________________________________________113
Figure 4.4.2-9. Yuma site run cr15m50 RMS recovered reflectance errors for new panels. ___________114
Table 4.4.2-1. Estimated atmospheric parameters from using different options in the inversion from sensor
radiance to ground reflectance algorithm. Note: The surface elevation is also coupled to the
x
pressure profile in the radiosonde and the water vapor amount is the total sun-target-sensor column
value._________________________________________________________________________114
Figure 7.3-1. 2nd pass recovered reflectance error for HYDICE Run 29 using NLLSSF for all options and
an isotropic averaging kernel for the PSF. ____________________________________________124
Figure 7.3-2. The 64% gray panel recovered reflectances from the 2nd pass NLLSSF with the phasefunction PSF and the flat averaging PSF. ____________________________________________125
xi
1. Introduction
For many years, the astronomical community has used spectroscopy to determine the
chemical composition of stellar objects. The atomic and molecular constituents of stars, planets, and
nebulae have been revealed by their unique spectra that in turn are due to their different properties of
absorption and emission of electromagnetic energy. The spectral signatures of these elements arise
from their electronic, vibrational, and rotational transitions. This information is also being extracted
from air and space-borne instruments to access properties about earth’s surface structure and the
composition of the atmosphere.
The analysis of stellar spectra is relatively straightforward because stars are composed
almost exclusively of elements in atomic form. Any molecules have dissociated due to the extremely
high temperatures. The spectra thus exhibit the well-defined narrow absorption lines of their
constituent elements. Based on the same spectral features, laboratory analysis can be used to
determine elemental constituents of a material. Spectra may be scanned at high resolution (i.e.,
narrow wavelength intervals) to measure the fine structure. Because these spectra are well
documented, chemical analysis is simple and repeatable.
It would be useful if the controlled approach of spectroscopy could be applied to airborne or
space-based imaging spectrometry of the earth. The calculus of atmospheric characterization and
identification of the constituents of ground objects would be simplified. Unfortunately, this
calculation is not trivial. The earth’s atmosphere is a complex mix of molecular and larger sized
compounds that are in flux spatially and temporally. To determine the scene content of an image
with confidence, the atmosphere must be characterized to sufficient accuracy to obtain ground
reflectance units to a half a reflectance unit or to estimate temperature parameters to a tenth of a
Kelvin.
To date, the best methods for extracting atmospheric information rely heavily on the
combination of ground-truth measurements of targets in the scene and ground-based atmospheric
measurements (for aerosol and water vapor determination) made with sun-photometers and
radiosondes. These measurements may be made only on days with high visibility. These truth data
allows an atmospherically corrected radiance image to be produced. The atmospheric data so
gleaned may be useful to climatologists for predicting and characterizing weather patterns, to
environmentalists for air pollution studies, and to the remote sensing scientist to remove the effects of
the atmosphere from the image in order to classify ground targets correctly.
Obtaining ground truth is an expensive, laborious, and time-consuming task. For physical
and economic reasons, few multispectral or imaging spectrometer missions measure actual
1
conditions simultaneously with image acquisition. To fill this computational void, algorithms have
been developed to extract atmospheric data directly from the spectra of individual pixels in the
hyperspectral image. All such algorithms use some form of radiative transfer model of the
atmosphere. These programs make certain assumptions about important radiometric parameters
that may result in gross errors in the attributes of the corrected image.
The purpose of this research is to further contribute to the precision of atmospheric
characterization by developing a total inversion algorithm that derives the estimated ground
reflectance of an object from the calibrated radiance at the sensor. This algorithm utilizes existing
atmospheric correction techniques, is radiometrically correct, is modular so that additional
techniques may be added, and is more rigorous in its treatment of radiometric parameters than
previous methodologies. Presently, there are different methods that are considered to be "state of the
art" for hyperspectral information extraction: the NonLinear Least Squares Spectral Fit method for
surface-pressure depth, columnar water vapor, and atmospheric visibility described by Green, (1989),
and the Atmospheric Pre-corrected Differential Absoprtion method for columnar water vapor
developed by Borel and Schläepfer, (1996). These algorithms have been tested in well-characterized
remote sensing environments and both are incorporated into the new atmospheric correction
algorithm.
In addition to the aforementioned methods, a new atmospheric visibility algorithm is added
which uses the atmospheric path radiance computed by the Regression Intersection Method. This
algorithm requires fewer computations (and thus shorter computation times) than NLLSSF and does
not require any user estimate of atmospheric visibility. Also, a new method to compute the target
surround contribution to upwelled radiance has been developed which utilizes the calculated aerosol
phase function parameters inside MODTRAN 4.
2
2. Background
2.1 A History of Hyperspectral Imaging
The advent of modern imaging spectrometry for earth remote sensing began at the Jet
Propulsion Laboratory about 1980. Prior to this time, remote sensing was limited to the analysis of
photographs of the earth based on a few algorithmic approaches to extract quantitative data. To a
large extent, the early efforts to develop sophisticated analytical techniques were hampered by the
limits to computing power and by the existing hardware technologies. The first device capable of
obtaining calibrated spectral information was the Thematic Mapper on Landsat 4 (1982) which
covered seven spectral bands in the visible, infrared, and far-infrared regions of the spectra. The
TM system delivered higher ground resolution, greater separation between spectral bands, and
better radiometric accuracy than previous space-based instruments (Kastner, 1985).
It was soon apparent to image analysts that the fuller spectral coverage and narrower
spectral bandwidths revealed much more information about the scene than previous designs. The
green (0.52-0.60µm) and red (0.63-0.69µm) bands could be used to distinguish differences in
vegetation and chlorophyll absorption better than ever before. Light in the blue-green band
penetrates water and therefore this band is used for oceanographic and hydrologic studies; data in
the SWIR (1.6µm) band could be used to differentiate snow and clouds, while spectra in the
2.2µm band can be used to differentiate different types of soil and rock. Thermal information from
band 6 spanned 10.4µm to 12.5µm; this band provided information about vegetation stress as
well as geologic and man-made structures (Kastner, 1985).
The success of the Landsat program spawned the further development of imaging
spectrometry culminating with the Shuttle Multispectral Infrared Spectrometer in 1981. SMIRR
acquired data over a 100-km wide ground track in 10 channels, three of which had narrow
bandwidths of 10nm located in the vicinity of 2.35 µm. They allowed the first spaceborne
identification of kaolinite and limestone by discriminating the unique absorption characteristics of
those minerals (Goetz, 1982).
Airborne Imaging Spectrometer (AIS)
3
The next phase in imaging spectrometry development was the AIS (Figure 2.1-1). This
instrument was designed explicitly for multispectral infrared imaging and used a 32x32 element
HgCdTe detector array with 10-bit quantization. The resolution of the spectrum was 9.3nm in the
1.2µm - 2.4 µm range (La Baw, 1987). Results obtained during terrain overflights indicated
significant geologic information potential. The spectra were sampled sufficiently finely for analysts
to identify spectra of specific minerals for unambiguous classification. At that time, atmospheric
models were not available so analysts used running averages of the acquired data (over all pixels);
the spectra were divided by this mean value which was an estimate of the atmospheric/solar
continuum. The result yielded a sampled spectrum with sufficient resolution for classification.
The early successes of AIS enabled NASA to upgrade the instrument (AIS II) with a 64x64
element HgCdTe array that extended the spectral range into the visible region of the spectra from
0.8 - 2.4 µm. AIS images definitely distinguish the different radiometric characteristics of ground
targets at altitude, but the performance was limited by its 7.3° FOV, low spatial resolution, and the
fact that it was not radiometrically calibrated.
Figure 2.1-1. Internal schematic of the AIS
4
The Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)
The success of AIS encouraged a demand for upgraded instrumentation to improve
mineral identification from spectral signatures. Further advances in infrared detector and scanner
designs led to the development of the prototype airborne VIS/NIR imaging spectrometer, which is
identified by its acronym AVIRIS (Figure 2.1-2). While AIS was built as an engineering testbed to
demonstrate that imaging spectrometers could acquire useful scientific data, AVIRIS was
proposed as a facility that would generate fully calibrated data to stimulate development of data
utilization and analysis methods (Vane, 1993). The emphasis had dramatically shifted from
proving the viability of image spectrometry to creating a scientific distribution resource with highquality calibrated data.
Figure 2.1-2. The AVIRIS instrument with labeled components and attributes (Vane, 1993).
5
AVIRIS includes a modified Kennedy-type optical scanner (Vane, 1993) fitted with custom
scanning and relay optics. The focal plane consisted of six 200µm diameter anti-reflection-coated
optical fibers connected to four spectrometers. The design gives greater area coverage and
spatial, spectral, and radiometric resolution. The Airborne Visible/Infrared Imaging Spectrometer,
in operation since 1987, utilizes detectors based on both silicon (for visible light) and indium
antimodide arranged in a line array to cover the spectral region from 0.41µm to 2.45µm in 224
channels with a resulting bandwidth of 0.010µm. NIST-traceable standards and state-of-the-art
field equipment were used for in-flight calibration. AVIRIS was designed to fly aboard NASA’s ER2 aircraft at an altitude of 20 km, thus generating an GIFOV of 20 meters and swath width of 12 km
(Porter, 1987).
An AVIRIS hyperspectral image is displayed somewhat differently than the typical 2dimensional RGB spatial image. The data output is in the form of an image cube; two axes of the
3-D data set are spatial, the third is spectral. Inherent in the spectral data is information about the
composition of the ground target and the atmosphere between the sensor and target. In fact, the
spectral sampling for AVIRIS was made fine enough to detect shifts in the chlorophyll spectrum of
the order of 0.010 to 0.040 µm at 0.7µm and resolve spectral features as narrow as those found in
minerals such as the kaolinite doublet at 2.2µm.
6
Figure 2.1-3. An AVIRIS image cube that shows spatial and spectral dimensions.
Imaging spectrometer data from AVIRIS has been applied to many other uses since its
acceptance by environmental scientists. The research communities in atmospheric science,
botany, hydrology, oceanography and remote sensing are applying this new imaging tool to gain
more information about the world.
The Hyperspectral Digital Imagery Collection Experiment (HYDICE)
The most advanced hyperspectral imaging spectrometer developed to date is the
Hyperspectral Digital Imagery Collection Experiment sensor (HYDICE) that was designed to
evaluate the utility of imaging spectroscopy in the area of civil applications (Rickard, 1993).
Specific applications include:
Environment - pollution detection
7
Geology - mineral detection and classification, surface materials, major rock types, altered
rocks
Hydrology - water quality, point and no point pollution
Archaeology - further characterization of known area, localize dig
Agriculture - type-Structure, texture, moisture of soils
Forestry - vegetation type mapping, quantification of biomass, stress detection
Oceanography - bathymetry, mapping littoral areas, water characteristics
Marine biology - characterizing surface environment
Endangered species - characterizing known environment
The sensor is a nadir-viewing pushbroom imaging spectroradiometer with a cryogenically cooled
InSb focal-plane array (Figure 2.1-4). It has a rather narrow ground swath of one kilometer at its
designed operating altitude of six kilometers; the linear dimension of a ground sample (pixel size)
is one to four meters depending on sensor altitude. The spectrum is sampled contiguously from
0.40 to 2.5 microns with spectral channels of nominal width 10nm. The most recently reported
signal-to-noise ratio was approximately 300 in the visible spectrum and close to 100 in the NIR @
5% reflectance, which is very close to AVIRIS. Major improvements in spatial resolution, signal-tonoise ratio, and radiometric accuracy make HYDICE an ideal instrument for determining the
applicability of hyperspectral imaging to the civil and military arenas. Hyperspectral imaging has
advanced to the state where development is not primarily for testbed instrumentation, but is now
for evaluating the use of the data and building operational systems (Rickard, 1993).
8
Figure 2.1-4. The HYDICE instrument
The Modular Imaging Spectrometer Instrument (MISI)
This research will use the latest in available technology to acquire the hyperspectral data
needed to study the atmosphere. The Digital Imaging and Remote Sensing Group at RIT has
constructed an imaging spectrometer called the Modular Imaging Spectrometer Instrument (MISI,
Figure 2.1-5) which is a line scanner with a 6” rotating mirror coupled to a Cassegrain telescope of
focal ratio 3.3. Two 0.5mm square silicon detectors for the measurements in the broad-band
visible spectrum and two 1.5mm fiber optics are placed at the primary focal plane to give a GIFOV
of 0.3 m and 1.0 m respectively at 0.3 km of altitude. The fibers lead to two separate 32-channel
spectrometers to cover the EM spectrum from 0.410µm to 1.020µm in 0.010µm spectral bands. A
pyramid mirror diverts some photons from the primary focal plane to five HgCdTe detectors for the
long-wave infrared region; secondary focal planes will be available in the SWIR and MWIR for
future use (Feng, 1995). An on-board calibration system consisting of two blackbodies for the
LWIR and a tungsten source for the visible completes this imaging system for gathering absolute
radiometrically calibrated data for remote sensing applications.
9
Figure 2.1-5. The Modular Imaging Spectrometer Instrument (MISI)
10
2.2 Information Extraction from Hyperspectral Data
Before delving too deeply into the technical aspects of imaging spectrometry, the definition
of hyperspectral imaging must be clear. Devices that collect multichannel, contiguous, narrowband imagery from the visible to the infrared portion of the electromagnetic spectrum are generally
referred to as "hyperspectral" sensors. In "ultraspectral" imaging, the bands cover a similar range
but are extremely narrow (on the order of 1-2nm in the visible and near infrared). In "multispectral"
imagery, the bandwidths typically are tens of nanometers wide and not necessarily contiguous. An
example of a hyperspectral sensor system is AVIRIS with 224 spectral bands, each with a 10nm
bandwidth, and covering the spectral range is 0.4µm to 2.4µm (Figure 2.2-1).
The power of the hyperspectral sensor rests in its ability to record an electromagnetic
profile with fine spectral resolution at each pixel within its field of view. Wavelength-dependent
characteristics in the reflectance or absorption spectra reveal important information about the
chemical make-up and types of atomic and molecular bonding in the material being targeted
(Goetz, 1985). Spectral features are the direct result of electronic and/or vibratory orbital energy
transitions at the atomic and/or molecular level due to photon absorption. Thus, the combination,
placement, and relative strength of the absorption feature(s) can be exploited for surface material
identification, evaluation, and analysis of internal processes.
11
Figure 2.2-1. Aerial spectral sampling of an AVIRIS scene showing the ground field of view,
spectral pixel samples, and sample spectrum.
Absorption is not the only determinant of the shape of the reflectance spectrum of a
material. Photon scattering, particle size, and porosity effects can cause linear and nonlinear
mixes of reflectance information. The path of a photon may resemble a random walk; a certain
percentage of photons are absorbed and the remainder are scattered in random directions by
each particle center. Larger particle grains have longer optical paths resulting in a higher
probability of absorption (Clark, 1984). With smaller grains, there are proportionally more surface
reflections per unit area compared to large grain sizes. Thus, as the grain size decreases, the
reflectance increases.
Spectral contrast is maximized (i.e. the absorption feature is more apparent) when the
particle diameter and the optical depth are approximately equal. Contrast depends strongly on the
12
difference between the absorption maximum and the absorption of the adjacent continuum
(Pieters, 1993). The continuum is defined as the “background absorption” onto which the other
absorption features are superimposed. For example, in Figure 2.2-2, the 2.2µm absorption
doublet is clearly seen against the continuum in the spectrum of the mineral "kaolinite". Because
of the complex, nonlinear scattering process, weak features not normally seen in transmittance are
sometimes enhanced in absorption and consequently spectral reflectance spectroscopy becomes
valuable as a diagnostic tool for target chemical make-up.
Figure 2.2-2. Laboratory spectrum of kaolinite showing the absorptions at 1.4µm and the
doublet at 2.2µm (arrows).
13
The complete utilization of hyperspectral reflectance spectroscopy is still developing.
Geologists are now able to map minerals in regions (e.g., the Cuprite Mining district in Nevada) by
employing imaging spectrometers such as AVIRIS (Figure 2.2-3).
14
Figure 2.2-3. Mineral mapping of the Cuprite mining region, Nevada with the Tricorder
algorithm (courtesy of Clark, USGS)
Algorithms such as "Tricorder" (Clark, 1991) compare the continuum-removed spectral features
from imaging spectrometer data to continuum-removed spectra from a reference library of
materials. Multiple absorption features are examined and the pixel is classified to the material in
the library data set with the most similar spectral absorption features.
Mineral mapping is only one of many uses of imaging spectrometer data. Plant species
and their condition also may be assessed using this technique (Figure 2.2-4). Potatoes sprayed
with defoliant show decreased overall absorption and a shift of the red edge of the chlorophyll
absorption to shorter wavelengths (Clark, 1995). Species differences can be discriminated by the
Tricorder algorithm based on shapes of the absorption spectra. For accurate classification, it is
important to have as complete a spectral reference library as possible.
15
Figure 2.2-4. Various spectra of potato plants with increasing chlorophyll levels top to
bottom (spectra courtesy of USGS).
It is clear that the reflectance spectrum derived from hyperspectral imaging can yield a
great deal of information about surface content in an image scene. Since absorption feature
signatures are indicators of chemical composition, many types of surface terrain may be classified
by matching these features to specific mineral, plant, or man-made object library spectra. What
has not been addressed is the impact of the atmosphere on the spectrum obtained from
hyperspectral imagery. The earth atmosphere leaves the imprint of its chemical composition on
the spectrum. The combination of atmospheric gases, water vapor, and suspended particulates
(known as "aerosols") interact with light throughout the entire spectrum. An example of the
influence of water vapor on atmospheric transmission is seen in Figure 2.2-5.
0 g/cm
2
1.0 g/cm
2
Figure 2.2-5. Column water vapor impact on atmospheric transmission spectrum from 0.861.017µm
Atmosphere constituents can have a significant effect on the spectrum of surface-leaving
radiance of an object. This effect is, of course, propagated to the derived reflectance spectrum of
the surface, making applications such as mineral mapping or plant-stress evaluation prone to
error. Many spectral surface features that modern advanced algorithms seek to identify are
altered by atmospheric interference.
Thus, it is imperative that the atmosphere be characterized and its effects removed from
the hyperspectral radiance spectrum. The methods for characterizing and correcting the effects of
16
the atmosphere on the sensor-acquired radiance spectrum are considered next in this discussion
in the review of NLLSSF and APDA.
2.3 Techniques for In-Scene Extraction of Atmospheric Parameters
2.3.1 The Atmospheric Pre-Corrected Differential Absorption
Technique (APDA)
The APDA method is a new technique that is a further refinement of the Continuum
Interpolated Band Ratio method (CIBR) (Bruegge, 1990; Green, 1989) and the ATREM method
(Gao et al., 1993). The governing radiometric equation for this algorithm is:
L ( λ)
= ρ( λ )
1
π
E 0 ( λ ) cos(
σ ) τ1 ( λ ) τ 2 ( λ ) + L atm ( λ )
(2-1)
where L(λ) is the radiance from one specific channel, ρ(λ) is the reflectance of the ground
(including adjacency effects), E0(λ) is the exoatmospheric irradiance, σ is the angle subtended
from sun-to-earth normal, τ1(λ) is the transmittance of the earth’s atmosphere from the sun to the
ground, τ2(λ) is the transmittance of the earth’s atmosphere from the ground to the sensor, and
Latm(λ) is the total atmospheric upwelled radiance. The radiative transfer code MODTRAN 4.0
also takes into account curved earth effects. It is assumed that index of refraction changes in the
atmospheric layers has a negligible effect at the sensor angular resolution.
The transmittance terms can be split further into parameters depending on water vapor
and on aerosols and atmospheric gas absorption:
τ 1 ( λ ) = τ 1 _ comp
τ1wv
τ 1 _ comp = τ1 _ aerosols
(2-2)
τ1 _ gases
(2-3)
17
Substituting into Equation (2-1) yields:
L ( λ)
where
1
 τ
E o cos σ τ1 _ comp τ 2 _ comp
= ρ
1 wv τ 2 wv + L atm ( λ )
 π

= L grnd ( λ ) τ1 wv τ 2 wv + L atm ( λ )
L grnd ( λ )
(2-4)
and is the total ground reflected radiance at the sensor in the absence of
atmospheric water vapor.
The radiances in the three channels can be written using this simplified equation where
the parameter "m" is the index of the measurement channel in the peak water-vapor-absorption
region centered on 0.94µm and r1 and r2 are the reference channels located in the atmospheric
“windows” for water vapor on each side of the absorption peak (i.e., τiwv,r1 = 1.0 & τiwv,r2 = 1.0).
Assuming a small difference in the center wavelengths of the given channels, the radiance in the
measurement channel can be approximated by a linear interpolation :
Lm
= [ ω r1 L grnd
+ L atm
, r1
+ ω r 2 L grnd , r 2 ] τ1 wv ,m ( PW ) τ 2 wv , m (PW )
, m (PW )
(2-5)
where:
ω r1 =
ω r2 =
λ r2 − λ m
(2-6)
λ m − λ r1
(2-7)
λ r 2 − λ r1
λ r2 − λ r1
By arranging Equation (2-5) to solve for the total transmission of water vapor and
substituting Lgrnd from Equation (2-4), the equation becomes very similar to the CIBR method but
with the additional upwelled radiance correction terms.
τ wv
,m
=
− L atm , m (PW )
− L atm ,r1 ) + ω r2 ( L r2 − L atm
Lm
ω r1 ( L r1
18
, r2
)
(2-8)
The path radiance corrections Latm,i contain functional parameters of terrain elevation,
channel center wavelength, and quantity of water vapor. Latm,i can be estimated by calculating the
total radiance at the sensor due to a zero albedo ground target with varying terrain height and
water vapor content (assuming a fixed aerosol optical depth). The accuracy is increased by an
iterative technique using water vapor contents retrieved from radiosonde profiles.
Equation (2-8) can be extended to multiple channels by calculating a regression line
through an arbitrary number of channels and evaluating the derived regression curve at the mean
center wavelength of the measurement channel(s). The numerator is the average of the
differences of the sensor radiance and the path radiance in the measurement channels. This is
the APDA equation for which the three-channel case is given in Equation (2-9):
R APDA
=
− L atm , m ] i
([ λ r ] j ,[L r − L atm , r ] j )|[ λ
[L m
LIR
(2-9)
m ]i
where LIR([x], [y])|a refers to the regression line y=ax+b for the points
y=Lr - Latm,r evaluated at x = λr in Equation (2-9). Essentially, this is a regression line across the
atmospheric “windows” surrounding the water-vapor absorption feature (L1 and L2) in the spectrum
(Figure 2.3-1). The denominator becomes the interpolated point L4 with the estimated upwelling
radiance subtracted. The numerator of Equation (2-9) is located at the wavelength of the trough of
the absorption feature (L3) in Figure 2.3-1. The subscripts i and j in Equation (2-9) refer to the
measurement and reference channels respectively.
Again, it must be made clear that the atmospheric windows at positions L1 and L2 in Figure
2.3-1 can be affected by water vapor in the atmosphere. For the purpose of this model, this effect
is considered to be negligent since the water vapor lines inherent in the band model are not close
to being saturated.
19
Figure 2.3-1. Linear regression across the 940nm water vapor band (courtesy of Daniel
Schlaepfer and Chris Borel).
An exponential approach similar to Beer’s Law is used to relate the R ratio to the
corresponding precipitable water vapor amount (PW):
τ wv
(PW )
≈ R APDA = e −( γ + α(PW )
β
)
(2-10)
where α, Β, and γ are the parameters of columnar water vapor content. This equation is
approximately true when the water vapor lines are not saturated. It is assumed that there is not
fog or near fog conditions which is reasonable since a very low percentage of remotely sensed
imagery is acquired or can be very useful under these circumstances. Solving Equation (2-10) for
the water vapor content:
20
PW ( R APDA )
− ln( R APDA
=(
α
1
)−γ β
)
(2-11)
The following APDA algorithm is used to compute the columnar water vapor content of a
given hyperspectral image (Schläepfer, 1996):
1. A radiative transfer program such as MODTRAN 4 is used to compute a LUT
containing both the total radiance at the sensor for an average reflectance background
(such as ρ=0.4) and the atmospheric upwelling radiance as a function of water content,
terrain elevation, wavelength, and atmospheric conditions. (The atmospheric conditions
are defined in the MODTRAN input file “tape5”.) The MODTRAN-derived radiances are
then convolved with the normalized sensor response function(s) to give sample radiance
values. Water content can be varied by scaling water vapor density in a standard
radiosonde file. Terrain height can be determined by using known topography information
or by using an empirical method developed by Schläepfer and Borel.
2. Determine the RAPDA values for the water vapor amounts specific to each MODTRAN
run by applying Equation (2-9).
3. Regress the random variables PW against RAPDA using the function in Equation (2-10)
and store the regression parameters α, β, and γ.
4. Assume some starting PW1 for the hyperspectral image pixels based on the
radiosonde profile and subtract the upwelling radiance term from the image.
5. Calculate the APDA ratio for the pixel and transform back into a PW2 via Equation (211) with the stored regression parameters.
6. With this improved estimate PW2, calculate the new Latm for substitution in Equation (29)
7. Calculate the R ratio for the image (pixel) again and inverse transform the ratio values
into a final PW3.
Previous experiments have shown that two iterations are sufficient to obtain good results.
Increasing the number of iterations can actually result in divergence since the errors may be
amplified.
21
Comparisons have been made between the ATREM-like CIBR method and the APDA
technique for retrieving columnar water vapor over dark, bright, and spectrally variable
backgrounds. The atmospheres for the comparisons were generated by MODTRAN. Many
reflectance spectra of minerals, man-made objects, and simulated vegetation were used with a
resulting water vapor error within +5% for most of the spectra (Schläepfer, 1996) as can be seen in
Figure 2.3-2. The authors consider this accuracy sufficient since current sensor calibration and
modeling errors are of the same order. No error analysis has been performed on APDA’s
dependence on atmospheric conditions (aerosol loadings, stratification, etc.), calibration errors,
and radiative transfer code uncertainties.
Figure 2.3-2. RMS relative error in % water vapor for 379 reflectance spectra using four
different water vapor retrieval techniques.
The next water vapor extraction technique reviewed in this section departs from the bandratio methodology and attempts to fit the spectrum in the water vapor absorption region to a curve
with variable parameters. The NonLinear Least Squares Spectral Fit (NLLSSF) technique allows
22
for more degrees of freedom to account for radiometric parameters and is consequently more
computationally intensive than APDA.
23
2.3.2 The NonLinear Least-Squares Spectral Fit Model (NLLSSF)
The NLLSSF technique developed by Green (1989) resembles the ATREM method (Gao,
et al., 1993) in that it is a complete atmospheric correction that inverts the governing radiative
transfer equation to solve for surface reflectance. Since the water vapor in this method is
calculated just before the inversion, all constituent modules of the algorithm up to and including the
column water vapor determination are covered in this section.
Upon inspection of the governing radiative transfer equation for a remotely sensed scene,
it is evident that a number of terms must be known to solve for apparent surface reflectance.
Elements such as atmospheric molecular absorptions and elemental scattering properties of the
surface, atmospheric aerosols, and the solar source must be characterized and included in the
generation of a model of a calibrated radiance spectra for a given scene (Green, 1996). If many of
the radiometric parameters can be known or closely estimated, a robust radiative transfer model
can be run with fewer flexible parameters. One by one, the flex parameters can be determined to
obtain a close estimation of what was detected at the sensor. The nonlinear least-squares
spectral fit is one such process that obtains an estimate of apparent ground reflectance by using a
governing radiative transfer equation and a radiative transfer model such as MODTRAN 4.
Because of the complex interaction of variables in a remotely sensed scene, the algorithm begins
with the user inserting parameters in the model that can be known and then estimates the terms
that are more difficult to obtain.
The algorithm to generate the model should include all known parameters of the remotely
sensed scene, such as the geometry of observation, time of day, latitude and longitude,
radiosonde data (if available), terrain height (if available), sensor altitude, and exoatmospheric
irradiance. The assignment of these parameters sets a constraint on the radiative transfer
algorithm with the goal of minimizing the degrees of freedom. From here, intelligent assumptions
must be made about the atmospheric composition, especially if radiosonde data are not available
for a baseline. Assumed parameters can include aerosol type, visibility, air pressure, temperature,
etc. Column water vapor is the flexible parameter in the atmospheric model.
With a baseline atmosphere, the only parameter(s) remaining in the radiative transfer
program are the reflectance characteristics of the ground object(s). If the spectral region of
24
interest is sufficiently narrow (as is true for the water vapor band), it may be possible to assume
that the object reflectance ρ is linear with wavelength λ. Thus, a model of reflectance can be built:
ρ = α + βλ
(2-12)
In some cases, there may be instances where nonlinear behavior occurs which is caused by some
quantified physical phenomenon, such as the absorption of liquid water in vegetation in the 0.861.0177µm water vapor band (Figure 2.3-3) or the chlorophyll feature at 0.7µm. This nonlinear
modeling can be easily added by introducing a scaled reflectance parameter to Equation (2-13)
where γ is the flexible scalar and ρvegetation(λ) is the reflectance curve of liquid water in vegetation
(or the reflectance curve of the chlorophyll band):
ρ = α + βλ + γρ vegetation ( λ )
(2-13)
25
Figure 2.3-3. Examples of a calculated water vapor transmittance spectrum and measured
reflectance spectra of vegetation and snow (Gao, 1993).
At this point, a model of the scene has been built with four flexible parameters: reflectance
bias (α), reflectance gain (β), proportion of nonlinearity due to surface leaf water (γ), and
atmospheric water vapor.
One method for solving for these parameters is a multivariate solution to a nonlinear leastsquares spectral fit (NLLSSF) between the spectral radiance measured by the hyperspectral
sensor and the spectral radiance calculated by a radiative transfer code, in this case MODTRAN 4.
Most multivariate solutions require estimates of the functions or their slopes to solve for the
parameters. Given the complexity of the radiative transfer models, use of these types of curvefitting routines is out of the question. The “best” curve-fitting routine in terms of efficiency and
speed for this model is a downhill simplex algorithm (Press, 1992), sometimes called the "amoeba"
curve-fitting technique, that is designed to find global minima or maxima of a function. The routine
name "amoeba" is descriptive of the way the simplex contorts in n-dimensional space as the
minimum of the function (with n number of varying parameters) is being sought (Figure 2.3-4).
For this model, the minimum difference between the MODTRAN 4-derived radiance and
the image radiance in their respective channels can be sought. A general flow of the amoeba
curve-fitting technique is shown in Figure 2.3-5.
26
Figure 2.3-4. Simplex changing shape as minimum is sought in two-dimensional space
(lower right frame has simplex contracting around calculated global minimum).
27
Figure 2.3-5. Flow chart of amoeba curve-fitting technique for columnar water vapor.
28
For assurance that an actual global minimum has been found by the amoeba rather than a
local minimum, it has been suggested by the algorithm creators that the algorithm be run a second
time. The initial parameters are the first pass final solutions. If the minimum is really global, the
amoeba will converge back down to the first pass solutions after a few iterations. This test is
addressed for the NLLSSF algorithm in the second pass through the atmospheric correction
algorithm (refer to Section 3.1).
Noise due to the sensor system and random photon arrivals is inherent in any real image.
The signal-to-noise ratio (SNR) can be increased by averaging sample values; the SNR increases
with the square root of the number of samples averaged if the noise is uncorrelated. For example,
the spectrum can be averaged over a 5x5-pixel area to reduce the noise in image radiance by a
factor of five. This averaging improves the estimate of the derived column water vapor amount in
the area of interest.
In the following modules, reference is made to a MODTRAN-generated LookUp Table
(LUT). To aid in the understanding of how NLLSSF works, brief procedures are outlined. Because
of the complexity of the LUT generation, a separate sub-section (Section 2.6) was created that
expounds on this topic in much greater detail. Suffice for the reader at this point that the LUT is a
multidimensional data structure that contains all the radiometric terms for the radiative transfer
equation as functions of surface elevation, visibility, water vapor, and wavelength. A caution
should also be given to the user of this technique. Since the dimensionality of this multivariate
data is fairly high, the NLLSSF technique needs initial values for the surface elevation, visibility,
and columnar water vapor that are close to the truth in order for the algorithm to converge to a
realistic set of radiometric values.
Module 1: Surface Pressure Height
The total radiance reaching a hyperspectral sensor is a function of the
absorption by well-mixed gases in the atmosphere in both source-to-target and target-to-sensor
paths. One of the strongest atmospheric gas absorption features is due to oxygen and spans the
spectral range from about 745nm to 785nm, with its peaks located at approximately 760nm (Figure
2.3-6). The oxygen band strength is calibrated to surface pressure elevation using the oxygen
band model in the MODTRAN 4 radiative transfer code. In practice, an LUT generated from
29
MODTRAN 4 contains the sun-ground-sensor direct radiance (Lgrnd), the upwelled path radiance
(Lu), the scattered downwelled radiance (LD), and the spherical albedo (S) of the atmosphere
above the surface, all as functions of a fixed sensor elevation and terrain height z. The
convolution of spectral radiance from MODTRAN 4 with the sensor response function for the final
LUT values is calculated. It should be noted that all of these terms are functions of wavelength.
0.003
0.0025
0.002
0.0015
0.001
MODTRAN Fit Radiance
AVIRIS Radiance
0.0005
0
0.74
0.745
0.75
0.755
0.76
0.765
0.77
0.775
0.78
0.785
Wavelength (µm)
Figure 2.3-6. A MODTRAN 4 NLLSSF spectrum and AVIRIS Boreas measured spectrum for
the oxygen band at 760nm .
The reflectance of the surface is modeled as a linear function of wavelength (Green,
1991b) as given in Equation (2-12) with a bias term (α) and a gain term. The aforementioned
parameters and z are allowed to vary to iteratively fit the governing radiative transfer equation
derived from Green, (1996) to the calibrated radiance at the sensor via NLLSSF:
L calc
_ sensor
( λ)
= L u ( λ) +
[L
ρ( λ )
grnd
1 − ρ( λ ) S( λ )
30
]
( λ) + L D ( λ )
(2-14)
where (1-ρ(λ)S(λ)) is a gain term for the trapping effect and the radiance vector from sun-toground-to-sensor is:
L grnd ( λ )
=
E 0 ( λ)
τ 1( λ) τ 2 ( λ)
π
cos
σ
(2-15)
where E0(λ) is the solar irradiance, τ1(λ) is the transmission from sun to the target, τ2(λ) is the
total transmission from the ground to the sensor, and σ is the solar zenith angle. (Equation 2-15
assumes that the ground target has Lambertian reflectance characteristics.)
The question may arise of the effect of the distance z from sensor to target on the surface
pressure depth pz. The depth of the 760nm oxygen band is proportional to the amount of oxygen
in the atmosphere between the sensor and target. Greater pressure means more column oxygen
and indicates a longer range from sensor to target. This being said, it should be noted that the
same baseline atmosphere is used at the beginning of this module, which is included in the
MODTRAN 4 carddecks for all z values. Essentially, the surface pressure parameter in the
carddeck is being scaled by z which produces a depth of the oxygen band absorption proportional
to p*z. For example, in Figure 2.3-7 the sensor is located at some fixed altitude with a true sensortarget range and surface pressure.
31
Figure 2.3-7. Surface pressure and elevation over target.
If the surface pressure given in the baseline carddeck is less than the actual atmospheric
pressure, the parameter pz will ultimately produce an oxygen absorption band depth that is less
than the oxygen absorption band depth from the image. Thus, increasing z will minimize the error
between real and predicted oxygen absorption as well as minimize the error between real and
predicted pz. It is not important that z be correct, but the parameter pz must be as close as
possible to the real value. Using the data from Figure 2.3-7:
SPE = 5 Km * 500Mb = 2500 Km Mb
(2-16)
where SPE is the surface pressure elevation. From the baseline atmosphere, surface pressure at
this elevation was 400Mb, thus the best predicted fit for the oxygen absorption band would
assume:
z
=
2500 KmMb
400 Mb
= 6.26 Km
(2-17)
The surface-pressure elevation would then be fixed and used as an atmosphere
parameter in the next module that estimates the aerosol-dependent visibility.
Module 2: Aerosol (Atmospheric Visibility)
The radiance scattered by atmospheric aerosols can be a significant contributor to the
total radiance reaching the sensor. The Mie scattering coefficient resulting from atmospheric
aerosols is proportional to
1
λ
. In this case, Mie scattering is significant in the range from 400 to
700nm owing to the extremely small size of the particles. This type of scattering is even more
pronounced at shorter wavelengths of the spectrum.
The NLLSSF algorithm is employed to fit the sampled calibrated radiance spectrum in the
range of strongest aerosol impact (see Figure 2.3-8). In this case, the flexible parameters in the
amoeba-fitting routine are: atmospheric visibility (a scalar for the aerosol number density),
32
reflectance bias, reflectance gain, and proportion of nonlinearity due the chlorophyll in vegetation.
Recall that the surface elevation has already been fixed from the previous routine.
The aspects of aerosol type (e.g., urban, rural, maritime, etc.) and scattering (e.g., single
or multi-scattering) are constrained by user-defined/estimated input to the MODTRAN 4 carddeck
before running the NLLSSF algorithm. For many of the acquisitions of high-visibility data made by
AVIRIS, the effect of aerosol scattering is strongest below λ=1µm. This allows the user to
constrain the range of the spectral curve from 0.4µm to 0.7µm or approximately 30 channels of
0.01µm bandwidth.
To calculate aerosol optical depth, the amoeba algorithm is employed which uses a
downhill simplex method to minimize a multidimensional function. In this case, the function to be
minimized is the absolute difference of the sensor-measured radiance and the radiance at the
sensor given by the governing radiative transfer equation (Equation 2-14) with parameter values
taken from MODTRAN 4.0 runs. Although there are a number of accepted multidimensional
minimization methods available for use in these calculations, the downhill simplex method is the
most practical selection. It requires only evaluations of functions (not derivatives) and is accepted
as the best method to use if the figure of merit is to “get something working quickly” for a problem
whose computational burden is small (Press, 1992). Another attractive aspect of the method is
that the fit parameters can easily be constrained without added computational burden. The routine
also can avoid local minima by restarting the algorithm at the place where it last ended to have
confidence about generating parameters from the global minimum.
To effectively incorporate this algorithm as the NLLSSF for the spectral curve, an LUT is
constructed from multiple runs of MODTRAN 4 where only the visibility is varied in predetermined
increments. Thus, when the amoeba routine calls the function evaluator subroutine (which uses
Equation 2-14 and subtracts it from the image pixel radiance value), any visibility parameter
between incremented values in the LUT can quickly be interpolated from the estimated visibility
being tested by the amoeba fit.
As stated previously, the primary variable is the atmospheric visibility, with three other
secondary parameters of α, β, and γ from the reflectance term ( Equation 2-13). An example of
the spectral curve generated from this routine is shown in Figure 2.3-8. To improve the SNR of the
data and the subsequent curve-fit, the data were averaged over a region of size 11-by-11 pixels.
33
The resulting 47.73km visibility is consistent with the typical values for aerosols in the ARM site
rural location.
HYDICE Run 29 NLLSSF Fit to Aerosols
0.02
0.018
0.016
0.014
0.012
0.01
0.008
MODTRAN Radiance
0.006
AVIRIS Radiance
0.004
0.002
0
0.4
0.45
0.5
0.55
0.6
0.65
Wavelength (µm)
Figure 2.3-8. NLLSSF for aerosols over the 16% ARM site gray panel .
34
0.7
Module 3: Total Column Water Vapor
Water vapor is by far the most significant absorbing constituent in the atmosphere over the
visible/NIR/SWIR spectral range. In addition, water vapor content in the atmosphere varies widely
in amount and distribution over space and time, even across topographically featureless regions
(Green, 1991b). Given the strength of this absorption feature, it is clear that total columnar water
vapor must be determined to accurately retrieve reflectance data for ground targets.
The final step in this algorithm computes the total columnar water vapor for an image pixel
by fitting the MODTRAN 4 derived spectral radiance at the sensor to the spectral radiance curve of
the 940nm water vapor absorption band. The parameters to be varied include the water vapor
amount and three terms in the reflectance equation (Equation 2-13). By this time, the surface
elevation (pressure-depth) and the atmospheric visibility have both been fixed from modules one
and two. Thus, the radiometry in the LUT is narrowed down so that the values can vary as a
function of different columnar water vapor amounts. The water vapor temperature is assumed to
be in equilibrium with the atmospheric layer(s).
To accelerate the computation, a LookUp Table (LUT) is generated from an estimated (or
actual) radiosonde profile with water-vapor density (as a function of altitude) in place of relative
humidity. Additional radiosonde files are created simply by scaling the water vapor densities to
create profiles with varying total columnar water vapor (PW). Carddecks for the MODTRAN 4
radiative transfer algorithm are created with each of the new radiosonde profiles and MODTRAN 4
then generates Lgrnd, Lu, LD, τ2, and S for each PW. The NLLSSF algorithm uses these data as a
LUT to fit the spectral radiance modeled by the radiation transfer code and the sensor-measured
spectral radiance between 850nm and 1050nm (Figure 2.3-9). Both visibility (aerosol loading) and
surface pressure elevation are constrained by the previous steps in the algorithm.
35
HYDICE Run 29 Fit to Water Vapor Feature
0.012
0.01
0.008
0.006
0.004
MODTRAN Fit Radiance
HYDICE Radiance
0.002
0
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
Wavelength (µm)
Figure 2.3-9. Water vapor spectral fit for the HYDICE Run29 16% gray panel (6.803 g/cm^2).
Using these parameters and the total column water vapor from this subroutine, the
governing radiative transfer equation (2-14) can be inverted to solve for apparent surface
reflectance. Figure 2.3-10 shows the derived reflectance (Tot_Inv) compared to surface ground
truth (Truth) for the ARM site gray panels. As can be seen, both measured spectral reflectance
curves agree well with NLLSSF-derived spectral reflectance.
36
Recovered Reflectance Comparison for Total Inversion Using ALL
NLLSSF Options on HYDICE Run 29
1
0.9
0.8
Truth 2%
Tot_Inv 2%
0.7
Truth 4%
Tot Inv 4%
0.6
Truth 8%
Tot Inv 8%
0.5
Truth 16%
Tot Inv 16%
0.4
Truth 32%
Tot Inv 32%
0.3
Truth 64%
Tot Inv 64%
0.2
0.1
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Wavelength (µm)
Figure 2.3-10. Calculated surface reflectance compared to measured field spectral
reflectance for the ARM site gray panels (from nominal 2% reflectance – 64% reflectance).
This concludes the discussion of atmospheric parameter extraction techniques for
hyperspectral imagery. APDA relies on a depth ratio of an absorption band to determine water
vapor while NLLSSF uses a curve-fitting routine to estimate parameters in the radiative transfer
equation.
37
2.4 Atmospheric Aerosols: Description and Existing Algorithms
2.4.1 Aerosol Properties
Aerosols are defined as solid or liquid airborne particles that are composed of various
materials and found in stratified layers of the earth’s atmosphere. Their sizes range from about
0.1µm to 10µm, though the sizes of condensation nuclei are typically about 0.01µm (Diner, 1994).
Natural sources such as dust storms, desert and soil erosion, biogenic emissions, forest and
grassland fires, and sea spray account for as much as 90% of the tropospheric aerosol loading,
with man-made sources making up the balance.
The chemical composition of aerosols is varied; the main contributing substance is sulfur
in the form of sulfates produced by the oxidation of gaseous sulfur dioxide generated as a byproduct of industrial activity (Horvath, 1996). About 80% of the mass is contained in particles of
size less than 1µm in diameter. The next most important substance is silicon, which has a bimodal
size distribution peaking at 0.7 and 3µm, and is mostly derived from soil. However, it has been
shown that submicrometer-sized silicon particle sources are typically due to coal-fired power plants
and the combustion of household waste. Calcium is another soil-derived aerosol and typically has
particle diameters greater than 3µm. Iron is commonly found in urban atmospheres and originates
either in industrial or power plant emissions. Iron particles have a not-too-well defined distribution
peak at d=0.7µm. Coarse particle sizes have been found ( d ≅ 3µm) and are attributed to road
dust in towns. Lead had been considered a tracer for automotive emissions in the past until the
barring of lead additives in gasoline. Most of these aerosol particles with d < 1µm are emitted by
incinerators and coal-fired power plants. Black carbon is the only light-absorbing aerosol in the
atmosphere and is derived mainly from diesel emissions. The size distribution peaks at d=0.25µm
and d=0.5µm; the former peak coincides with the size of diesel particles in exhaust gases. Due to
traffic factors, no other aerosol element exhibits such a large difference in atmospheric density
between inner city and suburban regions.
The effect of atmospheric aerosols on the earth biosphere is presently under intense study
by the scientific community. One of the most ambitious studies is incorporated in the MISR (MultiAngle Imaging Spectroradiometer) project at the Jet Propulsion Laboratory in Pasadena,
California. The scientific objectives of the MISR aerosol retrievals are:
38
1) To study the spatial and temporal variability of aerosols in the earth’s atmosphere and
determine their effect on climate,
2) To improve the knowledge of the sources, sinks, and global budget
of aerosols,
3) To characterize aerosols in the atmosphere and incorporate them
in radiative transfer and scattering algorithms to make better
quantitative estimates of
absolute surface reflectances.
The third goal of the MISR project also is the goal of this research effort. For many years,
the remote sensing community has strived to make quantitative assessments of surface-leaving
radiance and reflectance from high altitude or spaceborne platforms. Attenuation of the sun by
absorption and scattering due to atmospheric aerosols can alter the solar radiance by:
1) Reflection off the atmosphere,
2) Multiple reflections between the surface and atmosphere, and
3) Scattering into the target-sensor path from nearby surface.
The amount and the direction of light scatter in the atmosphere depend strongly on the
ratio of the aerosol particle size to the wavelength of the incident light. When the particles are
much larger than λ, the scattering is best explained by Mie theory. The atmospheric density of
aerosol particles is usually characterized by one or two mean particle size components in a lognormal distribution (Shettle & Fenn, 1979). This distribution is given by:
dN ( r )
dr

Ni

=
ln( 10 ) • r • σi
i =1 
2
∑
 (log(

exp −

2π
r ) − log( ri ))
2σ
2
i
2


(2-18)
where N(r) is the cumulative number density of particles of radius r, σ is the standard deviation of
the distribution, and ri and Ni are the mode radius and the number density of the ith mode.
39
Figure 2.4-1. Typical particle size distribution curves for a rural aerosol type.
Since the presence of aerosols in the atmosphere can seriously degrade the accuracy of
the surface radiative properties throughout the visible spectral bands, a robust and computationally
feasible algorithm to extract aerosol properties from in-scene data would greatly enhance existing
atmospheric correction techniques. The following sections briefly review existing algorithms for
aerosol property determination from calibrated hyperspectral imagery.
2.4.2 The Fourier Transform Method
The construction of the Multi-angle Imaging Spectroradiometer (MISR) at JPL has
motivated the development of algorithms that make use of the multidirectional viewing angles to
better characterize the radiative properties of ground targets and the composition and contribution
of the atmosphere in remote sensing. One of these techniques makes use of the spatial contrast
in the acquired multiangle imagery and compares the amplitudes of the spatial Fourier transforms
at all frequencies. An initial guess is made for the bulk optical aerosol properties, such as optical
40
depth τ, single-scattering albedo s, and the size distribution. The Fourier components of the
surface reflectance are compared to establish the quality of the first guess. Then the aerosol
properties are subtly changed and the next guess is computed. The process is repeated until the
RMS residuals indicate the best estimate of all aerosol properties. In all cases, the retrieval is
constrained by the information provided by the multiangle imagery. The algorithm is unusable with
nadir-only image acquisitions because of the need for multiple-angle data in the computations.
An assumption is made that the atmosphere is homogeneous over the image and that the
surface albedo variations in that region can be utilized to estimate the aerosol properties. The
governing radiative transfer equation for the directional surface reflectance inversion process is
(Diner, 1985):
 1 2π
= R + e µ π −1  ∫ ∫ r (x , y )
0 0

−τ
I(x , y )
π−
1
1 2π 1 2 π
D µ ′ d µ ′ d φ′  +
∫ ∫ ∫ ∫ (T ( x , y ) ∗ r (x , y )

D µ′
) d µ ′′
(2-19)
d φ ′′ d µ′′ d φ ′′
0 0 0 0
where x, y are the spatial image coordinates, R is the path radiance, τ is the opacity of the
atmosphere, D is the total radiance incident at the surface, T is the upward diffuse transmittance, r
is the surface reflectance, µ is the cosine of the view angle, and * denotes convolution. All terms
depend on view and sun angles and view azimuthal angle with respect to the sun position, where
"view angle" is defined as the azimuthal angle between the sun and the along-track direction of the
sensor. This equation can be restated in radiometric terms consistent with the notation of this
paper:
L sensor
= L u + τ2 ρ
cos
σ′
[
L grnd
+ L downwelled
]+ [ ∗ ρ(
T
L grnd
+ L downwelled
)cos σ′ ]
(2-20)
where σ´ is the view angle of the surface to the incident radiance. The last term on the right
describes the surface-leaving radiance being blurred by the diffuse-field point spread function
(PSF) of the atmosphere. The filter theorem of the Fourier transform allows the convolution to be
41
recast into a multiplication in the frequency domain. The spectrum of upward diffuse transmittance
decreases in magnitude with increasing frequency and acts like a lowpass filter on the surface
reflectance spatial structure.
The reflectance structure is modeled as:
ρ( ξ , η; cos σ, cos σ′ , φ − φ ′) = ρ ( ξ, η; cos σ ) + ρ ( ξ , η; cos σ) cos( φ − φ ′)
(2-21)
ρ(0 , 0 ; cos σ , cos σ ′, φ − φ ′) =
(2-22)
0
1
A ( ξ, η) ∗ ρ n (0 , 0 ; ξ , cos
σ ′, φ − φ ′)
ρ n ( ξ, η) = A ( ξ, η) ∗ρ n ( ξ , cos σ ′, φ − φ ′)
(2-23)
where A is the transformed hemispherical albedo of the surface image and r is the 1-D normalized
directional reflectance spectrum. It also can be shown that:
A ( ξ, η) ρ(cos
σ) =
L sensor ( ξ, η; cos
e
−τ
cos σ
[S
1
( φ2 −
σ , φ1 − φ 0 ) S 1 ( φ 2 − φ 0 )
φ0 ) − S 1 ( φ1 − φ 0 ) ]S 0
−
L sensor ( ξ, η; cos
e
−τ
cos σ
[S
1
(φ2
σ, φ2 − φ 0 ) S 1 ( φ1 − φ 0 )
− φ0 ) − S 1 ( φ1 − φ0 ) ]S 0
(2-24)
where the S-functions are the components of the atmospheric optical transfer function (OTF) which
suppress high-frequency information. Analysis of complex-valued parameters is avoided by taking
absolute values. Equation (2-24) is the radiative transfer function that is iterated to retrieve A and
uses two distinct azimuthal observation angles.
The Simplified Algorithm (Martonchik, 1992)
1) The algorithm first estimates the aerosol opacity, single-scattering albedo, and phase function.
The corresponding upwelled radiance (Lu), upward diffuse transmittance (T), and total downward
directed radiance (Lgrnd+Ldownwelled) are then computed.
42
2) The DC component of the Fourier transform of the multi-angle images is used to iterate on the
Fourier transform of Equation (2-19) by substituting in Equation 2-21 for r to solve for A(0, 0)ρ0 and
A(0, 0)ρ1. The surface reflectance structure ρ(0, 0) is constructed via Equation (2-22) and used to
update Lgrnd+Ldownwelled and to recalculate the suppression functions S0 and S1. The iteration
procedure continues until the value of Lgrnd+Ldownwelled converges.
3) At nonzero spatial frequencies, solve for
A ( ξ, η) ρ
0
and
A ( ξ, η) ρ
1
by using Equation (2-24).
The surface structure is incrementally constructed using Equation (2-23) in the multi-angle
acquisition and tracking the RMS residuals between the curves at all spatial frequencies. The
average of the aerosol parameter at the minimum residual for each curve gives the “best” estimate
of the scene atmosphere. This is illustrated in Figures 2.4-2 and 2.4-3. The frequency
representation of reflectance corresponding to the best estimate for all parameters is then
transformed to the space domain to produce the best estimate of the reflectance value in each
pixel of the image.
Figure 2.4-2. Retrieved directional reflectance shape residuals for various spatial wave
numbers (Martonchik, 1992).
43
Figure 2.4-3. Retrieved directional reflectance shape residuals for various spatial wave
numbers (Martonchik, 1992).
It should be noted that this procedure must be realized within individual wavelength bands
and must be repeated for each band when a multiangle hyperspectral image is analyzed. This
routine was tested for synthetic imagery having two fixed aerosol parameters with very good
results (Figures 2.4-2 and 2.4-3). No results of a test where three aerosol parameters were varied
are documented in the literature.
2.4.3 The Principal Components Method
This routine for retrieving aerosol properties from remotely sensed imagery was developed
by the same authors who constructed the Fourier Transform method reviewed in section 2.4.2
(Martonchik, 1992). In the Fourier Transform method, angle-dependent power functions of the
nonzero frequencies were used to construct empirical orthogonal functions (EOFs) which
described the surface component of the observed radiance (Martonchik, 1996). The best estimate
of the aerosol optical depth was that which minimized the residuals between the observed (sensor)
radiances and the modeled radiances computed using the EOF expansion of the total at-the-
44
surface radiance. In this technique, the FFT is unnecessary and the EOFs are constructed directly
from the individual pixel radiances in the image.
In this algorithm, the governing radiative transfer equation is simply written as:
L sensor (x , y )
= L atm + L direct
(x , y ) + L diffuse
(2-25)
where Latm is the path radiance, Ldirect is the direct solar radiance component from the surface to
the sensor, and Ldiffuse is the diffuse radiance from the surface to the sensor. All three terms
depend on the observer-view and sun angles and observer-azimuth angle with respect to sun
position. Only the direct radiance component is considered to vary spatially in this radiative
transfer function (RTF).
The image scene is divided into 4x4 pixel subscenes and the aerosol is estimated for
each. Since aerosol loading is assumed to be constant over the entire image, the results for all
subscenes are averaged at the end. The EOFs required to run the aerosol algorithm are the
eigenvectors associated with the real-valued, scatter matrix. These eigenvectors are constructed
from the reduced pixel radiances. Reduced pixel radiances are defined as the sensor radiance
value of the pixel minus the average radiance of the pixel-averaged 4x4 subscene in which it is
located. The assumption is that this process removes the path and the diffuse radiance which are
assumed identical for each pixel in the subscene. Thus, the reduced pixel radiance is given by:
L reduced ( x , y )
= L sensor
(x , y ) −
1
4
4
∑ ∑ L sensor
16 i =1 j =1
( i , j)
(2-26)
over the 4x4 image subsection where i, j are the pixel coordinates within the subsection. The
scatter matrix can be constructed where each element can be represented as:
C pq
=
∑ ∑ L reduced
x
y
( x , y , p )L reduced (x , y , q )
45
(2-27)
where p, q are used to indicate different viewing geometries. The eigenvectors of C are the
solutions to the equation:
10
∑C
q =1
p ,q
f n , q= λ n f n , p
(2-28)
The λn’s are the real, positive eigenvalues of fn. Since MISR has five forward and five
rearward camera look angles, there is a total of ten eigenvectors and associated eigenvalues.
Every image pixel would have a ten-element vector of reduced radiances and could be expanded
in terms of an orthonormal set:
=
L reduced ( x , y , p )
10
∑A n
n =1
x,y
(2-29)
fn , p
where the A matrix contains the principal components of the reduced radiance multiangle vector.
If a single spatially variable surface bidirectional reflectance factor (BRF) is said to be a
descriptor of the view angle variability of a surface within an image subsection (individual pixel
reflectances can still differ), the reduced pixel radiances obey the linear relation:
L reduced (x , y , p )
= c′
L reduced ( x ′ , y ′, p )
=c
f1, p
(2-30)
Thus, it follows that if the correct path radiance and diffusely transmitted radiances are subtracted
from the average radiance at the sensor (in the 4x4 subsection), then the resulting pixel-averaged
surface function must also be proportional to f1:
L sensor , i
− L atm
,i
− L diffuse
,i
= a 1 f1 , i
(2-31)
When the correct aerosol parameters are unknown, the best estimate of the parameters is the
minimum least-squares difference between the left and right side of Equation (2-31). This can be
expressed as:
46

= ∑  L sensor
i = 1
10
D (mod el , τ aer )
,i
− L atm
, i (mod
el , τ aer ) − L diffuse
, i (mod
el , τ aer

) − ∑ a n fn , i 

n =1
(2-32)
N
with the expansion coefficients obtained from:
10
an
=∑
i =1
(L
sensor , i
− L atm
, i (mod
el , τ aer ) − L diffuse
, i (mod
)f
el , τ aer )
n ,i
(2-33)
Only eigenvalues greater than 0.05l1 are used in the summation, (i.e., Nmax<10). The minimum D
corresponds to the best estimate of optical depth for that N. The best overall aerosol optical depth
for the image subsection is obtained by a weighted average over all N optical depths:
τ best
 N Max 1

 ∑ N τN 
 N =1 D

=
 N Max 1 
 ∑

 N =1 D N 
D eff
=
(2-34)
and:
N
N
Max
∑
N
=1
D
(2-35)
−N
A weighted average using the aerosol optical depth and corresponding Deff is then computed for
all 16-pixel subsections in the image.
In preliminary tests, the algorithm appeared to extract realistic aerosol optical depths for
the multiangle scene tested. Since no atmospheric truth data were obtained for the image
acquisition, the algorithmic procedure cannot be considered as validated.
47
2
This concludes the listing of aerosol extraction algorithms available for hyperspectral
imagery. Of these, only the NLLSSF technique has been used with actual image data with some
success. The aerosol NLLSSF algorithm by Green, (1989) has the advantage in that it extracts
the visibility parameter of aerosols and assumes a fixed standard deviation of the particle
distribution. However, the user must assume some particular set of atmospheric aerosols such as
an urban, rural, maritime, or other MODTRAN aerosol mixture.
The Fourier transform technique, while novel in its approach, is too computationally
intensive to incorporate into a total atmospheric algorithm. The Principal Component approach
may prove to be robust enough and computationally realistic for total atmospheric correction, but it
depends on the multiple-view angle imagery that only the MISR sensor can provide. The intriguing
aspect of this approach is its use of a spatially blurred image as part of the determination of
atmospheric aerosols. Since aerosols cause the most scattering of light in the visible region, the
incorporation of this phenomenon in the fit of aerosol bulk properties may be important.
While the Principal Component method may be useful, it is as yet untested and is
applicable only to MISR imagery (multiangle and multispectral). What is sorely needed is an
algorithm that can be utilized with more common types of sensors, such as line scanners.
For reasons previously stated, none of the aerosol algorithms are planned to be used with
the exception of the NLLSSF technique which may be part of larger, more comprehensive aerosol
extraction routine.
48
2.5 Review of the Radiative Transfer Process
Before reviewing the comprehensive atmospheric correction algorithm in detail, it is useful
to describe the paths of photons that transfer solar energy since both APDA and NLLSSF use this
radiometry to estimate the atmospheric component(s). This is key because well-modeled
radiometry can be applied to the sensor radiance so that the atmospheric correction algorithm can
derive an estimated ground reflectance.
Given the surface elevation, columnar water vapor, and visibility for a hyperspectral image,
the radiometric parameters can then be retrieved from an LUT generated previously by multiple
MODTRAN 4 runs. The radiometric parameters used in the LUT will be defined in this section
along with the radiative transfer process. Then the construction of the actual LUT will be described
in Section 2.6.
Since all work in this research is done in the visible and near-infrared regions, the thermal
emissive contributions to the total sensor radiance are assumed to be zero. There is also the
assumption that no shape factor is present due to objects or terrain and that the spectral
reflectance properties of the surface or target are Lambertian. In the simple single scattering case,
the total radiative transfer equation reduces to:
L sensor
= L grnd ρ + L upwelled
(2-36)
where Lsensor is the total radiance measured at the sensor by a detector element, Lgrnd is the direct
solar radiance from the sun to the target to the sensor (including transmissive effects of the
atmosphere as shown in Figure 2.5-1),
49
Figure 2.5-1. Direct solar radiance path.
ρ is the surface reflectance of the target, and Lu is the upwelled atmospheric radiance which has
no interaction with the target or surround (Figure 2.5-2). All of these terms are functions of
wavelength.
Figure 2.5-2. Atmospheric scattered upwelling radiance
If the earth's atmosphere caused only a single scattering event per photon, the work of a
remote sensing scientist would be a lot less challenging. However, earthbound photons in the
ultraviolet and visible portions of the spectrum frequently are scattered two or more times before
they reach the sensor because of molecular interaction (Rayleigh scattering), aerosols (Mie
50
scattering), and a Rayleigh-aerosol coupled interaction. Modeling this multiple scattering in the
radiative transfer equation warrants the inclusion of additional terms to account for non-target
direct solar photons that scatter into the sensor path:
L sensor
=
(
L grnd
+ L downwelled
(1.0 -
ρS)
) +L
π
ρ
upwelled
+
sensor _ height
∑
h =0
2
2π
∑ ∑ ρ( θ, φ)L env ( θ, φ, h )
θ= 0 φ= 0
(2-37)
where Ldownwelled is the scattered atmospheric radiance onto the target including transmissive
effects of the atmosphere,
Figure 2.5-3. Scattered solar downwelling radiance.
S is the spherical albedo of the atmosphere, (1.0-ρS) in the denominator is derived from a series
that accounts for successive reflections and scattering between the surface and the atmosphere
(Vermote, E. et al., 1997) also called the trapping effect (Figure 2.5-4).
51
Figure 2.5-4. Trapping effect radiance.
Figure 2.5-5. Environmental or adjacency radiance.
Lenv is the direct and scattered solar radiance that interacts with a surround area with
reflectance ρ(θ,φ) and is scattered into the target-sensor path (Figure 2.5-5), θ is the angle from
nadir (looking downward from the sensor) to where the surround area is located, and φ is the
azimuthal angle where the surround area is located.
The last term in the summation Equation 2-37 is often referred to as the "environmental or
adjacency effect radiance" because it includes photon interactions with ground areas outside of
the target. Presently in MODTRAN 4.0 radiative transfer calculations, the reflectance of the
surround areas are assumed to be equal to that of the target area. For homogeneous land cover
areas this assumption holds true, but usually not with most scene content. This problem leads to
one of the efforts in this research, since there appears to be a lack of algorithms that account for a
52
spatially nonhomogeneous reflective surround . In terms of the atmospheric optical effect, the
question becomes: What is the atmospheric point spread function (PSF)?
To account for nonhomogeneity in the surround of the scene, it is useful to visualize a
ground-projected block or grid of sensor pixels with each having reflectance ρ(θ,φ)). This block is
spatially weighted to account for the scattered fraction of radiance received at the sensor in its
instantaneous field of view (IFOV); see Figure 2.5-6. The resulting sum of the spatially weighted
ρ(θ,φ)) values is the average reflectance (ρavg). The grid of spatial weights can be thought of as
the estimate of the atmospheric PSF since the "point" or projected area of the detector element
receives energy from outside of the confines of the sensor IFOV.
ρ avg = ∑ ∑ W (i , j)ρ (i , j)
i
(2-38)
j
Note: In Equation 2-38 the Cartesian coordinates (i,j) have been substituted for polar
coordinates of the ground pixels (θ,φ).
The value of the environmental/adjacency radiance at the sensor reflected from a 100%
reflector (Lenv) can then be extracted from MODTRAN (given fixed atmospheric parameters) and
multiplied by this average reflectance of the surround to yield the estimated adjacency-effect
radiance. Since the trapping-effect radiance also includes interaction with the surround, the
average reflectance can also be substituted for ρ in the series. After a numerical estimate is
substituted for the series, the radiative transfer equation becomes:
L sensor
=
(L
grnd
+ L downwelled
(1 .0
− ρ avg S )
)ρ + L
upwelled
53
+ ρ avg L env
(2-39)
Figure 2.5-6. The sensor ground-projected pixel grids containing the fractional
contributions of the ground reflectance at each atmospheric layer height. These grids are
summed over the layers to eventually generate the spatial weighting for the ground
reflectance.
The assumption of use of the average reflectance is valid only if the target is not much
darker than the surround. If a dark target lies on a bright surround, the actual trapping effect
radiance will be very small since the last photon interactions result in reflection of a very small
percentage of the trapped radiance. As a side note, even though the same PSF was used for the
trapping effect in Equation 2-39 (i.e the ρ=ρavg substitution), it is known that the trapping effect
PSF is much larger and broader. Further research in this area could be performed to develop the
weighting (and kernel size) for better estimation of the gain effect in trapping effect radiance.
Solving Equation 2-39 for the ground reflectance of the target yields the equation:
ρ=
(L
sensor
− L upwelled − ρavg
(L
grnd
L env
+ L downwelled
)(1 .0 − ρ S )
)
avg
54
(2-40)
Equation 2-39 and its complement 2-40 is included as a choice for the radiative transfer
equation in the comprehensive atmospheric correction algorithm. In the event that the user does
not wish to include the Lenv radiometric parameter, an alternative governing equation for a single
pass through the algorithm may be selected:
L sensor
=
(L
grnd
) +L
+ L downwelled τ 2 ρ
(1 .0
− ρ S)
(2-41)
upwelled
As inferred in Equation 2-38, to estimate ρavg, it is necessary to already have a spectral
reflectance map. This requires t a first pass through the atmospheric correction code where ρavg is
assumed to be equal to the target reflectance within the sensor IFOV. Once the
radiometric parameters are determined by locking in the surface elevation, aerosol dependent
visibility, and columnar water vapor amount (via iterations with NLLSSF, APDA, or another
technique), Equation (2-39) may be inverted to solve for the target reflectance for the first run by
substituting ρ=ρavg:
ρ=
(L
(L
grnd
+ L downwelled
sensor
− L upwelled
) (L
+ L env +
)
sensor
− L upwelled
)S
(2-42)
This first-pass reflectance map becomes either the end product or the map that contains
ρ(i,j) values for use in Equation 2-38. The last step in the first run is the determination of the
spectral atmospheric PSF (or W(i,j)) that dictates the amount of blur that is applied image-wide
(and band-by-band) to the first-pass reflectance map (see Section 3.5) via convolution. The first
pass reflectance map convolved with the PSF is then used for ρavg in the second run. Once the
average reflectance map ρavg is derived, the second pass through the correction algorithm uses
Equation 2-40 for the inversion-to-ground-reflectance formula.
The next section addresses the generation of the Look-Up Table (LUT) with MODTRAN
4.0 that contains the radiometric parameters for different atmospheres as well as a general
overview of the atmospheric correction algorithm.
55
2.6 The Radiometry LUT and the Atmospheric Correction Algorithm
In order to finally solve Equation 2-40 or 2-42 for estimated ground reflectance, a quick
overview is needed of the steps in the comprehensive atmospheric correction algorithm. First, a
radiometrically calibrated hyperspectral image is chosen to invert to obtain the ground reflectance.
Secondly, an estimated atmospheric profile is chosen and the necessary parameters needed to
construct a MODTRAN carddeck are substituted, either from measurement or estimates by the
user. This becomes the base carddeck to use for making a full LUT.
Since NLLSSF, APDA, and the techniques developed in this research attempt to fit the
estimated radiance profile at the sensor (see Section 2.3.1 and 2.3.2), a number of atmospheric
conditions with their associated radiometric parameters must be determined. It must be
remembered that if the surface elevation (or surface-pressure-depth), visibility, or water-vapor
amount is changed, then the radiative transfer terms in the atmosphere also change. Thus, for the
purposes of this correction algorithm, the LUT must contain all radiometric parameters in Equation
2-40 for each combination of surface elevations, visibilities, and water vapor amounts as functions
of wavelength.
To begin, a range and increment step is chosen for each atmospheric parameter to be
solved. For example, the range ofsurface elevations can be from 0.0 km to 0.8 km in 0.1 km
increments, the visibility from 10.0 to 70.0km in 10 km increments, and the water vapor from 0.0 to
5.5g/cm2 in 0.75 g/cm2 increments. For every combination, the base MODTRAN carddeck is
altered , a run of MODTRAN is performed, the radiometric parameters are convolved with the
sensor response, the radiometric parameters needed for Equation 2-39 are linked with the
atmospheric parameter combination and then are placed in an organized data structure as the
LUT. The LUT becomes a complete database of radiometry that can easily be accessed for any
specific combination of surface elevation, visibility, and water vapor. Combinations that fall in
between the discrete intervals can be interpolated to obtain the necessary radiometry.
Once the LUT has been completed, the first pass of the comprehensive algorithm can
begin. The user can select which techniques to use to solve for surface elevation, visibility, and
water vapor. For this example, a user may select NLLSSF to solve all three atmospheric
parameters. The algorithm proceeds to Box A in Figure 2.6-1 and NLLSSF is used to solve for the
56
surface elevation of each pixel. The procedure repeats until all the pixels in the image have been
assigned a surface elevation.
Figure 2.6-1. Overview of the atmospheric correction algorithm.
NLLSSF iterates through the LUT the surface elevation dimension to find the combination
of radiometric parameters that will minimize the error between the image pixel radiance and
Equation 2-39, where ρavg=ρ is assumed. The aerosol-dependent visibility and columnar water
vapor must be estimated by the user for this step, usually by using one value fo rthe entire image
(for each parameter). As stated in Section 2.3.2, the NLLSSF routine must begin close to the truth
for convergence to a realistic solution.
With the surface elevation fixed, the algorithm moves to Box B in Figure 2.6-1 where the
NLLSSF solves for the aerosol-dependent visibility. The visibility that results in the least radiance
error for an image radiance value is used. The algorithm assigns a visibility to each pixel. At this
point, it is easy to see that essentially the algorithm moves through the 3-D LUT by constraining
one dimension after another to converge on the best "atmosphere" for the image pixel.
57
With the surface elevation and visibility fixed, the NLLSSF goes to Box C in Figure 2.6-1
where it iterates on the atmospheres until the best fit is found for the water vapor feature at
940nm. Again, the algorithm proceeds through the image pixel-by-pixel to assign a water vapor to
each pixel. The algorithm then proceeds to Box D in Figure 2.6-1 where it extracts the radiometric
parameters from the LUT that correspond to the solved surface elevation, visibility, and water
vapor from the previous three steps. Equation 2-42 is used to solve for the ground reflectance.
Once the recovered spectral reflectance is written to an image file for each pixel, the first pass is
complete.
The next step is to calculate the atmospheric PSF (see Section 3.5) and convolve this with
the first-pass reflectance image to yield a ρavg image (Box E). Once complete, the algorithm
repeats starting from Box A in Figure 2.6-1 using Equation 2-39 to fit the image pixel (sensor)
radiance. At Box D, the algorithm then uses Equation 2-40 to solve for reflectance (for each pixel)
using the radiometric terms that correspond to the fixed atmospheric parameters obtained in the
second pass.
58
3. Components of the Atmospheric Correction Algorithm
3.1 Overview of the Complete Algorithm
The APDA and NLLSSF technique were reviewed in Section 2.3 and the comprehensive
atmospheric correction algorithm was presented in Sections 2.5 and 2.6. Since the existing
components have been described previously, it is necessary to establish some order in the
computations of parameters. The sequence of the atmospheric characterization thus consists of
the following steps:
1) estimation of terrain height
2) determination of aerosol properties (by estimating the atmospheric visibility and defining an
aerosol type),
3) extraction of total column water vapor, and
4) estimation of the atmospheric PSF to account for surround effects.
(Note: From numerous trials, it has been determined that the aerosol properties must be
computed before estimating the water vapor estimation so that the atmospheric
"windows" (i.e. the wings) around the .94µm water vapor feature at .86µm and 1.0µm
have a better fit to the sensor radiance.)
Before exploring the composition of this atmospheric correction algorithm further reasons
for its development must be stated. First and foremost, the remote sensing community needs a
comprehensive atmospheric correction algorithm to obtain estimated ground reflectance from
calibrated multispectral and hyperspectral images. A second reason is that there is no
comprehensive correction algorithm that contains a large assortment of options for inverting
sensor radiance measurements to ground reflectance. The options such as APDA and NLLSSF
are not presently available in modular and useable forms. The third reason for this algorithm is
that in addition to including a large assortment of correction approaches, a new technique for
determining atmospheric visibility (and subsequently the aerosol properties) called the Regression
Intersection Method for Aerosol Correction (RIMAC) has been developed to work in this modular
environment. The last reason is that a new method for determining the contribution of the target
surround is presented which uses the built-in functionality of MODTRAN 4. This new method has
59
the potential for being able to use a generic set of PSFs given that the atmospheric layer profile
has relative humidities less than 95%.
With these reasons being established for a foundation, the components and atmospheric
characterization sequence in this atmospheric correction algorithm can be reviewed.
Figure 3.1-1 presents the atmospheric correction or inversion algorithm modules. The
atmosphere PSF routine is considered an intermediate step and is included in Figure 2.6-1. The
following list is a breakdown of the options available in the algorithm for solving for three
atmospheric parameters:
Parameter
Options
Surface elevation
Default or truth data
NLLSSF (fits O2 band)
Aerosol-Dependent
Visibility
Default or truth data
NLLSSF (fits .4-.7µm bands)
RIMAC (fits .55-.7µm bands)
Columnar Water
Vapor
Default or truth data
NLLSSF (fits H2O band)
APDA (fits H2O band)
Other options include the user's choice of one of two passes through the algorithm and
choices of radiative transfer equations (see Section 2.5). From Figure 3.1-1, it can be seen how
the options are combined to obtain the best model of the atmosphere given the image pixel
radiance. The algorithm then proceeds to invert the sensor radiance to ground reflectance.
60
Figure 3.1-1. The components of atmospheric correction and their flow to derive the
estimated ground reflectance (illustration courtesy of Nina Raqueño)
61
In all references to reflectance units in this research, the range is assumed to be 0.0 to 1.0
reflectance units. Zero reflectance is a completely black non-reflecting target, while a reflectance
of 1.0 means that the target reflects 100% of the incident light.
3.2 Terrain Height
Only Green’s method of NLLSSF is used to calculate the surface pressure elevation
(Section 3.3.2). Using the 760nm oxygen absorption band, an iterative routine is employed to fit
the model sensor radiance from MODTRAN to the acquired spectral radiance data for each pixel
(left middle module in Figure 3.1-1). The reflectance is modeled with a gain and bias as a
function of wavelength. A preconditioning step prior to running the amoeba routine performs a
fast linear fit between the first and last channel of the oxygen bands to initialize the reflectance
gain and bias using the atmospheric defaults.
This routine is incorporated into the new atmospheric correction routine as the first step. If
the surface elevation is known, this NLLSSF module can be switched off and a default elevation
used instead.
3.3 Aerosols
One option to determine the atmospheric visibility given an aerosol type is Green's
NLLSSF (in top right Figure 3.1-1). Once again, a pre-conditioning step is run to initialize the
amoeba routine. The default atmospheric condition radiometric parameters are used, except the
surface elevation is set to the solution of the previous step. The reflectance is linearly modeled
with the 400nm and 700nm bands and the vegetation scalar is found by multiplying the NDVI by
2.5. This multiplier for the NDVI is an empirically-derived value that appears to give a fairly
accurate vegetation fraction on a per-pixel basis. The multiplier is meant to help estimate in a preconditioning step and is not used to compute the final vegetation scalar in the actual fit routine.
The reflectance is modeled with a gain, bias, and a spectral scaled vegetation reflectance curve to
compensate for the non-linear chlorophyll reflectance as a function of wavelength. The NLLSSF is
then used on all the bands in the range from 400nm - 700nm. As in the previous subsection, a
default value for visibility can be used instead.
62
3.3.1 Non-Unique Radiometric Solutions for Aerosols
The original proposed goal in this area of research was to develop an inscene algorithm to
extract the bulk atmospheric aerosol properties from the image. Before this effort was undertaken,
it was deemed prudent to investigate how the microproperties of the aerosols affect the
macroscopic property of radiance at the sensor and the subsequent recovery of true surface
reflectance. The ideal case was chosen where the atmosphere was generated by MODTRAN and
the parameters were used to invert to ground reflectance.
To set up this test, a standard rural aerosol model was chosen with a number density that
matched a 15km meteorological visibility for 70% relative humidity. The MODTRAN radiometry
using the default mode radius and standard deviation for the small and large particle aerosol
component was used as "truth":
Small Aerosol Large Aerosol
Mode Radius
0.02846µm
St. Deviation
0.35µm
Number density 27037 p/cm3
0.4571µm
0.4µm
3.38 p/cm3
Cases where other combinations of aerosol number density and standard deviation were
sought that could invert from sensor radiance to reflectance with no greater error than 0.01
reflectance units. A rural aerosol was chosen that corresponded to 12.5 km visibility at 70%
relative humidity with particle density of 30945 particles/cm3 for the small particle and 3.87/cm3 for
the large particle. The standard deviation of the small particle density was changed until the
reflectance inversion error from "truth" matched the given tolerance. This same procedure was
followed for aerosol number density for a visibility of 17 km: 23911 small particle, 2.99 large
particle. The mode radii remained at the MODTRAN default for 70% humidity conditions. After
many MODTRAN runs with different user-defined aerosols specified in Card 2D2, the recovered
reflectance error tolerances for an average 0.18 albedo ground target were found. The limits were
an “equivalent” aerosol atmosphere in the 12.5 km visibility case with σ=0.34µm standard
deviation and in the 17 km visibility case σ=0.36µm standard deviation.
63
"Equivalent" Rural Aerosol Single & Multiple Scattering Atmospheres
(Error in Recovered Surface Albedo 0.01 or Less)
0.39
0.38
0.37
0.36
2
R = 0.9837
0.35
0.34
0.33
0.32
17000
19000
21000
23000
25000
27000
29000
31000
33000
35000
37000
Aerosol Number Density (particles/cm^3)
Figure 3.3.1-1. The regression line shows the non-unique combinations of aerosol standard
deviation and number density that yield equivalent atmospheres at 410nm.
Figure 3.3.1-1 shows a plot of the equivalent aerosol parameters that could be used as a
LUT in the spectral region of 410nm where the majority of scattering due to aerosols takes place.
Thus, by choosing a number density (e.g., visibility parameter) between the two extremes, you
could find a suitable standard deviation that would compute the ground reflectance from the
sensor radiance within 0.01 reflectance units. Assuming the MODTRAN model of the atmosphere
is true, the data show that there are non-unique aerosol properties that can yield the "same"
radiance at the sensor. For a range of atmospheres, it is not necessary to devise a complex and
run-time intensive algorithm to solve for non-unique bulk aerosol properties. A quantitative
solution to the radiative transfer equation can be found using an "equivalent" aerosol property(s)
essentially by employing the already fixed aerosol distribution standard deviation in MODTRAN
and then simply changing the relative humidity and visibility parameters. It should be noted that
the visibility parameter is closely related to the aerosol particle number density and humidity
64
(Shettle & Fenn, 1979). For the scope of this research, it was determined that solving for aerosol
visibility is sufficient for non-unique determination of the bulk properties.
3.3.2 The Regression Intersection Method for Aerosol Correction
(RIMAC)
A new in-scene option for estimating the atmospheric aerosols via the visibility (see at the
top left in Figure 3.1-1) is the Regression Intersection Method for Aerosol Correction (RIMAC).
Derived from the Regression Intersection Method to estimate atmospheric upwelled radiance
(Crippen, 1987) (Gaddis et al., 1996), this technique assumes that the majority of the upwelled
radiance is a function of aerosol scattering in the 550nm - 700nm wavelength range. A substantial
advantage of utilizing RIM is that it provides statistically derived results from the actual image data
with no atmospheric or other scene information needed. By comparison, the NLLSSF technique
relies on a starting estimate that is close to truth in order to obtain realistic atmospheric parameters
and subsequently yield a good inversion to reflectance. NLLSSF also is constrained by the
reflectance modeled as a linear function of wavelength for a given band range (with some
nonlinearity accounted for in specific bands).
The RIM depends on classification that can identify homogeneous areas of varying
spectral contrasts in the terrain. Lack of spectral contrast can lead to gross errors in the estimated
upwelled radiance. The method also assumes that the spectral bands are inherently registered.
As implemented, an unsupervised ISODATA classification is done by a noninteractive ENVI
calculation or a previously constructed supervised classification map is used to define class
regions of homogeneity. Ineligible class distributions are identified for lack of compactness by
using a standard deviation cutoff for each band (Barnes, 1997). Once ineligible distributions are
discarded, the spectral digital counts (DC) of the image are loaded for each of the classes.
Starting from the first band and using band pairs, a regression is performed on the DCs for each
class to extrapolate toward the origin and the intersections of all the class regressions are
calculated from the combinations of the first band with the others (Figure 3.3-1).
65
Figure 3.3-1 Example of In-Class Distributions in Two Bands
(Barnes, 1997)
The maximum hard limit for acceptable class regression line intersections is set by the
"toe" of the image histogram in the dark pixel region (for example, see Max_Int in Figure 3.3-1).
This requirement was put in place so that the resulting RIM-derived total upwelling radiance could
not be a value greater than the dark pixel radiances in the image. The absolute histogram
minimum could very well be either a dead or noise contaminated pixel. In the case of this
algorithm, the minimum number of pixels in the dark bin was set to ten. The minimum intersection
cutoff value is set to a DC of zero so that the RIM-derived upwelling radiance cannot be negative.
Intersections above and below the hard limits are discarded from consideration. An example of
the acceptable range limits for the intersection coordinates is given by the red lines in Figure 3.3-1.
Once a cluster of acceptable intersections are found for the band pair, the mean (or
median) value is determined and the transformed DC becomes the total upwelling radiance value
for the first band of the comparison. This process is then repeated for the second and subsequent
bands. See Figure 3.3-2 for a general flow chart of the algorithm.
66
Figure 3.3-2 RIMAC Flow Chart
The total upwelling radiance in this case is defined as:
L Total _ Upwelled
= L env ρavg + L atmos
_ upwelled
(3-1)
where Lenv is the radiance contribution of the target surround, ρavg is the average reflectance of the
surround, and Latmos_upwelled is the atmospheric radiance component. Light is highly scattered by
the atmosphere in the blue region of the spectrum from ~390nm to 500nm. Unfortunately, this
increased scatter also reduces the apparent contrast within a defined class in the scene. As
stated previously, the integrity of the RIM is highly dependent on class contrast. This is easily
understood by referring to Figure 3.3-1. As the contrast within a class in the two bands of interest
decreases, the distribution becomes increasingly circular. The correlation of the class distribution
decreases and the validity of performing a regression analysis becomes questionable.
Furthermore, even if a regression analysis can somehow be justified, the regression lines for the
classes have a high probability of either diverging, being parallel, or converging outside of the hard
67
limits. To avoid the low contrast spectral region, but still include bands where the aerosol
signature is apparent, the spectral range used for RIMAC has been set at 550nm-700nm. It
should be noted that these spectral limits have been derived from analyses on a very small image
set. Below about 500nm, the total upwelled radiance from the RIM method appears to be
underestimated with the error increasing into the blue region of the spectrum. Further work is
needed in this area to determine if the 550-700nm spectral range is the "best" for the total
upwelled radiance estimation.
The total upwelling radiance as defined by Equation 3-1 has no target interaction at all; it
is a function only of the scattering of the atmosphere defined by the aerosol phase function and
some interaction from the target surround. Using the radiometry from a MODTRAN 4.0 generated
LUT, a nonlinear fit can be performed to find the least-squared spectral error between the RIMderived total upwelled radiance and a MODTRAN calculated atmosphere for a specified visibility.
However, the average reflectance of the target surround has must somehow be estimated.
Before the NLLSSF can be performed to solve for the aerosol-specific visibility parameter,
one of two methods can be used to estimate ρavg. If the hyperspectral image spectral range
includes a 2200nm band, then a ratio method developed by Kaufman (1997) can be used to
estimate ρavg for the image. The average image spectra is calculated and since the multiple
scattering terms in the 2200nm band in the radiative transfer equation are negligible, a simplified
lower-dimensionality inversion to reflectance is performed:
ρ=
(L
sensor
− L atmos_upwelled
E s cos(
σ ) τ1 τ 2
π
)
(3-2)
where Latmos_upwelled is the non-target/surround interactive upwelling radiance component scattered
from the atmosphere, Es is the exo-atmospheric irradiance from the sun, σ is the solar zenith
angle, τ1 is the sun-target transmission term, and τ2 is the target-sensor transmission term.
Kaufman's correlation predicts that the reflectance in the 660nm band is approximately
half that of the 2200nm band (Kaufman, 1997). Once the reflectance for the 2200nm band is
estimated, the 660nm reflectance can be estimated by multiplying the 2200nm band reflectance by
68
0.5. Since this estimate is for image-wide spectra, it is assumed that the reflectance from 550nm700nm is constant and equal to the 660nm Kaufman estimate.
A least-squares spectral fit is performed by varying only the aerosol visibility to match the
RIM-derived total radiance value via Equation 3-1. If the spectral response of the sensor does not
include a 2200nm band, a simple NLLSSF on the RIM-derived total upwelled radiance is
performed on the 550-700nm bands where the average target surround is assumed to be a linear
function of wavelength in this region. There are three parameters to vary with this latter option, as
opposed to one in Kaufman's, method: the aerosol-specific visibility, the reflectance bias, and the
reflectance gain terms.
The aerosol-specific visibility that corresponds to the MODTRAN-derived total upwelled
radiance with the least-squares spectral fit to the RIM-derived total upwelled radiance is then
assigned to the image. Since there is only one visibility value that is derived from the RIMAC, it is
assumed that the user is aware that this amount is an average visibility over the entire image area.
Another words, the visibility is assumed to fairly homogeneous over the image area. For real
imagery this is certainly not true, but if the aerosol loading varies only slightly over the scene, then
the errors generated by using the scene average visibility will be small. This is not a visibility on a
per-pixel basis as in the NLLSSF technique; when this module is complete, it assigns the same
visibility to all pixels in the image.
3.4 Column Water Vapor
The user would select either NLLSSF, APDA, or a default columnar water vapor value for
the image, as seen at the bottom of Figure 3.1-1. If Green’s NLLSSF method is chosen, Equation
(3-1) would be used with ρavg=ρ for the first pass of the algorithm and then Equation (3-1) for the
second pass. The pre-conditioning step for the amoeba routine is the same as the previous steps
for the reflectance gain and bias, but the liquid water vapor scalar is determined by using CIBR in
the 975nm absorption band.
It should be noted that adding the downwelled terms to the APDA ratio equation was
deemed unnecessary and would add substantially to computer runtimes. This is because of
multiple recursion with MODTRAN runs at three or more wavelengths.
69
3.5 The Atmospheric Point Spread Function (PSF)
As previously mentioned, the earth's atmosphere is a far from perfect transmitter of
electromagnetic energy. This is true not only because of absorption that varies by wavelength, but
also because of Rayleigh scatter due to well-mixed gases and Mie scatter from much larger
suspended dust and organic debris. As reviewed in Section 2.5, some fraction of the total number
of photons that arrive at the sensor have had no interaction with the target in the sensor IFOV
(instantaneous field of view). The atmospheric upwelling radiance (Figure 2.5-2) has no
interaction with the ground so its contribution can be estimated with Rayleigh and Mie scattering
models. However, the other atmospheric pathway referred to as the "environmental" or
"adjacency" radiance, does interact with the ground. In this case, the direct and diffuse
components of solar radiation reflect from the surround of a target that in turn are scattered by the
atmosphere into the IFOV of the sensor (Figure 2.5-5).
To characterize the adjacency radiance contribution, it is first necessary to estimate the
aerosol visibility so that the aerosol-induced scattering can be calculated for the numerous
atmospheric layers between the target and sensor. The aerosol phase function P(θ,λ) can then
be calculated for each layer 'h' of the atmosphere. P(θ,λ) defines the angular distribution of light
that scatters into the direction θ per steradian in a homogeneous scattering medium. The phase
function also is the energy distribution that governs the fractional scattering contribution of the
reflected radiance from a given surround pixel that scatters into the nadir-viewing sensor path
(Figure 3.5-1).
70
Figure 3.5-1. Atmospheric path for light scattered into the sensor path from a surround
ground-projected pixel (green) and contributes to the irradiance leaving the target groundprojected pixel (red).
In theory, the atmospheric PSF has infinite support. However, the contribution of surround
radiance from a given ground-projected pixel is known to drop off substantially with increasing
angle to nadir because of increasing atmospheric transmission and the forward-scattering nature
of the aerosol phase function. To describe this entire radiative transfer process mathematically,
the total environmental contribution can be written:
L env_total ( λ )
=
τlayer (h ) 2 π
∫
π
2
∫ ∫ L( θ , φ , λ) P ( θ , λ, H )T2 ( θ, λ ) ρ ( θ, φ, λ
)d τ sin(
θ )d θ d φ
τlayer (1) φ =0 θ= 0
(3-3)
71
where θ is the angle of the surround location from nadir, ϕ is the azimuthal angle of the surround
location , L(θ,ϕ,λ) is the solar ground radiance which is incident on a surround pixel of reflectance
ρ(θ,ϕ,λ), P(θ,λ,Η) is the aerosol layer phase function (dependent on both aerosol composition
and relative humidity H), T2(θ,λ) is the transmission of surround pixel radiance
to the sensor, dτ is the atmospheric layer optical depth, and sin(θ)dθdϕ is
the solid angle that the unit cross-section of the sensor IFOV presents to
the surround pixel (Otterman and Fraser, 1979).
The geometry can be observed by referring to Figure 3.5-2.
Further computations on the solid angle determination can be seen in
Appendix A. However, MODTRAN 4.0 already calculates the resolved
environmental radiance (in this case using a 1.0 albedo ground target)
which is included in the LUT. The interest for this algorithm section is to
calculate the PSF or the ground reflectance weighting function for this
MODTRAN-derived radiance value.
72
Figure 3.5-2. The geometry for the solid angle of what the source (the surround pixel) sees
of the unit cross-section of the IFOV.
With the finite supports of the PSF defined as a grid of i × j ground-projected pixels, it can easily
be shown that the unnormalized grid values are defined as:
PSF unnorm (i, j)
= ∑
P( θ , λ )
Ω(i, j)
layers
e
-( τ 2a sec θ+τ 2b )
∆τ
layer
(3-4)
where θ is the angle made by the center of the pixel [i,j] of the surround with the nadir-view of the
center (target) pixel as seen from the layer height, P(θ,λ) is the aerosol phase function
for the layer, Ω is the solid angle subtended by the unit cross-section as seen by the i, jth
surround pixel, τ2a is the surround pixel-to-unit layer cross-section optical depth, τ2b is the unit
layer cross-section-to sensor optical depth, and ∆τlayer is the aerosol layer optical depth. To
calculate the fractional contribution of each surround pixel to the scattered radiance, it is
73
necessary to normalize the PSF (i.e the PSF must integrate to unity). However, when this
normalization is performed, the approximately equal aerosol layer optical depths cancel, leaving:
∑ P( θ , λ
PSF(i, j)
=
)
Ω(i,
j) e -( τ 2a sec θ+ τ 2b )
layers
∑ ∑ ∑ P( θ, λ
i
)
Ω(i, j)
e
-( τ 2a sec θ+τ 2 b )
(3-5)
j layers
Since the goal is a convolution kernel used to weight the first-pass recovered ground
reflectance values, the logic for this computation is easily followed. The magnitude of the resolved
environmental radiance vector generated by MODTRAN 4 in the LUT inherently contains the
optical depths that were cancelled out of Equation (3-5). Thus, in the context of the image, this
normalized PSF weighting function can be thought of as a band-dependent convolution kernel. To
computationally derive θ inside MODTRAN, the additional parameter of IFOV in milliradians must
be added to a special tape5 in order to calculate the solid angle, the layer heights and the pixel
center distances from nadir. Again, the index of refraction differences in the atmospheric layers is
assumed to have a negligible effect on the ground spot variation or shape of the atmospheric PSF.
At this point it should be mentioned that no skew correction is performed on the PSF to
account for the surround effects of target pixels that are not directly beneath the sensor.
Reinersman and Carder (1995) did Monte Carlo simulations with AVIRIS imagery that show the
skewness of the PSF is very small at least up to 15 degree off-nadir (which is the half-extent of the
AVIRIS field of view). Also, the PSF only accounts for Mie scattering and does not include
Rayleigh scattering or Rayleigh-aerosol scattering interaction. Again, Reinersman and Carder
(1995) work estimated that scattering effects other than Mie accounted for only a maximum of 5%
of the of the PSF in the blue region where scattering due to aerosols is greatest. Thus, a more
complex PSF generating process would buy only a small amount of scattering contribution that
most likely is at or below the noise level of the entire radiative transfer system.
The surface plots of the spectral kernels give a conceptual view of the scattering
contribution from each pixel. Figure 3.5-3 shows 11×11 kernels with AVIRIS-sized ground pixels
and the fractional scattering contributions at the sensor in the 405nm band and the 2100nm band.
74
As would be expected, there is much less scattering in the short-wave infrared than there is in the
blue region of the spectrum where scattering from atmospheric aerosols dominates.
Figure 3.5-3. Fractional scattering contribution kernel in the 402nm AVIRIS band (left) and
the 2100nm band (right) for a rural aerosol.
The surface plots in Figure 3.5-3 also match the predicted shapes of spectral atmospheric PSFs
from the work of Reinersman and Carder (1995).
This is also the case in Figure 3.5-4 that shows the atmospheric PSF for the HYDICE Run
29 scene at 400nm (Band 2) and 2100nm (Band 166). Notice that because HYDICE was flown at
a much lower altitude than AVIRIS, the fractional contributions from the surround pixels when the
respective spectral bands are compared are less than what is seen in Figure 3.5-3. This would be
expected since there would be less atmosphere between the ground and sensor and consequently
less scattering as well. The PSF also is different because the IFOV for HYDICE is 0.5 milliradians,
while the AVIRIS IFOV is 1.0 milliradians.
75
Figure 3.5-4. Fractional scattering contribution kernel (PSF) in the 400nm HYDICE band (left)
and the 2100nm band (right) for a rural aerosol.
For comparison, the PSF from the desert aerosol in the cr08m33 Western Rainbow scene
is also presented in Figure 3.5-5. The shape of the PSF is quite different due to the fact that the
scattering phase function must be very isotropic. This parabolic shape is also very similar to
Henyey-Greenstein phase function used for multiple scattering.
Figure 3.5-5. Fractional scattering contribution kernel (PSF) for a desert aerosol in all
bands.
In the final calculation of the total environmental/adjacency effect radiance at the sensor,
the magnitude of the resolved radiance also is very important. The resolved
76
environmental/adjacency radiance vector is the environmental radiance at the sensor if the ground
reflectance were 100%. In Figure 3.5-6, this is much less at 2100nm than at 402nm. This is
intuitive because the Mie scattering due to aerosols declines steadily from the blue into the
infrared and near-infrared region. Figures 3.5-4 and 3.5-5 also illustrate how the environmental
radiance can act like a gain factor for the for the PSF since it is driven by the scattering optical
depth. Even though the scattering optical depths were canceled out in Equation 3-5, they are still
accounted for in the MODTRAN-derived resolved environmental radiance vector. Generally the
longer the wavelength, the lower the scattering optical depth and thus the lower the total scattered
radiance. This is statement is considered to be true only in the bands of the solar continuum and
is invalid when volcanic dust, clouds, or other large particles are present in the optical path.
Adjacency Effect Radiance for HYDICE Run 29
0.012
0.01
0.008
0.006
0.004
0.002
0
0.4
0.65
0.9
1.15
1.4
1.65
1.9
2.15
2.4
Wavelength (µm)
Figure 3.5-6. The resolved environmental/adjacency radiance vector from HYDICE Run 29.
A large part of this work was then extraction of the shape of the atmospheric PSF from
MODTRAN, but just as important is the magnitude of the resolved environmental radiance vector.
77
In fact, the magnitude of the radiance gives the relative importance of the PSF; if the magnitude if
is very small, the shape of the PSF doesn’t really have a large effect in the overall radiative
transfer equation. On the other hand, if the magnitude is large (see Figure 3.5-6 in the blue
region), the shape of the atmospheric PSF will greatly affect the recovered ground reflectance.
Figure 3.5-7 shows a plot of the different radiance components from the HYDICE run 29 scene
and by just visually comparing the environmental radiance (Lenv) to the other components, it can be
ascertained how influential in the overall radiative transfer that it will be.
Radiometric Parameters for HYDICE Run 29
0.03
0.025
0.02
Lgrnd
Lu
0.015
Ld
Lenv
0.01
0.005
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Wavelength (µm)
Figure 3.5-7. The different radiance components from the HYDICE Run 29 scene (the
radiance components shown do not include interaction with the ground target).
Once the spectral "kernels" have been calculated, the kernels or PSFs are convolved with
the first-pass reflectance image to yield the estimate for the average reflectance of the surround
for each pixel in each band. A second pass can then be done through the inversion algorithm
using Equation 2-39.
78
79
4. Results and Discussion of Inversion from Sensor Radiance to Ground
Reflectance Units
The total inversion of sensor radiance to estimated ground reflectance was performed on
eight hyperspectral images from four different geographical locations and environmental
conditions. For each image, a number of different atmospheric parameter estimation options were
used and the results were compared to the ground truth target spectral reflectance. All spectral
reflectance errors were plotted from 400nm-1800nm with the exception of the AVIRIS Boreas
image because the truth data only extended from 400nm-900nm. The SWIR spectral range was
omitted for the HYDICE runs due to unresolved issues with the radiometric calibration in these
bands. For all the following plots, the definition of spectral reflectance error is the recovered
reflectance from the inversion minus the ground truth.
The spectral reflectance RMS error was calculated for all cases from 400nm- ~1350nm
with bands omitted that had estimated optical depths greater than 0.4. Because the 940nm water
vapor bands were used to estimate columnar water vapor, they were not omitted in the RMS
computation.
4.1 HYDICE Run 29 ARMs Site Image
The atmospheric characterization and reflectance inversion tools were applied to a June
24, 1997 HYDICE data collection over the DOE ARM site in Oklahoma. Because of this location,
the MODTRAN aerosol selected for the LUT used by the inversion algorithm was the rural model.
For this collection, several well-characterized gray reflective panels were deployed for ground truth
as shown in Figure 4.1-1.
80
Figure 4.1-1. HYDICE ARM site gray panels (photo on right courtesy of MTL).
These panels had nominal reflectance, of 2, 4, 8, 16, 32, and 64%. For evaluation
purposes, the difference in reflectance in each band was computed for each panel. The image
selected from this collect was HYDICE Run29 since it is an image that has proved radiometrically
reliable in previous research work and has only a few clouds in the sky at horizon level (as seen
from ground truth photos). The following are the results of the inversions from sensor radiance to
ground reflectance for HYDICE Run 29.
81
Error in Recovered Reflectance for HYDICE Run 29
Using Default (Truth) Options
0.1
0.05
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2% Delta r
4% Delta r
8% Delta r
-0.05
16% Delta r
32% Delta r
64% Delta r
-0.1
-0.15
-0.2
Wavelength (µm)
Figure 4.1-2. Plot of reflectance error for the inversion to reflectance using the truth
(default) data from the time of acquisition .
Error in Recovered Reflectance for HYDICE Run 29 Using Def_RIMAC_NL Options
0.1
0.05
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2% Delta r
4% Delta r
8% Delta r
-0.05
16% Delta r
32% Delta r
64% Delta r
-0.1
-0.15
-0.2
Wavelength (µm)
Figure 4.1-3. Plot of reflectance error for the inversion to reflectance using the truth
(default) surface elevation, RIMAC for the aerosol visibility, and NLLSSF for the columnar
water vapor.
82
Error in Second Pass Recovered Reflectance for HYDICE Run 29
Using Def_RIMAC_NL Options
0.1
0.05
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2% Delta r
4% Delta r
8% Delta r
-0.05
16% Delta r
32% Delta r
64% Delta r
-0.1
-0.15
-0.2
Wavelength (µm)
Figure 4.1-4. Same options as 4.1-3 after second pass.
Error in Recovered Reflectance for HYDICE Run 29 Using NLavg_RIMAC_NL
Options
0.1
0.05
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2% Delta r
4% Delta r
8% Delta r
-0.05
16% Delta r
32% Delta r
64% Delta r
-0.1
-0.15
-0.2
Wavelength (µm)
Figure 4.1-5. Plot of reflectance error for inversion to reflectance using the image-wide
average NLLSSF for surface elevation, RIMAC for the aerosol visibility, and NLLSSF for the
columnar water vapor.
83
Error in Recovered Reflectance for HYDICE Run 29 Using
All NLLSSF Options
0.1
0.05
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2% Delta r
4% Delta r
8% Delta r
-0.05
16% Delta r
32% Delta r
64% Delta r
-0.1
-0.15
-0.2
Wavelength (µm)
Figure 4.1-6. Run29 plot of reflectance error using NLLSSF for all options.
Error in Second Pass Recovered Reflectance for
HYDICE Run 29 Using All NLLSSF Options
0.1
0.05
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2% Delta r
4% Delta r
8% Delta r
-0.05
16% Delta r
32% Delta r
64% Delta r
-0.1
-0.15
-0.2
Wavelength (µm)
Figure 4.1-7. Run29 plot of reflectance error after second pass with NLLSSF for all options.
84
Error in Recovered Reflectance for HYDICE Run 29 Using NLavg_RIMAC_NL
Options
0.1
0.05
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2% Delta r
4% Delta r
8% Delta r
-0.05
16% Delta r
32% Delta r
64% Delta r
-0.1
-0.15
-0.2
Wavelength (µm)
Figure 4.1-8. Run29 plot of reflectance error using image-wide average NLLSSF for
elevation, RIMAC for visibility, and NLLSSF for columnar water vapor.
Estimated Image-Wide Reflectance Error for HYDICE Run 29 from
Def_RIM_NLLSSF 2nd Pass (average of all panel reflectances less than 18%)
0.02
0.015
0.01
0.005
0
Avg Reflectance Error
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
-0.005
-0.01
-0.015
-0.02
-0.025
-0.03
-0.035
-0.04
-0.045
-0.05
Wavelength (microns)
Figure 4.1-9. Estimated image-wide reflectance error for ground targets of 18% reflectance
or less.
85
0.09
0.08
0.07
0.06
Default
0.05
NLLSSF
Def_RIMAC_NL
0.04
NLavg_RIMAC_NL
NLLSSF 2nd Pass
Def_RIMAC_NL 2nd Pass
0.03
0.02
0.01
0
2
4
8
16
32
64
ARMs Site Gray Panel Nominal Reflectance
Figure 4.1-10. RMS reflectance error comparison for ARM site panels.
Elevation
Aerosol Vis
Water Vapor
Default
Default
RIMAC
NLLSSF
NLavg
RIMAC
NLLSSF
NLLSSF
Default
RIMAC
NLLSSF
2nd Pass
NLLSSF
2nd Pass
Surface
Elevation
(km)
Visibility
(km)
Water
Vapor
(g/cm^2)
0.315
0.315
0.414
0.417
0.315
1.133
58.00
34.56
33.32
47.73
34.62
48.0551
5.146
6.75
6.874
6.803
7.45
6.939
Table 4.1-10. Estimated atmospheric parameters from using different options in the
inversion from sensor radiance to ground reflectance algorithm. Note: The surface elevation is
also coupled to the pressure profile in the radiosonde and the water vapor amount is the total sun-targetsensor column value.
For all combinations of options used in the inversion, the data show good patterns of
agreement that deteriorate somewhat toward the blue region in the first-pass runs. The error in
86
the blue end of the spectrum is largely due to error in the aerosol term. Note how the second pass
through the algorithm, which accounts for aerosol scattering from the surround, dramatically
improved the errors in this region, though some error persists. The fine spectral shape to the error
is most likely to be due to differences between the instrument spectral calibration and the
MODTRAN spectral radiometry models. There also is a bit more error in the second pass with the
RIMAC option. It appears that some error may be due to assumptions about the aerosol
scattering in RIMAC, but the difference in RMS error is only 0.005 reflectance units (which is the
error tolerance for this algorithm).
This test case is presented first since the ARM site HYDICE collection represents the best
available characterized data set. Extensive ground truth, radiosonde, and weather conditions
were logged for this acquisition and the HYDICE sensor has been used for several years, thus
improving the reliability of the data. This being the case, the real benchmark for recovering
reflectances are the default or truth runs. Figure 4.1-9 has been presented to give a metric of how
well the algorithm would perform given a scene with these atmospheric conditions. From Figure
4.1-10, it can clearly be seen that the great majority of the inversions with various options were
equal to or better than using the truth data (within standard error). This result is very important
since the inversion algorithm yielded equivalent or better recovered spectral reflectance curves of
the ground targets as would be retrieved from an expensive and time-consuming extended field
campaign.
It is also readily apparent that the RIMAC compares favorably with the NLLSSF method in
the recovery of ground target reflectance. The aerosol-dependent visibility is somewhat different
between the two (Table 4.1-1), but it must be remembered that the RIMAC visibility is an imagewide parameter and the NLLSSF value is the average of 6 pixels in the center of the gray panels.
The results validate that the RIMAC is a useful tool in acquiring an estimate of aerosol-dependent
visibility when no close estimate of this parameter is available and when fast computation times
are important (NLLSSF has much longer run times).
87
This test also validates the use of an atmospheric PSF based on the MODTRAN-derived
radiometry and the aerosol scattering phase function. The reflectance recovery error in the blue
region was reduced significantly by using the second pass through the algorithm and utilizing the
spatially varying reflectance contribution of the surround to the radiance at the sensor. As a side
note, these trials included an inversion to reflectance which used a simple average over the extent
(11×11 pixels). See Appendix C for a very interesting analysis with this single image sample.
4.2 AVIRIS Boreas Image
This image was acquired by AVIRIS on September 17, 1994 for studies of the boreal
forest in Canada. The ground truth was taken from observation towers at four different sites in the
spectral region from 400-900nm. The chart legends identify each of these ground truth sites by
pixel position (column, row) in the original AVIRIS scene. Because of the clarity of the image, a
test inversion was run in single scattering mode to compare with the multiple scattering runs. Only
one set of options for inverting to reflectance from the single scattering is presented since all
combinations of options yielded virtually identical results. A truth or default test was not performed
with this image since the radiosonde data did not coincide with the acquisition and the truth
aerosol-dependent visibility is unknown. It was assumed that the aerosol model was rural.
Error in Recovered Reflectance for Four Ground Truth Sites in AVIRIS Boreas
Imagery (NL_RIMAC_NL Single Scattering Model)
0.06
0.04
0.02
0
400
450
500
550
600
650
700
-0.02
750
800
850
900
Diff 535_97
Diff 193_256
Diff 250_290
-0.04
Diff 144_195
-0.06
-0.08
-0.1
-0.12
Wavelength (nm)
88
Figure 4.2-1. Boreas plot of reflectance error using the single scattering radiative transfer
model from Equation (2-36).
Error in Recovered Reflectance for Four Ground Truth Sites in AVIRIS
Boreas Imagery (Def_RIMAC_NLLSSF Multiple Scattering)
0.04
0.02
0
400
450
500
550
600
650
700
750
800
850
900
-0.02
-0.04
Diff 535_97
Diff 193_256
Diff 250_290
-0.06
Diff 144_195
-0.08
-0.1
-0.12
-0.14
Wavelength (nm)
Figure 4.2-2. Boreas inversion error using truth (default) elevation, RIMAC for aerosols, and
NLLSSF for columnar water vapor.
Error in Recovered Reflectance for Four Ground Truth Sites in AVIRIS Boreas
Imagery (NLLSSFavg_RIMAC_NLLSSF Multiple Scattering Model)
0.04
0.02
0
400
450
500
550
600
650
700
750
800
850
900
-0.02
-0.04
Diff 535_97
Diff 193_256
Diff 250_290
-0.06
Diff 144_195
-0.08
-0.1
-0.12
-0.14
Wavelength (nm)
89
Figure 4.2-3. Boreas error using image-wide average NLLSSF elevation, RIMAC for
aerosols, and NLLSSF for columnar water vapor.
Error in Recovered Reflectance for Four Ground Truth Sites in AVIRIS
Boreas Imagery (NLLSSF Multiple Scattering Model)
0.04
0.02
0
400
450
500
550
600
650
700
750
800
850
900
-0.02
Diff 535_97
-0.04
Diff 193_256
Diff 250_290
-0.06
Diff 144_195
-0.08
-0.1
-0.12
-0.14
Wavelength (nm)
Figure 4.2-4. Boreas inversion error using NLLSSF for all options.
Error in Recovered Reflectance (Second pass) for Four Ground Truth Sites
in AVIRIS Boreas Imagery (NLLSSF Multiple Scattering Model)
0.04
0.02
0
400
450
500
550
600
650
700
750
800
850
900
-0.02
Diff 535_97
-0.04
Diff 193_256
Diff 250_290
-0.06
Diff 144_195
-0.08
-0.1
-0.12
-0.14
Wavelength (nm)
90
Figure 4.2-5. Boreas inversion error for second pass with all NLLSSF options.
Comparison of Different Inversion Techniques from AVIRIS
Boreas Image in Multiple Scattering Model
0.06
0.05
0.04
NLavg_RIMAC_NL
Def_RIMAC_NL
0.03
NLLSSF
NLavg_RIMAC_NL 2nd Pass
NLLSSF 2nd Pass
0.02
0.01
0.00
Diff 535_97
Diff 193_256
Diff 250_290
Diff 144_195
Truth Pixel Evaluated
Figure 4.2-6. AVIRIS Boreas multiple scattering RMS recovered reflectance errors.
Elevation
Aerosol Vis
Water Vapor
Default
RIMAC
NLLSSF
NLavg
RIMAC
NLLSSF
NLLSSF
NLavg
RIMAC
NLLSSF
2nd Pass
NLLSSF
2nd Pass
Surface
Elevation
(km)
Visibility
(km)
Water Vapor
(g/cm2)
0.315
0.426
0.427
0.324
0.318
69.999
69.999
53.73
69.999
69.71
3.313
3.281
3.26
3.26
3.24
Table 4.2-1. Estimated atmospheric parameters from using different options in the inversion
from sensor radiance to ground reflectance algorithm. Note: The surface elevation is also coupled
to the pressure profile in the radiosonde and the water vapor amount is the total sun-target-sensor column
value.
It is clear from viewing the plots from Figures 4.2-1 to 4.2-5 that the spectral reflectance
errors were nearly identical for all multiple scattering runs without regard to the choice of
atmospheric parameter options. The RMS errors for the single scattering cases (not shown) is
91
actually less than that of the multiple scattering model cases, but the spectral error is considerably
flatter over all the wavelengths in the latter cases. The rounded aerosol shape in the blue region is
not apparent when the multiple scattering radiative transfer model was used. Thus, the multiple
scattering model must be the correct model, but there must be other causes that contribute to the
reflectance recovery error.
The most likely explanation for both the magnitude of the reflectance recovery error and
the "vegetation" shape of the spectral error is that the AVIRIS pixels include darker (less reflective)
ground cover. The area covered by an AVIRIS pixel is a fairly large area of approximately 20
meters square. The total area covered by the spectral reflectance ground truth from the
observation tower was much smaller. The inclusion of dark or shaded soil as well as shaded parts
of the canopy would decrease the total integrated reflectance spectra of a 20-meter-square area;
this is especially true in the more vegetative reflective region above 700nm. The reflectance error
is the difference between the estimated reflectance and the truth reflectance. With the thin
atmosphere evident in Table 4.2-1, it is obvious that not many more photons can be gained at the
sensor (the solar source is largely transmitted). Spectra can only be corrected by mixing the pixel
with appropriate fractions of ground dark cover.
This test case only supports the validity of the RIMAC in that it stays with the NLLSSF
technique for estimating the aerosol-dependent visibility almost to the maximum at the visibility
contained in the MODTRAN-generated LUT.
From the Boreas image, it can plainly be seen that the pixels surrounding the four target
pixels are fairly homogeneous. In this case, it would be expected that the use of the PSF and the
second pass through the algorithm would not improve recovery of the reflectance. This is
observed in Figure 4.2-6 that neither of the two second-pass trials are measurably better than the
first-pass results.
4.3 HYDICE Western Rainbow Image (Low Altitude)
The Western Rainbow HYDICE image set is a sample of the collection that took place on October
21, 1995. This first image set was acquired by the HYDICE sensor at an altitude of 1.52 km and is
referred to as the low altitude set. Two groups of characterized reflectance panels of nominal
92
reflectance 2%, 12%, 24%, 36%, 48%, and 60% were placed in the desert environment of the
Yuma proving grounds in southern Arizona. The MODTRAN LUT used the desert aerosol model.
One group of reflectance panels is referred to as “Old” since these panels have faded due
to exposure to the elements. However, they are still well characterized with field-truth reflectance
measurements at the time of acquisition. The other group is referred to as “New” since these
panels had no apparent fading and were most likely used for the first time in this collection. The
images of the "Old" and "New" panels are actually subimages of a single HYDICE scene; if fact the
panels were located are fairly close to one another. The reason why two subscenes were cut from
the original large scene is that all of the full Western Rainbow HYDICE scenes were reclassified.
Permission was granted for this research to use only these two subscenes; this is also the case
for the high-altitude Western Rainbow scene cr15m50. The following plots are spectral reflectance
errors using different combinations of inversion techniques.
4.3.1 Cr08m33 Old Panels
Error in Recovered Reflectance for cr08m33 Using Default (Truth)
Options with Old Panels
0.1
0.08
0.06
0.04
0.02
2% Delta r
12% Delta r
24% Delta r
0
400
36% Delta r
600
800
1000
1200
-0.02
1400
1600
1800
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.3.1-1. Recovered reflectance error for cr08m33 old panels using all default (truth)
for options.
93
Error in Recovered Reflectance for cr08m33 Using DEF_RIMAC_NL Options
with Old Panels
0.1
0.08
0.06
0.04
0.02
2% Delta r
12% Delta r
24% Delta r
0
36% Delta r
400
600
800
1000
1200
1400
1600
1800
-0.02
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.3.1-2. Recovered reflectance error for cr08m33 old panels using default (truth) for
elevation, RIMAC for visibility, and NLLSSF for water vapor.
Error in Recovered Reflectance for cr08m33 Using NLavg_RIMAC_NL
Options on Old Panels
0.1
0.08
0.06
0.04
0.02
2% Delta r
12% Delta r
24% Delta r
0
400
36% Delta r
600
800
1000
1200
-0.02
1400
1600
1800
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.3.1-3. Recovered reflectance error from cr08m33 old panels using image-wide
average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor.
94
Error in Second Pass Recovered Reflectance for cr08m33 Using
NLavg_RIMAC_NL Options on Old Panels
0.1
0.08
0.06
0.04
0.02
2% Delta r
12% Delta r
24% Delta r
0
400
36% Delta r
600
800
1000
1200
1400
1600
1800
-0.02
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.3.1-4. Second pass recovered reflectance error from cr08m33 old panels using
image-wide average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor.
Error in Recovered Reflectance for cr08m33 Using
NLLSSF Options with Old Panels
0.1
0.08
0.06
0.04
2% Delta r
0.02
12% Delta r
24% Delta r
0
400
36% Delta r
600
800
1000
1200
-0.02
1400
1600
1800
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.3.1-5. Recovered reflectance error from cr08m33 old panels using NLLSSF for all
options.
95
Error in Second Pass Recovered Reflectance for cr08m33 Using
NLLSSF Options with Old Panels
0.1
0.08
0.06
0.04
2% Delta r
0.02
12% Delta r
24% Delta r
0
36% Delta r
400
600
800
1000
1200
1400
1600
1800
48% Delta r
-0.02
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.3.1-6. Second pass recovered reflectance error from cr08m33 old panels using
NLLSSF for all options.
Average Image-Wide Reflectance Error for HYDICE Run cr08m33 from NLLSSF
2nd Pass
(average of Old panel reflectances less than 18%)
0.02
0.015
0.01
Avg Reflectance Error
0.005
0
400
-0.005
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
-0.01
-0.015
-0.02
-0.025
-0.03
-0.035
-0.04
-0.045
-0.05
Wavelength (nm)
Figure 4.3.1-7. Estimated image-wide reflectance error for ground targets of 18% reflectance
or less.
96
0.06
0.05
0.04
Default
NLLSSF
Def_RIMAC_NL
0.03
NLavg_RIMAC_NL
NLLSSF 2nd Pass
NLavg_RIMAC_NL 2nd
Pass
0.02
0.01
0
2
12
24
36
48
60
Yuma Site Gray Panel Nominal Reflectance
Old Panels Run cr08m33
Figure 4.3.1-8. Yuma site run cr08m33 RMS recovered reflectance errors for old panels.
Elevation
Aerosol Vis
Water Vapor
Default
NLavg
RIMAC
NLLSSF
NLLSSF
NLavg
RIMAC
NLLSSF
2nd Pass
NLLSSF
2nd Pass
Surface
Elevation
(km)
Visibility
(km)
Water
Vapor
(g/cm^2)
0.265
0.459
0.496
0.797
0.807
70.00
68.64
52.779
45.798
51.851
2.146
1.571
1.552
1.431
1.435
Table 4.3.1-1. Estimated atmospheric parameters from using different options in the
inversion from sensor radiance to ground reflectance algorithm. Note: The surface elevation is
also coupled to the pressure profile in the radiosonde and the water vapor amount is the total sun-targetsensor column value.
97
4.3.2 Cr08m33 New Panels
Error in Recovered Reflectance for cr08m33 Using Default (Truth)
Options on New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.3.2-1. Recovered reflectance error for cr08m33 new panels using default (truth)
options.
Error in Recovered Reflectance for cr08m33 Using DEF_RIMAC_NL Options
on New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.3.2-2. Recovered reflectance error for cr08m33 new panels using default (truth) for
elevation, RIMAC for visibility, and NLLSSF for water vapor.
98
Error in Recovered Reflectance for cr08m33 Using NLavg_RIMAC_NL
Options for New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.3.2-3. Recovered reflectance error from cr08m33 new panels using image-wide
average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor.
Error in Second Pass Recovered Reflectance for cr08m33 Using
NLavg_RIMAC_NL Options for New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.3.2-4. Second pass recovered reflectance error from cr08m33 new panels using
image-wide average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor.
99
Error in Recovered Reflectance for cr08m33 Using
NLLSSF Options for New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.3.2-5. Recovered reflectance error from cr08m33 new panels using NLLSSF for all
options.
Error in Second Pass Recovered Reflectance for cr08m33 Using
NLLSSF Options for New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.3.2-6. Second pass recovered reflectance error from cr08m33 new panels using
NLLSSF for all options.
100
0.11
0.1
0.09
0.08
Default
0.07
NLLSSF
Def_RIMAC_NL
0.06
NLavg_RIMAC_NL
0.05
NLLSSF 2nd Pass
NLavg_RIMAC_NL 2nd
Pass
0.04
0.03
0.02
0.01
0
2
12
24
36
48
60
Yuma Site Gray Panel Nominal Reflectance
New Panels Run cr08m33
Figure 4.3.2-7. Yuma site run cr08m33 RMS recovered reflectance errors for new panels.
Elevation
Aerosol Vis
Water Vapor
Default
NLavg
RIMAC
NLLSSF
NLLSSF
NLavg
RIMAC
NLLSSF
2nd Pass
NLLSSF
2nd Pass
Surface
Elevation
(km)
Visibility
(km)
Water Vapor
(g/cm^2)
0.265
0.5087
0.514
0.815
0.813
70.00
65.08
48.27
44.888
37.37
2.146
1.53
1.504
1.42
1.413
Table 4.3.2-1. Estimated atmospheric parameters from using different options in the
inversion from sensor radiance to ground reflectance algorithm. Note: The surface elevation is
also coupled to the pressure profile in the radiosonde and the water vapor amount is the total sun-targetsensor column value.
This set of imagery presented a different problem when viewing both the recovered
reflectance and reflectance errors for each of the panels. The first observable artifact is the
"ringing" at the location of the 760nm oxygen band and the major water-vapor absorption features
101
due to a difference between the spectral locations of these features in the HYDICE imagery and
the MODTRAN database. In fact, all recovered spectra for this run are noisy due to this spectral
misalignment. This could very likely be a result of a spectral miscalibration with HYDICE at this
early acquisition date. The channel wavelength band center locations in HYDICE depend on the
atmospheric pressure. This is a consequence of the prism dispersion element used in the
HYDICE instrument. Any error in atmospheric pressure or in the pressure compensation
calculation for HYDICE would be propagated into a spectral shift from the truth band center(s).
All of the first-pass recovered reflectance spectra had errors that increased as the blue
region was approached. The errors in the blue region were decreased significantly by a second
pass through the algorithm. Again, this validates the use of the atmospheric point spread function
to accounting for the target surround contributions. But, the error still indicates that some
parameter(s) were not accounted for or incorrectly calculated.
This error could be due to the MODTRAN database phase function incorrectly modeling
the real atmosphere, background effects (i.e. shape factor) not accounted for in the radiative
transfer equation, the panels having some nonuniform BRDF, or some other radiative transfer
modeling error. Since both "Old" and "New" panel images were obtained from the same image
and are located in the same general, it would be expected that the recovered reflectance error
would be approximately equal for both. This is certainly not the case.
For an example, compare Figure 4.3.1-6 and 4.3.2-6. The error is much greater for the
"New" panel image even though the estimates of atmospheric parameters for each image were
similar. Since the error is negative, it means that more photons are needed at the sensor to
recover a higher reflectance value. Making the atmosphere thinner (i.e., increasing the visibility)
will not increase the flux at the sensor to any great degree since the visibility is already very high.
The most likely path to increase the number of photons in the model is to add a shape factor to the
atmospheric downwelling radiance term (Schott, 1997) and account for solar energy reflecting from
a nearby structure or object onto the panels. By virtue of the error being highest in the blue,
vegetation is excluded from being the object. It is most likely that the newer panels may have
been placed in a small gulley or ravine and some sunlight reflected from nearby (minerals?)
objects onto the new panels. This explanation would also account for the larger recovered
reflectance error being associated with the brighter panels; the higher the reflectance of the panel,
102
the larger the portoin of reflected radiance that would return to the sensor. Presently, the radiative
transfer equations included in this atmospheric correction algorithm are inadequate to compensate
for this effect. A more complex equation must be incorporated which would include the radiative
transfer path from a nearby object scaled by a shape factor that represents (the solid angle
fraction of the hemisphere "seen" by the panels), and scaling (reducing) of the atmospheric
downwelled radiance by the remaining hemispherical fraction.
The shape factor would also need to be known or closely estimated and the spectral
reflectance of the sand would also be required to improve upon the recovered panel spectral
reflectance. Another reasonable solution would be that the BRDF for the new panels was not
uniform and the reflectance decreased steeply in the blue. Moisture on the panels would certainly
affect the BRDF.
Since the error bias is fairly flat and still negative for the "Old" panels, it is safe to assume
that some small shape factor due to the presence of sand mounds could have increased the
photon flux onto the panels.
As in the HYDICE Run 29 case, the RIMAC method is comparable to the NLLSSF method
in that the RMS errors and spectral reflectance errors were usually very similar. The RIMAC
aerosol visibility was always closer to the measured ground truth parameter than the result from
the NLLSSF method. Also the RIMAC performed very well considering that the recovered
reflectance spectra contained so much noise from the spectral misalignment. It should be noted
that the bands used in the RMS error calculations were trimmed from that stated at the beginning
of this section. An effort was made to exclude the bands that exhibited ringing from the absorption
band spectral misalignment where the spectral features from the MODTRAN 4 model(s) were
shifted slightly with respect to the sensor spectra.
Figure 4.3.1-7 has been presented to give a metric of how well the algorithm would
perform given a scene with these atmospheric conditions and the spectral calibration of the
instrument at that time.
4.4 HYDICE Western Rainbow Image (High Altitude)
This is the second Western Rainbow HYDICE image set of the collection effort that took
place on October 21, 1995 at the Yuma proving grounds. This image set was acquired by the
103
HYDICE sensor at an altitude of 3.114km and is referred to as the "high-altitude set". As stated
previously in Section 4.3, both the Old and New panel images from this acquisition were cut from
the same original HYDICE scene. The following plots are the result of different combinations of
parameter estimation techniques used on these images to derive ground reflectance from the
sensor radiance. The MODTRAN LUT generated for the inversion used the desert aerosol model.
4.4.1 Cr15m50 Old Panels
Error in Recovered Reflectance for cr15m50 Using Default (Truth)
Options with Old Panels
0.1
0.08
0.06
0.04
0.02
2% Delta r
12% Delta r
24% Delta r
0
400
36% Delta r
600
800
1000
1200
-0.02
1400
1600
1800
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.4.1-1. Recovered reflectance error for cr15m50 old panels using default (truth)
options.
104
Error in Second Pass Recovered Reflectance for cr15m50 Using Default
(Truth) Options with Old Panels
0.1
0.08
0.06
0.04
2% Delta r
0.02
12% Delta r
24% Delta r
0
36% Delta r
400
600
800
1000
1200
1400
1600
1800
-0.02
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.4.1-2. Second pass recovered reflectance error for cr15m50 old panels using
default (truth) options.
Error in Recovered Reflectance for cr15m50 Using DEF_RIMAC_NL Options
with Old Panels
0.1
0.08
0.06
0.04
0.02
2% Delta r
12% Delta r
24% Delta r
0
400
36% Delta r
600
800
1000
1200
-0.02
1400
1600
1800
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.4.1-3. Recovered reflectance error for cr15m50 old panels using default (truth) for
elevation, RIMAC for visibility, and NLLSSF for water vapor.
105
Error in Second Pass Recovered Reflectance for cr15m50 Using
DEF_RIMAC_NL Options with Old Panels
0.1
0.08
0.06
0.04
0.02
2% Delta r
12% Delta r
24% Delta r
0
400
36% Delta r
600
800
1000
1200
1400
1600
1800
-0.02
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.4.1-4. Second pass recovered reflectance error for cr15m50 old panels using
default (truth) for elevation, RIMAC for visibility, and NLLSSF for water vapor.
Error in Recovered Reflectance for cr15m50 Using NLavg_RIMAC_NL
Options on Old Panels
0.1
0.08
0.06
0.04
0.02
2% Delta r
12% Delta r
24% Delta r
0
400
36% Delta r
600
800
1000
1200
-0.02
1400
1600
1800
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.4.1-5. Recovered reflectance error from cr15m50 old panels using image-wide
average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor.
106
Error in Second Pass Recovered Reflectance for cr15m50 Using
NLavg_RIMAC_NL Options on Old Panels
0.1
0.08
0.06
0.04
0.02
2% Delta r
12% Delta r
24% Delta r
0
36% Delta r
400
600
800
1000
1200
1400
1600
1800
-0.02
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.4.1-6. Second pass recovered reflectance error from cr15m50 old panels using
image-wide average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor.
Error in Recovered Reflectance for cr15m50 Using
NLLSSF Options with Old Panels
0.1
0.08
0.06
0.04
2% Delta r
0.02
12% Delta r
24% Delta r
0
400
36% Delta r
600
800
1000
1200
-0.02
1400
1600
1800
48% Delta r
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.4.1-7. Recovered reflectance error from cr15m50 old panels using NLLSSF for all
options.
107
Error in Second Pass Recovered Reflectance for cr15m50 Using
NLLSSF Options with Old Panels
0.1
0.08
0.06
0.04
0.02
2% Delta r
12% Delta r
24% Delta r
0
36% Delta r
400
600
800
1000
1200
1400
1600
1800
48% Delta r
-0.02
60% Delta r
-0.04
-0.06
-0.08
-0.1
Wavelength (nm)
Figure 4.4.1-8. Second pass recovered reflectance error from cr15m50 old panels using
NLLSSF for all options.
Estimated Image-Wide Reflectance Error for HYDICE Run cr15m50 from NLLSSF
2nd Pass (average of Old panel reflectances less than 18%)
0.02
0.015
0.01
Avg Reflectance Error
0.005
0
400
-0.005
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
-0.01
-0.015
-0.02
-0.025
-0.03
-0.035
-0.04
-0.045
-0.05
Wavelength (nm)
Figure 4.4.1-9. Estimated image-wide reflectance error for ground targets of 18% reflectance
or less.
108
0.06
0.05
0.04
Default
NLLSSF
Def_RIMAC_NL
0.03
NLavg_RIMAC_NL
Default_2nd Pass
NLLSSF 2nd Pass
0.02
Def_RIMAC_NL 2nd Pass
NLavg_RIMAC_NL 2nd
Pass
0.01
0
2
12
24
36
48
60
Yuma Site Gray Panel Nominal Reflectance
Old Panels Run cr15m50
Figure 4.4.1-10. Yuma site run cr15m50 RMS recovered reflectance errors for old panels.
Elevation
Aerosol Vis
Water Vapor
Default
Default
RIMAC
NLLSSF
NLavg
RIMAC
NLLSSF
NLLSSF
NLavg
RIMAC
NLLSSF
2nd Pass
NLLSSF
2nd Pass
Surface
Elevation
(km)
Visibility
(km)
Water Vapor
(g/cm^2)
0.265
0.265
0.479
0.480
0.787
0.787
70.0
66.11
69.83
69.887
69.64
69.64
2.0784
2.103
2.078
2.078
2.02
2.02
Table 4.4.1-1. Estimated atmospheric parameters from using different options in the
inversion from sensor radiance to ground reflectance algorithm. Note: The surface elevation is
also coupled to the pressure profile in the radiosonde and the water vapor amount is the total sun-targetsensor column value.
109
4.4.2 Cr15m50 New Panels
Error in Recovered Reflectance for cr15m50 Using Default (Truth)
Options on New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.4.2-1. Recovered reflectance error for cr15m50 new panels using default (truth)
options.
Error in Second Pass Recovered Reflectance for cr15m50 Using Default
(Truth) Options on New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.4.2-2. Second pass recovered reflectance error for cr15m50 new panels using
default (truth) options.
110
Error in Recovered Reflectance for cr15m50 Using DEF_RIMAC_NL Options
on New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.4.2-3. Recovered reflectance error for cr15m50 new panels using default (truth) for
elevation, RIMAC for visibility, and NLLSSF for water vapor.
Error in Second Pass Recovered Reflectance for cr15m50 Using
DEF_RIMAC_NL Options on New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.4.2-4. Second pass recovered reflectance error for cr15m50 new panels using
default (truth) for elevation, RIMAC for visibility, and NLLSSF for water vapor.
111
Error in Recovered Reflectance for cr15m50 Using NLavg_RIMAC_NL
Options for New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.4.2-5. Recovered reflectance error from cr15m50 new panels using image-wide
average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor.
Error in Second Pass Recovered Reflectance for cr15m50 Using
NLavg_RIMAC_NL Options for New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.4.2-6. Second pass recovered reflectance error from cr15m50 new panels using
image-wide average NLLSSF elevation, RIMAC for visibility, and NLLSSF for water vapor.
112
Error in Recovered Reflectance for cr15m50 Using
NLLSSF Options for New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.4.2-7. Recovered reflectance error from cr15m50 new panels using NLLSSF for all
options.
Error in Second Pass Recovered Reflectance for cr15m50 Using
NLLSSF Options for New Panels
0.1
0.05
0
400
600
800
1000
1200
1400
1600
1800
2% Delta r
-0.05
12% Delta r
24% Delta r
36% Delta r
48% Delta r
-0.1
60% Delta r
-0.15
-0.2
-0.25
Wavelength (nm)
Figure 4.4.2-8. Second pass recovered reflectance error from cr15m50 new panels using
NLLSSF for all options.
113
0.12
0.11
0.1
0.09
0.08
Default
NLLSSF
0.07
Def_RIMAC_NL
0.06
NLavg_RIMAC_NL
Default_2nd Pass
0.05
NLLSSF 2nd Pass
0.04
Def_RIMAC_NL 2nd Pass
0.03
NLavg_RIMAC_NL 2nd
Pass
0.02
0.01
0
2
12
24
36
48
60
Yuma Site Gray Panel Nominal Reflectance
New Panels Run cr15m50
Figure 4.4.2-9. Yuma site run cr15m50 RMS recovered reflectance errors for new panels.
Elevation
Aerosol Vis
Water Vapor
Default
Default
RIMAC
NLLSSF
NLavg
RIMAC
NLLSSF
NLLSSF
NLavg
RIMAC
NLLSSF
2nd Pass
NLLSSF
2nd Pass
Surface
Elevation
(km)
Visibility
(km)
Water Vapor
(g/cm^2)
0.265
0.265
0.479
0.479
0.812
0.810
70.0
66.504
59.79
69.747
49.32
69.58
2.0784
2.097
2.036
2.054
1.986
1.98
Table 4.4.2-1. Estimated atmospheric parameters from using different options in the
inversion from sensor radiance to ground reflectance algorithm. Note: The surface elevation is
also coupled to the pressure profile in the radiosonde and the water vapor amount is the total sun-targetsensor column value.
The amount of spectral ringing in this set of imagery is much less than in the low-altitude
run cr08m33, but some misalignment is still apparent judging from the residual noise in the
spectral reflectance errors for all of the panels. However, the recovered reflectance spectra using
any combination of options was acceptable. The recovered spectral reflectance error was again
114
larger in the blue region after the first-pass inversion. This was especially true for the "New"
panels, and in particular for the 48% and 60% gray panels. Again, this indicates that the "New"
panel scene exhibited nonuniform BRDF or some topography that must be considered using a
more complex radiative transfer equation (as stated at the end of Section 4.3.2). As in previous
examples, Figure 4.4.1-9 &4.4.1-10 are presented as the metric for the expected performance of
the algorithm.
The modeled adjacency effect from the PSF and second pass through the algorithm again
resulted in less error in the blue region. It appears that using an weighted averaged value of the
ground reflectance for the adjacency and the trapping effect radiance results in a better inversion
to ground reflectance than staying with the assumption that the surround reflectance is equal to
the target reflectance (as in the first-pass run). The total RMS spectral error was less for any of
the second-pass combinations with the exception in the reflectance recovery of the nominal 2%
panel.
The RIMAC again had comparable results with the NLLSSF technique for aerosols in the
spectral reflectance recovery and in the total RMS error.
115
5. Summary
A complete modular algorithm for inverting hyperspectral imagery from sensor radiance to
ground reflectance has been constructed and validated. This algorithm incorporates existing and
new methodologies for estimating the atmospheric parameters of surface-pressure depth, aerosoldependent visibility, and columnar water vapor. It provides a much-needed tool for removing the
atmosphere from hyperspectral images and facilitates the analysis of the ground reflectance
imagery.
A new method referred to as the Regression Intersection Method for Aerosol Correction
(RIMAC) has been developed and has peformed favorably when compared to the existing
NLLSSF method. The algorithm option combinations in which the RIMAC has been used has
resulted in very acceptable reflectance imagery. The RIMAC is a very useful module in that it is an
in-scene method that requires no estimate of aerosol visibility by the user and reduces the
computer run times when compared to iterative techniques such as the downhill simplex method in
NLLSSF.
A new concept has been tested by adding an environmental/adjacency effect to the
radiative transfer equation in MODTRAN 4.0 that does not need Monte Carlo methods or ray
tracing to determine the contribution of the surround to the target sensor radiance. It is assumed
that the total environmental or adjacency radiance can be estimated by:
1) Assuming that the MODTRAN-derived sensor radiance from a surround with unit 1.0
albedo is the summation of equivalent radiance values from discrete directions on the
ground that surround the target within a specified projected solid angle. This quantity can
be referred to as the resolved adjacency radiance vector.
2) Convolving a convolution kernel derived from a scattering phase function by a close
estimate of the ground (the first-pass reflectance image). This results in an average
reflectance weighting value for each pixel that can be multiplied by the resolved adjacency
radiance vector to give an estimate of the total scattered radiance contribution from the
surround.
116
A new method and a new term for the radiative transfer equation has been developed for
use during a second pass through an algorithm to derive ground reflectance from sensor radiance.
The resolved adjacency vector is the environmental/adjacency radiance that is multiplied by the
weighted average reflectance of the target surround. The success of the algorithm in reducing the
recovered spectral reflectance error in the blue/green regions of the spectrum and reducing the
total RMS spectral reflectance error has been documented.
The mean error in recovered reflectance for the earth albedo average of 0.18 (or less) is
approximately 0.01 reflectance units (Figure 5-1). This shows that the reflectance recovery
compared to truth is very good for average reflectors on the earth surface. Some of this error can
be attributed to the sample size of the ground truth being unequal to ground-projected detector
pixel on the panel, while the remainder is most likely atmospheric/spectral modeling error.
Another observation can be made from Figure 5-1. One of the reasons that the
reflectance recovery is so accurate for targets of 18% reflectance and below is that the surround
(i.e., average earth reflectance) is usually very close to 18%. Thus this algorithm has no problem
with high reflectance targets themselves, but rather it is the large contrast between the bright
target and the (average 18%) surround with the subsequent complexity of atmospheric scattering
that is difficult to model. The reflectance recovery of very dark targets on a bright reflecting
surround such as sand would also yield higher errors (with a double or multiple scattering
atmosphere). This difficult problem has been addressed by deriving an estimated atmospheric
PSF from the aerosol scattering phase function in this research work.
117
6. Considerations for Future Work
The total inversion from sensor radiance to ground reflectance algorithm was built to be
modular so that new atmospheric parameter methods could be added as they were developed.
However, there is still the consideration of the long MODTRAN run times to construct the LUT for
use in the total inversion process. All of the MODTRAN runs have been run with an 8 stream
multiple scattering option which is 100 times longer than running Isaac's Two Stream multiple
scattering. Further research to find suitable spectral anchor points for a specified sensor range
should be undertaken. If these anchor points could be specified, then the spectral scale factors
could be calculated to convert an Isaac's Two Stream MODTRAN run into a DISORT run. The
radiance error this approximation technique would yield is unknown, but investigation appears
attractive if two orders of magnitude of run time could be taken off the LUT generation needed for
the total inversion algorithm.
From the standpoint of recovering accurate ground reflectances, one of the largest
sources of errors appears to be spectral miscalibration or lack of spectral alignment with the
MODTRAN atmospheric model. The AVIRIS spectral match appears to be very good (Figure 4.24), however the HYDICE spectral error curves do not appear smooth (Figures 4.1-3 and 4.3.1-4).
It is easy to see that the error from the spectral mismatch (the “jaggys” in the recovered reflectance
curve) is almost a large as the mean level error of the reflectance for many of the HYDICE cases
(especially in the Western Rainbow data). Before too much more research effort is devoted to the
atmospheric radiative transfer model included in this total inversion algorithm, a focused study and
correction needs to be developed for spectral alignment or spectral re-calibration. Once a good
spectral correction algorithm adjusts for the spectral misalignment, it will be much easier to analyze
the recovered reflectance error in terms of adjusting or adding some parameter(s) in the radiative
transfer equation.
It is clear in all the plots on recovered reflectance error that most of the error is located in
the blue region which is where scattering due to aerosols are dominant. More work needs to be
done with aerosols in composition, relative abundance, and especially the scattering phase
function of the particles to recover truth reflectances more accurately in the blue-green spectral
region.
118
Further research could also be done in the generation of the atmospheric point spread
weighting function for multiple scattering. Possibly the Henyey-Greenstein function could be
added with input for MODTRAN-generated spectral asymmetry parameters which is all that is
needed for this simple function. The challenge would be to determine what the kernel size should
be to convolve with the first pass reflectance image. Related to this topic is that fact that the
11x11 pixel window size selected for this research work was chosen for convenience of use and
moderate coverage. For multiple scattering solutions particularly in the blue-green region of the
spectrum, it is very likely the window size for the PSF will have to be optimized.
Another module that could be investigated is incorporating a cloud shape factor in the
radiative transfer equation so that inversions to reflectance could be done with imagery where the
sky was contaminated with clouds. In this case the radiance coming from the cloud could be
modeled as:
L cloud
=
E s cos(
σ) τ1 τ 2 ρcloud
π
(6-1)
where Es is the solar irradiance, σ is the solar zenith angle, τ1 is the sun-cloud target path, τ2 is
target sensor path and ρcloud is the average reflectance of the cloud. The cloud shape factor or
fraction of the sky covered in clouds would be F and the downwelling radiance component would
be scaled by 1-F. If the cloud/sky fraction was not known, possibly some type of iterative
technique such as NLLSSF could be utilized to fit the sensor radiance.
These ideas are only a few that are shared in this text. Research into new and faster
techniques is taking place as this document is being written. It is hoped that this algorithm will be
a steeping stone and a useful tool for imaging scientists in the remote sensing field to use and
build on.
119
7. Appendix
7.1 Appendix A: Computation of Off-Axis Solid Angle of Sensor IFOV
Cross-Section
The IFOV (instantaneous field-of-view) of the sensor at some altitude H2 can be thought
of as a projected four-sided pyramid with the peak at the sensor and the base being the groundprojected object pixel at surface elevation H1. A source can be defined as the radiance reflecting
from a surround pixel at distance y from the object pixel. At some layer altitude h, the source
"sees" the altitude projected object as a slice of the IFOV at some angle θ (see Figure 3.5-3). The
angle θ is measured at the center of the altitude projected object pixel at height h between the
optical axis line at nadir to the line projected from the center of the object pixel at height h to the
center of the surround pixel at ground level. The area of the object pixel at height h can be
defined as:
Aobject = ((H2-h)ϕ)2
(A-1)
where ϕ is the IFOV in radians. The squared distance from the object pixel center at height h to
the center of the surround pixel at altitude H1 can be defined as:
r2 = (h-H1)2 + y2
(A-2)
The easy method for this computation is to first compute the total fraction of the
hemisphere that the surround pixel sees of the object pixel at height h. The total area of the
hemisphere is:
Ahemi = 4πr2
(A-3)
Then the fraction of the hemisphere that the object pixel at height h and angle θ is:
120
F
=
A object cos(
A hemi
θ)
=
((H 2 − h ) ϕ )2 cos( θ)
(
4 π (h
− H 1) 2 + y 2
)
(A-4)
Since the total steradians in a hemisphere is 4π, then the solid angle subtended by the
object pixel at height h and angle θ as viewed by the "source" is:
Ω=
F
4π
=
((H 2 − h ) ϕ )2 cos( θ)
((h − H 1)
2
+y2
(A-5)
)
which can be simplified further by using an identity:
Ω=
(( H 2 − h ) ϕ)2 cos 3 ( θ )
(A-6)
((h − H 1) )
2
121
7.2 Appendix B: Addition to Loop.f of MODTRAN 4.0 Source Code
SMSOLL=SMSOLL+SUBINT(INTRVL)*SOLLAY
LOP 0580
160
CONTINUE
LOP 0581
IKP1=IK+1
ANGLE=0.0
TEMP_PHASE=PHASEF(1,V,AH1(IKP1),ANGLE,ARH(IKP1))
GRND_PIX=(H1-H2)*IFOV*0.001
C Test to see if the phase function value is greater than zero.
C This algorithm uses only aerosol 1 which goes from 0-2km in
C altitude.
IF(TEMP_PHASE.GT.0.0)THEN
IF((TEMP_PHASE.GT.0.0).AND.(HOLDER.EQ.0))HOLDER=IK
IF(TX(9).NE.0.0)OPT_UPLYR(IK)=-LOG(TX(9))
DO 162 J=1, 11
DO 163 K=1,11
C
PRINT*, V
C
Calculate the distance from the center (target) pixel
C
on the ground to the surround pixel.
DIST=SQRT((((K-6)*GRND_PIX)*((K-6)*GRND_PIX)+
1
((J-6)*GRND_PIX)*((J-6)*GRND_PIX)))
C
Calculate the slant angle from nadir that the surround
C
pixel is located from the layer height object pixel.
SLANT_ANGLE(IK,J,K)=ATAN(DIST/(AH1(IK)-H2))
C
PRINT*, "DIST=", DIST
C
PRINT*, AH1(IKP1), H1,H2
C
PRINT*, H1-AH1(IK), AH1(IK)-H2
C
Find the solid angle that the "source" surround pixel
C
sees of the layer height object pixel.
OMEGA_PIX=((H1-AH1(IK))*IFOV*0.001)*
1
((H1-AH1(IK))*IFOV*0.001)*
2
COS(SLANT_ANGLE(IK,J,K))*
3
COS(SLANT_ANGLE(IK,J,K))*
4
COS(SLANT_ANGLE(IK,J,K))/((AH1(IK)-H2)*
5
(AH1(IK)-H2))
C
PRINT*, "OMEGA=",OMEGA_PIX
C
Calculate the phase function value for the radiance
C
vector at the layer height (AH1(IK)-H2) coming from
C
ground grid position J, K.
TEMP_PHASE=PHASEF(1,V,AH1(IKP1),SLANT_ANGLE(IK,J,K)*
1
DEG,ARH(IKP1))
C
Multiply the phase function value by the solid angle
C
subtended by the layer height object pixel.
SCAT_FUNC(IK,J,K)=TEMP_PHASE*OMEGA_PIX
C
PRINT*, "PHASE FUNC=",SCAT_FUNC(IK,J,K)
IF((J.EQ.1).AND.(K.EQ.1))THEN
C
PRINT*, AH1(IKP1), TEMP_PHASE, SCAT_FUNC(IK,J,K)
C
PRINT*, OMEGA_PIX
122
ENDIF
163
CONTINUE
162
CONTINUE
C
PRINT*, " "
ENDIF
IF(IK.EQ.IKMAX)THEN
C
Loop to begin summing the unitless scattering phase function
C
values over all the layer heights for the entire 11x11 grid.
DO 164 LAYER_INCR=HOLDER, IKMAX
DO 165 J=1, 11
DO 166 K=1, 11
IF(TX(9).NE.0.0)THEN
C
Calculate the total transmittance from the surround pixel
C
at grid position J, K to the layer height object pixel to
C
the sensor height. This is only the ground-to-sensor
C
transmission; the transmission from sun to ground is
C
assumed to be the same for all the ground pixels on the
C
grid.
TEMP_TAU=EXP(-((OPT_UPLYR(IKMAX)-OPT_UPLYR(LAYER_INCR))
1
/COS(SLANT_ANGLE(LAYER_INCR,J,K))+
2
OPT_UPLYR(LAYER_INCR)))
ENDIF
IF(TX(9).EQ.0.0)TEMP_TAU=0.0
C
Multiply the phase by the total transmission term.
SUM_PHASE_FUNC(J,K)=SUM_PHASE_FUNC(J,K)+
1
SCAT_FUNC(LAYER_INCR,J,K)*TEMP_TAU
IF((J.EQ.1).AND.(K.EQ.1))THEN
C
PRINT*, "SUM PHASE"
C
PRINT*, SLANT_ANGLE(LAYER_INCR,J,K)*DEG
C
PRINT*, AH1(LAYER_INCR+1), OPT_UPLYR(IKMAX)
C
PRINT*, OPT_UPLYR(LAYER_INCR), TEMP_TAU,
C 1
SCAT_FUNC(LAYER_INCR,J,K)
C
PRINT*, SUM_PHASE_FUNC(J,K)
C
PRINT*," "
ENDIF
166
CONTINUE
165 CONTINUE
C
PRINT*," "
164 CONTINUE
ENDIF
C PRINT*, " "
IF(NOPRNT.LE.-1)THEN
LOP 0582
123
7.3 Appendix C: Analysis of the HYDICE Run 29 NLLSSF 2nd Pass
Reflectance Inversion Using An Isotropic Atmospheric PSF.
Much time and effort has been spent attempting to model the atmospheric PSF to more
rigorously implement the radiance contribution at the sensor due to the adjacency effect. This
brief addendum is added to answer the question of: Why go through all the bother of deriving and
extracting the scattering due to the aerosol phase function when possibly a simple averaging
kernel might do just as well (or better)? Figure 7.3-1 shows the results in the form of recovered
reflectance error in the manner of Section 4.
Error in Flat Average Second Pass Recovered Reflectance for
HYDICE Run 29 Using All NLLSSF Options
0.1
0.05
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2% Delta r
4% Delta r
8% Delta r
-0.05
16% Delta r
32% Delta r
64% Delta r
-0.1
-0.15
-0.2
Wavelength (µm)
Figure 7.3-1. 2nd pass recovered reflectance error for HYDICE Run 29 using NLLSSF for all
options and an isotropic averaging kernel for the PSF.
When these results are compared directly with Figure 4.1-7, it can be seen that the simple
kernel actually has a bit less error in the far blue region than when using the phase functionderived kernel. The spectral reflectance errors are approximately equal at around 0.450µm and
124
from there to about 0.8µm the error for the simple kernel is progressively the poorer performer.
Then , an interesting thing happens at around 0.825µm out to about 1.3µm. The recovered
reflectance error becomes much less for the simple averaging kernel. The matches to the truth
reflectance for the 64% gray panel are clearly seen in Figure 7.3-2 with the "flat_avg" curve being
the one derived from the isotropic PSF.
Comparison of Recovered Reflectance for the 64% Gray Panel from
HYDICE Run 29
0.7
0.6
0.5
0.4
Truth
NLLSSF_avg
NLLSSF_Flat_avg
0.3
0.2
0.1
0
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Wavelength (µm)
Figure 7.3-2. The 64% gray panel recovered reflectances from the 2nd pass NLLSSF with the
phase-function PSF and the flat averaging PSF.
It is this researcher's opinion that there are two different things happening at different
places in the spectrum with the effectiveness of the radiative transfer equation process. First, in
the region from 0.4-0.45µm it is quite obvious from looking at the corresponding optical depths in
MODTRAN tape7 from this scene that double and multiple scattering is occurring (Van de Hulst,
1957). The PSF that is derived in this research work models only a single scattering event from
the surround pixel to the sensor. As explained at the end of Section 3.5, the PSF for multiple
125
scattering is much broader and isotropic than the single scattering models. Thus, in this trial, the
isotropic averaging kernel did a better job modeling the multiple scattering events below 0.45µm.
But, as the spectral optical depths decreased with increasing wavelength and a single scattering
effect became dominant, the phase function derived PSF was a better performer. This result
would be expected.
But, explaining the better performance in reflectance recovery from 0.825-1.3µm is
requires some thought into another process. In Figure 3.5-6, it can clearly be seen that the
magnitude of the resolved environmental radiance is very small above 0.8µm. It is certainly not of
the order to make a noticeable difference in the recovery of reflectance. However, refer to
Equation 2-39. The ρavg term was not only used in the environmental/adjacency radiance
parameter. It was substituted for ρ (the ground target reflectance) in the trapping effect radiance
series as well. Here is where the answer may lie.
In theory, the atmospheric PSF when applied to the trapping effect is very broad. The
series in the denominator of equation 2-37 and 2-39 models the multiple reflections of the
"trapped" photons from the surround and the target until they head in the nadir direction toward the
sensor. In a small 11x11 pixel window of the scene it may very well appear that this particular PSF
appears almost isotropic. This may explain why the isotropic averaging PSF worked so well in this
region of the spectrum; it more correctly modeled the trapping effect PSF than the one derived
from the aerosol phase function. Thus, from this one sample image, the conclusion could be
drawn that a ρavg derived from a different PSF must be used in the trapping effect series to
correctly model this process in the radiative transfer equation. Given these preliminary results with
this well characterized hyperspectral image, a further investigation into the trapping effect radiance
PSF certainly is in order.
126
7.4 Appendix D: The User's Manual for the Atmospheric Correction
Algorithm "Total Inversion"
127
User’s Manual for
Total Inversion
A Modular Algorithm for Retrieving Ground Reflectance from Calibrated Sensor Radiance
By Lee C. Sanders and Rolando Raqueño
August 11, 1999
128
TABLE OF CONTENTS
1.
INTRODUCTION______________________________________________________________ 2
2.
ATMOSPHERIC MODTRAN LUT GENERATION STEPS __________________________ 3
2.1.
2.2.
2.3.
3.
3.1.
3.2.
3.3.
3.4.
3.5.
3.6.
CREATE A MODTRAN LUT TREE_______________________________________________4
DISTRIBUTING, MONITORING, RESTARTING, AND VERIFYING THE MODTRAN LUTT ______10
APPLY THE APPROPRIATE SENSOR RESPONSE TO CREATE THE FINAL APDA/GREEN LUT ___21
SETTING UP FOR RUNNING TOTAL INVERSION _______________________________ 27
REQUIRED COMMAND LINE INPUTS _____________________________________________27
FILES NEEDED FOR PROGRAM INPUT ____________________________________________30
OPTIONAL FILES: ___________________________________________________________31
OUTPUTS _________________________________________________________________32
OPTIONAL OUTPUT __________________________________________________________33
OTHER CONSIDERATIONS: ____________________________________________________35
4.
PROCEDURE ________________________________________________________________ 37
5.
APPENDIX __________________________________________________________________ 41
5.1.
SAMPLE SCRIPT ____________________________________________________________41
1
1. Introduction
Total inversion is a modular program designed to be used on
radiometrically calibrated hyperspectral images in order to invert the
sensor radiance to estimated ground reflectance. Since the algorithm
has components that are in IDL, Fortran, C++, non-interactive ENVI
calls, and Unix awk scripts, it is highly recommended that the user set
up this algorithm on a system running Unix with the appropriate
compilers and ENVI installed. No guarantees are forwarded for this
algorithm as it now stands to be installed and used in a Windows, DOS,
or Macintosh OS. It should be noted that it is assumed that the user
already has MODTRAN 4.0 revision 3 installed on their system; it is
necessary since the environment variables for the MODTRAN databases
need to be set for the user's system.
This algorithm has three subsections that are optionally selected to solve
for the parameters of surface-pressure depth (elevation given a pressure
profile in radiosonde), aerosol model-dependent visibility, and columnar
water vapor. The package also includes the Look-Up Table (LUT)
generator for creating the radiometric database needed by Total
Inversion. The Total Inversion algorithm has three different selections for
the radiative transfer equation which depend either the appropriateness
of the model (single or multiple scattering) or whether the user is in the
first pass or second pass of the algorithm. The second pass of the
algorithm is designed to use the weighted average reflectance image to
scale the adjacency and trapping effect radiance.
The first pass of the algorithm produces for output a reflectance cube of
the same dimensions as the input hyperspectral image, an average
2
reflectance image derived from the 11x11 convolved input image, an
image information cube that contains the solved parameters for each
pixel (defined in the header file), a scaled water vapor tiff image, and a
scaled surface elevation tiff image. After running the routine to generate
the atmospheric PSF, the average reflectance image from the first pass is
over-written with the PSF-weighted average reflectance image for input
into the second pass. The second pass algorithm produces a new
reflectance cube and new image info cube.
2. Atmospheric MODTRAN LUT Generation Steps
Modified:
Fri Jun 4 08:56:02 EDT 1999
The following document describes the procedures to create an MODTRAN
atmospheric lookup table (LUT) for use as input into the APDA, GREEN.
and RIMAC methods implemented by Lee Sanders. The current version
supported for this implementation is MODTRAN 4.0 revision 3 for UNIX
workstations (OSF alpha's, Sun sparcs, and LINUX alphas).
Because these lookup tables can take over 1600 MODTRAN runs to
create,
the procedures outlined here have been developed to ease the logistics
of distributing these MODTRAN runs over the different CPU's in the
center. You will have the flexibility of targeting some or all of the
CPU's at your disposal (you should contact the appropriate person
if you plan to use CPU's under the ownership of labs outside of DIRS).
This distribution of processes insures a timely generation of LUT data
and also allows portions of the LUT cases to be processed should an
error be encountered in some of the runs or some of the CPU's become
3
unavailable. Tools have also been developed to check the validity of the
MODTRAN runs
and also monitor the number of MODTRAN cases that have been
completed.
Once the runs have been completed, an assembly process is applied to
the finished lookup table. This will generate a single file that contains all
the necessary data extracted from each of the MODTRAN runs.
The following sections will describe in detail each of the steps that
are necessary to produce a final LUT file. These sections will cover the
following topics
2.1
Creating the MODTRAN Lookup Table Tree (LUTT).
2.2.
Distributing, Monitoring, Restarting, and Verifying the
MODTRAN LUTT
2.3.
Assembling and Applying a Sensor Response the Final LUT file
N.B. Any scripts that are referenced in this document will reside in
/dirs/common/bin. Please make sure that this is in your path and that
it
comes before ~rvrpci/bin (this will insure that you are using the
most stable version of the scripts and not running some experimental
version that we may be working with).
2.1 Create a MODTRAN LUT tree
The process involves creating a directory tree for a given baseline
atmospheric case. This is accomplished by invoking the shell
4
script called "make_modtran_lut_tree.csh" which require two files
as part of its input arguments.
The first part is a baseline MODTRAN card deck and the second part
is a configuration file. The usage is shown below
% create_modtran_lut_tree.csh baseline_case baseline.cdk \
baseline.config
The first argument, "baseline_case", is the root name of the
atmospheric case which will be created (this directory should not
exist yet). This is a directory that will contain subdirectories
of the different MODTRAN cases.
The second argument is a standard MODTRAN input card deck
"baseline.cdk" which will be used as the starting point of all the
subsequent cases defined by the third argument "baseline.config".
Before running "create_modtran_lut_tree.csh" it would be wise to
check if this MODTRAN carddeck will run on all the architectures
that you plan to use. There are some cases in which the code will
run to completion on some architectures (most likely OSF alpha's) and
abort on others (Linux-alpha's and SUN sparc's). While this will
not screen out all cases, it will give an initial indication of
whether or not your carddeck is valid.
N.B. A common error that has been encountered by users is forgetting to
set the multiple scattering flag ( 5th field of the first card) to 1
to activate multiple scattering. If you do not do this, the file
spheralb.dat will not be generated and no spherical albedo data
5
will be available.
This third file configures how specific parameters in the card decks
are modified and how the directory structure of the tree will be
arranged.
The following shows how "baseline.config" might look like
############################################################
#
#Minimum Aerosol Value
#Maximum Aerosol Value
#Aerosol Value Increment
10.0
20.0
10.0
#Mininum Elevation Value
#Maximum Elevation Value
#Elevation Value Increment
0.315 1.215 0.1
#Minimum Water Vapor Value
0.05
#Maximum Water Vapor Value
2.25
#Water Vapor Value Increment
0.2
#Minimum Albedo Value
#Maximum Albedo Value
0.0 1.0
#Albedo Value Increment
1.0
#######################################################
######
6
The entry of the values is free format with leading "#" for comments.
The structure of the tree is currently setup such that the
the subdirectory names at the different depths reflect the parameters
listed below
aerosols
elevations
water_vapor
albedo
Each of the above subdirectories will contain children directories
which have numeric names reflecting the appropriate parameter value
for that case. The range of values and number of directories are
determined by the minimum, maximum, and increment values specified
in
the configuration file ("baseline.config").
As this directory tree is created, the different versions of
"baseline.cdk" are modified and placed in the appropriate directory.
Makefiles are also created at each level to allow the MODTRAN
runs to be started at any level of the tree.
The following is an example run and output of
"create_modtran_lut_tree.csh"
% create_modtran_lut_tree.csh boreas_mult boreas_mult.cdk
boreas_mult.conf
Aerosol directories are [km visibility] 10.0 20.0 30.0 40.0 50.0 60.0 70.0
7
Elevation directories are [km] 0.315 0.415 0.515 0.615 0.715 0.815
0.915 1.015 1.115 1.215
Water vapor directories are [scale factor] 0.05 0.25 0.45 0.65 0.85 1.05
1.25 1.45 1.65 1.85 2.05 2.25
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 0.05]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 0.25]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 0.45]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 0.65]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 0.85]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 1.05]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 1.25]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 1.45]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 1.65]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 1.85]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 2.05]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.315, 2.25]
Water vapor directories are [scale factor] 0.05 0.25 0.45 0.65 0.85 1.05
1.25 1.45 1.65 1.85 2.05 2.25
Processing [aerosol, elevation, water vapor] directory [10.0, 0.415, 0.05]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.415, 0.25]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.415, 0.45]
Processing [aerosol, elevation, water vapor] directory [10.0, 0.415, 0.65]
.
.
.
8
Water vapor directories are [scale factor] 0.05 0.25 0.45 0.65 0.85 1.05
1.25 1.45 1.65 1.85 2.05 2.25
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 0.05]
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 0.25]
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 0.45]
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 0.65]
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 0.85]
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 1.05]
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 1.25]
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 1.45]
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 1.65]
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 1.85]
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 2.05]
Processing [aerosol, elevation, water vapor] directory [70.0, 1.215, 2.25]
N.B. Because the runs may take several days, it is sometimes wise to
create
a MODTRAN LUT tree (LUTT) case that has a "coarse" increment for the
various parameters in the configuration file and an input carddeck that
has a
very coarse sampling of the spectral range. By doing this, you can make
a quick validation to establish that the ranges that you are trying to
use are reasonable and will run to completion. This is especially
helpful if this is your first time running a LUTT because you can
quickly run through all the steps without having to wait for a full
LUT.
Once this process is complete, the different cases can now be run
9
as detailed in Section 2.2.
2.2 Distributing, Monitoring, Restarting, and Verifying the MODTRAN LUT
Now that you have the "tree" created, you will need to start the
different cpu's processing this tree. Before you can do this, you
will need to identify the cpu's that you want to use and create
what is known as an ".rhosts" file in your home directory
(cf. man rhosts). An example ".rhosts" file might look like the
following.
rocky.whatsomattau.edu your_username
bullwinkle.whatsomattau.edu your_username
.
.
.
natasha.whatsomattau.edu your_username
boris.whatomattau.edu your_username
This file essentially allows you to "rsh" commands on other machines.
In other words, you can execute commands on another CPU without
logging in with a password. If you have this file set correctly,
you can test it by giving a command similar to the one below.
% rsh rocky.whatsomattau.edu w
This will execute the "w" command on the CPU
"rocky.whatsomattau.edu"
10
You will only need to setup this file once, but you will need to
update it with new CPU names if you find other CPU's that you want to
be able to use.
Checking for MODTRAN Availability on different CPU's:
Because the state of these machines may not always be known, it would
be
prudent to find out if MODTRAN is accessible in the form of the
command
"modtran4.bat". This can be done by executing the command
called "check_modtran_availability.csh"
The usage of this command is as follows.
% check_modtran_availability.csh cpu_list
The file, "cpu_list", will contain the candidate CPU's that you want
to utilize. As an example, you can group the fast CPU's into
a file called "fast_cpus" such as the one below. (A file called
all_cpus is located in /dirs/common/bin and contains a list,
probably outdated, of some of the CPU's in the Center).
titan
saturn
exeter
defiant
reliant
excelsior
11
cdom
haise
crippen
grissom
lovell
It is customary to put this file inside the root of the MODTRAN tree
directory that will be processed just to keep things in a centralized
location.
Now let us assume that the computer "haise" is not working properly
either because it is offline or the disk containing "modtran4.bat" is not
mounted properly.
When you execute this command using the CPU list "fast_cpus"
% check_modtran_availability.csh fast_cpus
You will get a file called "fast_cpus.good" and "fast_cpus.bad". The file
"fast_cpus.good" will contain the CPU list.
titan
saturn
exeter
defiant
reliant
excelsior
cdom
crippen
12
grissom
lovell
The other file, "fast_cpus.bad" will contain the CPU list
haise
You now have a list of valid CPU's that should, in theory, be able to
process
your MODTRAN runs. As for the CPU's in "fast_cpus.bad", report it to
Bob K. or Sue Michel so that they can make modtran4.bat accessible to
you so that you can utilize these additional CPU's. It may also be
prudent to see
if a particular CPU is heavily loaded with jobs. For this, you can use
the monitor_loads.csh command which will give you the following output.
% monitor_loads.csh
titan : 14:39 up 4 days, 6:32, 12 users, load average: 1.43, 1.28, 1.23
saturn : 14:39 up 4 days, 6:25, 8 users, load average: 0.37, 0.15, 0.13
exeter : 14:39 up 4 days, 6:04, 8 users, load average: 0.00, 0.00, 0.00
defiant : 14:39 up 4 days, 6:04, 1 user, load average: 0.00, 0.00, 0.00
reliant : 14:39 up 4 days, 6:04, 2 users, load average: 0.02, 0.18, 0.18
excelsior : 14:39 up 4 days, 6:04, 8 users, load average: 0.32, 0.35,
0.39
pile1 : 2:31pm up 5:47, 0 users, load average: 0.00, 0.00, 0.00
pile2 : 2:31pm up 5:46, 0 users, load average: 0.08, 0.02, 0.01
pile3 : 2:32pm up 2:36, 0 users, load average: 0.00, 0.00, 0.00
13
cdom : 2:39pm up 4 day(s), 18:08, 1 user, load average: 0.66, 0.80,
0.79
hubble : 2:36pm up 4 day(s), 5:42, 0 users, load average: 0.21, 0.15,
0.16
corona : 2:37pm up 4 day(s), 5:42, 0 users, load average: 0.24, 0.16,
0.16
keyhole : 2:38pm up 4 day(s), 5:42, 0 users, load average: 0.08, 0.02,
0.02
narwhal : 2:41pm up 5:48, 0 users, load average: 0.10, 0.03, 0.02
lacrosse : lacrosse.cis.rit.edu: Connection timed out
haise : 2:40pm up 4 day(s), 6:07, 0 users, load average: 0.11, 0.09,
0.09
crippen : 2:39pm up 4 day(s), 6:06, 2 users, load average: 0.18, 0.09,
0.09
lovell : 2:49pm up 4 day(s), 6:07, 0 users, load average: 0.02, 0.01,
0.01
grissom : 2:41pm up 4 day(s), 6:06, 1 user, load average: 2.86, 2.86,
3.02
carpenter : 2:38pm up 4 day(s), 6:03, 0 users, load average: 0.08,
0.02, 0.02
aldrin : 2:40pm up 4 day(s), 6:05, 0 users, load average: 0.09, 0.02,
0.02
young : 2:41pm up 4 day(s), 6:05, 0 users, load average: 0.11, 0.03,
0.02
cooper : 2:42pm up 4 day(s), 6:05, 0 users, load average: 0.10, 0.02,
0.02
ride : 2:44pm up 4 day(s), 6:03, 0 users, load average: 0.08, 0.02,
0.02
14
schirra : 2:45pm up 4 day(s), 6:03, 0 users, load average: 0.09, 0.02,
0.02
swigert : 2:56pm up 4 day(s), 6:04, 0 users, load average: 0.06, 0.02,
0.02
shepard : 2:56pm up 4 day(s), 6:06, 0 users, load average: 0.06,
0.02, 0.02
slayton : 2:58pm up 4 day(s), 6:05, 0 users, load average: 0.06, 0.02,
0.02
kepler : 2:40pm up 4 day(s), 6:05, 2 users, load average: 0.00, 0.05,
0.29
white : 2:39pm up 2:19, 0 users, load average: 0.05, 0.02, 0.02
conrad : 2:45pm up 2:19, 0 users, load average: 0.08, 0.02, 0.02
Depending on the load averages ( the numbers represent of jobs in
the run queue for the past 5, 30, and 60 seconds ) you may want to
delete a CPU from the list if it already has a job running. You
can start the jobs specifically for a given CPU later when the
process load goes down.
We can now start the MODTRAN runs by
giving the following command.
The command that you will be using initially is called
"distribute_modtran_runs.csh"
The usage for this command is the following
% distribute_modtran_runs.csh cpu_list_file absolute_path_to_tree
15
The cpu_list_file in this case would be the "fast_cpus.good" that has been
screened and generated by "check_modtran_availability.csh"
Now you want to choose a slow CPU that you will not be using for
MODTRAN processing and designate this as your MASTER CPU. It
should
not be in either your "good" or "bad" cpu list. It's role will be
to spawn the different MODTRAN processes so you don't want it to do
any other processing other than just spawning. You can then execute
the following command
The argument absolute_path_to_tree would be something like
/dirs/home/rvrpci/boreas/boreas_mult
From any machine, you should now be able to give the command that
looks like something below.
% distribute_modtran_runs.csh all_cpus.good
/dirs/home/rvrpci/boreas/boreas_mult &
[1] 16897
% Processing titan
[1] 16787
[1] 16813
[1] + Done
start_modtran_runs.csh titan
/dirs/home/rvrpci/boreas/boreas_mult
Processing saturn
[1] 19777
[1] 16566
16
.
.
.
Note that there will be a slight delay between each of the CPU's. This
delay
is intentional in order to keep too many processes from being created at
one
time.
Once the runs have been started, you will want to monitor the progress
of the runs as well as the loads on the CPUS. There are two commands
that you will be able to use for this.
The first command is "verify_modtran_runs.csh". You should run this
in the root directory of the LUT because this will generate a
file called "verify_modtan_runs.log"which looks like the file below
Tue Jun 1 08:52:29 EDT 1999
**** 1680 MODTRAN runs are currently running or have been succesfully
completed ****
**** out of 1680 runs ****
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
17
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
.
.
.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
STARTED on grissom: Sun May 30 23:50:24 EDT 1999 -------------------- :
./aerosols/50.0/elevations/1.215/water_vapor/0.25/albedo/1.0/proces
s.log
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
STARTED on corona.cis.rit.edu: Tue Jun 1 03:17:38 EDT 1999 ----------------- :
./aerosols/70.0/elevations/1.215/water_vapor/0.25/albedo/1.0/proces
s.log
+++++++++++++++
STARTED on lacrosse.cis.rit.edu: Tue Jun 1 04:17:36 EDT 1999 ----------------:
./aerosols/70.0/elevations/1.215/water_vapor/1.85/albedo/1.0/proces
s.log
++++
This log will tell you how many processes have completed or are
18
currently running. The CPU name and starting times of the processes
currently running are also listed. In some cases, the process may
have actually terminated. You can determine this by looking at the
start day and see if it makes sense. If the start date is more
than a day old, then the process probably terminated prematurely.
You can also use "monitor_loads.csh" to check if there is anything
running on the specific CPU's. If the loads are low, then the
MODTRAN process probably aborted.
There are several ways of restarting these aborted processes.
You can restart it by logging into a fast CPU that is not heavily
loaded and going directly to that directory (e.g.
./aerosols/50.0/elevations/1.215/water_vapor/0.25/albedo/1.0/ )
and giving the command
% gmake clean
command followed by a
% gmake &
or if you know that all the processes in the "verify_modtran_runs.log"
are all stalled or dead, you can give the following command.
% clean_stalled_cases.csh
This command will go to all the listed directories and "clean up" the
files so that they can be restarted again. Since you may only have
19
a few cases left to rerun, you may want to send them to a few
fast CPU's using the following command
% start_modtran_runs.csh titan
/dirs/home/rvrpci/boreas/boreas_mult
The usage is similar to distribute_modtran_runs.csh except the first
argument is an actual CPU name instead of a file containing CPU names.
You can also conceivably give an absolute path to the specific directory
of the case (e.g.
/dirs/home/rvrpci/boreas/boreas_mult/aerosols/50.0/elevations/1.215
/water_vapor/0.25/albedo/1.0 ) or you can give the absolute path to the
tree root directory. In the latter case, the process will traverse the tree
until it finds the unprocessed cases.
You will know that you have a fully processed MODTRAN tree when you
have run "verify_modtran_runs.csh" and have a log file that contains
all "+"'s , i.e.,
Tue Jun 1 12:52:29 EDT 1999
**** 1680 MODTRAN runs are currently running or have been succesfully
completed ****
**** out of 1680 runs ****
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
20
.
.
.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++
You can now proceed to the next step which is the assembly of the
final lookup table from the results of all these MODTRAN runs.
2.3 Apply the appropriate sensor response to create the final APDA/GREEN LUT
Once all the data is in place in the modtran tree directories,
the final sensor specific lookup table can now be generated.
21
In order for this to be generated, a sensor response file need
to be created and copied into the MODTRAN case root directory.
Below is a sample head and tail of an AVIRIS response file giving
the number of spectral points followed by the band centers and
FWHM values (in [nm] )at each spectral point.
224
373.4 9.9
382.94 9.82
392.51 9.76
...
2483.6 11.78
2493.43 11.75
2503.26 11.72
The command to start this process given a sensor response called
"baseline.rsp" (which should also be placed in the directory
"baseline_case") is the following
% assemble_lut.csh baseline_case baseline.rsp
This will create a file called "baseline.rsp.lut" in the directory
"baseline_case"
This process will take a while because it has to convolve the
file "spheralb.dat" into a file called "spherical_albedo.dat".
The process is currently serial and has not been parallelized.
22
This will be one of the improvements that needs to be incorporated
in future upgrades.
To check if the LUT is valid, you should run the command
"verify_assemble_lut.csh" which has the following usage.
% verify_assemble_lut.csh boreas_mult.rsp.lut
If the script completes without any errors such as the output below,
the you should now have a lookup table that is compatible with the
APDA and GREEN atmospheric corrections methods.
% verify_assemble_lut.csh hydice_cr15m50.rsp.lut
a = read_aerosol_elevation_water_vapor_data( 'hydice_cr15m50.rsp.lut' )
IDL Version 5.0 (sunos sparc). Research Systems, Inc.
Installation number: 13722-0.
Licensed for use by: RIT Center for Imaging Science
For basic information, enter "IDLInfo" at the IDL> prompt.
% Compiled module:
READ_AEROSOL_ELEVATION_WATER_VAPOR_DATA.
% Compiled module: STRIP_OUT_COMMENTS.
Number of Visibibility Entries =
7.00000
Number of Elevation Entries =
10.0000
Number of Water Vapor Entries =
Number of Spectral Points =
12.0000
209.000
Fri Jun 4 09:43:50 EDT 1999
23
N.B. A log of this output is also saved in the file called
"verify_assemble_lut.log" in your current working directory
(just a reminder, unless specified, you should be working inside
the top of your modtran lut tree).
The rest of this documents contains miscellaneous notes that you
may need to refer to in unusual cases. For the most part, however,
you will only need to follow the steps presented to this point.
In the event that you find any anomalous behaviors, please contact
mailto:rolando@cis.rit.edu and notify him of the specific conditions
that are causing the process to fail.
MISCELLANEOUS NOTES:
Dead Process Cases:
On occasion, you will inadvertently put the master CPU that spawns all
the processes in your CPU list. When you do this, what you will find is
that you will run out of process slots when it tries to process the
different cases. When you do a "verify_modtran_runs.csh" and look at
the file "verify_modtran_runs.log" you will show cases that look like
the following.
.
.
.
:
24
./aerosols/60.0/elevations/0.615/water_vapor/1.45/albedo/0.0/proces
s.log
:
./aerosols/60.0/elevations/0.615/water_vapor/1.45/albedo/1.0/proces
s.log
.
.
.
You would usually see a hostname and start date in these cases. But
because the CPU has maxed out the user process slots, it cannot
generate the appropriate information. Unfortunately, these cases
get tagged as if they executed to completion. So, in order to restore
them back to an uncompleted state, you can use the
"clean_dead_process_cases.csh"
This command will go to all these directories and restore them back
for other CPU's to process. In general, you should not have to use
this command as long as you make sure that you have one CPU as your
master CPU.
Utility routines:
distribute_modtran_runs.csh
start_modtran_runs.csh
verify_modtran_runs.csh
monitor_loads.csh
25
clean_stalled_cases.csh
Utility routines to be implemented:
check_carddeck.csh
# This routine will run a single carddeck
# case on an alpha (titan), sun (crippen),
# and a linux-alpha (pile1)
count_modtran_cases.csh # This routine will look for "makefiles"
# to get a tally of the number of modtran
# runs that need to be executed in a
# particular tree.
According to Lee S. the units of radiance coming out of the tape 7 files
generated by modtran35 is in Watts/(cm^2 sr cm^-1)
26
3.0 Setting Up for Running Total Inversion
There are a number of objects the user must have in a working directory
in order to run Total_Inversion. Some are required and others are
optional depending on what combination of parameter estimation
techniques are selected. Be sure to check the source code package to see
if there are sample files already included that can be edited for the user’s
purpose. The following is a list of objects required for the
total_inversion.pro command line (these are all the files or options that
prompt the user when the program “mk_total_inv_cddk.pro” is run), files
that the program will look for, and a detailed description of the program’s
output(s). If all the required images and file are checked off, the Total
Inversion algorithm can be initiated.
3.1 Required Command Line Inputs
Check over the list in this section and then run the program
“mk_total_inv_cddk.pro” in order to build a carddeck to run Total
Inversion.
O2_image_file -
An PxMxN hyperspectral image in integer (2-byte) data
format and band-interleaved-by-pixel (.bip). This
image
is used for the NLLSSF method in calculating the
surface-pressure elevation from the 760nm oxygen
band.
(Typically a 5x5 convolved version of the original
hyperspectral image [real_image].)
image_file -
An PxMxN hyperspectral image in integer (2-byte) data
format and band-interleaved-by-pixel (.bip). This
image
is used for the NLLSSF method in calculating the
total columnar water vapor from the 940nm band.
27
The original NLLSSF by Green did not specify a
convolved image for this module. If it is desired to
retain the original NLLSSF, the same image file name
as [real_image] may be used here. Otherwise, this file
name should be possibly a 3x3, 5x5 or other convolved
image that is derived from real_image. This option is
included mainly in case the user finds it desirable to
use
a convolved image for an improved SNR.
real_image -
An PxMxN hyperspectral image in integer (2-byte) data
format and band-interleaved-by-pixel (.bip) used for
inversion from sensor radiance to ground reflectance.
image_11x11_file An PxMxN hyperspectral image in integer (2byte) data
format and band-interleaved-by-pixel (.bip). This
image
is used for the NLLSSF method in calculating the
visibilty from a given aerosol type in the spectral
range of 400-700nm. (Typically an 11x11 convolved
version of the original hyperspectral image
[real_image].)
spectral_rsp_file - A 2xP ascii data file defining the Gaussian spectral
response function for each channel. The first column
is the band center wavelength (in nanometers) and the
second column is the Full-Width Half-Maximum of the
Gaussian (in nanometers).
channels the
P; the number of channels (bands in ENVI terms) in
hyperspectral image.
col
the
M; the number of columns (samples in ENVI terms) in
hyperspectral image.
rows -
N; the number of rows (lines in ENVI terms) in the
hyperspectral image.
gain -
The scalar needed to convert the integer (2-byte) digital
count into floating point radiance units. (This value is
28
usually defined in AVIRIS or HYDICE .gain files that
are
received with the images.) If gain value is not
constant,
see below under FILE INPUT and the file gain.dat.
*NOTE: The program does expect a scalar value for
this
term even if you have a pre-determined "gain.dat" file.
If
the file gain.dat exists in the working directory, the
program will use it for input and over-write the scalar
value.
conversion_fac-
Floating point value to convert image radiance units to
Watts/cm^2/sr/nm.
For AVIRIS images: 0.001
For HYDICE images: 0.0001
LUTname-
Filename of the existing 3-D Look-Up Table with
various atmospheric spectral radiometeric parameters
generated by MODTRAN 4.0.
cst_elevation -
Integer value to select the method of surface elevation
in the scene:
-1 Set to default constant (truth or estimated
surface elevation value in km contained in
"surf_scene_info.dat") [Fast]
0 Run NLLSSF for surface-pressure depth,
but
do it once with an image-wide average.
[Medium]
1 Run NLLSSF for surface-pressure depth for
each pixel. [Slow]
wv_switch -
Integer value to select the method of extraction for
columnar water vapor:
0
Set to default constant (truth or estimated
total
columnar water vapor amount) value in
"wv_scene_info.dat". Total columnar water
vapor is defined as the sum of the suntarget
29
and target-sensor vertical water columns in
grams/cm2. [Fast]
1
Run NLLSSF for columnar water vapor for
each pixel. [Slow]
2 Run APDA for columnar water vapor for each
pixel. [Medium]
use_rim_data -
Integer value to select the method of determining
atomspheric visibility:
-1 Set to default constant (truth or estimated
visibility value for the aerosol type) in
"aerosol_scene_info.dat" [Fast]
0 Run NLLSSF to derive visibility for each
pixel.
[Slow]
1 Use RIM method to derive visibility
to be used for the whole scene. [Medium]
inv_selection -
Integer value to select the radiative transfer equation
to use when inverting from sensor radiance to ground
reflectance. For a first run, this option MUST be set
to 0 or -1. If it is desired that the adjacency effect
in the radiative transfer equation use the average
surround reflectance from a previous total inversion
run
(rho_avg_image.bip), total_inversion.pro can be
run a second time with this option set to 1.
-1 Use the Big Equation without Lenv (this option
may
also be selected if the LUT was generated with a
single scattering atmosphere model).
0 Lenv is included in the Big Equation (for use
with a
multiple scattering atmosphere model LUT
only).
1 (Second pass ONLY) Make second pass
through total_inversion.pro and invert
to reflectance using the average reflectance
of the surround and Lenv.
3.2 Files Needed for Program Input
'leaf_water.dat'
A 2xN ascii data file of reflectance for green grass.
30
The first column is wavelength in microns where the
wavelength range is greater than that of spectral
response file and the unit increment is 0.001 micron.
The second column consists of the grass reflectance
where the range of from 0 (no reflectance) to 1.0
(100% reflectance). *NOTE: This file should be an
included part of the Total_Pkg directory.
'surf_scene_info.dat' The 2x3 ascii data file where the first column data
are
the starting values for the NLLSSF for: reflectance
bias,
reflectance gain, and the terrain elevation [km],
respectively. The second column consists of the
respective plus/minus range for each parameter.
'wv_scene_info.dat' The 2x4 ascii data file where the first column
consists
of starting values for NLLSSF for: reflectance bias,
reflectance gain, scalar for liquid water vapor
amount,
and the total columnar water vapor amount
in [g/cm2], respectively. The second column consists
of
the respective plus/minus range for each parameter.
'aerosol_scene_info.dat' The 2x4 ascii data file where the first column
data
are starting values for NLLSSF for: reflectance
bias,
reflectance gain, scalar for liquid water vapor
amount, and visibility in units of [km],
respectively.
The second column consists of the respective
plus/minus range for each parameter.
3.3 Optional Files:
'gain.dat'
-
A 1xP column vector file containing the gain coefficients
for each channel that is multiplied by the DC in the
image
31
to get radiance for each pixel. If this file does not exist,
the gain is set to the required scalar value from the
command line input. This file may be needed for sensors
that have different gain factors due to separate
spectrometers.
'classmap.bsq' -
If you are using the RIMAC option, it is required
that the program find the file 'classmap.bsq'. If the
file does not exist, the program 'm_class.pro' will
do an unsupervised classification and create the
class map file. If a different classification method
than ISODATA in ENVI is wished to be used, the user
must then create a class map (before running this
inversion code) using the method of their choice and
call
the file 'classmap.bsq'. The inversion program will
then
find the user-created file and process it.
3.4 Outputs
If inv_selection=0 or inv_selection=-1 (First Pass)
'ModBE_wAdj.bip' Spectral reflectance image where the reflectance of the
surround was assumed to be the same as the target in
the
radiative transfer equation. Size: MxNxP
'ModBE_rho_av.bip'
If this is after the first pass through the
algorithm and the atmospheric PSF has not yet
been calculated, then this file is the spectral
reflectance image derived from the input 11x11
convolved hyperspectral image. This image will
be over-written when the Phase Function
algorithm is invoked. This image is required
input for a second run of total_inversion.pro
when inv_selection=1.
'image_info2.bsq' An MxNx12 image that contains solved parameters for
each pixel in the hyperspectral image for the first pass
through the algorithm. (See ENVI header at the end of
total_inversion.pro for a description for each layer.)
32
'image_z.tif'
monchromatic
An MxN TIFF image representing a scaled
typographic map of the image scene.
'image_wv2.tif'
monchromatic
An MxN TIFF image representing a scaled
map of the atmospheric water vapor.
If inv_selection=1 (Second Pass)
'ModBE_wNew_Adj.bip' Final spectral reflectance image where the
average reflectance value of the target was used
for the surround reflectance in the radiative
transfer equation.
'*.*.hdr'
ENVI file headers for any of the previously mentioned
reflectance images.
'image_info2_2ndpass.bsq'
'image_z.tif'
monchromatic
An MxNx12 image that contains solved
parameters for each pixel in the
hyperspectral image for the 2nd pass
through the algorithm. (See ENVI header
at the end of total_inversion.pro for a
description for each layer.)
An MxN TIFF image representing a scaled
typographic map of the image scene.
'image_wv2.tif'
monchromatic
An MxN TIFF image representing a scaled
map of the atmospheric water vapor.
3.5 Optional Output
When building the carddeck, the program will ask if the user wishes to
have amoeba iteration information output for one pixel position. If the
user chooses yes [Y], then the IDL keywords SET_PIXEL_COL and
SET_PIXEL_ROW are set. When set, all the information from EACH
iteration in amoeba is output to the screen for this pixel position in the
image. This information can be used for debugging purposes or to plot
33
some of the data to see how well amoeba is fitting the feature curves. It
is strongly suggested that you redirect this data into a file at the start of
the program since it amoeba outputs a great deal of data.
Ex: If the total inversion carddeck is called inversion.cdk:
Enter at the command prompt:
idl<inversion.cdk>output_data.dat
Also, if you selected wv_switch=2, a file called ‘mch.dat’ and ‘refch.dat’
were created that contain a list of the array positions of the measurement
channels and the reference channels, respectively. To find which
channel wavelength these correspond to, simply type
nl –v0 name_of_spectral_response_file
and then the line numbers will correspond to the file numbers. The
channel wavelengths should be within these constraints:
For ‘refch.dat’, the first grouping should be for the atmospheric
window before the 0.94µm water vapor absorption feature between
0.86 and 0.886µm. The second grouping (there are no spaces or
gaps between the groupings) should be between 0.986 and 1.04µm
for the atmospheric window after the 0.940µm water vapor feature.
For ‘mch.dat’, the file numbers should correspond to wavelengths
on the trough of the 0.94µm water absorption feature between 0.93
and 0.96µm.
If you have corrupted data (e.g. noisy bands, pattern noise, bad pixels) in
ANY of these bands in your image, you need to edit those out of your
images (and the .rsp file AND the LUT!).
34
3.6 Other Considerations:
For CIS users, your IDL_DIR variable must be set to the DIRS copy of
IDL in order to enable the non-interactive ENVI calls. As of 7/8/99, you
can change this by typing: setenv IDL_DIR /dirs/archs/rsi/idl_5 at the
command prompt.
This set of programs contains Unix commands that are spawned from
IDL as well as non-interactive ENVI calls. The non-interactive ENVI calls
are only with the RIM option, but Unix commands are laced throughout
the code. If you run on an OS other than Unix, you MUST go through
the source code and see if you can make appropriate changes that work
in that operating system. (Highly suggest a grep on the word "spawn" to
see where the Unix calls are made.) No guarantees on this code if run on
any other OS than Unix.
Also, make sure if you created your .bip images on a Sun, you use a Sun
when you run total_inversion. If you created them on an alpha, make
sure you run total_inversion on an alpha. The header files for the images
are not read in to check the endian type. If you have images created on a
different architecture than you are running this algorithm on, it is easier
to run ENVI on the native architecture, take in the image, and write them
out again. The other option is to use the “swap_endian.pro” routine in
IDL in the source code to swap the endians for each of the input images,
but this option is discouraged unless it is unavoidable.
35
In the event that amoeba does not converge for a pixel, you will see
values of
-1 in the information vector in image_info2.bsq at the same position.
The
program will not abort when this occurs, but the reflectance data (which
will be bogus)will still be saved in image_info2.bsq.
36
4.0 Procedure
This is a suggested procedure to assist the user in running Total
Inversion with a minimum of run-time mistakes that result in restarting
the program. A sample Unix script is included in the Appendix to help
the user along.
1) Create a working directory. Copy the entire contents of Total_Pkg,
Phase_Pkg, and your default value MODTRAN 4.0 carddeck (the one that
the LUT generation was based) into the working directory. Copy the
MODTRAN_Phase folder and RIMAC folder into your working directory.
Compile the code in each of the folders using the provided makefiles.
Copy “rim” into the working directory from RIMAC.
2) Open the LUT in a text editor to determine the range and number of
sensor channels that have radiometric parameters. Then inspect and
change the .rsp file and all the images to be used to make sure the exact
bands (that are in the LUT) are in each one. If one image or .if the .rsp
file is different, the spectral misalignment will cause “ringing” by the
absorption features in the resulting recovered reflectance cube.
3) Start IDL in your working directory and run the program
“mk_total_inv_cddk.pro”. (There are no arguments for this procedure,
but you should have a list from Section 2.0 of the pathnames to the
needed files and images.) Answer all the questions at the prompt. Make
sure the full pathnames of the images or files are typed in if those images
or files are not found in the working directory. After the procedure is
complete, a new file called “inversion.cdk” is created in the working
directory (which the user may rename at their convenience).
37
4) Set up the default (truth or estimated) surface elevation, visibility, and
columnar water vapor values in “surf_scene_info.dat” (1st column, 3rd
row), “aerosol_scene_info.dat” (1st column, 4th row), and
“wv_scene_info.dat” (1st column, 4th row), respectively. If you do not
know the values, refer to the MODTRAN carddeck you copied into the
working directory in step 1 or use the values supplied in the sample files.
5) For debugging purposes or to just get a data file to track amoeba as it
does iterative fits on the absorption features, vi into total_inversion.pro
and go a few lines down from where the procedure begins to where you
see ‘set_pixel_row’ and ‘set_pixel_col’. If you set the row and column of
one pixel of interest in the image you are working on, the fit data will
print to the screen (or may be redirected into a file). Remember that
these variables are array indices, so you have to subtract 1 from the
actual row and column numbers when you set the values for
‘set_pixel_row’ and ‘set_pixel_col’.
6) Because this program has non-interactive ENVI calls, you must run
with the DIRS version of IDL. To do this, simply set the IDL_DIR
environment variable with this command: setenv IDL_DIR
/dirs/archs/rsi/idl_5.
7) Now you should be ready to run the first pass by typing at the
prompt:
idl<inversion.cdk>debug.data
(See step 5 for a description of the redirect into debug.data.)
8) When the first run is complete and you wish to do the second pass
through the algorithm, you may opt to run the Phase Function programs
that generate the new rho_average_image and over-writes the image
38
created during the first pass. The user at this point may also choose to
just use rho_average image from the first pass which is a smoothed
version of the ModBE_wAdj.bip (with an 11x11 averaging kernel). To get
the atmospheric PSF weighted rho average image made, you must start
by editing the file ‘idl_script2’ which is included as a sample. The first
argument for the “mk_rho_avg_image.pro” program is the instantaneous
field of view (IFOV) of the sensor in milliradians. The second argument is
the name of the MODTRAN 4.0 carddeck you copied into the directory in
step 1. The third argument is the name you wish the new MODTRAN 4.0
carddeck that this program creates. The fourth argument is the filename
(full path name) of the spectral response file.
9)..Start the phase program by typing: idl<idl_script2 . The program
will create a new MODTRAN 4.0 carddeck with the information from
image_info2.bsq, run a special MODTRAN 4.0 routine to extract the
scattering phase function data, and then convolves the first pass
reflectance image with the spectral kernels (or scaled atmospheric PSFs).
The output is a reflectance cube called “ModBE_rho_av.bip”. (This
output over-writes the file of the same name created at the end of the
first pass.)
10) When step 9 is completed, simply put inversion.cdk into a text editor
and change the second to last entry (the last numerical entry) from0 or –
1 to a 1. Then run this slightly changed inversion.cdk through the
algorithm again: idl<inversion.cdk>debug_2ndpass.data At the end of
the program, a reflectance cube called “ModBE_wNew_Adj.bip” is created
which is the second pass estimation of the ground reflectance.
39
40
5.0 Appendix
5.1 Sample Script
Script started on Fri Jul 16 11:09:41 1999
Yes, Master [201] % Yes, Master [201] % mkdir Def_cr050
Yes, Master [202] % cp Total_Pkg/* Def_cr050
Yes, Master [203] % mkdir Old
Yes, Master [204] % mkdir New
Yes, Master [205] % cp ../Total_Pkg/* Old
Yes, Master [206] % cp ../Total_Pkg/* New
Yes, Master [207] % cp /dirs/home/lcs3555/Phase_Func/Phase_Pkg_Execute/* Old
Yes, Master [208] % cp /dirs/home/lcs3555/Phase_Func/Phase_Pkg_Execute/* New
Yes, Master [209] % cd Old
Yes, Master [210] % idl
IDL Version 5.0.3 (OSF alpha). Research Systems, Inc.
Installation number: 10230-0.
Licensed for use by: The Digital Imaging and Remote Sensing Lab
For basic information, enter "IDLInfo" at the IDL> prompt.
IDL> mk_total_inv_cddk
% Compiled module: MK_TOTAL_INV_CDDK.
This IDL program constructs an input carddeck for the total
radiometric inversion to ground reflectance algorithm "total_inversion.pro".
NOTE: Before this step is executed, make sure that the bands in
your LUT correspond EXACTLY to those in the image(s).
(e.g. if your LUT only includes bands 5-15, then your
.bip images should only have bands 5-15.
Enter the name of the .bip image to be used for the 760nm
oxygen band surface-pressure depth NLLSSF algorithm.
By Greens example, this image is usually a 5x5 convolved
version of the original.
: /dirs/home/lcs3555/Western_Rainbow/cr15m50/old_cr15m50_5x5_crppd.bip
Enter the name of the .bip image to be used for the 940nm
water vapor band NLLSSF algorithm. This option is included
in the case that the signal-to-noise ratio needs improvement
from the original image. This may be a 5x5 kernel or greater
convolved image from the original. If no improvement in SNR is
needed, simply enter the name of the original .bip image.
: /dirs/home/lcs3555/Western_Rainbow/cr15m50/old_cr15m50_5x5_crppd.bip
Enter the name of the .bip image for inversion from sensor
radiance to ground reflectance.
: /dirs/home/lcs3555/Western_Rainbow/cr15m50/old_cr15m50_crppd.bip
Enter the name of the .bip image to be used for the 400nm-700nm
NLLSSF algorithm. This image is typically an 11x11 convolved
version of the original.
41
: /dirs/home/lcs3555/Western_Rainbow/cr15m50/old_cr15m50_11x11_crppd.bip
Enter the name of the spectral response file.
NOTE: this file must be a two column array with the first column
the center wavelength of the band in nm and the second
column the FWHM in nm. The number of rows must correspond
EXACTLY to the number and placement of the bands in the image.
: /dirs/home/lcs3555/Western_Rainbow/cr15m50/hydice_cr15m50_crppd.rsp
Enter the number of columns in the image:50
Enter the number of rows in the image:50
Enter the number of channels:209
Enter the channel gain term to convert image DC to radiance:75.0
Enter the conversion factor to convert radiance to Watts/cm^2/sr/nm:0.0001
Enter the name of the Look-Up
Table:/dirs/home/rvrpci/yuma/new_yuma_cr15m50/new_yuma_cr15m50.rsp.lut
If the elevation of the scene to be:
Set to default constant (value in "surf_scene_info.dat"); Enter -1
Constant over the scene, but have NLLSSF figure it out from
the scene average pixel; Enter 0
Calculated by NLLSSF for each pixel; Enter 1
: -1
Selection for calculating aerosol visibility:
Set to default constant (value in "aerosol_scene_info.dat")
Enter -1
Use NLLSSF to derive the aerosol visibility;
Enter 0
Use the RIM method to derive the aerosol visibility;
Enter 1
: -1
Selection for columnar water vapor calculation:
Set to default constant (value in "wv_scene_info.dat")
Enter 0
Use NLLSSF to derive the columnar water vapor;
Enter 1
Use APDA to derive the columnar water vapor;
Enter 2
:0
Selection to use average reflectance in Big Equation (1-S*rho_average)
NOTE: This option MUST be set to 0 or -1 for any first run!!
On the first run, total_inversion.pro will make an 11x11
convolved reflectance image. If you wish a second run to
use rho_av; Enter 1
Otherwise, Enter 0 if you wish Lenv in the Big Equation
Enter -1 to use a Big Equation without Lenv.
:0
42
Enter the name of the LUT .config file.
: /dirs/home/rvrpci/yuma/new_yuma_cr15m50/new_yuma_cr15m50.conf
IDL> exit
Yes, Master [211] % setenv IDL_DIR /dirs/archs/rsi/idl_5
Yes, Master [212] % idl<rtcr050>junk
IDL Version 5.0.3 (OSF alpha). Research Systems, Inc.
Installation number: 10230-0.
Licensed for use by: The Digital Imaging and Remote Sensing Lab
For basic information, enter "IDLInfo" at the IDL> prompt.
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
Compiled module: TOTAL_INVERSION.
Compiled module: FIND_BANDPASSES_FOR_NLLSSF.
Compiled module: PRO_CONV_REFL.
Compiled module: READ_AEROSOL_ELEVATION_WATER_VAPOR_DATA.
Compiled module: STRIP_OUT_COMMENTS.
Compiled module: ELEVATION_WATER_SERIES_GIVEN_AEROSOL.
Compiled module: ELEVATION_SERIES_GIVEN_A_WATER_VAPOR.
Compiled module: INTERPOLATE_WATER_VAPOR_SERIES.
Compiled module: INTERPOLATE_ELEVATION_SERIES.
Compiled module: WATER_VAPOR_SERIES_GIVEN_AN_ELEVATION.
Compiled module: INVERT_TO_REFLECTANCE.
Compiled module: CREATE_DYNAM_TIFF.
Compiled module: LINFIT.
Compiled module: WRITE_TIFF.
Program caused arithmetic error: Floating divide by 0
Program caused arithmetic error: Floating underflow
Program caused arithmetic error: Floating illegal operand
Yes, Master [213] % idl<idl_script2
IDL Version 5.0.3 (OSF alpha). Research Systems, Inc.
Installation number: 10230-0.
Licensed for use by: The Digital Imaging and Remote Sensing Lab
For basic information, enter "IDLInfo" at the IDL> prompt.
% Compiled module: MK_RHO_AVG_IMAGE.
% Compiled module: MOMENT.
avg_vis=
70.0000
avg_elevation=
265.009
avg_water_vapor=
0.801049
% Compiled module: MAKE_NEW_CARDDECK_FROM_ORIGINAL.
ML & locator=
33
0
0.00142450
Digital Imaging and Remote Sensing Lab
MODTRAN 4.0
A beta-version developed by Lee Sanders
(lcs3555@cis.rit.edu) for phase function
information extraction.
43
cond_tape10
5252
/dirs/home/lcs3555/Western_Rainbow/cr15m50/hydice_cr15m50_crppd.rsp
50
50
209
% Compiled module: M_CONVERT.
% Compiled module: FILEPATH.
% Compiled module: STR_SEP.
% Restored file: ENVI_UTL.
exit m_convert
Yes, Master [216] % cp rtcr050 rtcr050b
Yes, Master [217] % vi rtcr050b
total_inversion,
'/dirs/home/lcs3555/Western_Rainbow/cr15m50/old_cr15m50_5x5_crppd.bip',
'/dirs/home/lcs3555/Western
_Rainbow/cr15m50/old_cr15m50_5x5_crppd.bip',
'/dirs/home/lcs3555/Western_Rainbow/cr15m50/old_cr15m50_crppd.bip', '/d
irs/home/lcs3555/Western_Rainbow/cr15m50/old_cr15m50_11x11_crppd.bip',
'/dirs/home/lcs3555/Western_Rainbow/cr15m50/h
ydice_cr15m50_crppd.rsp', 50,
50,
209, 75.0000,
0.000100000,
'/dirs/home/rvrpci/yuma/new_yu
ma_cr15m50/new_yuma_cr15m50.rsp.lut',
-1,
-1,
0,
0,
'/dirs/home/rvrpci/yuma/new_yuma_cr15m
50/new_yuma_cr15m50.conf'
~
~ [H [53B"rtcr050b" 1 line, 606 characters [
Yes, Master [220] % idl<rtcr050b>junk_2ndpass
IDL Version 5.0.3 (OSF alpha). Research Systems, Inc.
Installation number: 10230-0.
Licensed for use by: The Digital Imaging and Remote Sensing Lab
For basic information, enter "IDLInfo" at the IDL> prompt.
%
%
%
%
%
%
%
%
%
%
%
%
%
%
Compiled
Compiled
Compiled
Compiled
Compiled
Compiled
Compiled
Compiled
Compiled
Compiled
Compiled
Compiled
Compiled
Compiled
module:
module:
module:
module:
module:
module:
module:
module:
module:
module:
module:
module:
module:
module:
TOTAL_INVERSION.
FIND_BANDPASSES_FOR_NLLSSF.
PRO_CONV_REFL.
READ_AEROSOL_ELEVATION_WATER_VAPOR_DATA.
STRIP_OUT_COMMENTS.
ELEVATION_WATER_SERIES_GIVEN_AEROSOL.
ELEVATION_SERIES_GIVEN_A_WATER_VAPOR.
INTERPOLATE_WATER_VAPOR_SERIES.
INTERPOLATE_ELEVATION_SERIES.
WATER_VAPOR_SERIES_GIVEN_AN_ELEVATION.
INVERT_TO_REFLECTANCE.
CREATE_DYNAM_TIFF.
LINFIT.
WRITE_TIFF.
44
209
% Program caused arithmetic error: Floating divide by 0
% Program caused arithmetic error: Floating underflow
% Program caused arithmetic error: Floating illegal operand
Yes, Master [221] % exit
Yes, Master [222] %
script done on Fri Jul 16 17:27:31 1999
45
8. References
Bohren, C., Huffman, D., Absorption and Scattering of Light by Small Particles, Wiley and Sons,
(1983).
Bruegge, C.J., Conel, J.E., Margolis, J.S., Green, R.O., Toon, G., Carrere, V., Holm, R.G., and
Hoover, G., “In-situ Atmospheric Water-Vapor Retrieval in Support of AVIRIS Validation”, Imaging
Spectroscopy of the Terrestrial Environment, SPIE Vol. 1298, pp. 150-163, (1990).
Clark, R.N., and Roush, T.L., “Reflectance Spectroscopy: Quantitative Analysis Techniques for
Remote Sensing Applications”, Journal of Geophysical Research, 89, 6329-6340, (1984).
Clark, R.N., Swayze, G.A., Gallagher, A., Gorelick, N., and Kruse, F., “Mapping with Imaging
Spectrometer Data Using the Complete Band Shape Least-Squares Algorithm Simultaneously Fit
to Multiple Spectral Features from Multiple Materials”, Proceedings of the Third Airborne
Visible/Infrared Imaging Spectrometer (AVIRIS) Workshop, JPL Publication 91-28, pp. 2-3, (1991).
Clark, R.N., King, T.V.V., Ager, C., and Swayze, G.A., “Initial Vegetation Species and
Senescence/Stress Mapping in the San Luis Valley, Colorado Using Imaging Spectrometer Data”,
Proceedings of the Summitville Forum ‘95, Colorado Geological Survey Special Publication 38, pp.
64-69, (1995).
Crippen, R. E., "The Regression Intersection Method of Adjusting Image Data for Band Ratioing",
International Journal of Remote Sensing, 8, No. 2, pp. 137-155, (1986).
Diner, D.J., Martonchik, J.V., “Influence of Aerosol Scattering on Atmospheric Blurring of Surface
Features”, IEEE Transactions on Geoscience and Remote Sensing, Ge-23, pp. 618-624, (Sept.
1985).
Diner, D.J., Abdou, W.A., Ackerman, T.P., Conel, J.E., Gordon, H.R., Kahn, R.A., Martonchik, J.V.,
Paradise, S.R., Wang, M., West, R.A., MISR: Level 2 Algorithm Theoretical Basis: Aerosol/Surface
Product, Part1 (Aerosol Parameters), JPL Publication D-11400, Rev.A, (December 1, 1994).
Feng, X., “Design and Performance of a Modular Imaging Spectrometer Instrument”, Rochester
Institute of Technology Dissertation, (1995).
Fraser, R.S., Kaufman, Y.J., “The Relative Importance of Aerosol Scattering and Absorption in
Remote Sensing”, IEEE Transactions on Geoscience and Remote Sensing, Ge-23, No. 5, pp. 625633, (1985).
Gao, B., Heidebrecht, K.B., Goetz, F.H., “Derivation of Scaled Surface Reflectances from AVIRIS
Data”, Remote Sensing of Environment, 44, pp. 165-178, (1993).
182
Gao, B.C., Goetz, A.F.H., Westwater, E.R., Conel, J.E., and Green, R.O., “Possible Near-IR
Channels for Remote Sensing Precipitable Water Vapor from Geostationary Satellite Platforms”,
Journal of Applied Meteorology, 32, p1794, (1993).
Goetz, A.F.H., Rowan, L.C., and Kingston, M.J., “Mineral Identification From Orbit: Initial Results
from the Shuttle Multispectral Infrared Radiometer”, Science, 218, pp.1020-1024, (1982).
Goetz, A.F.H., Vane, G., Solomon, J.E., Rock, B.N., “Imaging Spectrometry for Earth Remote
Sensing”, Science, 228, no 4704, pp. 1147-1153, (1985).
Green, R.O., Carrére, V., and Conel, J.E., “Measurement of Atmospheric Water Vapor Using the
Airborne Visible/Infrared Imaging Spectrometer”, American Society of Photogrammetry and
Remote Sensing, Workshop Image Processing, Sparkes, Nevada, (1989).
Green, R. O., Conel, J. E, Margolis, J. S., Bruegge, C. J., Hoover, G. L., An Inversion Algorithm for
Retrieval of Atmospheric and Leaf Water Absorption from AVIRIS Radiance with Compensation for
Atmospheric Scattering”, Proceeding of the Third Airborne Visible/Infrared Imaging Spectrometer
(AVIRIS) Workshop, JPL Publication 91-28, pp. 51-61, (1991b).
Green, R. O., Roberts, D. A., Conel, J. E, “Estimation of Aerosol Optical Depth, Pressure
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