3.3.2 LTSK1
Atmospheric Correction and Reflectance Algorithm
A. Algorithm Outline(1) Algorithm Code:LTSK 1(2) Product Code:ACLC(3) PI names:

G18 Dr. Alfredo Huete(4) Overview of algorithm (Standard level)
Algorithm objectives
The algorithm has the following objective:
To atmospherically correct the composited, normalized radiances for "Rayleigh scattering andozone absorption" on a per-pixel basis.
B. Theoretical Description(1) Methodology and Logic Flow
A general flowchart describing atmosphere correction is presented in figure 1.
Atmospheric correction is performed after the temporal mosaicking to reduce processing loads
and disk space as only one image is processed every composite period (16-day). Rayleighscattering and ozone absorption are corrected with the assistance of ancillary data provided by
GAIT, such as the TOVS data set and GTOPO30. Much of the computation during atmosphericcorrection requires intensive CPU time due to floating point processing.

GLI Algorithm Description

3.3.2-1

Figure 1: Flow diagram for the Atmospheric Correction and Reflectance Algorithm(LTSK1).

GLI Algorithm Description

3.3.2-2

(2) Physical and Mathematical Aspects of the Algorithms
Atmospheric Radiative Transfer Modeling Algorithm

GLI atmospheric correction for land is conducted for Rayleigh scattering and Ozone
absorption. Much of the computation during atmospheric correction requires intensive
CPU time due to floating point processing. Therefore, this algorithm is adopted
methodology by using Look-Up tables (LUTs). GLI land atmospheric correction has
some assumptions as the following items.

* Ozone layers are above molecular layer* All molecules are above aerosols* System of (aerosol layer + ground surface) is assumed as Lambertian* Horizontally homogeneousRayleigh scattering and ozone absorption are corrected with the assistance of ancillarydata NOAA/TOVS data set and GTOPO30. GLI observed reflectance at Top-OfAtmosphere is described as the followi ng equation:

whereis GLI observed reflectance derived from composite algorithm,

ozone transmittance,

is path radiance,

is downward transmittance,

upward transmittance,is spherical albedo, andisisis Rayliegh/Ozone correctedreflectance, which is output of this algorithm. The path radiance, upward and downward
transmittance and spherical albedo were tabulated as functions of optical thickness ofRayleigh scattering (), view and illumination angles. Then, these four values will be
retrieved based on the values offor each pixel at each land channel based on the
pixel elevation, BPF, and STSG (Sun-Target-Sensor Geometry).
relates toelevation through standard pressure and temperature (US62), which can be calculatedwith GTOPO30. And

GLI Algorithm Description

can be derived from NOAA/TOVS data.

3.3.2-3

(2) Calibration and Validation(3) Quality Control and Diagnostic Information:
The algorithm will include a portion dealing with Quality Assurance (QA) issues. The
goal of the QA is to guarantee a better data quality and consistency both spatially and temporally.
Inconsistent products may depict spatial and temporal variations in their values unrelated to
Earth’s surface states and processes. In order to prevent such data consistency problems andpoor data quality of that kind, it is necessary to develop such an algorithm. The GLI atmosphericcorrection will have a built- in QA/QC routine to warrant the data quality. figure 15 shows anexample of such a QA/QC product.

Fill value (no land or failure)
Solar zenith angle > 65
50% of Daily data is missing
View zenith < 45
Highest quality
High solar and view angle

GLI Algorithm Description

3.3.2-4

Figure 15: Example of QA/QC map for GLI(4) Exception Handling
Exception handling is the technique adopted to account for unforeseen situations. Missing
data, missing ancillary data, sensor behavior, floating point error during computation, data out ofrange and so on. In a generic approach, any time the algorithm does not perform as designed, thedata will generate an exception handler. However, during the run the algorithm will use a genericsuccess flag to track the execution of the different parts. Anytime an exception handler isgenerated the pixel value will not be updated (VI's case) and most probably a pre-determinedvalue (-300, -2000) will be appended instead. When the atmospheric correction algorithm fails ascheme was designed that consists of using a set of fill values generated before the compositing
takes place.
(5) Constraints, Limitations, Assumptions
As proposed in phase one, the atmospheric correction will only be concerned with Rayleigh andOzone. Three major shortcomings are noted here:
1) No account for BRDF
2) No account for aerosol over land
2) Not account for water vapor
For the time being we advise that aerosol correction should be applied at a later stage and on a
per demand basis. The BRDF product, by which data will be normalized to "nadir" view angles
could be adopted if research, and funding permits.

GLI Algorithm Description

3.3.2-5

(6) Suggestions and Recommendations
We will be looking into the feasibility, should the need arise, of extending the radiativetransfer methods described in this ATBD in order to potentially accommodate calculations ofaerosol scattering (based plausibly upon current climatological models of tropospheric andstratospheric haze geographic and altitudinal distributions) and water vapor absorption in thevisible and near-IR. Incorporation of the latter effect into our present code would follow thelines we have discussed regarding our treatment of ozone discussed elsewhere in this report. A
full- fledged treatment on a global scale of the extinction of sunlight by small airborne particles
is of course tremendously more difficult to achieve. It's important to realize at this stage, that
correction for aerosol is being applied by the ocean group, and we are identifying means ofcoordinating our work. The data flow-diagram proposed by GAIT and limitations in resources
will make some of these tasks hard to apply. Overall, we are confident in the current status of ourresearch, and hope to extend the GLI contribution to the remote sensing community by devisingbetter and sounder techniques for data production.

GLI Algorithm Description

3.3.2-6

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3.3.2-13

E. APPENDIX 1
Summary of the ESFT Technique: Application to CH4 Absorption in Saturn for the
λ = 1.7 - 2.6 µm Spectral Region
The “exponential-sum- fitting of transmittances” (ESFT) technique has been in generaluse for some time as a numerical means for evaluating absorption coefficients for a variety ofmolecular species. The ESFT method is especially attractive for use in the determination ofeffective absorption coefficients for gases in planetary atmospheres where the multiple scatteringof light by haze and cloud aerosols is important. A host of “band-model” formulations forcalculating the transmittance of sunlight through layers of “clean” gas abound. Suchparameterization of line strength and line spacing for complex absorption bands like thoseexhibited by CH4 and H2 O is quite satisfactory for traditional RLM studies of planetaryatmospheres. But as soon as small particles are envisaged to be mixed-in with the gaseous
constituents, band - model representations of spectral line optical depths are rendered intractablefor use in scattering models.
The underlying rationale for adopting the ESFT approach is as follows: because there isno correlation whatsoever between the magnitude of the absorption coefficient and the frequencyof the radiation, a transformation can be made from k(ν) to k(u), i.e., the absorption coefficient
as a function of frequency can be recast as an “effective” absorption coe fficient, keff , which is afunction of the optical path u. The transmittance is:

T ( u) = ( ∆υ )−1 ∫ exp( − kv u)dυ
The ESFT methodology is not too dissimilar from an approach known as the “kdistribution”. As Goody and Yung (1989) point out, it is sufficient to know what fraction f(k)dkof the frequency domain ν can be represented by absorption coefficients between k and k + dk.
No importance is attached to the location in frequency space of a given value of k. An expression
entirely is:

T ( u) = ∫ f ( k ) exp( − ku )dk
where f(k)dk is the k-distribution function. It is readily recognizable that f(k) is the inverse
Laplace transform of T(u).

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The ESFT approach circumvents the necessity of evaluating the in-verse Laplacetransform. ESFT is inherently a numerical analysis problem, and as such it is intrinsically illconditioned. The specific set of algorithms we used to determine the effective CH4 k’s,
originated with Asano and Uchiyama (1987). They have extended the traditional ESFT technique
to incorporate an iterative non-linear least squares fitting of an ordered set of the effective k’s.
The work of Asano and Uchiyama represents an improvement in a real, practical sense overmany previous implementations of the ESFT technique. Their approach relies on the preselection of a set of weights, wi , such thatT ( u) ≅ ∑ wi exp( − ki u)

These weights can be quite accurately determined once a preferred quadrature scheme isadopted. The heart of the Asano and Uchiyama ESFT procedure is the successive correction of
the ki ‘s for the set of fixed wi ‘s. The virtue of this extended ESFT technique is its ability to finda best-fitting set of ki ‘s for a wide range of absorber amounts, u, which might not necessarily beequally spaced.
Kerola (1989, private contributions) developed the FORTRAN code. It was imp lemented
in conjunction with Tomasko for modeling CH4 absorptions in Titan’s near-IR and visible
spectrum. The program was structured in a fashion to permit direct assessment of the standard
deviation of the transmittances computed via ESFT versus those obtained from wide-bandlaboratory measurements of transmittances made at NASA Ames Research Center. The Ames
laboratory data was generated by Giver (1990). Best-fit values for a monochromatic absorption
coefficient, kν , and a pressure coefficient, yν , were obtained by Giver from comparison of his
experimental data to that given in the Malkmus random-band model. The transmittance in the
Malkmus model is:
1/2 k uv
TM = exp − 2π yv p + 1 − 1  π y v p  The pressure parameter, yν, is the ratio of the line width at 1 atmosphere to the mean line spacing.
It has units of atm -1. The atmospheric pressure is p (in atm). The Ames measurements weremade at 3 temperatures: T= 112 K, 188 K, and 295 K. The full Ames dataset extends from about
3770 cm -1 to close to 9000 cm -1 . The spectral transmittances are recorded at every 10 cm -1 . In

GLI Algorithm Description

3.3.2-15

our Saturn modeling (Kerola, 1994), we performed the exponential-sum fitting on spectralintervals 50 cm -1 wide, spanning the region 3785 - 5995 cm-1 Our efforts included only the low
and mid-temperature Ames datasets. We used a linear extrapolation of the ki ‘s over temperature.
For most of the CH4 bands, the effective levels probed in Saturn’s troposphere are slightly colder
than about 100 K.
As a matter of computational ease and accuracy, the ESFT code was designed to use 8point Gaussian quadrature for the determination of the weights. The most important final outputof the program is a set of 8 best- fit ESFT k’s. These “equivalent” absorption coefficients arearranged so that they are in ascending order (i.e, k1 < k2 < k3 , etc). 8 ki values are generated foreach spectral interval (∆ν = 50 cm -1 ), and for each atmospheric pressure p. For each spectralinterval, TM (ui) is computed using equal spacing in the logarithm of absorber amount. The initial
guess for the absorption coefficient is given by:ki( 0 ) =

ln Ti
ui

60 values of ui were calculated. Two conditions of convergence involve either iterating at most
100 times or ending the iterations when the relative RMS. error is less than 0.2 percent.
Convergence is often quite rapid, taking typically less than a couple dozen iterations for mostspectral bands, and for most pressures.

GLI Algorithm Description

3.3.2-16