MODTRAN Cloud and Multiple Scattering
Upgrades with Application to AVIRIS
A. Berk,* L. S. Bernstein,* G. P. Anderson,† P. K. Acharya,*
D. C. Robertson,* J. H. Chetwynd,† and S. M. Adler-Golden*
R
ecent upgrades to the MODTRAN atmospheric radiation code improve the accuracy of its radiance predictions, especially in the presence of clouds and thick aerosols, and for multiple scattering in regions of strong
molecular line absorption. The current public-released
version of MODTRAN (MODTRAN3.7) features a generalized specification of cloud properties, while the current
research version of MODTRAN (MODTRAN4) implements a correlated-k (CK) approach for more accurate
calculation of multiply scattered radiance. Comparisons
to cloud measurements demonstrate the viability of the CK
approach. The impact of these upgrades on predictions for
AVIRIS viewing scenarios is discussed for both clear and
clouded skies; the CK approach provides refined predictions for AVIRIS nadir and near-nadir viewing. Elsevier Science Inc., 1998
INTRODUCTION
Downward-viewing airborne and spaceborne imaging
spectrometers such as the AVIRIS instrument provide
valuable information on Earth surface properties for a
variety of applications. To properly interpret these measurements, both atmospheric attenuation and path radiances need to be modeled. MODTRAN (Berk et al.,
1989; Kneizys et al., 1988), the Air Force Research Laboratory/Geophysics Directorate moderate spectral resolution (2 cm⫺1) background radiance and transmittance
model, has been widely used to analyze AVIRIS data due
to its computational speed and its ability to model molec-
ular and aerosol/cloud emissive and scattered radiance
contributions as well as the atmospheric attenuation. The
accuracy of MODTRAN, typically 2–5% in transmittance
(Bernstein et al., 1996a; Anderson et al., 1993), has been
confirmed through extensive validation against both measurements and the line-by-line (LBL) high spectral resolution model, FASCODE (Clough et al., 1988).
Recently, several new features have been introduced
into MODTRAN which improve its predictive capabilities under cloudy and/or heavy aerosol loading conditions. The newly released MODTRAN3.7 allows the default model clouds to be varied (altitudes, thickness,
etc.), clouds to be overlaid, and user-specified clouds
to be easily defined via explicit water and ice particle
profiles and spectral optical properties (extinction coefficients, scattering albedos, etc.). In addition, MODTRAN4, which is currently under development, introduces a correlated-k (CK) algorithm which significantly
improves the accuracy of radiance calculations, particularly for multiple scattering in spectral regions containing
strong molecular line absorption.
This paper briefly discusses MODTRAN’s radiance
transport methodology, focusing on scattered radiance
and on the MODTRAN3.7 and MODTRAN4 upgrades.
Initial comparisons between predictions and airborne
measurements of a solar illuminated cumulus cloud top
are presented, and the influence of the CK upgrade on
AVIRIS scenarios is demonstrated with two illustrative
calculations.
RADIANCE CALCULATION OVERVIEW
* Spectral Sciences, Inc., Burlington, Massachusetts
† Air Force Research Laboratory, Geophysics Directorate, Hanscom AFB, Massachusetts
Address correspondence to A. Berk, Spectral Sciences, Inc., 99 S.
Bedford St., #7, Burlington, MA 01803. E-mail: [email protected]
Received 27 May 1996; revised 23 April 1998.
REMOTE SENS. ENVIRON. 65:367–375 (1998)
Elsevier Science Inc., 1998
655 Avenue of the Americas, New York, NY 10010
The radiance observed from a down-looking sensor is
comprised of many components, as illustrated in Figure 1.
Typically, the quantity to be determined from these measurements is the spectrally dependent surface reflectance
function or albedo. For a near-infrared (NIR) and visible
0034-4257/98/$19.00
PII S0034-4257(98)00045-5
368
Berk et al.
Figure 1. Overview of MODTRAN source emission contributions.
(VIS) sensor such as AVIRIS, the dominant contribution
to the observed radiance is the surface-scattered sunlight. In the limit in which atmospheric attenuation and
scatter are negligible, the reflectance function is simply
the ratio of the observed spectral radiance to the solar
spectral irradiance (the normalized ratio includes a factor
of p steradians over the cosine of the solar zenith angle).
In reality, other radiance components and atmospheric
absorption are present. The “data correction” usually involves forward calculations with a comprehensive radiative transport model such as MODTRAN.
The basic approach in MODTRAN is to approximate
the atmosphere and Earth surface as a sequence of quasihomogeneous layers for which the individual layer radiance contributions from each of the source terms depicted in Figure 1 is considered. The surface is treated
as a layer of infinite opacity, an opaque boundary with
variable emissivity/reflectivity. Spherical refraction geometry effects are incorporated into calculation of path
sums and scattering angles, although multiple scattering
radiances are based on plane-parallel models. Approximate corrections are made for the effects of inhomogeneous distributions of temperature and species concentrations within the atmospheric layers. The approximate
layer radiance models used in MODTRAN derive from
the general solution to the radiative transport equation
for an absorbing-scattering atmosphere,
冮
Ta
DI⫽
J(T) dT ,
(1)
Tb
where DI is the radiance contribution from a single layer
along the line of sight, T denotes the transmittance to
the observer, J(T) is the total source term (i.e., the sum
of the individual terms in Fig. 1), and Ta and Tb are the
total path transmittances between the observer and the
beginning and end of the layer, respectively. For notational simplicity, the explicit dependence of DI and the
other quantities in Eq. (1) on frequency m is omitted, and
all quantities are 1 cm⫺1 interval averages unless otherwise noted. The total path radiance is obtained by summing the layer radiances along the line of sight.
Equation (1) is exact for monochromatic radiation, following from formal integration of the differential expression for I (Chandrasekhar, 1960), and is the starting
premise for band model formulations; in both cases, the
problem is to determine the appropriate layer and/or
layer boundary transmittances and source terms.
Transmittance Calculation
In MODTRAN3.7 and the developmental MODTRAN4
the band model transmittance algorithms are essentially
the same as in previous versions. The transmittance is
calculated for each 1 cm⫺1 bin using: 1) band model
parameters for molecular line absorption based on HITRAN96 (Rothman, personal communication, 1996; Rothman et al., 1992), with a approximate treatment of line
tails extending across multiple bins; 2) extinction coefficients for continuous and quasicontinuous molecular absorptions, such as the H2O (Clough et al., 1989) and N2
continua, CFC and HNO3 vibrational bands, and electronic transitions (Anderson et al., 1990) of O2, O3, etc.;
and 3) extinction coefficients for water particulates (i.e.,
clouds, fogs, and rain) and aerosols. Total transmittance
is calculated as a product of individual species transmittances, and multilayer paths are modeled using Curtis–
Godson averaging (Curtis, 1952; Godson, 1953). Calculations of equivalent widths, line tail contributions, and
Lorentz half-width temperature scaling have recently
been refined. Details of the MODTRAN band model
transmittance algorithm in general and recent refine-
Atmospheric Radiation Modeling Application to AVIRIS
369
Planck blackbody function. In practice, due to temperature variations within the layer and the steep temperature dependence of the Planck function, converging the
calculation through fine layering is very computationally
intensive. An alternative approach, widely used in monochromatic codes (Clough et al., 1992), is to use coarser
layering (⯝1 km resolution in the lower atmosphere)
with the “linear-in-tau” approximation. [A similar approach
for band models has been suggested by Cornette (1992)].
In this approximation, the source variation within a layer
is given by
Ds⬘
DJ,
J(s⬘)⫽Ja⫹
Ds
(3)
Ds⫽1n(Ta/Tb),
(4)
Ds⬘⫽1n(Ta/T),
(5)
where
⫺1
Figure 2. Comparison of MODTRAN4 to FASCODE 5 cm
transmittances for a nadir view through the U.S. Standard
Atmosphere from 20 km altitude. Differences between model
predictions are offset by 1.2.
ments in particular are found in recent articles and reports (Bernstein, 1996a; Berk, 1996).
To illustrate the accuracy of the band model transmittance approach, MODTRAN4 and FASCODE transmittances are compared at 5 cm⫺1 resolution (FWHM)
between 1600 nm and 2500 nm in Figure 2. FASCODE
itself has been extensively validated directly against measurements and has an accuracy of better than 1% for atmospheric transmittances. The current calculations were
performed for a nadir view from 20 km altitude using
the U.S. Standard Atmosphere. In regions of moderate
transmittance, differences between FASCODE and MODTRAN predictions fluctuate about the zero line with
maximum deviations of approximately 0.03. These results
represent an improvement over earlier comparisons between MODTRAN and FASCODE for multiple layers
paths (Bernstein, 1996a). The improvements are a result
of an increased spectral resolution in the treatment of
line tail absorption within MODTRAN. The remaining
discrepancies are attributed to underprediction of line
overlap and oversimplification of line strength distributions. The largest differences in Figure 2 are halved if
two pairs of line strength and line spacing band model
parameters are used instead of one pair to model the
transmittance in each spectral bin. Incorporation of this
upgrade and other refinements to the band model transmittance model is part of an ongoing effort.
Radiance from Direct Thermal Emission
For sufficiently fine layering, any variation in the source
term within the layer can be made negligible, and Eq.
(1) simplifies to
DI⫽(Ta⫺Tb)J,
(2)
where, for thermal emission, J is proportional to the
and DJ⫽Jb⫺Ja. Ds⬘ represents an effective incremental
optical depth from boundary a and Ds is the total effective optical depth across the layer. For monochromatic
radiation (i.e., obeying Beer’s law), Ds⬘ is the actual optical depth, and Eq. (3) is nearly exact for thermal emission when the temperature in the layer varies linearly
with density and scattering is negligible. Substituting
Eqs. (3), (4), and (5) into Eq. (1) yields the following
expression for the layer radiance contribution:
1⫺e⫺Ds
DI⫽Ta Ja⫺e⫺DsJb⫹
DJ .
Ds
冢
冣
(6)
Although it is not as rigorous when applied to nonmonochromatic band model calculations such as those in
MODTRAN, the linear-in-tau approximation still gives
good results and has therefore been chosen for both the
direct thermal emission and the two-stream (thermal and
solar) multiple scattering radiance components in MODTRAN3.7. In particular, Eq. (6) has the correct behavior
in the following limits: 1) as Ds→∞, the opaque limit is
attained, DI→Ta Ja and only emission from the front surface of the layer is observed; and 2) for a constant source
function, Ja⫽Jb, Eq. (2) is recovered, that is, DI⫽(Ta⫺Tb)
Ja. The linear-in-tau expression does not reduce to the
correct weak-line limit for a non-uniform species distribution, and MODTRAN adjusts the direct thermal far
boundary source term Jb to account for this (Clough et
al., 1992).
For more accurate results, a correlated-k (CK) approach, described later in this article, is used to convert
the MODTRAN band model calculations into a set of
equivalent monochromatic calculations. In this way, the
full accuracy of the linear-in-tau approximation is preserved. Other successful approaches have also been explored (Bernstein, 1995; Berstein et al., 1996a).
Accounting for scattering, the direct thermal source
function for Eq. (6) is given by Eq. (7):
370
Berk et al.
J⫽(1⫺x)B(H),
(7)
where x is the single scattering albedo and B(H) is the
Planck blackbody function evaluated at the local temperature H.
For monochromatic calculations, the single scattering albedo is rigorously defined for a homogeneous layer
by Eq. (8):
Dss
,
x⫽
Dss⫹Dsa⫹Dsm
(8)
where Dss is the layer vertical scattering optical depth,
Dsa is the vertical absorption optical depth due to particle and molecular continuum absorption, and Dsm is the
spectrally rapidly varying vertical optical depth due to molecular line absorption. The problem in defining x for a
band model code is in determining an effective spectralinterval average value for the molecular optical depth.
This can only be done approximately; no single effective
value Dsm can be determined a priori that accurately reproduces exact monochromatic results averaged over the
finite spectral interval. The approach adopted in MODTRAN is to define an effective molecular optical depth
using
Dsm⫽ln(Tm,a/Tm,b) ,
(9)
where Tm,a and Tm,b are the cumulative molecular band
model transmittances to the bottom and top layer boundaries for a vertical path from the ground.
This approach for defining molecular line absorption
layer vertical optical depths preserves the correct qualitative effects of molecular line absorption on scattering;
however, it can produce poor quantitative results if the
monochromatic Dsm’s exceed Dsa in a large fraction of
the spectral interval. In the AVIRIS down-looking sensor
scenario, if a given spectral interval contains one weak
line and one strong line, the strong line can be absorbed
in the top part of the atmosphere, while the weak line
can penetrate all the way down to the surface and back
to space. Under this circumstance, the effective molecular optical depth for the bottom layers of the atmosphere
are incorrectly represented by Eq. (9). This problem is
addressed in the CK approach discussed later.
Atmospheric Scattering of Thermal and
External Sources
The radiance sources in Figure 1, other than direct thermal emission, involve scattering of radiation originating
from other layers or external sources. Both thermal (skyshine and earthshine) and solar (or lunar, if specified) radiation are scattered by the Earth’s surface and by atmospheric particulates such as background and volcanic
aerosols, water and ice cloud particles, and boundary layer
fogs. Molecular or Rayleigh scattering is more important
at shorter wavelengths (NIR and UV/VIS) where the solar
contributions dominate. MODTRAN models the single
scatter solar radiation accounting for the solar spectrum
(Kurucz, 1992; 1994), the curvature of the Earth, refractive geometry effects (Ridgway et al., 1982; Gallery et al.,
1983; Kneizys et al., 1983), and a general scattering phase
function. Multiple scattering, which is much more difficult
to treat accurately, is handled with a plane-parallel atmospheric approximation (Anderson, 1983) and a Henyey–
Greenstein phase function. The Henyey–Greenstein functions are good for modeling fluxes, but less accurate when
used to predict radiant intensities.
Single Scattering Source Term and Layer Radiance
The single scattering source term is given by Eq. (10):
T
J⫽xP(h)I0 0 ,
T
(10)
where P(h) is the scattering phase function at scattering
angle h, I0 is the irradiance at the top of the atmosphere,
T is the transmittance from the scattering point to the observer, and T0 is the transmittance for the L-shaped path
from the external source to the observer. Rather than using the linear-in-tau approximation for J, MODTRAN assumes that log(T0) varies linearly with Ds⬘ and that xP(h)
is constant within the layer; this yields the correct monochromatic single scatter radiance for an isolated layer.
The approach was validated by comparison to UV measurements in the upper stratosphere (Minschwaner et al.,
1995). The resulting layer radiance is given by Eq. (11):
DI⫽Ta
冤DsDs ( J ⫺J e )冥 ,
a
b
⫺Ds
(11)
0
where Ds0 is the difference between log(T0) for the path
through scattering point a and log(T0) for the path through
scattering point b.
Multiple Scattering Source Term and Layer Radiance
MODTRAN provides two models for evaluating the scattered thermal and multiply scattered solar radiances: a
simple but faster two-stream model (Isaacs et al., 1987;
1986; Meador and Weaver, 1980) and the more accurate
but slower DISORT N-stream discrete ordinate method
(Stamnes et al., 1988; Stamnes and Swanson, 1981; Goody
and Yung, 1989). Both models calculate upwelling F⫹ and
downwelling F⫺ fluxes at layer boundaries by performing
lower and upper hemispherical integrations. The source
term for scattered thermal and multiply scattered solar radiance is a product of the scattering albedo and the flux
scattered towards the observer. In the two-stream
method, all hemispherical integrations are performed
with a 1-point Gaussian quadrature ignoring azimuthal
dependencies, and J has the form as shown in Eq. (12):
x
J⫽ [(1⫺b)F⫺⫹bF⫹] ,
p
(12)
where coefficient b is the integral of the scattering phase
function over the lower hemisphere at the path zenith
angle (Wiscombe and Grams, 1976). DISORT performs
Atmospheric Radiation Modeling Application to AVIRIS
the zenith integrations using N/2 Gaussian quadrature
points. Both methods assume Beer’s law extinction, an
inadequate approximation for MODTRAN’s band models.
The CK approach developed for MODTRAN4 overcomes
this limitation, as described below.
371
nential) behavior of the transmittance, whereas band
model transmittances do not follow Beer’s law. To properly integrate MODTRAN with these scattering algorithms, the transmittance for a given layer must be expressed as a weighted sum of exponential terms:
imax
MODTRAN3.7 CLOUD/RAIN
MODELS UPGRADE
The cloud/rain models in MODTRAN3.7 (Berk, 1995)
allow for generalized specification of layering and optical
and physical properties as well as the presence of multiple overlapping and nonoverlapping clouds. The cloud
models affected are the MODTRAN cumulus and stratus
clouds, both with and without rain (cloud/rain models
1–10). The upgrades include: 1) adjustable cloud parameters (thickness, altitude, vertical extinction, column
amounts, humidity, and scattering phase functions); 2)
decoupling of clouds from aerosols; 3) introduction of ice
particles; 4) user-defined water droplet, ice particle, and
rain rate profiles; 5) user-defined cloud spectral properties; and 6) output of cloud/rain profiles and spectral data
to the “tape6” file.
The decoupling of the cloud and aerosol models has
a number of implications. Clouds and aerosols can coexist at a single altitude, or clouds can be modeled with no
aerosol profiles included. When clouds and aerosols coexist, the cloud water droplets, cloud ice particles, and
aerosol particles may all have different scattering phase
functions. The single scatter solar contribution for each
component is properly combined. However, for multiple
scattering a single effective phase function is required. It
is defined using the “scattering optical depth”-weighted
Henyey–Greenstein asymmetry factor which was previously used to combine only the aerosol and molecular
multiple scattering contributions (Isaacs et al., 1986).
Cloud profiles are merged with the other atmospheric profiles (pressure, temperature, molecular constituent, and aerosol) by combining and/or adding new
layer boundaries. Any cloud layer boundary within half a
meter of an atmospheric boundary layer is translated to
make the layer altitudes coincide; new atmospheric layer
boundaries are defined to accommodate the additional
cloud layer boundaries.
ADDITION OF A CORRELATED-k CAPABILITY
TO MODTRAN
Addition of a CK capability (Lacis and Oinas, 1991; Goody
and Yung, 1989) in MODTRAN4 provides an improved
means for calculating atmospheric radiances including the
effects of multiple scattering (Bernstein et al., 1996b).
Since MODTRAN computes molecular transmittance using a narrow-band model, it is not suitable for direct interfacing with standard multiple scattering algorithms.
This is because these algorithms require Beer’s law (expo-
T⫽ 兺 Dgi e⫺Kiu ,
i⫽1
(13)
where the Dgi are weighting factors and the Ki are monochromatic absorption coefficients.
The use of real time LBL simulation or inverse Laplace transformation to derive the (Dgi, Ki) pairs during
a MODTRAN run is much too slow to be of practical
value. Creation and storage of temperature and pressure
dependent CK look-up tables for each molecule contributing to each 1 cm⫺1 spectral bin is also not a practical
alternative. The basic approach and key assumptions of
the CK implementation developed for MODTRAN4 are
described below; further details are provided elsewhere
(Bernstein et al., 1996b).
MODTRAN’s transmittance model for a single molecular species is based on four parameters: 1) the integrated line strength S in each 1 cm⫺1 spectral bin, 2) an
effective number of equivalent line n in the bin, 3) the
average pressure-broadened Lorentz line width cL, and
(4) the Doppler line width cD. In MODTRAN’s band
model algorithm, the transmittance is approximated from
these parameters using analytical expressions for a set of
n identical lines randomly located in the bin. In MODTRAN4, the cumulative distribution g(k) of absorption
coefficients k associated with this set of lines serves as
the starting point for the CK calculation.
From g(k) distributions for selected values of the
line parameters n, cL, and cD, a “k-distribution” table of
discrete g,k pairs was constructed. (Different values of S
were not required, as they simply scale the k values.)
The ranges of line parameter values covered by this table
were chosen to be compatible with radiative transfer calculations extending up to 70 km altitude, covering the
spectral range from 0 to 25,000 cm⫺1 (above 25,000 cm⫺1
all molecular absorption in MODTRAN is treated as
continua), and including all of the MODTRAN atmospheric species. The g values were selected so that the
k-distribution with the largest dynamic range in k would
have each decade of k values covered by approximately
three gi,ki pairs. This tabulation required a fixed grid of
33 g values ranging from g0⫽0 to g32⫽1. For low altitude
paths, fewer g values are required, and an approach for
optimally combining the subintervals is presently being
developed.
At run time, the line parameters are calculated for
each layer and spectral bin, and interpolated between the
table values to generate the appropriate k-distributions.
The effective absorption coefficients Ki for the subintervals
Dgi⫽gi⫺gi⫺1 [see Eq. (13)] are defined to insure that the
integral averaged subinterval transmittances are preserved.
372
Berk et al.
When only one molecular species is present in a spectral bin, the CK calculation of transmittance is straightforward and matches the band model. A single pseudogas
can be defined for multiple molecular species with fixed
mixing ratios (Goody et al., 1989). Varying mixtures of individual species are more difficult to model. Generally, the
assumption is made that absorption among different molecular species is uncorrelated, or equivalently that their
transmittances are multiplicative. In terms of the k-distribution formulation, the combined transmittance for M
overlapping gases is given by the multiple sum of the M
distributions. This approach is computationally very intensive, requiring iMmax separate calculations. To alleviate
the computational burden, the iMmax absorption coefficients
can be ordered and combined into a smaller set (Lacis
and Oinas, 1991). For the MODTRAN4 CK implementation, an alternative, approximate approach is used. The
net MODTRAN band model transmittance (assumed to
be the product of the individual species transmittances)
is calculated for each layer. A CK calculation is then performed and iteratively adjusted to match this net transmittance. For the CK calculation, effective species-averaged values for cL and cD and a first-guess value for n,
the effective number of equivalent lines, are determined.
n is then adjusted and the K’s recalculated until the CK
transmittance matches the band model value.
The resulting single-layer K’s are combined assuming perfect spectral correlation among the subintervals to
give the total path transmittance as shown in Eq. (14):
imax
T⫽ 兺 Dgi e⫺兺j Kijuj ,
i ⫽1
(14)
where j denotes the sum over layers. This approach eliminates the need to model the optical path as an equivalent homogeneous layer using Curtis–Godson averaging.
Comparisons performed to date between MODTRAN4 and FASCODE for vertical paths indicate that
MODTRAN4’s transmittance accuracy is comparable to
that of MODTRAN3.7, consistent with proper matching
of a single-layer band model transmittances by the CK
approach. Additional comparisons over a wider range of
geometries are planned.
DATA-MODEL COMPARISONS FOR A
SUNLIT CLOUD
As part of the initial validation of MODTRAN’s multiple
scattering algorithms, comparisons were made between
spectral measurements of a sunlit cumulus cloud top (Malherbe et al., 1995), predictions from MODTRAN4, and
calculations from another radiative transport code, NAULUM (Malherbe et al., 1995). The measurements were
performed by the ONERA and CELAR research agencies (France) from an aircraft using the SICAP circular
variable filter cryogenic spectrometer (1500–5500 nm,
2% resolution).
Figure 3. A comparison between SICAP Measurements (Malherbe et al., 1995) and model predictions for a solar illuminated cumulus cloud top with a 137⬚ relative solar azimuth
angle.
A typical spectrum is shown in Figure 3. Here the
aircraft is at 3.0 km altitude, the cloud top altitude is
2.5 km, the sensor line-of-sight (LOS) zenith angle is
104⬚, and the solar zenith and relative azimuth angles are
48⬚ and 137⬚, respectively. The CELAR cloud characterization was adopted for the MODTRAN simulations.
The cumulus cloud was modeled with a homogeneous
liquid water droplet density of 0.68 g/m3 from 0.1 km to
2.5 km altitude. Water droplet single scattering albedos
(Hansen et al., 1970) for a mean spherical particle radius
of 8 lm were entered at a 0.05 lm spectral resolution.
MODTRAN4 results at 10 cm⫺1 spectral resolution
(0.2% at 2000 nm) using the two-stream multiple scattering model (Isaacs et al., 1986; 1987; Meador and
Weaver, 1980) are shown and are in good agreement
with the data, although the data appear to be offset by
10–20 nm. Similar results were obtained with MODTRAN3.7 and with the discrete ordinates model DISORT (Stamnes and Swanson, 1981; Stamnes et al., 1988)
run with eight streams over a limited spectral subregion.
In addition, Figure 3 shows a calculation using ONERA’s
NAULUM code (Malherbe et al., 1995), which is also in
good agreement with the data and MODTRAN results;
NAULUM assumes a plane parallel atmosphere, appropriate for this case but not for general applications.
Figure 4 shows an additional SICAP data-model
comparison, but with a LOS zenith angle of 95⬚ and,
more importantly, a solar relative azimuth angle of 11⬚.
In this forward scattering case, MODTRAN4 underpredicts the measurements by about a factor of two because
the multiple scattering model averages over the azimuthal
dependence. MODTRAN does account for the relative
azimuth angle in single scattering, but single scattered
radiation accounts for less than 20% of the total radiance
in this example. The NAULUM calculation is an im-
Atmospheric Radiation Modeling Application to AVIRIS
Figure 4. A comparison between SICAP measurements (Malherbe et al., 1995) and model predictions for a solar illuminated cumulus cloud top with a 11⬚ relative solar azimuth
angle.
provement over MODTRAN4 because it models the azimuthal distribution of radiation in its plane-parallel discrete ordinates multiple scattering algorithm. DISORT
can also model azimuthal variations, but currently only
for plane-parallel atmospheres (Stamnes, personal communications, 1996); the development and integration into
MODTRAN of a curved-Earth, refractive path DISORT
routine which models solar azimuth dependencies is being pursued. For nadir-viewing geometries, such as
AVIRIS, solar azimuth geometry effects are minimized.
373
Figure 5. A comparison between MODTRAN3.7 and MODTRAN4 radiances for nadir viewing of the Earth through a
cirrus cloud with a 75⬚ solar zenith angle. The differences
between MODTRAN radiances are plotted offset by 0.08
lW sr⫺1 cm⫺2/nm.
MODTRAN3.7 and MODTRAN4 mid-IR and near-IR
radiances are compared for a nadir view of the MODTRAN model altostratus cloud (ICLD⫽2). The observer
is at 20 km altitude and the solar zenith angle is again
set to 75⬚. The cloud/rain model upgrade was used to
introduce finer layering near the cloud top (12 layers
were placed between 3.0 km and 3.5 km altitude). Inaccurate fluxes result from the multiple scattering algorithms if the original coarser layering is used. Even with
the finer layering, MODTRAN3.7 radiances exceed
those from MODTRAN4 by up to 20%.
SUMMARY
APPLICATIONS TO AVIRIS MEASUREMENTS
The primary focus of AVIRIS is characterization of the
Earth’s surface using nadir and near-nadir views. For
many such applications, the upgrade from MODTRAN3.7
to MODTRAN4 will have only a minor effect on the
data analysis. Under clear sky or thin cirrus conditions,
differences between MODTRAN3.7 and MODTRAN4
down-looking radiances from 20 km in the 400–2500 nm
spectral region are generally small. However, when multiple scattering is a sizable fraction of the total radiance,
the differences can be significant in absorption bands.
For example, Figure 5 shows down-looking radiances
predicted by MODTRAN3.7 and MODTRAN4 in the
center of the 1.9 lm H2O band. These calculations were
performed with a 1-km-thick cirrus cloud at 10 km altitude (0.14 vertical extinction at 550 nm), a solar zenith
angle of 75⬚, and using the MODTRAN grass (Vegetation A) surface albedos (Mustard, 1991). Within the 1.9
lm band region, MODTRAN3.7 radiances exceed those
from MODTRAN4 by up to 10%.
For views of solar-illuminated opaque clouds, the
MODTRAN4 upgrades are more critical. In Figure 6,
Several upgrades to MODTRAN have been developed
which lead to improvements in the calculation of radiaFigure 6. A comparison between MODTRAN3.7 and MODTRAN4 radiances for nadir viewing of the MODTRAN model
altostratus cloud with a 75⬚ solar zenith angle. The differences
between MODTRAN radiances are plotted offset by 7 lW
sr⫺1 cm⫺2/nm.
374
Berk et al.
tion scattering from clouds and aerosols. The cloud/aerosol models now allow for generalized layering and specification of physical and optical properties. A new CK
radiative transfer model leads to more accurate multiple
scattering calculations, particularly in spectral regions
containing strong molecular line absorption. It has been
shown that multiple scattering contributions can be important even for an optically thin solar-illuminated cirrus
cloud in the near-IR through visible spectral regions;
thus, these MODTRAN upgrades will lead to improved
data analyses and atmospheric/surface property retrievals
from down-looking sensors, such as AVIRIS, whose data
are often “contaminated” by subvisual clouds.
This work has been sponsored by the DOD/DOE/EPA interagency Strategic Environmental Research and Development Program (SERDP) and funded through Air Force contracts F1962893-C-0049 and F19628-91-C-0083 to Phillips Laboratory, Hanscom AFB, Bedford, Massachusetts. The authors express their
appreciation to H.E. Snell (Atmospheric and Environmental Research, Inc.) for performing FASCODE calculations, to S. Miller
(Geophysics Directorate, Phillips Laboratory) for technical and
administrative oversight of this effort, to W. Cornette (National
Imagery and Mapping Agency) for insightful technical discussions, and to P. Simoneau (Office National d’Etudes et de Recherches Aerospatiales) for providing an advance copy of the
(Malherbe et al., 1995) manuscript and for permission to include their measurements and calculations in this article.
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