Earth Interactions
Volume 8 (2004)
Paper No. 7
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Copyright Ó 2004, Paper 8-007; 4,089 words, 7 Figures, 0 Animations, 3 Tables.
http://EarthInteractions.org
Mapping Surface Broadband
Emissivity of the Sahara Desert Using
ASTER and MODIS Data
Kenta Ogawa*
USDA/ARS Hydrology and Remote Sensing Laboratory, Beltsville, Maryland, and School
of Engineering, University of Tokyo, Tokyo, Japan
Thomas Schmugge
USDA/ARS Hydrology and Remote Sensing Laboratory, Beltsville, Maryland
Received 19 August 2003; accepted 30 October 2003
ABSTRACT: Surface broadband emissivity in the thermal infrared region is
an important parameter for the studies of the surface energy balance. This paper
focuses on estimating a broadband window emissivity from the Advanced
Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and
Moderate Resolution Imaging Spectrometer (MODIS) data. Both sensors are on
board the NASA Earth Observing System (EOS) Terra satellite, which was
launched in 1999. First, several definitions of the broadband emissivity were
investigated, and it was found that the emissivity integrated between 8 and 13.5
lm is the best for estimating the net longwave radiation under clear-sky
conditions. Then, a method to estimate broadband emissivity at the continental
scale was developed. The method uses two regressions. The first regression is to
relate the broadband emissivity to the emissivities for the five ASTER channels
using measured emissivities in the laboratory from spectral libraries. The
second regression relates the broadband emissivity map from ASTER data to
* Corresponding author address: Kenta Ogawa, Hitachi Ltd., 4-6 Kanda-Surugadai ChiyodaKu, Tokyo 101-8010, Japan.
E-mail address: [email protected]
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the emissivity and reflectance derived from MODIS data. The first regression
was used for mapping the broadband emissivity using ASTER data in a 500 km
3 1400 km area of North Africa, which includes Tunisia, eastern Algeria, and
western Libya. This emissivity map was used to calibrate the second regression,
which was applied to MODIS data and generated a broadband emissivity map
over North Africa and the Arabian Peninsula. The range of the broadband
emissivity was found to be between 0.85 and 0.96 for the desert area. The
resulting broadband emissivity maps and the methodology for generating them
will contribute to future climate modeling studies.
KEYWORDS: Surface broadband emissivity, ASTER, Longwave net
radiation
1. Introduction
Accurately characterizing the surface emissivity is necessary for correctly
determining the longwave radiation leaving the surface, and thus, for determining
the surface radiation budget. This is particularly true for nonvegetated arid regions.
Therefore, emissivity is an important parameter for climate studies (Prabhakara and
Dalu, 1976; Wilber et al., 1999; Zhou et al., 2003a). For example, for a daily
average surface temperature of 295 K and a clear and dry sky, the daily averaged
net longwave radiation is about 135 W m2 and the net shortwave radiation is
between 150 and 200 W m2, depending on the solar geometry and the
atmospheric condition. Thus, an uncertainty of 10% in broadband emissivity
corresponds to the uncertainty between 15 and 20 W m2 in net longwave radiation
because the uncertainty in calculated net longwave radiation is approximately
proportional to the uncertainty of broadband emissivity for given surface and air
temperatures as shown in Equation (3) in section 2. For the net radiation, this
uncertainty in emissivity is comparable to an uncertainty of 7%–9% in albedo. The
range of 10% in broadband emissivity is observed for nonvegetated surfaces;
therefore, the accurate emissivity information in an arid region is important.
Furthermore, a set of sensitivity tests with a climate model (Zhou et al., 2003b)
indicates that a decrease of soil broadband emissivity by 0.1 could increase surface
temperature by 1.1 K and air temperature by 0.8 K in the Sahara Desert. However,
a constant and uniform emissivity is often used in model parameterizations for land
surface energy balance studies and numerical weather predictions (Blondin, 1991;
Bonan, 1996; Wood et al., 1997) because the information on the spatial variation of
emissivity is limited. Ogawa et al. (Ogawa et al., 2003) have shown that there are
large spatial variations (0.81–0.95) of window emissivity (e8–12) for the desert
region around Tunisia. Prabhakara and Dalu (Prabhakara and Dalu, 1976) mapped
the surface emissivity with 100-km resolution using the Nimbus-4 infrared
interferometer spectrometer (IRIS) and found that emissivity at 9 lm varied from
0.65 to 0.90. A map with a finer spatial resolution provided by the Advanced
Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and Moderate
Resolution Imaging Spectrometer (MODIS) data would be a useful improvement
for our understanding of the land–atmosphere interaction.
ASTER (Yamaguchi et al., 1998) is a sensor developed by the Ministry of
Economy, Trade and Industry (METI) in Japan and is on board the National
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Table 1. The center wavelengths of ASTER and MODIS in the thermal infrared
region.
ASTER channel
k (lm)
MODIS channel
10
11
12
13
14
29
8.29
8.63
9.08
10.66
11.29
8.55
31
11.03
32
12.02
Aeronautics and Space Administrations’s (NASA’s) Earth Observing System
(EOS) Terra satellite launched in 1999. ASTER has five channels in the thermal
infrared region (TIR) with 90-m spatial resolution. It is possible to estimate spectral
emissivities for the five channels using the temperature–emissivity separation
(TES) algorithm (Gillespie et al., 1998). MODIS is also on board the Terra satellite
and has 10 channels in the TIR. Three channels (29, 31, and 32) are in the
atmospheric window and can be used to observe the land surface with a 1-km
resolution. Table 1 shows the center wavelengths for the TIR channels of ASTER
and MODIS. ASTER has advantages in spatial resolution and a larger number of
channels in the TIR, thus making it easier to compare with laboratory and fieldscale measurements and to estimate accurate broadband emissivities. MODIS has
the advantages of spatial coverage and frequency of observations. We take
advantage of both sensors to accurately map the emissivity of large areas.
In this paper, we describe the method used to estimate broadband emissivity and
the results for the Sahara Desert. We focus only on the desert area because the
largest variation of emissivity is expected to be observed there. It also helps to
simplify the issue because temporal variations of emissivity and effects of
vegetation are minimal. We examine the definition of broadband emissivity. Then
we describe the regression approach that is used for mapping the broadband
emissivity from ASTER and MODIS data. We show the emissivity map of the
Sahara Desert from ASTER and MODIS data derived using regressions. Finally,
we validate the resulting emissivity map using additional ASTER data.
2. Method
2.1. The definition of broadband emissivity for estimating the net
longwave radiation
In the studies of the surface radiation budget and surface energy balance, the
surface emissivity is used to estimate the net longwave radiation. The net longwave
radiation Ln is the difference between upwelling irradiance emitted by the surface
L" and the downwelling irradiance from the sky L# and is given by
Ln ¼ L" L# ;
ð
ð
¼ ½ek Bk ðTs Þ þ qk Lak dk Lak dk;
ð
ð
¼ ½ek Bk ðTs Þ þ ð1 ek ÞLak dk Lak dk;
ð
¼ ek ½Bk ðTs Þ Lak dk;
ð1Þ
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Figure 1. The effective temperature of downwelling atmospheric radiation. The
difference from the surface temperature is much larger inside the
atmospheric window region (8–13.5 lm) than outside.
where qk is surface reflectance and La is downwelling atmospheric radiance. We
assumed that the observed land surface is under thermodynamic equilibrium and
follows Kirchhoff’s law; that is, qk¼ 1 – ek, in Equation (1). Equation (1) can be
expressed using the sky brightness temperature, Tsky,k:
ð
Ln ¼ ek ½Bk ðTs Þ Bk ðTsky;k Þdk:
ð2Þ
Figure 1 shows the Tsky,k of the U.S. Standard Atmosphere, 1976 calculated with
MODTRAN4. When the surface temperature Ts is close to the near-surface air
temperature Ta, the difference between Ts and Tsky,k is very small outside of the
atmospheric window region (8–13.5 lm). Therefore, the major contribution to the
net longwave radiation is in this region (8–13.5 lm) and the impacts of the
emissivity change in other wavelength regions are expected to be small.
For the studies of land surface models, the net longwave radiation is usually
expressed using a broadband emissivity eBB and a broadband absorptivity a
[Rowntree, 1991; Bonan, 1996; Campbell and Norman, 1998, see their Equations
(11.14) and (11.15) on p. 176] because the precise spectral emissivity of soil is
unknown for most areas. If we assume that the broadband emissivity is equal to the
broadband absorptivity and integrated over all wavelengths, Ln in Equation (2) is
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Ln ¼ eBB rTs4 aLa ;
¼ eBB ðrTs4 La Þ:
ð3Þ
For practical calculations of the broadband emissivity, ek1k2 can be defined as
Rk2
ek Bk ðTs Þdk
ek1k2 [ k1k2
R
;
ð4Þ
Bk ðTs Þdk
k1
where Ts is surface temperature,1 Bk is Planck’s function, and ek is spectral
emissivity. Here k1 and k2 are the wavelength ranges for the integration. An
important question is, ‘‘What is the appropriate wavelength range, k1 and k2, for
realistic estimation of the net longwave radiation?’’
We analyzed several definitions of the broadband emissivity to decide the
wavelength range of k1 and k2 for estimating the net longwave radiation. We
examine the two ranges, 8–12 and 3–14 lm, from our previous studies (Ogawa et
al., 2002; Ogawa et al., 2003), and an additional one, 8–13.5 lm. We examine 8–
13.5 lm because the wavelength region corresponds to the atmospheric window
region described in Figure 1. Emissivity spectra of 314 samples were used for the
values of ek. These spectra are part of the ASTER Spectral Library (see online at
http://speclib.jpl.nasa.gov/ ), the University of California Santa Barbara’s MODIS
Emissivity Library (Snyder et al., 1997), and our 57 soil samples. MODTRAN4
(Berk et al., 1999) and its U.S. Standard Atmosphere, 1976 profile were used to
calculate Lak. The comparisons of Ln have been done2 for three surface temperatures,
Ts ¼Ta, Ts ¼Taþ8, and Ts ¼Taþ15, where Ta is the near-surface air temperature,
288.15 K from the U.S. Standard Atmosphere, 1976. We selected these three
temperatures to cover a typical diurnal variation of the difference from Ta.
Considering the three wavelength ranges for broadband emissivity (e8–13.5, e8–12,
e3–14), the optimum window is e8–13.5, where estimation bias of net longwave
radiation is smallest for typical conditions3 (Figure 2). The narrower window, e8–12
1
Broadband emissivity is insensitive to surface temperature, Ts, for common surface
temperatures. We used Ts ¼ 300 K for the calculation of ek1k2 (Ogawa et al., 2002).
2
We note that the wavelength region for this analysis is limited to between 3 and 14 lm
because the available emissivity spectra data only cover this wavelength range. But this limitation
does not significantly affect the result because the 3–14-lm region contains the major part of the net
longwave radiation. The portion of the net longwave radiation included in 3–14 lm is from 84% (Ts
¼ Ta þ 15) to 97% (Ts ¼ Ta) from the U.S. Standard Atmosphere, 1976 and a blackbody surface.
Furthermore, the limited laboratory measurements of minerals in the 5–45-lm range indicate that
the emissivity value at wavelengths longer than 14 lm has little effect on the broadband emissivity
(Ogawa et al., 2002).
3
We note that when the above analysis was done for the other five atmospheric profiles
available in MODTRAN4, it was found that e8–13.5 gave the most accurate Ln for the drier
atmospheres: midlatitude winter, subarctic summer, and subarctic winter. Minor underestimations
of Ln were observed for the wetter atmospheres: tropical and midlatitude summer.
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Figure 2. The comparison of the calculated net longwave radiation (Ln) from
emissivity spectra with estimated Ln from the broadband emissivity.
Each point represents an emissivity spectrum from spectral libraries.
Here e8–13.5 shows the best results for all three temperatures.
underestimates the net longwave radiation because the emissivity at 12–13.5 lm is
generally higher and the radiation at this wavelength range affects the net longwave
radiation but is not accounted for in the e8–12 calculation. As a result, e8–12 is too
low to use in Equation (3). The wider window, e3–14, overestimations the actual net
longwave radiation because the atmospheric opacity in the 6–8-lm range limits the
effect of the high emissivity in this range. The importance depends on the
difference between Ts and Tsky and, as shown in Figure 1, it is small in this
wavelength region. As a result, e3–14 is too low to use in Equation (3). In this paper,
we use e8–13.5 as an estimator of the broadband emissivity.
2.2. Estimating the broadband emissivity from ASTER channel
emissivities
First, we used a regression to map the broadband emissivity, e813.5, from the
emissivities for the five ASTER channels, ech. Both e813.5 and ech are calculated
using the emissivity spectral libraries and a regression relation is developed
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Table 2. Coefficients used for the regression (4). The coefficient of a10 was
dropped by the stepwise regression because that was not statistically
significant.
a10
a11
a12
a13
a14
c
0.000
0.121
0.194
0.323
0.113
0.242
between them. The details of this approach are described in Ogawa et al. (Ogawa et
al., 2002; Ogawa et al., 2003). The broadband emissivity, e813.5 is given by
e813:5 ¼
14
X
ach ech þ c;
ð5Þ
ch¼10
where ach and c are the coefficients of the regression. We calculated the coefficients
using the 314 emissivity spectra described above. The rms error of the predicted
e8–13.5 by the regression was 0.0041. The coefficients are given in Table 2. The
broadband emissivity estimated by this regression is used to calibrate and validate
the second regression described below. We note that this linear relationship can be
applied to 90-m resolution ASTER data because the spectral emissivities of its
image pixel are considered to be approximately a linear combination of the
components included in the pixel (Gillespie, 1992).
2.3. Estimating the broadband emissivity from MODIS emissivity/
reflectance
The second regression is for extending the map to continental scales using a
relationship between 1) the broadband emissivity mapped by ASTER data using
Equation (4) and 2) the emissivity and reflectance data from MODIS. The spectral
emissivity for the MODIS TIR channels can be estimated using a physically based
algorithm, which uses the day/night pairs of TIR data in seven MODIS bands for
simultaneously retrieving surface temperatures and band-averaged emissivities
(Wan and Li, 1997).
We assume the following relationship:
e813:5 ¼ a þ b emaxmin þ c q2:13 ;
ð6Þ
where q2.13 is the reflectance for MODIS channel 7 at 2.13 lm and emaxmin is the
difference between the maximum emissivity for the three MODIS channels (29, 31,
and 32) and the minimum (similar to MMD for the TES algorithm; Gillespie et al.,
1998). The coefficients of this regression are a, b, and c. We used emaxmin rather
than the spectral emissivity value itself because we found that the agreement of
emaxmin between MODIS and ASTER is better than that for the emissivity values
when we compared the channels of both sensors at similar wavelengths. There are
several studies that discuss mapping emissivity using MODIS data or its
comparison with ASTER data (Petitcolin and Vermote, 2002; Minnis et al.,
2002; Jacob et al., 2004). Typically, we have found that the MODIS band-31
emissivity displays a greater range of values than is observed for the ASTER band
13 or is expected from laboratory data. Further investigations of the comparison of
ASTER and MODIS emissivities are necessary to quantify this discrepancy.
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Figure 3. The broadband emissivity derived from ASTER data around Tunisia.
Channel 7 was chosen because its correlation with the broadband emissivity was
highest of all the MODIS reflective channels (Zhou et al., 2003a). The surface
reflectivity of soils and rocks is determined by their mineral composition, as is their
emissivity. Generally, quartz-rich (SiO2) sand has a higher reflectivity and a lower
emissivity, but mafic minerals with lower SiO2 contents generally have a lower
reflectivity and a higher emissivity, thus the empirical relation between the
reflectivity and emissivity.
3. Results
We used these two regressions with ASTER and MODIS data acquired over the
Sahara Desert for mapping the broadband emissivity. The ASTER and MODIS
products from the U.S. Geological Survey’s EROS Data Center (EDC, see online
at http://lpdaac.usgs.gov/ ) were used. First, we used 258 scenes of the ASTER
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Figure 4. (top) Emissivity and (bottom) reflectance derived from MODIS data.
Emissivity data are from MOD11B1 products on 1–5 Nov 2001. The
image represents the emissivity of channel 29 (8.55 lm). The
reflectance data are from the MOD43 product on 8–23 May 2002.
The reflectance image shows RGB as channels 1, 4, and 3,
respectively. Both products are distributed in about 5-km resolution.
level-2 emissivity product (see online at http://edcdaac.usgs.gov/aster/ast_05.asp)
collected over a 500 km 3 1400 km area of North Africa around Tunisia, including
a part of Algeria and Libya in 2001 and 2002. To generate this level-2 emissivity
product, atmospheric profiles from the Global Data Assimilation System (GDAS;
Kalnay et al., 1990) operated by National Centers for Environmental Prediction
(NCEP) were used for the atmospheric correction. The uncertainties in these
profiles contribute to errors in the final emissivity product. The temporal emissivity
variation caused by the changes of soil moisture, vegetation fraction, and the
atmospheric profile uncertainty could have been a problem when we used the
emissivity products. However, the observed temporal variations of the emissivity
were insignificant (less than 0.02 in most cases) when we considered the
differences of emissivity for overlapping areas observed on different days. We
applied Equation (4) to these products and generated the broadband emissivity map
shown in Figure 3. The range of emissivity is between 0.85 and 0.96 for the desert
area. The low value, between 0.86 and 0.88 (shown in blue), is located in a sand
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Figure 5. Comparison of the broadband emissivities from ASTER data with the
values estimated from MODIS data for the calibration area around
Tunisia.
dune area (around 318N, 98E), and the high between 0.92 and 0.96 (shown in red)
is located in the Hamada de Tinrhert Mountains (around 308N, 118E).
To further study the effect of atmospheric profile uncertainty and the TES
method, we generated simulated observation data using the 314 emissivity spectra
(described earlier) and MODTRAN4 simulations with the U.S. Standard
Atmosphere, 1976 for the surface target at 0-m altitude with 300 K. The main
cause of errors in the atmospheric correction is the uncertainty in the water vapor
amount (Tonooka, 2001). Therefore, we varied the water vapor by 620% in the
MODTRAN4 simulation and applied the TES method to extract temperatures and
emissivities. Then we derived the broadband emissivities using the linear
regression [Equation (5)] and compared with the broadband emissivity calculated
Table 3. Coefficients used for the regression (5). The correlation coefficient is R
and r is the standard deviation.
Coefficients
R
r
Constant (a)
emaxmin (b)
q2.13 (c)
0.986
—
—
0.226
0.89
0.061
0.0757
0.81
0.096
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Figure 6. The broadband emissivity map of the Sahara Desert derived from
the regressions. Water and vegetated area are masked using a
land-cover map by USGS and given fixed values.
from the original emissivity spectra with Equation (4). The resulting rms error of
the broadband emissivity was 0.0132. This value is an estimate of the expected
error of ASTER-based broadband emissivity caused by 1) uncertainty of water
vapor and 2) the use of an empirical relationship in the TES method.
Using this emissivity map (Figure 3) and the MODIS data of the same area, we
calibrated Equation (5). The MODIS products shown in Figure 4 [MOD11B2
Figure 7. Comparison of the broadband emissivities from ASTER data with the
values estimated from MODIS data in the validation area shown in the
upper left. This area is covered with 115 scenes of ASTER data.
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(online at http://edcdaac.usgs.gov/modis/mod11l2.asp) for emissivity data, and
MOD43 (online at http://ivanova.gsfc.nasa.gov/outreach/EOSDIS_CD_01_v2/
docs/modisprod.htm) for reflectance data] were used for the calibration. The
calibrated coefficients are shown in Table 3. In Figure 5, the results from Equation
(5) are compared with the ASTER results. The residual rms difference in the
calibration of this regression is small (0.0085). Finally, we applied this regression
to the MODIS data for all of North Africa and generated the broadband emissivity
map (Figure 6; land cover map by USGS is available online at http://
edcdaac.usgs.gov/glcc/glcc.html). The range of emissivity is approximately the
same as that for the ASTER data around Tunisia, that is, between 0.85 and 0.96 for
the entire area. Dataset 1 includes the broadband emissivity value in this map. The
areas with low emissivity (blue in Figure 6) correspond to bright or red areas in the
reflectance map in Figure 4. These areas correspond to sand dunes in the soil map
of the Natural Resources Conservation Service of the U.S. Departments of
Agriculture (see online at http://www.nrcs.usda.gov/technical/worldsoils/
mapindex/ ).
We validated this map using 115 scenes of ASTER data acquired over other
parts of North Africa. Figure 7 shows the comparison between the emissivity
estimated from MODIS data and that determined directly with ASTER data. The
rms difference was 0.0114. Despite the difference of resolutions between ASTER
and MODIS, the results indicate that the regression provides a good estimation of
the broadband emissivity.
As described above, the rms error in the broadband emissivity from ASTER data
using Equation (4) is estimated to be 0.0132. The total error is roughly estimated to
be the square root of the sum of the squares of the broadband emissivity error by
ASTER data and the difference between ASTER estimates and MODIS estimates,
0.017(¼ =0:01322 þ 0:01142 ), if we assume the errors are independent.
4. Summary and conclusions
In this paper, we showed that the emissivity integrated between 8 and 13.5 lm was
the best for estimating the net longwave radiation. A broadband emissivity map for
the desert area of North Africa was generated using two regressions: the first to
relate the broadband emissivity to the five ASTER channel emissivities, and the
second to relate the broadband emissivity to the MODIS products. The expected
rms error was estimated to be 0.017 based on the analysis using emissivity spectral
libraries and the validation data. The range of the broadband emissivity was found
to be between 0.85 and 0.96 for the desert area. The resulting broadband emissivity
maps and the methodology for generating them will contribute to future climate
modeling. A preliminary example of this is given in the recent paper by Zhou et al.
(Zhou et al., 2003b) who found that a decrease of 0.1 in emissivity caused about a
18C change in both ground and air temperatures. This study used the emissivity
results presented here in the Community Land Model applied to North Africa.
Acknowledgments. This study was supported by the ASTER Project of NASA’s EOSTerra Program. The ASTER Spectral Library was provided by the Jet Propulsion Laboratory,
California Institute of Technology, Pasadena, California. The authors wish to thank Dr. Simon
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Hook from NASA JPL and Dr. Liming Zhou from Georgia Institute of Technology for useful
suggestions and comments on this study.
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