Abstract - We simulate effects of the atmosphere and surface emissivity on the thermal infrared spectral signature in six proposed thermal channels, for ...
EFFECTS OF THE ATMOSPHERE AND SURFACE EMISSIVITY ON THE THERMAL INFRARED SPECTRAL SIGNATURE MEASURED FROM MODIS-N Zhengming Wan and Jeff Dozier
Center for Remote Sensing and Environmental Optics University of California, Santa Barbara, CA 93106
Abstract - We simulate effects of the atmosphere and surface emissivity on the thermal infrared spectral signature in six proposed thermal channels, for measurements of surface temperature, of MODIS-N (Moderate Resolution Imaging Spectrometer Nadirmode). Conditions for the simulations include a variety of atmospheric profiles over a wide elevation range, with difkrent visibilities near the Earth’s surface under cloud-free conditions. Calculated or measured spectral emissivities for various land surfaces-snow, clay, coarse sand and fine sand-range from 0.55 to 1.0. The upwelling band-averaged radiance at the top of the atmosphere can be exprcssed with three terms: surface emittance, reflection of the downward radiance at the surface, and the atmospheric path radiance. The model separates effects of surface temperature and emissivity from those of the atmosphere; it also includes effects of solar radiation on the medium wavelength infrared bands from 3.5 to 4.lp.m. This parameterized model is useful for development of practical algorithms for deriving surface temperature and emissivities from multi-channel MODIS-N thermal data.
3. land-surface temperature has a much larger range; and 4. reflected solar radiation and surface topography cause additional complications. Land-surface temperature cannot be accurately estimated without corrections for the atmosphere and surface emissivity, even if the radiometric measurement is taken near the surface. A land-surface temperature model appropriate to a range wide enough to cover all these variations has to be developed from accurate radiative transfer simulations. We investigate the effects of the atmosphere, surface emissivity and solar radiation on the thermal infrared spectral signature measured from space and then develop parameterized models based on results from radiative transfer simulations. SURFACETEMPERATUREMEASUREMENTS
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Laboratory Measurements Emitted spectral radiance L into direction p=cose, the viewing angle normal to the surface, at wavelength h and thermodynamic temperature T, is the product of spectral emissivity and the Planck function,
Keywords: surface temperature, thermal infrared, emissivity, atmospheric corrections.
h is Planck‘s constant, c the velocity of light, and k Boltzmann’s constant. For the dimensions to be correct, h must be in meters.
INTRODUCTION
Land-surface temperature is one of the key parameters in the study of processes on regional and global scales, combining the results of all surface-atmosphere interactions and energy fluxes between the atmosphere and the ground [ l , 21. Therefore, the ability to accurately determine thermodynamic land-surface temperature is essential to many scientific problems in the Global Change Research Program [3] and to management of renewable resources [4]. However, ground temperatures over land are hard to measure directly, because of their high spatial and temporal variability and the disturbance by any thermometer. Only remote sensing technique can provide a practical and efficient means for measurement of land-surface temperature at regional and global scales. The proposed MODIS instrument on the Earth Observing System @ O S ) satellites, the first of which is planned for launch in 1997, will provide six thermal channels for this purpose [ 5 ] .
The brighmess temperature Tb(h) can be found by solving the Planck function for temperature, given the emitted spectral radiance. The brighmess temperature for a given wavelength is thus the temperature of a blackbody that emits the same amount of radiation at that wavelength.
For a non-blackbody surface, measured spectral radiance is the combination of the surface emittance and the background radiation reflected by the surface,
Uh,1.0= E@, p) B(h, Ts)+ 2n 1
I Jp,fr(h,
~3
~
Q*)u~,-P’,~ ’ ) d p ’ d + ’
’
7
9
(2)
00
where L(h,-p’,Q’) is the background radiance to the surface. Directional emissivity &(A, p) and the bidirectional reflectancedistribution function f r are coupled by Kirchhoffs law,
Remote sensing of land-surface temperatures is more difficult than remote sensing of sea-surface temperature because of combined uncertainties: 1. land-surface spectral infrared emissivity is usually unknown or changing; 2. the atmosphere varies more dynamically, and the boundary layer over land is not so closely coupled to surface properties as it is over the ocean;
2n 1
I
F) = 1 - I p * f r ( l ; Q ’ ) ~ P * ~ Q ’ . ~
‘
9
(3)
00
Therefore, one has to pay particular attention to the background radiation distribution, surface BRDF and instrument calibration in order to accurately measure surface temperature and emissivity [6].
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Ground Measurements - The spectral signature obtained by ground measurements is composed of surface thermal emittance and atmospheric and solar radiation reflected by the surface,
Table I. Spectral Characteristicsof MODIS-N Thermal Bands
L(h. cl) = [1 + a(h)lE@, j.0 B(h, T,) +
I
2rr 1
jcl’f,(cl;~’.~’)L(h,-cl‘,~’)dcl’d~’,
2 3 4 5 6
(4)
0 0
where a(h)is a small factor that accounts for the effect of atmospheric backscattering and surface reflectivity on the hemispherical surface thermal radiance. Although there is ample evidence that the emissivities of land surfaces vary with viewing angle [7, 8, 9, lo], there are few spectral, angular emissivity data available. We therefore make the simplifying assumption that land surfaces are Lambertian, up to about 40’ from nadir, so emissivity and the BRDF are independent of viewing angle. Then equation 4 becomes
bandwidth (nm) 180 50 50 300 500 500
emittance, as shown in Figure 1. Therefore, we include an accurate solar correction model so that we can use daytime data from these three bands.
4
I
L(h, P) = [ 1 + a(h)l~ ( hcl), B(h, T,) +
-E(h, cl11 [E&) + (5) where Eu and Es are the atmospheric thermal irradiance and solar irradiance. After convolution with the sensor spectral response function, h will be replaced by the band number j . .-lu
center wavelength (Pm) 3.750 3.959 4.050 8.550 11.030 12.020
band
0.3 ”.. . _
..... solar zenith 30”
‘..
__-
lalbedo
7
,303
solar zeniiri ou-
-_
...
Satellite Measurements - The thermal infrared spectral signature measured from satellite-bome sensors may be expressed as
273
Lo’) = t 10’) 11 + aW1 EO’) BO’,T,) +
.-
7c1[1-~0’)1 [t20’)EuO’) + t30’)EAj)I+
Lu0’) +-%W.
--- --
- -- -- -
0
(6)
I
I
3.5
tiu), i = 1 , 2 , 3 are three effective transmission coefficients for band
j : for surface thermal emittance, atmospheric downward thermal
I
3.7 3.9 wavelength (pm)
I
4.1
Figure 1. Solar reflectance and surface thermal emittance in
irradiance reflected by the surface, and solar irradiance reflected by the surface. Lu is the atmospheric upward thermal radiance, and L, is path radiance resulting from scattering of solar radiation.
w ,-2 w- I =- 1
SIMULATION RESULTS AND ANALYSIS
RADIATIVE TRANSFER SIMULATIONS
Atmospheric Transmittance - Figure 2 shows the transmittance
Radiative Transfer Model - We apply the interaction principle and discrete-ordinate method [ l l ] to solve the radiative transfer equation in a vertically inhomogeneous and horizontally parallel Earth-atmosphere system. The LOWTRAN code [12] provides atmospheric profiles (temperature, pressure, water vapor density, ozone density, and aerosol density) for several “standard” atmospheres: U.S. standard, mid-latitude spring/ summer, mid-latitude fall/winter, subarctic springlsummer, and subarctic fall/winter. LOWTRAN also provides absorption values for atmospheric gases and scattering and absorption properties of several common aerosols at a spectral resolution of 20cm-’. A rural aerosol distribution, whose density depends on surface visibility, applies to all atmospheric profiles in the elevation range from 0 to 2km. In the elevation range from 2 to lOkm is the background tropospheric aerosol; from 10 to 30km; is the background stratospheric aerosol. Snow, clay, fine sand, and coarse sand are used as examples of flat land surfaces. Their calculated or measured spectral emissivities range from 0.55 to 1.0 [13]. We also use a grey body as a reference surface in order to highlight the spectral features of atmospheric effects.
values of the Summer Mid-Latitude atmospheric profile with surface visibilities 23 km and 6.5 km at elevations 0 and 2 km. Change of surface elevation causes greater effects in the 8 to 13 pregion than in the medium wave infrared region from 3 to 4 p because of more water vapor absorption. The effect of aerosols on atmospheric transmission is about the same in these two wavelength regions, as the comparison between the different visibilities shows. 1.oo
-I
___
l I ..i
0.75 transmittance
Sensor Spectral Specification - Spectral characteristics of six MODIS-N thermal bands designed for clouds and land-surface temperature measurements are given in Table I.
4
0.00
I
3
Solar Radiation - In the 3-5 pm medium wave infrared (MWIR)
region, where MODIS-N thermal bands 1 to 3 are allocated, solar radiation reflected by land surfaces with moderate values of reflectivity could be comparable to or larger than surface thermal
I 4
-
vis 23 km elev 2 km vis 23 km elev 0 km
..... vis 6.5 km elev 0 km
j I I I I 7 8 9 10 wavelength (pm)
I 11
I 12
I 13
Figure 2. Transmittance of the Summer Mid-LatitudeAtmosphere
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Surface-Leaving Radiance - We use the simulation results for the Summer Mid-Latitude atmosphere with visibility 23 km as example calculations for equation 6. The correction factor a is negligible for surface albedo values up to 0.40 under average aerosol loading, bccause the atmospheric backscattering is only about 0.5%. In some heavy aerosol conditions, this assumption may cause a temperature crror up to 1 K for highly reflective surfaces. Table I1 shows the atmospheric and solar effects on a fresh snow surface, which has a small albedo (0.01-0.02) throughout the whole thermal infrared region. The solar reflectance is significant in medium wave infrared bands for snow, despite its low albedo.
100 -
surface temperature ~
------
75 -
273K 313K
band no.
Table II. Atmospheric and Solar Effects on Surface-Leaving Radiance Over Snow 0-
MODIS-N thermal band (see Table I) 1 2 3 4 5 6
Ts f°KI
contribution
265 265
surface atmosphere
99.0 1.0
99.4 0.6
99.1 0.9
99.2 0.8
99.3 0.7
98.6 1.4
273 273
surface atmosphere
99.3 0.7
99.6 0.4
99.4 0.6
99.4 0.6
99.4 0.6
98.8 1.2
265 265 265
surface atmosphere reflected solar
72.7 0.8 26.5
83.8 0.5 15.7
88.3 0.8 10.9
99.2 0.8
99.3 0.7
98.6 1.4
0.0
0.0
0.0
273 273 273
surface atmosphere reflected solar
80.3
88.5 0.4 11.1
91.8
0.5
99.4 0.6
99.4 0.6
98.8 1.2
7.7
0.0
0.0
0.0
I
I
I
0.7
0.8
0.9
Parameterized Model - The signature received by medium wave infrared sensors, such as bands 1 through 3 of MODIS-N, depends on the viewing geometry, because of the angular dependence of the atmospheric scattering phase function. In the example of Summer Mid-Latitude atmosphere and solar zenith angle 30", 6LslLs ranges from -0.007 to 0.024 in the viewing angle range 0 to 54". Detailed calculations depend on profiles of aerosol optical properties (optical depth, single scattering albedo, and phase function). For clarity, we only illustrate the azimuth-averaged case in the following model.
solar zenith angle 30" (values in per cent of total)
19.2
I
0.6
surface emissivity Figure 3. Temperature and emissivity influences on surface thermal emittance contribution to MODIS-N signatures, a s measured from space
no solar effect (values in per cent of total)
0.5
I
0.5
In order to separate the efkcts of surface temperature and emissivity from those of the atmosphere, we apply two special surface conditions to radiative transfer simulations: 1. a blackbody surface temperature of absolute zero,i.e. Ts= 0, E = 1; 2. a reflective surface whose temperature is absolute zero, i.e. T, = 0, E < 1.
Similar simulations for a grey-body surface with variable albedo value from 0 to 0.5 over a wide temperature range show that even for albedo 0.05, the atmospheric thermal term may be as high as 6T = 2 K in MODIS-N thermal bands 4 to 6. If Ts = 273°K and albedo is 0.05, the solar reflectance can be as large as the surface thermal emittance in band 1. If albedo =0.2, the solar reflectance can be 5x the surface thermal emittance.
Table 111 shows three effective transmission coefficients in Equation 6 for the Summer Mid-Latitude atmosphere under a clear-sky condition with solar zenith angle 30". This equation can express all the simulated band-averaged radiance measured from MODIS-N for viewing angles up to 54" for a wide range of surface temperature and emissivity: 263K
