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Estimating surface temperatures from satellite thermal infrared data—A simple formulation for the atmospheric effect
REMOTE SENSING OF ENVIRONMENT 13:353-361
353
Estimating Surface Temperatures from Satellite Thermal Infrared Data--A Simple Formulation for the Atmospheric Effect*
JOHN C. PRICE H~tdrology Laboratory, Plant Physiology Institute, Beltsville, Maryland
In recent years the availability of high spatial resolution thermal infrared'data from satellites has prompted the use of energy budget models relating satellite-derived surface temperatures to surface moisture, near-surface thermal inertia, energy exchange with the atmosphere, etc. However, correction of the high spatial resolution satellite data for atmospheric water vapor effects can represent a substantial computational burden unless simplifying assumptions are utilized. A simple formulation is developed and its applicability tested by application to standard meteorological soundings at a time near the overpass of an NOAA operational satellite. It appears that reasonable estimates of surface temperature (_+ 2-3°C) are readily obtained for areas of order 100-300 km2.
1. Introduction Recent advances in remote sensing technology have improved the quality (especially the spatial resolution) of thermal infrared measurements to the extent that detailed studies of surface thermal properties can be carried out. The Landsat 3 satellite carried a thermal infrared sensor capable of (240 m) 9" observations, which unfortunately did not perform well in orbit (Price, 1981). The Heat Capacity Mapping Mission satellite (NASA, 1978) acquired (600 m) a spatial resolution data, the Advanced Very High Resolution Radiometer (AVHRR), which is carried on NOAA satellites, acquires (1.1 km)2 data of much higher radiometric quality than that previously available from operational satellites (Kidwell, 1979), and the Thematic Mapper on Landsat satellites D and D' will provide (120 m) 2 thermal infrared data. *Contribution from USDA-ARS, Hydrology Laboratory, Plant Physiology Institute, Beltsville, Maryland. ©Elsevier Science Publishing Co., Inc., 1983 52 Vanderbilt Ave., New York, NY 10017
Data with high precision and spatial resolution are suitable for geologic studies (Watson, 1975), and for possible agricultural applications, such as estimation of surface moisture characteristics (Carlson et al., 1981; Price, 1982), because the field of view resolves many ground features. This permits relatively unambiguous comparison of satellite data with ground truth measurements. One would expect utilization of these data following appropriate research verification. However, a conceptionally simple but computationally demanding problem, namely, correcting satellite infrared measurements for atmospheric effects, complicates the reduction of remotely sensed data to readily interpretable values of surface temperature. It is thus worthwhile to develop a formulation which facilitates application of this atmospheric correction. The formulation described here represents a simple linear approximation to the solution of the radiative transfer equation. Consideration of a sample data set suggests that in relatively undisturbed 0034-4257/83/$3.00
354
(anticyclonic) meteorological conditions the formulation is applicable to large areas (100s of km on a side) with errors of a few degrees C. Infrared radiative transfer is reviewed briefly in See. 2, and the analytic simplification is described. Application to a sample data set is carried out in Sec. 3, and the implications for remote sensing are summarized briefly.
J. c. PRICE
could be used to establish reliable values for the radiative transfer coefficient. The intensity I x of radiation at wavelength ~ (/~m) passing through an absorbing/emitting medium with absorption coefficient k x (m2kg-1) is described by the equation (e.g., Chandrasekhar, 1960, p. 9). d/x =
ds
2. Effect of the Atmosphere in the 10-12-1~m Window For cloud-free locations the 10-12-/xm spectral interval is relatively transparent to radiation, except for the effects of atmospheric water vapor. Although neglect of absorption and emission by CO 2, 0 3, etc., in the present treatment may cause small errors, the major potential error sources arise from uncertainty in the estimation of the absorption coefficient k for water vapor, and from the need to use such radiosonde data as are available for atmospheric temperature and moisture profiles. The influence of aerosols is generally an order of magnitude smaller than molecular effects, except when the atmosphere is hazy (McClatchey et al., 1971). Imbault (1979) has carried out an extensive review of theory and experimental data on water vapor absorption in the 10-12-/xm region of the spectruna. The considerable scatter in experimental data is due to the difficulty in obtaining measurable absorption in the laboratory because the gas is so transparent, or in measuring accurately moisture concentrations and temperature when long path length experiments are conducted outdoors. In principle, a program of aircraft measurements, such as those of Schott and Tourin (1975) or Becker et al. (1979),
-kxpn2°(Ix + Bx)'
(1)
where s is the path length (m), PH20 the density (kgm-a) of the water vapor, and B is the black body emission as given by the Planck function Bx(T ) =
C1
~S[exp(C2/XT )- I ] W m - 2 s r - 1/~m-1"
Here T is the temperature (K), C 1 = 1.19 ×10 s W m - 2 - s r - l / z m 4 and C2 = 1.439 × 104/~m K. Following Imbault, the value of k x given by Kneizys et al. (1980) is used: k x = 10.13
(eexp[18OO(1/T- 1/296)] + 0.002(p- e))
× (4.18 + 5578e exp( - 78.7/~)), where p and e are atmospheric pressure and vapor pressure of water in millibars (1 m b - 10 2 Pa). Integration of Eq. (1) requires knowledge of atmospheric temperature and moisture as functions of height. These may be obtained from radiosonde data (NOAA-Environmental Data and Information Service), except that the data are generally given as functions of pressure. Thus a change of variable through the
ESTIMATING SURFACE TEMPERATURES
355
hydrostatic equation 1
dp
100 dz
dp (dscos O)
The equation expresses the fact that the satellite observed radiation is linearly related to ground emission. One may define a satellite brightness temperature (TBB) from the radiance measurement,
= _ p~g
is appropriate TBB = B - ' [ / ( s a t e l l i t e ) ] ,
dlx = kxq (I x + Bx), dp 100gcos 0
where B function:
where O is the nadir angle of observation (O = 0 for vertical observations), q is the mixing ratio = P H 2 o / ( P H 2 o + Pair), t h e factor 100 arises from expressing p in millibars, and g is the acceleration of gravity (9.8 ms - 2). A formal integration is now possible (Chandrasekhar, 1960), e.g., I x ( p ) = Ix(Po)e -~xO'°'n) + fn°dp, e - ~(no. p')
1
is the inverse of the Planck
B - 1(i ) = C 2 / M n [ 1 + C 1 / ( ~ 5 I )]. For modest temperature intervals (e.g., _ 20 ° about temperatures of order 300 K) the Plank hmction and its inverse are nearly linear at thermal infrared wavelengths (Slater, 1980). Thus Eq. (3) may be reduced to a simple expression relating surface temperatures to satellite observed brightness temperature.
.-1p
× kxqBx/(lOOgcos O),
(4)
T, =
(2)
+ Z,
(5)
where Tg is the ground brightness temperwhere Ix(P o) is the upward radiance at the earth's surface and the optical depth zx has been introduced:
ature,
a= "rx(Po, p ) = fp;'°dp'kxq/(lOOgcos O). is related to the transmittance (the symbol a is used to avoid confusion with temperature T) by ax(p0, p ) = e - ,x(po,n~ The integral on the right of Eq. (2), representing atmospheric emission, is independent of surface radiation. Denoting this sky emission term by s, dropping the subscripts h, and carrying the integral to satellite altitude (0 pressure) I(satellite) = a l o ( g r o u n d ) + s.
(3)
OTBB~o
and
fl = T 1 - aTBm.
It is recommended that the slope a be evaluated at surface air temperature To, with the constant term fl evaluated at T1 = TO+ 10 °, representing the fact that day surface temperatures may be appreciably warmer than air temperature. 1 Since a and s must be evaluated numerically, it is reasonable to obtain a and fl by
IA ro~zaxN listing for the computation of a and fl from meteorological soundings may be obtained from the author.
356
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290
295
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315
320
COMPUTED
SATELLITE
BRIGHTNESS
TEMPERATURE
FIGURE 1. Sudace temperature as a hmction ot satellite brightness temperature as given by numerical integration for a sounding (Peoria) described in See. III. Equation (5) yields a virtually identical line.
munerical means. Analytic expressions for a and fl are derived in the Appendix. Thus, over a moderate temperature range, surface temperature is linearly related to satellite observed brightness temperature (Fig. 1). 3. Spatial Variability The utility of Eq. (5) depends on the spatial variability of a and ft. This may be estimated through analysis of meteorological soundings which are acquired routinely for weather forecasting pttrposes.
Examination of satellite imagery from June and July of 1980 lead to selection of the morning of July 24, 1980 as a case study. Satellite imagery from 1400z of this day showed the central United States to be virtually cloud-free, from northern Wisconsin and Michigan to south Texas, and from eastern Colorado and New Mexico to Ohio and Alabama. An area this size corresponds to roughly 3 × 106 individual data points at the (1.1 kin) 2 spatial resolution of the Advanced Very High Resolution Radiometer carried on NOAA operational satellites. Such large data sets illustrate the need for straight-
ESTIMATING SURFACE TEMPERATURES
forward implementation of the atmospheric correction procedure. Nearly coincident radiosonde data for the area were acquired from the National Climatic Center, Ashville, N.C. The 13 stations selected are scattered along the 1600-km swath of satellite data (Fig. 2). For each sounding the temperature and humidity profiles were input to the radiative transfer computation [Eq. (2)], after which the coefficients a and/3 were computed. These values as well as the precipitable water and computed optical depth are given in Table 1. Although the coefficients a and /3 vary considerably from station to station, these variations tend to cancel each other when the total atmospheric correction is obtained. Thus the difference (~T) between the surface temperature and the satellite observed brightness temperature for two assumed values of surface temperature, 290 K and 310 K, were calculated. (2-m air temperatures at the 12z soundings ranged from 286.4 K at Flint, Mich., to 297.0 K at Stephenville, Tex.). From BT29o and ~T31o (Table 1), it is clear that the variation of the atmospheric correction is relatively small, i.e., from 3.0 to 4.9 K at 310 K, for the large central region of the United States on the date selected. An exception is evident in the data: the Jackson, Miss. sounding was significantly more moist than the others, leading to increased values of the atmospheric correction. This increased humidity is evidenced by scattered clouds in the Jackson area. In most cases cloud-free satellite images will be accompanied by lower than average atmospheric moisture content. The satellite thermal infrared data were examined and yielded surface tempera-
357
tures generally a few degrees warmer than air temperatures, as would be expected. A precise comparison of the satellite predicted surface temperatures with ground measurements would best be accomplished over a large uniform water surface, as with the NOAA operational sea surface temperature product (NOAA, 1980). From a practical point of view the error in using Eq. (5) in establishing land surface temperatures is associated with the time and space difference between the meteorological sounding and the satellite observation, the need to assume a value for surface emissivity, possible variation of the satellite calibration, etc. It thus appears that for undisturbed synoptic conditions, and given relatively minor topographic variability (which influences the optical depth of the atmosphere because moisture is concentrated in the lowest layers of the atmosphere), one may utilize meteorological sounding data to reduce satellite thermal infrared measurements to ground surface temperahares over moderate-sized areas. In practice one may utilize a single nearby sounding to compute a and ~, or else interpolate among a number of soundings. The results in Table 1 for 8T do not represent the extreme values of the atmospheric correction, nor of the possible errors resulting from computations using radiosonde data. Generally the atmospheric effect increases near midday, when the ground temperature may exceed 320-330 K during the summer. In such cases the atmospheric correction may exceed 10 °, as can be seen by extrapolation of ~T29o and ~T310 in Table 1. In addition by international convention radiosonde observations are taken near 00z and 1200z, thus missing the midday warming of the lower atmosphere in the
358
J.C. PRICE
FIGURE 2. Visibleimagery acquired by the NOAA-6Advanced Very High ResolutionRadiometer at 14:26z, July 24, 1980.
359
ESTIMATING SURFACE TEMPERATURES TABLE 1
Atmospheric Corrections--July 24, 1980, 1200z
LOCATION St. Cloud, MN Green Bay, WI Flint, MI Omaha, NE Peoria, IL Topeka, KS Salem, IL Monett, MO Nash~lle, TN Oklahoma City, OK N. Little Rock, AR StephenviUe, TX Jackson, MS
PBECIPITABLE WATER (em) 1.76 1.97 1.95 2.97 2.14 2.57 1.69 2.14 2.19 2.44 2.56 2.32 3.43
OPTICAL DEPTH 0.169 0.207 0.223 0.288 0.249 0.275 0.163 0.232 0.272 0.193 0.336 0.276 0.555
United States. As a reasonable estimate one may expect errors up to a few degrees C from use of Eq. (5) over areas comparable to a Landsat image, i.e., (100-300 km) 2, with the errors dependent on the degree of temporal and spatial interpolation of the radiosonde data. Of course, these distances may be decreased greatly in meteorologically active situations. To this point the effect of nonunit emissivity of the ground has not been discussed. For the 10-12-/~m spectral region emissivity values generally range between 0.95 and 0.99 (Taylor, 1979). Also, at these wavelengths I - T a'5 (Slater, 1980, Fig. 9.10). Thus from the radiance temperature TgsB given by Eq. (5) one may obtain the physical temperature Tgv using the relation
a 1.176 1.221 1.238 1.308 1.268 1.305 1.171 1.250 1.300 1.190 1.376 1.298 1.695
8T29o
8T310
51.1 63.9 63.3 89.1 77.3 88.7 49.4 72.8 87.2 54.5 - 109.7 - 87.8 - 203.2
0.0 0.2 0.6 0.0 0.2 0.2 0.2 0.2 0.1 0.5 0.6 1.1 1.0
3.0 3.8 4.4 4.7 4.5 4.5 3.1 3.8 4.5 3.7 4.9 3.5 7.2
-
or
4.5
(aT~at+ fl)"
(6)
This equation is well suited for obtaining satellite estimates of surface temperahire from high spatial resolution thermal infrared data.
Dr. Y. Kaufinan provided useful comments and suggestions concerning the manuscript.
Appendix Given Eq. (3) in the form I(TBB) =
aI(Tg)+s, the Planck function and its inverse, it is required to express
OT,
a-= 3TB---~
and fl - TO+ 1 0 - otTBm
in terms of known quantities. Let x = C2/ X and g = C 1/Xs, so that
so that
T~ = TgSB/c~/45 ----'1'~-Bd~~
fl
+ c
TBB = x/ln(1 + g/[aI(Tg)+ s]).
360
j. C. PRICE
T h e n a is determined by differentiation
1 aTBB 7"0= ~ = ~
(--X)
(ln(1 + v/[al(r,)+ s]}) Y
(l + y/[aI(Tg)+ s]}
(-a) (alg+s) ~ 1
age *~to
a
(l+y/[aI(To)+S])
X
• O, -aI(r,) -'-~g
o,
X
To[aI(To)+s] In{1 + v/[aI(To)+s]}
Given a, it is straightforward to find 13: /~ = (TO+ 10)
- ax/In(1 + v / [ a I ( T o + 10)+ s]}.
References Becker, F., Blumenroeder, D., Hechinger, E., Hourani, A., Ramey, B., Trautman, J., Dechambenoy, C., and Pellegrin, A. (1979), Measurement and mapping of absolute surface temperature of water surface by remote sensing, 13th ERIM Symposium on Remote Sensing of Environment, Ann Arbor, Michigan. Carlson, Toby N., Dodd, J. K., Benjamin, S. G., and Cooper, J. N. (1981), Satellite estimation of surface energy balance, moisture availability and thermal inertia,/. Appl. Meteorol. 20:60-87. Chandrasekhar, S. (1960), Radiative Transfer, Dover, New York. Imbauh, Daniele (1979), Determination de la temperature de surface de l'ocean par radiometric differentielle, thesis, Universit6
Pierre and Marie Curie, Paris, France, 163 pp. Kidwell, Katherine B. (1979), NOAA Polar Orbiter Users Guide, National Climatic Center, Washington, D.C., pp. 2.3.12.3.10. Kneizys, F. X., Shettle, E. P., Gallery, W. O., Chetwynd, L. H., Jr., Abreu, L. W., Selby, J. E. A., Fenn, R. W., and McClatchey, R. A. (1980), Atmospheric transmittance/ radiance: Computer Code Lowtran 5, Environmental Research Papers, No. 697, Air Force Geophysics Laboratory, Hanscom AFB, Bedford, Mass., pp. 57-60. McClatchey, R. A., Fenn, R. W., Selby, J. E. 2. A., Volz, F. E., and Garing, J. S. (1971), Optical Properties of the Atmosphere (Revised), Environmental Research Paper No. 354, Air Force Cambridge Research Laboratories, p. 24. NASA (1978), Heat Capacity Mapping Mission User's Guide, Goddard Space Flight Center, Greenbelt, Md. (revised 1980), 120 pp. NOAA-Environmental Data Service, National Climatic Center, Ashville, N. C. NOAA (1980), Environmental Satellite Service Catalog of Products, 3rd ed., U.S. Department of Commerce, Washington, D.C., pp. 73-83. Price, John C. (1981), The Contribution of Thermal Data in Landsat Multispectral Classification, Photo. Eng. Remote Sens. 47:229-236. Price, John C. (1982), Estimation of regional scale evapotranspiration through analysis of satellite thermal infrared data, /. IEEE Trans. Geosci. Remote Sens., to be published. Schott, J. R., and Tourin, R. H. (1975), A completely airborne calibration of aerial infrared water temperatttre measurements, in Proceedings of the Tenth International Symposium on Remote Sensing of Environment, Environmental Research Institute of Michigan, Ann Arbor, MI, pp. 78-87. Vol. 1.
ESTIMATING SURFACE TEMPERATURES
361
Slater, Philip N. (1980), Remote Sensing, Watson, K. (1975), Geologic applications of Optics and Optical Systems, Addison-Westhermal irdrared imagery, Proc. IEEE ley, Reading, Mass., pp. 246, 247. 63:128-137. Taylor, S. Elwynn (1979), Measured Emissivity of Soils in the Southeast United States, Received 1 September 1982; revised 2 December 1982. Remote Sens. Environ. 8:359-364.
353
Estimating Surface Temperatures from Satellite Thermal Infrared Data--A Simple Formulation for the Atmospheric Effect*
JOHN C. PRICE H~tdrology Laboratory, Plant Physiology Institute, Beltsville, Maryland
In recent years the availability of high spatial resolution thermal infrared'data from satellites has prompted the use of energy budget models relating satellite-derived surface temperatures to surface moisture, near-surface thermal inertia, energy exchange with the atmosphere, etc. However, correction of the high spatial resolution satellite data for atmospheric water vapor effects can represent a substantial computational burden unless simplifying assumptions are utilized. A simple formulation is developed and its applicability tested by application to standard meteorological soundings at a time near the overpass of an NOAA operational satellite. It appears that reasonable estimates of surface temperature (_+ 2-3°C) are readily obtained for areas of order 100-300 km2.
1. Introduction Recent advances in remote sensing technology have improved the quality (especially the spatial resolution) of thermal infrared measurements to the extent that detailed studies of surface thermal properties can be carried out. The Landsat 3 satellite carried a thermal infrared sensor capable of (240 m) 9" observations, which unfortunately did not perform well in orbit (Price, 1981). The Heat Capacity Mapping Mission satellite (NASA, 1978) acquired (600 m) a spatial resolution data, the Advanced Very High Resolution Radiometer (AVHRR), which is carried on NOAA satellites, acquires (1.1 km)2 data of much higher radiometric quality than that previously available from operational satellites (Kidwell, 1979), and the Thematic Mapper on Landsat satellites D and D' will provide (120 m) 2 thermal infrared data. *Contribution from USDA-ARS, Hydrology Laboratory, Plant Physiology Institute, Beltsville, Maryland. ©Elsevier Science Publishing Co., Inc., 1983 52 Vanderbilt Ave., New York, NY 10017
Data with high precision and spatial resolution are suitable for geologic studies (Watson, 1975), and for possible agricultural applications, such as estimation of surface moisture characteristics (Carlson et al., 1981; Price, 1982), because the field of view resolves many ground features. This permits relatively unambiguous comparison of satellite data with ground truth measurements. One would expect utilization of these data following appropriate research verification. However, a conceptionally simple but computationally demanding problem, namely, correcting satellite infrared measurements for atmospheric effects, complicates the reduction of remotely sensed data to readily interpretable values of surface temperature. It is thus worthwhile to develop a formulation which facilitates application of this atmospheric correction. The formulation described here represents a simple linear approximation to the solution of the radiative transfer equation. Consideration of a sample data set suggests that in relatively undisturbed 0034-4257/83/$3.00
354
(anticyclonic) meteorological conditions the formulation is applicable to large areas (100s of km on a side) with errors of a few degrees C. Infrared radiative transfer is reviewed briefly in See. 2, and the analytic simplification is described. Application to a sample data set is carried out in Sec. 3, and the implications for remote sensing are summarized briefly.
J. c. PRICE
could be used to establish reliable values for the radiative transfer coefficient. The intensity I x of radiation at wavelength ~ (/~m) passing through an absorbing/emitting medium with absorption coefficient k x (m2kg-1) is described by the equation (e.g., Chandrasekhar, 1960, p. 9). d/x =
ds
2. Effect of the Atmosphere in the 10-12-1~m Window For cloud-free locations the 10-12-/xm spectral interval is relatively transparent to radiation, except for the effects of atmospheric water vapor. Although neglect of absorption and emission by CO 2, 0 3, etc., in the present treatment may cause small errors, the major potential error sources arise from uncertainty in the estimation of the absorption coefficient k for water vapor, and from the need to use such radiosonde data as are available for atmospheric temperature and moisture profiles. The influence of aerosols is generally an order of magnitude smaller than molecular effects, except when the atmosphere is hazy (McClatchey et al., 1971). Imbault (1979) has carried out an extensive review of theory and experimental data on water vapor absorption in the 10-12-/xm region of the spectruna. The considerable scatter in experimental data is due to the difficulty in obtaining measurable absorption in the laboratory because the gas is so transparent, or in measuring accurately moisture concentrations and temperature when long path length experiments are conducted outdoors. In principle, a program of aircraft measurements, such as those of Schott and Tourin (1975) or Becker et al. (1979),
-kxpn2°(Ix + Bx)'
(1)
where s is the path length (m), PH20 the density (kgm-a) of the water vapor, and B is the black body emission as given by the Planck function Bx(T ) =
C1
~S[exp(C2/XT )- I ] W m - 2 s r - 1/~m-1"
Here T is the temperature (K), C 1 = 1.19 ×10 s W m - 2 - s r - l / z m 4 and C2 = 1.439 × 104/~m K. Following Imbault, the value of k x given by Kneizys et al. (1980) is used: k x = 10.13
(eexp[18OO(1/T- 1/296)] + 0.002(p- e))
× (4.18 + 5578e exp( - 78.7/~)), where p and e are atmospheric pressure and vapor pressure of water in millibars (1 m b - 10 2 Pa). Integration of Eq. (1) requires knowledge of atmospheric temperature and moisture as functions of height. These may be obtained from radiosonde data (NOAA-Environmental Data and Information Service), except that the data are generally given as functions of pressure. Thus a change of variable through the
ESTIMATING SURFACE TEMPERATURES
355
hydrostatic equation 1
dp
100 dz
dp (dscos O)
The equation expresses the fact that the satellite observed radiation is linearly related to ground emission. One may define a satellite brightness temperature (TBB) from the radiance measurement,
= _ p~g
is appropriate TBB = B - ' [ / ( s a t e l l i t e ) ] ,
dlx = kxq (I x + Bx), dp 100gcos 0
where B function:
where O is the nadir angle of observation (O = 0 for vertical observations), q is the mixing ratio = P H 2 o / ( P H 2 o + Pair), t h e factor 100 arises from expressing p in millibars, and g is the acceleration of gravity (9.8 ms - 2). A formal integration is now possible (Chandrasekhar, 1960), e.g., I x ( p ) = Ix(Po)e -~xO'°'n) + fn°dp, e - ~(no. p')
1
is the inverse of the Planck
B - 1(i ) = C 2 / M n [ 1 + C 1 / ( ~ 5 I )]. For modest temperature intervals (e.g., _ 20 ° about temperatures of order 300 K) the Plank hmction and its inverse are nearly linear at thermal infrared wavelengths (Slater, 1980). Thus Eq. (3) may be reduced to a simple expression relating surface temperatures to satellite observed brightness temperature.
.-1p
× kxqBx/(lOOgcos O),
(4)
T, =
(2)
+ Z,
(5)
where Tg is the ground brightness temperwhere Ix(P o) is the upward radiance at the earth's surface and the optical depth zx has been introduced:
ature,
a= "rx(Po, p ) = fp;'°dp'kxq/(lOOgcos O). is related to the transmittance (the symbol a is used to avoid confusion with temperature T) by ax(p0, p ) = e - ,x(po,n~ The integral on the right of Eq. (2), representing atmospheric emission, is independent of surface radiation. Denoting this sky emission term by s, dropping the subscripts h, and carrying the integral to satellite altitude (0 pressure) I(satellite) = a l o ( g r o u n d ) + s.
(3)
OTBB~o
and
fl = T 1 - aTBm.
It is recommended that the slope a be evaluated at surface air temperature To, with the constant term fl evaluated at T1 = TO+ 10 °, representing the fact that day surface temperatures may be appreciably warmer than air temperature. 1 Since a and s must be evaluated numerically, it is reasonable to obtain a and fl by
IA ro~zaxN listing for the computation of a and fl from meteorological soundings may be obtained from the author.
356
J.C. PRICE 320
s15
PEORIAIL , LINOIS
/
310 uJ iv, I-
<
305
aLU L
:E
'"
I-
300
¢0
111 Z
I--r
295
a,m
,,,
290
0 M.
ca
285
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/ 275
I
I
I
I
I
I
I
I
I
280
285
290
295
300
305
310
315
320
COMPUTED
SATELLITE
BRIGHTNESS
TEMPERATURE
FIGURE 1. Sudace temperature as a hmction ot satellite brightness temperature as given by numerical integration for a sounding (Peoria) described in See. III. Equation (5) yields a virtually identical line.
munerical means. Analytic expressions for a and fl are derived in the Appendix. Thus, over a moderate temperature range, surface temperature is linearly related to satellite observed brightness temperature (Fig. 1). 3. Spatial Variability The utility of Eq. (5) depends on the spatial variability of a and ft. This may be estimated through analysis of meteorological soundings which are acquired routinely for weather forecasting pttrposes.
Examination of satellite imagery from June and July of 1980 lead to selection of the morning of July 24, 1980 as a case study. Satellite imagery from 1400z of this day showed the central United States to be virtually cloud-free, from northern Wisconsin and Michigan to south Texas, and from eastern Colorado and New Mexico to Ohio and Alabama. An area this size corresponds to roughly 3 × 106 individual data points at the (1.1 kin) 2 spatial resolution of the Advanced Very High Resolution Radiometer carried on NOAA operational satellites. Such large data sets illustrate the need for straight-
ESTIMATING SURFACE TEMPERATURES
forward implementation of the atmospheric correction procedure. Nearly coincident radiosonde data for the area were acquired from the National Climatic Center, Ashville, N.C. The 13 stations selected are scattered along the 1600-km swath of satellite data (Fig. 2). For each sounding the temperature and humidity profiles were input to the radiative transfer computation [Eq. (2)], after which the coefficients a and/3 were computed. These values as well as the precipitable water and computed optical depth are given in Table 1. Although the coefficients a and /3 vary considerably from station to station, these variations tend to cancel each other when the total atmospheric correction is obtained. Thus the difference (~T) between the surface temperature and the satellite observed brightness temperature for two assumed values of surface temperature, 290 K and 310 K, were calculated. (2-m air temperatures at the 12z soundings ranged from 286.4 K at Flint, Mich., to 297.0 K at Stephenville, Tex.). From BT29o and ~T31o (Table 1), it is clear that the variation of the atmospheric correction is relatively small, i.e., from 3.0 to 4.9 K at 310 K, for the large central region of the United States on the date selected. An exception is evident in the data: the Jackson, Miss. sounding was significantly more moist than the others, leading to increased values of the atmospheric correction. This increased humidity is evidenced by scattered clouds in the Jackson area. In most cases cloud-free satellite images will be accompanied by lower than average atmospheric moisture content. The satellite thermal infrared data were examined and yielded surface tempera-
357
tures generally a few degrees warmer than air temperatures, as would be expected. A precise comparison of the satellite predicted surface temperatures with ground measurements would best be accomplished over a large uniform water surface, as with the NOAA operational sea surface temperature product (NOAA, 1980). From a practical point of view the error in using Eq. (5) in establishing land surface temperatures is associated with the time and space difference between the meteorological sounding and the satellite observation, the need to assume a value for surface emissivity, possible variation of the satellite calibration, etc. It thus appears that for undisturbed synoptic conditions, and given relatively minor topographic variability (which influences the optical depth of the atmosphere because moisture is concentrated in the lowest layers of the atmosphere), one may utilize meteorological sounding data to reduce satellite thermal infrared measurements to ground surface temperahares over moderate-sized areas. In practice one may utilize a single nearby sounding to compute a and ~, or else interpolate among a number of soundings. The results in Table 1 for 8T do not represent the extreme values of the atmospheric correction, nor of the possible errors resulting from computations using radiosonde data. Generally the atmospheric effect increases near midday, when the ground temperature may exceed 320-330 K during the summer. In such cases the atmospheric correction may exceed 10 °, as can be seen by extrapolation of ~T29o and ~T310 in Table 1. In addition by international convention radiosonde observations are taken near 00z and 1200z, thus missing the midday warming of the lower atmosphere in the
358
J.C. PRICE
FIGURE 2. Visibleimagery acquired by the NOAA-6Advanced Very High ResolutionRadiometer at 14:26z, July 24, 1980.
359
ESTIMATING SURFACE TEMPERATURES TABLE 1
Atmospheric Corrections--July 24, 1980, 1200z
LOCATION St. Cloud, MN Green Bay, WI Flint, MI Omaha, NE Peoria, IL Topeka, KS Salem, IL Monett, MO Nash~lle, TN Oklahoma City, OK N. Little Rock, AR StephenviUe, TX Jackson, MS
PBECIPITABLE WATER (em) 1.76 1.97 1.95 2.97 2.14 2.57 1.69 2.14 2.19 2.44 2.56 2.32 3.43
OPTICAL DEPTH 0.169 0.207 0.223 0.288 0.249 0.275 0.163 0.232 0.272 0.193 0.336 0.276 0.555
United States. As a reasonable estimate one may expect errors up to a few degrees C from use of Eq. (5) over areas comparable to a Landsat image, i.e., (100-300 km) 2, with the errors dependent on the degree of temporal and spatial interpolation of the radiosonde data. Of course, these distances may be decreased greatly in meteorologically active situations. To this point the effect of nonunit emissivity of the ground has not been discussed. For the 10-12-/~m spectral region emissivity values generally range between 0.95 and 0.99 (Taylor, 1979). Also, at these wavelengths I - T a'5 (Slater, 1980, Fig. 9.10). Thus from the radiance temperature TgsB given by Eq. (5) one may obtain the physical temperature Tgv using the relation
a 1.176 1.221 1.238 1.308 1.268 1.305 1.171 1.250 1.300 1.190 1.376 1.298 1.695
8T29o
8T310
51.1 63.9 63.3 89.1 77.3 88.7 49.4 72.8 87.2 54.5 - 109.7 - 87.8 - 203.2
0.0 0.2 0.6 0.0 0.2 0.2 0.2 0.2 0.1 0.5 0.6 1.1 1.0
3.0 3.8 4.4 4.7 4.5 4.5 3.1 3.8 4.5 3.7 4.9 3.5 7.2
-
or
4.5
(aT~at+ fl)"
(6)
This equation is well suited for obtaining satellite estimates of surface temperahire from high spatial resolution thermal infrared data.
Dr. Y. Kaufinan provided useful comments and suggestions concerning the manuscript.
Appendix Given Eq. (3) in the form I(TBB) =
aI(Tg)+s, the Planck function and its inverse, it is required to express
OT,
a-= 3TB---~
and fl - TO+ 1 0 - otTBm
in terms of known quantities. Let x = C2/ X and g = C 1/Xs, so that
so that
T~ = TgSB/c~/45 ----'1'~-Bd~~
fl
+ c
TBB = x/ln(1 + g/[aI(Tg)+ s]).
360
j. C. PRICE
T h e n a is determined by differentiation
1 aTBB 7"0= ~ = ~
(--X)
(ln(1 + v/[al(r,)+ s]}) Y
(l + y/[aI(Tg)+ s]}
(-a) (alg+s) ~ 1
age *~to
a
(l+y/[aI(To)+S])
X
• O, -aI(r,) -'-~g
o,
X
To[aI(To)+s] In{1 + v/[aI(To)+s]}
Given a, it is straightforward to find 13: /~ = (TO+ 10)
- ax/In(1 + v / [ a I ( T o + 10)+ s]}.
References Becker, F., Blumenroeder, D., Hechinger, E., Hourani, A., Ramey, B., Trautman, J., Dechambenoy, C., and Pellegrin, A. (1979), Measurement and mapping of absolute surface temperature of water surface by remote sensing, 13th ERIM Symposium on Remote Sensing of Environment, Ann Arbor, Michigan. Carlson, Toby N., Dodd, J. K., Benjamin, S. G., and Cooper, J. N. (1981), Satellite estimation of surface energy balance, moisture availability and thermal inertia,/. Appl. Meteorol. 20:60-87. Chandrasekhar, S. (1960), Radiative Transfer, Dover, New York. Imbauh, Daniele (1979), Determination de la temperature de surface de l'ocean par radiometric differentielle, thesis, Universit6
Pierre and Marie Curie, Paris, France, 163 pp. Kidwell, Katherine B. (1979), NOAA Polar Orbiter Users Guide, National Climatic Center, Washington, D.C., pp. 2.3.12.3.10. Kneizys, F. X., Shettle, E. P., Gallery, W. O., Chetwynd, L. H., Jr., Abreu, L. W., Selby, J. E. A., Fenn, R. W., and McClatchey, R. A. (1980), Atmospheric transmittance/ radiance: Computer Code Lowtran 5, Environmental Research Papers, No. 697, Air Force Geophysics Laboratory, Hanscom AFB, Bedford, Mass., pp. 57-60. McClatchey, R. A., Fenn, R. W., Selby, J. E. 2. A., Volz, F. E., and Garing, J. S. (1971), Optical Properties of the Atmosphere (Revised), Environmental Research Paper No. 354, Air Force Cambridge Research Laboratories, p. 24. NASA (1978), Heat Capacity Mapping Mission User's Guide, Goddard Space Flight Center, Greenbelt, Md. (revised 1980), 120 pp. NOAA-Environmental Data Service, National Climatic Center, Ashville, N. C. NOAA (1980), Environmental Satellite Service Catalog of Products, 3rd ed., U.S. Department of Commerce, Washington, D.C., pp. 73-83. Price, John C. (1981), The Contribution of Thermal Data in Landsat Multispectral Classification, Photo. Eng. Remote Sens. 47:229-236. Price, John C. (1982), Estimation of regional scale evapotranspiration through analysis of satellite thermal infrared data, /. IEEE Trans. Geosci. Remote Sens., to be published. Schott, J. R., and Tourin, R. H. (1975), A completely airborne calibration of aerial infrared water temperatttre measurements, in Proceedings of the Tenth International Symposium on Remote Sensing of Environment, Environmental Research Institute of Michigan, Ann Arbor, MI, pp. 78-87. Vol. 1.
ESTIMATING SURFACE TEMPERATURES
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Slater, Philip N. (1980), Remote Sensing, Watson, K. (1975), Geologic applications of Optics and Optical Systems, Addison-Westhermal irdrared imagery, Proc. IEEE ley, Reading, Mass., pp. 246, 247. 63:128-137. Taylor, S. Elwynn (1979), Measured Emissivity of Soils in the Southeast United States, Received 1 September 1982; revised 2 December 1982. Remote Sens. Environ. 8:359-364.