Science in China Series D: Earth Sciences © 2008
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Correlation-based temperature and emissivity separation algorithm CHENG Jie1,3†, LIU QinHuo1,3, LI XiaoWen1,2, XIAO Qing1, LIU Qiang1 & DU YongMing1,2 1
State Key Laboratory of Remote Sensing Science, Jointly Sponsored by the Institute of Remote Sensing Applications of Chinese Academy of Sciences and Beijing Normal University, Beijing 100101, China; 2 Beijing Key Laboratory of Environmental Remote Sensing and City Digitalization, Beijing Normal University, Beijing 100875, China; 3 Graduate University of Chinese Academy of Sciences, Beijing 100049, China
Based on analyzing the relationship between the atmospheric downward radiance and surface emissivity, this paper proposes a correlation criterion to optimize surface temperature during the process of temperature and emissivity separation from thermal infrared hyperspectral data, and puts forward the correlation-based temperature and emissivity separation algorithm (CBTES). The algorithm uses the correlation between the atmospheric downward radiance and surface emissivity to optimize surface temperature, and obtains surface emissivity with this temperature. The accuracy of CBTES was evaluated by the simulated thermal infrared hyperspectral data. The simulated results show that the CBTES can achieve high accuracy of temperature and emissivity inversion. CBTES has been compared with the iterative spectrally smooth temperature/emissivity separation (ISSTES), and the comparison results show that they have relative accuracy. Besides, CBTES is insensitive to the instrumental random noise and the change of atmospheric downward radiance during the measurements. As regards the nonisothermal pixel, its radiometric temperature changes slowly with the wavenumber when its emissivity is defined as r-emissivity. The CBTES can be used to derive the equivalent temperature of nonisothermal pixel in a narrow spectral region when we assumed that the radiometric temperature is invariable in the narrow spectral region. The derived equivalent temperatures in multi-spectral regions in 714―1250 cm−1 can characterize the change trend of nonisothermal pixel’s radiometric temperature. correlation, temperature and emissivity separation, nonisothermal pixel, thermal infrared, remote sensing
Land surface temperature (LST) is one of the key parameters to characterize the land-surface physical processes on a regional as well as global scale[1]. LST is integrative results of reciprocity between land, ocean, and atmosphere. Therefore, it is an important parameter in the study of many environmental models[2], for example: 1) matter and energy exchange between atmosphere and land surface; 2) numerical weather prediction; 3) global ocean circulation; 4) global climatic change, etc. Surface emissivity is a physical quantity which mainly depends on surface’s compositions and texture. Surface emissivity can be used in the field of target identification and ― mineral mapping[3 5]. In the temperature inversion with surface emissivity known as a prior, the determination of
surface emissivity affects the precision of LST, and the uncertainty of surface emissivity has become one of the key parameters that constrain the improvement of precision of LST retrieval[6]. Temperature and emissivity separation are the basis and key problems of thermal infrared remote sensing[7]. Temperature and emissivity inversion from the radiometric measurements of thermal infrared remote sensor is also an ill-posed problem even if we have obtained the Received September 27, 2007; accepted December 27, 2007 doi: 10.1007/s11430-008-0022-7 † Corresponding author (email:
[email protected]) Supported by the National Knowledge Innovation Program of CAS (Grant Nos. KZCX3-SW-338-2 and KZCX2-YW-313), the National Natural Science Foundation of China (Grant Nos. 40501042, 40671139 and 40701123), and National Basic Research Program of China (Grant No. 2007CB714400)
Sci China Ser D-Earth Sci | Mar. 2008 | vol. 51 | no. 3 | 357-369
accurate atmospheric parameters. Some approximations and assumptions must be taken to make the under-determined equation well determined. Several temperature and emissivity separation algorithms with different approximations and assumptions have been put ― forward[8 17]. The rationality of these approximations and assumptions in the algorithms has become the key factor affecting the precision of temperature and emissivity inversion. With the development of infrared sensor techniques, the hyperspectral infrared sensors have been provided with the preliminary ability of practicality. The improvement of spectral resolution gives prominence to the object’s spectral characteristic, produces stable constraints with physical meanings, makes the under-determined equation well determined, and improves the accuracy of temperature and emissivity inversion finally.
+ ∫ ρb,i (θi , φi ,θ r , φr ) Latm↓, j (θi , φi ) cos θi dΩi .
Assuming surface is lambertian, according to the Kirchhoff’s law, the at-sensor radiance is given as L j (θ r , φr ) = ε j (θ r , φr ) B j (Ts ) + (1 − ε j (θ r , φr )) Latm↓, j , (3) where Latm↓, j is the equivalent atmospheric downward radiance (This term will be called the atmospheric downward radiance later), which is given as 1 Latm↓, j = ∫ Latm↓, j (θi , φi ) cos θi dΩi . (4) π 2π Once we obtained an estimated value Tˆ of surface temperature, surface emissivity can be calculated with eq. (5):
ε j (θ r , φr ) =
L j (θ r , φr ) − Latm↓, j . B (Tˆ ) − L j
1 Algorithm’s principle 1.1 The relationship between the atmospheric downward radiance and surface emissivity The general formulation of the band radiance received by the thermal infrared sensor can be expressed as L j (θ r , φr ) = τ j (θ r , φr )ε j (θ r ,φr ) B j (Ts ) + Latm↑, j (θ r , φr )
+ τ j (θ r , φr ) ∫ ρb,i (θi , φi ,θ r , φr ) Latm↓, j (θi ,φi ) cos θi dΩi , 2π
(1) where L j (θ r , φr ) is the at-sensor directional radiance,
τ j (θ r , φr ) is
the
total
atmosphere
transmittance,
ε j (θ r , φr ) is the directional emissivity, B j (Ts ) is the radiance emitted by a blackbody at the surface temperature Ts , which can be calculated with Planck’s law,
Latm↑, j (θ r , φr ) is the upward radiance directly emitted by the atmosphere between the sensor and surface, ρb,i (θi , φi ,θ r , φr ) is the bi-directional reflectance distribution function (BRDF), and Latm↓, j (θi , φi ) is the downward radiance emitted and diffused by the total atmosphere. In the field measurements, the distance between the sensor and surface is about one meter, and the influence of atmosphere in the path can be neglected. So, equation (1) can be approximated as[18] L j (θ r , φr ) = ε j (θ r , φr ) B j (Ts ) 358
(2)
2π
(5)
atm ↓ , j
The accuracy of surface temperature is very crucial in the temperature and emissivity separation. The derived surface emissivity spectrum will remain atmospheric emission lines if the derived surface temperature is inaccurate, as shown in Figure 1. The data used to generate Figure 1 were simulated data. The atmospheric model used in the simulation is 1976 US Standard Atmosphere; the spectral resolution is 1 cm−1; surface emissivity is the mean of soil emissivity in the ASTER spectral library; the true surface temperature is 300 K. When the derived surface temperature is not equal to 300 K, the calculated emissivity with eq. (5) will remain atmospheric emission lines, and the intensity of residual atmospheric emission lines mainly depends on the original intensity of the lines in the atmospheric downward radiance. When the derived surface temperature is less than 300 K, the derived surface emissivity is greater than the true value, and surface emissivity is correlated with the atmospheric downward radiance positively. When the derived surface temperature is greater than 300 K, the derived surface emissivity is less than the true value, and surface emissivity is correlated with the atmospheric downward radiance negatively. The degree of correlation depends on the bias of the derived temperature. The larger the bias, the better the correlation (here, the correlation means the absolute value of coefficient between surface emissivity and the atmospheric downward radiance). However, the true surface emissivity has nothing to do with the atmospheric downward radiance in theory.
CHENG Jie et al. Sci China Ser D-Earth Sci | Mar. 2008 | vol. 51 | no. 3 | 357-369
Figure 1
1097―1141 cm−1 spectral region. (a) Atmospheric downward radiance; (b) emissivity curves correspond to different soil temperatures.
1.2 Correlation-based temperature and emissivity separation algorithm (CBTES)
CBTES uses the correlation between the atmospheric downward radiance and surface emissivity to optimize surface temperature, assumes surface emissivity and the atmospheric downward radiance as vectors X and Y with n dimension, generates a series of temperatures which centered around the maximum brightness corresponding to the ground-leaving radiance at an interval of instrument noise equivalent delta temperature (NEDT), calculates surface emissivity Xi corresponding to each given temperature with eq. (5) and then calculates the correlation between Xi and Y. The optimal value of the surface temperature is the one possessing minimum correlation. Once we obtained the surface temperature, surface emissivity can be derived with eq. (5) from the sensor’s radiometric measurements and the derived surface temperature: X ⋅Y , X i ∈ Rn ,Y ∈ Rn , corr(i ) = i (6) Xi Y optimalT = Ti
min(abs(corr(i )))
,
(7)
where corr is the coefficient between the vectors X i and Y, the symbol · represents inner product, || || is the module of the vector, abs represents absolute value. Eqs. (6) and (7) are the correlation criterion of surface temperature optimization.
2 Analysis and discussion 2.1 The accuracy of temperature and emissivity retrieval
CBTES obtains the optimal temperature based on the
correlation criterion, and then calculates surface emissivity with sensor’s radiometric measurements and this temperature. The accuracy of surface temperature will definitely influence the accuracy of the following surface emissivity calculation. So the first thing we should do is to investigate the accuracy of surface temperature before investigating the accuracy of surface emissivity on the premise that CBTES can achieve high accuracy of surface temperature. The accuracy of CBTES is evaluated by simulated data. The spectral resolution of the simulated data is 1 cm−1. The atmospheric downward radiance was simulated with the atmospheric radiative transfer code MODTEAN 4.0. We used the atmospheric downward radiance of 53° to replace the equivalent atmospheric ― downward radiance[19 21]. The atmosphere models we used were: 1976 US Standard Atmosphere (abbreviated as standard atmosphere), mid-latitude summer, midlatitude winter, sub-arctic summer, sub-arctic winter, and tropical atmosphere. Surface emissivities selected were soil emissivities in the ASTER spectral library and vegetation emissivities in the MODIS USCB spectral library. The reason why we selected these kinds of samples is that they are typical type of land cover and represent two kinds of typical spectral characteristics, vegetation emissivity is similar to water and snow, their spectral contrast is low, soil emissivity is similar to the rock, and their spectral contrast is high. The simulated ground-leaving radiance and atmospheric downward were added an instrumental random noise of 2.5e−9 W·cm−2·sr−1·cm−1, which was the labeled noise equivalent spectral radiance (NESR) of the spectrometer
CHENG Jie et al. Sci China Ser D-Earth Sci | Mar. 2008 | vol. 51 | no. 3 | 357-369
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BOMEM FTIR MR 304. Two quantities were used to evaluate the accuracy of CBTES: temperature bias and root mean of squared error (RMSE). Temperature bias was used to evaluate the accuracy of surface temperature retrieval and RMSE was used to evaluate the accuracy of surface emissivity retrieval. Their definitions were given as T = abs(Tˆ − T ), (8) bias
true
N
RMSE =
∑ (ε i,inv − ε true )2 i =1
, (9) N where Tbias is temperature bias, Ttrue is the true temperature, εi,inv is the emissivity retrieved with CBTES, εtrue is the true or mean value of emissvity, εtrue is the true emissivity when calculating emissivity RMSE of each band, and εtrue is the mean value of emissivity when calculating the RMSE of each emissivity sample. (1) Accuracy of temperature retrieval. In the simulation, surface emissivities are the mean value of soil emissivities in the ASTER spectral library and vegetation emissivities in the MODIS USCB spectral library. Table 1
Surface temperatures were centered on the bottom layer temperature of temperature profile of each atmosphere model at 5 K interval and within the range of 30 K. For each given surface temperature, we generated 200 simulated data, retrieved surface temperature and emissivity with CBTES, and calculated the temperature bias. Then we obtained 200 temperature biases for each given surface temperature, and took its mean as the accuracy of surface temperature retrieval. Different spectral regions in 714-1250 cm−1 have been selected to retrieve surface temperature with CBTES based on the intensity of atmosphere emission lines and their sensitivity to the temperature bias. We found CBTES can achieve high accuracy of temperature retrieval in 1097-1141 cm−1 and 1097 - 1125 cm−1 through simulated calculation. The results are shown in Tables 1 and 2. Temperature bias is less than 0.08 K in 1097―1141 cm−1 when surface temperature is higher than or equal to the bottom layer temperature of atmosphere profile. Temperature biases are relatively large when surface temperature is lower than the bottom layer temperature of atmosphere profile of mid-latitude summer, sub-arctic
Algorithm’s temperature retrieval accuracy when the surface emissivity is the mean of soil emissivity in the ASTER spectral librarya)
T (K) 273.1 278.1 283.1 288.1 0.02(0.03) 0.02(0.03) 0.03(0.04) 0.04(0.05) Tbias(K) T (K) 279.2 284.2 289.2 294.2 Mid-latitude summer 3.56(0.01) 0.38(0.02) 0.01(0.02) 0.01(0.03) Tbias (K) T (K) 257.2 262.2 267.2 272.2 Mid-latitude winter Tbias (K) 0.03(0.03) 0.03(0.04) 0.03(0.05) 0.04(0.07) T (K) 272.2 277.2 282.2 287.2 Sub-arctic summer 0.31(0.02) 0.01(0.02) 0.02(0.03) 0.02(0.04) Tbias (K) T (K) 242.2 247.2 252.2 257.2 Sub-arctic winter Tbias (K) 0.03(0.06) 0.03(0.08) 0.04(0.11) 0.05(0.14) T (K) 284.7 289.7 294.7 299.7 Tropical atmosphere 2.01(1.87) 1.59(0.01) 3.04(0.02) 0.01(0.03) Tbias (K) a) The value in parentheses means that the spectral region used in CBTES is 1097―1125 cm−1. Standard atmosphere
Table 2 librarya)
298.1 0.06(0.09) 304.2 0.02(0.06) 282.2 0.07(0.10) 297.2 0.04(0.06) 267.2 0.05(0.20) 309.7 0.01(0.06)
303.1 0.08(0.10) 309.2 0.03(0.07) 287.2 0.07(0.12) 302.2 0.05(0.08) 272.2 0.07(0.26) 314.7 0.01(0.07)
Algorithm’s temperature retrieval accuracy when the surface emissivity is the mean of vegetation emissivity in the MODIS UCSB spectral
T (K) 273.1 278.1 283.1 288.1 1.04(0.02) 0.01(0.01) 0.01(0.02) 0.01(0.02) Tbias(K) T (K) 279.2 284.2 289.2 294.2 Mid-latitude summer Tbias (K) 3.23(0.01) 0.41(0.01) 3.07(0.01) 0.01(0.02) T (K) 257.2 262.2 267.2 272.2 Mid-latitude winter Tbias (K) 0.02(0.03) 0.02(0.03) 0.02(0.04) 0.02(0.03) T (K) 272.2 277.2 282.2 287.2 Sub-arctic summer Tbias (K) 0.37(0.01) 3.47(0.02) 0.01(0.02) 0.01(0.02) T (K) 242.2 247.2 252.2 257.2 Sub-arctic winter Tbias (K) 0.03(0.05) 0.04(0.05) 0.03(0.05) 0.04(0.06) T (K) 284.7 289.7 294.7 299.7 Tropical atmosphere Tbias (K) 2.02(1.92) 2.81(0.01) 3.07(0.01) 0.01(0.01) a) The value in parentheses means that the spectral region used in CBTES is 1097―1125 cm−1. Standard atmosphere
360
293.1 0.05(0.06) 299.2 0.02(0.04) 277.2 0.06(0.08) 292.2 0.03(0.05) 262.2 0.05(0.17) 304.7 0.01(0.04)
293.1 0.01(0.02) 299.2 0.01(0.02) 277.2 0.02(0.04) 292.2 0.02(0.02) 262.2 0.04(0.08) 304.7 0.01(0.01)
CHENG Jie et al. Sci China Ser D-Earth Sci | Mar. 2008 | vol. 51 | no. 3 | 357-369
298.1 0.02(0.03) 304.2 0.01(0.02) 282.2 0.03(0.04) 297.2 0.01(0.02) 267.2 0.04(0.08) 309.7 0.01(0.02)
303.1 0.02(0.03) 309.2 0.01(0.02) 287.2 0.03(0.05) 302.2 0.01(0.03) 272.2 0.05(0.09) 314.7 0.01(0.02)
summer and tropical atmosphere, resulting from the singular emissivity introduced during the process of surface temperature optimization, and we will discuss the reason in section 2.5. Temperature bias is less than 0.11 K in 1097-1125 cm−1 except for tropical atmosphere when surface temperature is lower than the bottom layer temperature of atmosphere profile. The accuracy of temperature retrieval in 1097-1125 cm−1 is better than 1097-1141 cm−1 when surface temperature is lower than the bottom layer temperatures of mid-latitude summer and sub-arctic summer; the temperature bias is less than 0.03 K. The temperature bias is less than 0.02 K when the surface temperature is lower than the bottom layer temperature of atmosphere profile of tropical atmosphere, and that surface temperature is 15 K lower than the bottom layer temperature is not included. High accuracy of surface temperature retrieval can be achieved through combining these two spectral regions because surface temperature can be deduced easily from measured ground-leaving radiance or other methods in the field measurements and air temperature can also be obtained from ground meteorological station. (2) Accuracy of emissivity retrieval. Based on the surface temperature retrieval results with CBTES in 1097-1141 cm−1, we selected the surface temperature range whose boundary temperature bias is less than 0.1 K to generate surface temperature randomly. Simulated data were generated with these temperatures, six atmosphere models, soil emissivities in the ASTER spectral library, and vegetation emissivities in the MODIS USCB spectral library. For each emissivity spectrum, 200 simulated data were generated. Surface temperatures were retrieved with CBTES in 1097-1141 cm−1, then surface emissivities in 714-1250 cm−1 were calculated. For each simulated datum, temperature bias and RMSE of each emissivity sample were derived subsequently.
For each emissivity spectrum, three quantities were obtained: the mean of temperature bias, the mean of sample RMSE, and RMSE of each band. For the soil emissivity or vegetation emissivity in the spectral library, we can also obtain three quantities: the mean of temperature bias of each emissivity spectrum, the mean of sample RMSE of each emissivity spectrum, and the mean of RMSE of each band of each emissivity spectrum. The mean of RMSE of each band of each emissivity spectrum was regarded as the accuracy of emissivity retrieval. In the extremity of 714-1250 cm−1, surface emissivity contains the residual atmospheric emission lines, so the RMSE is relatively large, the RMSE is less than 0.003 in other spectral regions (Figures 2 and 3). The temperature bias is less than 0.07 K and the RMSE of sample is less than 0.011 (Table 3). 2.2 Comparison with ISSTES
We also used ISSTES to retrieve surface temperature and emissivity with the same data as above. Three quantities used to evaluate the algorithm were also calculated and compared with those derived with CBTES. Figures 2 and 3 show the RMSE of emissivity derived from those two algorithms. Table 3 gives temperature bias and sample RMSE derived from those two algorithms. We can see from those two figures that: (1) The emissivity being soil emissivity in the ASTER spectral library. When the atmosphere models are standard atmosphere and mid-latitude winter, the accuracy of emissivity derived with those two algorithms is comparative; when the atmosphere models are mid-latitude summer, sub-arctic summer and sub-arctic winter, the accuracy of emissivity derived with CBTES is higher than that derived with ISSTES; when the atmosphere model is tropical atmosphere, the accuracy of emissivity derived with CBTES is lower than that derived with ISSTES.
Table 3 The accuracy of CBTES and ISSTES when the emissivity is soil emissivity in the ASTER spectral library or vegetation emissivity in the MODIS USCB spectral librarya) Atmosphere model
Tbias (K)
RMSE
CBTES
ISSTES
CBTES
Standard atmosphere
0.03(0.02)
0.02(0.01)
0.009(0.008)
0.007(0.008)
ISSTES
Mid-latitude summer
0.02(0.01)
0.07(0.01)
0.009(0.002)
0.011(0.001)
Mid-latitude winter
0.03(0.03)
0.02(0.01)
0.006(0.004)
0.004(0.003)
Sub-arctic summer
0.07(0.02)
0.08(0.08)
0.011(0.010)
0.013(0.013)
Sub-arctic winter
0.03(0.05)
0.10(0.11)
0.006(0.011)
0.008(0.009)
Tropical atmosphere 0.04(0.02) 0.01(0.01) 0.002(0.001) 0.001(0.001) a) The value in parentheses is the accuracy of CBTES and ISSTES when the emissivity is vegetation emissivity in the MODIS USCB spectral library.
CHENG Jie et al. Sci China Ser D-Earth Sci | Mar. 2008 | vol. 51 | no. 3 | 357-369
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Figure 2 RMSE of soil emissivity corresponding to different atmosphere models. (a) Standard atmosphere; (b) mid-latitude summer; (c) mid-latitude winter; (d) sub-arctic summer; (e) sub-arctic winter; (f) tropical atmosphere.
(2) The emissivity being vegetation emissivity in the MODIS USCB spectral library. When the atmosphere models are sub-arctic summer and sub-arctic winter, the accuracy of emissivity derived with CBTES is higher than that derived with ISSTES; when the atmosphere 362
models are standard atmosphere, mid-latitude summer, mid- latitude winter and tropical atmosphere, the accuracy of emissivity derived with CBTES is a litter lower than that derived with ISSTES. From those analyses, we concluded that their accu-
CHENG Jie et al. Sci China Ser D-Earth Sci | Mar. 2008 | vol. 51 | no. 3 | 357-369
Figure 3 RMSE of vegetaion emissivity corresponding to different atmosphere models. (a) Standard atmosphere; (b) mid-latitude summer; (c) mid-latitude winter; (d) sub-arctic summer; (e) sub-arctic winter; (f) tropical atmosphere.
racy is comparative. 2.3 Algorithm’s sensitivity to the instrumental random noise
The instrumental random noise is one of the factors to influence the algorithm’s accuracy. The algorithm’s sen-
sitivity to the instrumental random noise was evaluated with simulated data. Standard atmosphere, vegetation emissivities in the MODIS USCB spectral library and randomly distributed temperature in the range of 278.1- 303.1 K were used to generate ground-leaving radiance
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and atmospheric downward radiance. 2-, 4-, 8-, and 16-fold instrumental random noise were added to the simulated data. 1097-1141 cm−1 spectral region was used to retrieve surface temperature with CBTES, and then surface emissivity was derived. The temperature bias is about 0.11 K (Table 4) and RMSE of emissivity is about 0.005 except the extremity of 714-1125 cm−1 (Figure 4) when the simulated data were added with 8-fold instrumental random noise, showing that CBTES is insensitive to the instrument random noise. 2.4 Algorithm’s sensitivity to atmospheric downward radiance error
In the field measurements, the atmospheric downward radiance was measured with a standard gold reflector. The time interval between ground-leaving radiance and the equivalent atmospheric downward radiance measurements depends on the settled instrument spectral resolution and scanning times. The actual atmospheric
Algorithm’s sensitivity to the instrumental random noise.
Figure 4 Table 4
Sample RMSE and temperature bias corresponding to different levels of instrumental random noise Instrumental noise level
Table 5
16
24
RMSE
0.008
1
0.020
0.023
0.035
0.052
0.063
Tbias(K)
0.02
0.03
0.05
0.11
0.21
0.31
2
4
8
Sample RMSE and temperature bias corresponding to different atmospheric downward radiance errors Atmospheric downward radiance error
364
downward radiance may be changed during the process of these two measurements. Standard atmosphere, soil emissivities in the ASTER spectral library and randomly distributed temperature in the range of 278.1-303.1 K were used to generate ground-leaving radiance and atmospheric downward radiance. 1%, 2%, 5%, and 10% errors of atmospheric downward radiance were added to the simulated atmospheric downward radiance. 1097- 1141 cm−1 spectral region was used to retrieve surface temperature with CBTES, and then surface emissivity was derived. As we can see from Figure 5 and Table 5, RMSE of emissivity is about 0.005 when the atmospheric downward radiance error was 5%, and RMSE of emissivity is about 0.01 when the atmospheric downward radiance error was 10% except the extremity of 714 - 1125 cm−1, and the corresponding temperature biases are 0.23 K and 0.46 K respectively, which shows that CBTES is insensitive to the atmospheric downward radiance error.
RMSE
1% 0.010
2% 0.014
5% 0.027
10% 0.035
Tbias(K)
0.05
0.09
0.23
0.46
CHENG Jie et al. Sci China Ser D-Earth Sci | Mar. 2008 | vol. 51 | no. 3 | 357-369
Figure 5
The algorithm’s sensitivity to the atmospheric downward radiance error.
2.5 Reason for partial larger errors of surface temperature retrieval
The reasons for partial large errors of surface temperature retrieval were analyzed with simulated data. The mid-latitude summer atmosphere model and mean value of vegetation emissivities in the MODIS UCSB spectral library were used to generate simulated data. The temperature of vegetation was assumed to be 284.2 K. Figure 6(a) gives the simulated ground-leaving radiance and the atmospheric downward radiance; Figure 6(b) gives the correlation of surface emissivity and the atmospheric downward radiance corresponding to different surface temperatures; Figure 6(c) gives the true emissivity and calculated emissivity located around two minima of correlation, one corresponds to the surface temperature of 283.79 K, the other corresponds to the surface temperature of 284.23 K. When the vegetation temperature was 283.79 K, the derived emissivity should be greater than the true value. However, the derived vegetation emissivity is less than the true value at 1136 cm−1 when the surface temperature was 283.79 K, the derived emissivity at 1136 cm−1 was singular value, which distorts the correlation between surface emissivity and the atmospheric downward radiance, as shown in Figure 6(c). The original correlation changed from a relative large value between zero and one to zero or a little value, even less than the cor-
relation corresponding to the optimal temperature. Hence, we can not obtain the accurate vegetation temperature. The reason for the introduction of unwonted emissivity can be penetrated from eq. (5) from the angle of numerical calculation: 1) The subtract operation reduced the signal noise ratio; 2) In the process of surface temperature optimization, surface temperature was generated randomly around the maximum brightness temperature calculated with the ground-leaving radiance at certain interval, and usually the interval equals the NEDT of instrument. Because the atmospheric downward radiance is constant during the surface temperature optimization, surface temperature is changing, when the difference between ground-leaving radiance and object’s blackbody radiation at its true temperature is in the same order as the instrumental random noise, that is to say, the numerator and denominator of eq. (5) without being affected by the instrumental random noise and the instrument random noise are in the same order as the instrumental random noise, and the probability of introducing unwonted singular emissivity is very great. 2.6 Consideration of nonisothermal pixel
Up to now, the temperature and emissivity separation algorithms in the literatures can only obtain an average equivalent temperature in the thermal infrared on the assumption that the pixel is isothermal, so does CBTES
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sothermal pixel so far[22 27]. The radiometric temperature of nonisothermal pixel will vary slowly with wavenumber when its emissivity is defined as r-emissivity[22]. Therefore, large error will be brought out definitely when we used an average equivalent temperature to replace the radiometric temperature of nonisothermal pixel in 714―1250 cm−1. We considered two kinds of typical nonisothermal pixel: 1) the mixed system composed of soil and vegetation. Their temperature difference is very large under the direct irradiation of sun; 2) pixel composed of naked soil or Gobi. Two components with different temperatures, illumination and shadow were formed due to the multi-shadow between components. We assumed that the nonisothermal pixel was composed of two components, each component is lambertian, the atmosphere state is the same within the pixel, the area ratios of two components are a1 and a2, component temperatures are T1 and T2, component emissivities are εj,1 and εj,2. The radiance received by the thermal infrared sensor can be expressed as ―
L j (θ r , ϕr ) = a1ε j ,1 B(T1 ) + a2ε j ,2 B(T2 ) + (1 − a1ε j ,1 − a2ε j ,2 ) Latm↓, j + e j ,
(10)
where L j (θ r , ϕ r ) is the at-sensor radiance of band j,
Figure 6 (a) Ground-leaving radiance and atmospheric downward radiance; (b) correlation corresponding to different vegetation temperatures; (c) true emissivity and calculated emissivity corresponding to different vegetation temperatures.
algorithm in this paper. Actually, nonisothermal and mixed pixel is a universal natural phenomenon. The temperature difference between components can achieve 20 K under the direct irradiation of the sun. There have been several different definitions of emissivity of noni366
and ej represents the contribution of multi-scattering between components. We took two kinds of nonisothermal pixel mentioned above as an example and used eq. (10) to generate simulated data to analyze the change of nonisothermal pixel’s radiometric temperature in 714-1250 cm−1 when its emissivity was defined as r-emissivity. The equivalent temperature of nonisothermal pixel in the narrow spectral regions was derived with CBTES using simulated data under the assumption that the radiometric temperature of nonisothermal pixel is unchanged approximately in the narrow spectral region. In the simulation, mid-latitude summer atmosphere model was used and the multi-scattering between components was ignored, and the detailed parameter setting can be seen in Table 6. εvegetation is the mean value of vegetation emissivities which come from the ASTER spectral library, and εsoil is the mean value of soil emissivities from the MODIS UCSB spectral library. For each kind of nonisothermal pixel, 200 simulated data were generated. The equivalent temperature of each narrow spectral region
CHENG Jie et al. Sci China Ser D-Earth Sci | Mar. 2008 | vol. 51 | no. 3 | 357-369
was derived with CBTES and its mean value was regarded as the final temperature (Table 7). As can be seen from Figures 7 and 8, the change of radiometric temperature of nonisothermal can achieve 0.4 K, and one average equivalent temperature derived with previous
algorithms can not embody the actual change of radiometric temperature.
Figure 7 The equivalent temperature derived with CBTES and the change trend of radiometric temperature of nonisothermal composed of soil and vegetation. (a) 10 K temperature difference; (b) 15 K temperature difference; (c) 20 K temperature difference.
Figure 8 The equivalent temperature derived with CBTES and the change trend of radiometric temperature of nonisothermal composed of vegetation. (a) 10 K temperature difference; (b) 15 K temperature difference; (c) 20 K temperature difference.
3 Conclusion and prospect This paper presents a new temperature and emissivity
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Table 6
Parameter setting of nonisothermal pixel simulation
Temperature difference (K) 10 15 20 10 15 20 Table 7
Component temperature (K) T1=289.2 T2=299.2 T1=289.2 T2=304.2 T1=289.2 T2=309.2 T1=289.2 T2=299.2 T1=289.2 T2=304.2 T1=289.2 T2=309.2
1 781―787
2 826―841
3 847―858
6
7
8
9
10
920―926
1064―1068
1104―1125
1160―1170
1192―1204
corresponding to different surface temperatures in a relatively narrow spectral region, so CBTES possesses high computing efficiency. Its potential applications lie in temperature and emissivity separation from space-borne hyperspectral data, for example, Atmospheric Infrared Sounder[28] (AIRS), Tropospheric Emission Spectrometer[29] (TES), and Infrared Atmospheric Sounding Interferometer[30] (IASI). They have the advantages of global coverage and short repeat cycle, which directly result in mass data needed to process. The mass data management needs temperature and emissivity separation algorithm with high computing efficiency, because the efficiency of temperature and emissivity separation will constrain the following temperature/moisture profile and trace gases retrieval. When the forest fire happens and the area of fire point is less than one pixel, the pixel is nonisothermal. CBTES may be used to identify the sub-pixel fire point through change of the equivalent temperature in narrow spectral region.
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2
Component area ratio a1=a2=0.5 a1=a2=0.5 a1=a2=0.5 a1=a2=0.5 a1=a2=0.5 a1=a2=0.5
Narrow spectral region used to derive the equivalent temperature
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1
Component emissivity ε1=εvegetation ε2=εsoil ε1=εvegetation ε2=εsoil ε1=εvegetation ε2=εsoil ε1=εsoil ε2=εsoil ε1=εsoil ε2=εsoil ε1=εsoil ε2=εsoil
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