Land Surface Temperature Retrieval from MODIS Data by Integrating Regression Models and the Genetic Algorithm in an Arid Region
">
<p>Location of the study area in mainland China.</p> ">
<p>Scatter plots between the atmospheric upwelling radiance of MODIS channel 31 and the other atmospheric parameters. (<b>a</b>) transmittances of channels 31 and 32; (<b>b</b>) upwelling radiance of channel 32.</p> ">
<p>Scatter plot between the simulated atmospheric upwelling radiance in MODIS channel 31 and differences in the at-sensor brightness temperatures of channel 31 and 32 (<span class="html-italic">T</span><sub>b31</sub>–<span class="html-italic">T</span><sub>b32</sub>).</p> ">
<p>The minimum (Min), mean (Mean), and maximum (Max) objective values of all the individuals in each generation during the iteration process.</p> ">
<p>Scatter plot between the estimated LST and the LST input to the MODTRAN4 code for the eighteen radiosonde profiles. The solid line corresponds to a 1:1 relation.</p> ">
<p>Spatial patterns of the land surface temperature in the study area retrieved by the RM-GA method and those provided by MODIS LST/emissivity products. A is vegetation, B is snow, C is gobi, and D is desert. The MODIS images were acquired on 6 July 2007. (<b>a</b>) LST at 04:05UTC retrieved with the RM-GA method. (<b>b</b>) LST at 04:05UTC provided by the MODIS LST/emissivity product. (<b>c</b>) LST at 15:10UTC retrieved with the RM-GA method. (<b>d</b>) LST at 15:10UTC provided by the MODIS LST/emissivity product.</p> ">
Abstract
:1. Introduction
2. Methodology
2.1. Study Area and Datasets
2.2. Regression Models for Atmospheric Parameters
2.3. Determination of LST with a Genetic Algorithm
- (1)
- Defining the ranges of and Ts: The ranges of and Ts are defined as 0.01 W·m−2·sr−1·μm−1 to 3.0 W·m−2·sr−1·μm−1 and 250.0 K to 340.0 K, respectively. The previous two ranges are set according to the conditions of the study area and our investigations of the radiosonde profiles, GDAS profiles, and MODIS LST/emissivity products. On the one hand, the maximum value of calculated based on all the in situ atmospheric radiosondes is 1.8821 W·m−2·sr−1·μm−1, appearing in the region with low elevation in summer. For all the GDAS profiles, over 98% of the simulated samples have lower than 3.0 W·m−2·sr−1·μm−1, and the GDAS profiles are found to overestimate the water vapor contents. On the other hand, a range of 250.0 K to 340.0 K covers most possible conditions in the study area, according to our finding based on MODIS LST products of the study area.
- (2)
- Defining the initial values of Ts and : Considering that the atmospheric effects in MODIS channel 32 are more significant than those in channel 31, the at-sensor brightness temperature of channel 31, Tb31, is used as the initial value of Ts. It is difficult to determine the initial value of because there is no knowledge about the atmospheric condition. However, we find that there is a significant correlation between and Tb31–Tb32 (see Figure 3). Their relationship can be written as:In total, 5486 samples are used to infer Equation (11). The adjusted R2 value of the regression is 0.964, and the correlation is significant at the 0.001 probability level, demonstrating that Equation (11) is sufficiently accurate to calculate the initial value of . Because of the searching and optimizing processes, the results generated by the GA are not significantly influenced by the initial values of the unknowns.
- (3)
- Designing the objective function of GA: The estimated Ts and should balance the radiative transfer equations. Therefore, the following function is used as the objective function to select appropriate individuals during iteration:where the objective value, F, should be close to 0.
- (4)
- Specifying the population size (Popsize), maximum number of generations (Maxgen), crossover fraction (Pc) and mutation fraction (Pm): These parameters may significantly influence the optimization of GA [50–52]. Determining these parameters is a repetitive process. A group of parameters derived from the simulation of a radiosonde profile, which were acquired at the Biandukou site on 5 July 2008, is used for an experiment. These parameters are an LST of 300.9 K, TOA spectral radiances of 9.3994 W·m−2·sr−1·μm−1 and 8.7839 W·m−2·sr−1·μm−1 for channels 31 and 32, respectively.
3. Sensitivity Analysis and Validations
3.1. Sensitivity Analysis
3.2. Validations
3.2.1. Validation with Simulation Datasets
3.2.2. Validation with In Situ LST Measurements
3.2.3. Comparisons with MODIS LST Products
4. Discussion
5. Conclusions
Acknowledgments
Conflicts of Interest
- Author ContributionsJi Zhou wrote the manuscript and was responsible for research design, data preparation and processing, and analysis. Xu Zhang contributed significantly to the radiative transfer simulation and validation. Wenfeng Zhan wrote the Matlab programs for the method proposed in this research and provided constructive comments and suggestions for developing the method. Huailan Zhang contributed to the sensitivity analysis part and made the maps in this paper.
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No. | SW Algorithm | Reference |
---|---|---|
1 | Ts = A0 + A1T11 + A2 (T11 −T12) | Ottlé and Vidal-Madjar (1992) [10] |
2 | Ts = A0 + A1T11 + A2 (T11 −T12) + A3 (T11 −T12)2 | François and Ottlé (1996) [11] |
3 | Ts = A0 + A1T11 + A2 (T11 −T12 )+ A3 T11ɛ11 + A4 (T11 −T12)(1− ɛ11)+ A5T12Δɛ | Price (1984) [12] |
4 | Ts = A0 + A1T11 + A2 (T11 −T12 )+ A3 (1 −ɛ) | Ulivieri and Cannizzaro (1985) [13] |
5 | Becker and Li (1990) [14], Wan and Dozier (1996) [15] | |
6 | Prata and Platt (1991) [16] | |
7 | Vidal (1991) [17] | |
8 | Ts = A0 + A1T11 + A2 (T11 −T12 )+ A3 (1−ɛ)+ A4Δɛ | Ulivieri et al. (1994) [18] |
9 | Ts = A0 +(A1 w + A2 w2 + A3 )T11 +(A4 w + A5 w2 + A6 )T12 + A7 w + A8 w2 | François and Ottlé (1996) [11] |
10 | Sobrino et al. (1991) [19] | |
11 | Ts = A0 + A1T11 +(A2 w + A3 )(T11 −T12 ) +(A4 w + A5 )(1−ɛ) +(A6 w + A7 )Δɛ | Ulivieri et al. (1994) [18] |
12 | Ts = A0 + A1T11 + A2 (T11 −T12 ) + A3 (T11 −T12 )2 +[( A4 w + A5 )T11 + ( A6 w + A7 ) ](1−ɛ) −[( A8 w + A9 )T11 + ( A10 w + A11 )]Δɛ | Coll et al. (1994) [20] |
13 | Ts = A0 + A1T11 + A2 (T11 −T12 )+ A3 (T11 −T12)2 + (A4 w + A5 )(1−ɛ)−(A6 w + A7)Δɛ | Sobrino and Raissouni (2000) [21] |
14 | Ts = A0 + A1T11 + A2 (T11 −T12) + A3 (T11 − T12)2 + (A4 w + A5) (1−ɛ) | Ma (2003) [22] |
15 | Ts = A0 + A1 w +[A2 + ( A3 w cosθ+ A4 )(1−ɛ11 ) −( A5 w + A6 )Δɛ](T11 +T12 ) +[A7 + A8 w + ( A9 + A10 w)(1−ɛ11 ) −( A11 w + A12 )Δɛ](T11 −T12 ) | Becker and Li (1995) [23] |
Temperature Range | MODIS Channel | a | b | Adjusted R2 | Significance Level | Sample Size |
---|---|---|---|---|---|---|
250 K–280 K | 31 | 0.1003 | −21.175 | 0.998 | 0.001 | 61 |
32 | 0.0902 | −18.637 | 0.998 | 0.001 | 61 | |
280 K–310 K | 31 | 0.1350 | −30.917 | 0.999 | 0.001 | 60 |
32 | 0.1169 | −26.110 | 0.999 | 0.001 | 60 | |
310 K–340 K | 31 | 0.1693 | −41.560 | 0.999 | 0.001 | 60 |
32 | 0.1422 | −33.966 | 0.999 | 0.001 | 60 |
Parameter | Error Range | Standard Deviation of the Error | Standard Deviation of the Absolute Error | MAE | RMSE |
---|---|---|---|---|---|
τ31 | −0.0189–0.0042 | 0.0059 | 0.0054 | 0.0080 | 0.0097 |
τ32 | −0.0221–0.0035 | 0.0044 | 0.0042 | 0.0098 | 0.0107 |
−0.0144–0.0517 | 0.0122 | 0.0098 | 0.0083 | 0.0128 |
Population Size (Popsize) | Maximum Generation (Maxgen) | ||||
---|---|---|---|---|---|
20 | 60 | 100 | 140 | 180 | |
10 | 2.7 | 1.1 | 0.3 | 0.7 | 0.6 |
30 | 0.3 | 0.4 | 0.5 | 0.3 | 0.3 |
50 | 0.5 | 0.5 | 0.3 | 0.3 | 0.3 |
70 | 0.4 | 0.4 | 0.3 | 0.3 | 0.3 |
90 | 0.3 | 0.4 | 0.3 | 0.3 | 0.3 |
Time | Crossover Fraction (Pc) | |||||
---|---|---|---|---|---|---|
0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | |
1 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 |
2 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.4 |
3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.4 |
4 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 |
5 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.5 |
LSE Error | LST Error Caused by δɛ31 | LST Error Caused by δɛ32 | ||||||
---|---|---|---|---|---|---|---|---|
Soil, VZA = 0 | Soil, VZA = 30 | Vegetation, VZA = 0 | Vegetation, VZA = 30 | Soil, VZA = 0 | Soil, VZA = 30 | Vegetation, VZA = 0 | Vegetation, VZA = 30 | |
−0.010 | 1.4 | 1.3 | 1.2 | 1.2 | 0.8 | 0.8 | 0.6 | 0.6 |
−0.008 | 1.1 | 1.1 | 0.9 | 0.9 | 0.6 | 0.6 | 0.5 | 0.5 |
−0.006 | 0.8 | 0.8 | 0.7 | 0.7 | 0.5 | 0.5 | 0.3 | 0.3 |
−0.004 | 0.5 | 0.5 | 0.5 | 0.5 | 0.3 | 0.3 | 0.2 | 0.2 |
−0.002 | 0.3 | 0.3 | 0.2 | 0.2 | 0.1 | 0.1 | 0.1 | 0.1 |
0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
0.002 | 0.3 | 0.3 | 0.2 | 0.2 | 0.1 | 0.1 | 0.1 | 0.1 |
0.004 | 0.5 | 0.5 | 0.5 | 0.5 | 0.3 | 0.3 | 0.2 | 0.2 |
0.006 | 0.8 | 0.8 | 0.7 | 0.7 | 0.4 | 0.4 | 0.3 | 0.3 |
0.008 | 1.1 | 1.1 | 0.9 | 0.9 | 0.5 | 0.5 | 0.4 | 0.4 |
0.010 | 1.4 | 1.4 | 1.2 | 1.2 | 0.6 | 0.6 | 0.5 | 0.5 |
LSE Error | LST Error Caused by δɛ31 | LST Error Caused by δɛ32 | ||||||
---|---|---|---|---|---|---|---|---|
Soil, VZA = 0 | Soil, VZA = 30 | Vegetation, VZA = 0 | Vegetation, VZA = 30 | Soil, VZA = 0 | Soil, VZA = 30 | Vegetation, VZA = 0 | Vegetation, VZA = 30 | |
−0.010 | 2.0 | 1.9 | 2.1 | 1.9 | 1.8 | 2.0 | 1.8 | 2.3 |
−0.008 | 1.6 | 1.5 | 1.7 | 1.6 | 1.7 | 2.2 | 1.9 | 2.4 |
−0.006 | 1.3 | 1.2 | 1.3 | 1.2 | 1.9 | 2.3 | 2.0 | 1.3 |
−0.004 | 0.9 | 0.8 | 0.9 | 0.8 | 0.9 | 0.7 | 2.2 | 0.7 |
−0.002 | 0.4 | 0.4 | 0.5 | 0.4 | 0.4 | 0.3 | 0.4 | 0.3 |
0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
0.002 | 0.5 | 0.4 | 0.5 | 0.5 | 0.3 | 0.3 | 0.3 | 0.3 |
0.004 | 1.1 | 1.1 | 1.2 | 1.0 | 0.6 | 0.5 | 0.6 | 0.6 |
0.006 | 2.2 | 1.6 | 2.3 | 1.5 | 0.8 | 0.8 | 0.9 | 0.8 |
0.008 | 2.5 | 2.7 | 2.7 | 2.8 | 1.1 | 1.0 | 1.1 | 1.0 |
0.010 | 2.7 | 2.9 | 2.8 | 3.1 | 1.3 | 1.2 | 1.4 | 1.2 |
Grid Location | Sample Size | MAE (K) | RMSE (K) |
---|---|---|---|
(100°E, 38°N) | 1495 | 0.8 | 1.0 |
(100°E, 39°N) | 1339 | 0.5 | 0.7 |
(98°E, 40°N) | 1326 | 0.6 | 0.8 |
(99°E, 40°N) | 1326 | 0.6 | 0.8 |
Total | 5486 | 0.6 | 0.9 |
Satellite | Location | Measured LST (K) | Estimated LST by RM-GA (K) | MODIS product (K) |
---|---|---|---|---|
Terra | 100.98°E, 38.22°N | 292.2 | 291.5 | 290.2 |
100.97°E, 38.26°N | 291.7 | 290.3 | 290.7 | |
Aqua | 100.98°E, 38.22°N | 294.2 | 294.0 | 294.4 |
100.97°E, 38.26°N | 294.3 | 293.1 | 294.1 |
Satellite and Sensor | ai1 (i = 1, 2, 3) | ai2 (i = 1, 2, 3) | ai3 (i = 1, 2, 3) | Adjusted R2 | Standard Error of Estimate |
---|---|---|---|---|---|
NOAA-7 AVHRR | 0 | −0.134 | 0.987 | 0.989 | 0.0097 |
0 | −0.181 | 0.981 | 0.986 | 0.0150 | |
−0.073 | 1.460 | −0.035 | 0.999 | 0.0290 | |
NOAA-9 AVHRR | 0 | −0.134 | 0.987 | 0.989 | 0.0096 |
0 | −0.178 | 0.985 | 0.986 | 0.0147 | |
−0.060 | 1.411 | −0.046 | 0.999 | 0.0330 | |
NOAA-11 AVHRR | 0 | −0.134 | 0.987 | 0.989 | 0.0097 |
0 | −0.180 | 0.983 | 0.986 | 0.0150 | |
−0.067 | 1.436 | −0.039 | 0.999 | 0.0302 | |
NOAA-12 AVHRR | 0 | −0.135 | 0.987 | 0.989 | 0.0098 |
0 | −0.181 | 0.976 | 0.986 | 0.0150 | |
−0.081 | 1.482 | −0.019 | 0.999 | 0.0240 | |
NOAA-14 AVHRR | 0 | −0.134 | 0.987 | 0.989 | 0.0097 |
0 | −0.186 | 0.976 | 0.985 | 0.0160 | |
−0.088 | 1.531 | −0.025 | 0.999 | 0.0298 | |
Terra ASTER | 0 | −0.133 | 0.986 | 0.989 | 0.0095 |
0 | −0.156 | 0.996 | 0.984 | 0.0132 | |
0 | 1.132 | −0.053 | 0.997 | 0.0397 | |
Landsat-8 TIRS | 0 | −0.135 | 0.984 | 0.988 | 0.0105 |
0 | −0.175 | 0.991 | 0.987 | 0.0143 | |
−0.030 | 1.299 | −0.071 | 0.999 | 0.0309 |
© 2014 by the authors; licensee MDPI, Basel, Switzerland This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).
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Zhou, J.; Zhang, X.; Zhan, W.; Zhang, H. Land Surface Temperature Retrieval from MODIS Data by Integrating Regression Models and the Genetic Algorithm in an Arid Region. Remote Sens. 2014, 6, 5344-5367. https://doi.org/10.3390/rs6065344
Zhou J, Zhang X, Zhan W, Zhang H. Land Surface Temperature Retrieval from MODIS Data by Integrating Regression Models and the Genetic Algorithm in an Arid Region. Remote Sensing. 2014; 6(6):5344-5367. https://doi.org/10.3390/rs6065344
Chicago/Turabian StyleZhou, Ji, Xu Zhang, Wenfeng Zhan, and Huailan Zhang. 2014. "Land Surface Temperature Retrieval from MODIS Data by Integrating Regression Models and the Genetic Algorithm in an Arid Region" Remote Sensing 6, no. 6: 5344-5367. https://doi.org/10.3390/rs6065344