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Sensitivity analysis of temperature-emissivity separation method commonly applied to hyperspectral data to various sources of errors is performed in this paper. In terms of resulting errors in the process of retrieving surface temperature, results show that: (1) Satisfactory results can be obtained for heterogeneous land surfaces and retrieval error of surface temperature is small enough to be neglected for all atmospheric conditions. (2) Separation of atmospheric downwelling radiance from at-ground radiance is not very sensitive to the uncertainty of column water vapor (WV) in the atmosphere. The errors in land surface temperature retrievals from at-ground radiance with the DRRI method due to the uncertainty in atmospheric downwelling radiance vary from −0.2 to 0.6K if the uncertainty of WV is within 50% of the actual WV; (3) Impact of the errors generated by the poor atmospheric corrections is significant, implying that a well-done atmospheric correction is indeed required to obtain accurate at-ground radiance from at-satellite radiance for successful separation of land-surface temperature and emissivity.
©2010 Optical Society of America
1. Introduction
On the basis of the smoothness of the spectral emissivity, Borel in 1998 [1] proposed a method to retrieve both Land Surface Temperature (LST) and emissivity from hyperspectral Thermal InfraRed (TIR) data. Following his work, we proposed in 2008 [2] a Downwelling Radiance Residual Index (DRRI) to separate LST and emissivity from atmospherically corrected hyperspectral TIR data.
This paper focuses on the sensitivity analysis of DRRI to various sources of measurement errors. Section 2 describes briefly the concept of DRRI. Section 3 presents the process of the data simulation. Section 4 analyzes the effect of heterogeneous surface and uncertainties of atmospheric corrections on the retrieval results. Finally, conclusions are made in section 5.
2. Principle of the Downwelling Radiance Residual Index (DRRI)
Since the natural land surface is not a blackbody, at-ground leaving radiance therefore contains both the surface thermal emission and the reflected atmospheric downwelling radiance. If the LST is not accurately estimated, the corresponding emissivity spectrum retrieved from at-ground radiance exhibits ‘downwelling radiance residual feature’, namely, there are some sharp convexities or concavities caused by the atmospheric absorption lines on the estimated emissivity spectrum. This residual feature can be quantified by a Downwelling Radiance Residual Index (DRRI) and can be computed with the estimated emissivity values at six groups of well-chosen channels, where the peak corresponding to strong atmospheric line absorption and valley corresponding to weak atmospheric absorption are used to depict the direction and magnitude of the downwelling radiance residual feature [2], the component DRRI is calculated by the selected channels in each group, namely:
where ε1,ε2 and ε3 denote the channel emissivities at the left, middle, and right channels in each group respectively. The final DRRI is the sum of the six DRRI components. According to the definition, the DRRI value is only a function of the estimated temperature and will be closed to zero if this temperature approaches the actual one. The Newton-Raphson algorithm [3] is employed to find LST which is the solution of equation DRRI = 0. Once LST is determined, the land surface spectral emissivities can be easily derived from the at-ground leaving spectral radiances. More detailed information on the development of DRRI can be referred to our previous work [2].3. Data simulation
Based on the 4A/OP (Operational Release for Automatized Atmospheric Absorption Atlas) [4], a hyperspectral thermal infrared atmospheric radiative transfer model, the at-ground/satellite spectral radiance can be simulated for different situations with various land surfaces and atmospheres. In this work, the at-ground/satellite spectral radiance database were simulated using the 4A/OP model with nine typical types of surfaces (four soils, two rocks, one water body and two types of vegetation) selected from JHU (The Johns Hopkins University) emissivity spectral database [5] and six atmospheric profiles from the TIGR (Thermodynamic Initial Guess Retrieval) atmospheric profiles data sets [6]. These six atmospheric profiles were chosen to take into account the large distribution range of air temperature at the first layer and total column precipitable water vapor (WV). Their characteristics are listed in Table 1 .
Table 1. Characteristics of TIGR profiles used in this work
Following the procedure described in Fig. 1 , the atmospheric parameters (downwelling radiance, upwelling radiance and transmittance) used in the atmospheric Radiative Transfer Equation (RTE) were simulated first using 4A/OP with the six atmospheric profiles for a spectral range varying from 785 to 985 cm−1 at a spectral interval of 0.25 cm−1 and the spectral resolution of 0.5cm−1. The RTE equation is showed below:
where Lsensor is the at-sensor radiance, ε is the land surface emissivity, B(Ts) is the blackbody radiance given by the Planck's law and Ts is the LST, Latm,d is the downwelling atmospheric radiance, τ is the total atmospheric transmittance between the surface and the sensor and Latm,u is the upwelling atmospheric radiance [7].Subsequently, the RTE is used to produce the at-ground/satellite radiance with these simulated atmospheric parameters, emissivity spectrum and various surface temperatures. All simulations are made for observation at nadir.
4. Errors analysis
The main sources of errors in the separation of temperature and emissivity by means of the DRRI are considered as follow:
4.1 Heterogeneity effect
In most remote sensing studies involving TIR measurements, only homogeneous isothermal surfaces have been considered. However, natural surfaces observed from space are usually heterogeneous, especially, at low spatial resolution. The heterogeneous and non-isothermal surface must be taken into account.
In order to investigate the DRRI’s applicability to the heterogeneous land surfaces, a complex heterogeneous land surface scheme depicted in Fig. 2 [8] was used to synthesize heterogeneous targets for various types of land surfaces. Targets are organized as a matrix with the nine different types of surfaces distributed in each column and row. The emissivities of the nine land surface types are shown in Fig. 3 . Each element of the matrix is a mixture of two types of surfaces and is further divided into pixels. Each type of surface in the row is assigned to have a unique temperature (300K), while three temperatures (280K, 300K and 320K) are assigned to three pixels in the column of each matrix element. Three mixing ratios of surface types in the row are set to be 75%, 50% and 25% for 3 pixels from up to bottom. Thus, there are totally pixels and ‘pure’ pixels (only one constituent) are in the diagonal of the matrix and others are all mixed with two different constituents and two different proportions. The emitted radiance of each pixel is given by:
in which f 1 and f 2 are the fraction of the two constituents, ε1 and ε2 are the land surface emissivity of the two constituents, T1 and T2 are the LST of two constituents, respectively.After having constructed the targets, three types of atmosphere in TIGR database (from moist (A1) to moderately moist (A3) and dry (A5)) are chosen (Table 1) to simulate the at-ground spectral radiances as shown in Fig. 1. The DRRI is then applied to these simulated data to obtain the retrieved LST and emissivities.
In order to analyze the accuracy of LST retrieved with the DRRI for heterogeneous surfaces, LST and emissivity need to be defined for heterogeneous non-isothermal surfaces in the target. As defined by Becker and Li [7], the emissivity of each heterogeneous pixel is the area-weighted average of emissivity of each surface type, while the actual surface temperature is simply defined as the mean temperature of wavenumber dependent surface temperatures over the spectral range used in this paper (from 785 to 985 cm−1) because variation of the wavenumber dependent surface temperatures is small and can be neglected in the spectral range 785 to 985 cm−1. According to the definitions given above, the errors of retrieved LST are calculated by subtracting the actual LST defined above from the retrieved one. The histogram of the retrieved LST errors due to the heterogeneous land surface effects for A3 atmosphere is shown in Fig. 4 . This figure illustrates that the estimated LST errors are small enough, which implies that the retrieval errors for heterogeneous land surfaces can be neglected compared with the errors that introduced by other error sources (as discussed below). Similar results are also found for the moist and the dry atmospheric conditions.
Fig. 4 Histogram of LST error induced by heterogeneous surface effects for moderately moist atmosphere (A3)
4.2 Sensitivity to the uncertainties in the atmosphere
4.2.1 Uncertainties of atmospheric downwelling radiance
In order to evaluate the sensitivity of the DRRI to the error of atmospheric downwelling radiance, following the data simulation scheme, at-ground hyperspectral TIR data were simulated with a specific atmosphere A4 and nine types of surface for a LST that equals to the air temperature at the first layer. The DRRI method is then applied to these simulated data with the incorrect atmospheric downwelling radiance estimated using 4A/OP model and WVs ranging from 0.3 to 2.0 times of the actual one in the atmosphere we used to simulate the TIR data. Figure 5(a) shows the errors of LST derived with different estimated atmospheric downwelling radiances for the A4 atmosphere. Similar work is also done to evaluate the DRRI on various atmospheric conditions (A1-A6) with an incorrect atmospheric downwelling radiances resulting from WVs = 0.1 to 2.0 times of the actual WVs. Figure 5(b) shows the errors of LST obtained for the six atmospheric conditions and a gray body with the constant emissivity value of 0.9.
Fig. 5 (a) Effect of atmospheric downwelling radiance error on LST retrieval for A4 atmosphere. The abscissa represents the water vapor content used to estimate the atmospheric downwelling radiance while the ordinate represents the LST error. Nine types of materials from rock to grass have been tested. (b) Effect of atmospheric downwelling radiance error on LST retrieval for different atmospheric conditions (A1-A6) with a gray body of emissivity = 0.9. The abscissa represents the WV scaling factors.
The results show that: 1) An error of 0.3-2.0 times of actual WV leads to an error of −0.3 to 1.8K on LST depending on the types of surfaces under the moderately moist atmospheric condition (A4); 2) As shown in Fig. 5(a), the errors in land surface temperature retrievals from at-ground radiance with the DRRI method due to the uncertainty in atmospheric downwelling radiance vary from −0.2 to 0.6K if the uncertainty of WV is within 50% of the actual WV. It is worth noting that the underestimation of water vapor content will lead to a large retrieved LST error. Same tendency is found in Fig. 5(b); 3) LST errors for vegetation and water surfaces are smaller than these for soils and rocks, probably due to the fact that vegetation and water have the smoother emissivity spectrum in the six well-chosen channels than soils and rocks; 4) As shown in Fig. 5(b), if there were no error of atmospheric downwelling radiance, the retrieved LST errors for dry atmosphere are larger than those for moist atmosphere.
4.2.2 Uncertainties of atmospheric upwelling radiance and transmittance
In order to investigate the effects of uncertainties of atmospheric correction on the retrieval results, we first generated the at-satellite radiances at different atmospheric conditions under original water vapor profiles, and then these radiances are corrected to the at-ground radiances using the atmospheric upwelling radiances and transmittances estimated with 4A/OP model and scaled water vapor profiles. DRRI is then employed to retrieve LST and Fig. 6 shows the errors of LST for A4 atmosphere and a gray body with the constant emissivity value of 0.9. The results indicate that the method is very sensitive to the accuracy of the atmospheric correction. The incorrect atmospheric correction will lead to a large error. It can be seen from this simulation (Fig. 6) that in the range of WV from −20% to 20% the error of LST varies from −4K to 6K. With the reduction of WV, for A3 atmosphere, in the range of WV from −20% to 20% the error of LST varies from −2K to 1K. With the increment of WV, much more errors are to be expected, which further confirms the importance of atmospheric correction. For A5 atmosphere, in the range of WV from −20% to 20% the error of LST varies from −6K to 10K.
Fig. 6 Effect of incorrect atmospheric correction errors on LST retrieval for A4 atmosphere with a gray body of emissivity = 0.9.
5. Conclusions
In this work, the hyperspectral simulated data has been simulated with 4A/OP and TIGR atmospheric profiles and JHU surface spectral database. Six selected TIGR atmospheric profiles and nine land surface types were used to produce the atmospheric parameters and land surface emissivities. The at-ground/satellite radiance was then simulated by the atmospheric RTE.
To analyze the sensitivity of the DRRI method to various measurement errors, after the application of the method to the simulated hyperspectral TIR data, the results of the retrieval temperatures show that: (1) Satisfactory results can be obtained for heterogeneous land surfaces and the error is small enough to be neglected for all atmospheric conditions. (2)Separation of atmospheric downwelling radiance from at-ground radiance is not very sensitive to the uncertainty of column water vapor (WV) in the atmosphere. The errors in land surface temperature retrievals from at-ground radiance with the DRRI method due to the uncertainty in atmospheric downwelling radiance vary from −0.2 to 0.6K if the uncertainty of WV is within 50% of the actual WV; (3) Impact of the errors generated by the poor atmospheric corrections is significant, implying that a well-done atmospheric correction is indeed required to obtain accurate at-ground radiance from at-satellite radiance for successful separation of land-surface temperature and emissivity. In a word, the proposed DRRI method is suitable for accurately retrieving LST if the atmospheric correction has been well performed, even for the heterogeneous and non-isothermal surfaces and the inaccuracy atmospheric downwelling radiance. It should be mentioned that all simulations are made for observations at nadir. Uncertainty and errors would increase for large viewing zenith angles.
Acknowledgments
This work was supported by the Hi-Tech Research and Development Program of China (863 Plan Program) under Grant 2006AA12Z121. The authors would like to sincerely thank NOVELTIS Inc. for providing the 4A/OP model, JPL for providing the JHU spectral library, and the Laboratoire de Meteorologie Dynamique for providing the TIGR database.
References and links
1. C. C. Borel, “Surface emissivity and temperature retrieval for a hyperspectral sensor,” in Proceedings of IEEE International Geoscience and Remote Sensing Symposium (Seattle, 1998), 1, pp. 546–549.
2. X. Wang, X.Y. OuYang, B.H.Tang, R.H. Zhang and Z.-L. Li, “A new method for temperature/emissivity separation from hyperspectral thermal infrared data,” in Proceedings of IEEE International Geoscience and Remote Sensing Symposium (Boston, Massachusetts, 2008), III, pp. 286–289, 2008.
3. The Newton-Raphson Method, http://www.math.ubc.ca/~clarkson/newtonmethod.pdf.
4. http://ara.lmd.polytechnique.fr/
5. http://speclib.jpl.nasa.gov/
6. http://ara.lmd.polytechnique.fr/htdocs-public/products/TIGR/TIGR.html
7. F. Becker and Z.-L. Li, “Surface temperature and emissivity at various scales: definition, measurement and related problems,” Remote Sens. Rev. 12, 225–253 (1995).
8. A. R. Gillespie, Department of Earth and Space Sciences, UW-ESS, Mailstop 351310, University of Washington, Seattle, W.A., 98195–1310 (personal communication, 1995)
