Open Access
Add to BibSonomy
Abstract
An adaptive Fourier neural operator (AFNO)-transformer model was developed to retrieve land surface temperature (LST) data from infrared atmospheric sounding interferometer (IASI) observations. A weight selection scheme based on linearization of the radiative transfer equation was proposed to solve the hyperspectral data channel redundancy problem. The IASI brightness temperatures and Advanced Very High Resolution Radiometer onboard MetOp (AVHRR/MetOp) LST product were selected to construct the training and test datasets. The AFNO-transformer performed effective token mixing through self-attention and effectively solved the global convolution problem in the Fourier domain, which can better learn complex nonlinear equations and achieve time-series forecasting. The root mean square error indicated that the LST in Eastern Spain and North Africa could be retrieved with an error of less than 2.5 K compared with the AVHRR/MetOp LST product. Moreover, the validation results from other time period data showed that the retrieval accuracy of this model can be less than 3 K. The proposed model provides a novel approach for hyperspectral LST retrieval.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Land surface temperature (LST) is an important parameter of land surface processes at regional and global scales [1–4]. Hyperspectral resolution thermal infrared (TIR) sounding data with a fine spectral resolution provides an effective way to obtain LSTs. Currently, many hyperspectral infrared sensors onboard satellites have been developed, such as the atmospheric infrared sounder (AIRS) [5], infrared atmospheric sounding interferometer (IASI) [6], infrared atmospheric sounding interferometer-New Generation (IASI-NG) [7] and cross-track infrared sounder (CrIS) [8]. However, according to the radiative transfer equation (RTE), LST is also coupled with land surface emissivity (LSE), and even if atmospheric correction has been performed, there will always be N + 1 unknowns (N emissivities in each channel and an unknown LST) for N equations. Thus, the retrieval of accurate LST data from remotely sensed hyperspectral TIR data has attracted considerable attention.
Various methods have been proposed to derive LSTs from at-sensor hyperspectral TIR observations. These methods can be classified into four types: temperature–emissivity separation, regression inversion, physical inversion, and machine learning methods. The temperature–emissivity separation method assumes that atmospheric correction has been completed and solves the underdetermined equation problem by adding physical constraints or reducing the number of unknowns in the equation to calculate the LST. For example, Borel et al. proposed an iterative spectrally smooth (ISSTES) method that defines a smoothness index: the closer the temperature is to the true temperature, the smaller the corresponding smoothness index [9–12]. Wang et al. designed a downwelling radiance residual index (DRRI) [13,14], and Ouyang et al. found that the differences between IASI observations and Moderate Resolution Imaging Spectroradiometer (MODIS)-derived LSTs using DRRI were no more than 2 K. Wang et al. represented LSE with continuous line segments to reduce the number of LSE unknowns and finally obtained LST [15,16]. Similarly, Liu et al. and Zhang et al. used emissivity eigenvectors (EVs) and wavelet transforms, respectively, to reduce the number of LSE unknowns [17,18]. On the other hand, regression inversion [19–21], physical inversion [22–31] and machine learning methods [32–35] can achieve LST retrieval without accurate atmospheric correction from hyperspectral TIR data. Physical inversion primarily provides initial values for iterative optimization and calculates the atmospheric radiance in the TIR with time-consuming; it can provide accurate results. The regression inversion model runs faster, albeit with a relatively lower accuracy. Currently, machine learning methods have attracted considerable attention for simultaneously retrieving land surface information from hyperspectral TIR data because of their ability to learn and recognize complex nonlinear patterns between satellite observations and land surface and atmospheric information [35–37]. A transformer model is a neural network architecture that automatically transforms one type of input into another type of output [38]. Inspired by the success of transformer scaling in natural language processing, effective token mixing through self-attention for vision transformers has been discussed owing to the significant reduction in the computational resources required for training [39]. Adaptive Fourier neural operator (AFNO) is an efficient token mixer that learns mixing in the Fourier domain. It frames token mixing as a continuous global convolution, and is independent of the input resolution [40]. To best of our knowledge, this study is the first attempt at achieving LST inversion with hyperspectral TIR IASI observations using a transformer model based on the AFNO operator, even when the atmospheric conditions are unknown. In the transformer model, we will use the real IASI observations and satellite LST products instead of simulated datasets as the training datasets to improve the applicability of the model in retrieving LST from actual satellite observations.
The remainder of this paper is organized as follows. Section II presents the methodology employed. The experiment with the retrieval results is presented and analyzed in Section III. The proposed method is applied and validated using real observations in Section IV. Finally, Section V presents the discussions and conclusions.
2. Methodology
2.1 Channel selection
Usually, there is close correlation between the hyperspectral data channels, leading to ill-conditioned retrieval problems and possibly reducing the accuracy of the retrieval target. In addition, if hundreds of channels in hyperspectral data are used for machine learning, the running time of the model will be significantly increased, and the computer processing power will be higher. Therefore, channel selection is a key issue in LST retrieval using hyperspectral TIR data. In this study, the sensitivity between the temperature and onboard observations was used to select the channels that contribute to temperature retrieval.
Assuming a cloud-free atmosphere under local thermodynamic equilibrium and neglecting the atmospheric scattering effects, the radiative transfer equation (RTE) at wavelength $\lambda $ can be expressed as follows [3]:
We can further obtain the first order variation of RTE as the following form [41]:
According to Eqs. (2) and (2c), the LST weight value ${W_{T{s_\lambda }}}$ can be adopted to select channels with a larger weight to facilitate the LST retrieval and realize the dimension reduction and noise reduction of the spectral samples.
2.2 AFNO-transformer model
Figure 1 shows the constructed AFNO transformer model. The inputs of the model were the LST dataset $Ts$ and the brightness temperature dataset $Tb$ from 1 to time t. $Tb$ in each channel was introduced into the model through the patch and position embedding layer to mix with the $Ts$ of the corresponding position and calibrate the corresponding position-coding data to ensure that $Tb$ and $Ts$ remained geographically matched. For the selected study area, the size of the satellite data $Tb$ collected during all time periods was integrated into $m^{\prime} \times \textrm{ch}$ dimensions, where $ch$ is the number of selected observation channels. Correspondingly, the dimension of the $Ts$ becomes $m^{\prime} \times 1$. Subsequently, according to the time series, the data were reorganized at fixed time intervals. Finally, the dimension of $Tb$ was the three-dimensional spatial dimension data: $i \times j \times ch$, $Ts$ was integrated into 2-dimensional spatial data with a dimension of $i \times j$. Among them, $i = j = \sqrt {m^{\prime}} $.
Before position embedding, we performed a two-dimensional convolution mixing operation on $Ts$ and $Tb$ data in each channel dimension to obtain feature information. The transformer model is processed internally in parallel, and if the input dimension is excessively large, a large number of calculations are required. Therefore, it is necessary to divide the input data and adopt an appropriate batch size x to reduce the dimensionality of the data (Fig. 2 (a)). Subsequently, the divided batch-sized convolution data and position-encoding information were input into L layers for the subsequent self-attention module (Fig. 2 (b)).
The proposed AFNO transformer model has two parts: encoding and decoding of the traditional transformer model. In the encoding part, we constructed L layers, including two token mixing layers. In the L layers, the AFNO operator was used to complete the spatial mixing operation. For each batch size area, for a continuous input $X \in D$ and kernel $\kappa $, the kernel integral at token s is expressed as:
With mixing tokens using the discrete Fourier transform, for the input token tensor $X \in {R^{h \times w \times d}}$, a block diagonal structure on d × d weight matrices W for each token was divided into k weight blocks of size d/k × d/k to reduce the parameter count. Consequently, the kernel operated independently on each block per token $({m,n} )\in [h ]\times [w ]$ as follows:
To avoid adaptive changes in new samples after weight learning, the tokens must interact and decide upon the passage of certain low- and high-frequency modes. A two-layer perceptron was adopted to associate static weight values back and forth to complete self-attention learning such that the model could be applied to new sample data. The MLP operation was used in the L layers to complete the channel-mixing operation and the weight data W was shared across all channels. For ($n,m$)-th token, Eq. (5) is applicable. The parameter count can be reduced because the weights ${W_1}$, ${W_2}$, and b are shared for all tokens.
Finally, after passing through several L layers, the model was sent to the multi-head attention structure of the decoder after a full dropout operation. For the decoding part, it combined the input data with the feature values of the encoder, and the output data was processed by a fully connected layer, the predicted LST data was obtained. To train this AFNO transformer model, training was performed by minimizing the mean-square error between the predicted and true values.
3. Experiments and results
3.1 Data
3.1.1 Remote sensing data
The IASI instrument is a Fourier transform spectrometer onboard the MetOp satellite. It is based on a Michelson interferometer coupled to an integrated imaging system that observes and measures the infrared radiation emitted from the Earth. The IASI L1c product contains infrared radiance spectra with a spectral sampling of 0.25 cm−1 (at 0.5cm−1 resolution after apodization). For each sounder pixel, it has 8461 spectral samples covering the range of 645–2760 cm-1. IASI with hundreds of channels provide rich spectral information to help us solve key parameters. IASI can not only help obtain atmospheric parameters, but also further explore the inversion of land surface parameters. In this paper, the brightness temperature extracted from the IASI L1c product was used to retrieve the LST using the transformer model.
The Advanced Very High Resolution Radiometer (AVHRR) is an optical/infrared imager with a spatial resolution of approximately 1 km onboard polar orbiting MetOp satellites. The satellite application facility on land surface analysis adopted a generalized split-window algorithm based on clear-sky measurements obtained from AVHRR/Metop to produce LST products [42]. The AVHRR/Metop Daily LST product (LSA-002) provides a composite of daytime and nighttime retrievals of LST with a sinusoidal grid centered at (0°N, 0°W) and a resolution of 0.01°${\times} $0.01°. Reiners et al. found that the AVHRR LST has an absolute deviation of 1.83 K from the in situ LST and a difference of 2.34 K from the MODIS product [43]. To eliminate the influence of time differences, AVHRR/Metop LST products were adopted to validate the model’s retrieval performance compared to the retrieval LST results of the IASI brightness temperatures. Furthermore, to achieve consistency in the spatial resolution and projection, the AVHRR/Metop LST products were reprojected and resampled to the parameters of the IASI L1c products.
3.1.2 Auxiliary data
In addition to the remote sensing data used to train the transformer model, simulated data containing typical atmospheric and surface parameters were added as auxiliary dataset. Here, 65 emissivity spectra were selected from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) spectral library to represent most land cover types [44], including 52 soil, 4 vegetation and 9 waters/snows/ice spectra. The Thermodynamic Initial Guess Retrieval (TIGR) dataset contains 2311 representative atmospheric profiles to describe atmospheric situations, from the surface to the top of the atmosphere, using the values of temperature, water vapor and ozone concentrations on a given pressure grid. Finally, 946 clear-sky atmospheric profiles (relative humidity > 90%) were selected from the TIGR dataset [45]; the bottom atmospheric temperature (${T_0}$) ranged as 230–320 K, and q ranged as 0.1–6.5 g/cm2. To build the auxiliary dataset and render the dataset more representative, ${T_0}$ values of the atmospheric profiles (from −10 to +15 K in steps of 5 K for ${T_0}$ < 280 K and from −5 to +20 K in steps of 5 K for ${T_0}$ ≥ 280 K) were used to simulate as the LST. The instrument noise can be simulated with white Gaussian noise with a noise equivalent temperature (NE$\varDelta $T) of 280 K to characterize the real IASI observations [41]. Finally, the radiative transfer model Operational Release for Automatized Atmospheric Absorption Atlas (4A/OP) simulated the at-sensor radiance, atmospheric upwelling radiance, downwelling radiance, and transmittance for the IASI with selected emissivities, atmospheric profiles, and a certain observation geometry.
3.2 Research area
The proposed AFNO-transformer model is universal, and we chose the regions of eastern Spain and North Africa to demonstrate its application (Fig. 3). The eastern Spain region has a temperate Mediterranean climate, and its terrain is dominated by plateaus, interspersed with mountains, forests and other vegetation. North Africa has a tropical desert climate, mostly consisting of plateaus and deserts. Therefore, these areas contain a variety of land surface coverage. Moreover, these areas mostly have a clear-sky. Thus, more IASI observations can be obtained, which is conducive to training and verification analysis.
3.3 Results
The spectral range of the simulated data was 645–1600 cm−1 to avoid contamination from solar components. To determine the retrieval channels for this model, we analyzed the simulated dataset with different combinations of land surface and atmospheric types to calculated LST weight value ${W_{T{s_\lambda }}}$ according to Eq. (2c). Channels with larger LST weights were selected to facilitate the LST retrieval. For each combination, we selected the channels with the top 15% weight values. Subsequently, the intersection of all selected channels with different combinations were obtained. We also analyzed the atmospheric window characteristics of the channels outside the intersection channels. Finally, 200 channels sensitive to surface information were selected to retrieve LSTs (Fig. 4).
The remote sensing dataset (IASI brightness temperature product and AVHRR/MetOp Daily LST product) was used in this model to construct the training and test datasets simultaneously. The time span of the remote sensing data was 2018–2020. For each research area, we selected the number of pixels with a size of 16${\times} $16, with time interval of 32 d. For t value of 4, the research data $Ts$ (the AVHRR/MetOp Daily LST product) were integrated into a 256 ${\times} $ 256 matrix, Tb (IASI Level 1C product) was a matrix of 256 ${\times} $ 256 ${\times} $ 200, and the batch size was set to 16. These datasets were the inputs of the L layers for the subsequent training.
We adopted the root mean square error (RMSE) and bias as indicators to validate retrieval accuracy. Figures 5 and 6 show the histograms of the residuals between the retrieved and referenced LSTs (AVHRR/MetOp Daily LST product is defined as the referenced LSTs) using the AFNO-transformer algorithm. The residuals between the retrieved and referenced LSTs for the eastern Spain and North Africa regions were predominantly located in the range of -5 K and 5 K (Figs. 5 and 6). In addition, the RMSEs between the estimated and referenced LSTs were 1.84 and 2.40 K for North Africa and eastern Spain, respectively. We found that the accuracy of the two research areas was different but very similar, indicating that the model was not greatly affected by regional characteristics and had a certain degree of universality. The difference in accuracy between the two study areas may be attributed to the fact that the selected North African region has a relatively uniform surface type.
3.4 Application
To further demonstrate the performance of this model, the AFNO-transformer method was applied to real IASI observations generated at other times. The timespan must be expanded and adjusted according to the selected date. The retrieval performance is shown separately for daytime and nighttime data. For the study area in eastern Spain, daytime and nighttime data on October 1, 2021, and April 27, 2021, were selected to show the retrieval accuracy. Whereas, daytime and nighttime data on January 2, 2021, and July 1, 2021, for the study area in North Africa were selected.
As shown in Figs. 7 and 8, we retrieved LST for daytime and nighttime data in different seasons using two research areas with the AFNO-transformer model. The size (number of pixels) of each study area was identical. Finally, compared with the AVHRR/MetOp LST product, the LST was retrieved with an accuracy of <3 K for April and October in Spain (Fig. 7) and <2.5 K for January and July in North Africa (Fig. 8). The retrieval accuracy trend was consistent with the accuracy of the above retrieval results. In Spain, the accuracy for October was better than that for April, which may be owing to the influence of the season on the inversion of the input data for April. We used the surrounding average value to complement the temperature in pixels partially covered by clouds. The LST data introduced in this section had a certain impact on the retrieval accuracy, although introducing actual satellite observations mixed with LST reduced certain errors. North Africa performed similarly in January and July. In addition, the temperature at night was more uniform; therefore, the LST retrieval accuracy at night was higher.
Fig. 7. Retrieval results in eastern Spain. (a) Daytime data obtained on April 27, 2021. (b) The nighttime data obtained on April 27, 2021. (c) Daytime data obtained on October 1, 2021. (d) The nighttime data obtained on October 1, 2021.
Fig. 8. Retrieval results in North Africa. (a) Daytime data obtained on January 2, 2021. (b) The nighttime data on January 2, 2021. (c) Daytime data on July 1, 2021. (d) The nighttime data on July 1, 2021.
It can be concluded that the AFNO-transformer model provides good and relatively accurate LST estimations for real IASI observations. It is reasonable to conclude that the application of the proposed AFNO-Transformer method to the IASI data yields an LST retrieval that coincides with that based on the AVHRR/Metop LST product.
4. Discussion and conclusion
When discussing LST retrieval using hyperspectral TIR data, simultaneous LST and LSE retrieval methods can accurately obtain LST and LSEs if atmospheric corrections are performed properly. However, accurate atmospheric profiles are usually not available synchronously with TIR measurements, which influences the retrieval accuracy of LST. Considering this problem, this study aimed to obtain high-precision LST under unknown atmospheric profiles. This study only discussed the relationship between IASI brightness temperature and LST and further proposed an AFNO-transformer model to provide accurate LST estimation in time series without atmospheric information.
The proposed model was trained and validated using actual IASI satellite observations and AVHRR/MetOp LST products. The simulated IASI dataset was used to accomplish the channel selection for this model. The RMSEs of the retrieved LST for the two selected areas of North Africa and Eastern Spain were 1.84 K and 2.4 K, respectively. For the two study areas, the proposed method was applied to the actual IASI observations obtained at other times. The retrieval performance for daytime data with an accuracy of < 3 K for North Africa and Eastern Spain was lower than that for nighttime data with an accuracy of <1.5 K. Our proposed method achieved a good LST accuracy with hyperspectral TIR data.
This study introduced a large number of real satellite observations and land surface products to ensure the universality of the model in real observation. However, for the proposed machine learning model, a large number of real observations that need to be prepared consume considerable time in data downloading and processing. Moreover, they require high computer performance, which is also a problem of this machine learning model. Improving the data and computer processing speeds is another problem in large-scale research. In addition, when choosing LST products, we did not use the commonly used MODIS LST but used AVHRR/MetOp LST products to avoid the influence of transit time on temperature. In future work, multiple LST products can be used to cross-validate the retrieval results, and a multi-angle observation retrieval model can be attempted.
Funding
Fundamental Research Funds for the Central Universities (BLX202169); National Natural Science Foundation of China (42201378).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. M. C. Anderson, J. M. Norman, W. P. Kustas, et al., “A thermal-based remote sensing technique for routine mapping of land-surface carbon, water and energy fluxes from field to regional scales,” Remote Sens. Environ. 112(12), 4227–4241 (2008). [CrossRef]
2. P. Dash, F. M. Göttsche, F. S. Olesen, et al., “Land surface temperature and emissivity estimation from passive sensor data: Theory and practice-current trends,” Int. J. Remote Sens. 23(13), 2563–2594 (2002). [CrossRef]
3. Z. L. Li, B. H. Tang, H. Wu, et al., “Satellite-derived land surface temperature: Current status and perspectives,” Remote Sens. Environ. 131, 14–37 (2013). [CrossRef]
4. J. Sun and L. Mahrt, “Determination of surface fluxes from the surface radiative temperature,” J. Atmos. Sci. 52(8), 1096–1106 (1995). [CrossRef]
5. H. H. Aumann, M. T. Chahine, C. Gautier, et al., “AIRS/AMSU/HSB on the aqua mission: Design, science objectives, data products, and processing systems,” IEEE Trans. Geosci. Remote Sens. 41(2), 253–264 (2003). [CrossRef]
6. F. Hilton, R. Armante, T. August, et al., “Hyperspectral earth observation from IASI:Five Years of Accomplishments,” Bull. Am. Meteorol. Soc. 93(3), 347–370 (2012). [CrossRef]
7. F. Bermudo, S. Rousseau, E. Pequignot, et al., “IASI-NG program: A new generation of Infrared Atmospheric Sounding Interferometer,” in 2014 IEEE Geoscience and Remote Sensing Symposium (2014), pp. 1373–1376.
8. H. J. Bloom, “The cross-track infrared sounder (CrIS): A sensor for operational meteorological remote sensing,” Int. Geosci. Remote Sens. Symp. 3(C), 1341–1343 (2001). [CrossRef]
9. C. Borel, “Iterative Retrieval of Surface Emissivity and Temperature for a Hyperspectral Sensor,” First JPL Work. Remote Sens. L. Surf. Emiss. (836), (1997).
10. C. C. Borel, “Surface emissivity and temperature retrieval for a hyperspectral sensor,” Int. Geosci. Remote Sens. Symp. 1(August 1998), 546–549 (1998). [CrossRef]
11. C. Borel, “ARTEMISS - an Algorithm to Retrieve Temperature and Emissivity from Hyper-Spectral Thermal Image Data,” 28th Annu. GOMACTech Conf.3–6 (2003).
12. C. Borel, “Error analysis for a temperature and emissivity retrieval algorithm for hyperspectral imaging data,” Int. J. Remote Sens. 29(17-18), 5029–5045 (2008). [CrossRef]
13. X. Wang, X. OuYang, B. Tang, et al., “A new method for temperature/emissivity separation from hyperspectral thermal infrared data,” Int. Geosci. Remote Sens. Symp. 3(1), 286 (2008). [CrossRef]
14. X. Ouyang, G. Kang, F. Zeng, et al., “Preliminary applications of a land surface temperature retrieval method to IASI and AIRS data,” Int. J. Remote Sens. 34(9-10), 3128–3139 (2013). [CrossRef]
15. N. Wang, H. Wu, F. Nerry, et al., “Temperature and emissivity retrievals from hyperspectral thermal infrared data using linear spectral emissivity constraint,” IEEE Trans. Geosci. Remote Sensing 49(4), 1291–1303 (2011). [CrossRef]
16. X. Lan, E. Zhao, Z. L. Li, et al., “An improved linear spectral emissivity constraint method for temperature and emissivity separation using hyperspectral thermal infrared data,” Sensors 19(24), 5552 (2019). [CrossRef]
17. X. Liu, W. L. Smith, D. K. Zhou, et al., “Principal component-based radiative transfer model for hyperspectral sensors: Theoretical concept,” Appl. Opt. 45(1), 201–209 (2006). [CrossRef]
18. Y. Z. Zhang, H. Wu, X. G. Jiang, et al., “Land surface temperature and emissivity retrieval from field-measured hyperspectral thermal infrared data using wavelet transform,” Remote Sens. 9(5), 454 (2017). [CrossRef]
19. D. K. Zhou, W. L. Smith, J. Li, et al., “Thermodynamic product retrieval methodology and validation for NAST-I,” Appl. Opt. 41(33), 6957 (2002). [CrossRef]
20. M. D. Goldberg, Y. Qu, L. M. McMillin, et al., “AIRS near-real-time products and algorithms in support of operational numerical weather prediction,” IEEE Trans. Geosci. Remote Sensing 41(2), 379–389 (2003). [CrossRef]
21. D. K. Zhou, A. M. Larar, X. Liu, et al., “Global land surface emissivity retrieved from satellite ultraspectral IR measurements,” IEEE Trans. Geosci. Remote Sensing 49(4), 1277–1290 (2011). [CrossRef]
22. J. Li, Z. Fengxian, and Z. Qingcun, “Simultaneous non-linear retrieval of atmospheric temperature and absorbing constituent profiles from satellite infrared sounder radiances,” Adv. Atmos. Sci. 11(2), 128–138 (1994). [CrossRef]
23. J. Li, J. Li, E. Weisz, et al., “Physical retrieval of surface emissivity spectrum from hyperspectral infrared radiances,” Geophys. Res. Lett. 34(16), 4–9 (2007). [CrossRef]
24. F. Aires, W. B. Rossow, N. A. Scott, et al., “Remote sensing from the infrared atmospheric sounding interferometer instrument 1. Compression, denoising, and first-guess retrieval algorithms,” J.-Geophys.-Res. 107(D22), 4619 (2002). [CrossRef]
25. F. Aires, W. B. Rossow, N. A. Scott, et al., “Remote sensing from the infrared atmospheric sounding interferometer instrument 2. Simultaneous retrieval of temperature, water vapor, and ozone atmospheric profiles,” J.-Geophys.-Res. 107(D22), 1–12 (2002). [CrossRef]
26. X. L. Ma, T. J. Schmit, and W. L. Smith, “A nonlinear physical retrieval algorithm - Its application to the GOES-8/9 sounder,” J. Appl. Meteor. 38(5), 501–513 (1999). [CrossRef]
27. M. Paul, F. Aires, C. Prigent, et al., “An innovative physical scheme to retrieve simultaneously surface temperature and emissivities using high spectral infrared observations from IASI,” J. Geophys. Res. 117(D11), 1–15 (2012). [CrossRef]
28. G. Masiello and C. Serio, “Simultaneous physical retrieval of surface emissivity spectrum and atmospheric parameters from infrared atmospheric sounder interferometer spectral radiances,” Appl. Opt. 52(11), 2428–2446 (2013). [CrossRef]
29. X. L. Ma, Z. Wan, C. C. Moeller, et al., “Retrieval of geophysical parameters from Moderate Resolution Imaging Spectroradiometer thermal infrared data: evaluation of a two-step physical algorithm,” Appl. Opt. 39(20), 3537 (2000). [CrossRef]
30. X. L. Ma, Z. Wan, C. C. Moeller, et al., “Simultaneous retrieval of atmospheric profiles, land-surface temperature, and surface emissivity from Moderate-Resolution Imaging Spectroradiometer thermal infrared data: extension of a two-step physical algorithm,” Appl. Opt. 41(5), 909 (2002). [CrossRef]
31. H. Ren, X. Ye, J. Nie, et al., “Retrieval of Land Surface Temperature, Emissivity, and Atmospheric Parameters From Hyperspectral Thermal Infrared Image Using a Feature-Band Linear-Format Hybrid Algorithm,” IEEE Trans. Geosci. Remote Sensing 60, 1–15 (2022). [CrossRef]
32. F. Aires, C. Prigent, W. B. Rossow, et al., “A new neural network approach including first guess for retrieval of atmospheric water vapor, cloud liquid water path, surface temperature, and emissivities over land from satellite microwave observations,” J. Geophys. Res. 106(D14), 14887–14907 (2001). [CrossRef]
33. F. Aires, A. Chédin, N. A. Scott, et al., “A regularized neural net approach for retrieval of atmospheric and surface temperatures with the IASI instrument,” J. Appl. Meteor. 41(2), 144–159 (2002). [CrossRef]
34. N. Wang, Z. L. Li, B. H. Tang, et al., “Retrieval of atmospheric and land surface parameters from satellite-based thermal infrared hyperspectral data using a neural network technique,” Int. J. Remote Sens. 34(9-10), 3485–3502 (2013). [CrossRef]
35. M. Chen, L. Ni, X. Jiang, et al., “Retrieving Atmospheric and Land Surface Parameters from At-Sensor Thermal Infrared Hyperspectral Data with Artificial Neural Network,” IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing 12(7), 2409–2416 (2019). [CrossRef]
36. K. Mao, J. Shi, H. Tang, et al., “A neural network technique for separating land surface emissivity and temperature from ASTER imagery,” IEEE Trans. Geosci. Remote Sensing 46(1), 200–208 (2008). [CrossRef]
37. X. Ye, H. Ren, J. Nie, et al., “Simultaneous Estimation of Land Surface and Atmospheric Parameters From Thermal Hyperspectral Data Using a LSTM–CNN Combined Deep Neural Network,” IEEE Geosci. Remote Sensing Lett. 19, 1–5 (2022). [CrossRef]
38. A. Vaswani, N. Shazeer, N. Parmar, et al., “Attention is all you need,” Adv. Neural Inf. Process. Syst. 30 (2017).
39. A. Dosovitskiy, L. Beyer, A. Kolesnikov, et al., “An Image is Worth 16 × 16 Words: Transformers for Image Recognition at Scale,” in International Conference on Learning Representations (2020).
40. J. Guibas, M. Mardani, Z. Li, et al., “Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers,” in International Conference on Learning Representations (2021).
41. X. Lan, E. Zhao, P. Leng, et al., “Alternative Physical Method for Retrieving Land Surface Temperatures from Hyperspectral Thermal Infrared Data: Application to IASI Observations,” IEEE Trans. Geosci. Remote Sensing 60, 1–12 (2022). [CrossRef]
42. Z. Wan and D. Jeff, “A generalized split-window algorithm for retrieving land-surface temperature from space,” IEEE Trans. Geosci. Remote Sensing 34(4), 892–905 (1996). [CrossRef]
43. P. Reiners, S. Asam, C. Frey, et al., “Validation of AVHRR Land Surface Temperature with MODIS and In Situ LST—A TIMELINE Thematic Processor,” Remote Sens. 13(17), 3473 (2021). [CrossRef]
44. A. M. Baldridge, S. J. Hook, C. I. Grove, et al., “The ASTER spectral library version 2.0,” Remote Sens. Environ. 113(4), 711–715 (2009). [CrossRef]
45. J. M. Galve, C. Coll, V. Caselles, et al., “An atmospheric radiosounding database for generating land surface temperature algorithms,” IEEE Trans. Geosci. Remote Sensing 46(5), 1547–1557 (2008). [CrossRef]
