RIFTES: An RTM- and iteration-free temperature-emissivity separation framework for accurate and efficient clear-sky land surface temperature retrieval

Bo-Hui Tang; Frank M. G\"ottsche; Huanyu Zhang; Menglin Si; Tian Hu; Yuanliang Cheng; Yun Jiang; Zhao-Liang Li

arxiv: 2606.03025 · v1 · pith:4UCQE2OYnew · submitted 2026-06-02 · ⚛️ physics.geo-ph

RIFTES: An RTM- and iteration-free temperature-emissivity separation framework for accurate and efficient clear-sky land surface temperature retrieval

Huanyu Zhang , Bo-Hui Tang , Yun Jiang , Menglin Si , Frank M. G\"ottsche , Tian Hu , Yuanliang Cheng , Zhao-Liang Li This is my paper

Pith reviewed 2026-06-28 07:50 UTC · model grok-4.3

classification ⚛️ physics.geo-ph

keywords temperature-emissivity separationland surface temperaturenon-iterative algorithmatmospheric correctiondeep residual networkremote sensingECOSTRESSABI

0 comments

The pith

A closed-form reformulation of temperature-emissivity separation retrieves land surface temperatures at 1.06 K RMSE without iterations or radiative transfer models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops RIFTES to replace the standard iterative temperature-emissivity separation procedure with a mathematically equivalent closed-form solution and to handle atmospheric correction through a physics-informed deep residual network. This targets clear-sky land surface temperature retrieval from instruments such as ECOSTRESS and ABI using only easily accessible parameters. If the reformulation holds, the approach reduces both error accumulation from iterations and the computational cost of full radiative transfer modeling while maintaining or improving accuracy over split-window, TES, and hybrid methods. Validation on simulations and global in-situ sites shows lower RMSE values and substantial speed gains.

Core claim

The iterative TES procedure can be rewritten as a non-iterative closed-form solution that is mathematically equivalent, and pairing it with a masking-enabled deep residual network for atmospheric correction produces an RTM-free and iteration-free framework that achieves 1.06 K RMSE in simulations, 1.51 K and 1.97 K on ECOSTRESS and ABI in-situ data, and cuts computation time by 74 percent and 62.5 percent relative to prior TES and hybrid algorithms.

What carries the argument

The non-iterative TES algorithm obtained by algebraic reformulation of the original iterative procedure into a closed-form expression that removes the need for iteration loops.

If this is right

RIFTES produces the lowest simulation RMSE of 1.06 K among split-window, TES, and hybrid methods while remaining stable under input uncertainty.
Applied to ECOSTRESS the method reduces in-situ RMSE by up to 24 percent; applied to ABI it reduces RMSE by up to 32 percent.
Overall runtime drops 74 percent versus standard TES and 62.5 percent versus the hybrid algorithm.
Atmospheric correction can optionally incorporate available constraints through the network masking mechanism without requiring a full RTM at runtime.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Because the solution is closed-form, large-scale global LST mapping could shift from batch processing to near-real-time pipelines on modest hardware.
The same algebraic rearrangement technique might be tested on other iterative remote-sensing inversions that currently rely on successive approximation.
Embedding radiative-transfer constraints inside the network could allow the method to operate when standard atmospheric profiles are missing or uncertain.

Load-bearing premise

The algebraic reformulation of the iterative TES steps produces results that are numerically identical to the original iterative version and do not change error behavior.

What would settle it

Running the closed-form solution and the original iterative TES on identical input radiances and emissivity spectra and finding that the two outputs differ by more than floating-point roundoff or that the closed-form version yields higher RMSE against validation temperatures.

Figures

Figures reproduced from arXiv: 2606.03025 by Bo-Hui Tang, Frank M. G\"ottsche, Huanyu Zhang, Menglin Si, Tian Hu, Yuanliang Cheng, Yun Jiang, Zhao-Liang Li.

**Figure 2.** Figure 2: Spatial distribution of selected validation sites. (a) Sites CNS, KIT, CDG, and FDU in Europe, (b) Site GBBp in Namibia, (c) SURFRAD sites in United States [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Figure 3: Detailed structure of the DRNNMM. The masking layer selectively applies a mask to PWV depending on its availability, which allows the model to flexibly accommodate both the presence and absence of PWV input. The basic principle of this layer is summarized as follows: { PWVmasked = PWV ⊙ mask mask ∈ {0, 1} (19) where ⊙ denotes the Hadamard product. Then, the input projection layer was used to extract shallo… view at source ↗

**Figure 4.** Figure 4: Overall workflow of the RIFTES framework for clear-sky LST retrieval. 3.4 Evaluation strategies Comprehensive simulation analysis and T-based validation were conducted in this study to validate the performance of various clear-sky LST retrieval methods, including SW, TES, RIFTES. These two evaluation strategies complement each other to provide more robust and credible validation results, as simulation data… view at source ↗

**Figure 9.** Figure 9: Comparison of RMSE values of the PWV-incorporated and PWV-free RIFTES algorithms across different LST and PWV bins. Panels (a) and (b) present RMSE values of the PWV-incorporated and PWV-free RIFTES algorithms. Numbers in parentheses indicate the number of samples. Panel (c) shows the RMSE differences (PWV-free RIFTES minus PWV-incorporated RIFTES). 4.2 T-based validation As the SW, TES, and ISW-TES algori… view at source ↗

**Figure 13.** Figure 13: Comparison of computational efficiency and retrieval accuracy among different methods. Accuracy metrics are derived from the T-based validation results in Section 4.2 [PITH_FULL_IMAGE:figures/full_fig_p030_13.png] view at source ↗

read the original abstract

This study proposes an RTM- and iteration-free TES (RIFTES) framework to improve both computational efficiency and retrieval accuracy of the temperature-emissivity separation (TES) algorithm for clear-sky land surface temperature (LST) retrieval. Based on physical derivations, a non-iterative TES algorithm was first developed by reformulating the original iterative procedure into a mathematically equivalent closed-form solution, thereby eliminating the need for cumbersome iterations. To further reduce error propagation risks and computational burdens, a deep residual neural network that integrates atmospheric radiative transfer physics was adopted to conduct atmospheric correction using easily accessible parameters, with a masking mechanism introduced to flexibly incorporate atmospheric constraints when available. Comprehensive validations demonstrate the effectiveness of the proposed algorithm. Simulation results show that RIFTES remains robust to input uncertainties and achieves the lowest root mean squared error (RMSE) of 1.06 K among representative existing algorithms, including split-window (SW), TES, and SW-TES hybrid methods. In-situ measurements from globally distributed sites were then used to evaluate the practical performance of RIFTES when applied to both the ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station (ECOSTRESS) and the Advanced Baseline Imager (ABI). The new algorithm achieves RMSE values of 1.51 K and 1.97 K for ECOSTRESS and ABI, respectively, reducing retrieval uncertainties by up to 24% and 32% compared with existing methods. Furthermore, by simplifying both the iterative procedure and atmospheric correction, RIFTES reduces the overall computational time by 74.0% and 62.5% compared with the TES and hybrid algorithms, respectively.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

RIFTES gives a closed-form non-iterative TES plus a physics residual net for atmospheric correction, with reported gains in speed and RMSE, but the exact equivalence of the reformulation is the part that still needs checking.

read the letter

The two things worth knowing are that the authors reformulated the usual iterative TES into a closed-form solution and then used a residual network that folds in radiative transfer physics for the atmospheric step, claiming both lower error and much less compute time.

They do show concrete numbers: 1.06 K RMSE on simulations, beating the SW, TES, and hybrid baselines, plus 1.51 K and 1.97 K on ECOSTRESS and ABI in-situ data with 24-32% error reduction and 62-74% faster run times. The masking trick in the network to bring in atmospheric constraints when available is a practical touch, and the overall framing stays grounded in the physical problem rather than treating it as pure black-box learning.

The soft spot is the central claim that the closed-form version is mathematically equivalent to the original iterative procedure. If the derivation drops higher-order terms or changes how the emissivity normalization is handled, the performance difference could partly reflect that change rather than a pure improvement. The abstract gives no derivation steps or side-by-side numerical checks across edge cases, so it is impossible to judge how tight the equivalence actually is. The in-situ results are useful but the training and validation details for the network are not visible here either.

This is aimed at groups doing operational clear-sky LST retrieval from sensors like ECOSTRESS or ABI who care about throughput on large archives. A reader who needs faster processing and is willing to test the closed-form step themselves could extract value. It is solid enough on the application side and the reported metrics to deserve a serious referee, even if the math section will need close scrutiny.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes the RIFTES framework for clear-sky land surface temperature (LST) retrieval. It first reformulates the standard iterative temperature-emissivity separation (TES) procedure into a non-iterative closed-form solution based on physical derivations. Atmospheric correction is then performed via a deep residual neural network that incorporates radiative transfer physics and includes a masking mechanism for optional atmospheric constraints. Simulation and in-situ validations (ECOSTRESS and ABI) are reported to show the lowest RMSE values (1.06 K in simulations; 1.51 K and 1.97 K in-situ) among split-window, TES, and hybrid baselines, together with 62.5–74 % reductions in computation time.

Significance. If the closed-form TES reformulation is numerically equivalent to the iterative version and the physics-informed network generalizes reliably, the work could meaningfully improve both accuracy and throughput for operational LST products. The explicit integration of radiative-transfer constraints into the network architecture is a constructive element that may aid robustness beyond purely data-driven approaches.

major comments (2)

[Abstract / non-iterative TES section] Abstract and the section describing the non-iterative TES development: the central claim that the reformulation produces a 'mathematically equivalent closed-form solution' is load-bearing for attributing the reported RMSE reductions to the new framework rather than to implementation differences. Explicit numerical verification (e.g., side-by-side comparison of LST and emissivity outputs across the full range of input emissivities, temperatures, and atmospheric states) is required to confirm that no discrepancies arise from neglected higher-order terms or altered normalization handling.
[Simulation results section] Simulation validation section: the reported RMSE of 1.06 K is presented without error bars, without the number of Monte-Carlo realizations, and without the precise ranges of input uncertainties. These details are necessary to establish whether the improvement over the SW, TES, and hybrid baselines is statistically significant rather than within the variability of the test ensemble.

minor comments (1)

[Abstract] The abstract states time reductions of 74.0 % and 62.5 % relative to 'the TES and hybrid algorithms' but does not name the exact reference implementations used for timing; this should be clarified for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment below and commit to revisions that strengthen the manuscript without altering its core claims.

read point-by-point responses

Referee: [Abstract / non-iterative TES section] Abstract and the section describing the non-iterative TES development: the central claim that the reformulation produces a 'mathematically equivalent closed-form solution' is load-bearing for attributing the reported RMSE reductions to the new framework rather than to implementation differences. Explicit numerical verification (e.g., side-by-side comparison of LST and emissivity outputs across the full range of input emissivities, temperatures, and atmospheric states) is required to confirm that no discrepancies arise from neglected higher-order terms or altered normalization handling.

Authors: We agree that explicit numerical verification strengthens the claim. The closed-form solution was obtained by algebraic rearrangement of the original iterative equations with no approximations or altered normalization; however, to address the concern directly we will add a new subsection (or appendix) containing side-by-side numerical comparisons of LST and emissivity outputs from both the iterative and closed-form implementations over the full range of input emissivities, temperatures, and atmospheric states used in the study. revision: yes
Referee: [Simulation results section] Simulation validation section: the reported RMSE of 1.06 K is presented without error bars, without the number of Monte-Carlo realizations, and without the precise ranges of input uncertainties. These details are necessary to establish whether the improvement over the SW, TES, and hybrid baselines is statistically significant rather than within the variability of the test ensemble.

Authors: We acknowledge the omission. In the revised manuscript we will report error bars on all RMSE values, state the exact number of Monte-Carlo realizations performed, and provide the precise ranges of input uncertainties (temperature, emissivity, and atmospheric parameters) so that readers can assess statistical significance of the reported improvements. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained reformulation plus independent NN training

full rationale

The paper's central step is a claimed mathematical reformulation of the existing iterative TES procedure into an equivalent closed-form solution based on physical derivations, followed by a separately trained deep residual NN for atmospheric correction using accessible parameters. No equations or claims reduce a prediction to a fitted input by construction, no self-citations are invoked as load-bearing uniqueness theorems, and no ansatz is smuggled via prior work. Validation uses external simulation benchmarks and in-situ measurements, so the reported RMSE improvements are not forced by the inputs themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review based on abstract only; no explicit free parameters, axioms, or invented entities are identifiable. The central claim rests on the asserted mathematical equivalence of the closed-form reformulation and the adequacy of the neural network for atmospheric correction.

pith-pipeline@v0.9.1-grok · 5867 in / 1270 out tokens · 33205 ms · 2026-06-28T07:50:14.088838+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

16 extracted references

[1]

Introduction Land surface temperature (LST) is a key parameter in the Earth surface system, controlling the exchange of energy and water between the land surface and atmosphere (Li et al., 2023; Li et al., 2013). LST reflects the thermal state of the land surface, and is therefore of great importance for a wide range of applications, such as climate chang...

2023
[2]

Data Two representative sensors were considered in this study to evaluate the cross- sensor performance of different algorithms. The first is NASA’s ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station (ECOSTRESS) (Fisher et al., 2020), which serves as a precursor to next-generation TIR missions and provides high-spatial-resolution (~70 m) ...

2020
[3]

Before iteration, the initial emissivity (i.e., 𝜀𝑖

Methods 3.1 Non-iterative TES algorithm 3.1.1 The original NEM module The original NEM module iteratively removes 𝑳𝒂𝒕𝒎↓ from 𝑳𝒈𝒓𝒅 to eliminate the atmospheric effect. Before iteration, the initial emissivity (i.e., 𝜀𝑖
[4]

Then, for the arbitrary i-th band of the sensor during the first iteration, its corresponding LST is calculated from Eq

for each band is set to the possible maximum value (e.g., 0.99 for gray bodies and 0.96 for non-gray bodies). Then, for the arbitrary i-th band of the sensor during the first iteration, its corresponding LST is calculated from Eq. (2) as follows: 𝑇𝑠,𝑖 1 =𝐵𝑖 −1[𝐿𝑖 𝑔𝑟𝑑−(1−𝜀𝑖 0)𝐿𝑖 𝑎𝑡𝑚↓ 𝜀𝑖 0 ] (5) where the superscript number denotes the iteration round. In t...
[5]

(6) where 𝑇𝑠,𝑁𝐸𝑀 1 represents the NEM LST after first iteration, and max(∙) denotes the maximum operation applied to a vector. After obtaining 𝑇𝑠,𝑁𝐸𝑀 1 , the emissivity value for the i-th band is updated as follows: 𝜀𝑖 1=𝐿𝑖 𝑔𝑟𝑑−(1−𝜀𝑖 0)𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 ) (7) Similarly, in the second iteration, the LST and LSE of the i-th band are calculated as follows:...
[6]

(9) indicates that 𝜀𝑖 1 ≤ 𝜀𝑖 0

=𝜀𝑖 0 (9) Eq. (9) indicates that 𝜀𝑖 1 ≤ 𝜀𝑖 0 . Therefore, the following relationship can be derived: 𝜀𝑖 1=𝐿𝑖 𝑔𝑟𝑑−(1−𝜀𝑖 0)𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 ) ≥𝐿𝑖 𝑔𝑟𝑑−(1−𝜀𝑖 1)𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 ) (10) By rearranging Eq. (5), 𝜀𝑖 0 can be expressed as follows: 𝜀𝑖 0= 𝐿𝑖 𝑔𝑟𝑑−𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑖 1)−𝐿𝑖 𝑎𝑡𝑚↓ (11) As 𝜀𝑖 0 is positive, if 𝐿𝑖 𝑔𝑟𝑑 > 𝐿𝑖 𝑎𝑡𝑚↓ , which is the most common ...
[7]

Conversely, for the rare case where 𝐿𝑖 𝑔𝑟𝑑 < 𝐿𝑖 𝑎𝑡𝑚↓ , 𝐵𝑖(𝑇𝑠,𝑖

> 𝐿𝑖 𝑎𝑡𝑚↓ . Conversely, for the rare case where 𝐿𝑖 𝑔𝑟𝑑 < 𝐿𝑖 𝑎𝑡𝑚↓ , 𝐵𝑖(𝑇𝑠,𝑖
[8]

Therefore, Eq

< 𝐿𝑖 𝑎𝑡𝑚↓. Therefore, Eq. (10) can be rearranged as follows: { 𝜀𝑖 1≥ 𝐿𝑖 𝑔𝑟𝑑−𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 )−𝐿𝑖 𝑎𝑡𝑚↓ when 𝐿𝑖 𝑔𝑟𝑑>𝐿𝑖 𝑎𝑡𝑚↓ 𝜀𝑖 1≤ 𝐿𝑖 𝑔𝑟𝑑−𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 )−𝐿𝑖 𝑎𝑡𝑚↓ when 𝐿𝑖 𝑔𝑟𝑑<𝐿𝑖 𝑎𝑡𝑚↓ (12) From Eqs. (8) and (12), LST of the i-th band in the second iteration follows: { 𝐵𝑖(𝑇𝑠,𝑖 2)=𝐿𝑖 𝑎𝑡𝑚↓+𝐿𝑖 𝑔𝑟𝑑−𝐿𝑖 𝑎𝑡𝑚↓ 𝜀𝑖 1 ≤𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 ) when 𝐿𝑖 𝑔𝑟𝑑 >𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑖 ...
[9]

confident clear

does not exceed 𝑇𝑠,𝑁𝐸𝑀 1 , and consequently, the NEM LST remains unchanged. Similarly, it is easy to know that the NEM LST will not change in the subsequent iterations. In other words, the NEM LST is already determined after the first iteration. Given this phenomenon, the NEM LSE (i.e., 𝜺𝑵𝑬𝑴) 14 can be directly derived from the maximum LST after the first...

1992
[10]

Specifically, both the conventional and non-iterative TES algorithms were applied to the simulation dataset for ECOSTRESS, estimating LST from error-free 𝑳𝒈𝒓𝒅 and 𝑳𝒂𝒕𝒎↓

Results 4.1 Simulation analysis 4.1.1 Comparison of the conventional and non-iterative TES algorithms A simulation analysis was first conducted to demonstrate the effectiveness of the new non-iterative TES algorithm. Specifically, both the conventional and non-iterative TES algorithms were applied to the simulation dataset for ECOSTRESS, estimating LST fr...

2025
[11]

3σ-Hampel identifier

Discussion 5.1 Impact of the number of residual blocks in DRNNMM The performance of neural networks generally varies with model capacity. To further assess its influence, the simulated training set for ECOSTRESS was used to train DRNNMM with the number of ResBlocks varying from 1 to 4. Subsequently, the corresponding loss values of DRNNMM with different m...

2025
[12]

Xingdian Talent Support Program

Conclusion LST is a fundamental parameter in TIR remote sensing. The TES and SW algorithms remain two most widely used methods for operational clear-sky LST retrieval, while both of them suffer from certain limitations. In recent years, hybrid methods combining the SW and TES algorithms have become increasingly popular. Nevertheless, these hybrid methods ...

2026
[13]

Remote Sens Environ 257, 112349

NASA’s surface biology and geology designated observable: A perspective on surface imaging algorithms. Remote Sens Environ 257, 112349. Cheng, J., Liang, S., Yao, Y., Zhang, X., 2013. Estimating the optimal broadband emissivity spectral range for calculating surface longwave net radiation. IEEE Geosci. Remote Sens. Lett. 10, 401–405. Cheng, Y., Wu, H., Li...

2013
[14]

IEEE Trans

A physics-based algorithm for the simultaneous retrieval of land surface temperature and emissivity from VIIRS thermal infrared data. IEEE Trans. Geosci. Remote Sens. 55, 563–576. Jia, A., Mallick, K., Upadhyaya, D., Hu, T., Szantoi, Z., Bhattacharya, B., Sekhar, M., Skoković, D., Sobrino, J.A., Ruiz, L., Boulet, G., 2025. Deriving a clear-sky soil moistu...

2025
[15]

Remote Sens

Satellite -derived land surface temperature: Current status and perspectives. Remote Sens. Environ. 131, 14–37. Liang, S., Wang, D., He, T., Yu, Y., 2019. Remote sensing of earth’s energy budget: synthesis and review. Int. J. Digital Earth 12, 737–780. Liang, S., Wang, K., Zhang, X., Wild, M., 2010. Review on estimation of land surface radiation and energ...

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[16]

Validation and consistency assessment of land surface temperature from geostationary and polar orbit platforms: SEVIRI/MSG and AVHRR/Metop. ISPRS J. Photogramm. Remote Sens. 175, 282–297. Wang, M., He, G., Hu, T., Yang, M., Zhang, Zhengjia, Zhang, Zhaoming, Wang, G., Li, H., Gao, W., Liu, X., 2024. Innovative hybrid algorithm for simultaneous land 42 surf...

2024

[1] [1]

Introduction Land surface temperature (LST) is a key parameter in the Earth surface system, controlling the exchange of energy and water between the land surface and atmosphere (Li et al., 2023; Li et al., 2013). LST reflects the thermal state of the land surface, and is therefore of great importance for a wide range of applications, such as climate chang...

2023

[2] [2]

Data Two representative sensors were considered in this study to evaluate the cross- sensor performance of different algorithms. The first is NASA’s ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station (ECOSTRESS) (Fisher et al., 2020), which serves as a precursor to next-generation TIR missions and provides high-spatial-resolution (~70 m) ...

2020

[3] [3]

Before iteration, the initial emissivity (i.e., 𝜀𝑖

Methods 3.1 Non-iterative TES algorithm 3.1.1 The original NEM module The original NEM module iteratively removes 𝑳𝒂𝒕𝒎↓ from 𝑳𝒈𝒓𝒅 to eliminate the atmospheric effect. Before iteration, the initial emissivity (i.e., 𝜀𝑖

[4] [4]

Then, for the arbitrary i-th band of the sensor during the first iteration, its corresponding LST is calculated from Eq

for each band is set to the possible maximum value (e.g., 0.99 for gray bodies and 0.96 for non-gray bodies). Then, for the arbitrary i-th band of the sensor during the first iteration, its corresponding LST is calculated from Eq. (2) as follows: 𝑇𝑠,𝑖 1 =𝐵𝑖 −1[𝐿𝑖 𝑔𝑟𝑑−(1−𝜀𝑖 0)𝐿𝑖 𝑎𝑡𝑚↓ 𝜀𝑖 0 ] (5) where the superscript number denotes the iteration round. In t...

[5] [5]

(6) where 𝑇𝑠,𝑁𝐸𝑀 1 represents the NEM LST after first iteration, and max(∙) denotes the maximum operation applied to a vector. After obtaining 𝑇𝑠,𝑁𝐸𝑀 1 , the emissivity value for the i-th band is updated as follows: 𝜀𝑖 1=𝐿𝑖 𝑔𝑟𝑑−(1−𝜀𝑖 0)𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 ) (7) Similarly, in the second iteration, the LST and LSE of the i-th band are calculated as follows:...

[6] [6]

(9) indicates that 𝜀𝑖 1 ≤ 𝜀𝑖 0

=𝜀𝑖 0 (9) Eq. (9) indicates that 𝜀𝑖 1 ≤ 𝜀𝑖 0 . Therefore, the following relationship can be derived: 𝜀𝑖 1=𝐿𝑖 𝑔𝑟𝑑−(1−𝜀𝑖 0)𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 ) ≥𝐿𝑖 𝑔𝑟𝑑−(1−𝜀𝑖 1)𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 ) (10) By rearranging Eq. (5), 𝜀𝑖 0 can be expressed as follows: 𝜀𝑖 0= 𝐿𝑖 𝑔𝑟𝑑−𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑖 1)−𝐿𝑖 𝑎𝑡𝑚↓ (11) As 𝜀𝑖 0 is positive, if 𝐿𝑖 𝑔𝑟𝑑 > 𝐿𝑖 𝑎𝑡𝑚↓ , which is the most common ...

[7] [7]

Conversely, for the rare case where 𝐿𝑖 𝑔𝑟𝑑 < 𝐿𝑖 𝑎𝑡𝑚↓ , 𝐵𝑖(𝑇𝑠,𝑖

> 𝐿𝑖 𝑎𝑡𝑚↓ . Conversely, for the rare case where 𝐿𝑖 𝑔𝑟𝑑 < 𝐿𝑖 𝑎𝑡𝑚↓ , 𝐵𝑖(𝑇𝑠,𝑖

[8] [8]

Therefore, Eq

< 𝐿𝑖 𝑎𝑡𝑚↓. Therefore, Eq. (10) can be rearranged as follows: { 𝜀𝑖 1≥ 𝐿𝑖 𝑔𝑟𝑑−𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 )−𝐿𝑖 𝑎𝑡𝑚↓ when 𝐿𝑖 𝑔𝑟𝑑>𝐿𝑖 𝑎𝑡𝑚↓ 𝜀𝑖 1≤ 𝐿𝑖 𝑔𝑟𝑑−𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 )−𝐿𝑖 𝑎𝑡𝑚↓ when 𝐿𝑖 𝑔𝑟𝑑<𝐿𝑖 𝑎𝑡𝑚↓ (12) From Eqs. (8) and (12), LST of the i-th band in the second iteration follows: { 𝐵𝑖(𝑇𝑠,𝑖 2)=𝐿𝑖 𝑎𝑡𝑚↓+𝐿𝑖 𝑔𝑟𝑑−𝐿𝑖 𝑎𝑡𝑚↓ 𝜀𝑖 1 ≤𝐵𝑖(𝑇𝑠,𝑁𝐸𝑀 1 ) when 𝐿𝑖 𝑔𝑟𝑑 >𝐿𝑖 𝑎𝑡𝑚↓ 𝐵𝑖(𝑇𝑠,𝑖 ...

[9] [9]

confident clear

does not exceed 𝑇𝑠,𝑁𝐸𝑀 1 , and consequently, the NEM LST remains unchanged. Similarly, it is easy to know that the NEM LST will not change in the subsequent iterations. In other words, the NEM LST is already determined after the first iteration. Given this phenomenon, the NEM LSE (i.e., 𝜺𝑵𝑬𝑴) 14 can be directly derived from the maximum LST after the first...

1992

[10] [10]

Specifically, both the conventional and non-iterative TES algorithms were applied to the simulation dataset for ECOSTRESS, estimating LST from error-free 𝑳𝒈𝒓𝒅 and 𝑳𝒂𝒕𝒎↓

Results 4.1 Simulation analysis 4.1.1 Comparison of the conventional and non-iterative TES algorithms A simulation analysis was first conducted to demonstrate the effectiveness of the new non-iterative TES algorithm. Specifically, both the conventional and non-iterative TES algorithms were applied to the simulation dataset for ECOSTRESS, estimating LST fr...

2025

[11] [11]

3σ-Hampel identifier

Discussion 5.1 Impact of the number of residual blocks in DRNNMM The performance of neural networks generally varies with model capacity. To further assess its influence, the simulated training set for ECOSTRESS was used to train DRNNMM with the number of ResBlocks varying from 1 to 4. Subsequently, the corresponding loss values of DRNNMM with different m...

2025

[12] [12]

Xingdian Talent Support Program

Conclusion LST is a fundamental parameter in TIR remote sensing. The TES and SW algorithms remain two most widely used methods for operational clear-sky LST retrieval, while both of them suffer from certain limitations. In recent years, hybrid methods combining the SW and TES algorithms have become increasingly popular. Nevertheless, these hybrid methods ...

2026

[13] [13]

Remote Sens Environ 257, 112349

NASA’s surface biology and geology designated observable: A perspective on surface imaging algorithms. Remote Sens Environ 257, 112349. Cheng, J., Liang, S., Yao, Y., Zhang, X., 2013. Estimating the optimal broadband emissivity spectral range for calculating surface longwave net radiation. IEEE Geosci. Remote Sens. Lett. 10, 401–405. Cheng, Y., Wu, H., Li...

2013

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IEEE Trans

A physics-based algorithm for the simultaneous retrieval of land surface temperature and emissivity from VIIRS thermal infrared data. IEEE Trans. Geosci. Remote Sens. 55, 563–576. Jia, A., Mallick, K., Upadhyaya, D., Hu, T., Szantoi, Z., Bhattacharya, B., Sekhar, M., Skoković, D., Sobrino, J.A., Ruiz, L., Boulet, G., 2025. Deriving a clear-sky soil moistu...

2025

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Remote Sens

Satellite -derived land surface temperature: Current status and perspectives. Remote Sens. Environ. 131, 14–37. Liang, S., Wang, D., He, T., Yu, Y., 2019. Remote sensing of earth’s energy budget: synthesis and review. Int. J. Digital Earth 12, 737–780. Liang, S., Wang, K., Zhang, X., Wild, M., 2010. Review on estimation of land surface radiation and energ...

2019

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Validation and consistency assessment of land surface temperature from geostationary and polar orbit platforms: SEVIRI/MSG and AVHRR/Metop. ISPRS J. Photogramm. Remote Sens. 175, 282–297. Wang, M., He, G., Hu, T., Yang, M., Zhang, Zhengjia, Zhang, Zhaoming, Wang, G., Li, H., Gao, W., Liu, X., 2024. Innovative hybrid algorithm for simultaneous land 42 surf...

2024