A robust framework for accurate land surface temperature retrieval: Integrating split-window into knowledge-guided machine learning approach

Abstract

Land surface temperature (LST) is a crucial parameter of the surface-atmosphere system, driving the water and heat exchange between the surface and the atmosphere. However, existing LST retrieval methods are highly sensitive to input errors. This study proposed a robust framework for retrieving LST, termed SW-NN, which integrates the physics-based Split-Window (SW) algorithm with a data-driven Neural Network (NN). The framework comprises of two main components: (1) a NN model that estimates SW coefficients as functions of key parameters such as brightness temperature (BT), water vapor content (WVC), land surface emissivity (LSE), and viewing zenith angle (VZA); and (2) a SW model that applies these coefficients to compute LST based on physical principles. By embedding the SW algorithm into the NN's loss function, this integrated design ensures that physical relationships guide the training process. The training data for the framework were generated by simulating satellite BT under a broad range of atmospheric and surface conditions using a radiative transfer model. To address the challenge of input errors, the proposed framework incorporates Gaussian noise into the training data to simulate realistic uncertainties in BT, WVC, and LSE. Specifically, noise with standard deviations of 0.05 K, 10 % of the WVC value, and 0.01 was added to BT, WVC, and LSE, respectively. Simulation analysis on an independent test set demonstrates that the proposed framework achieves a theoretical root-mean-square error (RMSE) of 0.60 K under the noise strategy, outperforming standalone NN and SW models. Sensitivity analysis, conducted using the same noise strategy applied during training, indicates that input errors affect LST retrieval by approximately 0.20 K, significantly enhancing the model's generalization and robustness. The proposed framework was also applied to MODIS data to retrieve LST, which was directly validated against global measurements from fifteen sites. Additionally, the proposed framework was compared with the NN method, the generalized split-window (GSW) method (MOD11 LST), and the Temperature Emissivity Separation (TES) method (MOD21 LST). The results showed that the proposed framework achieved an RMSE of 1.99 K, outperforming the NN method (RMSE = 2.08 K) and the GSW method (RMSE = 2.52 K), and performing comparably to the TES method (RMSE = 2.03 K). Further analysis in arid areas, where LSE accuracy is relatively lower, showed that the proposed framework improved the RMSE to 1.94 K compared to MOD11 LST, which had an RMSE of 3.02 K, utilizing the same LSE inputs. The proposed framework leverages the SW model's mechanism and the NN model's nonlinear fitting capability. It also demonstrates high robustness against input error, particularly LSE error. In summary, the proposed framework achieves robust and accurate LST retrieval, offering interpretability and a significant improvement over existing methods designed for sensors with two thermal infrared channels, especially in challenging environmental conditions. The proposed framework is available at https://github.com/YL-Cheng-IGSNRR/SW-NN.