Strong impact of topography on Land Surface Temperature (LST) has limited its use on flat terrain. I am currently working on extracting LST data from band 10 Landsat 8 for a mountainous area. I have read that it is necessary to apply topographic normalization to the LST if the study area has a complex terrain. Is there any recommendation on what method or tools I should use?

Do topographic correction methods for LST differ from the ones used for surface reflectance?

The only reference I could find for topographic correction for LST is from Malbéteau et al. (2017)

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