Exploring a minimal Convolutional Linear-Regression Model for Urban Land Surface Temperature estimation

With rising urbanization and extreme heat events, effective monitoring of urban heat stress is essential. Satellite-derived land surface temperature (LST) is valuable for this task, but current technologies face a trade-off between spatial resolution and revisit frequency, leading to gaps in high resolution thermal data. While numerous methods for downscaling coarse resolution imagery exist, their increasing complexity and variability make it challenging to standardize accuracy and identify key improvement factors. In response, we introduce the Convolutional Linear-Regression Model (CLRM), a minimal complexity approach that focuses on two key assumptions: (i) correlations between LST at different times and spatial resolutions are considered without additional variables, and (ii) these correlations are modelled using linear relationships. Unlike the conventional fusion-based methods, CLRM leverages temporal correlations to perform pixel-wise linear interpolations, thereby avoiding the complexities of pixel unmixing, and eliminating the need for a fine resolution reference image. We use CLRM to generate Landsat 8 imagery at 30 m resolution using data from Moderate-resolution Imaging Spectroradiometer (MODIS) and the Spinning Enhanced Visible and Infrared Imager (SEVIRI) over Madrid, Brussels, and Helsinki, representing three different climate regions. CLRM achieves robust accuracy, with a mean absolute error (MAE) of approximately 1.5 °C, a root mean square error (RMSE) typically below 2 °C - aligning with the error ranges reported for LST downscaling methods in the literature. Finally, we apply CLRM to reconstruct the high-resolution daily LST profile over Madrid, illustrating its potential for improved urban heat monitoring and thermal data enhancement.