Impact of Physical Constraints on Deep Learning-Based Downscaling Predictions of Temperature

Deep-learning models are often considered “black boxes,” and the physical properties of meteorological variables can provide prior knowledge and enhance model interpretability. Analyzing the relationships among meteorological variables as input factors and constructing loss functions based on the physical properties of the output meteorological variables are crucial for understanding and improving deep-learning-based downscaling predictions. To address this research gap, high-resolution (0.05º) predictions from Days 1–9 were obtained during the summer of 2023 for the lower reaches of the Yangtze River using the U-Net deep learning framework and ECMWF low-resolution (0.5º) daily maximum 2-m temperature forecasts. Considering that the 2-m temperature is influenced by multiple factors such as topography and environmental airflow, four input factors were considered: high-resolution elevation fields (elevation), ECMWF low-resolution 10-m zonal winds (U), 10-m meridional winds (V), and direct output daily maximum 2-m temperature (DMO) forecasts. The utilization of a combination of all four input factors led to a significant reduction in the root mean square error of the predictions, decreasing from 2.497 ºC in the original ECMWF forecast to 2.155 ºC. This improvement was determined through an analysis comparing the downscaling performance rates associated with various combinations of the four input factors. Additionally, an examination was conducted to assess the contribution of each individual input factor towards minimizing forecast errors. Elevation made the largest contribution, reaching 0.31ºC, whereas DMO contributed 0.25ºC. As the forecast time increased, the contributions of elevation and DMO tended to decrease and increase, respectively. Considering the two physical properties (continuity and change-angle fidelity) between adjacent grid points in the output field, hybrid loss functions were constructed separately, making the physical characteristics of the predicted field closer to the true value. This study identifies three essential components for achieving high-precision and trustworthy forecasts: input factor significance assessment, interpretable artificial intelligence framework development, and physical consistency verification. Furthermore, it proposes a randomized perturbation method to quantify input contributions, revealing that elevation and DMO exert significant influences on temperature downscaling predictions.