Impact of Physical Properties among Meteorological Variables in Deep Learning-based Downscaling Prediction: A Case for Daily Maximum Temperature

Deep learning models are often considered as "black boxes," and the physical properties of meteorological variables can provide prior knowledge and enhance the interpretability of the models. Analyzing the relationships among meteorological variables as input factors and constructing loss functions based on the physical properties of output meteorological variables are crucial for understanding and improving deep learning-based downscaling predictions. In the summer of 2023 in the middle and lower reaches of the Yangtze River, using the U-Net deep learning framework and based on the European Centre for Medium-Range Weather Forecasts (ECMWF)'s low-resolution (0.5º) daily maximum 2-meter temperature forecasts, high-resolution (0.05º) predictions (1 to 9-day forecasts) were obtained. Considering that the 2-meter temperature is influenced by multiple factors such as topography and environmental airflow, four input factors were included: high-resolution elevation fields (Elevation), ECMWF's low-resolution 10-meter east-west wind (U), 10-meter north-south wind (V), and directly output daily maximum 2-meter temperature (DMO) forecasts. By comparing the downscaling effects of different combinations of input factors, it was found that using a combination of all four input factors significantly reduced the root mean square error of the predictions, from 2.497 ºC of the original ECMWF forecast to 2.155 ºC. The contributions of each input factor in correcting forecast errors were also analyzed, revealing that Elevation had the largest contribution, reaching 0.31 ºC, while DMO contributed 0.25 ºC. As the forecast time increases, the contribution of Elevation (DMO) tends to decrease (increase). 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. Introducing the Random Generation Method, it quantifies the importance of input factors and reveals that Elevation and DMO have significant impacts on temperature downscaling predictions, providing crucial insights for understanding and improving deep learning.