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 (1–9 d) were obtained in the summer of 2023 for the middle and lower reaches of the Yangtze River using the U-Net deep learning framework and ECMWF low-resolution (0.5) 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. 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, as based on a comparison of the downscaling performance rates of different combinations of the four input factors. The contribution of each input factor to reducing the forecast errors were also analyzed. 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. A random generation method was employed to quantify the importance of the input factors, and elevation and DMO had significant impacts on the temperature downscaling prediction. These results demonstrate that appropriately accommodating the physical relationships between input and output variables is beneficial for deep learning.