Impact of Physical Constraints on Deep Learning-Based Downscaling Prediction of 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 prediction. In summer 2023 over the middle and lower reaches of the Yangtze River, using the U-Net deep learning framework and based on the ECMWF low-resolution (0.5º) daily maximum 2-m temperature forecasts, high-resolution (0.05º) predictions (1–9-day forecasts) were obtained. 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 wind (U), 10-m meridional wind (V), and directly output daily maximum 2-m temperature (DMO) forecasts. By comparing the downscaling effects of different combinations of the four 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 2.497ºC of the original ECMWF forecast to 2.155ºC. The contribution of each input factor to reducing the forecast errors were also analyzed, revealing that Elevation had the largest contribution, reaching 0.31ºC, while DMO contributed 0.25ºC. 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. A random generation method was employed to quantify the importance of input factors and the results reveal that Elevation and DMO have significant impacts on temperature downscaling prediction. The above results demonstrate that appropriately accommodating the physics relationships among input and output variables are beneficial for deep learning.