Convolutional Graph Neural Network with Novel Loss Strategies for Daily Temperature and Precipitation Statistical Downscaling over South China

Traditional meteorological downscaling methods face limitations due to the complex distribution of meteorological variables, which can lead to unstable forecasting results, especially in extreme scenarios. To overcome this issue, we propose a convolutional graph neural network (CGNN) model, which we enhance with multilayer feature fusion and a squeeze-and-excitation block. Additionally, we introduce a spatially balanced mean squared error (SBMSE) loss function to address the imbalanced distribution and spatial variability of meteorological variables. The CGNN is capable of extracting essential spatial features and aggregating them from a global perspective, thereby improving the accuracy of prediction and enhancing the model's generalization ability. Based on the experimental results, CGNN has certain advantages in terms of bias distribution, exhibiting a smaller variance. When it comes to precipitation, both UNet and AE also demonstrate relatively small biases. As for temperature, AE and CNNdense perform outstandingly during the winter. The time correlation coefficients show an improvement of at least 10% at daily and monthly scales for both temperature and precipitation. Furthermore, the SBMSE loss function displays an advantage over existing loss functions in predicting the 98th percentile and identifying areas where extreme events occur. However, the SBMSE tends to overestimate the distribution of extreme precipitation, which may be due to the theoretical assumptions about the posterior distribution of data that partially limit the effectiveness of the loss function. In future work, we will further optimize the SBMSE to improve prediction accuracy.