Prediction of Tropical Pacific Rain Rates with Over-parameterized Neural Networks

The prediction of tropical rain rates from atmospheric profiles poses significant challenges, mainly due to the heavy-tailed distribution exhibited by tropical rainfall. This study introduces over-parameterized neural networks not only to forecast tropical rain rates, but also to explain their heavy-tailed distribution. The prediction is separately conducted for three different rain types (stratiform, deep convective, and shallow convective) observed by the Global Precipitation Measurement satellite radar over the West and East Pacific regions. Atmospheric profiles of humidity, temperature, and zonal and meridional winds from the MERRA-2 reanalysis are considered as covariates. Although over-parameterized neural networks are well-known for their double descent phenomenon, little has been explored for their applicability to real-world datasets and capability of capturing the tail behavior of data. In our results, over-parameterized neural networks accurately predict the rain rate distributions and outperform other machine learning methods. Spatial maps show that over-parameterized neural networks successfully describe spatial patterns of each rain type across the tropical Pacific. We also obtain the covariate importance for each over-parameterized neural network to provide insights into the key factors driving the predictions, with humidity being the overall most important category. These findings highlight the capability of over-parameterized neural networks in predicting the distribution of the rain rate and explaining extreme values.