A Neural-network-based Alternative Scheme to Include Nonhydrostatic Processes in an Atmospheric Dynamical Core

Here, a nonhydrostatic alternative scheme (NAS) is proposed for the grey zone where the nonhydrostatic impact on the atmosphere is evident but not large enough to justify the necessity to include an implicit nonhydrostatic solver in an atmospheric dynamical core. The NAS is designed to replace this solver, which can be incorporated into any hydrostatic models so that existing well-developed hydrostatic models can effectively serve for a longer time. Recent advances in machine learning (ML) provide a potential tool for capturing the main complicated nonlinear-nonhydrostatic relationship. In this study, an ML approach called a neural network (NN) was adopted to select leading input features and develop the NAS. The NNs were trained and evaluated with 12-day simulation results of dry baroclinic-wave tests by the Weather Research and Forecasting (WRF) model. The forward time difference of the nonhydrostatic tendency was used as the target variable, and the five selected features were the nonhydrostatic tendency at the last time step, and four hydrostatic variables at the current step including geopotential height, pressure in two different forms, and potential temperature, respectively. Finally, a practical NAS was developed with these features and trained layer by layer at a 20-km horizontal resolution, which can accurately reproduce the temporal variation and vertical distribution of the nonhydrostatic tendency. Corrected by the NN-based NAS, the improved hydrostatic solver at different horizontal resolutions can run stably for at least one month and effectively reduce most of the nonhydrostatic errors in terms of system bias, anomaly root-mean-square error, and the error of the wave spatial pattern, which proves the feasibility and superiority of this scheme.