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

Abstract

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.

摘要

大气非静力效应随水平分辨率的提高不断增强, 当分辨率上升到一定临界范围即“灰色地带”时, 其对大气模式动力框架有明显影响, 但仍不足以证明必须在框架中包含非静力隐式求解器. 本文针对上述问题, 旨在发展一套非静力替代求解方案(NAS)来取代传统的非静力隐式积分求解, 使得非静力求解过程成为一个可以自由融入任意静力模式的模块, 从而延长已有成熟的静力模式的使用寿命. 近年来机器学习相关的研究表明该方法具有强大的非线性模拟能力, 十分适合应用于非静力替代求解方案的开发. 本文基于WRF大气模式非静力框架的干斜压波理想试验, 选取了一种经典的机器学习算法——全连接神经网络算法来挑选最优输入特征以及构建求解方案. 该算法的目标变量为非静力倾向在相邻两个时刻的向前差, 挑选的最优输入特征分别为上一时步的非静力倾向, 以及当前时步静力框架的位势高度、 气压的不同差分形式和位温. 基于以上特征构建的非静力求解方案能够有效模拟出非静力倾向项的时空分布特征. 将该方案耦合至WRF模式静力框架后, 模式积分稳定, 实现了对非静力过程的一个月长期稳定模拟. 针对不同分辨率试验, 该方案从系统偏差、 距平均方根误差以及斜压波空间模态误差三个方面均能够有效降低模式的非静力误差, 证明了该方案在不同分辨率下的可行性和优越性.

Electronic Supplementary Material to

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