Today’s weather forecast and climate projection are based on Numerical Weather Prediction (NWP) models and General Circulation Models (GCM). Due to the ubiquitous turbulence in atmospheric boundary layer and convection, directly resolving all the dynamic scales is prohibiting with current computational capacity. Thus, NWP models and GCMs run on a relatively low-resolution grid and represent sub-grid scale (SGS) effects on the resolved scales with parameterization schemes. Traditional turbulence parameterization schemes are commonly built on heuristic assumptions and tuned without coupling with the resolved-scale physics and other SGS physical parameterizations, so in some weather and climate regimes at least, they exhibit considerable uncertainties and low fidelity. With the development...[ Read more ]

Today’s weather forecast and climate projection are based on Numerical Weather Prediction (NWP) models and General Circulation Models (GCM). Due to the ubiquitous turbulence in atmospheric boundary layer and convection, directly resolving all the dynamic scales is prohibiting with current computational capacity. Thus, NWP models and GCMs run on a relatively low-resolution grid and represent sub-grid scale (SGS) effects on the resolved scales with parameterization schemes. Traditional turbulence parameterization schemes are commonly built on heuristic assumptions and tuned without coupling with the resolved-scale physics and other SGS physical parameterizations, so in some weather and climate regimes at least, they exhibit considerable uncertainties and low fidelity. With the development of machine learning techniques, the feasibility of data-driven parameterizations has been investigated in a lot of recent studies. Taking the evolution of Kelvin-Helmholtz instability in the barotropic vorticity equation (BVE) as a prototype problem, here we first perform supervised a priori training on classic deep learning models such as multi-layer perceptron (MLP) and convolutional neural network (CNN). The input data for the machine learning models are coarse-grained physical variables, the training targets are computed in advance and the training procedure is free from the feedback of the numerical solver, therefore this style of training is named a priori training. We evaluate the influence of training features and loss functions on the training procedure and offline performance. A novel deep generative model called conditional variational autoencoder (CVAE) is also applied for training a parameterization scheme and it outperforms the classical models in terms of validation and offline accuracy. Although they present accurate offline predictions, these a priori trained models perform poorly in the online test, in which the machine learning models are coupled with the numerical solver of the BVE. Beyond the a priori training approach, we also study a model consistent training strategy, which employs a numerical solver with automatic differentiation included in the loss function and enables the interaction between the solver and deep learning model during the training phase. The simulation performance is improved significantly with this new training strategy, revealing a promising strategy of for developing new atmospheric models with differentiable numerical solvers and deep-learning-based physical parameterizations.