Learning model parameters from observations by combining data assimilation and machine learning

Parametrization of microphysics as well as parametrization of processes in the surface and boundary layers typically contain several tunable parameters. The parameters are not observed and are only crudely known. Traditionally, the numerical values of these model parameters are chosen by manual model tuning, leading to model errors in convection permitting numerical weather prediction models. More objectively, parameters can be estimated from observations by the augmented state approach during the data assimilation or by combing data assimilation with machine learning (ML).

If the parameters are updated objectively according to observations, they are flexible to adjust to recent conditions, their uncertainty is considered, and therefore the uncertainty of the model output is more accurate. To illustrate benefits of online augmented state approach, Ruckstuhl and Janjic (2020) show in an operational convection-permitting configuration that the prediction of clouds and precipitation is improved if the two-dimensional roughness length parameter is estimated. This could lead to improved forecasts of up to 6 h of clouds and precipitation. However, when parameters are estimated by the augmented state approach, stochastic model for the parameters needs to be pre-specified to keep the spread in parameters. Alternatively, Legler and Janjic (2022) investigate a possibility of using data assimilation for the state estimation while using ML for parameter estimation in order to overcome this problem. We train two types of artificial neural networks as a function of the observations or analysis of the atmospheric state.  The test case uses perfect model experiments with the one-dimensional modified shallow-water model, which was designed to mimic important properties of convection. Through perfect model experiments we show that Bayesian neural networks (BNNs) and ensemble of point estimate neural networks (NNs) are able to estimate model parameters and their relevant statistics. The estimation of parameters combined with data assimilation for the state decreases the initial state errors even when assimilating sparse and noisy observations.