Combining data assimilation and machine learning to estimate parameters of a convective‐scale model

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 148; no. 743; pp. 860 - 874
• Main Authors: Legler, S., Janjić, T.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.01.2022; Wiley Subscription Services, Inc
• Subjects: Artificial intelligence; Bayesian analysis; Bayesian neural network; Boundary conditions; Boundary layers; Convection; convective‐scale data assimilation; Data assimilation; Data collection; EnKF; Errors; layer‐wise relevance propagation; Machine learning; Mathematical models; Microphysics; Modelling; Neural networks; Numerical schemes; Orography; Parameter estimation; Parameters; Prediction models; Probability theory; Rainfall forecasting; Scale models; Statistical analysis; Statistical methods; Strong winds; Training; Weather forecasting; Winds
• DOI: 10.1002/qj.4235
• ISSN: 0035-9009

Errors in the representation of clouds in convection‐permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of the numerical schemes determining the evolution of humidity and temperature, but large contributions are due to the parametrization of microphysics and the parametrization of processes in the surface and boundary layers. These schemes typically contain several tunable parameters that are either not physical or only crudely known, leading to model errors. Traditionally, the numerical values of these model parameters are chosen by manual model tuning. More objectively, they can be estimated from observations by the augmented state approach during the data assimilation. Alternatively, in this work, we look at the problem of parameter estimation through an artificial intelligence lens by training two types of artificial neural network (ANN) to estimate several parameters of the one‐dimensional modified shallow‐water model as a function of the observations or analysis of the atmospheric state. Through perfect model experiments we show that Bayesian neural networks (BNNs) and Bayesian approximations 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. The sensitivity to the number of ensemble members, observation coverage and neural network size is shown. Additionally, we use the method of layer‐wise relevance propagation to gain insight into how the ANNs are learning and discover that they naturally select only a few grid points that are subject to strong winds and rain to make their predictions of chosen parameters. We train a Bayesian neural network (BNN) and an ensemble of point estimate neural networks (NN) to estimate several model parameters and their uncertainty as a function of the atmospheric state. Experiments with the one‐dimensional modified shallow‐water model show that the BNN and the NN are able to estimate the model parameters and their relevant statistics. In addition, once combined with data assimilation for the state estimation, the state errors decreased even when assimilating sparse and noisy observations.