Exploring a neural network-based background-error covariance model

Data assimilation of atmospheric observations traditionally relies on variational and Kalman filter methods. Several ideas of merging data assimilation with machine learning have emerged in recent years. One possibility would be to perform variational data assimilation in the latent space of an autoencoder (AE). In our approach, we define and minimise the three-dimensional variational (3D-Var) data assimilation cost function there to determine the analysis that optimally fuses simulated observations and the encoded 24-hour neural network forecast (background), accounting for their errors. Similar to several previous studies, the latent space has Gaussian properties, which are favourable for variational data assimilation, and the climatology-based background-error covariance (B) matrix measured and represented in the latent space turns out to be quasi-diagonal, which, together with the cost function manipulation, leads to a vast computation process speed-up.  

The main focus of this presentation is to study the physical feasibility of the analysis increments that we obtain using a multilevel multivariate AE and the U-net type neural network forward model (NNfwd) in this kind of framework. The analysis increments after observing geopotential in the midlatitudes give a multivariate geostrophic pattern, obey the thermal wind balance, and resemble some distinctive local features, such as orography and land-sea distribution. Also, the magnitude of the analysis increment at the observation location and its standard deviation closely match their theoretical values, and the impact of the observation reasonably fades with distance in both horizontal and vertical directions. On the other hand, assimilating increased moisture in the tropics leads to increments that align with the physics of the emerging tropical convective cloud systems despite the clouds and precipitation not being explicitly forecasted by the AE and NNfwd. Also, the increments after assimilating the observations in the tropics seem to distinguish between the local horizontal length scales. Finally, we study the plausibility of the model response after running the forecast with NNfwd using the analysis as the initial condition.