Neural variational Data Assimilation with Uncertainty Quantification using SPDE priors
Résumé
Such a strategy turns out to be very efficient to improve the mean state estimation, but still needs complementary developments to quantify its related uncertainty. In this work, we use the theory of Stochastic Partial Differential Equations (SPDE) and Gaussian Processes (GP) to estimate both space-and time-varying covariance of the state. Our neural variational scheme is modified to embed an augmented state formulation with both state and SPDE parametrization to estimate. We demonstrate the potential of the proposed framework on a spatio-temporal GP driven by diffusionbased anisotropies and on realistic Sea Surface Height (SSH) datasets. We show how our solution reaches the OI baseline in the Gaussian case. For nonlinear dynamics, as almost always stated in DA, our solution outperforms OI, while allowing for fast and interpretable online parameter estimation
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