Section: New Results

Objective 3 – Non-parametric inference

The forecasting and reconstruction of ocean and atmosphere dynamics from satellite observation time series are key challenges. While model-driven representations remain the classic approaches, data-driven representations become more and more appealing to benefit from available large-scale observation and simulation datasets. In [12],  [13] and [4], we investigate the relevance of recently introduced neural network representations for the forecasting and assimilation of geophysical fields from satellite-derived remote sensing data. As a case-study, we consider satellite-derived Sea Surface Temperature time series off South Africa, which involves intense and complex upper ocean dynamics. Our numerical experiments report significant improvements in terms of reconstruction performance compared with operational and state-of-the-art schemes.

Data assimilation methods aim at estimating the state of a system by combining observations with a physical model. When sequential data assimilation is considered, the joint distribution of the latent state and the observations is described mathematically using a state-space model, and filtering or smoothing algorithms are used to approximate the conditional distribution of the state given the observations. The most popular algorithms in the data assimilation community are based on the Ensemble Kalman Filter and Smoother (EnKF/EnKS) and its extensions. In [14], we investigate an alternative approach where a Conditional Particle Filter (CPF) is combined with Backward Simulation (BS). This allows to explore efficiently the latent space and simulate quickly relevant trajectories of the state conditionally to the observations. We also tackle the difficult problem of parameter estimation. Indeed, the models generally involve statistical parameters in the physical models and/or in the stochastic models for the errors. These parameters strongly impact the results of the data assimilation algorithm and there is a need for an efficient method to estimate them. Expectation-Maximization (EM) is the most classical algorithm in the statistical literature to estimate the parameters in models with latent variables. It consists in updating sequentially the parameters by maximizing a likelihood function where the state is approximated using a smoothing algorithm. In this paper, we propose an original Stochastic Expectation-Maximization (SEM) algorithm combined to the CPF-BS smoother to estimate the statistical parameters. We show on several toy models that this algorithm provides, with reasonable computational cost, accurate estimations of the statistical parameters and the state in highly nonlinear state-space models, where the application of EM algorithms using EnKS is limited. We also provide a Python source code of the algorithm.