High-resolution data assimilation through stochastic subgrid tensor and parameter estimation from 4DEnVar

In this paper, we explore a dynamical formulation allowing to assimilate high-resolution data in a large-scale fluid flow model. This large-scale formulation relies on a random modelling of the small-scale velocity component and allows to take into account the scale discrepancy between the dynamics and the observations. It introduces a subgrid stress tensor that naturally emerges from a modified Reynolds transport theorem adapted to this stochastic representation of the flow. This principle is used within a stochastic shallow water model coupled with an 4DEnVar assimilation technique to estimate both the flow initial conditions and the inhomogeneous time-varying subgrid parameters. The performance of this modelling has been assessed numerically with both synthetic and real-world data. Our strategy has shown to be very effective in providing a more relevant prior/posterior ensemble in terms of the dispersion compared to other tests using the standard shallow water equations with no subgrid parameterization or with simple eddy viscosity models. We also compared two localization techniques. The results indicate the localized covariance approach is more suitable to deal with the scale discrepancy-related errors.