Abstract
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.
Highlights
The numerical simulation of all the scales of geophysical fluid flows, up to the smallest dissipation scales, remains nowadays completely intractable due to the dimension of the problem to handle
We focus on the specification through highresolution image data assimilation of the dynamics model uncertainties
In order to evaluate the robustness of the proposed scheme and the effectiveness of the stochastic model, we carried out one test with the model under uncertainty and two tests on the “standard-model” in which no subgrid parameterization is introduced and the ensemble is generated by perturbing the initial condition state with the uncertainties computed a few time steps after the starting of the experiment
Summary
The numerical simulation of all the scales of geophysical fluid flows, up to the smallest dissipation scales, remains nowadays completely intractable due to the dimension of the problem to handle (which scales as the cube of the Reynolds number). The simplest method consists in introducing random forcing terms into the flow dynamics equations Another way of considering the stochastic nature of the neglected scales is to study directly the governing differential equations driven by stochastic processes. Recent studies show that the quality of the ensemble spread can be significantly improved by perturbing the initial condition and some parameters related to the dynamics (Wei et al, 2013; Yang et al, 2015) Those facts advocate the setup of physically relevant stochastic dynamical models coupling the random production terms and the dissipation term. Results and discussions with some concluding remarks are provided
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