Subgrid-scale Parametrization of Unresolved Processes



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Subgrid-scale parametrizations aim to take into account effects of processes that occur and evolve on scales below the model grid size. It is one of essential research areas in atmosphere, ocean and climate science. In this study, we derive stochastic parametrization schemes that approximate and incorporate the effects of unresolved processes in a reduced equation for local averages in flux difference discretization of partial differential equations. Our aim is to develop a reduced model which reproduces stationary statistics of the full model. In the first part, we develop a parametrization using generative adversarial networks (GAN) to sample subgrid fluxes the effective equation for local averages in in two spatially discretized systems - in forced Burgers' equation and in forced one-dimensional shallow water equations. We demonstrate that stationary statistics of the full model are emulated quite well by the reduced model. Some experiments on short-term prediction and sensitivity to changes in forcing and scale are also done. In the second part, we derive subgrid fluxes using stochastic mode reduction to obtain a reduced equation for the resolved variables (local spatial averages) in finite-volume discretization of inviscid Burgers equation. The reduced model improves the truncated model and gives accurate estimate of some stationary statistics of the full model.



stochastic parametrization, subgrid-scale parametrization, generative adversarial networks, Burgers' equation, shallow water equations


Portions of this document appear in: Alcala, J., Timofeyev, I. Subgrid-scale parametrization of unresolved scales in forced Burgers equation using generative adversarial networks (GAN). Theor. Comput. Fluid Dyn. (2021).