Parameter estimation in the stochastic superparameterization of two-layer quasigeostrophic flows
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Parameter estimation in the stochastic superparameterization of two-layer quasigeostrophic flows Estimation of subgrid-scale modeling parameters in the stochastic superparameterization of two-layer quasigeostrophic turbulence Yoonsang Lee * Correspondence:
[email protected] Mathematics Department, Dartmouth College, 27 N Main St, Hanover, NH 03755, USA The author is supported by NSF DMS-1912999 and the Burke award at Dartmouth College
Abstract Geophysical turbulence has a wide range of spatiotemporal scales that requires a multiscale prediction model for efficient and fast simulations. Stochastic parameterization is a class of multiscale methods that approximates the large-scale behaviors of the turbulent system without relying on scale separation. In the stochastic parameterization of unresolved subgrid-scale dynamics, there are several modeling parameters to be determined by tuning or fitting to data. We propose a strategy to estimate the modeling parameters in the stochastic parameterization of geostrophic turbulent systems. The main idea of the proposed approach is to generate data in a spatiotemporally local domain and use physical/statistical information to estimate the modeling parameters. In particular, we focus on the estimation of modeling parameters in the stochastic superparameterization, a variant of the stochastic parameterization framework, for an idealized model of synoptic scale turbulence in the atmosphere and oceans. The test regimes considered in this study include strong and moderate turbulence with complicated patterns of waves, jets, and vortices. Keywords: Stochastic parameterization, Multiscale, Parameter estimation, Quasigeostrophic turbulence Mathematics Subject Classification: 65C20, 76F55, 86-08
1 Introduction Geophysical fluid systems involve a tremendously wide range of spatiotemporal scales. In the atmosphere and oceans, the spatial scale varies from millimeters to tens of thousands of kilometers, while the timescale varies from seconds to hundreds of years [33,36]. In the numerical simulation of such systems, it is essential to develop a multiscale prediction model that is tractable by the current (or the near future) generation computing powers. A
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challenge in multiscale modeling is that the unique and relevant properties of such systems are characterized by a complex interplay of different scale dynamics. Quasigeostrophic turbulence includes regimes where there is a kinetic energy transfer from small to large scales, an inverse cascade of energy [5,7], and the small (or unresolved subgrid) scale affects and is affected by the large (or resolved coarse) scale. Therefore, it is crucial to represent the effect of unresolved small scale, either analytically or numerically, to close the large-scale dynamics, which is called subgrid-scale parameterization in geophysical fluid systems. There are several classes of subgrid-scale parameterization strategies fo
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