Towards subgrid-scale parameterizations constrained by first principles and with climate dependence - Stamen Dolaptchiev

Abstract

Joint work with Ulrich Achatz, Ilya Timofeyev, Ulrike Löbl and Adrey Gritsun

Abstract: Efficient modeling of the atmospheric dynamics often requires the development of subgrid-scale (SGS) parameterizations. The reliability of any SGS parameterization increases if the parameterization is based on first principles as much as possible. In the first part of the talk a method is presented for deriving effective stochastic models for the time-evolution of spatial averages (resolved variables) in finite-difference discretizations of the governing equations using a stochastic mode reduction technique. This method relies on i) the existence of a time-scale separation in the dynamics of the resolved and SGS variables and ii) the assumption that the fast SGS self-interactions can be modeled by an empirical Ornstein-Uhlenbeck process. A conservative discretization of the Burgers equation is used as particular example to illustrate the approach.

In the second part of the talk we discuss how a climate dependence can be introduced in the SGS parameterization. Empirical parameters are inevitable in nearly every SGS parameterization and often they are objectively tuned using the statistics of an unperturbed climate.
However, they might be not valid if the climate changes. The fluctuation-dissipation-theorem predicts the change in the statistics of the perturbed climate and thus allows to correct the empirical parameters. This approach is applied within the framework of a low-order quasi-geostrophic barotropic model on the sphere with an empirical linear closure