Climate Dependence in Empirical Parameters of Subgrid-Scale Parameterizations using the Fluctuation–Dissipation Theorem

Abstract

Abstract Many subgrid-scale (SGS) parameterizations in climate models contain empirical parameters and are thus data dependent. In particular, it is not guaranteed that the SGS parameterization still helps the model to produce the correct climate projection in the presence of an external perturbation (e.g., because of climate change). Therefore, a climate dependence of tuning parameters is proposed, using the fluctuation–dissipation theorem (FDT). The FDT provides an estimation of the changes in the statistics of a system, caused by a small external forcing. These estimations are then used to update the SGS parameterization. This procedure is tested for a toy atmosphere given by a quasigeostrophic three-layer model (QG3LM). We construct a low-order climate model for this toy atmosphere, based on a reduced number of its empirical orthogonal functions (EOFs), equipped with either an empirical deterministic or an empirical stochastic SGS parameterization. External forcings are considered that are either a local anomalous heat source in the extratropics or a global dynamical forcing represented by individual EOF patterns. A quasi-Gaussian variant of the FDT is able to successfully update the SGS parameterization leading to an improvement in both amplitude and correlation between the low-order climate model and the QG3LM, in case of a perturbed system. The stochastic closure exhibits nearly no improvement compared to the deterministic parameterization. The application of a more sophisticated non-Gaussian FDT algorithm (i.e., the blended short-time/quasi-Gaussian FDT) yields only marginal improvement over the simple quasi-Gaussian FDT.