Open Access

Martin Pieroth

• State-of-the-art climate models contain, to a significant degree, empirical components. In particular, subgrid-scale (SGS) parameterizations are usually highly tuned against observations or high-resolution model data. While this enables the models to minimize the error during hindcasts, it is not guaranteed that it yields a benefit for climate projections because of climate change. In this thesis the Fluctuation-Dissipation theorem (FDT) is used to update the statistics of the system in the presence of an external forcing. If the empirical parameters are tuned objectively to the data (i.e., they depend on the statistics of the data), then they might be updated with the FDT. This ansatz is tested within a framework of a semi-empirical model (SEM) based on the leading variance patterns of a quasigeostrophic three-layer model (QG3LM) and supplemented by a purely data-driven parameterization. We show that the FDT is able to successfully update the tuning parameters of the data-driven SGS closure, resulting in a systematic improvement in model performance in comparison to an untreated SEM. Ideally, SGS parameterizations should contain little to no tuning parameters. Thus, complementary to the FDT approach we investigate a stochastic SGS closure constrained by first principles that is calculated using the stochastic mode reduction (SMR). The SMR allows for an analytic derivation of the SGS closure from the model equations while requiring only minimal tuning. We successfully apply the SMR to the QG3LM and construct the reduced stochastic model (RSM). Furthermore, we show that the RSM is more robust against an external forcing than the SEM. Additionally, we find that, under appropriate conditions, the FDT is able to update the empirical parts of the RSM. Yet, only for the response in mean streamfunction the RSM provides useful results, while the response in covariance of the streamfunction is incorrect for most cases. Nevertheless, we obtain a remarkably accurate response in both moments for the RSM in an idealized setting. In combination with the results of the FDT study this indicates that the considered RSM is too low dimensional and encourages us to investigate the response of larger RSMs in the future.