Dr Christian Franzke
FRANZKE: Systematic Strategies for Stochastic Climate Modeling The climate system has a wide range of temporal and spatial scales for important physical processes. Examples include convective activity with an hourly time scale, organized synoptic scale weather systems on a daily time scale, extra-tropical low-frequency variability on a time scale of 10 days to months, to decadal time scales of the coupled atmosphere-ocean system. An understanding of the processes acting on different spatial and temporal scales is important since all these processes interact with each other due to the nonlinearities in the governing equations. Most of the current problems in understanding and predicting the climate system stem from the multi-scale nature of the climate system in that all of the above processes interact with each other and the neglect and/or misrepresentation of some of the processes lead to systematic biases of the resolved processes and uncertainties in the climate response. A better understanding of the multi-scale nature of the climate system will be crucial in making more accurate and reliable weather and climate predictions. In my presentation I will discuss systematic strategies to derive stochastic models for climate prediction. The stochastic mode reduction strategy accounts systematically for the effect of the unresolved degrees of freedom and predicts the functional form of the effective reduced equations. These procedures extend beyond simple Langevin equations with additive noise by predicting nonlinear effective equations with both additive and multiplicative (state-dependent) noises. The stochastic mode reduction strategy predicts rigorously closed form stochastic models for the slow variables in the limit of infinite separation of time-scales.