Systematic Stochastic Modeling of Climate Variability

Christian Franzke
Courant Institute of Mathematical Sciences

The climate system has a wide range of time scales for important physical processes, ranging from organized synoptic scale weather systems on a daily scale, extra-tropical low-frequency variability on interannual time scales, to decadal scales of the coupled atmosphere-ocean system. An understanding of the different time scales is important since all these time scales interact with each other due to the nonlinearities in the governing equations. The spatial structure of extra-tropical variability can be described by a few teleconnection patterns. The two most prominent examples are the North Atlantic Oscillation (NAO) and the Pacific-North American (PNA) pattern. These teleconnection patterns explain a large amount of the total variability, have a strong impact on surface climate and are related to climate change.

In atmosphere-ocean science, these slowly evolving large-scale structures, and their statistical behavior, are often of the most interest, and yet the computational power of complex climate models is spent on resolving the smallest and fastest variables in the system. Stochastic modeling with the non-essential degrees of freedom represented stochastically provide computationally feasible alternatives for calculating the statistical behavior of the climatological relevant slow variables.

In my talk I will present successful applications of a systematic stochastic modeling approach to simple, yet realistic models of the atmosphere. The systematic stochastic mode reduction procedure eliminates the fast evolving processes, associated with e.g. synoptic scale weather systems, in a systematic way and predicts deterministic correction terms and both additive and multiplicative noises. This procedure extends beyond simple linear Langevin equations with additive noise by predicting nonlinear correction terms and both additive and multiplicative (state-dependent) noises. These correction terms and noises account for the neglected interactions between the resolved and unresolved modes and involve only minimal regression fitting of the unresolved degrees of freedom. The more slowly evolving processes, for example atmospheric teleconnection patterns like the NAO and PNA, are treated explicitly as prognostic equations. Such reduced models are much more computationally efficient for long climate simulations and ensemble forecasts and will lead to deeper understanding of the slow dynamics of the climate system.

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