UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Parametrization and multiple time scale problems with non-Gaussian statistics related to climate dynamics Thompson, William F.


Many problems in climate modelling are characterized by their chaotic nature and multiple time scales. Stochastic parametrization methods can often simplify the analysis of such problems by using appropriate stochastic processes to account for degrees of freedom that are impractical to model explicitly, such that the statistical features of the reduced stochastic model are consistent with more complicated models and/or observational data. However, applying appropriate stochastic parametrizations is generally a non-trivial task. This is especially true when the statistics of the approximated processes exhibit non-Gaussian features, like a non-zero skewness or infinite variance. Such features are common in problems with nonlinear dynamics, anomalous diffusion processes, and multiple time scales. Two common topics in stochastic parameterization are model parameter estimation and the derivation of reduced stochastic models. In this dissertation, we study both of these topics in the context of stochastic differential equation models, which are the preferred formalism for continuous-time modelling problems. The motivation for this analysis is given by problems in atmospheric or climate modelling. In Chapter 2, we estimate parameters of a dynamical model of sea surface vector winds using a method based on the properties of differential operators associated with the probabilistic evolution of the wind model. The parameter fields we obtain allow us to reproduce statistics of the vector wind data and inform us regarding the limitations of both the estimation method and the model itself. In Chapter 3, we derive reduced stochastic models for a class of dynamical models with multiple time scales that are driven by α-stable stochastic forcing. The results of Chapter 3 are applied in Chapter 4, where we derive a similar approximation for processes that are driven by a fast linear process experiencing additive and multiplicative Gaussian white noise forcing. The results of these chapters complement previous results for systems driven by Gaussian white noise and suggest a possible dynamical mechanism for the appearance of α-stable stochastic forcing in some climatic time series.

Item Citations and Data


Attribution-NonCommercial-NoDerivs 2.5 Canada