Ergodic Theory of Smooth Dynamical Systems and Statistical Properties of Geophysical Flows in West Africa

This dissertation develops original results in the ergodic theory of smooth dynamical systems with applications to the statistical description of geophysical flows, with a specific application domain centred on the atmospheric dynamics and oceanic circulation patterns governing West African monsoon variability and the interannual rainfall variability of Nigeria and the broader West African Sahel. Ergodic theory provides the rigorous mathematical foundation for interpreting statistical observations of deterministic dynamical systems as time averages converging to spatial averages on invariant measures, and its application to geophysical flows offers a principled framework for climate statistics that transcends empirical data fitting. The dissertation proves novel decay of correlations results for a class of partially hyperbolic flows modelling the dynamics of the West African monsoon, using the transfer operator spectral theory approach of Baladi and extending existing results to the case of non-compact phase spaces appropriate to global atmospheric dynamics. Abstract statistical limit theorems, including the central limit theorem and invariance principle for observables of the geophysical flow, are established rigorously under the correlation decay assumptions, providing theoretical foundations for statistical climate analysis. New results on the existence and statistical properties of physical measures for flows with singularities modelling monsoon onset transitions are developed. Applications to the statistical analysis of interannual rainfall variability in the Sahel zone of North West Nigeria, using reanalysis data from the European Centre for Medium-Range Weather Forecasts, validate the theoretical framework. Keywords: ergodic theory, smooth dynamical systems, transfer operators, West African monsoon, statistical climate