Modeling studies of ocean circulation using inverse methods and bifurcation theory

We present a study of the ocean circulation using state of the art numerical and data assimilation techniques. The second chapter of the thesis presents the development and application of generalized inversion to a simple dynamical model of Lake Kinneret. The intent was to develop the necessary tools to implement variational assimilation scheme in the realm of a simple model and data set. We were able to determine the spatially nonuniform wind pattern and distinguish it clearly from the effect of assuming a spatially uniform wind. We present statistical evidence for our finding that the two layer model contained sufficient detail to describe the physics of internal waves and residual circulation embedded in the data. We were also able to determine the time and location of an outcropping event that resulted in a fish kill event. The third chapter presents an in depth study of the multiple steady states of the Kuroshio south of Japan using a limited area 2 layer quasigeostrophic model. This study enabled us to understand the possible nature of the transitions and the dynamical nature of the steady states. The last chapter is a refinement of the understanding of the Kuroshio using the assimilation of satellite data to explain the recent transition from a non-large meander to a large meander and its opposite. The assimilation procedure can be seen as the test of a null hypothesis consisting of a prior estimate of the model and data discrepancy. The result of the assimilation gives us posterior statistics that permit us to draw error bars on the model dynamics. From these posterior statistics, we can determine if the model contains sufficient dynamics to explain physics present in the altimetry data.