Stochastic models for unresolved scales in ocean flows

The large-scale ocean circulation is strongly influenced by mesoscale turbulent eddies. Mesoscale ocean eddies exist on spatial scales in an approximate range of 10-100 km. Therefore, global climate models need grid resolutions smaller than 10 km in their ocean component in order to directly resolve these turbulent motions. Due to computational limitations, such high resolution is still infeasible in current climate models, and the effects of turbulent eddies must be parameterized. In this thesis we propose novel stochastic methodologies for eddy parameterization. A key assumption for the developed methodologies is the availability of reference data, albeit in small amounts relative to the problem dimensionality. This reference data can come from such places as real-life observations or highly resolving, but restricted, simulations. This enables us to propose data-driven stochastic parameterizations that are informed by empirical references in addition to physical insight. We use the stochastic parameterizations to drive reduced models that, otherwise, would omit most mesoscale features. We show that these stochastic models accurately reproduce both the key statistical and physical criteria of the references. Additionally, this thesis presents solutions to define our methodologies in a memory-efficient way for global ocean model applications.