A Stochastic Parametrization of Ocean Mesoscale Eddies

The ocean contains a vigorous mesoscale eddy field which evolves over time scales from weeks to months and is important in establishing the ocean's circulation and tracer properties. Mesoscale eddies have spatial scales of approximately 10 to 100km and are therefore a subgrid scale process in current climate models such that their effect needs to be parametrized. Current parametrizations of mesoscale eddies are bulk parametrizations which are not derived from first principles. The parametrizations for example do not account for the fluctuations in subgrid transports or do not represent upscale turbulent cascades therefore leading to model error in the representation of present and future climate change. The goal of our study is to construct a stochastic parameterization of ocean mesoscale eddies in order to account for such effects and to account for model error associated with the uncertainty in the parameters. The parametrization is constructed by using first principles and the output of a high resolution model to derive statistics of the eddy source term as function of the resolved scales. The parametrization is first derived in a quasi-geostrophic model in a double-gyre configuration to provide a tractable framework. Probability density functions of the eddy source term conditional on the intrinsic resolved large scale dynamics are calculated from the model and therefore capture the key fluctuations associated with mesoscale eddies and their impact on the mean flow. The conditional probability density functions are then implementated as the basis for a new parametrization of mesoscale eddies in a coarse resolution model. The results of the implementation of the stochastic parametrization are shown to dramatically improve the representation of the mean flow, its variability at most frequencies and the kinetic energy power spectrum as function of wavelength. Some preliminary results of the model in forecast mode and quantification of model error will be discussed.