A Stochastic Approach to Representing Unresolved Mesoscales in Ocean Circulation Models

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Ocean models are indispensable tools for understanding, estimating, and predicting ocean dynamics. A key challenge in the construction of accurate ocean models is the fact that computational resources preclude direct resolution of all physical scales; depending on their intended use, the next generation of global ocean models will have horizontal spatial resolutions from 1 degree to 1/10 degree. Models at the coarser end of this range, which support longer-term ensemble forecasting (e.g. climate prediction) and reanalysis applications, are unable to represent the scale of the most energetic dynamics, the mesoscale, over large regions of the globe. Mesoscale eddies (on order 100 km) play a leading role in the transport of heat and biogeochemical tracers, and the parameterization of their effects in global ocean models has a long history. High-resolution models support shorter-term forecasting and studies of ocean dynamical processes, but they are too expensive for long-term or large-ensemble applications. An emerging paradigm in modeling the effects of unresolved scales in ocean (and atmosphere) models is based on the observation that unresolved small-scale dynamics interact with resolvable dynamics in a non-deterministic way; the net tracer transports associated with these unresolved scales are stochastic, and require stochastic models. The construction of accurate, stochastic models of real physical fields is a young field of research, as is the field of stochastic parameterization into computational ocean models. This project will significantly extend both these fields by bringing to bear sophisticated statistical models and systematic Bayesian optimization to ocean modeling. The project will also provide training for a post-doctoral fellow at the intersection of physical oceanography and applied mathematics. It will strengthen collaborations between university-based researchers and scientists at the National Center for Atmospheric Research (NCAR) through the Community Earth System Model (CESM) Ocean Model Working Group (OMWG). A stochastic model of the global mesoscale eddy field will be developed. A stochastic parameterization of mesoscale eddies will be implemented and tested in the 1-degree version of the ocean component of the CESM version 3.This project aims to develop a framework for stochastic parameterization of tracer transports in the coarse- resolution ocean model setting used for long-term or large ensemble applications. Unlike other approaches that model the transport directly, the stochastic approach models the eddy velocity and tracer anomaly fields directly, and uses them to construct realistic tracer fluxes. This idea has recently begun to be developed in the context of eddy-permitting ocean models to model 'backscatter' that energizes the partially resolved mesoscale eddies, but only in the past year or two has it begun to be developed in the coarse-model case, which is significantly different than the eddy-permitting case. It is particularly important to develop realistic stochastic parameterizations for coarse models though, because the ensemble-simulation scenarios for which these coarse models are increasingly used require realistic patterns of eddy-driven large-scale variability. The uncertainty associated with mesoscale eddy transports absolutely must be included in the models via realistic stochastic parameterizations for the conclusions of these studies to be accurate. A benefit of this approach is that the eddy fields are easier to model and observe than the transport; the approach also results in realistic non-Gaussian tracer flux distributions. The approach works within the Gent-McWilliams (GM) framework and results in a stochastic parameterization of the eddy bolus velocity. The project has two main components: (i) the development of a stochastic model of the eddy field, and (ii) the implementation, thorough testing, and validation of the associated stochastic parameterization in an IPCC-class global climate model. Both components will involve close collaboration with scientists in the Community Earth System Model (CESM) Ocean Model Working Group (OMWG) at NCAR.