Superparmeterization in Ocean Modeling Using General Multiscale Techniques: A Deep- Convection Case Study Employing ESMF.

Multiscale approaches allow explicit modeling of the many different phenomena that are present in real ocean dynamics. In this work we use multiscale-superparameterization approach to efficiently model oceanic deep- convection. We present results and methodology for a multiscale simulation in which several hundred high-resolution, two-dimensional, non-hydrostatic process models are coupled, as separate ESMF components, to a large-scale hydrostatic ocean model. One process model is embedded in each grid cell of the large-scale three-dimensional hydrostatic model. The process models take the place of conventional one-dimension empirical parameterizations, producing a simulation more accurately grounded in underlying physical equations. The individual MITgcm process models, and the hydrostatic MITgcm model into which they are embedded, are implemented as ESMF components. The ESMF library is used to orchestrate data flows between components and to steer the overall computation, including spreading the workload over multiple parallel processors. We measure the impact of our approach, in terms of both improved numerical accuracy and computational cost, by comparing quantitative metrics with respect to a fully resolved, three-dimensional, non-hydrostatic "ground- truth" simulation. In comparison with a purely hydrostatic numerical experiment, the time evolving state and statistics of the multiscale system are found to be significantly closer to the ground-truth model solution. For example, in the embedded simulation, the slanting of convective plumes due to large scale flow vertical shear is reproduced and higher order statistics, such as the variance and skewness of the model fields, are all much closer to the ground-truth model solution. The improved accuracy of the multi-scale model is achieved for a computational cost far less than that of a fully resolved non-hydrostatic model. By exploiting parallelism amongst the embedded models, we can achieve a wall-clock time to solution that is a small multiple of a pure hydrostatic simulation. The approach we have taken is by no means limited to parameterization of deep convection and can be generalized fairly broadly. For example mixed-layer processes, biogeochemical processes, eddy flux coefficients could all be estimated by appropriate local, prognostic sub-models that are then coupled to a larger scale model, provided the factors and analysis we described are appropriately considered.