A framework for variational data assimilation with superparameterization

Superparameterization (SP) is a multiscale computational approach wherein a large scale atmosphere or ocean model is coupled to an array of simulations of small scale dynamics on periodic domains embedded into the computational grid of the large scale model. SP has been successfully developed in global atmosphere and climate models, and is a promising approach for new applications, but there is currently no practical data assimilation framework that can be used with these models. The authors develop a 3D-Var variational data assimilation framework for use with SP; the relatively low cost and simplicity of 3D-Var in comparison with ensemble approaches makes it a natural fit for relatively expensive multiscale SP models. To demonstrate the assimilation framework in a simple model, the authors develop a new system of ordinary differential equations similar to the two-scale Lorenz-'96 model. The system has one set of variables denoted (Y-i), with large and small scale parts, and the SP approximation to the system is straightforward. With the new assimilation framework the SP model approximates the large scale dynamics of the true system accurately.