Stochastic Parametrization using Compressed Sensing: Application to the Lorenz-96 Atmospheric Model

Growing set of optimization and regression techniques, based upon sparse representations of signals, to build models from data sets has received widespread attention recently with the advent of compressed sensing. In this paper, sparse approximations in high-dimensional spaces are used to build models (vector fields) to emulate the behavior of the fine-scale process, so that explicit simulations become an online benchmark for parameterization. Observations are assimilated during the integration of low-dimensional built model to provide predictions. We outline how the parameterization schemes developed here and the low-dimensional filtering algorithm can be applied to the Lorenz-96 atmospheric model that mimics mid-latitude atmospheric dynamics with microscopic convective processes.