  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. This paper
deals with the parameterization of the Lorenz-96 model with two time-scales
that mimics mid-latitude atmospheric dynamics with microscopic convective
processes. Compressed sensing is 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. We apply compressed sensing,
where the sparse recovery is achieved by constructing a sensing/dictionary
matrix from ergodic samples generated by the Lorenz-96 atmospheric model, to
parameterize the unresolved variables in terms of resolved variables.
Stochastic parameterization is achieved by auto-regressive modelling of noise.
We utilize the ensemble Kalman filter for data assimilation, where observations
(direct measurements) are assimilated in the low-dimensional stochastic
parameterized model to provide predictions. Finally, we compare the predictions
of compressed sensing and Wilk's polynomial regression to demonstrate the
potential effectiveness of the proposed methodology.
