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

TL;DR

This paper introduces a novel stochastic parameterization method for the Lorenz-96 atmospheric model using compressed sensing to efficiently emulate unresolved processes, enhancing data assimilation and model accuracy.

Contribution

It applies compressed sensing for sparse model recovery in atmospheric dynamics, combining it with stochastic auto-regressive noise modeling and data assimilation techniques.

Findings

Compressed sensing effectively models unresolved variables.

Auto-regressive noise improves stochastic parameterization.

Method outperforms polynomial regression in predictions.

Abstract

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.