Multiplicative non-Gaussian model error estimation in data assimilation

TL;DR

This paper introduces a novel method for estimating non-Gaussian model errors in data assimilation using partial observations, improving error characterization and forecast accuracy in complex systems.

Contribution

It presents a new approach for estimating sub-grid scale process errors with partial data, capturing complex non-Gaussian error structures for better data assimilation.

Findings

Error estimates outperform existing methods.

Improved forecast accuracy demonstrated in Lorenz 96 system.

Effective for systems with different time scale separations.

Abstract

Model uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub-grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many existing Stochastic Parameterization schemes are only applicable when knowledge of the true sub-grid scale process or full observations of the coarse scale process are available, which is typically not the case in real applications. We present a methodology for estimating the statistics of sub-grid scale processes for the more realistic case that only partial observations of the coarse scale process are available. Model error realizations are estimated over a training period by minimizing their conditional sum of squared deviations given some informative covariates (e.g. state of the system), constrained by available observations and assuming that the observation errors are smaller than the model errors. From these realizations a conditional probability distribution of additive model errors given these covariates is obtained, allowing for complex non-Gaussian error structures. Random draws from this density are then used in actual ensemble data assimilation experiments. We demonstrate the efficacy of the approach through numerical experiments with the multi-scale Lorenz 96 system using both small and large time scale separations between slow (coarse scale) and fast (fine scale) variables. The resulting error estimates and forecasts obtained with this new method are superior to those from two existing methods.