Monotone conservative strategies in data assimilation

TL;DR

This paper explores how preserving monotonic properties in data assimilation can improve forecast accuracy, especially for systems governed by SPDEs or PDEs with monotone characteristics, by combining SSP time-stepping and nonlinear solving strategies.

Contribution

It demonstrates that monotone ensemble solutions in particle filters can enhance forecast skill and are compatible with advanced degeneracy avoidance techniques.

Findings

Monotone ensemble solutions improve forecast skill.

Compatibility of monotone methods with tempering-jittering.

Monotonic properties can be leveraged for better data assimilation.

Abstract

This paper studies whether numerically preserving monotonic properties can offer modelling advantages in data assimilation, particularly when the signal or data is a realization of a stochastic partial differential equation (SPDE) or partial differential equation (PDE) with a monotonic property. We investigate the combination of stochastic Strong Stability Preserving (SSP) time-stepping, nonlinear solving strategies and data assimilation. Experimental results indicate that a particle filter whose ensemble members are solved monotonically can increase forecast skill when the reference data (not necessarily observations) also has a monotone property. Additionally, more advanced techniques used to avoid the degeneracy of the filter (tempering-jittering) are shown to be compatible with a conservative monotone approach.