A square root approach to incorporating model error in ensemble methods

Model error, despite its varied sources, is typically written as a stochastic noise term for the purposes of data assimilation (DA). Accounting for model error improves uncertainty quantification and is essential in sequential DA in order to prevent filter divergence. The two most common techniques for dealing with model error are multiplicative inflation and additive noise. In the context of ensemble methods, we propose a novel approach based on the square root methodology developed for the EnKF analysis step, which we duplicate into the forecast step. The technique boils down to a right-multiplication by a "transform matrix", and is a particularly benign update mechanism thanks to its linearity. Further advantages include covariance structure preservation, modularity, and a minimal ensemble disarrangement (optimal transport) quality. Benchmarks from twin experiments with simple, prototype, nonlinear dynamics indicate improved performance over additive and multiplicative techniques.