Extending the square root method to account for additive forecast noise in ensemble methods

TL;DR

This paper extends the square root method for ensemble Kalman filters to deterministically account for forecast noise, reducing sampling errors and improving performance in low-order dynamical systems.

Contribution

It introduces a deterministic transform approach for model noise in EnKF, enhancing dynamical consistency and addressing ensemble subspace limitations.

Findings

Improved accuracy over traditional additive noise methods

Reduced sampling errors in ensemble forecasts

Enhanced performance in twin experiments with simple dynamics

Abstract

A square root approach is considered for the problem of accounting for model noise in the forecast step of the ensemble Kalman filter (EnKF) and related algorithms. The primary aim is to replace the method of simulated, pseudo-random, additive noise so as to eliminate the associated sampling errors. The core method is based on the analysis step of ensemble square root filters, and consists in the deterministic computation of a transform matrix. The theoretical advantages regarding dynamical consistency are surveyed, applying equally well to the square root method in the analysis step. A fundamental problem due to the limited size of the ensemble subspace is discussed, and novel solutions that complement the core method are suggested and studied. Benchmarks from twin experiments with simple, low-order dynamics indicate improved performance over standard approaches such as additive, simulated noise and multiplicative inflation.