The impact of ensemble filter definition on the assimilation of temperature profiles in the tropical Pacific

The traditional analysis scheme in the Ensemble Kalman Filter (EnKF)
uses a stochastic perturbation or randomization of the measurements
which ensures a correct variance in the updated ensemble. An
alternative so-called deterministic analysis algorithm is based on a
square-root formulation where the perturbation of measurements is
avoided. Experiments with simple models have indicated that ensemble
collapse is likely to occur when deterministic filters are applied to
nonlinear problems. In this paper the properties of stochastic and
deterministic ensemble analysis algorithms are evaluated in an
identical-twin experiment using an ocean general-circulation model.
In particular, the implications of the use of deterministic Ensemble
Square-Root Filters (EnSRF) for ensemble spread are investigated. An
explanation is presented for the observed collapse, and a simple
solution based on randomization of the analysis ensemble anomalies is
examined. A one-year assimilation run with this improved EnSRF is found
to produce Gaussian distributions, similar to the EnKF.