  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.
