  We propose a method to account for model error due to unresolved scales in
the context of the ensemble transform Kalman filter (ETKF). The approach
extends to this class of algorithms the deterministic model error formulation
recently explored for variational schemes and extended Kalman filter. The model
error statistic required in the analysis update is estimated using historical
reanalysis increments and a suitable model error evolution law. Two different
versions of the method are described; a time-constant model error treatment
where the same model error statistical description is time-invariant, and a
time-varying treatment where the assumed model error statistics is randomly
sampled at each analysis step. We compare both methods with the standard method
of dealing with model error through inflation and localization, and illustrate
our results with numerical simulations on a low order nonlinear system
exhibiting chaotic dynamics. The results show that the filter skill is
significantly improved through the proposed model error treatments, and that
both methods require far less parameter tuning than the standard approach.
Furthermore, the proposed approach is simple to implement within a pre-existing
ensemble based scheme. The general implications for the use of the proposed
approach in the framework of square-root filters such as the ETKF are also
discussed.
