  This chapter describes a novel approach for the treatment of model error in
geophysical data assimilation. In this method, model error is treated as a
deterministic process fully correlated in time. This allows for the derivation
of the evolution equations for the relevant moments of the model error
statistics required in data assimilation procedures, along with an
approximation suitable for application to large numerical models typical of
environmental science. In this contribution we first derive the equations for
the model error dynamics in the general case, and then for the particular
situation of parametric error. We show how this deterministic description of
the model error can be incorporated in sequential and variational data
assimilation procedures. A numerical comparison with standard methods is given
using low-order dynamical systems, prototypes of atmospheric circulation, and a
realistic soil model. The deterministic approach proves to be very competitive
with only minor additional computational cost. Most importantly, it offers a
new way to address the problem of accounting for model error in data
assimilation that can easily be implemented in systems of increasing complexity
and in the context of modern ensemble-based procedures.
