Deterministic treatment of model error in geophysical data assimilation

TL;DR

This paper introduces a deterministic approach to model error in geophysical data assimilation, deriving evolution equations for error moments and demonstrating its effectiveness and computational efficiency in various models.

Contribution

It presents a novel deterministic framework for modeling and incorporating model error into data assimilation, applicable to complex environmental models.

Findings

Deterministic error modeling is competitive with standard methods.

The approach is easily integrated into existing assimilation systems.

It performs well in low-order and realistic models.

Abstract

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.