[p2] Model-related issues


Accounting for model error in strong constraint 4DVar

Katherine Howes (University of Reading), Alison Fowler (University of Reading) and Amos Lawless (University of Reading)


The strong constraint formulation of four-dimensional variational data assimilation (4DVar) assumes that the model used in the process perfectly describes the true dynamics of the system. However, this assumption often does not hold and the use of an erroneous model in strong constraint 4DVar can lead to a sub-optimal estimation of the initial conditions. We show how the presence of model error can be correctly accounted for in strong constraint 4D-Var by allowing for errors in both the observations and the model when considering the statistics of the innovation vector. We demonstrate that when these combined model error and observation error statistics are used in place of the standard observation error statistics in the strong constraint formulation of 4DVar, a statistically more accurate estimate of the initial state is obtained.
The calculation of the combined model error and observation error statistics requires the specification of model error covariances, which in practice are often unknown. We present a method to estimate the combined statistics from innovation data that does not require explicit specification of the model error covariances. The theory is illustrated with simple numerical experiments.