[p2] Mathematical aspect


Accounting for Model Error: Weak-Constraint 4D-Variational Data Assimilation

N. K. Nichols (University of Reading), A. El-Said (University of Reading), A. S. Lawless (University of Reading)


The behaviour of the weak-constraint four-dimensional variational data assimilation problem (wc4DVAR) and its sensitivity to the input data governing the problem are investigated here. The aim of wc4DVAR is to provide a statistically optimal estimate of the state of a dynamical system given an imperfect model of the system, a model forecast, and observations of the states over time. It differs from conventional strong constraint 4DVAR by providing estimates for the model errors as well as the states. We consider two formulations of the wc4DVAR problem - the model error and state estimation formulations - and examine these as a function of observation accuracy and configuration; forecast accuracy and error covariance structure; model error variance and correlation length scales; and assimilation window length. The variational problems are solved by a gradient iteration procedure. We investigate the behaviour of the convergence of the two formulations via numerical examples. Results are shown using a linear advection model with periodic boundary conditions. Although the optimization problems are mathematically equivalent, we show that the two formulations exhibit very different performance characteristics when the data are varied.