Impact of correlated observation errors on the conditioning of variational data assimilation problems

Summary An important class of nonlinear weighted least‐squares problems arises from the assimilation observations in atmospheric and ocean models. In variational data assimilation, inverse error covariance matrices define weighting problem. For observation errors, a diagonal matrix (i.e., uncorrelated errors) is often assumed for simplicity even when errors are suspected to be correlated. While accounting observation‐error correlations should improve quality solution, it also affects convergence rate minimization algorithms used iterate solution. If process stopped before reaching full convergence, which usually case operational applications, solution may degraded if correctly accounted for. this article, we explore influence correlation () on preconditioned conjugate gradient (PCG) algorithm applied one‐dimensional (1D‐Var) We design idealized 1D‐Var system include two key features more complex systems: use background as preconditioner (B‐PCG); diffusion operator model spatial . Analytical numerical results with show strong sensitivity B‐PCG parameters diffusion‐based Depending parameter choices, correlated can either speed up or slow down convergence. practice, compromise required specifications between staying close best available estimates one hand ensuring an adequate other.