Estimation of the optimal interpolation parameters in a quasi-geostrophic model of the Northeast Atlantic using ensemble methods

Abstract The SOPRANE operational forecasting system is based on a quasi-geostrophic (QG) model of the Northeast Atlantic. The assimilation scheme used to constrain the model consists of a Reduced Order Optimal Interpolation (ROOI) using an Extended Kalman Filter (EKF) formulation. Corrections to the model fields at the surface are consistent with satellite along track data and a priori statistical information on the forecast error. The required forecast error variance is updated using an estimation of the time evolution of the analysis error variance (taken as the initial condition error variance). A correlation function C then leads to the forecast error covariance matrix. However, our knowledge on these statistics is poor. We then achieve ensemble forecast experiments based on perturbed initial condition fields so as to estimate initial condition error growth and check if the ROOI hypothesis is relevant. Tests on six different initial ensembles of 140 members, integrated over 35 days, have been performed to correctly determine characteristics of the initial condition statistics. We can clearly show the strong correlation between local dynamics and spatial repartition of the error growth, which concentrates on the most energetic regions. Some interannual variability patterns can also be found. This leads to the computation of a new ensemble, with statistics consistent with what is observed in the previous experiments. Time propagation of the initial condition error variance, the C matrix and its parameters are estimated. It shows a northward decrease of the error correlation radii and a westward propagation of the errors. There is an interannual and spatial variation of C, on the contrary to what is stated in the SOPRANE ROOI scheme. Moreover, the increase error variance in time is also correlated with the dynamics.