Detecting unstable structures and controlling error growth by assimilation of standard and adaptive observations in a primitive equation ocean model

Abstract. Oceanic and atmospheric prediction is based on cyclic analysis-forecast systems that assimilate new observations as they become available. In such observationally forced systems, errors amplify depending on their components along the unstable directions; these can be estimated by Breeding on the Data Assimilation System (BDAS). Assimilation in the Unstable Subspace (AUS) uses the available observations to estimate the amplitude of the unstable structures (computed by BDAS), present in the forecast error field, in order to eliminate them and to control the error growth. For this purpose, it is crucial that the observational network can detect the unstable structures that are active in the system. These concepts are demonstrated here by twin experiments with a large state dimension, primitive equation ocean model and an observational network having a fixed and an adaptive component. The latter consists of observations taken each time at different locations, chosen to target the estimated instabilities, whose positions and features depend on the dynamical characteristics of the flow. The adaptive placement and the dynamically consistent assimilation of observations (both relying upon the estimate of the unstable directions of the data-forced system), allow to obtain a remarkable reduction of errors with respect to a non-adaptive setting. The space distribution of the positions chosen for the observations allows to characterize the evolution of instabilities, from deep layers in western boundary current regions, to near-surface layers in the eastward jet area.