Variational assimilation of altimeter data into a non-linear ocean model: temporal strategies

Abstract
In this paper, we explore the use of the adjoint method in the oceanographic context for assimilating satellite altimeter data. Experiments with simulated altimeter data are performed in a multi-layer quasigeostrophic ocean model. The interest is mainly with controlling the mesoscale eddy active ocean circulation observed in the mid-latitudes. Due to the surface nature of the observations, one key aspect in the success of assimilation is its ability to transfer the surface data information downwards to the deep flows. Test experiments are performed first, in a coarse resolution regional basin within which several eddies are interacting on the f-plane and second, in a high resolution basin size domain on the ß-plane which mimics the Gulfstream-like behavior of mid-latitude jets and western boundary currents and the associated eddy system. As a matter of fact, it is found that the length of the assimilation cycle is crucial to the success of this assimilation. Short assimilation cycles may be efficient in the control of surface flows but rather ineffective with respect to the downward penetration of information. Conversely, long assimilation cycles lead to rather coherent results in terms of efficiency on the vertical but this global efficiency is poor, especially identifying the initial control state. It is suggested that an efficient assimilation strategy can be constructed by dividing the global time sequence in several time sub-periods the individual duration of which must be less than the typical predictability time scale of the flow. However, the whole assimilation cycle must be long enough and larger than the vertical penetration time scale. A "sliced assimilation" strategy which satisfies these conditions is studied in which the assimilation period is divided into equal-length time-intervals. With this approach, an acceptable accuracy can be reached for the recovery of the final flow state. This meets the requirements of the "filtering" objectives of data assimilation and therefore the "forecast" purposes. A so-called "progressive assimilation" strategy is also studied in which successive iterations of increasing durations are performed in order to progressively improve the control of the initial state control variable. This more expensive strategy is more adequate for "smoothing" objectives.