Continuous assimilation in an open domain of the northeast Atlantic: 1. Methodology and application to AthenA‐88

Abstract

A scheme to perform suboptimal intermittent assimilation in an open‐ocean, quasi‐geostrophic model is presented and applied to the assimilation of altimeter data in a domain of the northeast Atlantic west of Ireland. Both simulated and real altimeter data are used. Three‐dimensional (3‐D) synoptic observation fields and error variance fields are derived from synoptic dynamic topography anomaly estimates, using an empirical orthogonal mode (EOF) vertical extension technique. The 3‐D estimates are suboptimally combined with the time‐dependent part of the forecast fields. Suboptimality here means that the combination does not directly use spatial correlations of errors; however, the 3‐D synoptic observation estimates used in the combination do contain error spatial statistical information. The resulting fields added to a mean model climatology are used as initial conditions for the model, which is integrated until a new dynamic topography anomaly estimate is available. Locally, the combination is optimal in the sense that it is based on the observational error variances, which reflect the measurement noise and the space‐time distribution of data, and that it minimizes the error variance of the results. A similar combination scheme using past as well as future observations is used to update the boundaries during model integration. Simulated surface topography anomaly maps, typical of the northeast Atlantic, are assimilated every 20 days for a 300‐day period, with different noise characteristics typical of altimetric sampling errors, in a three‐level version of the model. The assimilation fields, especially the vorticity at deeper levels, converge toward the reference fields. The convergence is obtained after O(100 days), regardless of the observational noise levels tested (up to −2 dB). Using a relevant observational error model seems to matter, in particular, the error level should not be underestimated. In the case of an 80‐day gap in the data inflow, the model predictability limits the reliability of the forecast beyond 20 days. The scheme makes the model converge back as soon as new observations are entered, with limited convergence loss due to the gap. The case of an unknown model climatology is also studied. Finally, the scheme is applied to Geosat altimeter data, added to the Robinson, Bauer and Schroeder annual climatology, in the AthenA‐88 cruise area, which is contained in the model box. The assimilation results compare favorably with hydrographical data from the cruise and help the synoptic interpretation of the observed phenomena.