On the efficiency of statistical assimilation techniques in the presence of model and data error

Abstract

Statistically based assimilation methods make use of error statistics. When these statistics apply to data, some aspects of them are known. However, model error statistics are at best poorly known. The variability of these error fields causes the strength of the assimilated signal to vary. This (spatial) variability, plus diffusion, can cause the assimilated signal to rapidly disappear, decreasing the impact of the data. Our demonstration uses a statistical method [from Oschlies and Willebrand, 1996], which assimilates sea surface height using vertical regressions. An idealized Gaussian depression of sea surface height about 10° in diameter was assimilated, using both the original statistical scheme and a scheme with a horizontally uniform regression coefficient, to test the effects of variability in model errors. Results indicated that the uniform scheme is more efficient in assimilation of sea surface height than the original scheme (in that assimilated information is lost less rapidly because of small‐scale mixing) for the simplified Gaussian problem, but predictive skill was not improved when assimilating over the full North Atlantic. The influence of interpolated satellite observation errors caused by limitations of satellite track coverage was also assessed, using a chessboard sea surface depression that would be induced from the (statistically) optimal combination of model and data. Artificial eddies on the scale of the satellite track intervals are induced by including the satellite errors in the ocean model. These eddies dissipate rapidly in the presence of mixing, taking with them much of the assimilated signal. We suggest a possible solution.