Sea surface topography fields of the tropical Pacific from data assimilation

Copyrighted by American Geophysical Union.Time series of maps of monthly tropical Pacific dynamic topography\ud anomalies from 1979 through 1985 were constructed by means of assimilation of tide\ud gauge and expendable bathythermograph (XBT) data into a linear model driven by\ud observed winds. Estimates of error statistics were calculated and compared to actual\ud differences between hindcasts and observations. Four experiments were performed\ud as follows: one with no assimilation, one with assimiation of sea level anomaly data\ud from eight selected island tide gauge stations, one with assimilation of dynamic\ud height anomalies derived from XBT data, and one with both XBT and tide gauge\ud data assimilated. Data from seven additional tide gauge stations were withheld from\ud the assimilation process and used for verification in all four experiments. Statistical\ud objective maps based on data alone were also constructed for comparison purposes.\ud The dynamic response of the model without assimilation was, in general, weaker\ud than the observed response. Assimilation resulted in enhanced signal amplitude in\ud all three assimilation experiments. RMS amplitudes of statistical objective maps\ud were only strong near observing points. In large data-void regions these maps show\ud amplitudes even weaker than the wind-driven model without assimilation. With\ud few exceptions the error estimates generated by the Kalman filter appeared quite\ud reasonable. Since the error processes cannot be assumed to be white or stationary,\ud we could find no straightforward way to test the formal statistical hypothesis that\ud the time series of differences between the filter output and the actual observations\ud were drawn from a population with statistics given by the Kalman filter estimates.\ud The autocovariance of the innovation sequence, i.e., the sequence of differences\ud between forecasts before assimilation and observations, has long been used as an\ud indicator of how close a filter is to optimality. We found that the best filter we\ud could devise was still short of the goal of producing a white innovation sequence.\ud In this and earlier studies, little sensitivity has been found to the parameters under\ud our direct control. Extensive changes in the assumed error statistics make only\ud marginal differences. The same is true for long time and space scale behavior of\ud different models with richer physics and finer resolution. Better data assimilation\ud results will probably require relaxation of the assumptions of stationarity and serial\ud independence of the errors. Formulation of such detailed noise models will require\ud longer time series, with the attendant problems of matching very different data sets