Statistical inference of weakly correlated subthermocline fields from satellite altimeter data
Authors: Hurlburt Harley E. , Fox Daniel N. , Metzger E. Joseph 
Published: February 2008

To initialize the barotropic and baroclinic modes, numerical ocean prediction models need information both above and below the main thermocline. Forecasts of upper ocean mesoscale variability using real and simulated data show high sensitivity to the Subthermocline pressure (STP) field. Results using simulated data indicate that the accuracy of this field may be the limiting factor on the time scale for mesoscale oceanic predictive skill. Satellite altimetry provides a potentially abundant source of sea surface height (SSH) data, but there is no comparable source of Subthermocline information on the horizon. We investigate statistical techniques to infer Subthermocline pressure anomalies from SSH data, a problem complicated by the weak correlation between the fields. This problem is addressed by using the degrees of freedom available in the data and by describing them in an efficient manner to suppress noise, eliminate unskilled or redundant estimators and to prevent ill‐conditioned matrix inversions. Multilinear regression, empirical orthogonal function (EOF) regression and principal estimator patterns are compared using data simulated by a numerical ocean model and error models. Numerous questions that need to be addressed for proper application of the statistical techniques are investigated. Topics include noise suppression and the impact of the noise on accuracy. These topics are studied as a function of decorrelation distance in the noise and the presence or absence of noise in dependent and independent data sets. In this context we also investigate dependent data set size requirements, the criteria for choosing estimators, the number, areal coverage, and spacing of sampling locations used in the estimators, the effect of the ocean dynamical regime on the results, the effects of ocean model imperfections or changes in population statistics on the results, SSH versus ΔSSH in an orbital repeat period as estimators, and the effect of orbital repeat period on Subthermocline estimates from ΔSSH data. In the presence of 40% rms noise the usual significance tests are much too conservative for this application. (However, we also found that EOFs calculated from spatially correlated, temporally uncorrelated noise can pass a popular EOF significance test based on uncorrelated noise.) Although more difficult to suppress than uncorrelated noise, correlated noise did not markedly increase the error in these tests. Spatial coverage of the estimators was found to be an important parameter, and four to five ascending‐or descending tracks per wavelength were sufficient for uniformly accurate estimates whether beneath or between altimeter tracks. In most of these tests, ΔSSH proved a better estimator than SSH, but for ΔSSH resolving the shortest major time scale is a necessity. High accuracy is not required for Subthermocline pressure anomalies to substantially enhance upper ocean forecast skill in a numerical ocean prediction model. In results to be reported elsewhere, a statistically inferred STP field substantially enhanced the skill of a Gulf Stream forecast model where the SSH was initialized from oceanic observations. The inferred STP field allowed the model to show forecast skill in comparison to persistence of the initial state.