Continuous assimilation of simulated Geosat altimetric sea level into an eddy‐resolving numerical ocean model: 2. Referenced sea level differences

Continuous assimilation of referenced altimetric sea level differences from the simulated Geosat Exact Repeat Mission (ERM) into a three-layer, wind-driven, quasi-geostrophic, eddy-resolving numerical ocean box model at mid-latitude was conducted utilizing an improved version of the optimal interpolation procedure found in Part I (White et al., this issue), forming the basis of an operational dynamical interpolation procedure to be used in subsequent gridding of real Geosat ERM altimetric sea level data. The major improvement over the dynamical interpolation method used in Part I was the inclusion of temporal decorrelation in the error covariance matrix and the introduction of noise into the system. As referenced altimetric sea level differences (i.e., differences referenced by the mean of the model) were observed from a control model integration in real model time by the simulated Geosat altimeter, attention focused upon the ability of the dynamical interpolation procedure to reconstruct a mesoscale eddy field resembling that of the control model integration. Results of this dynamical interpolation procedure were compared with those of a statistical (i.e., optimum) interpolation procedure in its ability to reconstruct the mesoscale eddy field in the western boundary extension current of the control model integration. A series of model integrations were made, with initial conditions independent from those of the control model integration (the latter taken to represent the observed mesoscale eddy field), where the dynamical interpolation of simulated referenced Geosat ERM altimetric sea level differences was found capable of reproducing the control model integration (i.e., explaining 80–90% of the control model variance) after only one repeat cycle (i.e., 17 days) of the ERM. This success was attributed to the use of time decorrelation in the error covariance (together with noise) to nudge the first-guess model upper level stream function field toward the corresponding observation field over a period of a few days, reducing the shock of inserting the observations into the model. The degree of similarity between the upper layer stream function of the updated model and the control model integration after one repeat cycle was, however, only marginally significantly greater than that achieved by statistical interpolation (i.e., explaining 65–90% of the control model variance), both interpolation procedures (i.e., dynamical and statistical) using covariance estimates that were determined a priori in both space and time. Two important advantages of the dynamical interpolation over the statistical interpolation became evident after three cycles (i.e., 51 days) of continuous assimilation of referenced simulated Geosat ERM altimetric sea level differences. First, mesoscale eddy activity in the middle and lower layers of the updated model integration began to resemble that of the model control integration (i.e., explaining 65% and 15% of the control model variance, respectively), without resorting to vertical statistical interpolation. Second, the spectral coherence between the upper layer stream function field of the updated model integration and that of the control model integration was symmetric with respect to direction of propagation, while the spectral coherence between the upper layer stream function field by statistical interpolation and that of the control model integration was not, with the latter robust enough only to detect the dominant westward propagating portion of the spectrum of mesoscale eddy activity and not the subdominant information. An important finding was the fact that both interpolation procedures were able to resolve wavelengths longer than the Nyquist (i.e., 280 km) dictated by the track separation distance, as expected, but both interpolation procedures were able to resolve periods (i.e., 12 days) much shorter than the Nyquist (i.e., 34 days) dictated by the exact repeat period.

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