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Manfred Wenzel and Jens Schröter


The mass budget of the ocean in the period 1993–2003 is studied with a general circulation model. The model has a free surface and conserves mass rather than volume; that is, freshwater is exchanged with the atmosphere via precipitation and evaporation and inflow from land is taken into account. The mass is redistributed by the ocean circulation. Furthermore, the ocean’s volume changes by steric expansion with changing temperature and salinity. To estimate the mass changes, the ocean model is constrained by sea level measurements from the Ocean Topography Experiment (TOPEX)/Poseidon mission as well as by hydrographic data. The modeled ocean mass change within the years 2002–03 compares favorably to measurements from the Gravity Recovery and Climate Experiment (GRACE), and the evolution of the global mean sea level for the period 1993–2003 with annual and interannual variations can be reproduced to a 0.15-cm rms difference. Its trend has been measured as 3.37 mm yr−1 while the constrained model gives 3.34 mm yr−1 considering only the area covered by measurements (3.25 mm yr−1 for the total ocean). A steric rise of 2.50 mm yr−1 is estimated in this period, as is a gain in the ocean mass that is equivalent to an eustatic rise of 0.74 mm yr−1. The amplitude and phase (day of maximum value since 1 January) of the superimposed eustatic annual cycle are also estimated to be 4.6 mm and 278°, respectively. The corresponding values for the semiannual cycle are 0.42 mm and 120°. The trends in the eustatic sea level are not equally distributed. In the Atlantic Ocean (80°S–67°N) the eustatic sea level rises by 1.8 mm yr−1 and in the Indian Ocean (80°S–30°N) it rises by 1.4 mm yr−1, but it falls by −0.20 mm yr−1 in the Pacific Ocean (80°S–67°N). The latter is mainly caused by a loss of mass through transport divergence in the Pacific sector of the Antarctic Circumpolar Current (−0.42 Sv; Sv ≡ 109 kg s−1) that is not balanced by the net surface water supply. The consequence of this uneven eustatic rise is a shift of the oceanic center of mass toward the Atlantic Ocean and to the north.

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Jens Schröter, Ulrike Seiler, and Manfred Wenzel


A variational inverse technique is applied to assimilate sea surface height (SSH) measurements into a simple eddy-resolving quasigeostrophic ocean model. The data used were measured by Geosat in the spring of 1987 in an area in the Gulf Stream extension. The assimilation technique minimizes the weighted least-squares difference between model and observations, while the dynamical model equations are satisfied exactly. Fitting the model to data by applying the adjoint technique allows us not only to solve for the best model trajectory in phase space but also the wind forcing and internal model parameters describing, for example, diffusion or stratification.

The method is first tested systematically by performing a number of identical twin experiments with model-produced “observations.” A hierarchy of ocean models is then applied to test their performance in assimilating two repeat cycles of Geosat sea surface height (SSH) measurements. The most successful model is nonlinear and baroclinic. It can fit the data to less than 5-cm rms difference, which is within the error estimates of the satellite measurements.

Special consideration is given to studying the possibilities and limitations of the retrieval of model parameters. It is found that the assimilation period has to exceed two repeal cycles of the satellite to determine model parameters. For longer assimilation periods, however, the discrepancy between the complex dynamics of the meandering Gulf Stream and the simple dynamics of the model becomes more and more apparent.

Verification of model results with an independent dataset shows that modeled currents compare reasonably well with in situ measurements made by drogued buoys.

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Marc H. Taylor, Martin Losch, Manfred Wenzel, and Jens Schröter


Empirical orthogonal function (EOF) analysis is commonly used in the climate sciences and elsewhere to describe, reconstruct, and predict highly dimensional data fields. When data contain a high percentage of missing values (i.e., gappy), alternate approaches must be used in order to correctly derive EOFs. The aims of this paper are to assess the accuracy of several EOF approaches in the reconstruction and prediction of gappy data fields, using the Galapagos Archipelago as a case study example. EOF approaches included least squares estimation via a covariance matrix decomposition [least squares EOF (LSEOF)], data interpolating empirical orthogonal functions (DINEOF), and a novel approach called recursively subtracted empirical orthogonal functions (RSEOF). Model-derived data of historical surface chlorophyll-a concentrations and sea surface temperature, combined with a mask of gaps from historical remote sensing estimates, allowed for the creation of true and observed fields by which to gauge the performance of EOF approaches. Only DINEOF and RSEOF were found to be appropriate for gappy data reconstruction and prediction. DINEOF proved to be the superior approach in terms of accuracy, especially for noisy data with a high estimation error, although RSEOF may be preferred for larger data fields because of its relatively faster computation time.

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