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Jens Schröter and Carl Wunsch

Abstract

Dynamical models driven by “observed” forcing fields (e.g., the wind) have a true solution uncertainty owing to observational errors in the driving. This uncertainty is usually hidden from view because conventional numerical methods do not easily calculate it. We explore with finite difference, nonlinear circulation models (one and two layer) the uncertainties in interesting flow properties, such as western boundary current trandport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies.

Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.

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Manfred Wenzel and Jens Schröter

Abstract

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

Abstract

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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Martin Losch, René Redler, and Jens Schröter

Abstract

The recovery of the oceanic flow field from in situ data is one of the oldest problems of modern oceanography. In this study, a stationary, nonlinear inverse model is used to estimate a mean geostrophic flow field from hydrographic data along a hydrographic section. The model is augmented to improve these estimates with measurements of the absolute sea-surface height by satellite altimetry. Measurements of the absolute sea-surface height include estimates of an equipotential surface, the geoid. Compared to oceanographic measurements, the geoid is known only to low accuracy and spatial resolution, which restricts the use of sea-surface height data to applications of large-scale phenomena of the circulation. Dedicated satellite missions that are designed for high precision, high-resolution geoid models are planned and/or in preparation. This study, which relies on twin experiments, assesses the important contribution of improved geoid models to estimating the mean flow field along a hydrographic section. When the sea-surface height data are weighted according to the error estimates of the future highly accurate geoid models GRACE (Gravity Recovery And Climate Experiment) and GOCE (Gravity Field and Steady-State Ocean Circulation Explorer), integrated fluxes of mass and temperature can be determined with an accuracy that is improved over the case with no sea-surface height data by up to 55%. With the error estimates of the currently best geoid model EGM96, the reduction of the estimated flux errors does not exceed 18%.

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