Search Results

You are looking at 1 - 8 of 8 items for

  • Author or Editor: Jens Schröter x
  • Refine by Access: All Content x
Clear All Modify Search
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.

Full access
Uwe Dobrindt and Jens Schröter

Abstract

A new inverse model to study the large-scale ocean circulation and its associated heat and freshwater budget is developed. The model relies on traditional assumptions of mass, heat, and salt conservation. A three-dimensional velocity field that is in steady state and obeys geostrophy is derived. Using this flow field, the steady-state advection–diffusion equations for temperature and salinity are solved and the corresponding density is calculated. An optimization approach is used that adjusts reference velocities to get model parameters close to observations so that the velocities are in geostrophic balance with the model density field. In order to allow a variable spatial resolution, the finite-element method is used. The mesh is totally unstructured and the three-dimensional elements are tetrahedra. Climatological hydrographic data, observations of sea surface height (SSH) from satellite altimetry, and wind data are assimilated in the model. The advantages of the finite-element method make it possible to use an easy representation of the model parameters on the tetrahedra. It is not difficult to find the adjoint form of the discrete equations. The unstructured mesh agrees well with the complex geometry of the bottom topography. The model is applied to the South Atlantic. First model results show that the upper-level circulation corresponds to the circulation known from literature. The volume transport through Drake Passage is constrained to be 130 Sv. The transports of water masses, heat, and salt across the open boundaries (Drake Passage, 30°S, 20°E) are in agreement with the literature. The formation rate of bottom water is 13.0 Sv and the heat transport across 30°S to the north is 0.64 PW.

Full access
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.

Full access
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%.

Full access
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.

Full access
Lars Nerger, Tijana Janjić, Jens Schröter, and Wolfgang Hiller

Abstract

In recent years, several ensemble-based Kalman filter algorithms have been developed that have been classified as ensemble square root Kalman filters. Parallel to this development, the singular “evolutive” interpolated Kalman (SEIK) filter has been introduced and applied in several studies. Some publications note that the SEIK filter is an ensemble Kalman filter or even an ensemble square root Kalman filter. This study examines the relation of the SEIK filter to ensemble square root filters in detail. It shows that the SEIK filter is indeed an ensemble square root Kalman filter. Furthermore, a variant of the SEIK filter, the error subspace transform Kalman filter (ESTKF), is presented that results in identical ensemble transformations to those of the ensemble transform Kalman filter (ETKF), while having a slightly lower computational cost. Numerical experiments are conducted to compare the performance of three filters (SEIK, ETKF, and ESTKF) using deterministic and random ensemble transformations. The results show better performance for the ETKF and ESTKF methods over the SEIK filter as long as this filter is not applied with a symmetric square root. The findings unify the separate developments that have been performed for the SEIK filter and the other ensemble square root Kalman filters.

Full access
Tijana Janjić, Lars Nerger, Alberta Albertella, Jens Schröter, and Sergey Skachko

Abstract

Ensemble Kalman filter methods are typically used in combination with one of two localization techniques. One technique is covariance localization, or direct forecast error localization, in which the ensemble-derived forecast error covariance matrix is Schur multiplied with a chosen correlation matrix. The second way of localization is by domain decomposition. Here, the assimilation is split into local domains in which the assimilation update is performed independently. Domain localization is frequently used in combination with filter algorithms that use the analysis error covariance matrix for the calculation of the gain like the ensemble transform Kalman filter (ETKF) and the singular evolutive interpolated Kalman filter (SEIK). However, since the local assimilations are performed independently, smoothness of the analysis fields across the subdomain boundaries becomes an issue of concern.

To address the problem of smoothness, an algorithm is introduced that uses domain localization in combination with a Schur product localization of the forecast error covariance matrix for each local subdomain. On a simple example, using the Lorenz-40 system, it is demonstrated that this modification can produce results comparable to those obtained with direct forecast error localization. In addition, these results are compared to the method that uses domain localization in combination with weighting of observations. In the simple example, the method using weighting of observations is less accurate than the new method, particularly if the observation errors are small.

Domain localization with weighting of observations is further examined in the case of assimilation of satellite data into the global finite-element ocean circulation model (FEOM) using the local SEIK filter. In this example, the use of observational weighting improves the accuracy of the analysis. In addition, depending on the correlation function used for weighting, the spectral properties of the solution can be improved.

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

Abstract

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.

Full access