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    Validation of ocean mass variability derived from the Gravity Recovery and Climate Experiment - Studies utilizing in-situ observations and results from a Finite Element Sea ice - Ocean Model
    The Gravity Recovery and Climate Experiment (GRACE) provides estimates of the Earth's time-variable and static gravity field with an unprecedented accuracy. As fluctuations of the gravity field on sub-annual time scales are mainly induced by mass redistribution on the Earth's surface, GRACE is potentially able to monitor oceanic mass variability and redistribution. Current gravity data products, however, suffer from aliasing effects due to insufficient accuracy of background models. This study compares different filter mechanisms and develops a new filtering approach which uses information on ocean circulation patterns derived from model simulations with the Finite Element Sea - Ice Ocean Model (FESOM). To obtain a realistic representation of the ocean mass budget on interannual time scales in the FESOM model, the computation of sea surface height is extended in order to consider the effect of surface freshwater fluxes and internal mixing. The river runoff forcing is modified to balance the net evaporation on long time scales. For validation, we utilize in-situ ocean bottom pressure (OBP) data from a global bottom pressure data base. For the correction of tides, variations derived from the tidal model (FES2004), also used as a background model in the GRACE data processing, are subtracted from the in-situ data. In general, the validation of GRACE-derived anomalies against in-situ time series indicates a good agreement between the two data sets. Especially, for the high latitude arrays GRACE captures a considerable part of the observed oceanic variability. Largest errors in the GRACE data are found in the tropical Atlantic, where the GRACE-derived OBP data from all data centers feature spurious variability which probably goes back to tidal aliasing and/or the large hydrological cycle over the Orinoco/Amazon river basin. Filtering the GRACE data with the new pattern-based approach improves the correlations between GRACE and in-situ OBP anomalies compared to conventional isotropic Gauss filtering. Focussing on the ocean domain, the filter reduces land leakage effects and introduces valuable information on the ocean circulation to the GRACE data, which helps to reduce errors and to identify geophysical signals in the gravity field solutions. As a first application, the improved GRACE data sets are utilized to study the relation between oceanic transport variability and cross-flow gradients of OBP anomalies. Maps of correlations between the Southern Annular Mode (which is the dominant mode of atmospheric variability in the Southern Ocean) and GRACE OBP anomalies reveal a circumpolar band of highly negative correlation around Antarctica closely following f/H contours. Although this spatial structure is already found for data filtered with an isotropic Gauss filter, correlations are further enhanced when using the new filter approach. Based on these results, this study supports previous findings indicating that SAM affects ACC transport variability at least on a month-to-month time scale.
    Dissertation
      355  181
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    Untersuchungen zur Variabilität im Südlichen Ozean mit dem Ozeanzirkulationsmodell BARBI
    The ACC is the largest ocean current system. This current is driven directly or indirectly by the strong westerly winds, and it is one major topic of this study to investigate the variability of the ACC transport through Drake Passage due to fluctuations in these westerly winds.It is demonstrated, that the relationship between the meanzonal windstress over the southern ocean and the transportthrough Drake Passage can be described by a simple lineardynamic model, which contains the barotropic and the baroclinictime scales. Another topic of this study is the propagation of Rossbywaves under the influence of topography and the connectionof the southern ocean with the equatorial and northernlatitudes via the interaction of Rossby waves, coastal andequatorial Kelvin waves.Furthermore, the relation between the transport and the bottom pressure on the one hand, and between transport and the meridionaldifference of potential energy on the other handis studied further with a channel model.
    Dissertation
      462  75
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    Numerical Investigation of Tidal Processes and Phenomena in the Weddell Sea, Antarctica
    In the framework of the BRIOS (Bremerhaven Regional Ice OceanSimulations), a three-dimensional tidal model was developed to investigate tidal processes in the southern Weddell Sea. The model is based on the free surface SCRUM (S-Coordinate Primitive Equation Ocean Model), modified to allow for the inclusion of the horizontal component of the Earth´s rotation vector, the equilibrium tide and ice shelves. Barotropic tides are simulated in a regional two-dimensional (x-y) configuration for the Atlantic Sector of the Southern Ocean. In this investigation, the semidiurnal M2 and S2 and the diurnal K1 and O1 frequencies are considered. For both semidiurnal constituents, maxima amplitudes are found in the southwestern corner of the Filchner-Ronne Ice Shelf (FRIS). Diurnal tides have higher amplitudes at the continental shelf break where they excite continental shelf waves of same period propagating in the along-slope direction. With the full three-dimensional model, baroclinic tidal currents are studied in the inner Weddell Sea, using an orthogonal curvilinear 3D grid. Semidiurnal and diurnal periods are considered, although the emphasis is on the superinertial frequencies at which free propagating internal tides can be generated at the latitude range of the inner Weddell Sea. The vertical structure of tidal currents in the southern continental shelf region and beneath FRIS are described in detail, including their seasonal variability. The model results show that tidal currents contribute significantly to the turbulent mixing at the shelf break of the southern Weddell Sea and beneath FRIS. They also suggest that tides have a direct effect on both water mass formation through mixing and on water mass modification through heat transport to the upper boundary layer, in the ice shelf cavities and by opening leads in the sea ice.
    Dissertation
      370  114
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    Analyse hydrographischer Schnitte mit Satellitenaltimetrie
    Dedicated satellite missions that will lead to high precision, high resolution geoid models are planned and/or in preparation. In this study, a particular method is presented that allows the use of sea surface height data, that is consistent with its error covariance. A first test of the model in a scenario with a small data set demonstrates some of the model´s characteristics. One has to handle the mathematical under-determination of the model by introducing sufficient prior information about the state of the ocean. This independent information could be taken from a hydrographic atlas. Twin experiments with a data set taken from a general circulation model of the FLAME group reveal the importance of improved geoid models for estimating the flow field along a hydrographic section. When the sea surface height data is weighted according to the error estimates of the future geoid models GRACE and GOCE integrated transports of volume and temperature can be determined with an accuracy that is improved over the case with no sea surface height data by 55%. With the error estimates of the currently available geoid model EGM96 the reduction of the estimated errors does not exceed 18%. The inverse model estimates integrated volume transports through the WOCE hydrographic section SR3, one of the choke point sections of the Antarctic Circumpolar Current, of 145-166 Sv. These values agree with the ones found by other authors. The error estimates range from 13 Sv without to 11 Sv with sea surface height data. The sea surface height data is referenced to the EGM96 geoid model and weighted according to its error covariance. Sea surface height data and an estimate of the sea surface height by the model are found to deviate from each other by more than the error estimates.
    Dissertation
      321  83
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    Tides on unstructured meshes
    Unstructured mesh methods offer flexibility in representing variable coastlines and bathymetries in ocean circulation models. They propose other advantages allowing, for example, to define high resolution in certain regions of global mesh without invoking nesting methods.However, already existing finite-difference structured mesh models often outperform them as their computations per mesh node are less expensive. Nevertheless, due to the big variety of discretizations possible with unstructured mesh methods - finite element or finite volume - and the freedom in mesh design, the existing setups are not necessarily optimal in terms of accuracy and numerical efficiency. The search for optimal approach presents an important direction of current research. This thesis partly contributes in this direction. Two finite element and one finite volume method are compared with respect to their ability to faithfully simulate tides on meshes of the European Continental Shelf. Judged by computational efficiency and the absence of stabilization the preference is given to the semi-implicit models based on finite volumes after Chen et al. (2003) or on the non-conforming finite element method.One of the proposed models is further validated in simulating M2 and K1 tidal constituents on a fine mesh. Its performance in balancing energy and calculating residual currents is analyzed. The influence of the open boundary condition is also discussed. The results obtained in this analysis indicate, that the model skills are more sensitive to errors in open boundary conditions and depth representation than to changes in the spatial or temporal discretization schemes. This dictates the next step - implementing algorithms that systematically improve model parameters and open boundary forcing. It is the second major goal of this thesis.In the thesis the adjoint model is generated by adapting automatic differentiation technique. It computes the sensitivities of a cost function, which is a measure for the misfit between observed and simulated model fields, with respect to the depth, the bottom friction coefficients and the open boundary values. The sensitivities are compared in M2 and K1 tidal simulations and on a coarse and fine meshes. Regions of strong sensitivities for each tidal constituent are identified. It turns out that the sensitivities on the coarse and fine meshes do not match. If mesh is coarse it is missing dynamics that are tuned. In contrast, on the fine mesh the sensitivities with respect to, for example, depth identify islands missing from the mesh. This suggests to use adjoint models for mesh refinements.Further, the adjoint model is coupled to a Broyden-Fletcher-Goldfarb-Shanno algorithm, and the parameters are optimized on the coarse mesh. The error in coastline representation and mesh resolution is partly projected on the parameter sensitivities, which leads to a tendency in less realistic values unless strong regularization is used. This shows that tuning parameters for the wrong reason is something that should be avoided. This thesis proposes to use the sensitivities first for mesh refinements and in a second step for parameter optimization.
    Dissertation
      354  177
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    Aspects of Ocean Circulation with Finite Element Modelling
    This thesis deals with development and evaluation of the three dimensional, nonstationary ocean model FEOM:sub:0:/sub: (basic version of the Finite Element Ocean Model FEOM). This model is based on the Finite Element Method (FEM) which allows for the use of unstructured grids with variable resolution. The first part of the thesis introduces the governing equations, the mathematical formulation as well as the discretisation using FEM. After introducing the discrete form of the equations some details on the numerical implementation are given.The second part of the thesis contains applications of FEOM:sub:0:/sub: to different oceanographic tasks under idealised conditions. Comparisons to analytical results as well as to results of other numerical models in corresponding experiments are presented.The first application investigates the propagation of waves in a stratified ocean. The model shows nice correspondence to theoretically obtained wave properties as well as to results of the Modular Ocean Model (MOM). The second investigation considers the wind driven ocean circulation, especially the resulting vertical structure of the flow field. The influence of topography is examined, the results coincide with the predictions of linear theory. Finally an idealised overflow scenario is investigated. The flow of dense water on a slope poses a special problem for numerical ocean models. An international intercomparison study (DOME: Dynamics of Overflow Mixing and Entrainment) was conceived in order to gain insight into the capabilities of different numerical models in reproducing this process. FEOM:sub:0:/sub: is applied to the idealised DOME setup with and without interior density stratification. In case of a homogeneous interior a variability in the overflow rate of several days shows up, the model gives a reasonable path of the plume and reproduces the theoretically obtained dependence of the overflow transport on Coriolis parameter and density structure.
    Dissertation
      401  196
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    Untersuchungen zum Einfluss des Ozeans auf die Rotation der Erde: Assimilation beobachteter Erdrotationsparameter mit einem globalen Ozeanmodell
    Changes in the oceanic current system and in the oceanic mass distribution alter the state of the Earth's free rotation which is characterised by length of day and polar motion. The study of this connection was the challenge and the subject of this thesis. To this end, the oceanic state was estimated by assimilating Earth rotation observations with a global ocean model. The considered time span was 1993 to 2002. Although assimilation is a well established tool in climate science the assimilation of Earth rotation observations with a global ocean model is done for the first time. Before the assimilation, the observations had to be projected onto the angular momentum of the ocean. Non-oceanic contributions were removed. The result of the assimilation procedure is a time varying ocean modelstate, i.e. a trajectory, that reproduces the Earth rotationobservations. This trajectory was studied to understand the generation of Earth rotation deviations by the oceans. The governing physical mechanisms could be identified: First, changes in length of day are attributed to changes in total ocean mass. These changes are determined by the surface freshwater flux from the atmosphere to the ocean. Changes in the ocean current system have a minor contributionto length of day changes. Second, the excitation of polar motion is connected to the inhomogeneous distribution of ocean mass. These inhomogeneities are a consequence of the wind and buoyancy-driven currents. The results of this non-uniform mass distributions are currents too, i.e. geostrophic currents. This way the oceanic excitation of polar motion splits up into contributions from currentsand mass distribution. Both contributions entail each other and are highly correlated.
    Dissertation
      431  274
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    Langfristige Variabilität der thermohalinen Zirkulation in einem gekoppelten Ozean-, Meereis-, Atmosphaerenmodell
    The heat and moisture transports by transient eddies in the EMBM are parameterized by diffusion. The coupled model reproduces many aspects of today´s oceanic circulation. The most interesting features of the coupled model are the sensitivity of the thermohaline circulation to changes in the configuration, the multidecadal variability in the ocean-sea ice system, and the behaviour of the thermohaline circulation during transitions between glacial and interglacial periods. A very strong thermohaline circulation develops in the coupled system that is not evident in the stand-alone ocean model. An interesting aspect of this behaviour is the existence of a maximum strength in the overturning. Beyond this maximum, evaporation in the subtropics cannot balance the northward salt-transport. As a result, the watermasses over the deep water production sites become fresher, leading to a collapse of the thermohaline circulation. The associated changes in the sea ice cover prevent the system to recover. Acceleration and breakdown of the thermohaline circulation is expected during glaciation periods, when freshwater is stored on continents and the oceanic stratification in the North Atlantic is weakened by a reduced continental run-off and by enhanced cooling of surface water. Under these conditions a stronger thermohaline circulation compared to the reference case was established. Salinity was redistributed such that the deep water became more saline than today. During the following equilibrium conditions without net fresh water storage on the continents, the coupled model reproduces the shallow and weak overturning cell and many other aspects of the glacial circulation. All experiments are characterised by a highly variable thermohaline circulation on multidecadal timescales. This variability is maintained by the negative feedback between the strength of the overturning and sea ice cover.
    Dissertation
      448  242
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    Variability of the ice-ocean system in the Pacific sector of the Southern Ocean: Numerical model studies
    In the framework of BRIOS (Bremerhaven Ice Ocean Simulations) a coupled ice-ocean model of the Southern Ocean was adapted to investigate the variability of the ice-ocean system in the Pacific sector of the Southern Ocean with a particular focus on the factors affecting dense water formation on the Ross Sea continental shelf. The sea ice regimes in the western and eastern Ross Sea were shown to be decoupled from each other with sea ice characteristics in the western Ross Sea determined predominantly by the local atmospheric conditions and those in the eastern Ross Sea by ice import from the Amundsen Sea. The resulting strong gradient in sea ice formation provides the thermohaline driving force for the shelf circulation. The cooling, salt input and subsequent deep convection during the seasonal cycle modifies the waters of the shelf inflow so that their density is sufficient participate in Antarctic Bottom Water formation.Model results show that the region around Ross Island and McMurdo Sound has a key role in controlling the exchange between the ice shelf cavity and the open ocean in the Ross Sea. Drainage of High Salinity Shelf Water through McMurdo Sound into the cavity in winter prevents brine accumulation and thus lowers High Salinity Shelf Water salinities to the range observed. This also affects the balance of Ice Shelf Water and High Salinity Shelf Water, the two parent water masses for the formation of Antarctic Bottom Water in the Ross Sea. The interannual variability of dense water characteristics is, however, predominantly controlled by variations in the shelf inflow through a sub-surface salinity and a deep temperature signal whose origin can be traced into the Amundsen and Bellingshausen Seas. The temperature anomalies are induced in the western Bellingshausen Sea where the meridional transport of Circumpolar Deep Water causes temperature anomalies at the continental shelf break.
    Dissertation
      491  148
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    Ein Inversmodell fuer den Suedatlantik mit der Methode der finiten Elemente
    The large scale flow field of the South Atlantic and its associated heat and fresh water budget are studied with an inverse model. The model relies on traditional assumptions of mass, heat and salt conservation. A 3-dimensional velocity field which is in steady state and obeys geostrophy is derived. Using this flow field, the steady state advective-diffusive equations for temperature and salinity are solved and the corresponding density is calculated. An optimization approach is used that adjusts reference velocities such that modeled temperature and salinity are close to observations and that velocities are in geostrophic balance with the modeled density field. In order to allow for a variable spatial resolution, the finite element method is used. Its mesh is totally unstructured and the 3-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 bottom topography. The model results show, that the reference velocities return the structure of the SSH data. In general the upper-level circulation corresponds to the circulation known from the literature. The volume transport through Drake Passage is constrained to be 130 Sv. At the open boundaries (Drake Passage, 30S, 20E) the mass, heat and salt transports are in agreement with the literature. This is also true for the transports of surface, intermediate, deep and bottom water.9.6 Sv of bottom water is formed in the South Atlantic.
    Dissertation
      466  136