Besides the warming of the ocean, sea level is mainly rising due to land ice mass loss of the major ice sheets in Greenland, the West Antarctic, and the Alaskan Glaciers. However, it is not clear yet how these land ice mass losses influence regional sea level. Here, we use the global Finite Element Sea-ice Ocean Model (FESOM) to simulate sea surface height (SSH) changes caused by these ice mass losses and combine it with the passive ocean response to varying surface loading using the sea level equation. We prescribe rates of fresh water inflow, not only around Greenland, but also around the West Antarctic Ice Sheet and the mountain glaciers in Alaska with approximately present-day amplitudes of 200, 100, and 50 Gt/yr, respectively. Perturbations in sea level and in freshwater distribution with respect to a reference simulation are computed for each source separately and in their combination. The ocean mass change shows an almost globally uniform behavior. In the North Atlantic and Arctic Ocean, mass is redistributed toward coastal regions. Steric sea level change varies locally in the order of several centimeters on advective time- scales of decades. Steric effects to local sea level differ significantly in different coastal locations, e.g., at North American coastal regions the steric effects may have the same order of magnitude as the mass driven effect, whereas at the European coast, steric effects remain small during the simulation period.

The Finite-Element Sea Ice Model (FESIM), used as a component of the Finite-Element Sea ice Ocean Model, is presented. Version 2 includes the elastic-viscous-plastic (EVP) and viscous-plastic (VP) solvers and employs a flux corrected transport algorithm to advect the ice and snow mean thicknesses and concentration. The EVP part also includes a modified approach proposed recently by Bouillon et al. (2013), which is characterized by an improved stability compared to the standard EVP approach. The model is formulated on unstructured triangular meshes. It assumes a collocated placement of ice velocities, mean thicknesses and concentration at mesh vertices, and relies on piecewise-linear (P1) continuous elements. Simple tests for the modified EVP and VP solvers are presented to show that they may produce very close results provided the number of iterations is sufficiently high.

The Finite Element Sea Ice-Ocean Model (FESOM) is the first global ocean general circulation model based on unstructured-mesh methods that has been developed for the purpose of climate research. The advantage of unstructured-mesh models is their flexible multi-resolution modelling functionality. In this study, an overview of the main features of FESOM will be given; based on sensitivity experiments a number of specific parameter choices will be explained; and directions of future developments will be outlined. It is argued that FESOM is sufficiently mature to explore the benefits of multi-resolution climate modelling and that its applications will provide information useful for the advancement of climate modelling on unstructured meshes.

Parameterization of mesoscale eddies is an important problem of modern ocean dynamics and modeling. The most widely used scheme is the so-called Gent-McWilliams parameterization, which describes the eddy-induced transport of tracers, including temperature, density, and isopycnal thickness (TH). An alternative scheme, proposed by Green and Welander, deals with parameterizing eddy fluxes of potential vorticity (PV). Many recent studies propose using it, for it includes the effect of eddy Reynolds stresses that may influence mean flows. These two schemes are compared in the simplest configuration of two-layer quasigeostrophic channel flow, which enables analytical solutions for zonal-mean fields. It is shown how the parameterizations shape the zonally averaged zonal velocity profiles, with special attention paid to the role of the Reynolds stresses and momentum conservation. The zonally averaged zonal velocity profiles are sensitive to the amplitude and profiles of TH and PV diffusivities. For small enough diffusivities the TH parameterization may lead to solutions resembling those for the PV parameterization if it uses the diffusivity of the latter; that is, it may mimic the impact of the Reynolds stresses on the mean flow.

In this article, the tsunami model TsunAWI (Alfred Wegener Institute) and its application for hindcasts, inundation studies, and the operation of the tsunami scenario repository for the Indonesian tsunami early warning system are presented. TsunAWI was developed in the framework of the German-Indonesian Tsunami Early Warning System (GITEWS) and simulates all stages of a tsunami from the origin and the propagation in the ocean to the arrival at the coast and the inundation on land. It solves the non-linear shallow water equations on an unstructured finite element grid that allows to change the resolution seamlessly between a coarse grid in the deep ocean and a fine representation of coastal structures. During the GITEWS project and the following maintenance phase, TsunAWI and a framework of pre- and postprocessing routines was developed step by step to provide fast computation of enhanced model physics and to deliver high quality results.

The western Ross Sea is one of the key sites for cross‐shelf water exchange around Antarctica. The mechanism through which tides affect the cross‐shelf exchange in the northwestern Ross Sea is investigated using numerical simulations. Tides are found to increase the high‐salinity shelf water (HSSW) outflow through the impact on the warm water intrusion of open ocean origin. The residual tidal currents are onshore along the Modified Circumpolar Deep Water pathway and therefore enhance its intrusion. Lighter ambient water adjacent to the HSSW increases the cross‐flow density gradient, thus strengthening the HSSW export. At the same time, the onshore residual current and increased dilution of the HSSW have the potential to reduce the export rate. Owing to the existence of opposite tidal effects, the strongest HSSW export happens at the intermediate tidal forcing strength. The amplification of tides on cross‐shelf exchange indicates that the relevant dynamical processes should be simulated or parameterized in climate models in order to adequately predict the ocean.

With the focus on the Southern Ocean circulation, results of assimilation of multi-mission-altimeter data and the GRACE/GOCE gravity data into the finite element ocean model (FEOM) are investigated. We use the geodetic method to obtain the dynamical ocean topography (DOT). This method combines the multi-mission-altimeter sea surface height and the GRACE/GOCE gravity field. Using the profile approach, the spectral consistency of both fields is achieved by filtering the sea surface height and the geoid. By combining the GRACE and GOCE data, a considerably shorter filter length can be used, which results in more DOT details. We show that this increase in resolution of measured DOT carries onto the results of data assimilation for the surface data. By assimilating only absolute dynamical topography data using the ensemble Kalman filter, we were able to improve modeled fields. Results are closer to observations which were not used for assimilation and lie outside the area covered by altimetry in the Southern Ocean (e.g. temperature of surface drifters or deep temperatures in the Weddell Sea area at 800m depth derived from Argo composite.)

The seasonal variability of Weddell Sea Bottom Water (WSBW) transport and its driving mechanisms are examined using FESOM simulations. Pronounced seasonal variability is present in both the Filchner shelf water export rate and the WSBW transport rate near the Antarctic Peninsula (AP) tip. The variabilities at both locations are linked to the surface wind forcing. The Filchner shelf water export rate responds to the onshore propagating density anomaly, which is caused by the wind‐induced variation of the isopycnal depression at the coast. The variability near the AP tip originates from upstream variations at the Filchner Depression and from seasonal variability of the Weddell gyre strength.

A mean dynamic ocean topography (MDT) has been computed using a high resolution GOCE (Gravity field and steady-state Ocean Circulation Explorer) gravity model and a new mean sea surface obtained from a combination of satellite altimetry covering the period 1992 October till 2010 April. The considered gravity model is GO-CONS-GCF-2-TIM-R3, which computes geoid using 12 months of GOCE gravity field data. The GOCE gravity data allow for more detailed and accurate estimates of MDT. This is illustrated in the Southern Ocean where the commission error is reduced from 20 to 5cm compared to the MDT computed using the GRACE gravity field model ITG-Grace2010. As a result of the more detailed and accurate MDT, the calculation of geostrophic velocities from the MDT is now possible with higher accuracy and spatial resolution, and the error estimate is about 7 cms−1 for the Southern Ocean.

Meltwater from the Greenland Ice Sheet (GIS) has been a major contributor to sea level change in the recent past. Global and regional sea level variations caused by melting of the GIS are investigated with the finite element sea-ice ocean model (FESOM). We consider changes of local density (steric effects), mass inflow into the ocean, redistribution of mass, and gravitational effects. Five melting scenarios are simulated, where mass losses of 100, 200, 500, and 1000 Gt/yr are converted to a continuous volume flux that is homogeneously distributed along the coast of Greenland south of 75 degrees N. In addition, a scenario of regional melt rates is calculated from daily ice melt characteristics. The global mean sea level modeled with FESOM increases by about 0.3 mm/yr if 100 Gt/yr of ice melts, which includes eustatic and steric sea level change. In the global mean the steric contribution is one order of magnitude smaller than the eustatic contribution. Regionally, especially in the North Atlantic, the steric contribution leads to strong deviations from the global mean sea level change. The modeled pattern mainly reflects the structure of temperature and salinity change in the upper ocean. Additionally, small steric variations occur due to local variability in the heat exchange between the atmosphere and the ocean. The mass loss has also affects on the gravitational attraction by the ice sheet, causing spatially varying sea level change mainly near the GIS, but also at greater distances. This effect is accounted for by using Green's functions. (C) 2011 Elsevier Ltd. All rights reserved.

Earth System modeling is indispensable for our understanding of current and future climate change. Here we will address one of its components, the ocean, capable of storing large amount of heat and thus influencing the climate on large time and space scales. Currently, numerical modeling of ocean general circulation is dominated by models formulated on regular meshes. Many of them are elaborated tools enabling a selection of various time-stepping techniques, advection schemes, physical parameterizations, vertical discretization and convenient initialization and data analysis tools. When it comes to selectively changing the resolution in an area of interest, there are several choices beginning from nesting (when a finer grid is included into a coarse one) to curvilinear coordinates stretched or squeezed locally to follow coastlines or deliver extra resolution to specific areas. Despite many successful applications of nesting, its difficulties are generally recognized, and it is generally a challenging task to seamlessly match fluxes (of momentum, tracers, mass) both ways (from coarse to fine and vice versa) while maintaining appropriate physical parameterizations.

Weekly surface loading variations are estimated from a joint least squares inversion of load-induced GPS site displacements, GRACE gravimetry and simulated ocean bottom pressure (OBP) from the finite element sea-ice ocean model (FESOM).In this study, we directly use normal equations derived from reprocessed GPS observations, where station and satellite positions are estimated simultaneously. The OBP weight of the model in the inversion is based on a new error model, obtained from 2 FESOM runs forced with different atmospheric data sets.Our findings indicate that the geocenter motion derived from the inversion is smooth, with non-seasonal RMS values of 1.4, 0.9 and 1.9 mm for the X, Y and Z directions, respectively. The absolute magnitude of the seasonal geocenter motion varies annually between 2 and 4.5 mm. Important hydrological regions such as the Amazon, Australia, South-East Asia and Europe are mostly affected by the geocenter motion, with magnitudes of up to 2 cm, when expressed in equivalent water height.The chosen solar radiation pressure model, used in the GPS processing, has only a marginal effect on the joint inversion results. Using the empirical CODE model slightly increases the annual amplitude of the Z component of the geocenter by 0.8 mm. However, in case of a GPS-only inversion, notable larger differences are found for the annual amplitude and phase estimates when applying the older physical ROCK models. Regardless of the used radiation pressure model the GPS network still exhibits maximum radial expansions in the order of 3 mm (0.45 ppb in terms of scale), which are most likely caused by remaining GPS technique errors.In an additional experiment, we have used the joint inversion solution as a background loading model in the GPS normal equations. The reduced time series, compared to those without a priori loading model, show a consistent decrease in RMS. In terms of the annual height component, 151 of the 189 stations show a reduction of at least 10% in seasonal amplitude.On the ocean floor, we find a positive overall correlation (0.51) of the inversion solution with time series from globally distributed independent bottom pressure recorders.Even after removing a seasonal fit we still find a correlation of 0.45. Furthermore, the geocenter motion has a significant effect on ocean bottom pressure as neglecting it causes the correlation to drop to 0.42. (C) 2011 Elsevier Ltd. All rights reserved.

Weekly ocean bottom pressure anomalies (OBP) are modeled using the Finite Element Sea-ice Ocean Model (FESOM). The model's OBP error, mostly unknown so far, is assessed by comparing two model simulations, each forced by different atmospheric forcing data sets. The mean estimated error of modeled OBP is found to be 0.04 m per 1.5 degrees x 1.5 degrees grid cell. The error varies strongly from 0.003 m in the equatorial region to 0.31 m in the Weddell and Ross Seas. We believe that the spatial variations of the errors are an important improvement over previous error models. The new error estimates are implemented in a joint inversion of Gravity Recovery and Climate Experiment (GRACE) gravity measurements, GPS site displacements and modeled OBP, resulting in a larger overall OBP weight in the inversion, most notably in the Polar Regions. Additionally, the inversion provides a global mass correction term to adjust the ocean mass budget of the model. The estimated term is used to correct the model's fresh water balance, making it consistent with GRACE and GPS on seasonal and longer timescales. All model results, weekly GRACE estimates and the inverse solutions are compared with measurements from in situ bottom pressure recorders. The newly estimated error model of the combination solution results in higher correlations than the previously used constant error model of the combination solution.

The relation between the sea surface height and the meridional transport across a zonal section at 26.5°N in the North Atlantic is studied by using an eddy resolving ocean state estimate simulated with the Massachusetts Institute of Technology general circulation model. It is shown that the correlation between the zonal sea surface height difference and transport can be substantially increased if the steric height contribution from the seasonal thermocline is removed. The latter explains a substantial part of sea surface height variability, but its effect on transport is weak. It is also found that the zonal steric height difference correlates well with the transport after the contribution of the seasonal thermocline has been removed. There is a similar agreement (with correlation coefficient of 0.63 for the full signal and 0.89 for the mean seasonal cycle) between the meridional transport and steric height based on observations from the Rapid Climate Change (RAPID) project.

We have studied the ability of the GRACE gravimetry mission and Jason-1 altimetry to resolve ice and glacier induced contributions to sea level rise, by means of a fingerprint method. Here, the signals from ice sheet and land glacier changes, steric changes, glacial isostatic adjustment and terrestrial hydrology are assumed to have fixed spatial patterns. In a joint inversion using GRACE and Jason-1 data the unknown temporal components can then be estimated by least-squares. In total, we estimate temporal components for up to similar to 80 individual patterns. From a propagation of the full error-covariance from GRACE and a diagonal error-covariance from Jason-1 altimetry we find that: (1) GRACE almost entirely explains the mass related parameters in the joint inversion, (2) an inversion using only Jason-1 data has a marginal ability to estimate the mass related parameters, while the steric parameters have much better formal accuracy. In terms of mean sea level rise the steric patterns have a maximum formal accuracy of 0.01 mm for an 11 week running mean. In general, strong negative error correlations (rho < -0.9) exists between the high and low elevation parts of the ice sheet drainage basins, when those are estimated independently. The largest formal errors found are in the order of 40 Gton for small high elevation sub-basins in the southern Greenland ice sheet, which are difficult to separate. In a simplified joint inversion, merging high and low elevation basins, we have investigated the ability of the GRACE and Jason-1 data to separate the geocenter motion into a present-day contribution and a contribution from glacial isostatic adjustment (CIA). We find that the CIA related signal is larger than the present-day component with a maximum of -0.71 mm/year in the Z direction. Total geocenter motion rates are found to be -0.28, 0.43. -1.08 mm/year for the X, Y and Z components, respectively. The inversion results have been propagated to the Jason-1 along-track measurements. Over the time period considered, we see that a large part of the variability in the Pacific, Atlantic and Indian ocean can be explained by our inversion results. The applied inversion method therefore seems a feasible way to separate steric from mass induced sea level changes. At the same time, the joint inversion would benefit from more advanced parameterizations, which may aid in fitting remaining signal from altimetry. (C) 2011 Elsevier Ltd. All rights reserved.

The tidal impact on overflow dynamics and bottom water production in the western Ross Sea is studied with the Finite Element Ocean Model, which allows embedding a mesh with 0.5 km resolution in a coarse resolution (30 km) setup without nesting. The simulated overflow properties inside and downstream of the western Ross Sea are described. The overflow exhibits pronounced variability at both daily and spring‐neap tidal time scales in the western Ross Sea. Tides increase mixing over both the outer shelf and upper slope there. Plume jets are shaped by tidal currents at a bathymetric bend west of the Drygalski Trough mouth, descending rapidly and supplying the bottom water. A fraction of shelf water remains over the shelf and propagates westward from the Ross Sea, but it does not contribute significantly to bottom water formation because of energetic mixing over the upper slope. Compared to a simulation without tidal forcing, tides (with the major K1 and O1 constituents) increase the outflow rate over the continental slope off Cape Adare by about 70%. A set of sensitivity experiments show that the rate of bottom water production is not a monotonic function of the tidal currents amplitude. Tidal forcing with intermediate strength leads to the most efficient bottom water formation.

The data available from satellite altimetry and Argo profiling buoys are combined into Inverse Finite Element Ocean model (IFEOM) for each of the years 1999 and 2008. The model solves for temperature and salinity fields that are close to measurements, respects stationary dynamical balances, and simultaneously produces estimates of the circulation. Several experiments have been performed to reconstruct the interannual variability. We show, that including altimetry improves the circulation picture. We estimate variability of transports and heat content as result of combined assimilation of Argo and altimetry.

Local volume and tracer balances in finite-element models which use continuous shape functions for elevation and tracers are written for patches of elements. Although the locally conserving nodal fluxes can be introduced at the postprocessing stage, they generally lead to an ambiguous definition of transports between two points of the computational mesh and are frequently impractical. Practical computation of transports involves either re-projection or interpolation which, in turn, causes imbalances. The output of Finite Element Ocean circulation Model run on several meshes including the North Atlantic is used to illustrate the ambiguities in transport computations. Simple approximate ways of estimating transports are also discussed. It is shown that imbalances/ambiguities can be significant on coarse (about one degree) unstructured meshes reaching several Sverdrups (106m3/s). This may hamper studies of ocean variability unless appropriate resolution is used.

We derive changes in ocean bottom pressure (OBP) and ocean mass by combining modeled ocean bottom pressure, weekly GRACE‐derived models of gravity change, and large‐scale deformation patterns sensed by a global network of GPS stations in a joint least squares inversion. The weekly combination allows a consistent estimation of geocenter motion, loading mass harmonics up to degree 30, and a spatially uniform mass correction term, which serves as a correction for forcing of the ocean model. We provide maps and time series of ocean mass and bottom pressure variations. Furthermore, we discuss the estimated geocenter motion and the estimated model correction. Our results indicate that the total ocean mass change is predominantly annual, with a maximum amplitude corresponding to 7.4 mm in October, which is in line with earlier work. The mean ocean bottom pressure (i.e., ocean plus atmospheric mass) shows an annual amplitude of 8.7 mm and is shifted forward by about 1.5 months. In addition, the solution exhibits typical autocorrelation times of about 2 weeks. A comparison with in situ bottom pressure time series in the southern Indian Ocean shows a good agreement, with correlations of 0.7–0.8. Based on these comparisons, we see that our results monitor realistic submonthly variations, which are strongest at high latitudes. The addition of GRACE data in the inversion is found to improve these high‐latitude variations and enables better separability of the geocenter motion from other unknowns. Increasing the OBP model error from 3 cm to 4.8 cm affects mainly the higher‐degree coefficients.