A Tailored Computation of the Mean Dynamic Topography for a Consistent Integration into Ocean Circulation Models

Geostrophic surface velocities can be derived from the gradients of the mean dynamic topography—the difference between the mean sea surface and the geoid. Therefore, independently observed mean dynamic topography data are valuable input parameters and constraints for ocean circulation models. For a successful fit to observational dynamic topography data, not only the mean dynamic topography on the particular ocean model grid is required, but also information about its inverse covariance matrix. The calculation of the mean dynamic topography from satellite-based gravity field models and altimetric sea surface height measurements, however, is not straightforward. For this purpose, we previously developed an integrated approach to combining these two different observation groups in a consistent way without using the common filter approaches (Becker et al. in J Geodyn 59(60):99–110, 2012; Becker in Konsistente Kombination von Schwerefeld, Altimetrie und hydrographischen Daten zur Modellierung der dynamischen Ozeantopographie 2012). Within this combination method, the full spectral range of the observations is considered. Further, it allows the direct determination of the normal equations (i.e., the inverse of the error covariance matrix) of the mean dynamic topography on arbitrary grids, which is one of the requirements for ocean data assimilation. In this paper, we report progress through selection and improved processing of altimetric data sets. We focus on the preprocessing steps of along-track altimetry data from Jason-1 and Envisat to obtain a mean sea surface profile. During this procedure, a rigorous variance propagation is accomplished, so that, for the first time, the full covariance matrix of the mean sea surface is available. The combination of the mean profile and a combined GRACE/GOCE gravity field model yields a mean dynamic topography model for the North Atlantic Ocean that is characterized by a defined set of assumptions. We show that including the geodetically derived mean dynamic topography with the full error structure in a 3D stationary inverse ocean model improves modeled oceanographic features over previous estimates.     

Passive tracers in a general circulation model of the Southern Ocean

Passive tracers are used in an off-line version of the United Kingdom Fine Resolution Antarctic Model (FRAM) to highlight features of the circulation and provide information on the inter-ocean exchange of water masses. The use of passive tracers allows a picture to be built up of the deep circulation which is not readily apparent from examination of the veloCity or density fields. Comparison of observations with FRAM results gives good agreement for many features of the Southern Ocean circulation. Tracer distributions are consistent with the concept of a global “conveyor belt” with a return path via the Agulhas retroflection region for the replenishment of North Atlantic Deep Water.     

Joint altimetric and in-situ data assimilation using the GRACE mean dynamic topography: a 1993–1998 hindcast experiment in the Tropical Pacific Ocean

The altimetric satellite signal is the sum of the geoid and the dynamic topography, but only the latter is relevant to oceanographic applications. Poor knowledge of the geoid has prevented oceanographers from fully exploiting altimetric measurements through its absolute component, and applications have concentrated on ocean variability through analyses of sea level anomalies. Recent geodetic missions like CHAMP, GRACE and the forthcoming GOCE are changing this perspective. In this study, data assimilation is used to reconstruct the Tropical Pacific Ocean circulation during the 1993–1996 period. Multivariate observations are assimilated into a primitive equation ocean model (OPA) using a reduced order Kalman filter (the Singular Evolutive Extended Kalman filter). A 6-year (1993–1998) hindcast experiment is analyzed and validated by comparison with observations. In this experiment, the new capability offered by an observed absolute dynamic topography (built using the GRACE geoid to reference the altimetric data) is used to assimilate, in an efficient way, the in-situ temperature profiles from the TAO/TRITON moorings together with the T/P and ERS1&2 altimetric signal. GRACE data improves compatibility between both observation data sets. The difficulties encountered in this regard in previous studies such as Parent et al. (J Mar Syst 40–41:381–401, 2003) are now circumvented. This improvement helps provide more efficient data assimilation, as evidenced, by assessing the results against independent data. This leads in particular to significantly more realistic currents and vertical thermal structures.     

Geoid and Sea Surface Topography Derived from ERS-1 Altimeter Data by the Adjoint Method

A method for splitting sea surface height measurements from satellite altimetry into geoid undulations and sea surface topography is presented. The method is based on a combination of the information from altimeter data and a dynamic sea surface height model. The model consists of geoid undulations and a quasi-geostrophic model for expressing the sea surface topography. The goal is the estimation of those values of the parameters of the sea surface height model that provide a least-squares fit of the model to the data. The solution is accomplished by the adjoint method which makes use of the adjoint model for computing the gradient of the cost function of the least-squares adjustment and an optimization algorithm for obtaining improved parameters. The estimation is applied to the North Atlantic. ERS-1 altimeter data of the year 1993 are used. The resulting geoid agrees well with the geoid of the EGM96 gravity model.     

Assimilating altimetric data to control the tropical instability waves: an observing system simulation experiment study

Tropical instability waves (TIWs) are not easily simulated by ocean circulation models primarily because such waves are very sensitive to wind forcing. In this study, we investigate the impact of assimilating sea surface height (SSH) observations on the control of TIWs in an observing system simulation experiment (OSSE) context based on a regional model configuration of the tropical Atlantic. A Kalman filtering method with suitable adaptations is found to be successful when altimetric data are assimilated in conjunction with sea surface temperature and some in situ temperature/salinity profiles. In this rather realistic system, the TIW phase is roughly controlled with a single nadir observing satellite. However, a right correction of the TIW structure and amplitude requires at least two nadir observing satellites or a wide swath observing satellite. The significant impact of orbital parameters is also demonstrated: in particular, the Jason or GFO satellite orbits are found to be more suitable than the ENVISAT orbit. More generally, it is found that as soon as adequate sub-sampling exists (with periods of 5–10?days), the length of the repetitivity cycle of orbits does not have a significant impact.     

Performance of GOCE and GRACE-derived mean dynamic topographies in resolving Antarctic Circumpolar Current fronts

Presently, two satellite missions, Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE), are making detailed measurements of the Earth’s gravity field, from which the geoid can be obtained. The mean dynamic topography (MDT) is the difference between the time-averaged sea surface height and the geoid. The GOCE mission is aimed at determining the geoid with superior accuracy and spatial resolution, so that a more accurate MDT can be estimated. In this study, we determine the mean positions of the Antarctic Circumpolar Current fronts using the purely geodetic estimates of the MDT constructed from an altimetric mean sea surface and GOCE and GRACE geoids. Overall, the frontal positions obtained from the GOCE and GRACE MDTs are close to each other. This means that these independent estimates are robust and can potentially be used to validate frontal positions obtained from sparse and irregular in situ measurements. The geodetic frontal positions are compared to earlier estimates as well as to those derived from MDTs based on satellite and in situ measurements and those obtained from an ocean data synthesis product. The position of the Sub-Antarctic Front identified in the GOCE MDT is found to be in better agreement with the previous estimates than that identified in the GRACE MDT. The geostrophic velocities derived from the GOCE MDT are also closer to observations than those derived from the GRACE MDT. Our results thus show that the GOCE mission represents an improvement upon GRACE in terms of the time-averaged geoid.     

Recovery of marine gravity anomalies from ERS1, ERS2 and ENVISAT satellite altimetry data for geoid computations over Norway

Free-Air Anomalies (FAA) for the Norwegian marine area including some parts of the North Sea, the Norwegian Sea and the Barents Sea are computed from satellite altimetry data. A total of 84 cycles of ERS2 along-track data, 25 cycles of ENVISAT along-track data and high density ERS1 data during its geodetic mission are used. The new geopotential model from the Gravity Recovery and Climate Experiment (GRACE) mission, GGM02S (Tapely et al., 2005) is used to compute the long wavelength contributions of the geoid and the FAA. To correct data for mean dynamic topography, the available Levitus climatology model (Levitus and Boyer, 1994) is used. Corrected data are then used to compute along-track gradients in each cycle-pass to suppress the orbital and the atmospheric errors below the noise level of the altimeter. Resulted gradients are then stacked and the east-west and the north-south components of the deflection of verticals are computed where ascending and descending tracks meet each other. Finally, the inverse Vening-Meinesz formula is implemented on the gridded deflections to compute FAA. Results are then compared with available marine and airborne data. Standard deviations of ± 4.301 and ± 6.159 mGal in comparison with airborne and marine FAA were achieved. Thereafter, the derived anomalies are combined with marine and airborne FAA together with the land FAA to compute a fine resolution geoid for Norway and the surrounding marine areas. This geoid is evaluated over sea and land with the synthetic geoid (the geoid derived from the mean sea surface by subtracting the mean dynamic topography) and Global Positioning System (GPS)-levelling and the standard deviations of the differences are ± 20.9 and ± 12.8 cm respectively. ali.soltanpour@ntnu.no, hossein.nahavandchi@ntnu.no, kourosh.ghazavi@ntnu.no     

A comparison of GOCE gravitational models with EGM2008

Four new gravity field models from GOCE, two of them combined with GRACE, are compared here with EGM2008. The objectives are to look into the differences in consecutive ranges of the spherical harmonic expansion globally as well as in selected geographical regions and in the regions of the various data sources used for EGM2008. In general, GOCE is able to contribute to improved global gravity models in the spherical harmonic range between 120 and 200 (and above). The agreement between EGM2008 and the GOCE models is very good in well-surveyed regions such as North America, Europe and Australia, with geoid RMS-differences on the order of 4–6 cm. In other regions, where the surface gravity data available for the development of EGM2008 were poor, such as South America, Africa, South-East Asia or China the RMS-differences are on a level of 30 cm. Here GOCE leads to a significant improvement. These findings are confirmed by the analysis of the areas of the various EGM2008 data sources. In the regions of the so-called “fill-in” data of EGM2008 RMS-geoid height differences are high. In Antarctica GOCE also gives important improvements in terms of spatial resolution and accuracy. In general, the agreement between EGM2008 and the GOCE-models up to degree and order (d/o) 200 is good, with a global (excluding the polar gaps of GOCE orbits, throughout) geoid difference RMS of 11 cm, in the ocean areas 8 cm and 20 cm in the continental areas. GOCE models are better suited for ocean circulation studies because no prior ocean information enters into the data reduction process, as it is the case when deducing gravity anomalies from an altimetric mean sea surface. On the other hand, the good consistency between GOCE-models and EGM2008 in ocean areas very likely indicates that the influence of ocean circulation information on EGM2008 is rather small. The four tested GOCE models behave similarly except at the highest latitudes where GOCE lacks data due to its orbit inclination of 96.5° and some form of regularization which has to be applied.     

A dynamically consistent analysis of circulation and transports in the southwestern Weddell Sea

An inverse model is applied for the analysis of hydrographic and current meter data collected on the repeat WOCE section SR4 in the Weddell Sea in 1989–1992. The section crosses the Weddell Sea cyclonic gyre from Kapp Norvegia to the northern end of the Antarctic Peninsula. The concepts of geostrophy, conservation of planetary vorticity and hydrostatics are combined with advective balances of active and passive properties to provide a dynamically consistent circulation pattern. Our variational assimilation scheme allows the calculation of three-dimensional velocities in the section plane. Current speeds are small except along the coasts where they reach up to 12 cm/s. We diagnose a gyre transport of 34 Sverdrup which is associated with a poleward heat transport of 28 × 10¹² W corresponding to an average heat flux of 15 Wm^–2 in the Weddell Sea south of the transect. This exceeds the estimated local flux on the transect of 2 Wm^–2. As the transect is located mostly in the open ocean, we conclude that the shelf areas contribute significantly to the ocean-atmosphere exchange and are consequently key areas for the contribution of the Weddell Sea to global ocean ventilation. Conversion of water masses occuring south of the section transform 6.6 ± 1.1 Sv of the inflowing warm deep water into approximately equal amounts of Weddell Sea deep water and Weddell Sea bottom water. The volume transport of surface water equals in the in-and outflow. This means that almost all newly formed surface water is involved in the deep and bottom water formation. Comparison with the results obtained by pure velocity interpolation combined with a hydrographic data subset indicates major differences in the derived salt transports and the water mass conversion of the surface water. The differences can be explained by deviations in the structure of the upper ocean currents to which shelf areas contribute significantly. Additionally a rigorous variance analysis is performed. When only hydrographic data are used for the inversion both the gyre transport and the poleward heat transport are substantially lower. They amount to less than 40% of our best estimate while the standard deviations of both quantities are 6.5 Sv and 37 × 10¹² W, respectively. With the help of long-term current meter measurements these errors can be reduced to 2 Sv and 8 × 10¹² W. Our result underlines the importance of velocity data or equivalent information that helps to estimate the absolute velocities.     

Turbulent viscosity optimized by data assimilation

As an alternative approach to classical turbulence modelling using a first or second order closure, the data assimilation method of optimal control is applied to estimate a time and space-dependent turbulent viscosity in a three-dimensional oceanic circulation model. The optimal control method, described for a 3-D primitive equation model, involves the minimization of a cost function that quantifies the discrepancies between the simulations and the observations. An iterative algorithm is obtained via the adjoint model resolution. In a first experiment, a k ± L model is used to simulate the one-dimensional development of inertial oscillations resulting from a wind stress at the sea surface and with the presence of a halocline. These results are used as synthetic observations to be assimilated. The turbulent viscosity is then recovered without the k + L closure, even with sparse and noisy observations. The problems of controllability and of the dimensions of the control are then discussed. A second experiment consists of a two-dimensional schematic simulation. A 2-D turbulent viscosity field is estimated from data on the initial and final states of a coastal upwelling event.     

Assimilation of geodetic dynamic ocean topography using ensemble based Kalman filter

Estimation of ocean circulation is investigated via assimilation of satellite measurements of the dynamic ocean topography (DOT) into the global finite-element ocean model (FEOM). The DOT was obtained by means of a geodetic approach from carefully cross-calibrated multi-mission altimeter data and GRACE gravity fields. The spectral consistency was achieved by consistently filtering both, the sea surface and the geoid. The filter length is determined by the spatial resolution of the gravity field and corresponds to approximately 241 km half width for the GRACE-based gravity field model ITG-Grace03s.The assimilation of the geodetic DOT was performed by employing a local singular evolutive interpolated Kalman (SEIK) filter in combination with the method of weighting of observations. It is shown that this approach leads to a successful assimilation technique that reduced the RMS difference between the model and the data from 16 cm to 5 cm during one year of assimilation. The ocean model returns an optimized mean dynamic ocean topography. The effects of assimilation on transport estimates across several hydrographic World Ocean Circulation Experiment (WOCE) sections show improvements compared to the FEOM run without data assimilation. As a result of the assimilation, DOT estimates are available in the polar or coastal regions where the geodetic estimates from satellite data alone are not adequate. Furthermore, more realistic features of the ocean can be seen in these areas compared to those obtained using the filtered data fields.     

Collinear and cross-over adjustment of Geosat ERM and Seasat altimeter data in the Mediterranean Sea

The computation of mean sea surface heights from a set of collinear Geosat ERM altimeter data tracks was carried out in a collinear adjustment, where 1 cy/rev cosine and sine coefficients for each track are estimated, so the differences between the collinear tracks are minimized. Then bias/tilt cross-over adjustments of stacked Geosat and Seasat altimetry were carried out. The problems with the free surface in the cross-over adjusted altimetric surface were treated using the absolute sea surface heights relative to the geoid model OSU89B. In a combined adjustment of the two altimeter data sets using cross-over and height informations simultaneously a RMS of the cross-overs of 0.080 m and a RMS of the sea surface heights relative to OSU89B of 0.611 m were obtained.     

MOM4_L40模式对全球海洋CFC-11分布的模拟及其通风能力评估

CFC-11是评估全球海洋环流模式的一个重要工具,海水中溶解的CFC-11被用来分析全球海洋模式的通风模拟.本文在中国气象局国家气候中心发展的40层全球海洋环流模式(MOM4_L40)增加了示踪物CFC-11模块,然后利用该模式研究了CFC-11在全球海洋中的分布,并评估了模式的通风能力.对CFC-11的海表浓度、柱总含量以及大洋剖面的垂直浓度分布和渗透深度进行了分析,结果表明,与观测相比,模式较好地再现了CFC-11在海洋表面的水平分布特征,CFC-11主要储存区位于西北大西洋、副热带北太平洋及南大洋,其浓度分布与温度分布梯度相反.沿三个大洋的5个剖面的CFC-11垂直分布模拟也与观测基本吻合.模式模拟的CFC-11分布情况与全球平均经向流函数吻合,在南大洋模拟效果更加接近观测值,深海模拟效果较好,渗透深度接近观测.同时,模拟与观测相比也存在偏差.比如在北大西洋主要的存储区域,模式低估了CFC-11的吸收,这与高纬的CFC-11向低纬过度输送有关,可能是受温盐环流和强迫资料的影响.总体来说,MOM_L40模式模拟大洋吸收的CFC-11总量是理想的,通过模拟被动示踪物CFC-11很好地再现了海洋的通风能力.     

Water mass distribution in Fram Strait and over the Yermak Plateau in summer 1997

The water mass distribution in northern Fram Strait and over the Yermak Plateau in summer 1997 is described using CTD data from two cruises in the area. The West Spitsbergen Current was found to split, one part recirculated towards the west, while the other part, on entering the Arctic Ocean separated into two branches. The main inflow of Atlantic Water followed the Svalbard continental slope eastward, while a second, narrower, branch stayed west and north of the Yermak Plateau. The water column above the southeastern flank of the Yermak Plateau was distinctly colder and less saline than the two inflow branches. Immediately west of the outer inflow branch comparatively high temperatures in the Atlantic Layer suggested that a part of the extraordinarily warm Atlantic Water, observed in the boundary current in the Eurasian Basin in the early 1990s, was now returning, within the Eurasian Basin, toward Fram Strait. The upper layer west of the Yermak Plateau was cold, deep and comparably saline, similar to what has recently been observed in the interior Eurasian Basin. Closer to the Greenland continental slope the salinity of the upper layer became much lower, and the temperature maximum of the Atlantic Layer was occasionally below 0.5 °C, indicating water masses mainly derived from the Canadian Basin. This implies that the warm pulse of Atlantic Water had not yet made a complete circuit around the Arctic Ocean. The Atlantic Water of the West Spitsbergen Current recirculating within the strait did not extend as far towards Greenland as in the 1980s, leaving a broader passage for waters from the Atlantic and intermediate layers, exiting the Arctic Ocean. A possible interpretation is that the circulation pattern alternates between a strong recirculation of the West Spitsbergen Current in the strait, and a larger exchange of Atlantic Water between the Nordic Seas and the inner parts of the Arctic Ocean.     

Impact of partial steps and momentum advection schemes in a global ocean circulation model at eddy-permitting resolution

Series of sensitivity tests were performed with a z-coordinate, global eddy-permitting (1/4°) ocean/sea-ice model (the ORCA-R025 model configuration developed for the DRAKKAR project) to carefully evaluate the impact of recent state-of-the-art numerical schemes on model solutions. The combination of an energy–enstrophy conserving (EEN) scheme for momentum advection with a partial step (PS) representation of the bottom topography yields significant improvements in the mean circulation. Well known biases in the representation of western boundary currents, such as in the Atlantic the detachment of the Gulf Stream, the path of the North Atlantic Current, the location of the Confluence, and the strength of the Zapiola Eddy in the south Atlantic, are partly corrected. Similar improvements are found in the Pacific, Indian, and Southern Oceans, and characteristics of the mean flow are generally much closer to observations. Comparisons with other state-of-the-art models show that the ORCA-R025 configuration generally performs better at similar resolution. In addition, the model solution is often comparable to solutions obtained at 1/6 or 1/10° resolution in some aspects concerning mean flow patterns and distribution of eddy kinetic energy. Although the reasons for these improvements are not analyzed in detail in this paper, evidence is shown that the combination of EEN with PS reduces numerical noise near the bottom, which is likely to affect current–topography interactions in a systematic way. We conclude that significant corrections of the mean biases presently seen in general circulation model solutions at eddy-permitting resolution can still be expected from the development of numerical methods, which represent an alternative to increasing resolution.     

Modelling the fine-structure of the geoid: Methods,data requirements and some results

The requirements for precise geoid models on local and regional scales have increased in recent years, primarily due to the ongoing developments in height determination by GPS on land, but also due to oceanographic requirements in using satellite altimetry for recovering dynamic sea-surface topography. Suitable methods for geoid computations from gravity data include Stokes integration, FFT methods, and least-squares collocation. Especially the FFT methods are efficient in handling large amounts of gravity data, and new variants of the methods taking earth curvature rigorously into account provide attractive methods for obtaining continental-scale, high-resolution geoid models. The accuracy of such models may be from 2–5 cm locally, to 50–100 cm on regional scales, depending on gravity data coverage, long wave-length gravity field errors, and datum problems. When approaching the cm-level geoid basic geoid definition questions (geoid or quasigeoid?) become very significant, especially in rugged areas. In the paper the geoid modelling methods and problems are reviewed, and some investigations on local data requirements for cm-level geoid prediction are presented. Some actual results are presented from Scandinavia, where a recent regional high-resolution geoid model yields apparent accuracies of 2–10 cm over GPS baselines of 50 to 2000 km.     

Topographic effects on the wind‐driven ocean circulation

Abstract

This is a study of the influence of bottom topography of an ocean basin on the wind‐driven, barotropic ocean circulation. A detailed investigation is made of the role of vorticity transfer to the ocean bottom in the presence of varying topography. It is shown that the wind‐driven gyre over the topography of the North Atlantic has a transport in the western part of the basin only half of that obtained in an ocean of constant depth.     

Estimating the 4DVAR analysis error of GODAE products

We explore the ocean circulation estimates obtained by assimilating observational products made available by the Global Ocean Data Assimilation Experiment (GODAE) and other sources in an incremental, four-dimensional variational data assimilation system for the Intra-Americas Sea. Estimates of the analysis error (formally, the inverse Hessian matrix) are computed during the assimilation procedure. Comparing the impact of differing sea surface height and sea surface temperature products on both the final analysis error and difference between the model state estimates, we find that assimilating GODAE and non-GODAE products yields differences between the model and observations that are comparable to the differences between the observation products themselves. While the resulting analysis error estimates depend on the configuration of the assimilation system, the basic spatial structures of the standard deviations of the ocean circulation estimates are fairly robust and reveal that the assimilation procedure is capable of reducing the circulation uncertainty when only surface data are assimilated.     

Reflection of equatorial Kelvin waves at eastern ocean boundaries Part II: Pacific and Atlantic Oceans

The effect of viscosity, non linearities, incident wave period and realistic eastern coastline geometry on energy fluxes are investigated using a shallow water model with a spatial resolution of 1/4 degree in both meridional and zonal directions. Equatorial and mid-latitude responses are considered. It is found that (1) the influence of the coastline geometry and the incident wave period is more important for the westward energy flux than for the poleward flux, and (2) the effect of the inclination of the eastern ocean boundary on the poleward energy flux, for the Pacific and Atlantic Oceans, decline as the period of the incident wave increases. Furthermore, the model simulations suggest that the poleward energy fluxes from meridional boundaries give plausible results for motions of seasonal and annual periods. For comparatively shorter periods, a realistic coastline geometry has to be included for more accurate results. It is recommended that any numerical model involving the reflection of baroclinic Rossby waves (of intraseasonal, seasonal or annual periods) on the eastern Pacific or Atlantic Oceans, should consider the effect of the coastline geometry in order to improve the accuracy of the results.