Barotropic Ocean Research Articles

Impact of short period, non‐tidal, temporal mass variability on GRACE gravity estimates

Using orbital simulations of the Gravity Recovery and Climate Experiment (GRACE) spacecraft, we examined the effects on gravity recovery due to short period, non‐tidal temporal mass variability in the atmosphere, ocean, and continental hydrology. We found that the magnitude of the aliasing error was strongly correlated with the power of the high‐frequency variability of the models. Degree error relative to measurement error increased by a factor of ∼20 due to atmospheric aliasing (corresponding to geoid anomalies of approximately 1 mm at 500 km wavelengths), by a factor of ∼10 due to the ocean model, and by a factor of ∼3 due to the continental hydrology model. De‐aliasing done with approximate models gave the greatest reduction in aliasing error for the mid‐degrees and higher. For the atmosphere, the residual error was ∼1/5 times that of the aliasing error. A barotropic ocean model reduced the aliasing error due to a baroclinic model to nearly the level of measurement noise.

Evidence of different ocean responses to atmospheric pressurevariations in the Atlantic, Indian and Pacific Basins as deduced fromERS-2 altimetric data

Abstract. The exponential increase in the use of altimeter data in oceanographic studies in the past two decades has improved the knowledge of the processes that govern the interaction between the ocean and the atmosphere. One of these processes is the response of the ocean to atmospheric pressure variations, which has been deeply analysed in the past. That response is based on the isostatic assumption used to establish a standard correction for altimetric purposes, the Inverse Barometer Correction (IBC). As a general rule, the ocean goes up/down 1cm when the atmospheric pressure goes down/up 1mbar. However, in light of recent works in some oceanic regions, discrepancies arise when the real response is compared to the hypothetical one. It is important to quantify this discrepancy, in order to improve the accuracy of the correction, which is one of the most significant geophysical corrections applied to altimeter records. Some aspects of this response remain unclear, such as the real space-temporal scales where IBC can be applied, the influence of wind, non-isostatic atmospheric pressure-driven signals, and the effect of aliasing from high frequency signals. This paper is an attempt to gain insight into this phenomenon. The data used are the residuals obtained between sea surface heights from the ERS-2 altimeter and the outputs of a global barotropic ocean model. Significant departures from the hypothetical isostatic response in all data series (spatial and temporal domain) have been found, especially in the case of altimeter records. By applying the collinear track method, we observe that the estimated Atlantic Ocean response is quite similar to the one deduced from the isostatic assumption at all latitudinal bands. Nonetheless, the Indian and Pacific Oceans show important departures from the hypothetical value at low latitudes. Results obtained with the crossover track method show important deviations at low latitudes in the three basins. In order to understand why the Atlantic Ocean response is different from the one obtained in the other two, we can infer some explanations based on the interaction of seasonal and intraseasonal signals with the isostatic one. Key words. Meteorology and atmospheric dynamics (ocean-atmosphere interactions). Oceanography: physical (sea level variations; remote sensing, instruments and techniques)

Small viscosity sharp estimates for the global attractor of the 2-D damped-driven Navier-Stokes equations

We consider in this article the damped and driven two-dimensional Navier-Stokes equations at the limit of small viscosity coefficiento! 0 + . In particular, we obtain upper bounds of the order o i1 on the fractal and Hausdorff dimensions of the global attractor for the system on the torus T 2 , on the sphere S 2 and in a bounded domain. Furthermore, in the case of the torus, we establish a lower bound of the order o i1 . This sharp estimate is remarkably smaller than the well established sharp bound for the dimension of the global attractor of the Navier-Stokes equations on the torus T 2 , which is of the order o i4/3 . This means that the damping/friction term plays a significant role in reducing the number of degrees of freedom in this two-dimensional model. This, we believe, is done by dissipating the energy at the large spatial scales which is transferred to these scales via the inverse cascade mechanism. Finally, we remark that the system of equations studied here is related to the Stommel-Charney barotropic ocean circulation model of the gulf stream.

Propagating Bottom Pressure Signals around Antarctica at 1–2-Day Periods and Implications for Ocean Modes

Abstract Previous studies of barotropic ocean dynamics have shown that several global normal modes are possible at periods between 1 and 2 days. The role of these modes in diurnal tidal dynamics is well documented, but finding evidence for their direct excitation by atmospheric forcing has remained elusive. Analyses of a barotropic ocean model and a limited number of bottom pressure records in the Southern Ocean described here provide evidence for large-scale, coherent signals propagating westward around Antarctica at 1–2-day periods. Phases are roughly consistent with the fundamental Kelvin wave structure underlying a number of normal modes with significant expressions in the Southern Ocean. Model and data results suggest the weak excitation of several of these normal modes by atmospheric pressure fluctuations. Strong dissipation also contributes to their weak amplitudes and makes it difficult to detect a truly global signal in the data.

Removing the separation singularity in a barotropic ocean with bottom friction

We consider western boundary outflow in a two-dimensional rectangular basin on a beta plane with bottom drag. The nature of the flow in the boundary layer is determined by a parameter λ which measures the nonlinearity of the flow. When λ is smaller than some critical value λ c, the boundary layer remains attached to the western wall, but as λ is increased above λ c, a separation bubble develops, and the point of separation moves south with increasing λ. If a classical boundary layer expansion as suggested by Prandtl, (Motion of Fluids with Very Little Viscosity, Technical Memo-452, NACA, Washington, DC, 1928) is attempted, a Goldstein separation singularity develops (Quart. J. Mech. Appl. Math. 1 (1948) 43). We show that if an alternative expansion is used inside the boundary layer, this singularity can be removed and the flow can be extended past separation.

Equilibrium surface elevation distribution in a baroclinic ocean with realistic bottom topography

The objective of this study is to theoretically determine the equilibrium surface elevation distribution for the given density field in the ocean with the realistic bottom topography. It is first experimentally demonstrated in a barotropic ocean model experiment that during the process of the geostrophic adjustment in the ocean with the realistic bottom topography the equilibrium surface elevation rapidly adjusts to the most stable state independent of initial conditions. It follows from this result that in a baroclinic ocean the equilibrium gradient of the potential energy that can be converted into the kinetic energy of the vertically averaged flow is rapidly minimized, giving the theoretical solution for the equilibrium surface elevation field. This application of the minimum potential energy principle is experimentally validated in a numerical model simulation of the free surface geostrophic adjustment in the North Atlantic.

Quality of wind stress fields measured by the skill of a barotropic ocean model: Importance of stability of the Marine Atmospheric Boundary Layer

The stability of the Marine Atmospheric Boundary Layer (MABL) plays an important role in the air‐sea exchange of momentum. Hence MABL's stability has an impact on the performance of numerical ocean models, which are driven by wind stress (along with other forcings). Here we investigate the effect of three wind stress parameterizations on the ability of a barotropic model to fit sea‐level measurements from the US‐French satellite TOPEX/POSEIDON (TP). We show that the wind stress parameterization that takes into account the stability of MABL enhances the model's skill to fit the TP data. Because the ocean shows a barotropic response primarily in high latitudes, the model's gain in skill is also in the high latitudes, where the probability of the MABL being unstable is in the 50% to 70% range.

Transformation of the Level of Barotropic Ocean under an Elliptic Region of Disturbances of a Baric Field

We study elevations of the level of a homogeneous ocean caused by a large-scale elliptic anomaly of the field of atmospheric pressure and determine the conditions under which Earth's rotation and the asymmetry of the region of disturbances of the baric field lead to significant deviations of the ocean level from its values given by the law of inverted barometer. Our investigation is based on the numerical analysis of the integral solution of the linear problem. It is shown that the deviations from the law of inverted barometer are especially pronounced in shallow-water regions, at high latitudes, and for strongly asymmetric regions of disturbances of atmospheric pressure.

Barotropic mode errors in an Indian Ocean model associated with the GWR method

Fast barotropic gravity waves in the ocean require that an efficient computational method is applied in ocean models used for climate simulations. The gravity wave retardation (GWR) method is a simple technique that slows down surface waves and allows a simple explicit integration to be used. Here the method is discussed and applied to a layer model of the tropical Indian Ocean subject to monthly climatological wind forcing. The errors introduced by the GWR method on the barotropic ocean circulation and sea surface elevation are analyzed. Comparison to a model integration with a flat bottom demonstrates that GWR integrations with a speed-up factor up to 16 indeed capture some influence of the bottom relief, in the sense that the GWR solutions have less error than if topography was ignored. Integrations with a speed-up factor of up to 8 are found to model the barotropic circulation well, implying that the GWR method can be applied to climate modelling.

Rapid ocean signals in polar motion and length of day

Non‐tidal variability in ocean currents and bottom pressure is substantial at short periods, but relating the associated signals in ocean angular momentum (OAM) to observed polar motion and length of day fluctuations has been difficult. Our simulations using a barotropic ocean model reveal a clear connection between the estimated OAM signals and both polar motion and length of day at periods of 3–10 days. The dynamic response of the oceans to barometric pressure plays an important role in the excitation of rapid rotation signals. The impact of OAM variability is most clear when using GPS‐based Earth orientation measurements with little temporal smoothing. Using the GPS series, and accounting for OAM in addition to atmospheric effects, yields substantial improvements in the excitation budget for rapid polar motion and length of day. The comparisons with Earth rotation data provide a useful check on the rapid ocean variability simulated by the barotropic model.

Modeling the high‐frequency barotropic response of the ocean to atmospheric disturbances: Sensitivity to forcing, topography, and friction

This study examines high‐frequency sea level variations forced by changes in surface atmospheric pressure and wind and their sensitivity to different forcing mechanisms, bottom topography resolution, and amount of friction in a barotropic ocean model. Optimal model performance, defined in terms of the explained variance in satellite altimeter and bottom pressure data, is found when using relatively strong friction, equivalent to a damping timescale of only a few days over the deep ocean, and topography with minimal smoothing. Spatial variations of the optimal friction parameter seem to reflect the roughness of bottom topography. The model demonstrates skill in simulating the wind‐driven response as well as the nonequilibrium response to atmospheric pressure variations.

Sensitivity of the attractor of the barotropic ocean model to external influences: approach by unstable periodic orbits

Abstract. A description of a deterministic chaotic system in terms of unstable periodic orbits (UPO) is used to develop a method of an a priori estimate of the sensitivity of statistical averages of the solution to small external influences. This method allows us to determine the forcing perturbation which maximizes the norm of the perturbation of a statistical moment of the solution on the attractor. The method was applied to the barotropic ocean model in order to determine the perturbation of the wind field which provides the greatest perturbation of the model's climate. The estimates of perturbations of the model's time mean solution and its mean variance were compared with directly calculated values. The comparison shows that some 20 UPOs is sufficient to realize this approach and to obtain a good accuracy.

Indirect effect of the atmosphere through the oceans on the Earth nutation using the torque approach

The atmosphere exerts a direct torque on the Earth, perturbing its rotation. Additionally, the atmosphere exerts pressure, gravitational, and friction forces on the ocean, which induce an indirect effect of the atmosphere on the Earth. The oceanic response consists of variable currents and mass fluxes. These effects change the oceanic torque on the Earth. As the atmosphere has a large diurnal cycle, the indirect torque also presents a large diurnal component. This indirect diurnal torque is investigated using a numerical barotropic ocean model. In particular, we show that a dynamic ocean model is essential to compute the indirect effect of the atmosphere on nutation, as the oceanic response is far from that predicted by a static model. We also point out that the response of the ocean is nevertheless highly correlated with the atmospheric signal for the diurnal timescale but with a large amplification. The amount of ocean bottom friction is found to have a substantial influence on the indirect diurnal torque acting on the Earth. The effect of this indirect torque on the Earth nutation is computed and found to be much larger than the precision of current nutation observations, but results are uncertain in light of discrepancies in the angular momentum and torque balance.

Antarctic Circumpolar Current response to zonally averaged winds

Coherence analysis techniques are used to compare Southern Ocean wind forcing with Antarctic Circumpolar Current transport. Winds are derived from five different products: ERS winds that have been bin‐averaged, weekly gridded ERS winds produced by the Centre ERS d'Archivage et de Traitement, 5 day winds from the Special Sensor Microwave Imager, analysis winds from the European Centre for Medium‐Range Weather Forecasts, and reanalysis winds from the National Centers for Environmental Prediction. Barotropic transport is estimated from the pressure difference between bottom pressure gauges deployed on either side of Drake Passage by Proudman Oceanographic Laboratory as part of the World Ocean Circulation Experiment. Surface transport is estimated from TOPEX altimetry. Results indicate that transport and wind forcing are coherent over a broad range of frequencies, corresponding to time periods of roughly 10–256 days. Highest coherences occur for winds at latitudes on the south side of Drake Passage. Barotropic ocean transport lags wind forcing not by a constant time interval but by a constant phase lag of about one eighteenth of a cycle at a broad range of frequencies, suggesting that the oceanic response to wind is controlled by both the tendency term and a frequency‐dependent viscous process. Surface transport lags by a longer phase interval. Wind stress curl north of Drake Passage is more coherent with transport than is wind stress curl in the latitudes of Drake Passage. Ocean transport lags wind stress curl, suggesting that transport fluctuations are not governed by a simple Sverdrupian vorticity balance. Like the observations, general circulation model transports from the Parallel Ocean Program and from the Parallel Ocean Climate Model are coherent with wind stress from the south side of Drake Passage and with wind stress curl from latitudes north of Drake Passage. Unlike the observations, model transport and bottom pressure vary almost simultaneously with the wind and do not replicate the observed phase lags, implying that the effective model viscosity may be too large.

Correction to “Assimilation of coastal acoustic tomography data into a barotropic ocean model”

Correction to “Assimilation of coastal acoustic tomography data into a barotropic ocean model”

Assimilation of coastal acoustic tomography data into a barotropic ocean model

A data assimilation technique was applied to analyze the first coastal acoustic tomography data, obtained in the Neko‐Seto Channel of the Seto Inland Sea, Japan on March 2–3, 1999. The ensemble Kaiman filter technique accompanied by the forecast of error covariances by means of the Monte Carlo method is found to be best fitted to the present problem because currents in the tomography region are dominated by the strongly nonlinear tidal vortices. Furthermore, the analyzed results are in better agreement with the shipboard ADCP results than those obtained by the inverse analysis of the travel time difference data for the pairs of acoustic stations.

Wind stress forcing of the North Sea 'pole tide'

We conduct numerical simulations of the wind forcing of sea level variations in the North Sea using a barotropic ocean model with realistic geography and bathymetry to examine the forcing of the 14 month ‘pole tide’, which is known to be anomalously large along the Denmark–Netherlands coast. The simulation input is the monthly mean surface wind stress field from the National Centers for Environmental Prediction (NCEP) reanalysis for the 40 year period 1958–1997. The ocean model output sea level response is then compared with 10 coastal tide gauge records from the Permanent Service for Mean Sea Level (PSMSL) over the same period of time. Besides the strong seasonal variations, several prominent quasi-periodicities exist near 7 years, 3 years, 14 months, 9 months and 6.5 months. Correlations and spectral analyses show remarkable agreement between the model output and the observations, particularly in the 14 month, or Chandler, period band. The latter indicates that the enhanced pole tide found in the North Sea along the Denmark–Netherlands coast is actually the coastal set-up response to wind stress forcing with a periodicity of around 14 months. We find no need to invoke a geophysical explanation involving resonance enhancement of the pole tide in the North Sea to explain the observations.

Physics of the 9-Month Variability in the Gulf Stream Region: Combining Data and Dynamical Systems Analyses

Using nonseasonal altimeter data and SST observations of the North Atlantic, and more specifically the Gulf Stream region, dominant patterns of variability are determined using multivariate time series analyses. A statistically significant propagating mode of variability with a timescale close to 9 months is found, the latter timescale corresponding to dominant variability found in earlier studies. In addition, output from a high resolution simulation of the Parallel Ocean Climate Model (POCM) is analyzed, which also displays variability on a timescale of 9 months, although not statistically significant at the 95% confidence level. The vertical structure of this 9-month mode turns out to be approximately equivalent barotropic. Following the idea that this mode is due to internal ocean dynamics, steady flow patterns and their instabilities are determined within a barotropic ocean model of the North Atlantic using techniques of numerical bifurcation theory. Within this model, there appear to be two different mean flow paths of the Gulf Stream, both of which become unstable to oscillatory modes. For reasonable values of the parameters, an oscillatory instability having a timescale of 9 months is found. The connection between results from the bifurcation analysis, from the analysis of the observations, and from the analysis of the POCM output is explored in more detail and leads to the conjecture that the 9-month variability is related to a barotropic instability of the wind-driven gyres.

The Influence of Negative Viscosity on Wind-Driven, Barotropic Ocean Circulation in a Subtropical Basin

Abstract In this paper, a new barotropic wind-driven circulation model is proposed to explain the enhanced transport of the western boundary current and the establishment of the recirculation gyre. In this model the harmonic Laplacian viscosity including the second-order term (the negative viscosity term) in the Prandtl mixing length theory is regarded as a tentative subgrid-scale parameterization of the boundary layer near the wall. First, for the linear Munk model with weak negative viscosity its analytical solution can be obtained with the help of a perturbation expansion method. It can be shown that the negative viscosity can result in the intensification of the western boundary current. Second, the fully nonlinear model is solved numerically in some parameter space. It is found that for the finite Reynolds numbers the negative viscosity can strengthen both the western boundary current and the recirculation gyre in the northwest corner of the basin. The drastic increase of the mean and eddy kinetic en...

On the “genetic memory” of chaotic attractor of the barotropic ocean model

The structure of attractor of barotropic ocean model is studied in this paper. Theorems of the existence of the attractor for the finite dimensional approximation of this model are proved as well as its convergence to the attractor of the model itself. Some properties of stationary solutions of this model and their stability are discussed. The structure of the attractor is partially explained by the sequence of bifurcations the system is subjected to by variations of leading parameters. The principal feature of the studied system is the existence of two “almost invariant” basins of chaotic attractor with very rare transitions between them. This is related to the rise of a couple of non-symmetric stable stationary solutions in the model with symmetric forcing. The “memory” of chaos appears also in the presence of maxima in the spectrum of energy. These maxima correspond either to the principal frequency of the limit cycle which arose in the Hopf bifurcation, or to the frequencies of the Feigenbaum phenomenon.