Parallel Ocean Program Research Articles

On the time‐mean state of ocean models and the properties of long range acoustic propagation

Receptions on three vertical hydrophone arrays from basin‐scale acoustic transmissions in the North Pacific during 1996 and 1998 are used to test the time‐mean sound‐speed properties of the World Ocean Atlas 2005 (WOA05), of an eddying unconstrained simulation of the Parallel Ocean Program (POP), and of three data‐constrained solutions provided by the estimating the circulation and climate of the ocean (ECCO) project: a solution based on an approximate Kalman filter from the Jet Propulsion Laboratory (ECCO‐JPL), a solution based on the adjoint method from the Massachusetts Institute of Technology (ECCO‐MIT), and an eddying solution based on a Green's function approach from ECCO, Phase II (ECCO2). Predictions for arrival patterns using annual average WOA05 fields match observations to within small travel time offsets (0.3–1.0 s). Predictions for arrival patterns from the models differ substantially from the measured arrival patterns, from the WOA05 climatology, and from each other, both in terms of travel time and in the structure of the arrival patterns. The acoustic arrival patterns are sensitive to the vertical gradients of sound speed that govern acoustic propagation. Basin‐scale acoustic transmissions, therefore, provide stringent tests of the vertical temperature structure of ocean state estimates. This structure ultimately influences the mixing between the surface waters and the ocean interior. The relatively good agreement of the acoustic data with the more recent ECCO solutions indicates that numerical ocean models have reached a level of accuracy where the acoustic data can provide useful additional constraints for ocean state estimation.

Failure analysis of parameter-induced simulation crashes in climate models

Abstract. Simulations using IPCC (Intergovernmental Panel on Climate Change)-class climate models are subject to fail or crash for a variety of reasons. Quantitative analysis of the failures can yield useful insights to better understand and improve the models. During the course of uncertainty quantification (UQ) ensemble simulations to assess the effects of ocean model parameter uncertainties on climate simulations, we experienced a series of simulation crashes within the Parallel Ocean Program (POP2) component of the Community Climate System Model (CCSM4). About 8.5% of our CCSM4 simulations failed for numerical reasons at combinations of POP2 parameter values. We applied support vector machine (SVM) classification from machine learning to quantify and predict the probability of failure as a function of the values of 18 POP2 parameters. A committee of SVM classifiers readily predicted model failures in an independent validation ensemble, as assessed by the area under the receiver operating characteristic (ROC) curve metric (AUC > 0.96). The causes of the simulation failures were determined through a global sensitivity analysis. Combinations of 8 parameters related to ocean mixing and viscosity from three different POP2 parameterizations were the major sources of the failures. This information can be used to improve POP2 and CCSM4 by incorporating correlations across the relevant parameters. Our method can also be used to quantify, predict, and understand simulation crashes in other complex geoscientific models.

Activation of the operational ecohydrodynamic model (3D CEMBS) – the hydrodynamic part

The paper describes the hydrodynamic part of the coupled ice-ocean model that also includes the ecosystem predictive model. The Baltic Sea model is based on the Community Earth System Model (CESM from NCAR – National Centre for Atmospheric Research). CESM was adopted for the Baltic Sea as a coupled sea-ice model. It consists of the Community Ice CodE (CICE, model version 4.0) and the Parallel Ocean Program (POP, version 2.1). The models are linked through a coupler (CPL7), which is based on the Model Coupling Toolkit (MCT) library. The current horizontal resolution is about 2km (1/48 degrees). The ocean model has 21 vertical levels and is forced by atmospheric fields from the European Centre for Medium Weather Forecast (ECMWF). A preliminary validation of the hydrodynamic module with in situ measurements and reanalysis from My Ocean (http://www.myocean.eu) has also been done. In the operational mode, 48-hour atmospheric forecasts provided by the UM model from the Interdisciplinary Centre for Mathematical and Computational Modelling of Warsaw University (ICM) are used. The variables presented on the website in real time for a 48-hour forecast are temperature, salinity, currents, sea surface height, ice thickness and ice coverage (http://deep.iopan.gda.pl/CEMBaltic/newlay/index.php). The embedded model of the marine ecosystem, like ice, is not taken into account in this paper.

A multi-resolution approach to global ocean modeling

A new global ocean model (MPAS-Ocean) capable of using enhanced resolution in selected regions of the ocean domain is described and evaluated. Three simulations using different grids are presented. The first grid is a uniform high-resolution (15km) mesh; the second grid has similarly high resolution (15km) in the North Atlantic (NA), but coarse resolution elsewhere; the third grid is a variable resolution grid like the second but with higher resolution (7.5km) in the NA. Simulation results are compared to observed sea-surface height (SSH), SSH variance and selected current transports. In general, the simulations produce subtropical and subpolar gyres with peak SSH amplitudes too strong by between 0.25 and 0.40m. The mesoscale eddy activity within the NA is, in general, well simulated in both structure and amplitude. The uniform high-resolution simulation produces reasonable representations of mesoscale activity throughout the global ocean. Simulations using the second variable-resolution grid are essentially identical to the uniform case within the NA region. The third case with higher NA resolution produces a simulation that agrees somewhat better in the NA with observed SSH, SSH variance and transports than the two 15km simulations. The actual throughput, including I/O, for the x1-15km simulation is the same as the structured grid Parallel Ocean Program ocean model in its standard high-resolution 0.1° configuration. Our overall conclusion is that this ocean model is a viable candidate for multi-resolution simulations of the global ocean system on climate-change time scales.

Interaction of ocean temperature advection, surface heat fluxes and sea ice in the marginal ice zone during the North Atlantic Oscillation in the 1990s: A modeling study

A moderately fine‐resolution (0.4°, 40 vertical levels), global, coupled ice‐ocean model was configured and run for 24 years (1979–2002), forced with high‐frequency National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) atmospheric fluxes. The model consists of the Los Alamos National Laboratory Parallel Ocean Program (POP) and sea ice model (CICE). The fidelity of the simulated mean climatological state and variability of key variables such as ice concentration, total ice area, ice thickness and drift were compared to observational data sets from satellite and ice drift buoy measurements. Basin‐scale changes in the lower atmosphere/surface ocean/sea‐ice in the simulated Arctic and Nordic Seas before and after the North Atlantic Oscillation (NAO) phase switch in 1995 were examined using winter composite analyses over the period 1990–1999. Ice cover changes between the two NAO phases were consistent with observations in that reduced concentrations were found in the Nordic and Barents Seas and increased values occurred in the Labrador Sea. Next we regionally evaluated the relative importance of winter anomalies of upper‐ocean mixed layer net heat fluxes and of ocean temperature advection on marginal ice zone variability in the Irminger, Greenland, and Barents Seas for this ten‐year period. We found that the net heat flux winter anomaly was at least four times more important than the winter anomaly of ocean temperature advection in the Greenland and Barents Seas, while it was twice as important in the Irminger Sea. The Ekman ocean temperature advection component generally dominated the geostrophic component in all three regions.

Rossby Waves and the Variability of the North Pacific Current during 2002–03

Abstract A numerical model, the Parallel Ocean Program (POP), with 0.25° horizontal spatial resolution and 28 vertical levels is used to simulate the circulation of the North Pacific Ocean for the time period 1960–2006. Spectral nudging is used so that model drift of the mean state over the 46-yr time period of the simulation is prevented while allowing for the prognostic evolution of the circulation at time scales that are not nudged. The simulation successfully reproduces a southward shift in the North Pacific Current in 2002–03 as calculated from scalar observations. It is suggested that this calculated shift may not be solely due to meridional current drift but also a consequence of the shifting intensity of two eastward-moving current bands separated by 300–500 km, a distance consistent with the Rhines scale (the scale at which the 2D turbulence cascade tends to be arrested), which implies an influence from Rossby waves that are heavily affected by nonlinearities. The simulation suggests that the North Pacific Current may indeed have been influenced by a Rossby wave–like disturbance. This disturbance could have been forced to a significant extent by the local winds, but there is also evidence in the model for a coastally generated Rossby wave–like disturbance. This coastal disturbance was generated during the 1997/98 ENSO and traveled westward from the coast at about 1 cm s−1, taking 3–5 yr to travel into the region of the North Pacific Current. The noncoastal portion of the disturbance, which was generated by the local winds away from the coast, propagated westward at about 1 cm s−1 as well.

Simulated eddy induced vertical velocities in a Gulf of Alaska model

Mesoscale eddies can distribute nutrients, heat and fresh water into the Gulf of Alaska (GOA) from the coastal margins. While many studies have investigated the physical characteristics of GOA eddies, their effects on passive-dispersive particles have not been previously simulated to investigate eddy induced upwelling. A climatologically forced Parallel Ocean Program simulation of the north Pacific Ocean with an online particle tracking scheme was used to simulate passive-dispersive particles in the Gulf of Alaska. In-eddy vertical Lagrangian velocities of the particles were calculated both inside and outside the eddies and showed upwelling rates are generally greater inside the eddies where the vertical velocities of the particles ranged from 0.2 to 0.7 m/day.

Near-Surface Eddy Heat and Momentum Fluxes in the Antarctic Circumpolar Current in Drake Passage

Abstract The authors present new estimates of the eddy momentum and heat fluxes from repeated high-resolution upper-ocean velocity and temperature observations in Drake Passage and interpret their role in the regional Antarctic Circumpolar Current (ACC) momentum balance. The observations span 7 yr and are compared to eddy fluxes estimated from a 3-yr set of output archived from an eddy-resolving global Parallel Ocean Program (POP) numerical simulation. In both POP and the observations, the stream-averaged cross-stream eddy momentum fluxes correspond to forcing consistent with both a potential vorticity flux into the axis of the Subantarctic Front (SAF) and a sharpening of all three main ACC fronts through Drake Passage. Further, the POP analysis indicates that the mean momentum advection terms reflect the steering of the mean ACC fronts and are not fully balanced by the eddy momentum forcing, which instead impacts the strength and number of ACC fronts. The comparison between POP and observed eddy heat fluxes was less favorable partly because of model bias in the water mass stratification. Observed cross-stream eddy heat fluxes are generally surface intensified and poleward in the ACC fronts, with values up to approximately −290 ± 80 kW m−2 in the Polar and Southern ACC Fronts. Interfacial form stresses FT, derived from observed eddy heat fluxes in the SAF, show little depth dependence below the Ekman layer. Although FT appears to balance the surface wind stress directly, the estimated interfacial form stress divergence is only an order of magnitude greater than the eddy momentum forcing in the SAF. Thus, although the eddy momentum forcing is of secondary importance in the momentum balance, its effect is not entirely negligible.

Simulation of Mixed Layer Depth in the Northeast Pacific Utilizing Spectral Nudging

Abstract A numerical model, the Parallel Ocean Program (POP), is used to run a 46-yr simulation of the North Pacific Ocean beginning in January 1960. The model has 0.25° horizontal resolution and 28 vertical levels, and it employs spectral nudging, which, unlike standard nudging, nudges only specific frequency and wavenumber bands. This simulation is nudged to the mean and annual Levitus climatological potential temperature and salinity. The model was forced with National Centers for Environmental Prediction (NCEP) mean monthly winds, sea level pressure, net heat flux, and rain rate. The simulated mixed layer depths (MLD) suggest significant shoaling of the MLD between 1970 and 2006, with faster rates in the northern Gulf of Alaska and slower rates to the west and south of Line Papa. The rates are of similar magnitude to those found in past studies and are consistent with the observed freshening and warming of the upper waters in the Gulf of Alaska. The rates are not spatially uniform, and the simulated MLD in the northeast Pacific actually deepens with time at some locations. These regions of increase form zonal bands in the simulation. The simulated MLD at Ocean Weather Station Papa (OWSP) shoals on average, but it is located close to one of these deepening bands. On average, the simulated, low-frequency MLD at OWSP gives a good indication of the MLD along Line Papa and in the Gulf of Alaska near Line Papa’s latitude. The correlation coefficient between the MLD at OWSP and the latitudinal average of the MLD within the greater Gulf of Alaska (with OWSP removed) is 0.7 at zero lag. The correlation coefficient between the MLD at OWSP and the latitudinal average along Line Papa alone (with OWSP removed) is 0.6 at zero lag. Observed variability of the MLD along Line Papa and at OWSP is reproduced by the model. However, there is considerable spatial variability in the simulated MLD in the Gulf of Alaska as a whole, so MLD variability at OWSP is not necessarily a good indicator of the MLD variability throughout the region. Over the span of the simulation, the low-frequency MLD variability in the Gulf of Alaska is better correlated to the North Pacific Gyre Oscillation (NPGO) than to either the Pacific decadal oscillation (PDO) or Southern Oscillation index (SOI).

Marine methane cycle simulations for the period of early global warming

Geochemical environments, fates, and effects are modeled for methane released into seawater by the decomposition of climate-sensitive clathrates. A contemporary global background cycle is first constructed, within the framework of the Parallel Ocean Program. Input from organics in the upper thermocline is related to oxygen levels, and microbial consumption is parameterized from available rate measurements. Seepage into bottom layers is then superimposed, representing typical seabed fluid flow. The resulting CH{sub 4} distribution is validated against surface saturation ratios, vertical sections, and slope plume studies. Injections of clathrate-derived methane are explored by distributing a small number of point sources around the Arctic continental shelf, where stocks are extensive and susceptible to instability during the first few decades of global warming. Isolated bottom cells are assigned dissolved gas fluxes from porous-media simulation. Given the present bulk removal pattern, methane does not penetrate far from emission sites. Accumulated effects, however, spread to the regional scale following the modeled current system. Both hypoxification and acidification are documented. Sensitivity studies illustrate a potential for material restrictions to broaden the perturbations, since methanotrophic consumers require nutrients and trace metals. When such factors are considered, methane buildup within the Arctic basin is enhanced. However, freshened polar surface waters act as a barrier to atmospheric transfer, diverting products into the deep return flow. Uncertainties in the logic and calculations are enumerated including those inherent in high-latitude clathrate abundance, buoyant effluent rise through the column, representation of the general circulation, and bacterial growth kinetics.

Transport of 137Cs to the Southern Hemisphere in an ocean general circulation model

137Cs originating from global fallout is transported into the ocean interior by advection and diffusion, and the 137Cs concentration is reduced by radioactive decay. 137Cs concentrations in the global ocean can be simulated by global integration of the coarse-resolution Parallel Ocean Program to understand the mechanism of material transport in the ocean. We investigated the transport mechanism of 137Cs to the Southern Hemisphere using an ocean general circulation model (OGCM) and compared the simulated results with observations of 137Cs concentrations in the Southern Hemisphere. 137Cs was deposited on the ocean surface mainly as global fallout originating from atmospheric nuclear weapons testing since 1945, and the global distribution of cumulative 137Cs deposition has been reconstructed from global measurements of 137Cs in rain, seawater, and soil. We estimated the global distribution of 137Cs deposition from 1945 to 2003 using these distribution data, 137Cs deposition data observed at the Meteorological Research Institute, Tsukuba, Japan, from 1958 to 2003, and 137Cs deposition data for 1945–1957 estimated from ice-core data. We compared the simulated results with 137Cs sections from the South Pacific, Indian, and South Atlantic Oceans obtained during the BEAGLE2003 cruise in 2003. The simulated 137Cs sections were in good agreement with the observations, except for the effects of mesoscale eddies, which not be simulated by the model because of its coarse resolution. OGCMs can simulate the general pattern of 137Cs distribution in the world’s oceans and improve our understanding of the transport mechanism leading to those 137Cs distributions on a time scale of several decades. The model simulation results suggest that the 137Cs deposited in the North Pacific advected to the South Pacific and Indian Ocean, and then to the South Atlantic over about four decades. The North Pacific is thus an important source area of 137Cs to the Southern Hemisphere.

Understanding Checkpointing Overheads on Massive-Scale Systems: Analysis of the IBM Blue Gene/P System

Providing fault tolerance in high-end petascale systems, consisting of millions of hardware components and complex software stacks, is becoming an increasingly challenging task. Checkpointing continues to be the most prevalent technique for providing fault tolerance in such high-end systems. Considerable research has focussed on optimizing checkpointing; however, in practice, checkpointing still involves a high-cost overhead for users. In this paper, we study the checkpointing overhead seen by various applications running on leadership-class machines like the IBM Blue Gene/P at Argonne National Laboratory. In addition to studying popular applications, we design a methodology to help users understand and intelligently choose an optimal checkpointing frequency to reduce the overall checkpointing overhead incurred. In particular, we study the Grid-Based Projector-Augmented Wave application, the Carr-Parrinello Molecular Dynamics application, the Nek5000 computational fluid dynamics application and the Parallel Ocean Program application—and analyze their memory usage and possible checkpointing trends on 65,536 processors of the Blue Gene/P system.

Isopycnal diffusivities in the Antarctic Circumpolar Current inferred from Lagrangian floats in an eddying model

Lagrangian subsurface isopycnal eddy diffusivities are calculated from numerical floats released in several regions of the Antarctic Circumpolar Current (ACC) of the 0.1° Parallel Ocean Program. Lagrangian diffusivities are horizontally highly variable with no consistent latitudinal dependence. Elevated values are found in some areas in the core of the ACC, near topographic features, and close to the Brazil‐Malvinas Confluence Zone and Agulhas Retroflection. Cross‐stream eddy diffusivities are depth invariant in the model ACC. An increase of Lagrangian eddy length scales with depth is masked by the strong decrease with depth of eddy velocities. The cross‐stream diffusivities average 750 ± 250 m2s−1around the Polar Frontal Zone. The results imply that parameterizations that (only) use eddy kinetic energy to parameterize the diffusivities are incomplete. We suggest that dominant correlations of Lagrangian eddy diffusivities with eddy kinetic energy found in previous studies may have been due to the use of too short time lags in the integration of the velocity autocovariance used to infer the diffusivities. We find evidence that strong mean flow inhibits cross‐stream mixing within the ACC, but there are also areas where cross‐stream diffusivities are large in spite of strong mean flows, for example, in regions close to topographic obstacles such as the Kerguelen Plateau.

Performance and Scalability Evaluation of ‘Big Memory’ on Blue Gene Linux

We address memory performance issues observed in Blue Gene Linux and discuss the design and implementation of ‘Big Memory’——an alternative, transparent memory space introduced to eliminate the memory performance issues. We evaluate the performance of Big Memory using custom memory benchmarks, NAS Parallel Benchmarks, and the Parallel Ocean Program, at a scale of up to 4,096 nodes. We find that Big Memory successfully resolves the performance issues normally encountered in Blue Gene Linux. For the ocean simulation program, we even find that Linux with Big Memory provides better scalability than does the lightweight compute node kernel designed solely for high-performance applications. Originally intended exclusively for compute node tasks, our new memory subsystem dramatically improves the performance of certain I/O node applications as well. We demonstrate this performance using the central processor of the LOw Frequency ARray radio telescope as an example.

Special Issue: Advances in High‐Performance Computing and Communications

Special Issue: Advances in High‐Performance Computing and Communications

Workload performance characterization of DARPA HPCS benchmarks

AbstractIt is critical to understand the workload characteristics and resource usage patterns of available applications to guide the design and development of hardware and software stacks of future machines. In this article, we analyze the workload performance characteristics of three large‐scale DARPA HPCS benchmarks: Hybrid Coordinate Ocean Model, Parallel Ocean Program, and Lattice Boltzemann Magneto‐Hydrodynamics Code while executing on IBM Power5+ processor machines. Our analysis is focused on the CPU/memory performance using Cycles Per Instruction (CPI) model and multiprocess communication performance using MPI traces. For each benchmark, we provide a high‐level performance analysis followed by the hotspot analysis for selected input parameters. Then we present a detailed workload performance characterization using CPI model with data from a unique set of performance counters available on the Power5+ processor system. From communication performance analysis, we describe the sources of load imbalances in the applications and identify the potential impediments to the scalability of the applications under large processor counts. We identify several sources of performance problems that are potential bottlenecks and discuss methods to ameliorate them. We also present a comparative analysis of these benchmarks to summarize the similarities and differences in their performance characteristics. Copyright © 2009 John Wiley & Sons, Ltd.

A decade of acoustic thermometry in the North Pacific Ocean

Over the decade 1996–2006, acoustic sources located off central California (1996–1999) and north of Kauai (1997–1999, 2002–2006) transmitted to receivers distributed throughout the northeast and north central Pacific. The acoustic travel times are inherently spatially integrating, which suppresses mesoscale variability and provides a precise measure of ray‐averaged temperature. Daily average travel times at 4‐day intervals provide excellent temporal resolution of the large‐scale thermal field. The interannual, seasonal, and shorter‐period variability is large, with substantial changes sometimes occurring in only a few weeks. Linear trends estimated over the decade are small compared to the interannual variability and inconsistent from path to path, with some acoustic paths warming slightly and others cooling slightly. The measured travel times are compared with travel times derived from four independent estimates of the North Pacific: (1) climatology, as represented by the World Ocean Atlas 2005 (WOA05); (2) objective analysis of the upper‐ocean temperature field derived from satellite altimetry and in situ profiles; (3) an analysis provided by the Estimating the Circulation and Climate of the Ocean project, as implemented at the Jet Propulsion Laboratory (JPL‐ECCO); and (4) simulation results from a high‐resolution configuration of the Parallel Ocean Program (POP) model. The acoustic data show that WOA05 is a better estimate of the time mean hydrography than either the JPL‐ECCO or the POP estimates, both of which proved incapable of reproducing the observed acoustic arrival patterns. The comparisons of time series provide a stringent test of the large‐scale temperature variability in the models. The differences are sometimes substantial, indicating that acoustic thermometry data can provide significant additional constraints for numerical ocean models.

Observation and origin of an interannual salinity anomaly in the Mozambique Channel

A positive salinity anomaly of 0.2 PSU was observed between 50 and 200 m over the years 2000–2001 across the Mozambique Channel at a section at 17°S which was repeated in 2003, 2005, 2006, and 2008. Meanwhile, a moored array is continued from 2003 to 2008. This anomaly was most distinct showing an interannual but nonseasonal variation. The possible origin of the anomaly is investigated using output from three ocean general circulation models (Estimating the Circulation and Climate of the Ocean, Ocean Circulation and Climate Advanced Modeling, and Parallel Ocean Program). The most probable mechanism for the salinity anomaly is the anomalous inflow of subtropical waters caused by a weakening of the northern part of the South Equatorial Current by weaker trade winds. This mechanism was found in all three numerical models. In addition, the numerical models indicate a possible salinization of one of the source water masses to the Mozambique Channel as an additional cause of the anomaly. The anomaly propagated southward into the Agulhas Current and northward along the African coast.

Estimates of bottom flows and bottom boundary layer dissipation of the oceanic general circulation from global high‐resolution models

This paper (1) compares the bottom flows of three existing high‐resolution global simulations of the oceanic general circulation to near‐bottom flows in a current meter database and (2) estimates, from the simulations, the global energy dissipation rate of the general circulation by quadratic bottom boundary layer drag. The study utilizes a data‐assimilative run of the Naval Research Laboratory Layered Ocean Model (NLOM), a nonassimilative run of NLOM, and a nonassimilative run of the Parallel Ocean Program z‐level ocean model. Generally speaking, the simulations have some difficulty matching the flows in individual current meter records. However, averages of model values of (the time average of the cube of bottom velocity, which is proportional to the dissipation rate) computed over all the current meter sites agree to within a factor of 2.7 or better with averages computed from the current meters, at least in certain depth ranges. The models therefore likely provide reasonable order‐of‐magnitude estimates of areally integrated dissipation by bottom drag. Global dissipation rates range from 0.14 to 0.65 TW, suggesting that bottom drag represents a substantial sink of the ∼1 TW wind‐power transformed into geostrophic motions.

Assessing eddy heat flux and its parameterization: A wavenumber perspective from a 1/10° ocean simulation

Diffusivities diagnosed from eddy heat fluxes in eddying models tend to show unphysically large positive and negative values. These have been attributed to rotational components that do not influence the heat budget. The rotational component of the horizontal eddy heat flux is diagnosed in the Southern Ocean of the 1/10° Parallel Ocean Program as a function of averaging lengthscale. At the scales at which most of the eddy heat flux energy occurs, the rotational component, as measured by its curl, accounts for more than 95% of the total flux, increasing to more than 99% with increasing lengthscale. Hence, rotational components are the dominant component of eddy fluxes even when they are averaged over scales larger than the eddy scales. The rotational component can be approximated by its projection along temperature variance contours; however this only accounts for a fraction of the total rotational component, leaving a residual that is still more rotational than divergent. The eddy heat flux can be parameterized as a function of averaging lengthscale using coherence analysis. The meridional eddy heat flux is most coherent with its parameterizations on lengthscales larger than 50°, but this coherence is due to the rotational component. The divergence of the eddy heat flux is most coherent with the divergence of the parameterizations on scales less than 4°, where the curl of the eddy heat flux has a minimum. Diffusivities estimated from the eddy heat flux show a high wavenumber dependence and are as high as 15 , 000 m 2 s - 1 , reflecting the presence of the rotational component. Using the divergence, more realistic, less wavenumber dependent values are estimated, ranging from 500 m 2 s - 1 within the ACC to 1000 m 2 s - 1 in the near surface ocean in the Agulhas Retroflection region.