Primitive Equation Ocean Model Research Articles

The performance of implicit ocean models on B- and C-grids

Fully-implicit primitive equation ocean models are useful to study the sensitivity of steady ocean flows to parameters, to determine bifurcations of these flows associated with instabilities and to use relatively large time steps in transient flow computations. This paper addresses a problem related to the origin of wiggles occurring in fully-implicit C-grid models. The situation considered is the computation of three-dimensional thermally-driven steady flows in a midlatitude spherical sector. We determine the reason why in a coarse resolution C-grid implicit model, the values of the lateral friction coefficients are restricted to far higher values than for the same B-grid model. The analysis also reveals why the B-grid discretization is superior for the computation of this type of flows.

Tide-topography interaction along the eastern Brazilian shelf

In the Tropics, continental shelves governed by western boundary currents are considered to be among the least productive ocean margins in the world, unless eddy-induced shelf-edge upwelling becomes significant. The eastern Brazilian shelf in the Southwest Atlantic is one of these, and since the slight nutrient input from continental sources is extremely oligotrophic. It is characterized by complex bathymetry with the presence of shallow banks and seamounts. In this work, a full three-dimensional nonlinear primitive equation ocean model is used to demonstrate that the interaction of tidal currents and the bottom topography of the east Brazil continental shelf is capable of producing local upwelling of South Atlantic Central Water, bringing nutrients up from deep waters to the surface layer. Such upper layer enrichment is found to be of significance in increasing local primary productivity.

The Effects of Mesoscale Eddies on the Stratification and Transport of an Ocean with a Circumpolar Channel

AbstractThe effects of eddies in a primitive equation ocean model configured in a single hemisphere domain with circumpolar channels at their poleward ends are investigated; in particular, two regimes for the mass balance in the channel are investigated. With small overlying winds, the channel stratification is largely set by diffusion operating in the gyre portion of the domain: the depth scale varies with a fractional power of the diffusivity but has little dependence on the wind stress. As the winds are increased, the depth becomes increasingly controlled by a tendency toward small residual circulation. In this limit, a scaling theory is derived for the stratification in the channel that predicts the overall depth of the thermocline as a power of the wind stress and that allows the eddy length scale to differ from the channel length scale. The predicted depth depends on the details of the closure chosen for the eddy buoyancy flux, but in general it varies as some fractional power of the wind stress, and a channel-only numerical simulation agrees well with this prediction. When a gyre region is added to the channel, vertical diffusion in the gyre exerts some control on the channel stratification even at higher winds, forcing the mass balance into a mixed regime in which both eddy and diffusive effects are important. The depth scale varies less with the wind stress than in a channel-only configuration, and the residual mean circulation in the channel is maintained by the convergence of cross-isopycnal eddy buoyancy fluxes.

The Warming of the California Current System: Dynamics and Ecosystem Implications

Abstract Long-term changes in the observed temperature and salinity along the southern California coast are studied using a four-dimensional space–time analysis of the 52-yr (1949–2000) California Cooperative Oceanic Fisheries Investigations (CalCOFI) hydrography combined with a sensitivity analysis of an eddy-permitting primitive equation ocean model under various forcing scenarios. An overall warming trend of 1.3°C in the ocean surface, a deepening in the depth of the mean thermocline (18 m), and increased stratification between 1950 and 1999 are found to be primarily forced by large-scale decadal fluctuations in surface heat fluxes combined with horizontal advection by the mean currents. After 1998 the surface heat fluxes suggest the beginning of a period of cooling, consistent with colder observed ocean temperatures. Salinity changes are decoupled from temperature and appear to be controlled locally in the coastal ocean by horizontal advection by anomalous currents. A cooling trend of –0.5°C in SST is driven in the ocean model by the 50-yr NCEP wind reanalysis, which contains a positive trend in upwelling-favorable winds along the southern California coast. A net warming trend of +1°C in SST occurs, however, when the effects of observed surface heat fluxes are included as forcing functions in the model. Within 50–100 km of the coast, the ocean model simulations show that increased stratification/deepening of the thermocline associated with the warming reduces the efficiency of coastal upwelling in advecting subsurface waters to the ocean surface, counteracting any effects of the increased strength of the upwelling winds. Such a reduction in upwelling efficiency leads in the model to a freshening of surface coastal waters. Because salinity and nutrients at the coast have similar distributions this must reflect a reduction of the nutrient supply at the coast, which is manifestly important in explaining the observed decline in zooplankton concentration. The increased winds also drive an intensification of the mean currents of the southern California Current System (SCCS). Model mesoscale eddy variance significantly increases in recent decades in response to both the stronger upwelling winds and the warmer upper-ocean temperatures, suggesting that the stability properties of the SCCS have also changed.

Developing a dynamically based assimilation method for targeted and standard observations

Abstract. In a recent study, a new method for assimilating observations has been proposed and applied to a small size nonlinear model. The assimilation is obtained by confining the analysis increment in the unstable subspace of the Observation-Analysis-Forecast (OAF) cycle system, in order to systematically eliminate the dynamically unstable components, present in the forecast error, which are responsible for error growth. Based on the same ideas, applications to more complex models and different, standard and adaptive, observation networks are in progress. Observing System Simulation Experiments (OSSE), performed with an atmospheric quasi-geostrophic model, with a restricted "land" area where vertical profiles are systematically observed, and a wider "ocean" area where a single supplementary observation is taken at each analysis time, are reviewed. The adaptive observation is assimilated either with the proposed method or, for comparison, with a 3-D VAR scheme. The performance of the dynamic assimilation is very good: a reduction of the error of almost an order of magnitude is obtained in the data void region. The same method is applied to a primitive equation ocean model, where "satellite altimetry" observations are assimilated. In this standard observational configuration, preliminary results show a less spectacular but significant improvement obtained by the introduction of the dynamical assimilation.

Lagrangian Data Assimilation in Multilayer Primitive Equation Ocean Models

Abstract Because of the increases in the realism of OGCMs and in the coverage of Lagrangian datasets in most of the world's oceans, assimilation of Lagrangian data in OGCMs emerges as a natural avenue to improve ocean state forecast with many potential practical applications, such as environmental pollutant transport, biological, and naval-related problems. In this study, a Lagrangian data assimilation method, which was introduced in prior studies in the context of single-layer quasigeostrophic and primitive equation models, is extended for use in multilayer OGCMs using statistical correlation coefficients between velocity fields in order to project the information from the data-containing layer to the other model layers. The efficiency of the assimilation scheme is tested using a set of twin experiments with a three-layer model, as a function of the layer in which the floats are launched and of the assimilation sampling period normalized by the Lagrangian time scale of motion. It is found that the assimilation scheme is effective provided that the correlation coefficient between the layer that contains the data and the others is high, and the data sampling period Δt is smaller than the Lagrangian time scale TL. When the assimilated data are taken in the first layer, which is the most energetic and is characterized by the fastest time scale, the assimilation is very efficient and gives relatively low errors also in the other layers (≈ 40% in the first 120 days) provided that Δt is small enough, Δt << TL. The assimilation is also efficient for data released in the third layer (errors < 60%), while the dependence on Δt is distinctively less marked for the same range of values, since the time scales of the deeper layer are significantly longer. Results for the intermediate layer show a similar insensitivity to Δt, but the errors are higher (exceeding 70%), because of the lower correlation with the other layers. These results suggest that the assimilation of deep-layer data with low energetics can be very effective, but it is strongly dependent on layer correlation. The methodology also remains quite robust to large deviations from geostrophy.

Evaluation of an eddy-permitting finite-element ocean model in the North Atlantic

A new version of the 3D finite-element primitive-equation ocean model (FEOM) based on tetrahedron partitioning of the computational domain is applied to simulate the North Atlantic circulation at eddy-permitting resolution (1/15°–2°). It relies on a horizontally refined mesh in regions of steep topography and allows the sloping bottom to be represented within the z-coordinate vertical discretization, similar to the so-called shaved-cell approach. It is the first time this approach is used to model large-scale ocean circulation. The FEOM performance in the North Atlantic is compared with that of the finite-difference models of similar resolution of the DYNAMO project. The meridional overturning circulation and heat transport of FEOM agree well with those of the DYNAMO project models, while the mean sea surface height demonstrates the presence of the Gulf Stream recirculation reproduced only by the ISOPYCNIC model of DYNAMO. The annual mean transports of the Gulf Stream and Deep Western Boundary Current at 27°N are of 37 Sv and 17 Sv with core velocities of about 1 m/s and 12 cm/s respectively. Due to flexibility in mesh refinement the FEOM provides a tool for modelling the influence of small-scale phenomena unresolved by current climate models on large-scale ocean circulation.

Wind‐induced, cross‐frontal exchange on Georges Bank: A mechanism for early summer on‐bank biological particle transport

Water exchange across the tidal‐mixing front on the southern flank of Georges Bank (GB) is examined using a two‐dimensional (2D) primitive equation ocean model. The model domain features a cross‐frontal transect including a June 1999 hydrographic (CTD)/ADCP study made as part of the U.S. GLOBEC Northwest Atlantic/Georges Bank program. The model was initialized with temperature and salinity fields taken on the 15 June 1999 CTD section and run prognostically with tidal forcing, measured winds, and representative surface heat flux. The results show that fluctuations of wind plus tidal mixing can play the following essential role in the short‐term transport of water and particles from the stratified region to the mixed region on GB in early summer, when stratification is just developing with a weak thermocline at a depth of about 10 m. First, a passing weather front drives a wind‐induced on‐bank Ekman transport of the upper part of the water column at the tidal‐mixing front and associated particles in the surface mixed layer. Then, when the wind relaxes or changes direction, the water in the on‐bank extension of the front (above the thermocline) mixes quickly through enhanced tidal motion in shallower depths of water. As a result, particles that are advected along the extended front stay in the previously well‐mixed region of the bank. Surface heating tends to increase the strength of the thermocline and reduce the thickness of the surface mixed layer. This in turn accelerates the on‐bank movement of the front under an easterly wind favorable for Ekman transport and thus enhances the on‐bank, cross‐frontal transport of particles. Since the wind‐induced, cross‐frontal on‐bank transport of water can occur episodically during passages of meteorological fronts, these could produce a larger net cross‐frontal flux than that produced by just tidal forcing on equivalent timescales. Therefore wind‐induced processes can be important in the on‐bank cross‐frontal flux of copepods and other zooplankton species that exhibit shallow maxima in their vertical distributions over the southern flank of GB in early summer.

Export pathways for river discharged fresh water in the northern Gulf of Mexico

A numerical simulation of the Gulf of Mexico (GoM) using the Navy Coastal Ocean Model (NCOM) is used to identify the pathways by which fresh water discharged by major rivers in the northern Gulf is exported away from the region. The NCOM, a new primitive equation ocean model with a hybrid sigma/geopotential level vertical coordinate, is described along with its application to the GoM region. Trajectories from surface drifters are analyzed to show evidence of the seasonally shifting alongshore and cross‐shelf transport in the region. The model results are used to determine the preferred locations and times of year for cross‐shelf and along‐shelf export of low‐salinity water from the northern GoM. The annual cycle of local wind stress plays an important role in shifting the export pathway of the fresh water discharged from the major rivers (primarily the Mississippi River) toward the east in the spring/summer, where it can be transported offshore by the currents associated with deep ocean mesoscale eddies, and toward the west in the fall/winter, where it is transported southward along the Mexican coastline as a coastally trapped current.

A Model of the Wind-Driven Seasonal Variability in the Tropical North Pacific, with Validation through Altimeter Data

Abstract The wind-driven seasonal variability in the tropical North Pacific Ocean is analyzed by means of a two-layer primitive equation ocean model implemented in an idealized Pacific extending from 30°S to 52°N and forced by an analytic seasonally varying wind stress field derived from ECMWF winds. The oceanic response in the tropical region is found to be mainly in the form of annual beta-refracted baroclinic Rossby waves radiating from the eastern boundary. Validation of these results with TOPEX/Poseidon (T/P) altimeter data is carried out. Zonal longitude–time diagrams of sea surface height anomalies and zonally integrated meridional transports computed from T/P data and from the winds through the Sverdrup relation by Stammer are compared with the corresponding quantities obtained from the model results. Such comparison shows that the model does capture the essential features of the wind-driven seasonal variability in the tropical North Pacific. The analysis of the model results, based also on sensit...

Data‐driven simulations of synoptic circulation and transports in the Tunisia‐Sardinia‐Sicily region

Data from a hydrographic survey of the Tunisia‐Sardinia‐Sicily region are assimilated into a primitive equations ocean model. The model simulation is then averaged in time over the short duration of the data survey. The corresponding results, consistent with data and dynamics, are providing new insight into the circulation of Modified Atlantic Water (MAW) and Levantine Intermediate Water (LIW) in this region of the western Mediterranean. For MAW these insights include a southward jet off the east coast of Sardinia, anticyclonic recirculation cells on the Algerian and Tunisian shelves, and a secondary flow splitting in the Strait of Sicily. For the LIW regime a detailed view of the circulation in the Strait of Sicily is given, indicating that LIW proceeds from the strait to the Tyrrhenian Sea. No evidence is found for a direct current path to the Sardinia Channel. Complex circulation patterns are validated by two‐way nesting of critical regions. Volume transports are computed for the Strait of Sicily, the Sardinia Channel, and the passage between Sardinia and Sicily.

Seasonal dynamics of the surface circulation in the Southern California Current System

Abstract The seasonal dynamics of the Southern California Current (SCC) is investigated using a primitive equation ocean model with real coastlines and topography. The model is tested with different wind forcing, and the resulting flow fields are compared to the mean and seasonal circulation inferred from long-term in situ observations (California Cooperative Oceanic Fisheries Investigation (CalCOFI)). The model integration forced with the output winds of a regional atmospheric model (RSM) best captures the statistics of the observed circulation, with a 0.9 correlation coefficient for the streamlines and 0.5 for the velocity fields. The model integrations reveal a pronounced linear response of the flow field to changes in winds on the shelf region. A dynamical feature inferred from CalCOFI hydrography, also suggested in TOPEX/ERS maps, is an annually recurrent westward propagation of SSH anomalies originated in the Southern California Bight (SCB) during the upwelling season. The RSM integration is the only one to capture the correct timing and spatial evolution of this process. We therefore use this model integration for guidance in constructing a dynamical framework to interpret the observed circulation and its variability. During the upwelling season in spring, there is an upward tilt of the isopycnals along the coast directly forced by the winds in the Bight. As the spring transitions to the summer the upwelling winds relax in the Bight but are still strong in the region offshore, approximately in correspondence of the continental slope (positive wind-stress curl condition). Anomalous denser waters in the location of the Southern California Eddy are maintained and reinforced by the combined interaction of the coastal/islands geometry and the wind-stress curl (through Ekman dynamics). The adjustment process to the denser water initiates a westward propagation of ocean density anomaly through Rossby waves, and reinforces the cyclonic gyre-like circulation of the SCE (increasing positive vorticity). Surface poleward flow, maintained by the positive wind-stress curl, is also reinforced in proximity of Point Conception as a consequence of the adjustment. During the summer the cyclonic gyre becomes increasingly unstable as the core of the ocean anomalies crosses the continental slope. Instability processes within the cyclonic region, characterized by a sharp increase in EKE, shed eddies that leave the region either drifting to the west or interacting with existing eddies in the region offshore. The EKE reaches a seasonal maximum at the end the summer in the cyclonic region, and in late fall further offshore where the eddies are fully developed. The shedding of eddies cannot be directly seen in the CalCOFI observations because of the sampling aliasing. For this point we rely on the strong suggestion of the model, which we assume is able to capture the leading order dynamics. Additional integrations with a linearized version of the model are also presented to reinforce our interpretation of the westward propagation of the isopycnal anomalous displacement associated with Rossby wave dynamics.

Response of an eddy‐permitting ocean model to the assimilation of sparse in situ data

The response of an eddy‐permitting ocean model to changes introduced by data assimilation is studied when the available in situ data are sparse in both space and time (typical for the majority of the ocean). Temperature and salinity (T&S) profiles from the WOCE upper ocean thermal data set were assimilated into a primitive equation ocean model over the North Atlantic, using a simple nudging scheme with a time window of about 2 days and a horizontal spatial radius of about 1°. When data are sparse the model returns to its unassimilated behavior, locally “forgetting” or rejecting the assimilation, on timescales determined by the local advection and diffusion. Increasing the spatial weighting radius effectively reduces both processes and hence lengthens the model restoring time (and with it, the impact of assimilation). Increasing the nudging factor enhances the assimilation effect but has little effect on the model restoring time.

An Unstructured Grid, Finite-Volume, Three-Dimensional, Primitive Equations Ocean Model: Application to Coastal Ocean and Estuaries

An unstructured grid, finite-volume, three-dimensional (3D) primitive equation ocean model has been developed for the study of coastal oceanic and estuarine circulation. The model consists of momentum, continuity, temperature, salinity, and density equations and is closed physically and mathematically using the Mellor and Yamada level-2.5 turbulent closure submodel. The irregular bottom slope is represented using a s-coordinate transformation, and the horizontal grids comprise unstructured triangular cells. The finite-volume method (FVM) used in this model combines the advantages of a finite-element method (FEM) for geometric flexibility and a finite-difference method (FDM) for simple discrete computation. Currents, temperature, and salinity in the model are computed in the integral form of the equations, which provides a better representation of the conservative laws for mass, momentum, and heat in the coastal region with complex geometry. The model was applied to the Bohai Sea, a semienclosed coastal ocean, and the Satilla River, a Georgia estuary characterized by numerous tidal creeks and inlets. Compared with the results obtained from the finite-difference model (ECOM-si), the new model produces a better simulation of tidal elevations and residual currents, especially around islands and tidal creeks. Given the same initial distribution of temperature in the Bohai Sea, the FVCOM and ECOM-si models show similar distributions of temperature and stratified tidal rectified flow in the interior region away from the coast and islands, but FVCOM appears to provide a better simulation of temperature and currents around the islands, barriers, and inlets with complex topography.

A Large-Scale Seasonal Modeling Study of the California Current System

A high-resolution, multi-level, primitive equation ocean model has been used to investigate the combined role of seasonal wind forcing, seasonal thermohaline gradients, and coastline irregularities on the formation of currents, meanders, eddies, and filaments in the entire California Current System (CCS) region, from Baja to the Washington-Canada border. Additional objectives are to further characterize the meandering jet south of Cape Blanco and the seasonal variability off Baja. Model results show the following: All of the major currents of the CCS (i.e., the California Current, the California Undercurrent, the Davidson Current, the Southern California Countercurrent, and the Southern California Eddy) as well as filaments, meanders and eddies are generated. The results are consistent with the generation of eddies from instabilities of the southward current and northward undercurrent via barotropic and baroclinic instability processes. The meandering southward jet, which divides coastally-influenced water from water of offshore origin, is a continuous feature in the CCS, and covers an alongshore distance of over 2000 km from south of Cape Blanco to Baja. Off Baja, the southward jet strengthens (weakens) during spring and summer (fall and winter). The area off southern Baja is a highly dynamic environment for meanders, filaments, and eddies, while the region off Point Eugenia, which represents the largest coastline perturbation along the Baja peninsula, is shown to be a persistent cyclonic eddy generation region.

Non-uniform adaptive vertical grids in one-dimensional numerical ocean models

It is demonstrated in this paper how the concept of general vertical coordinates can be exploited for constructing adaptive grids in primitive equation ocean models. The term adaptive is used here in the sense of coordinate iso-surfaces which follow certain internal structures of the flow in such a way that higher vertical resolution is obtained in locations where vertical gradients are large. The internal structures considered here are shear and stratification. In this paper, one-dimensional models are applied in order to demonstrate the ability of such grid adaptation methods to follow internal structures even in flow situations dominated by vertical mixing processes. Here, a variational approach is considered for the generation of grids which results in a diffusion equation for the vertical coordinate. The method is tested for five different idealised and realistic scenarios with the result that the discretisation error can be significantly reduced in comparison to equidistant Cartesian grids. Some recommendations for extending these methods for three-dimensional models are given at the end of this paper.

Tidal Mixing in the Southern Weddell Sea: Results from a Three-Dimensional Model

Abstract A three-dimensional primitive equation ocean model is used to study the magnitude and distribution of tidal mixing in the southern Weddell Sea. The contributions of (i) semidiurnal barotropic constituents M2 and S2, (ii) internal tides, and (iii) diurnal barotropic tides are considered. Computed elevation cotidal charts are generally consistent with our knowledge and observations for the region. The model reproduces maximum semidiurnal tidal elevations of about 1.6 m and 1.0 m for M2 and S2, respectively. An internal tide of moderate strength is generated over the slope, propagating in the alongslope direction but rapidly dissipating. On the continental shelf, a thick benthic boundary layer (150 m) develops due to the proximity of the critical latitude for the M2 constituent. Typical M2 and S2 baroclinic tidal currents at the shelf break are 7 and 4 cm s−1, respectively. In general, the tidal currents produce strong mixing in the bottom boundary layer at the shelf break and on the shelf leading t...

Dynamics of a Buoyancy-Driven Coastal Jet: The Gaspé Current

A primitive equation ocean model is applied to the process study of the Gaspé Current and cyclonic circulation over the northwestern Gulf of St. Lawrence (NWG). The model is driven by river discharge and barotropic boundary flows. Two types of model domains are used: an idealized basin with a flat bottom and piecewise coastline, and a realistic basin with model-resolved NWG bathymetry. The model domains are initially filled with horizontally uniform but vertically stratified waters. The river discharge is expressed in terms of lower salinity and a weak barotropic inflow in the upper waters at the estuary head. The early developments of the estuarine plume and coastal current system driven by the river discharge are qualitatively similar in both basins. After a short-period adjustment, a buoyant plume is developed near the estuary mouth, with a surface-intensified coastal current advecting the estuarine water seaward in the direction of Kelvin wave propagation. The coastal current initially follows the coastline closely but later becomes unstable with backward-breaking waves developed along the outer edge of the current. The kinetic energy analysis reveals that the plume–current system is baroclinically unstable with the transient motions resulting primarily from the mean available potential energy. With the river discharge at the head as the only driving force, the offshore front of the estuarine plume expands continuously seaward, leading to a large-scale anticyclonic circulation over the NWG. The addition of a barotropic westward jet along the Quebec shore, however, is able to restrain the seaward expansion of the offshore front of the plume, and therefore form a large-scale cyclonic motion over this region.

Effects of river inputs into the Bay of Bengal

The effect of river runoff in the Bay of Bengal is examined using a reduced gravity primitive equation ocean model coupled to an atmospheric boundary layer model. Model simulations are carried out by including river discharges as surface freshwater forcing at the mouths of the rivers. To assess the effect of river inputs on the dynamics and thermodynamics of the tropical Indian Ocean, parallel simulations are carried out by neglecting the river inputs. Additionally, another set of parallel runs without penetrative radiation loss through the mixed layer is carried out. The freshwater flux due to rivers results in lower salinities and shallower mixed layers, as expected. However, the influence of this additional freshwater flux into the bay is rather counterintuitive. With the inclusion of river discharges more heat is absorbed by the ocean, but sea surface temperatures are slightly cooler in the bay because of enhanced entrainment cooling of the shallower mixed layer, enhanced penetrative radiation, and an enhanced effect of latent heat loss on the temperature tendency. This is despite the greater latent heat loss when river input is neglected. Conversely, neglect of penetrative radiation results in a shallower but slightly warmer mixed layer with river input. River input and penetrative radiation each affect the mixed layer depths, the salinity and temperature structure, and currents in the Bay of Bengal, but they have a small effect on SST. Annual SST, averaged over the Bay of Bengal, is only 0.1°C colder with river input. Neglecting penetrative radiation in the river run results in an increase of only 0.2°C for the annual SST. The lack of persistence of a barrier layer in the bay helps regulate SST even in the presence of enhanced buoyancy forcing due to river input. Averaged over the bay, a barrier layer forms as mixed layer detrainment occurs, and the thermocline deepens just after the southwest monsoon and the northeast monsoon. The barrier layer is short‐lived in each case it is eroded by mixing. The effect of riverine input in the bay is not confined to the surface waters. A pool of cold anomaly (−1°C) and fresher waters is centered near 100 m depth in the bay with riverine input. This cold pool beneath the mixed layer allows entrainment cooling of the mixed layer to be more effective, even though mass entrainment is lower relative to the case neglecting river input. The more diffuse thermocline in the bay is consistent with enhanced vertical mixing despite the large positive buoyancy forcing.

The use of simulated drifters to estimate vorticity

A primitive equation ocean model is used to generate trajectories of simulated clusters of drifters in the California Current (CC) region. These trajectories allow us to evaluate a least squares (LS) method of estimating vorticity and vertical velocity along a cluster's path. Two clusters provide examples of successful and less successful estimates of vorticity and vertical velocity. Our analysis quantifies the dependence of estimate quality on several parameters that can be used as error predictors in the LS estimate of vorticity: cluster separation, number of drifters in a cluster, and cluster shape. A combination of cluster separation and ellipticity shows the most promise as an indicator of quality for the vorticity estimate.