GLOBAL OCEAN SIMULATIONS WITH AN ISOPYCNIC ... - CiteSeerX

GLOBAL OCEAN SIMULATIONS WITH AN ISOPYCNIC COORDINATE MODEL RAINER BLECK, SHAN SUN

Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida 33149, USA

SUMNER DEAN

Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA

1 Introduction Poleward heat transport by atmospheric and oceanic currents is a vital link in the complex machinery that maintains the earth's climate. In the atmosphere, much of this heat transport is accomplished by transient eddies (cyclones and anticyclones) embedded in strong, hydrodynamically unstable zonal currents circling the earth in west to east directions. Ocean currents { excepting the one that ows around Antarctica { cannot move along a latitude circle without sooner or later running into a continent. As a result, oceanic circulation systems tend to form closed loops (\gyres") within individual basins, even if driven entirely by zonal winds. Hence, the ocean exhibits a phenomenon we do not generally see in the atmosphere, namely, strong, persistent currents

owing in meridional directions. The presence of meridional ocean currents implies that meridional heat transport by the ocean varies with longitude. The atmosphere is likely to take note of these regional dierences and will react for example, by forming more storms in regions where warm water ows poleward than in regions where cold water ows equatorward. It is easy to understand then, that the physical parameters de ning the climate on the eastern side of a continent can dier noticeably from those on the western side, and that these dierences are linked to the strength of the ocean currents. Since many ocean currents are primarily wind-driven, it is also easy to see how regionally altered storm activity can feed back on the strength of the oceanic circulation and thus on the oceanic heat transport. It is this mutual interaction between the atmosphere and the ocean that stands in the way of a \static" model of the earth's climate. As the human population grows and natural resources are being stretched to their limits, our vulnerability to climate uctuations will increase, and eorts 1

must be made to understand and predict these uctuations. Many basic features of the ocean circulation can be explained using the analytical tools of geophysical uid dynamics. However, the complexities of the coupled ocean-atmosphere system are such that they can best be investigated with a tool that only recently has become available: numerical simulation. Computer models suitable for this purpose are quite complex because they need to have atmospheric, oceanic, and land surface components. In this article, we will focus on the oceanic component. Speci cally, we will describe recent advances made in the design of ocean models in which the traditional roles of water density and height as dependent and independent variables are reversed. This switch may seem inconsequential from the point of view of the governing dierential equations (after all, the laws of physics remain the same) but it has a profound eect on the properties of the numerically obtained solutions. Readers interested in the state of ocean modeling in general are referred to a recent review article by McWilliams 10 . Together with the OPYC model developed by J.Oberhuber 11 at the Max Planck Institute for Meteorology in Hamburg (Germany), the Miami Isopycnic Coordinate Ocean Model 2 3 (MICOM) is one of two \general-purpose" isopycnic models available to the community today. Unlike OPYC, MICOM presently lacks a sea ice component, but it has numerical attributes that allow it to run fairly eciently at high resolution on Massively Parallel Processors: the governing equations are hyperbolic and time integration is fully explicit. This article will focus on global simulation results obtained by running MICOM on one particular MPP: the Connection Machine CM-5 built in the early 1990's by Thinking Machines, Inc., and installed at Los Alamos National Laboratory. ;

2 Ocean Modeling in Isopycnic Coordinates Sunlight, the source of oceanic heating, penetrates the ocean only to a depth of a few hundred meters. Thus, the ocean is essentially a medium heated from above. In most oceanic locations, a thin layer of warm water overlies a massive layer of cold water. The cold bottom water is being replenished continuously from relatively small polar regions where atmospheric circulation anomalies or other factors allow the formation of water masses that possess sucient negative buoyancy to sink to the bottom. Centuries or millennia later, this water comes into contact with the surface again because it eventually lls up the basin. During the intervening time, the thermal properties of the deep water remain virtually unchanged. In view of the huge heat capacity of the world ocean, a serious \climate drift" can and will occur in coupled ocean-atmosphere simulations if the al2

gebraically approximated governing equations do not keep the cold subsurface water thermally insulated from the warm surface water. One possible way to remedy this problem is to reverse, as indicated above, the independent and dependent variables. This amounts to replacing the dierential equations governing oceanic motion in Cartesian geometry by an analogous set depicting the ocean as a stack of quasi-immiscible, variable-depth layers which exchange properties such as temperature only to the extent found in nature. This approach to ocean simulation has become known as isopycnic modeling { isopycnic because model layers are typically chosen to be layers of constant potential density (the density a uid parcel acquires after being brought adiabatically to a prescribed reference pressure). The isopycnic approach requires numerical tools that were not available 30 years ago when the rst global ocean circulation models were developed, and even today are not as robust as one would like them to be. Nevertheless, isopycnic modeling has recently acquired considerable momentum, spawning the work presented here. The dynamical \kernel" of an isopycnic model is a set of prognostic equations resembling the so-called shallow-water equations. The three primary prognostic variables are the x and y components of horizontal momentum in each layer and the thickness of each layer. While model layers are prohibited from inadvertently exchanging material properties, they do communicate through hydrostatically transmitted pressure forces. Thus, the hydrostatic equation is an integral part of the set of the governing equations. Since water density is a function of both temperature (T ) and salinity (S ), a prognostic equation for either T or S must also be included in each layer. T , S , and the vertical coordinate  (potential density) are not independent of each other but must satisfy an equation of state. The ocean is kept in motion by a combination of wind and buoyancy forces { radiation, sensible and latent heat ux, precipitation and evaporation. In order to accommodate buoyancy forcing in a model that treats buoyancy ( density) as an independent variable, density in the uppermost model layer is permitted to vary both horizontally and in time. This allows the model to interact with the overlying atmosphere in the same way that a conventional ocean model would. However, a variable-density layer does not totally solve the problem of how to force density in a density coordinate model; it only passes the problem from the ocean surface to the rst interior layer interface. There, buoyancy uxes must be translated into interlayer mass uxes { a nontrivial problem given the \discord" between the continuously varying density eld in the top layer and the discrete density structure in the model's interior. a

a Because of the near-incompressibility of seawater, the terms density and potential density will be used synonymously in this article.

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It is convenient to let the uppermost model layer represent the surface mixed layer. Its thickness is the depth to which wind stirring and surface buoyancy uxes are able to maintain a turbulent state. Buoyancy loss to the atmosphere, which destabilizes the water column, acts as a source of turbulence kinetic energy (TKE). Any excess TKE is used to mix up denser water from below 7 ; the mixed layer then deepens at the expense of the uppermost interior layer(s). On the other hand, if buoyancy gain stabilizes the column, turbulence decreases and the mixed layer shrinks. In an isopycnic model this requires water to be transferred from the mixed layer to the interior layers. Because of the discrete interior density structure, the numerical implementation of this so-called detrainment process is too complex to be described here. It is worth pointing out that the annual cycle of mixed layer growth and retreat is a process of utmost importance, because it eciently transmits T; S signals from the surface to the oceanic interior, occasionally all the way to the bottom. While any model depicting the ocean as a stack of immiscible layers, isopycnic or not, would be able to suppress numerically induced vertical heat diffusion, isopycnic coordinate models oer the additional advantage of correctly simulating the horizontal diusive spreading of water mass properties. Mixing in strati ed uids occurs preferentially along surfaces in which displaced

uid parcels remain neutrally buoyant, i.e., along potential-density surfaces. By solving nite-dierence transport equations for T and S along such surfaces, an isopycnic coordinate model can, to a large extent, mask numerical dispersion errors as isopycnic diusion. The situation is somewhat complicated by the fact that compressibility of seawater, while generally small and often negligible, depends strongly on temperature and salt content (thermobaricity). One consequence is that the slope of potential-density surfaces in water masses of nonuniform salinity depends on the choice of reference pressure. Another consequence is the following: if two water parcels of dierent salinity and pressure are chosen such that parcel A, after neutrally buoyant lateral displacement, ends up next to parcel B, the opposite is not true; that is, an attempt to laterally displace parcel B in the direction of parcel A will cause it to \miss" parcel A. This phenomenon renders neutral surfaces multi-connected 9 . Thermobaric eects become important in the deep ocean where density contrasts are minimal and pressure eects are large. The usual practice of lifting water parcels to the surface ( guratively speaking) to determine their potential density is de nitely not advisable if they are brought up from a depth of 4 or 5 km. One could try to reduce the magnitude of this problem by using an abyssal pressure surface as reference level for potential density 12 , but this would lead to a misrepresentation of near-surface water mass properties. To 4

minimize the eect of thermobaricity in studies involving the total oceanic depth range, an intermediate reference level { say, 2000 m { is probably the best choice. The question of how to de ne coordinate layers that remain optimally aligned with neutrally buoyant surfaces in a variable-salinity environment and how to take thermobaricity into consideration is a matter of ongoing research.

3 A Near-Global Coarse-Mesh Simulation Experiment In our global experiments conducted to date, MICOM has been con gured with 16 layers (a surface mixed layer plus 15 isopycnic layers) on a horizontal grid spanning the latitude range 69S { 64N. We have experimented with several grid resolutions. A multi-century simulation is presently underway on a 128256 point mesh (referred to below as the 1.4 experiment) while a multidecadal simulation has recently begun on an 8251600 point mesh (the 0.225 experiment). Some experiments have also been carried out on 0.35 and 2 grids. In all cases, grid cells are de ned as squares on a Mercator map. Thus, while longitudinal grid resolution (in degrees) is uniform, the actual mesh size in x and y direction (in meters) on the sphere decreases poleward with the cosine of latitude. Initial conditions for these simulations are derived from climatological data 8 . In contrast to past practices in global ocean circulation modeling, thermal forcing in our experiments is not formulated as Newtonian relaxation to observed oceanic surface T and S elds; instead, it is based on seasonally varying atmospheric data. Speci cally, our forcing elds consist of: wind stress, atmospheric temperature and humidity, all derived from the Comprehensive Ocean Atmosphere Data Set (COADS); precipitation inferred from the NOAA microwave sounder; net radiation from the Oberhuber atlas; and freshwater input from 14 major rivers and the polar ice caps. This type of forcing was chosen in anticipation of MICOM's future use in coupled climate simulations where ocean surface conditions cannot be prescribed because they are part of the solution. There are obvious shortcomings in the present round of global experiments due to the absence of the Arctic Ocean and the lack of an ice model. Special boundary conditions applied along the northern and southern boundaries can overcome these de ciencies to some extent. The traditional method consists of restoring the mass eld near arti cial lateral boundaries to prescribed hydrographic conditions. In isopycnic models, one can alternatively prescribe diapycnal (= interlayer) mass uxes near the boundary which mimic the water mass conversion taking place in regions outside the model domain. An exper5

iment testing several methods of imposing such lateral boundary conditions is in progress. The lateral boundary problem will go away once we extend the model domain to the North Pole and add a sea ice model. This work has begun. We intend to cover the polar cap with a bipolar coordinate system whose two poles are located over land. The resulting grid connects smoothly to the Mercator grid and we call it the Pan-Am grid because of its resemblance to the familiar airline logo. Emphasis in our present analysis of model output is on climate-relevant processes, primarily the vertical-meridional overturning circulation often referred to as the global conveyor belt 5 , and the associated 3-dimensional diapycnal mass ux eld. The latter is driven in the model by three processes: (i) the annual mixed-layer advance/retreat; (ii) interior diapycnal mixing, and (iii) imposed lateral boundary conditions. Our focus on diapycnal mass transport is not surprising, given the (relatively) clean separation between isopycnal and diapycnal processes in MICOM-class models. 3.1 Zonally averaged overturning in individual basins To convey the model's view of how the three major oceans interact in maintaining the global thermohaline (i.e., buoyancy-driven) circulation, we plot in Fig. 1 the streamfunction of the zonally and time-averaged vertical-meridional mass

ux in each basin. These results are based on our baseline 1.4 experiment in which no eort is made to incorporate the eect of the Arctic Ocean. The abscissa is labeled in deg latitude while ordinate labels indicate layer potential densities in sigma units (density in kg/m3 minus 1000). Contours are labeled in units of Sverdrups (Sv), where 1 Sv = 106 m3 =s. In the Atlantic (upper left panel) we see an interhemispheric overturning cell, fed by water entering at the latitude of the Cape of Good Hope at the surface and exiting at depth. The cell is remarkably steady in this multi-century simulation but has declined from a value in the low 20s to slightly below 20 Sv at year 400. The maximum northward heat ux associated with this cell at year 400 is 0.9 PW (1 PW = 1015W). Given the absence of an Arctic basin or of boundary conditions mimicking its role, the Atlantic overturning rate is surprisingly close to observational estimates, which are in the 25 { 28 Sv range. One possible contributing factor is our method of basing evaporation on a xed, though seasonally varying, atmospheric humidity eld; this causes water that is slightly too warm relative to climatology to become too salty as well. The resulting buoyancy loss creates a positive feedback on the maintenance of the overturning cell.

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Figure 1: 5-year averaged mass transport in the vertical-meridional plane, zonally averaged over 3 individual ocean basins and the world ocean as a whole, from the 1.4 experiment. Solid/dashed lines indicate counterclockwise/clockwise rotation looking east. Contour interval: 2 Sv. Abscissa: longitude; ordinate: density ( units).

In order to represent the meridional overturning in the Paci c and Indian Ocean basins in streamfunction form, the ow through the Indonesian passage had to be subtracted from one basin and added to the other. The strength of this through ow in the present simulation is  15 Sv, half again as strong as the observational estimate. The residual circulation shows barely 3 Sv upwelling in the abyssal Indian Ocean (upper right panel) while the equatorial Paci c (lower left panel) appears as the place where wind-driven Ekman layer divergence brings a small portion of the global conveyor belt water back to the surface. The excessive Indonesian through ow rate, which may also be viewed as an excessive counterclockwise circulation around Australia, greatly distorts the meridional heat transport in the model; heat actually moves equatorward in the South Paci c, making the Indian Ocean the only basin transporting heat 7

poleward in the southern hemisphere. The likely cause is low through ow impedance, related to the absence of the Lesser Sunda Islands from our 1.4 bathymetry. The zonally averaged overturning circulation in all basins and the Southern Ocean combined is shown in the lower right panel of Fig. 1 Noteworthy features are the shallow, thermally indirect Deacon cell in the southern ocean and the extent to which the conveyor belt circulation involves upwelling near Antarctica. The meridional heat ux associated with this pattern exhibits peak values of +1.4 PW at 16N and -0.7 PW at 16 S. Note that the model produces no Antarctic Bottom Water (AABW). AABW formation is presently inhibited by our crude method of distributing ice melt water uniformly in longitude and time along the northern and southern model boundaries. 3.2 Annually averaged diapycnal ux elds

Figure 2: 5-year average of vertical mass ux (m/yr) through bottom of mixed layer, from the 1.4 experiment. Positive numbers indicate downward motion. Note exponentially expanding contouring interval. Sea-surface height contours added to indicate surface ow. Contour interval: 20 cm.

More detailed geographic information about the vertical branches of the thermohaline circulation can be gleaned from maps of interlayer mass transport. A striking example of the type of information obtainable from an isopycnic model is the vertical mass ux through the bottom of the mixed layer. In Fig. 2 we show this ux averaged over 5 years, again from the baseline 1.4 experiment. Note the exponentially expanding color scale. 8

The largest transport values in Fig. 2 are seen in the Labrador Sea, where the southward owing Labrador Current impinging on the North Atlantic Current (the extension of the Gulf Stream) \subducts" 1500 m of water every year, and in the east-central Paci c where water upwells into the mixed layer at a rate of almost 1000 m per year. In the extratropics, upwelling appears to be associated with poleward- owing ocean currents (examples: Gulf Stream, Somali Current) and with regions subjected to cyclonic wind stress. Downwelling in the extratropics takes place where currents ow equatorward (examples: Falkland and Labrador Currents) and/or where the wind stress is anticyclonic. Subduction is generally de ned as the transfer of water from the surface mixed layer to the strati ed ocean interior. Of particular interest is the amount of water which, after being subducted during the springtime mixed-layer retreat, migrates far enough equatorward during the summer to escape next fall's re-entrainment into the mixed layer. (Equatorward motion is called for because the maximum wintertime mixed-layer depth increases strongly poleward.) For the purpose of this discussion, we will only consider water as having been subducted if it escapes re-entrainment in the following winter. This more narrowly de ned subduction process is physically relevant because it determines the rate at which the ocean interior is being \ventilated". A precise diagnosis of this so-de ned subduction process would require evaluating the strength of the meridional ow in relation to the slope of the late-winter mixed-layer interface. MICOM's variable-depth slab-type mixed layer allows this transport to be diagnosed approximately as a vertical mass exchange. In a nutshell, an equatorward- owing current will tend to advect the mixed-layer interface equatorward. From a local perspective, this is seen as mixed-layer deepening. The model, sensing a discrepancy between the new mixed-layer depth and the equilibrium depth implied by the local surface TKE input, will try to remove the discrepancy. The amount of water thereby transferred from the mixed layer to the layer(s) below matches the amount that earlier would have crossed the interface horizontally, had the interface not been carried along with the motion. This mechanism also works in the other direction: a current pushing a tilted mixed-layer interface poleward is likely to cause the model to locally deepen the mixed layer, thereby transferring water from the thermocline to the mixed layer. Fig. 3 shows the 5-year averaged vertical mass ux through one of the model's lowest layer interfaces. This plot strikingly reveals that the model in our baseline 1.4 experiment produces bottom water in only one region of the world ocean: the western Labrador Sea. In the real world, the major bottom water source regions are the Greenland-Iceland-Norwegian (GIN) Sea in the 9

Figure 3: Diapycnal mass ux (m/yr) through a near-bottom layer interface, from the 1.4 experiment. See Fig. 2 for further details.

North and the Weddell Sea in the South. The lack of bottom water coming out of the GIN Sea can be understood because the computational domain ends at the edge of that basin. Interestingly, the model minimizes the impact of the geographic truncation by shifting bottom water production to the Labrador Sea. Of more concern is the lack of Antarctic Bottom Water production. The reason for this defect was given earlier. It is possible that the absence of an AABW generation mechanism helps maintain the robust interhemispheric overturning circulation seen in Fig. 1. The ascending branch of this circulation shows up in Fig. 2 as the yellow region near the southern domain boundary, indicating large-scale upwelling at a rate of up to 100 m per year. 3.3 Interannual and Interdecadal Variability The 1.4 experiment is approaching half a millennium at the time of this writing, making it possible to look at the long-term steadiness of the model's thermohaline circulation. Note that the ocean in this experiment is driven by atmospheric elds containing no interannual variability. An important question to address is whether the model contains internal multi-year variability modes, i.e., modes that cannot be explained by variability in the forcing functions. Two 400-year long time series presented in Figs. 4 and 5 suggest that such long-term internal variability is indeed present in the model. The overturning rate of the North Atlantic, sampled at 30 day intervals, is shown in Fig. 4.

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Figure 4: Atlantic overturning rate (Sv) as a function of time, from the 1.4 experiment.

The general decline in overturning strength is interspersed with episodes of strengthening, some of which taper o within a few years while others, notably the one initiated at year 250, have eects discernible for several decades. There is also evidence of uctuations on the 5-to-10 year time scale. Note that Fig. 4 suggests a mean overturning rate of about 25 Sv at year 400, while Fig. 1 indicates a mean overturning rate of no more than 20 Sv. This discrepancy is due to the fact that the streamfunction reaches its maximum at dierent locations in latitude-density space in the course of a model year. The time-averaged circulation thus appears to be weaker. The second time series (Fig. 5) shows the Indonesian through ow rate, another possible measure of the strength of the global conveyor belt. The variability here is somewhat higher than in the previous gure, and the uctuations in the two time series appear rather uncorrelated. Therefore, the 11

Figure 5: Indonesian through ow rate (Sv) as a function of time, from the 1.4 experiment.

simpli ed notion that conveyor belt water entering the Atlantic is made up entirely of Paci c water having passed through the Indonesian passage is not borne out in this experiment. Work has not progressed to the stage where we can explain the nature of the variabilities shown in Figs. 4 and 5. Suce it to say that the thermohaline circulation, while surprisingly robust in this experiment, does undergo uctuations on multi-year to multi-decadal time scales. Heat transport uctuations associated with this internal variability are likely to have relevance for climate prediction and thus require further study. 3.4 Tracer transport by abyssal currents. Tracer transport calculations are an eective way of assessing the realism of the thermohaline circulation in an ocean model. As discussed earlier, the de-

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Figure 6: Passive tracer distribution in the 2 = 37:11 layer after 30 years, from the 2.0 experiment.

pendence of sea water compressibility on salinity and temperature is a problem when it comes to comparing the relative buoyancy of abyssal water masses having dierent T; S properties. Choosing a deeper reference pressure is a partial solution to this problem. The tracer transport calculations shown below were therefore conducted with a version of MICOM that references potential density to the pressure at 2000 m. Horizontal mesh size in these experiments is 2.0 . Figs. 6 and 7 show the distribution of a passive tracer introduced in two geographic regions where the model generates bottom water, namely, the Labrador Sea and the Weddell Sea. (Bottom water formation in the Weddell Sea is achieved in this experiment somewhat arti cially by not dumping fresh water, representing Antarctic ice runo, into the Weddell Sea.) Tracer concentration is permanently set to 100% in the surface mixed layer in the regions mentioned. Every spring, some of this \tagged" water gets injected into interior layers as a by-product of mixed-layer detrainment. In addition, the Mediterranean basin is kept permanently saturated with tracer which then leaks into the Atlantic basin through isopycnic diusion. Figs. 6 and 7 show conditions 30 years after initiation of the tracer release in two abyssal layers, 2 = 37:11 and 2 = 37:17 (2 is potential density referenced to 2000 m). Outside their source regions, these layers are typically found at depths exceeding 4 km. Shading indicates the amount of tracer-laden water (in meters) present in each layer. In both gures, Labrador Sea water is seen to ow southward along the American continent, though at dierent 13

Figure 7: Passive tracer distribution in the 2 = 37:17 layer after 30 years, from the 2.0 experiment.

rates; in Fig. 6, a tongue more than 100 m thick has crossed the equator. Water carrying the Mediterranean tracer spreads northward at a slower speed. The Mid-Atlantic Ridge works as a temporary barrier to the two water masses. Other bottom topography features, such as the Bermuda rise, appear as white holes in the tracer plots. Most of the water injected into deep layers in the Weddell Sea is seen to be semi-stationary, but a small amount (note the exponential grey scale) gets drawn into the Antarctic Circumpolar Current. In the faster- owing layer (Fig. 6), some of this water has reached the Paci c by year 30 and is turning north. In the lower layer (Fig. 7), which receives most of the Weddell Sea deep water, we nd up to 650 m of tracer-laden water. Some of it can be seen owing north through gaps in the Scotia Ridge and into the Argentine Basin where at year 30 it has reached a thickness of 25 m. The patterns shown in Figs. 6 and 7 are in qualitative agreement with evidence regarding the Atlantic overturning rate obtained from tracer measurements 6 .

4 A Near-Global Fine-Mesh Simulation Experiment As mentioned in the beginning, poleward heat transport in the extratropical atmosphere is accomplished primarily by transient eddies which arise from a special type of hydrodynamic instability { barotropic and baroclinic instability 14

{ of the basic zonal jet streams. Climate simulation with a numerical model that is too \coarse" to resolve the spatial structure of these weather-producing instabilities would be out of the question. It was also mentioned that the oceanic circulation is characterized by, among other things, mean meridional currents. Thus, one could expect the ocean to be capable of transporting heat poleward without resorting to barotropic and baroclinic instabilities of its basic current system. This possibility raises the following question: could one simulate the oceanic component of the climate system with a model that fails to spatially resolve eddies produced by these instabilities? The question is important because the preferred scale of barotropic/baroclinic instabilities is 10 times smaller in the ocean than in the atmosphere (100 versus 1000km, roughly speaking). An eddy-resolving ocean simulation, carried over a prescribed time interval, therefore requires 10 times the number of time steps and is consequently 1000 times as expensive as an eddy-resolving atmospheric simulation. The answer to the question posed above is not known at this time, mainly because computers capable of performing global eddy-resolving ocean simulations have only become available in the last 5 years. One speci c purpose of the simulations described in this article is to investigate the sensitivity of the poleward heat transport to grid resolution. Unfortunately, the eddy-resolving 0.225 simulation mentioned earlier and described in more detail below has not advanced far enough to draw rm conclusions in this regard. At the time of this writing, the 0.225 experiment has passed the 4-year mark. Initial conditions for this run were obtained from the 1.4 experiment at year 150. Atmospheric forcing elds for the two experiments are identical. There are some dierences, necessitated by the multi-purpose nature of this expensive simulation: The domain has been extended slightly in north-south direction, and the bottom-water forming capabilities of the truncated ocean basins (GIN Sea to the north and the inner Weddell Sea to the south) are mimicked by prescribing modest diapycnal uxes in the appropriate geographic regions. The obvious course to take in order to isolate the eect of grid resolution on the meridional heat transport will be to start a non-eddy-resolving 1.4 experiment under identical geographic and forcing conditions. We will limit the discussion of the 0.225 experiment to a few examples of phenomena of general oceanographic interest that have begun to emerge in this simulation. Seagoing oceanographers studying numerical model output are often perplexed by the short life span of simulated ocean eddies, a phenomenon attributed to excessive numerical damping. To demonstrate the presence of eddies in the model solution, we show in Figs. 8 and 9 snapshots of the eddy 15

Figure 8: Snapshot of sea surface height (cm) near the tip of Africa, from the 0.225 experiment.

population in the Agulhas and Brazil Current retro ection regions, respectively. Eddies spawned near the tip of Africa are believed to be part of the global conveyor belt, i.e., they carry warm water of Indian and Paci c Ocean origin into the Atlantic. Likewise, eddies forming in the region where the Brazil Current turns oshore propagate conveyor belt water up the Brazil coast and into the Caribbean where it merges with the Gulf Stream system. The eld shown in Fig. 8 is sea surface height, an approximate streamfunction for surface velocity vectors similar to the pressure eld on a weather map. Thus, the circular and oval features directly mark the eddies we are interested in. The eld shown in Fig. 9, on the other hand, is surface salinity. Here, the eddy motion must be inferred from swirls and cresent-shaped streaks in the salinity eld. We chose salinity because it demonstrates that the 16

Figure 9: Snapshot of surface salinity (g/kg) in the Caribbean basin and subtropical western Atlantic, from the 0.225 experiment.

current traversing the Caribbean basin on its way to the Gulf of Mexico { the future Gulf Stream { is a mixture of Sargasso Sea water (purple because of its high salinity) and equatorial water (yellow due to out ow from the Amazon). The Sargasso Sea component represents a circulation that is con ned to the North Atlantic and is primarily wind-driven, whereas the water moving up the Brazil coast represents, at least in part, the thermally driven interhemispheric conveyor belt ow. Returning to the question of eddy longevity in numerical models, we track in Fig. 10 an eddy that originates in the Brazil Current retro ection region and can be easily followed to the extreme western Caribbean. Since the salinity eld loses much of its contrast after passing the Lesser Antilles, we contour in Fig. 10 the vorticity eld. The sequence of maps was selected from plots made 17

Figure 10: Sequence of surface vorticity elds in the Caribbean basin and adjacent regions, from the 0.225 experiment. Time increases upward. Numbers shown in the color bar represent the arctangent of vorticity 105 sec.

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at 10-day intervals. At the beginning of the sequence (bottom of Fig. 10) the eddy in question is marked by the vorticity minimum (or extremum of negative vorticity) on the far right. The second snapshot, counting from the bottom, marks the time when the eddy encounters the Lesser Antilles. Note the red streamers of vorticity emerging from gaps in the island chain. A short time later, these streamers have merged to re-create a weakened version of the original eddy. In the third snapshot, the vorticity signature of this eddy is shown as a prominent red streak centered on 75W. One month later, the eddy arrives in the semi-enclosed basin bordered by Nicaragua and Panama. Downstream of that location, the ow is forced to curve cyclonically around the Honduran/Nicaraguan landmass. To make it around that bend, the eddy's vorticity must now be converted from curvature to shear vorticity. It is here where the eddy signature becomes diuse. In the fourth snapshot (second from the top), a green speck o the Yucatan coast at 21.5N marks a vorticity perturbation likely caused by the former eddy. The perturbation enters the billowing meander in the Gulf of Mexico just before the meander rolls up into a cuto eddy. The separated eddy is shown in the nal (uppermost) snapshot. An observer trained in vorticity-oriented weather forecasting techniques might be tempted to speculate that, based on the evidence presented in Fig. 10, eddy shedding in the Gulf of Mexico is modulated by the arrival of vorticity perturbations from the Caribbean. The 0.225 mesh size used in the present experiment, while nominally eddy resolving, is probably not sucient to determine the relevance of such a chain of events. A 0.08 mesh size, used in Atlantic basin simulations reported elsewhere 4, may be required to investigate this matter further { not to mention additional observations.

5 Summary and Outlook Many features in our quasi-global solutions appear realistic, but various simpli cations made in setting up these experiments have left their mark. Particularly unrealistic is the treatment of ice melt along the edge of the Antarctic continent which is presently parameterized as a seasonally invariant line source of fresh water along the southern domain boundary. This steady in ux of fresh water prevents formation of Antarctic Bottom Water in our simulations. Letting the ocean end at 65N and thus omitting the Greenland-IcelandNorwegian Sea is another shortcoming; this one likely aects the production rate and properties of North Atlantic Deep Water. The fact that the 1.4 model appears to be \comfortable" with forcing 19

elds representing present-day atmospheric conditions, at least on a 400-year time scale, is perhaps the most noteworthy result. The relative stability of the thermohaline circulation in this particular suite of experiments is in marked contrast to experiments by other investigators. One possible explanation is that our method of prescribing an atmospheric state is more tolerant of the model's ideosyncracies than the traditional method of nudging the model's surface T; S elds. In other words, we conjecture that penalizing the model for discrepancies between the modeled and the actually observed oceanic state interferes with its ability to develop and maintain a steady thermohaline circulation. The notion that inappropriate surface boundary conditions can lead to catastrophic events such as periodic conveyor belt breakdowns, and that the global thermohaline circulation is in fact more robust than presently assumed, deserves further study. words, we conjecture that by not penalizing the model for discrepancies between the modeled and the actually observed oceanic state we allow it to develop and maintain a relatively steady thermohaline circulation. The notion that inappropriate surface boundary conditions can lead to catastrophic events such as periodic conveyor belt breakdowns, and that the global thermohaline circulation is in fact more robust than presently assumed, deserves further study. Work has begun to correct three of MICOM's present shortcomings:  Model grid points associated with isopycnic layers lighter than the surface mixed layer, which presently sit idle, will be put to use in providing at least some rudimentary vertical resolution in the mixed layer.  An option to reference model potential density to nonzero pressure will be added to improve adherence of deep coordinate surfaces to neutral surfaces 9 . At the same time, thermobaric eects on compressibility will be added.  For numerical eciency reasons, the vertically averaged (barotropic) velocity and pressure eld is advanced in time separately from the rest of the 3-dimensional motion eld 1 . This mode splitting is imperfect at present, leading to \leakage" of information between the two modes which impacts overall numerical stability. What makes work with layer models such as MICOM most rewarding is the ability to establish cause-and-eect links. For example, if the model is found to produce too little or too much of a particular water mass (say, subtropical 18 water or AABW), the internal layer structure allows one to quickly trace the water mass to its source region. An inspection of the boundary conditions 20

or model physics at that particular location usually pinpoints the cause of the de ciency and suggests a remedy. Ideally, one wants a model that does everything right. The next best thing to a perfect model, however, is a model whose defects are tractable and thus can be removed over time.

Acknowledgments This work is sponsored by the U.S. Dept. of Energy under the Computer Hardware, Advanced Mathematics, and Model Physics (CHAMMP) program, and by the National Science Foundation under grant No. OCE92-06643.

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11. Oberhuber, J. M., 1993: Simulation of the Atlantic circulation with a coupled sea ice-mixed layer-isopycnal general circulation model. Part I: model description. J. Phys. Oceanogr., 23, 808{829. 12. Lynn, R. J., and J. L. Reid, 1968: Characteristics and circulation of deep and abyssal waters. Deep Sea Res., 15, 577{598.

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