Contents 1. Introduction 2. Modeling Philosophy 3. Idealized, static polynyas 4. Time dependent polynyas 5. Shelf edge processes 6. Interannual variability 7. References

Modeling the Formation and Offshore Transport of Dense Shelf Water from High-Latitude Coastal Polynyas D. Chapman Senior Scientist, WHOI G. Gawarkiewicz Associate Scientist, WHOI The research described here was originally supported by the Arctic System Science (ARCSS) program at NSF, and more recently by the Western Arctic Shelf-Basin Interactions (SBI) project, which is co-sponsored by NSF through ARCSS and by the High-Latitude Dynamics Program at ONR. The fundamental goal of SBI is to understand the physical and biogeochemical processes that link the arctic shelves, slope and deep basins within the context of global change. The focus of SBI is the region including Bering Strait and the Chukchi and Beaufort Shelves (Figure 1). Our focus has been to understand the physical processes that modify the shelf water and exchange shelf water with deep basin water.

1. Introduction           

Directly beneath the ice cover of the deep Arctic basins is a 50-100 m layer of relatively fresh water that is near the freezing temperature. This surface layer is separated from the underlying warmer, saltier Atlantic water by the cold halocline layer, in which the temperature is near freezing while the salinity increases rapidly with depth. The cold halocline water is not a simple mixture of the surface layer and the Atlantic water. Aagaard et al. (1981) suggested that the cold halocline layer must be maintained by the lateral injection of cold, salty water; the most likely source being from the broad, shallow Arctic continental shelves where cooling rapidly reduces the temperature to near freezing and salt rejection accompanying ice formation can increase the salinity (and, hence, density) of the shelf waters.

	Figure 1: Map of the region of interest for the Western Arctic Shelf-Basin Interactions (SBI) project. Arrows indicate the directions of known mean flows through Bering Strait and across the Chukchi Shelf (click here for more details). [Larger image]

The Chukchi Shelf is a good candidate for such dense-water formation because (i) it is very shallow (40-50 m deep), (ii) there is a large seasonal variation in ice cover (i.e. seasonal ice formation), (iii) there are persistent wind-driven coastal polynyas in which ice can form at about ten times the seasonal rate, and (iv) there is little freshwater runoff to reduce the salinity of the shelf water.

The basic scenario is as follows. A mean transport of about 0.8 Sverdrups (1 Sv = 10^6 m^3/s) of relatively fresh and warm Pacific water flows through Bering Strait onto the shallow Chukchi Shelf (Figure 1). This flow splits into several branches as it crosses the shelf before possibly entering the Canada Basin. (Click here for details of this circulation.) During it's transit, it may be modified considerably by atmospheric cooling and ice formation processes. Our initial goal was to understand the ocean response to salt rejection during ice formation in a coastal polynya:

1. What ocean circulation is induced by a coastal polynya?
2. How dense can the water beneath a coastal polynya become?
3. How does the dense water move across the shelf and into the deep basin?
4. How much dense water can coastal polynyas produce?

2. Modeling Philosophy           

Numerical modeling studies can be grouped into two broad categories: (1) full-physics simulations, and (2) process studies. Full-physics simulations attempt to use a comprehensive model with complete physics, the most realistic geometry, forcing and boundary conditions either to reproduce existing observations or to predict future behavior. In our view, it is often difficult to isolate and understand individual processes that are embedded among many processes in such models. Frequently, the "numerical data" must be analyzed in the same manner as real ocean observations, making the interpretation unclear.

Process studies attempt to gain an understanding of some basic underlying physics by studying one or more processes in specific circumstances. Generally, the model geometry, forcing and/or boundary conditions are simplified in order to isolate the processes of interest, often involving parameterizations of effects for which a full model would be overly complicating. For example, we often study the ocean response to wind forcing by applying a stress to the ocean surface, in order to avoid using a full atmospheric model. Likewise, we can study the ocean response to ice formation in a coastal polynya by imposing a surface density flux to represent salt rejection, perhaps based on satellite images of ice distribution and estimates of heat flux, without a full ice-dynamics model. The results of process studies are universal, so they are useful for building intuition and are easily applied to new situations.

We have adopted the process study approach in our research. The choices of model, model domain, coastline and bathymetry depend on the particular scenario being considered, and we simplify the forcings, boundary conditions and/or geometry where appropriate in order to reduce the complexity of the dynamical system while maintaining enough dynamics to understand the important processes. We are ultimately interested in applying the results to observable situations, so we add more realism to the scenarios as we progress, trying not to compromise our likelihood of understanding the results.

3. Idealized, static polynyas           

We began with the simplest coastal polynya scenario we could imagine -- a static polynya of specified size and shape with an imposed salt flux at the surface to mimic the primary effect of salt rejection accompanying ice formation (Figure 2). The coastline is assumed straight and the bottom slopes gently away from the coast. We ignore the details of wind forcing and ice dynamics, and assume a constant ice formation rate (i.e. constant surface buoyancy flux).

Figure 2: Schematic of the geometry of our idealized, static polynya. A surface salt (or density) flux is applied within the half-elliptical region adjacent to the straight coastline (colored red). Initially the density of water beneath the salt flux increases. Geostrophic currents develop along the edge of the polynya, as indicated by the arrows. Eventually, this rim current develops instabilities that grow into eddies and move away from the polynya, carrying the denser water with them (Figure 3). [Larger image]

The ocean starts from rest. The water beneath the polynya becomes denser than the surrounding water, creating a density front along the edge of the polynya. This front adjust toward geostrophy, developing currents along the front -- clockwise at the surface and counter-clockwise at the bottom (Figure 2). The front is unstable, so any perturbations of the frontal currents (e.g. where the front intersects the coastal boundary) grow and form eddies that break away from the front and carry dense water with them. This is the mechanism by which the dense water is carried across the shelf. It does not flow as a smooth gravity current, but rather is carried by small-scale (15-30 km diameter), intense eddies with swirl velocities of 20-30 cm/s. The eddies move slowly offshore as counter-rotating vortex pairs with translation speeds of 1-2 cm/s (Figure 3). More details can be found in Gawarkiewicz and Chapman (1995).

With continued buoyancy forcing, the eddies eventually carry the dense water offshore as fast as the surface flux can increase the density, so a quasi-equilibrium is reached in which the density increase beneath the polynya is fairly constant (Figure 4). A simple theory, based on the approach of Visbeck, Marshall and Jones (1996), allows us to estimate the time it takes to reach this quasi-equilibrium and the maximum density increase produced by the polynya, as a simple algebraic function of polynya size and shape, water depth, and buoyancy forcing (Chapman and Gawarkiewicz, 1997).

These results have helped in the understanding of some recent laboratory experiments on convection in a two-layer fluid (Narimousa, 1996). Surface cooling sometimes causes the upper layer fluid to penetrate through the interface into the lower layer, while sometimes it does not. Our simple theoretical estimates of the quasi-equilibrium density increase explain this behavior (Chapman, 1997). If the parameters are such that the increased density in the upper layer at equilibrium is larger than the density difference across the interface, then convection will penetrate into the lower layer. If the equilibrium density increase is less than the density difference across the interface, the dense water remains lighter than the lower layer water, and hence it remains in the upper layer.

	Figure 3: Plan views of the density increase at the bottom at three different times for an idealized, static polynya. A constant surface density flux is imposed within the white half-ellipse adjacent to the coastline. The colorbar indicates the density increse in kg/m^3. [Larger image]	Figure 4: Average density increase near the coast, within the polynya region, as a function of time during the calculation shown in Figure 3 (cyan curve). Initially, the increase is linear because the water stays within the polynya. After the eddies carry the denser water away from the polynya (after about day 12), the density increase reaches a quasi-steady value. The yellow curve indicates the density increase if no eddies formed. [Larger image]

An important aspect of our specified polynya is the thin ice region surrounding the polynya over which the ice formation rate (i.e. surface buoyancy flux) decays from its maximum in the polynya to zero outside the polynya, where the water is totally ice covered. If this region is large, eddy formation can be delayed, and a much larger density increase can be produced within the polynya before the quasi-equilibrium is reached. Thus, the width of the forcing decay region appears explicitly in the theoretical estimates described above. The relation of these estimates to those without the forcing decay region, and the transition between the two cases, has been explored in Chapman (1998).

We have examined some effects of bottom topography and ambient alongshelf currents on the formation and offshore transport of dense water from coastal polynyas. First, we included a single submarine canyon that intersected the original idealized, static polynya (Chapman and Gawarkiewicz, 1995). The basic formation of dense water eddies was qualitatively identical to the smooth topography cases. However, eddies that happen to move into the canyon quickly cascade down the steep canyon walls and are channeled offshore as an intermittent gravity current that rides along the right wall of the canyon into deeper water (Figure 5). The gravity current tends to "pulse" as each eddy passes. The current is slow and strongly stratified, so little mixing with ambient fluid takes place, in marked contrast to gravity currents associated with large overflows, e.g. the Mediterranean Sea. The model features are consistent with recent observations of dense water currents in Barrow Canyon (Weingartner et al., 1998).

An ambient alongshelf current carries water out of the polynya during ice formation, thereby reducing the density increase for a given surface buoyancy flux. Furthermore, the distribution of water with increased density is altered substantially. Surprisingly, an alongshelf current can inhibit the tendency of dense water eddies to enter submarine canyons because the alongshelf current itself tends to follow isobaths and flow around the canyon, carrying the dense water eddies with it (Figure 6). This suggests the combined importance of ambient shelf currents and bottom topography in determining the pathways of dense water transport across continental shelves. Details are found in Chapman (2000).

Figure 5: Plan views of the density anomaly at the bottom at four different times for an idealized, static polynya with a constant surface density flux (as in Figure 3), but with a submarine canyon intersecting the polynya (indicated by the black depth contours). As eddies move close to the canyon, they slide down the steep canyon walls and flow along the canyon axis as a slow and intermittent gravity current. The colorbar shows the density increase in kg/m^3. [Larger image]	Figure 6: Plan views of the density increase at the bottom at four different times for an idealized, static polynya, but with an alongshelf current from left to right of 10 cm/s imposed at the left boundary of the model. A constant surface density flux is imposed within the white half-ellipse adjacent to the coastline. The colorbar indicates the density increase in kg/m^3. The dashed contours are isobaths, indicating a submarine canyon crossing the shelf at x=125 km. Note that the dense water does NOT flow down the canyon, despite moving directly toward the canyon edge. Instead, the alongshelf current flows around the canyon head, almost parallel to the isobaths, carrying the dense water eddies with it. [Larger image]

The estimates for the quasi-equilibrium density increase and time to reach this equilibrium depend on a proportionality coefficient that represents the efficiency with which eddies transport dense water across the front at the polynya edge. This has traditionally been treated as an unknown constant that is estimated by fitting numerical, laboratory and observed responses. In an attempt to understand this coefficient from dynamical principles, Spall and Chapman (1998) developed a theoretical model in which cross-frontal heat (or density) flux is accomplished by heton pairs. They showed that the unknown coefficient can be estimated reasonably well as the ratio of the cross-frontal translation velocity of the heton pairs to the along-frontal current speed.

4. Time-dependent polynyas           

Figure 7: Average density increase near the coast, within the polynya region, as a function of time for a calculation forced with a time-varying polynya based on estimates of observed polynya width and surface density flux for the Chukchi Shelf during the winter of 1991-1992 (cyan curve). As in the idealized cases, the density increases rapidly until eddies form and carry the dense water away from the polynya region, producing a quasi-equilibrium. The yellow curve indicates the density increase if the yearly averaged forcing is applied and held costant for the entire period. The details are different, but the yearend product is comparable. [Larger image]

The static polynya studies assume that the polynya remains open with a fixed shape and that the ice formation rate is constant. Of course, real polynyas open and close on time scales of days to weeks, with their shapes varying tremendously. In fact, polynyas may not remain open long enough for the quasi-equilibrium to be reached. To address these issues, an investigation of the ocean response to time-dependent polynyas has been made (Chapman, 1999).

The opening and closing of the polynya was modeled using the Pease (1987) model in which polynya width is determined by a balance between the surface wind stress blowing the newly formed ice offshore (opening the polynya) and the new ice formation (closing the polynya). Using idealized atmospheric variables (air tempreature and wind speed), as well as estimates based on observations, it was shown that the ocean basically integrates the effects of short-duration polynyas and behaves in much the same manner as the idealized, static polynyas. The density within the polynya increases with each successive polynya until eddies form and begin to carry the dense water away from the polynya region. The density increase is then limited, despite additional polynya events throughout the winter. The time-dependent response is nearly the same as if the polynya were static and forced with the seasonally averaged surface buoyancy flux, suggesting that the simple algebraic estimates of density increase may be useful even for variable polynyas on longer time scales (Figure 7).

5. Shelf-edge processes           

The effect of dense water transport across an idealized continental shelf has important implications for exchange between the shallow continental shelves and the deep ocean basins within the Arctic Ocean. Gawarkiewicz (2000) found that dense water eddies are capable of inducing flows which cross the shelfbreak. Using ambient (linear) stratification which is typical of the Chukchi Shelf, and forcing typical of coastal polynyas, the dense water was injected over the continental slope at a depth of 100 m, roughly the depth of the shelfbreak (Figure 8). A theoretical estimate of this depth of maximal transport of dense water was developed, which depended on both the strength of the surface buoyancy forcing in the coastal polynya as well as the strength of the ambient stratification.

A key result of this work is that fluxes from the shelf to the slope are highly variable in both time and space (Figure 9), depending on the detailed trajectory and structure of individual eddies as they reach the shelfbreak. We anticipate that future observations will show similar complex behavior in terms of cross-shelfbreak fluxes, with large variations on time scales of days and spatial scales of order 10 kilometers.

Figure 8 : Along-slope distribution of a passive tracer seaward of the shelfbreak after 90 days of a model run. The maximum concentrations are at a depth of 90 to 120 meters, which is similar to the depth of the shelfbreak. The tracer was initialized next to the coast, within an idealized coastal polynya. [Larger image]	Figure 9: Time series of (negative) buoyancy fluxes across the shelfbreak (y=50 km), and slope (y=62 and 73 km) from dense eddies crossing the shelfbreak. Note the large day to day variability at the shelfbreak as individual eddies cross. [Larger image]

6. Interannual variability           

Figure 10: Distribution of density increases and volumes for each of 21 winters (1978-1998), generated by forcing an idealized model of the Chukchi Shelf with estimates of polynya width and surface density flux based on observed meteorological data and a simple polynya model. The colorbar on the right shows the density anomalies in kg/m3. Note the high degree of interannual variability and wide range of density increases. [Larger image]

Several estimates have been made of the total amount of dense water capable of feeding the cold halocline layer that could be produced on Arctic continental shelves by coastal polynya processes (e.g. Cavalieri and Martin, 1994; Winsor and Bjork, 2000). These results are based on estimates of salt rejected during ice formation, which is then available to increase the density of the shelf water. However, the studies have not included a dynamical ocean model to determine the actual density increase from the polynyas. Therefore, Winsor and Chapman (2001) have used the polynya model of Winsor and Bjork (2000) to force an idealized ocean model to estimate the dense water production on the Chukchi Shelf for the winters of 1978-1998.

Results show that the density increase during typical winters is substantially less than expected from previous estimates. Only in a few of the years is the density increase enough (when added to the density of the Bering Strait inflow) to produce cold halocline water. There is considerable interannual variability in both the volume of dense water produced and the maximum density increase (Figure 10). These results are consistent with the intermittency of dense water found on the Chukchi Shelf and suggest that other sources of cold halocline water are probably important.

7. References           

Aagaard, K., L. K. Coachman, and E. Carmack, 1981. On the halocline of the Arctic Ocean. Deep-Sea Res., 28A, 529-545.

Cavalieri, D.J. and S. Martin, 1994. The contributions of Alaskan, Siberian, and Canadian coastal polynyas to the cold halocline layer of the Arctic Ocean, J. Geophys. Res., 99, 18343-18362.

Chapman, D.C., 1997. A note on isolated convection in a rotating, two-layer fluid, J. Fluid Mech., 348, 319-325.

Chapman, D.C., 1998. Setting the scales of the ocean response to isolated convection, J. Phys. Oceanogr., 28, 606-620.

Chapman, D.C., 1999. Dense water formation beneath a time-dependent coastal polynya, J. Phys. Oceanogr., 29, 807-820.

Chapman, D.C., 2000. The influence of an alongshelf current on the formation and offshore transport of dense water from a coastal polynya, J. Geophys. Res., 105, 24007-24019.

Chapman, D.C. and G. Gawarkiewicz, 1995. Offshore transport of dense shelf water in the presence of a submarine canyon, J. Geophys. Res., 100, 13373-13387.

Chapman, D.C. and G. Gawarkiewicz, 1997. Shallow convection and buoyancy equilibration in an idealized coastal polynya, J. Phys. Oceanogr., 27, 555-566.

Gawarkiewicz, G. and D.C. Chapman, 1995. A numerical study of dense water formation and transport on a shallow, sloping continental shelf. J. Geophys. Res., 100, 4489-4507.

Gawarkiewicz, G., 2000. Effects of ambient stratification and shelfbreak topography on offshore transport of dense water on continental shelves, J. Geophys. Res., 105, 3307-3324.

Narimousa, S., 1996. Penetrative turbulent convection into a rotating two-layer fluid, J. Fluid Mech., 321, 299-313.

Pease, C. H., 1987. The size of wind-driven coastal polynyas, J. Geophys. Res., 92, 7049-7059.

Spall, M.A. and D.C. Chapman, 1998. On the efficiency of baroclinic eddy heat transport across narrow fronts, J. Phys. Oceanogr., 28, 2275-2287.

Visbeck, M., J. Marshall and H. Jones, 1996. Dynamics of isolated convective regions in the ocean, J. Phys. Oceanogr., 26, 1721-1734.

Weingartner, T.J., D.J. Cavalieri, K. Aagaard and Y. Sasaki, 1998. Circulation, dense water formation, and outflow on the northeast Chukchi Shelf. J. Geophys. Res., 103, 7647-7661.

Winsor, P. and G. Bjork, 2000. Polynya activity in the Arctic Ocean from 1958 to 1997, J. Geophys. Res., 105, 8789-8803.

Winsor, P. and D.C. Chapman, 2001. Distribution and interannual variability of dense water production from coastal polynyas on the Chukchi Shelf, J. Geophys. Res., submitted.

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