LAURIE PADMAN, Earth and Space Research, Seattle, Washington 98102-3620
ROBIN ROBERTSON, College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331-5503
We have built an eight-constituent, nonlinear, finite-difference model of barotropic tides in the Weddell and Scotia Seas and have used this model to investigate some possible effects of tides on the large-scale circulation and hydrography of the region. We summarize the model, then consider the influence of tides on the generation of mixing in the pycnocline, particularly near the shelf break and near the ice front of the Filchner-Ronne Ice Shelf (FRIS).
The model is described in detail in Robertson, Padman, and Egbert (in press). In brief, the domain extends from 83°10'S to 55°00'S and from 84°00'W to 10°00'E, thus including the ocean cavities under the FRIS and other ice shelves. Over most of the domain, we obtained bathymetry from the ETOPO-5 database, which provides depths on a 1/12° global grid, but modifications to the model bathymetry were made in several regions where more recent data have become available. Bathymetry based on satellite altimetry and aircraft gravimetric surveys, as well as depth measurements from Ice Station Weddell (LaBrecque and Ghidella 1992) was used in the western Weddell Sea in the region 73°S to 65°S and 60°W to 44°W. Under the FRIS, measurements of water-column thickness were used instead of bathymetry (Vaughan et al. 1994). An Arakawa-C grid was used, with a grid spacing of 1/6° in longitude and 1/12° in latitude, resulting in a 565 x 339 array.
For this first modeling effort, we chose a two-dimensional, depth-integrated barotropic model, therefore ignoring variations of currents with depth. The model uses the mass conservation and depth-integrated shallow-water momentum equations, including the pressure and coriolis terms, astronomical forcing, bottom friction, and lateral viscosity. Eight tidal constituents were modeled, four semidiurnal and four diurnal. For land boundaries, both the no-normal flow and no-slip conditions were used. At open ocean boundaries, we used tide-height coefficients obtained from "TPXO.3," an updated version of the global inverse tidal solution described in Egbert, Bennett, and Foreman (1994) and based on assimilation of approximately 3 years of TOPEX/Poseidon altimetry data. After model stabilization, the elevation time series were harmonically analyzed for 45 days, producing fields of the amplitude and phase for each tidal constituent. The velocity components were also harmonically analyzed for 45 days to obtain estimates of the major and minor axes, inclination, and phase for the tidal ellipses.
Our primary interest in Weddell Sea tides is in their potential to lead to mixing of various water masses. This expectation of mixing is based on our experience with ocean turbulence data collected in the Arctic Ocean (see Padman 1995) and the hypothesis of Foster, Foldvik, and Middleton (1987) that ocean mixing near the shelf break in the Weddell Sea might be greatly enhanced by tides. There are several dynamical mechanisms by which tides can lead to mixing, but most are too complicated to explain in useful detail in this report. Instead, we consider here only essentially qualitative estimates of the potential for mixing as a function of geographic location.
The simplest correlation we can imagine is between mixing and total tidal energy density. This latter measure can be usefully understood in terms of a spatially dependent average tidal current speed, áU(x,y)ñ , that is calculated from time series based on all modeled tidal constituents (figure). Typical values over the deep basins are small, frequently less than 3 centimeters per second (cm s-1). Over the continental shelves, · áU(x,y)ñ normally exceeds 10 cm s-1 and sometimes exceeds 1 meter per second (m s-1). The largest values can occur at quite strategic locations for significant mixing processes in the Weddell Sea. For example, energetic tidal currents (predominantly semidiurnal) occur at the front of the FRIS. These currents perform a dual function of not only creating mixing where Ice Shelf Water and Western Shelf Water interact but also straining the sea-ice cover and, thus, permitting a greater coupling between the ocean and atmosphere. Another region of considerable interest is around the southern shelf break, where much of the mixing of water masses that determines the ultimate temperature-salinity properties of Weddell Sea Bottom Water and Antarctic Bottom Water occurs. In particular, note the very high currents near General Belgrano Bank; currents here are primarily associated with diurnal tides.
A more complicated, but still essentially qualitative, model of mixing by tides via internal tide generation (Sjöberg and Stigebrandt 1992) has been applied by us to the Weddell Sea to map the likely mixing "hot spots." A simple calculation in which all the generated baroclinic tidal energy is dissipated through diapycnal mixing in the pycnocline predicts a regional mean heat flux of about 20 watts per square meter (W m-2) in the Weddell Sea, consistent with recent estimates of the heat loss from the Warm Deep Water (WDW) in the Weddell Gyre. As expected, mixing is concentrated near the upper slope, particularly in the southern Weddell Sea. The Sjöberg and Stigebrandt (1992) model, unfortunately, cannot deal with forced baroclinic tides south of each tidal constituent's "critical latitude," i.e., the latitude at which the constituent's frequency equals the local coriolis frequency, nor does it allow for a flux of tidal energy into higher frequency internal waves that could then also contribute to mixing rates (Padman 1995). We are, therefore, now concentrating on running a more realistic, vertically stratified numerical model forced offshore by the principal semidiurnal barotropic tide (M 2 ), and preliminary results suggest that mixing will be very intense near the M 2 critical latitude of 74°29'S, which lies near the oceanographically important southern shelf break.
We have not yet run our tidal model coupled to a general circulation (wind- and thermohaline-forced) model or with realistic sea-ice cover. Our results to date demonstrate, however, that tides are a major component of the total oceanic kinetic energy in the Weddell Sea and may dominate as the source of turbulent kinetic energy and mixing in regions of significant water mass formation and modification. For these reasons, plus the tides' ability to modify sea-ice characteristics such as average concentration and roughness, we conclude that tides cannot be neglected in attempts to quantify the formation rates of such globally significant water masses as Antarctic Bottom Water. Finally, we note that sensitivity studies by us indicate that the poor available bathymetric information, particularly for the southern and western shelves, is a critical limiting factor to our ability to model tides accurately. Increasing the physical sophistication of models cannot overcome the deficiencies caused by the poor bathymetry.
This research was supported by National Science Foundation grants OPP 93-17319 and OPP 96-15524.
Egbert, G.D., A.F. Bennett, and M.G.G. Foreman. 1994. TOPEX/POSEIDON tides estimated using a global inverse model. Journal of Geophysical Research , 99(C12), 24821-24852.
Foster, T.D., A. Foldvik, and J.H. Middleton. 1987. Mixing and bottom water formation in the shelf break region of the southern Weddell Sea. Deep-Sea Research , 34, 1771-1794.
LaBrecque, J.L., and M.E. Ghidella. 1992. Estimates of bathymetry, depth to magnetic basement, and sediment thickness for the western Weddell Basin. Antarctic Journal of the U.S. , 27(5), 68-70.
Padman, L. 1995. Small-scale physical processes in the Arctic Ocean. In W.O. Smith and J.M. Grebmeier (Eds.), Arctic oceanography: Marginal ice zones and continental shelves. Coastal and estuarine studies (Antarctic Research Series, Vol. 49). Washington, D.C.: American Geophysical Union.
Robertson, R., L. Padman, and G.D. Egbert. In press. Tides in the Weddell Sea. In S. Jacobs and R. Weiss (Eds.), Oceans, ice, and atmosphere: Interactions at the antarctic continental margin (Antarctic Research Series Vol. 75). Washington, D.C.: American Geophysical Union.
Sjöberg, B., and A. Stigebrandt. 1992. Computations of the geographical distribution of the energy flux to mixing processes via internal tides and the associated vertical circulation in the ocean. Deep-Sea Research , 39, 269-291.
Vaughan, D.G., J. Sievers, C.S.M. Doake, G. Grikurov, H. Hinze, V.S. Pozdeev, H. Sandhäger, H.W. Schenke, A. Solheim, and F. Thyssen. 1994. Map of the subglacial and seabed topography; Filchner-Ronne-Schelfeis/Weddell Sea, Antarktis, scale 1:2,000,000. Frankfurt am Main, Germany: Institut für Angewandte Geodäsie.