Person:

Tziperman, Eli

The problem of determining the (eastern boundary) basic stratification and the buoyancy-driven circulation of the oceans is addressed. A global integral constraint relating the interior stratification and the air-sea heat fluxes is derived, based on the condition that the total mass of water of given density is constant in a steady state ocean. This constraint is then applied to two simple analytic models: The first is a continuous nonlinear diffusive model of the lower mid-depth and bottom circulation below the influence of the wind-driven circulation. It shows the tendency of the vertical density profile to look like an exponential profile in the presence of mixing. The integral constraint is used to relate the stratification and circulation of the bottom and mid-depth waters to the air-sea heat fluxes at the surface, where the deep densities outcrop. The second model is a layered one of the wind-driven circulation, mid-depth, and bottom water. The eastern boundary stratification of the model is determined from the air-sea heat fluxes, using the integral constraint and a parameterization of the mixing processes in layer models. A two gyre mid-depth circulation is found, driven by the cross-isopycnal diffusive velocities and affected by the variations in the depth of the main thermocline above it. The bottom circulation in both models is similar to that of the Stommel-Arons model.

Air-sea heat fluxes affect the deep buoyancy-driven flows not by direct cooling or heating, but through the formation of water masses that sink and spreak in the deep ocean. Thermal boundary conditions for the interior thermocline problem seem to require specification of the air-sea heat fluxes in addition to the specification of the density distribution at the base of the Ekman layer. Cross-isopycnal mixing processes are a crucial part of the dynamics, although numerically small. Together with the air-sea heat fluxes, they determine the basic vertical stratification of the wind-driven and deep circulation.

The relation between the circulation calculated from averaged hydrographic data (such as the Levitus data), and the actual time average circulation is examined using a CTD dataset which provides both time and space coverage of a region of the Mediterranean Sea. The connection between eddy mixing coefficients calculated from hydrographic data and the eddy fluxes (u′T′) they are intended to parameterize is also considered.

An inverse model is used to calculate circulation and mixing coefficients from the time average data. Then, the actual time averaged circulation is estimated by averaging six realizations of the instantaneous velocity field, and mixing coefficients are calculated by directly parameterizing the eddy fluxes of heat and salt.

Comparing the results obtained by the different procedures, it is concluded that the horizontal time average circulation can be reliably estimated from averaged and smoothed climatological data, but that it is nearly impossible to obtain physically meaningful mixing coefficient from such data.

An efficient procedure is presented for analyzing oceanographic observations with the aid of a general circulation model. Poorly known model parameters, such as eddy-mixing coefficients, surface forcing and tracer boundary fluxes, can be calculated by fitting model results to observations. Optimal estimates for all model fields, including the observed ones, can then be computed by running the model with the best-fit values of the calculated parameters. Information about the resolution and the error-covariances of the model parameters can be computed. This information is shown to be very valuable for critically evaluating how well the data determine the parameter's values. An adjoint model, similar in structure to the numerical model, uses information on model-data misfit to improve estimates of the unknown model parameters, and improve the fit to observations. The procedure is illustrated using simulated data and a simple, barotropic, nonlinear, quasi-geostrophic model. Examples are discussed in which friction parameters, wind forcing, and the steady-state circulation are determined from simulated vorticity and streamfunction observations.

Motivated by the Mediterranean outflow into the North Atlantic, a simple diffusive layer model of a deep buoyancy-driven circulation driven by a middepth inflow from the eastern boundary is developed. Cross-interfacial velocities are allowed and are related to the stratification through a density equation. The horizontal circulation, cross-interfacial (vertical) velocities, and density stratification are all coupled and are determined by the model as part of the solution. The importance of water masses injected into the ocean interior in driving the deep circulation is demonstrated. The inflow from the eastern boundary turns northward before reaching the western boundary current region and flows along the eastern boundary. The westward distance traveled by the inflow before turning northward can be derived by considering the dissipation of long westward traveling Rossby waves by the vertical density diffusion. Layers above and below the inflow are also set in motion, and their circulation is southward along the eastern boundary, opposite to the direction of the circulation in the inflow layer. The vertically integrated circulation of the model is similar to that in a Stommel-Arons model with the mass source on the eastern boundary: Most of the inflow flows to the western boundary current region, spreads there along the boundary, and reenters the interior as a broad northward current.

A finite difference linear inverse model is applied to hydrographic data from six summer and fall cruises in a small area (250 × 200 km) of the eastern Mediterranean sea. The temperature and salinity equations are used to form a linear set of equations for the reference geostrophic velocities and the mixing coefficients, which are then solved by singular value decomposition.

Advection by the horizontal velocities is the dominant process affecting the temperature and salinity fields in the region, and the model successfully resolves the horizontal velocities. Mixing and vertical advection are smaller by an order of magnitude, and the model cannot fully resolve the mixing coefficients and vertical velocities.

The six velocity fields calculated from the data indicate a very strong variability that makes it difficult to identify a repeating summer or fall circulation patterns on the scale of the region covered by the data.

An appendix contains the details of a new procedure for including linear inequalities in the solution of a rank deficient system of linear equations.