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A Vertical Structure Module for Isopycnal Ocean Circulation Models

Kirk Bryan, Princeton Univ.

Summary

The ultimate value of ocean models in climate research depends on their ability of simulate the observed state of the oceans as indicated by actual measurements. Great progress has been made, but existing models which can be used for the long time scales of climate change of the order of centuries still do not provide a very satisfactory simulation of key climatic processes such as water mass formation in the subpolar oceans. Ocean models based on Cartesian coordinates have been well tested and their drawbacks are well known. Models based on a moving vertical coordinate have the potential to provide a much more accurate simulation of the advection and lateral mixing in the main thermocline, but are not 'mature' enough at present to gain widespread acceptance in the climate modeling community. This project is aimed at providing a module for representing the non-adiabatic processes in such a model and organizing the vertical structure. The module can then be inserted in the 'dynamic core' of existing models and used by the modeling community.

At present there are more than four efforts to develop isopycnal ocean models in the United States. However, all the research efforts could be considered subcritical. At present each of the models have been developed somewhat independently and the results cannot easily be rigorously compared. At the most recent meeting at Miami it was decided to agree on a common framework for cooperation in isopycnal model development. In this frame work models would be "unbundled", so that different components could be exchanged and compared.

The present effort in Princeton is aimed towards developing the vertical component of a hybrid model. The hybrid coordinate will be a fixed function of pressure in the upper ocean mixed layer, but will become a moving coordinate in the statically stable areas of the main thermocline. The formulation of mixing is based on the KPP of Large et al (1994) , which is widely used in ocean modeling. For defining the vertical density coordinate in statically stable areas of the thermocline our package uses the 'orthobaric density' scheme developed by De Szoeke et al (2000) at Oregon State University. This scheme has the advantage of defining a global coordinate which is a much more accurate representation of the local vertical and horizontal isopycnal gradients than any other method proposed to date.

The vertical module would ordinarily be called by the main model program at each time step. The package contains the following procedures:

1. The KPP scheme is used to compute the vertical mixing coefficients, which depend on stratification, vertical shear of the current and the proximity of the air-sea interface.
2. These coefficients are then used to calculate diffusion of temperature , salinity and the horizontal velocity.
3. The new values of temperature and salinity are used to calculate the Oregon State 'orthobaric density' profile. Where inversions exist, Cartesian coordinate reference pressures replace the previous interface pressures.
4. In stable parts of the water column the interfaces are 'nudged' up and down so that the orthobaric densities are relaxed back to the reference values, which are specified in the initial conditions.
5. Thus an entirely new set of interface pressures are created. In a final step the temperature and salinity is remapped from the old set of vertical coordinates to the new set.

To test the vertical package we have run a problem for a one-dimensional ocean which has a uniform salinity, but is driven by a varying heat flux at the surface. The heat flux varies on an annual cycle, creating a seasonal thermocline through the vertical mixing specified by KKP mixing. Physically, this test corresponds to an annual cycle in the high latitude oceans where the upper thermocline is eliminated in winter and reforms every summer. As a reference case we have specified Cartesian coordinates with uniformly spaced grid points in pressure. The solution for this case is shown in Figure 1. This is compared with the solution for a more typical hybrid case in Figure 2.

Figure 1 Potential temperature as a function of depth and time for a reference case with evenly spaced pressure grid points. The ordinate is depth in meters and the abscissa is time in days. The solution is after 10 years of integration.

Figure 1 and Figure 2 show a reasonable qualitative agreement, but considerable experimentation was required to achieve this. It was found to be very important to specify the reference levels in such a way that no abrupt discontinuities of resolution will exist at the base of the depth of convective penetration. One approach was to smooth the spacing of the interfaces at each time step. The best results were achieved without smoothing and simply specifying the reference pressures for the Cartesian part of the grid to have a spacing proportional to the local pressure. This provides high resolution in the surface mixed layer and a resolution that matches that of the isopycnal layers at the base of the convective layer.

Figure 2 The same as for Figure 1 except that the calculation is carried out on a hybrid vertical grid.

Comparison with observations can only be carried out when this package is inserted into a three-dimensional model. At first this will be tried out in the HIM (Robert Hallberg) isopycnal model at the Geophysical Fluid Dynamics Laboratory of NOAA. With the completion of the multi-processor code for the HYPOP isopycnal model at Los Alamos (John Dukowicz, John Baumgardner, William Lipscomb).

For more information on this contact:

Dr. Kirk Bryan, Senior Research Scholar
AOS Program, Sayre Hall, Princeton University
Phone: 609-258-3688
kbryan@splash.princeton.edu

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