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A Vertical Structure Module for Isopycnal Ocean Circulation Models

Kirk Bryan, Princeton Univ.

Summary

The credibility of ocean models for climate research depends on their ability to simulate the observed state and natural variations of the oceans as indicated by actual measurements. Existing models, which can be used for simulating the long time scales of climate change of the order of centuries, still do not provide a very satisfactory treatment 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.

The present effort in Princeton is aimed towards developing the vertical component of a hybrid model as a nearly independent module that could be used in a variety of ‘core' isopycnal models that are under development. The hybrid vertical 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 parameterization of Large et al (1994) , which is widely used in ocean modeling. At present the vertical density coordinate in statically stable areas of the thermocline our package is based the 'orthobaric density' scheme developed by De Szoeke et al (2000) at Oregon State University. This feature can easily modified if another definition of the vertical coordinate appears more advantageous.

The approach to implementing the hybrid model is based on vertical remapping. At each time step temperature and salinity are mixed vertically using the KPP parameterization. Next the water column is regridded by interpolation. In stable areas the interfaces are made to coincide with reference target ‘orthobaric densities'. In unstable areas the interfaces are made to coincide with previously determined reference depths. As a final step temperatures and salinities are interpolated to the new vertical grid in such a way that temperature and salinity are conserved. We believe that the proposed method is inherently simpler than that of the HYCOM model at the Univ. of Miami, but all advantages and the disadvantages of this remapping approach will not be known until tests are carried out in a the actual geometry of the World Ocean.

Effort over the last year has been devoted to the complex task of porting the one-dimensional mixing module to a three-dimensional, ‘core' isopycnal model. Since the HYPOP model being developed at LANL is still being tested, we have used the HIM model designed by Robert Hallberg available at GFDL. The HIM has recently been recoded in Fortran 90, which made the task much easier.

A test problem has been designed, which will be used to compare different methods of modelling the upper ocean. To test the hybrid ocean vertical package we require a three-dimension geometry, which includes both actively convecting regions and stably stratified regions. A special concern is the accurate estimation of horizontal pressure gradients in the model. It is well known that ocean models can compute accurate horizontal gradients in horizontal or isopycnal coordinates. Special care must be taken in the general case, which will apply to the transition regions which lie between areas of active convection and stably stratified regions.

Figure 1 (above) A plan view of the test basin showing the temperature and the velocity field in an upper layer of the hybrid version of the HIM model.

Our test geometry is an enclosed box ocean of uniform depth which is only 180 km by 180 km and 4 km deep. A circularly symmetric heating is imposed at the surface.

The water is initially heated at the center and cooled along the edges. The temperature and density differences created in this way are smoothed out by the horizontal transfer of heat by the velocity field. Figure 1 shows an anticyclonic flow pattern which would be expected for a warm anomaly near the surface surrounded by colder and denser water.

Figure 2 A vertical cross section from the model. (upper panel) The penetration of the temperature field into the hybrid model. The lateral exchange of heat by the model circulation prevents a deep penetration of the imposed temperature anomalies.(lower panel) The configuration of the hybrid coordinate surfaces. Note the coordinate surface is pushed upwards in response to surface heating at the center and downwards in response to cooling at the edges.

Our future plan is to calculate reference solutions based on a finely spaced Z coordinate vertical grid and use that to test our hybrid grid sytem in a three-dimensional framework, as we have already done in one-dimension. With the completion of the multi-processor code for the HYPOP isopycnal model at Los Alamos (John Dukowicz, John Baumgardner, William Lipscomb) it will be possible repeat the same test calculations using the HYPOP isopycnal core model. We anticipate that there will be unique problems in adapting various core isopycnal models to our new isopycnal system.

For further information on this subject 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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