***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.

![](media/image1.jpeg){width="3.002083333333333in" height="2.25in"}

*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.

![](media/image2.jpeg){width="3.002083333333333in" height="2.25in"}

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