Climate Modelling Group
School of Earth and Ocean Sciences


CORC Review Document to Scripps Institution of Oceanography
for NOAA OFFICE OF GLOBAL PROGRAMS


Subcontractor: University of Victoria


CORC REPORT PERIOD: May 1, 1994 through March 31, 1996

Agency: National Oceanic and Atmospheric Administration, Office of Global Programs

Project Title: The Lamont/Scripps Consortium for Climate Research - Dynamical Modeling of Climate Change.

NOAA Award No: NA47GP0188

Principal Investigator: Andrew Weaver

Project Period: May 1, 1994 through April 30, 1997

Performance Report Completed: March 25, 1996



1 Project goals

In the original proposal I noted that the development of a quantitative understanding of decadal-century climate variability was in its early stages. The modelling and prediction of decadal-century scale climate variability needed to be refined and expanded through a hierarchy of both coupled and uncoupled ice/ocean/atmosphere models. Model simulations must be carefully analysed and compared to both existing and future observations.

Together with research associates and students, I proposed to use existing models and develop new models for the purpose of large scale ocean/climate prediction on the decadal timescale. I further proposed to undertake a comparison of these different models with the purpose of understanding their individual shortcomings/assets. One of the major goals of this project was to obtain an analysis of the stability and variability properties of the global ocean thermohaline circulation (hereafter THC).

Since further advances in the understanding of the ocean's role in climate on the decadal timescale can only be obtained using coupled models, another goal of this proposal was to develop a global OGCM for the purpose of coupling it to an AGCM. The fully coupled atmosphere-ocean-ice GCM would then be used for climate change/prediction simulations. This later project was to involve collaboration with the Canadian Centre for Climate Modelling and Analysis (CCC).

2 Description of work originally proposed

The original proposal had five specific projects to:

* examine the structure, stability and variability properties of the THC in a global OGCM. The climatology of the global ocean model would be checked using CFC tracer data.

* develop a finite element, semi-Lagrangian OGCM.

* couple an energy balance climate model (EBM) to OGCMs of increasing complexity to investigate the role of simple atmospheric feedbacks on the stability and variability properties of the THC.

* Couple both thermodynamic and dynamic ice models to the aforementioned GCMs to investigate ice-ocean and ice-ocean-atmosphere feedbacks on the stability and variability of the global THC.

* Use simple zonally-averaged models to understand the stability and variability properties of the THC.

3 Project Accomplishments

Below I provide details regarding the accomplishments obtained through funding from the NOAA Consortium on the Ocean's Role in Climate. I have provided details under a more diverse range of subheadings than listed in the bullets above. All of the original proposed projects are on track as detailed below. It is unlikely that a global finite-element OGCM will be developed given the reduction of support from NOAA. I am presently seeking alternate funding sources in an attempt to keep this project going. Nevertheless, the groundwork for this project has been set and a global, finite-element barotropic model has been developed as have semi-Lagrangian advection algorithms for implementation into the model (see sections 3.7 and 3.8 below).

I decided to combine the projects involving the coupling of an OGCM to an EBM with the project involving the coupling of an OGCM to ice models. We have instead developed a coupled energy-moisture balance atmosphere model (EMBM)/thermodynamic ice model (TIM)/OGCM. By developing a fully coupled model we alleviated potential problems with surface boundary conditions.

3.1 Development of a coupled EMBM-OGCM-TIM

In process studies of the ocean's role in climate, mixed boundary conditions are often employed in which the salt flux is fixed, while a restoring condition on temperature is maintained. It is widely recognized that such an approach has serious deficiencies in its representation of the atmosphere. Through NOAA funding, Hughes and Weaver (1996), as a first step towards developing a better boundary condition for salinity, accounted for the physically-observed dependence of evaporation on SST. They showed that the stability and variability properties of the THC were largely unchanged when this new boundary condition was incorporated.

Using the fact that the timescale of atmospheric variability is generally short compared to the decadal-interdecadal timescales of interest here, an EMBM has been developed (Fanning and Weaver, 1996) for use in studying the ocean's role in climate change and variability. Since the timescale of variability of the cryosphere lies between that for the atmosphere and ocean, a simple thermodynamic ice model (Semtner, 1976) (which includes heat insulation and brine rejection) was also incorporated. This EMBM relates all components of the atmospheric system to only two prognostic variables: surface air temperature and specific humidity. In this manner, the model includes the primary hydrological and thermodynamic processes within the climate system, yet utilizes only modest computer resources, making it useful for coupled ocean-atmosphere studies on climate timescales.

Initial testing under fixed climatological sea surface temperature (SST) and surface wind conditions yields surface air temperatures, specific humidities and surface fluxes which are comparable to direct estimates. Precipitation compares less favorably with observations. As an extension to the climatological forcing case, a simple perturbation experiment in which the 1955-59 pentad was compared to the 1970-74 pentad by driving the model under the respective SST fields has also been conducted. The model exhibits a global air temperature decrease in the latter pentad of 0.27deg.C (comparable to direct estimates) with cooling in the northern hemisphere, and warming in the southern hemisphere. Such large scale cooling in the atmospheric model is driven by local changes in the prescribed SST fields, subsequently smoothed by atmospheric diffusion of heat.

In another project the EMBM has been coupled to the realistic geometry global OGCM described by Weaver and Hughes (1996). Precipitation over land was returned to the oceans through a series of river drainage basins, and we allowed for the water vapor-planetary longwave feedback. Although no flux adjustments are employed, this coupled climate model faithfully represents deep water formation in the North Atlantic and Southern Ocean, with upwelling throughout the Pacific and Indian oceans. Water mass characteristics in the vertical compare very favorably with direct (see Fanning and Weaver, 1996).

3.2 Simulation of the Younger Dryas event

The use of models to simulate past climatic events is an important avenue of investigation if one is to have confidence in their application to future climatic changes. To this end, as part of the Abrupt Climate Change component of the Consortium Science Plan we have undertaken a simulation of the Younger Dryas event (hereafter YD). The realistic geometry, global, coupled OGCM-EMBM is currently being used to investigate the transition between the last glaciation and the present Holocene. During the transition, an abrupt return to glacial climatic conditions, known as the YD occurred. The YD cold episode was particularly pronounced in regions bordering the North Atlantic, and is evidenced in northern European and maritime Canadian lakes and bogs; North Atlantic marine sediments; and northwestern European and central Canadian glacial moraines. Although strongest in the northern Atlantic region, further evidence indicates the impacts of the YD were felt throughout the globe.

While the exact cause of the YD is still unknown, a general consensus has emerged that it was linked to an oceanographic phenomena. The amplification of the YD signal in the northeastern North Atlantic suggests a primary role for the THC, particularly North Atlantic deepwater (NADW) production. The question naturally arises as to what source could supply the necessary excess freshwater needed to reduce NADW formation. The obvious sources are the polar ice caps and the Laurentide and Fennoscandian ice sheets (LIS and FIS, respectively). The traditional viewpoint is that the YD was triggered by the diversion of meltwater (due to the retreating LIS) from the Gulf of Mexico to the St. Lawrence (Broecker et al., 1988). However, the fact that deep water is usually formed in local high-latitude regions of small extent suggests that not only the amount, but also the location of meltwater introduced is crucial for interrupting the North Atlantic Conveyor.

We are currently conducting experiments to reinvestigate the climatic implications of the geographical and temporal change in the runoff from the LIS and FIS, utilizing estimated meltwater and precipitation runoff from drainage basins in and around the North Atlantic, before, during, and after the YD (Teller, 1990). While Maier-Reimer and Mikolajewicz (1989), using an ocean-only model, found they were capable of shutting down NADW production within 200 years from the time they deflected 347 km3/yr from the Gulf of Mexico into the St. Lawrence valley (roughly half that estimated to have occurred). Our results suggest the traditional meltwater diversion theory is incapable of inducing a shutdown of NADW. If, however, we apply the runoff estimates previous to the YD, the conveyor is pushed to the brink, allowing the diversion of LIS waters to completely halt NADW production. In an additional experiment we will consider the role of the FIS meltwater on the YD climate. These results will be written up for publication shortly.

3.3 Oceanic poleward heat transport and decadal variability as a function of OGCM resolution

One of the most important roles of the ocean in climate is its transport of heat from low to high latitudes. A fundamental, yet unanswered, question regarding the ocean's role in climate is whether or not eddies are important in transporting heat and salt poleward. Numerous studies (e.g., Cox, 1985; Bryan, 1986; Boening and Budich, 1992; Drijfhout, 1994) have suggested that eddies do not play a significant role and that the North Atlantic heat/salt transport is dominated by the meridional overturning transport.

All of the above works suffer from a major shortcoming since all the experiments were conducted using ocean-only models. In the limit of specified fluxes of heat and freshwater, the oceanic heat and salt transports are necessarily predetermined at equilibrium since the divergence of the transport gives the zonally-averaged flux. Thus, whether or not eddies are resolved will not change the total heat or salt transport at equilibrium. All of the above studies also used restoring boundary conditions on temperature and salinity. While these boundary conditions do not impose an exact constraint on the oceanic poleward heat and salt transports at equilibrium, they do largely determine the thermocline structure and hence may clamp the ability of the ocean models to freely regulate its heat and salt transport.

Five experiments have been conducted with a single hemisphere (60deg. x 60deg.) EMBM/OGCM, driven by zonally uniform wind stress and solar insolation forcing, with horizontal resolution ranging from 4deg. x 4deg. to 0.5deg. x 0.5deg.. Poleward heat transport is shown to significantly increase from coarse to finer resolution. Our coupled atmosphere-ocean model results contradict earlier studies mentioned above which showed that the time-variant (eddy) component of poleward heat transport counteracts increases in the time mean flow. This is perhaps related to the relatively short integration times utilized by these previous works. An additional mechanism may be the inclusion of salinity in our analysis. Previous works utilized buoyancy forcing alone so that eddies were aligned along isopycnals and hence no net heat transport occurs by their presence. In the present work, isotherms and isopycnals no longer coincide and a net heat transport can be expected if eddies propagate across isopycnals. Even though the net oceanic heat transport has not converged, the net planetary heat transport has converged owing to the strong constraint of energy balance at the top of the atmosphere. Consequently, the atmospheric heat transport is reduced to offset the increasing oceanic heat transport. Currently we are extending the resolution studies to 1/4deg. x 1/4deg.

Of particular importance in this study is that spontaneous decadal variability is found to exist in the 0.5deg. x 0.5deg. resolution case (in both coupled and uncoupled models). We find the variability is strongly linked to the value of the horizontal diffusivity utilized in the model. Increasing the diffusivity from 200 m2/s to 500 m2/s is enough to destroy the variability, while decreasing the diffusivity from 500 m2/s to 200 m2/s (in the 1deg. x 1deg. case) is capable of inducing the variability.

3.4 Flux adjustments and their influence in coupled models

During the last two years, a global ocean model was developed in collaboration with Warren Lee of the CCC for coupling to the CCC AGCM. Two versions of this model now exist: the first version is a high resolution model (1.8deg. x 1.8deg. x 29 levels) which has now been coupled to the CCC AGCM to investigate the climatic response to increasing atmospheric greenhouse gases and aerosols. The second version of the model is of slightly coarser resolution (3.6deg. x 1.8deg. x 19 levels) and is currently being used to understand the structure, stability and variability of the global ocean THC.

The surface heat and freshwater fluxes from equilibrium OGCM and AGCM climates have been examined in order to determine the minimum flux adjustment required to prevent climate drift upon coupling (Weaver and Hughes, 1996). It was shown that a dramatic climate drift of the coupled system is inevitable unless ocean meridional heat and freshwater (salt) transports are used as constraints for tuning the AGCM present-day climatology. It was further shown that the magnitude of the mismatch between OGCM and AGCM fluxes is not as important for climate drift as the difference in OGCM and implied AGCM meridional heat and freshwater (salt) transports. Hence a Minimum Flux Adjustment was proposed, which is zonally-uniform in each basin and of small magnitude compared to present flux adjustments. This minimum flux adjustment acts only to correct the AGCM implied oceanic meridional transports of heat and freshwater (salt).

We are also investigating the role of flux adjustments on interdecadal climate variability. The numerical simulations of Delworth et al. (1993), using the GFDL coupled model revealed interdecadal variability of the THC in the North Atlantic. It is not clear to what extent the variability in that study is preconditioned by the heat and salt flux adjustment fields required to prevent climate drift in the coupled model. It is also unclear whether or not this variability is linked to coupled ocean-atmosphere dynamics or to ocean dynamics alone. In order to do elucidate this, the GFDL coupled model has been adapted to our local IBM cluster. The oceanic part of this model is now being run under fixed-flux boundary conditions, made up of atmospheric fluxes (diagnosed from the atmospheric model at equilibrium) and the flux adjustment terms. If similar variability as in the fully coupled experiments is found, we can conclude that the variability is due to internal ocean dynamics alone.

3.5 Decadal variability in OGCMs with various subgrid-scale boundary layer parameterizations

During the last decade, the tuning of large-scale ocean models towards observations has been achieved by adjusting tracer mixing processes and surface boundary conditions. However, few alternatives to the traditional Laplacian closure of Reynolds stress have been implemented in OGCMs. The influence of the momentum dissipation parameterization and dynamical boundary conditions is not likely to be negligible at coarse-resolution and is worth being precisely evaluated. Therefore, an ocean model has been developed for a coarse-resolution, box-geometry, mid-latitude beta-plane, based on the planetary geostrophic equations and allowing for different choices of momentum dissipation (linear, harmonic, biharmonic or none) and associated boundary conditions (no-slip, free-slip or vorticity closure). These models were first compared to the GFDL OGCM with the same geometry and forcing to validate the planetary geostrophic dynamics. Results from this analysis will be written up shortly.

Of particular importance to the NOAA Consortium is the effect that different momentum dissipation parameterizations have on the internal decadal-interdecadal variability found in ocean models. Through the use of these efficient ocean models we have found that atmospheric forcing plays the leading role in generating decadal variability in ocean models: flux boundary conditions are the most likely to allow variability as no damping applies to surface anomalies, although the spatial distribution is important. A parameter sensitivity study of the oscillatory behaviour has also been carried out. Results suggest that the horizontal tracer diffusivity has a critical damping effect, while increasing the vertical diffusivity strongly enhances the oscillations. The parameterization or even inclusion of convection is found not to be necessary in sustaining the decadal variability, although it is necessary to remove static instabilities. As pointed out by Winton (1996), the variation of the Coriolis parameter with latitude is not necessary, so saying that Rossby wave propagation is not important for the oscillations. Greatbatch and Peterson (1995) proposed an explanation in terms of Kelvin waves propagating around the basin. This mechanism was investigated by moving the boundaries or by forcing an f-plane model with a symmetric (about the meridional centre of the basin) heat flux. None of these major changes remove the oscillatory behavior; therefore we conclude that Kelvin wave propagation is not important for the oscillation. As the variability is mainly observed in the region of separation of the western boundary current, we are now looking at 2-layer and 2-dimensional models to investigate an advective mechanism, as originally proposed by Weaver and Sarachik (1991).

3.6 Climate Variability as a function of mean climatic state

An interesting phenomenon which I observed in Weaver (1993) was that for different equilibria obtained under normal, 2xCO2, 4xCO2 and 8xCO2 forcing in coupled GCMs (and in the uncoupled CCC AGCM), the total planetary heat transport was fairly constant (in a global warming or cooling scenario there was net heat loss or gain by the planetary system but at equilibrium, the radiation balance at the top of the atmosphere was similar). This phenomenon was exploited in the coupled atmosphere-ocean box model developed by Tang and Weaver (1995). The results of this simple model suggest, as did the uncoupled ocean experiments of Weaver and Hughes (1994), that as the earth warms, the hydrological cycle intensifies and hence the THC becomes more variable.

3.7 Finite element modelling

A diagnostic, finite element, barotropic ocean model has been developed and used to simulate the mean circulation in the North Atlantic (Myers and Weaver, 1995). With the inclusion of the joint effect of baroclinicity and relief (JEBAR), the Gulf Stream is found to separate at the correct latitude off Cape Hatteras. Results suggest that the JEBAR term in three key regions (offshore of the separation point in the path of the main jet, along the slope region of the North Atlantic Bight and in the central Irminger Sea) is crucial in determining the separation point. The transport driven by the bottom pressure torque component of JEBAR, dominates the solution, except in the subpolar gyre, and is also responsible for the separation of the Gulf Stream. Excluding high latitudes (in the deep water formation regions) density variations in the upper 1000m of the water column govern the generation of the necessary bottom pressure torque in the model. Examination of results from the WOCE - Community Modelling Effort (CME) indicates that the bottom pressure torque component of JEBAR is underestimated by almost an order of magnitude, when compared to the diagnostic results. The reason for this is unclear, but may be associated with the diffuse nature of the CME model thermocline as suggested by the diagnostic model's sensitivity to the density field above 1000m.

The finite element model was then used to study the circulation of the North Pacific Ocean (Myers and Weaver, 1996). With the inclusion of the JEBAR term, the model produced a very realistic picture of the circulation. All major currents were reproduced with the calculated transports agreeing well with the observations. The effect of using different wind stress climatologies was also examined. Due to the dominance of the JEBAR term in the solution, the resulting circulations were all similar. Analysis of the seasonal cycle in the model supports Sakamoto and Yamagata (1995) in that JEBAR rectification can explain the decreased amplitude of the seasonal cycle and the out of phase relationship between observations and the predictions of flat-bottomed Sverdrup theory. Finally, density fields from 1955-1959 and 1970-1974 were used to examine aspects of interpentadal variability in the North Pacific Ocean.

3.8 The Development of Semi-Lagrangian Advection Algorithms for Ocean Models

In the initial phases of this NOAA project we began working on the development of semi-Lagrangian advection algorithms appropriate for use in ocean models. The Marotzke et al. (1988) model of the zonally-averaged 2-D THC was used as the test model. To determine the extent to which the accuracy and efficiency of the model depended on the numerical integration scheme, the test problem was solved independently using an explicit finite difference method and three implicit methods: a finite difference, a finite element and an upwind scheme. Integrations of the model to several equilibria were performed to determine the accuracy, efficiency and stability of each integration scheme as a function of time step. For the same level of accuracy the time step used in the semi-Lagrangian scheme was found to be at least five times greater than that employed in the case of the implicit methods. The time step used in the implicit methods in turn were at least six times greater than those needed in the explicit integration of the governing equations. It was further shown that Dirichlet, Neumann and mixed boundary conditions could be handled efficiently with the semi-Lagrangian method. The semi-Lagrangian method was also applied in the usual three-time level and two-time level interpolating versions as well as in a non-interpolating, three-time level version. The two-time level scheme further doubled the speed of the time integration step for the same level of accuracy, beyond that which was achieved using the three-time level scheme. The non-interpolating scheme did not eliminate the damping introduced by the interpolation. Hence we concluded that the two-time level semi-Lagrangian advection method was best suited for ocean climate studies. These results are detailed in Das and Weaver (1995).

3.9 A Mechanism for Interdecadal Variability in the Subpolar North Atlantic

The statistical relationships between various components of the subpolar North Atlantic air-sea-ice climate system were examined in order to investigate potential processes involved in interdecadal climate variability. It was found that SST anomalies concentrated in the Labrador Sea region have a strong impact upon atmospheric sea level pressure anomalies over Greenland, which in turn influence the transport of freshwater and ice anomalies out of the Arctic Ocean, via Fram Strait. These freshwater and ice anomalies are advected around the subpolar gyre into the Labrador Sea affecting convection and the formation of Labrador Sea Water. This has an impact upon the transport of North Atlantic Current water into the subpolar gyre and thus, also upon sea surface temperatures in the region. An interdecadal climate feedback loop was therefore proposed as an internal source of climate variability within the subpolar North Atlantic. Through the lags associated with the correlations between different climatic components, observed horizontal advection timescales, and the use of Boolean Delay Equation models, the timescale for one cycle of this feedback loop was determined to have a period of about 21 years.

3.10 CFCs and global ocean models

Robitaille and Weaver (1995) examined three sub-grid scale mixing parameterizations (lateral/vertical; isopycnal/diapycnal; Gent and McWilliams, 1990 -- GM) using a global ocean model in an attempt to determine which yielded the best ocean climate. Observations and model CFC-11 distributions, in both the North and South Atlantic, were used in the model validation (see attached figure for the South Atlantic results). While the isopycnal/diapycnal mixing scheme did improve the deep ocean potential temperature and salinity distributions, when compared to results from the traditional lateral/vertical mixing scheme, the CFC-11 distribution was significantly worse due to too much mixing in the southern ocean. The GM parameterization, on the other hand, significantly improved the deep ocean potential temperature, salinity and CFC-11 distributions when compared to both of the other schemes. The main improvement came from a reduction of CFC uptake in the southern ocean where the "bolus" transport canceled the mean advection of tracers and hence caused the Deacon Cell to disappear. These results suggest that the asymmetric response found in CO2 increase experiments, whereby the climate over the Southern Ocean does not warm as much as in the northern hemisphere, may be an artifact of the particular sub-grid scale mixing schemes used.

Due to the reduction of vertical mixing when the GM scheme was incorporated, numerical problems associated with vertical grid Peclet violations were found to occur. A flux-corrected transport (FCT) scheme (Gerdes et. al 1991) was therefore implemented into the GFDL OGCM and the consequences of using this advection scheme to eliminate these numerical problems are being investigated. Several integrations comparing mixing and advection schemes, in a simple model, demonstrate that it may be necessary to use a more sophisticated advection scheme (like FCT) when using isopycnal mixing parameterizations.

4 Ties to Other Projects

The research conducted through funding from this NOAA proposal has close ties with a number of other national and international projects. The knowledge gained from this research is of importance to international CLIVAR and WOCE activities in which I participate and collaborate extensively (I am co-Chair of the Canadian National Committee for WOCE). My interactions and collaborations with both the CCC and more recently with the NOAA GFDL are continuing. We now have a version of the GFDL coupled model running on our local workstations which is of a complexity between the simple coupled EMBM-TIM-OGCM and the CCC Coupled model.

5 Relevance to the Climate and Global Change Program

The research undertaken in this proposal is fundamental to two main components of the Climate and Global Change Program. While it is clear that the main emphasis of this research is on the role of the ocean in climate and global change, there has been some indirect evidence to underline the importance of properly representing clouds (especially marine stratocumulus clouds) in global coupled models (see section 3.4). Therefore one central goal of the Climate and Global and Change Program is being directly addressed:

* Reduction in the uncertainty of effects of clouds and ocean heat storage on climate and hence in the range of predictions of global warming over the next century

Many of the modelling and data analysis studies discussed in section 3 concerned the development of a detailed understanding of decadal-interdecadal climate variability. Most of the emphasis was on the region surrounding the North Atlantic Ocean. Thus a second goal of the Climate and Global Change Program is also being directly addressed:

* Predictions of anthropogenic interdecadal changes in regional climate in the context of statistics for natural, unpredictable, interannual and interdecadal variability.

6 Conceptual Plans and Priorities

Over the next three years I hope to continue improving our understanding of the mechanisms of decadal-interdecadal climate variability through the development of increasingly more sophisticated coupled models. The coupled EMBM-TIM-OGCM represents the simplest form of our coupled modelling studies. We shall continue to use it to explore simple thermodynamic feedbacks and gain insight into what results we might expect and which experiments we should undertake with the more complicated GFDL and CCC coupled models. In addition, the GFDL coupled model will be used to investigate questions concerning the existence of variability in the coupled climate system and how it varies as the mean climatic state changes (i.e, does the decadal-interdecadal climate variability found in the coupled model change as CO2 is increased in the atmosphere. Since the GFDL coupled model is far more computationally efficient than the CCC coupled model, it is hoped that the insight we gain from it will allow us to better streamline the future experiments we perform with the more sophisticated CCC coupled model.

References not in attached list:

Gent, P.R. and J.C. McWilliams, 1990: Isopycnal Mixing in Ocean Circulation Models, J. Phys. Oceanogr., 20, 150-155.

Boening, C.W. and R.C. Budich, 1992: Eddy dynamics in a primitive equation model: Sensitivity to horizontal resolution and friction. J. Phys. Oceanogr., 22, 361-381.

Broecker, W.S., M. Andree, W. Wolfli, H. Oeschger, G. Bonani, J. Kennett and D. Peteet, 1988: The chronology of the last deglaciation: Implications to the cause of the Younger Dryas event. Paleoceanogr., 3, 1-19.

Bryan, K., 1986: Poleward buoyancy transport in the ocean and mesoscale eddies. J. Phys. Oceanogr., 16, 927-933.

Cox, M.D., 1985: An eddy resolving numerical model of the ventilated thermocline, J. Phys. Oceanogr., 15, 1312-1324.

Delworth, T., S. Manabe and R.S. Stouffer, 1993: Interdecadal variations of the THC in a coupled ocean-atmosphere model. J. Climate, 6, 1993-2011.

Drijfhout, S.S., 1994: Heat transport by mesoscale eddies in an ocean circulation model. J. Phys. Oceanogr., 24, 353-369.

Gerdes, R., C. Koeberle and J. Willebrandt, 1991: The influence of numerical advection schemes on the results of ocean general circulation models. Clim Dynamics 5, 211-226.

Greatbatch, R.J. and K.A. Peterson, 1996: Interdecadal variability and oceanic thermohaline adjustment. J. Phys. Oceanogr., in press.

Maier-Reimer, E. and U. Mikolajewicz, 1989: Experiments with an OGCM on the cause of the Younger Dryas, Max Planck Institute fur Meteorologie, Report #39, 13 pp.

Marotzke, J., P. Welander and J. Willebrand, 1988: Instability and multiple steady states in a meridional-plane model of the thermohaline circulation. Tellus, 40A, 162-172.

Sakamoto, T. and T. Yamagata, 1995: Seasonal transport variations of the wind-driven oceaqn circulation in a two-layer planetray geostrophic model with a continental slope. J. Mar. Res., submitted.

Semtner, A.J., 1976: A model for the thermodynamic growth of sea ice in numerical investigations of climate. J. Phys. Oceanogr., 6, 379-389.

Teller, J.T., 1990: Meltwater and precipitation runoff to the North Atlantic, Arctic, and Gulf of Mexico from the Laurentide Ice sheet and adjacent regions during the Younger Dryas, Paleoceanogr., 5, 897-905.

Weaver, A.J., 1993: The oceans and global warming. Nature, 364, 192-193.

Weaver, A.J., and E.S. Sarachik, 1991: Evidence for decadal variability in an ocean general circulation model: an advective mechanism. Atmos.-Ocean, 29, 197-231.

Winton, M., 1996: The role of horizontal boundaries in parameter sensitivity and decadal-scale variability of coarse-resolution ocean general circulation models. J. Phys. Oceanogr., 26, 2.


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