Climate Modelling Group
School of Earth and Ocean Sciences

NSERC World Ocean Circulation Experiment Collaborative Special Project

Progress Report and Budget: WOCE Fiscal Year 1993/94

Principal Investigator:
Dr. Andrew J. Weaver
School of Earth and Ocean Sciences
University of Victoria
PO Box 1700
Victoria, British Columbia

tel: (250) 472-4001
fax: (250) 472-4004
Project Title: Ocean Modelling /Model Development

My NSERC/WOCE grant has been used to fund my research into the role of the ocean in climate change/variability. In particular, I have been focussing on the stability and variability properties of the thermohaline circulation. Over the past two years I have written two review articles on this topic (Weaver, 1994; Weaver & Hughes, 1992). I have also recently begun to develop simple coupled models for the purpose of studying feedbacks in the coupled atmosphere-ocean system. The NSERC/WOCE grant has been used to either partially or fully support one MSc student (T. Wohlleben), six PhD students (A. Fanning, T. Hughes, P. Myers, T. Reynaud, D. Robitaille and L. Zhang) and three research associates (S. Das, R. Outerbridge and B. Tang).

Together with my students and research associates, I have either submitted or have had a number of manuscripts appear over the last year. Briefly, Weaver et al. (1993) was a detailed sensitivity analysis of the stability and variability properties of the thermohaline circulation. We showed how thermohaline variability on fundamental timescales (diffusive, meridional overturning and horizontal advective) could be excited depending on the relative importance of thermal vs freshwater vs wind forcing. T. Hughes and I also wrote a manuscript concerning the existence of multiple equilibria in an idealized global ocean model (Hughes & Weaver, 1994). Under present day forcing we showed that there was a clear preference for the "conveyor belt" equilibrium. Furthermore, our model results suggest that there are three possible modes for the North Atlantic conveyor: 1) the present day "normal" state; 2) a state with no North Atlantic overturning (colder); 3) a state with enhanced thermohaline overturning (warmer).

In a paper which recently appeared in Nature (Weaver & Hughes 1994) we further showed how transitions between these modes could be excited through stochastic atmospheric forcing. This theory provides a possible explanation for the recent, and highly publicized, Greenland ice core data for the Eemian (GRIP 1993). That is, we specifically addressed the question: "Why would the stability of our present Holocene be different from that of the Eemian interglacial?", and quantitatively showed that the difference could be linked to an enhanced hydrological cycle associated with the warmer mean climate of the Eemian. Recent coupled atmosphere-ocean simulations (Manabe & Stouffer 1993) of the climatic response to increasing atmospheric CO2, for which I was asked to write a Nature News & Views (Weaver 1993), have also noted that the hydrological cycle intensifies as the climate warms. If the variability found in the GRIP ice core data is corroborated then the Eemian interglacial may therefore offer us a glimpse as to the type of rapid climate variability which we might expect in a future climate warmed through anthropogenic greenhouse gas emissions. The policy implications of this work were recently submitted (jointly with an economist, C. Green at McGill University), upon invitation, and subsequently accepted for publication in a US public policy journal (Weaver and Green, 1994) and I have been contacted by numerous MLAs, government officials, newspapers, radio and television stations to discuss the implications of these findings (see some attached samples and the list below).

An interesting phenomenon which I observed in writing the News & Views piece was that for different equilibria obtained under normal, 2xCO2, 4xCO2 and 8xCO2 forcing in coupled GCMS (and indeed in the uncoupled Canadian Climate Centre atmospheric GCM), 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 & Weaver (1994). The results of this simple coupled model suggest, as did the uncoupled ocean experiments of Weaver & Hughes (1994), that if the earth were to warm by a few degrees then we might expect rapid climate variability as seen in the last interglacial period.

In an another project (Weaver et. al., 1994) we used the "observed" North Atlantic P-E field, Levitus sea surface temperature (SST) and Hellerman and Rosenstein wind stress data to drive a "realistic" geometry North Atlantic OGCM. In our experiments we found 20 year self-sustained variability of the thermohaline circulation (and hence the poleward heat transport) which was driven by changes in Labrador Sea convection. This is an important result as there have been many observations of decadal variability in and around the North Atlantic. Indeed, an MSc student, T. Wohlleben, working under my supervision, is currently analysing many of these observations in an attempt to statistically quantify mechanisms for interdecadal climate variability. She is currently writing up her thesis and will defend this summer. An article on this work will be written up and submitted to Atmosphere-Ocean this summer. Over the last year I have been working on a detailed scaling analysis of the thermohaline circulation under both Neumann and Dirichlet boundary conditions. This scaling analysis is being compared with the results of a "converted GFDL general circulation model". That is, the normal GFDL code has been stripped to be purely baroclinic (as there is no wind forcing, nonlinear terms in the momentum equation, bottom friction or topography, the barotropic mode is zero and hence all this code has been removed). Furthermore, the tracer and salinity equations have been combined into one "conservation of potential density" equation so that there is no equation of state. Finally, Dirichlet boundary conditions have been implemented directly instead of using the more normal relaxation boundary condition.

A PhD student (T. Reynaud) who was funded under the first round of NSERC/WOCE and jointly supervised by Richard Greatbatch and me, recently submitted his PhD thesis and will defend this thesis later this month. Two research articles have been/ will be written from this thesis. In the first of these (Reynaud et al. 1994a) we analysed archived data from the Labrador Sea region of the North Atlantic. Several diagnostic models were used to study the climatological mean summer circulation in the area. In the second paper (Reynaud et al. 1994b), which will be submitted later this summer, we have extended this analysis to examine interdecadal changes in the circulation and water mass properties of the Labrador Sea.

My NSERC/WOCE grant proposal also provided funds to start developing simple coupled models to understand the role of feedbacks in the coupled air-sea system. To this end, A. Fanning, a PhD student, has developed a diffusive heat transport energy balance model (EBM) and tested it in both simplified and global domains. The EBM is loosely based upon the models of Budyko (1969), Sellers (1969), and North (1975). We have extended these models to allow coupling with the GFDL-MOM ocean general circulation model (Geophysical Fluid Dynamics Laboratory Modular Ocean Model, Pacanowski et al., 1993) by allowing latent, sensible and radiative heat transfers between the ocean and atmosphere. In an effort to completely couple the ocean-atmosphere system, a moisture balance equation has also been added to the EBM so that freshwater fluxes can be predicted for the ocean model. Currently, tests are being carried out in an effort to tune the moisture balance to present climatology. A version of the ocean model has been partially coupled to the EBM, however, the final version will also include the prediction equations for precipitation currently under testing.

L. Zhang has been developing a zonally averaged coupled ocean-ice-atmosphere model for the purpose of investigating coupled air-sea-ice climate interactions and for comparing with the more complicated three-dimensional models (discussed in the preceding paragraph). The zonally averaged ocean model is based on the formulation of Wright and Stocker (1991), in which geostrophy is used in the momentum equations and the zonally averaged east-west pressure gradient is parameterized in terms of the meridional pressure gradient. This model has been coupled with a zonally-averaged atmosphere EBM with the evaporation minus precipitation prescribed following the work by Stocker et. al. (1992). The atmospheric EBM is based on the model of Sellers (1969), while the ice model is a 1-D thermodynamic model (Semtner, 1976) including heat insulation and brine rejection.

Dr. B. Tang recently spent spent two weeks at Athens to develop a box model for the Mediterranean thermohaline circulation, collaborating with A. Lascaratos of University of Athens. They (Tang et al., 1994) found that the current estimates of the surface heat flux, the ocean temperature and salinity structure, and the thermohaline circulation of the Mediterranean Sea are not consistent, and proposed that either the surface heat flux be lower than currently believed or the lateral mixing in the intermediate water play a more important role. A similar study can be carried out for the global ocean. We are extending this analysis further using the global model discussed below to examine the influence of Mediterranean outflow on the global thermohaline circulation.

I have also been working collaboratively with Warren Lee in the Canadian Climate Centre to develop a global model which will be coupled to the Canadian Climate Centre for the purpose of undertaking climate change/variability forecasts. The model is now complete and we are currently writing up two papers to submit shortly. Weaver and Lee (1994) will describe the methodology and climatology of the model and Lee and Weaver (1994) will describe a detailed sensitivity analysis to model parameters/forcing fields.

Over the past months, T. Hughes has completed the development of a 19-level global ocean model based on the the higher resolution (vertically and horizontally) world ocean model mentioned above. The equilibria under both restoring and mixed boundary conditions on temperature and salinity (the restoring T and S values adapted from the Levitus data atlas) and Hellerman and Rosenstein observed wind, are satisfactory and close to the accepted climatology. The steady state obtained under wind and buoyancy flux forcing taken directly from the CCC atmospheric model is however very different. It features deep water formation in the Pacific and Indian Oceans rather than the Atlantic and Antarctic, and meridional heat and salt transports quite unlike the observed. A final step will be to infer the flux corrections needed for this atmospheric model to produce an acceptable ocean circulation when running in coupled mode. T. Hughes should complete her PhD by the end of the summer and I will take her on as a research associate at that time.

In another project, T. Hughes is obtaining a preliminary estimate of the importance of sea surface temperature-evaporation feedback for natural internal variability in the ocean. This is accomplished with an uncoupled model within the context of mixed boundary conditions by prescribing a fixed Bowen ratio and net radiation profile, allowing the latent heat flux to be deduced. Different simple schemes for redistributing the new precipitation are compared given the impossibility of representing clouds. The evaporative feedback is evaluated in three case studies taken from Weaver et al (1993) which exhibit spontaneous decadal, century and millennial timescale variability respectively.

Finally, T. Hughes is involved in a collaboration with D. Wright (Bedford Institute) and C. Vreugdenhil (Netherlands) to compare the dynamics of zonally-averaged and three-dimensional ocean circulation models, with the goal of improving the parameterisation of zonal pressure gradients necessary in the former.

Dr. S. Das was initially working on the development of semi-Lagrangian advection algorithms for implementation into the Bryan-Cox model. Only the advection-diffusion equation governing the tracers are to be treated with the help of the semi-Lagrangian scheme in the first instance. We have decided not to incorporate the semi-Lagrangian schemes into the Bryan-Cox model as we thought it would be more useful, for large-scale ocean circulation models, to develop our own model where the momentum equations are diagnostic rather than prognostic. This model is currently being coded up for comparison with the other global ocean models mentioned above.

As a preliminary step he used the Marotzke et al. (1988) model of the zonally averaged two-dimensional thermohaline circulation. The model's governing equations were solved under a variety of boundary conditions. To determine the extent to which the accuracy and efficiency of the calculations depended on the numerical integration scheme, the test problem was solved independently using an explicit finite difference (leap-frog in time, centered difference in space) 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 eliminated the damping introduced by the interpolation. Hence, this method stands out as a viable time integration scheme for the climate models which are normally run for thousands of years. We concluded that the three-time level, non-interpolating semi-Lagrangian advection method was best suited for ocean climate studies. These results are summarized in Das and Weaver (1994).

Subsequently, Dr. Das has taken up the study of the full set of thermocline equations in Cartesian co-ordinates using the semi-Lagrangian algorithm . The scheme will be applied to the tracer equations only as the momentum equations will be diagnostic with frictional boundary layers. The algorithm has already been tested in its interpolating form using the cubic-Lagrange interpolation scheme on a rotating cone problem. The non-interpolating form for the three-dimensional form is also working. Dr. Das is now applying the schemes to the advection-diffusion equations. Since the 1970's, a considerable amount of atmospheric and oceanographic data of freon (CFC) 11 and 12 have been accumulated. The surface data can be introduced in ocean circulation models to predict the distribution of freon with depth. When compared with observations, this can be use as a tool to verify the ability of the model to reproduce the present day climatology. This has been done using the Bryan-Cox GCM for the North Atlantic with a horizontal resolution of 1 degree by 1 degree, and the GFDL MOM version of the code (Pacanowski et al., 1993) for the same region at a resolution of 2 degree by 2 degree. The next step will be to apply the same surface freon distribution but to a global ocean model. Also the differences in the results when using an isopycnal mixing scheme (following the method in Gent and McWilliams, 1990) as opposed to more traditional schemes will be examined. Once the model can reproduce present-day freon distribution, we will be able to use it in a predictive mode to project oceanic freon distribution and water mass formation rates following different freon-release scenarios. The project involving the development of a finite-element global primitive equation ocean model is also proceeding well. To this date both the time-dependent and steady nonlinear, spherical coordinate, barotropic vorticity equation have been coded up (see Myers and Weaver, 1994). The model has also been run in diagnostic mode to try and address the question of Gulf Stream separation (Myers et al., 1994). Several important numerical problems were overcome: These included the treatment of islands and the handling of no-slip boundary conditions using finite-elements; the generation of cyclic elements using a grid-generation package (for the global model) and the handling of cyclic boundary conditions.


Budyko, M.I., 1969: The effect of solar radiation variations on the climate of the earth. Tellus, 21, 611-619.
Gent, P. R. and J.C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150-155.
GRIP Project Members, 1993. Climate instability during the last interglacial period recorded in the GRIP ice core. Nature, 364, 203-207.
Manabe, S. and R.J. Stouffer, 1993: Century-scale effects of increased atmospheric CO2 on the ocean-atmosphere system, Nature, 364, 215-218.
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.
North, G.R., 1975: Theory of energy balance climate models. J. Atmos. Sci. 32, 2033-2043.
Pacanowski, R., K. Dixon and A. Rosati, 1993: The GFDL Modular Ocean Model Users Guide, GFDL Ocean Group Technical Report #2, 46pp.
Sellers, W.D., 1969: A global climatic model based on the energy balance of the earth-atmosphere system. J. Appl. Meteorol. 8, 392-400.
Semtner, A.J., 1976: A Model for the Thermodynamic Growth of Sea Ice in Numerical Investigations of Climate. J. Phys. Oceanogr., 6, 379-389.
Stocker, T.F., Wright, D.G. and L.A. Mysak, 1992: A Zonally Averaged, Coupled Ocean-Atmosphere Model for Paleoclimate Studies. J. Climate, 5 773-797.
Wright, D.G. and T.F. Stocker, 1991: A Zonally Averaged Ocean Model for the Thermohaline Circulation. Part 1: Model Development and Flow Dynamics. J. Phys. Oceanogr.,21, 1713-1724.

5. Other Relevant Information

The principal investigator, A. Weaver, currently sits on the United Nations Steering Group for Global Climate Modelling and has recently been asked to sit on the United Nations Climate Variability (CLIVAR) scientific steering committee on decadal-century timescale variability. He is also a lead author for Chapter 10 of the United Nations Intergovernmental Panel for Climate Change (IPCC) 1995 Scientific Assessment. Furthermore, he is a principal investigator in the NOAA consortium on the ocean's role in climate.

In September 1993, he coordinated a meeting of the Canadian WOCE modelling community at the Institute of Ocean Sciences which immediately followed the annual SGGCM and international WOCE NEG meetings (see enclosed CEOR report).

6. Presentations Given by the Principal Investigator

1. Decadal-millennial internal oceanic variability in coarse resolution ocean general circulation models 2. On the sensitivity of the thermohaline circulation in ocean general circulation models to the vertical eddy diffusivity 3. Some numerical considerations for ocean climate models 4. The ocean's thermohaline circulation and climate: coupled model developments in Canada 5. Ocean/climate modelling and the Canadian Centre for Climate 6. Decadal-millennial climate variability: observations and theory 7. The ocean as a source for rapid interglacial climate fluctuations

Conference presentations given by others

1. Myers, P.G. and A.J. Weaver, 1993: Development of a global steady-state finite-element barotropic model. Lecture presented at 27th Annual Congress of the Canadian Meteorological and Oceanographic Society, Fredricton, New Brunswick, June 8-11.

2. Hughes, T.M.C. and A.J. Weaver, 1993: Multiple equilibria of an asymmetric two-basin ocean model. Lecture presented at 27th Annual Congress of the Canadian Meteorological and Oceanographic Society, Fredricton, New Brunswick, June 8-11.

3. Tang, B. and A.J. Weaver, 1994: Climate stability as deduced from an idealized coupled atmosphere-ocean model. Poster presented at the 1994 Ocean Sciences Meeting, San Diego, California, February 21-25.

4. Lee, W.G.. and A.J. Weaver, 1994: Sensitivity of a global OGCM climatology to external forcing, internal parameters and topography. Poster presented at the 1994 Ocean Sciences Meeting, San Diego, California, February 21-25.

5. Myers, P.G. and A.J. Weaver, 1994: The barotropic circulation of the North Atlantic from a finite element model. Lecture presented at XIX General Assembly of the European Geophysical Society, Grenoble, France, April 25-29, 1994.

7. Publications and preprints arising

Research Articles which A. Weaver was involved in and which were funded by the NSERC/WOCE operating grant.

1. Weaver, A.J., J. Marotzke, P.F. Cummins and E.S. Sarachik, 1993: Stability and variability of the thermohaline circulation. J. Phys. Oceanogr., 23, 39-60.

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

3. Weaver, A.J., and. T.M.C. Hughes, 1994: Rapid interglacial climate fluctuations driven by North Atlantic ocean circulation. Nature, 367, 447-450.

4. Hughes, T.M.C. and A.J. Weaver, 1994: Multiple equilibria of an asymmetric two-basin ocean model. J. Phys. Oceanogr., 24, 619-637.

5. Weaver, A.J., 1994: Decadal-millennial internal oceanic variability in coarse resolution ocean general circulation models. In:The Natural Variability of the Climate System on the 10100 Year Time-Scales, National Academy Press, in press.

6. Weaver, A.J., Aura, S.M., and P.G. Myers, 1994: Interdecadal variability in a coarse resolution North Atlantic model. J. Geophys. Res., Observation and Modeling of North Atlantic Deep Water Formation and its Variability, Special Edition, in press.

7. Reynaud, T.H., Weaver, A.J. and Greatbatch, R.J. 1994a: Summer mean circulation in the western North Atlantic. J. Geophys. Res., submitted.

8. Tang, B., and A. J. Weaver, 1994: Climate stability as deduced from an idealized coupled atmosphere-ocean model. Clim. Dyn., submitted.

9. Weaver, A.J., and C. Green, 1994: Global climate change/variability: Action or adaptation to increasing greenhouse gases? - Lessons from the past. Invited paper submitted to Forum for applied research and public policy, in press.

10. Myers, P.G. and A.J. Weaver, 1994: A diagnostic barotropic finite element ocean circulation model. J. Atmos. Ocean. Tech., submitted.

11. Das, S.K. and A.J. Weaver, 1994: Semi-Lagrangian advection algorithms for ocean circulation models. J. Atmos. Ocean. Tech., submitted.

Publications (To be submitted shortly)

1. Weaver, A.J., 1994: A scaling analysis of the thermohaline circulation: Comparison with an ocean general circulation model. To be submitted to J. Phys. Oceanogr.

2. Lee, W.G. and A.J. Weaver, 1994: Sensitivity analysis of a global ocean general circulation model. To be submitted to Atmos.-Ocean.

3. Weaver, A.J. and W.G. Lee, 1994: A global OGCM for coupling to the Canadian Climate Centre AGCM. To be submitted to Atmos.-Ocean.

4. Wohlleben, T., and A.J. Weaver, 1994: Decadal variability of the North Atlantic climate system. To be submitted to Atmos.-Ocean.

5. Reynaud, T.H., Weaver, A.J. and R.J. Greatbatch, 1994b: Interdecadal changes in the circulation of the western North Atlantic. To be submitted to J. Geophys. Res.

6. Tang, B., A. Lascaratos and A.J. Weaver, 1994: What cools Levintine intermediate water? To be submitted to Geophys. Res. Let.

7. Myers, P.G., A.F. Fanning and A.J. Weaver, 1994: On the cause of Gulf Stream separation. To be submitted to J. Phys. Oceanogr.

Other research articles which were written by people either fully or partially funded through the NSERC/WOCE operating grant awarded to A. Weaver.

1. Wright, D.G., C.B. Vreugdenhil and T.M.C. Hughes,, 1994: Vorticity dynamics and zonally averaged ocean circulation models. submitted to J. Phys. Oceanogr.

2. Lardner, R.W. and S.K. Das, 1994: Optimal Estimation of Eddy Viscosity for a Quasi-Three-Dimensional Numerical Tidal and Storm Surge Model. Int. J. Num. Meth. Fluid., 18, 295-312.

3. Tang, B., 1994: Periods of linear development of the ENSO cycle and POP forecast experiments. J. Clim., in press.

4. Tang, B., G. Flato and G. Holloway, 1994: A study of Arctic sea ice and sea level pressure using POP and neural network methods. Atmos.-Ocean, in press.

5. Robitaille, D.Y., L.A. Mysak and M.S. Darby, 1994: A Box Model Study of the Greenland Sea, Norwegian Sea, and Arctic Ocean. Clim. Dyn., submitted.

Technical Reports and Other Publications in 1993

1. Weaver, A.J., and T.M.C. Hughes, 1993: Stability and variability of the thermohaline circulation and its link to climate. CEOR Report No. 93-1, University of Victoria.

2. Weaver, A.J., Aura, S.M., and P.G. Myers, 1993: Interdecadal variability in a coarse resolution North Atlantic model. CEOR Report No. 93-2, University of Victoria.

3. Hughes, T.M.C. and A.J. Weaver, 1993: Multiple equilibria of an asymmetric two-basin ocean model. CEOR Report No. 93-3, University of Victoria.

4. Weaver, A.J., 1993: Climate commentary off the mark. Commentary in the editorial section of the Victoria Times Colonist, page A5, Wednesday, August 18, 1993.

5. Weaver, A.J., and. T.M.C. Hughes, 1993: The ocean as an internal source for rapid interglacial climate fluctuations. CEOR Report No. 93-6, University of Victoria.

6. Weaver, A.J., 1993: CNC WOCE Workshop: Agenda & Abstracts. CEOR Report No. 93-7, University of Victoria.

7. Tang, B., and A. J. Weaver, 1993: Climate stability as deduced from an idealized coupled atmosphere-ocean model. CEOR Report No. 93-9, University of Victoria.

8. Weaver, A.J.: Global climate change/variability: Action or adaptation to increasing greenhouse gases? - Lessons from the past. CEOR Report No. 93-10, University of Victoria.

9. Weaver, A.J., and C. Green, 1994: Global climate change/variability: Action or adaptation to increasing greenhouse gases? - Lessons from the past. C2GCR Report No. 94-1, McGill University.

10. Weaver, A.J., 1994: Model instabilities. In: World Climate Research Programme, WOCE Numerical Experimentation Group: Report of the 8th Meeting (NEG-8) and workshop on ocean models for climate research. WOCE Report No. 117/94, WOCE International Project Office, Wormley (pages 9-10).

11. Weaver, A.J., 1994: Long-term oscillations of the ocean. In: World Climate Research Programme, WOCE Numerical Experimentation Group: Report of the 8th Meeting (NEG-8) and workshop on ocean models for climate research. WOCE Report No. 117/94, WOCE International Project Office, Wormley (pages 21-22).

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