Climate Modelling Group
School of Earth and Ocean Sciences


Climate Research Network

Collaborative Research Agreement at the University of Victoria on Behalf of the Canadian Institute for Climate Studies and Environment Canada
(#11 CICS-Global Oceans)



Progress Report:

October 1, 1996

1. Principal Investigator

Andrew Weaver

2. Institution

School of Earth & Ocean Sciences
University of Victoria
PO Box 1700
Victoria, BC, V8W 2Y2

3. Details of Projects

The purpose of the #11 CICS -- Global Oceans grant is to allow Dr. A. Weaver to participate in the continued development of the Canadian Climate Centre (CCC) coupled atmosphere-ocean model and to act as the Scientific Leader of the Ocean Modelling Division of the CCC. In addition, it allows him to conduct research into developing improved global ocean models for the purpose of coupling them with the CCC AGCM.

A copy of previous progress reports are available on the world wide web at:

http://wikyonos.seos.uvic.ca/projects/CCC-Global-Progress.html
http://wikyonos.seos.uvic.ca/projects/CCC-Global-Progress2.html
http://wikyonos.seos.uvic.ca/projects/CCC-Global-Progress3.html
http://wikyonos.seos.uvic.ca/projects/CCC-Global-Progress4.html
http://wikyonos.seos.uvic.ca/projects/CCC-Global-Progress5.html
http://wikyonos.seos.uvic.ca/projects/CCC-Global-Progress6.html


This progress report highlights the work conducted during the 1996 fiscal. Some reference to earlier funded CICS Global Oceans research is also made. <

3.1 Oceanic poleward heat transport as a function of OGCM resolution

The idealized climate model (consisting of an energy-moisture balance atmosphere, thermodynamic ice, and an ocean general circulation model, hereafter referred to as the EMBM-TIM-OGCM -- see Fanning and Weaver, 1996a) previously developed by A. Fanning (a PhD. student) has been utilized to study the influence of horizontal resolution and parameterized eddy processes on the poleward heat transport in the climate system. The results have recently been submitted for publication in Journal of Climate (Fanning and Weaver, 1996b).

Model results suggest that as resolution is varied from 4o to 0.25o the oceanic heat transport steadily increases. Owing to the strong constraint imposed by the radiation balance at the top of the atmosphere, the planetary (ocean plus atmosphere) heat transport changes little throughout our resolution experiments. As a consequence, the atmospheric heat transport generally decreases to offset the increasing oceanic transport.

The increase in oceanic heat transport as resolution increases is in contrast to previous ocean-only model studies (e.g., Cox, 1985; Bryan, 1987; Böning and Budich, 1992; Drijfhout, 1994). This result is also evidenced in a parallel series of ocean-only experiments where forcing is diagnosed from our 4o coupled model's equilibrium state (e.g. Haney, 1971; Han, 1984). Although heat transport is generally higher in the coupled model, both models behave similarly, with the primary increases occurring in the baroclinic gyre component of the oceanic heat transport.

The conspicuous absence of an eddy transport compensation mechanism is in contrast to previous ocean-only model studies. Boning and Budich (1992) found eddy length-scales ranging from 50 to 175 km in their 1/6o model study. The highest resolution case studied here (0.25o) is adequate to resolve some of these features, and spectral analysis of the basin mean kinetic energy density reveals variability (above 95% significance) in the range weeks to a year. Such time scales are consistent with those found by Cox (1985,1987).

To investigate this contradiction further, an additional set of ocean-only experiments (more closely approximating the earlier studies) were performed. In particular we wished to test whether an inclusion of salinity forcing (and hence a breakdown of the non-acceleration theorem -- eg. McDougall, 1984; Cox, 1985; Bryan, 1991; Drijfhout, 1994) could explain the differences in our results. Results suggest this is not the case, however. Restoring to temperature alone (as in previous studies) results in higher heat transports than the thermal/haline case (due to haline effects on the baroclinic overturning transport). The latter two experiments are consistent with our previous cases, again increases in the baroclinic gyre transport result in an increasing oceanic heat transport.

The thermocline adjustment time scale due to a perturbation (e.g. induced upon switching resolution) should be that for a first mode baroclinic Rossby wave to cross the basin. Owing to the generally short integration time of these studies (generally 10 years or less at highest resolution) it is not clear whether the time-variant compensation noted is eddy generated or rather an aliased Rossby wave signal (see Cox, 1985,1987). The poleward oceanic heat transport can be scaled as TO ~ V delta(T) where delta(T) is the contrast between an average thermocline temperature and an average deep water temperature, and V is an average northward transport in the thermocline (with southward transport below). Although the thermocline may undergo adjustment on a baroclinic Rossby wave time scale, the surface to deep water contrast is set by an advective spin up time scale (order of hundreds of years). Therefore, earlier studies involving rather short integration times are not sufficient to remove the transients at deep levels (on long advective time scales), or allow full equilibration of the meridional overturning circulation.

Although the identification of an eddy compensation mechanism found in previous studies may be due to the rather short integration times employed, additional factors exist which may explain the differences we note. Cox, (1985); Boning and Budich, (1992); and Drijfhout, (1994) each employed an idealized continental shelf along the western boundary with a promitory at approximately 35oN. Sufficient nonlinearity, along with inertial overshoot could give rise to enhanced eddy activity. Additionally, previous studies utilized biharmonic closure schemes at highest resolution. Here we chose not to do so since a change in closure ultimately alters the 'control' of the experiment.

Spontaneous decadal-intradecadal scale variability is found to exist in our higher resolution experiments. The intradecadal scale variability (period 3-5 years) is linked to the nonlinear advection terms in the momentum equations. This variability is similar to that noted by Cox (1985,1987) who found a 4-4.5 year variation in his model. Such variability (period 3 years) was also noted by Boning and Budich (1992). Spontaneous decadal scale variability is also found in our present study and its existence is intimately linked to the value of the horizontal diffusivity we employ. Increasing the diffusivity in our high resolution cases (below 0.5o) is enough to destroy the variability, while decreasing the diffusivity in our moderately coarse resolution cases (above 1o) is enough to induce the variability.

The decadal oscillation we describe is a thermally driven advective-convective oscillation, characterized by the turning on and shutting off of convective activity in the northwestern corner of the model domain (cf. Weaver et al., 1994; Greatbatch and Zhang, 1995). The fact that decadal scale variability exists in an idealized coupled ocean-atmosphere model (which does not employ flux adjustments) is an intriguing result. While our model is highly idealized, the question naturally arises: is the variability found in more complete coupled models (e.g. Delworth et al., 1994) a feature of the coupled state, or determined by the flux adjustment employed as suggested by Weaver et al. (1994), and Greatbatch and Zhang (1995). These results point to the importance of higher resolution in the ocean component of coupled models, revealing the existence of richer decadal-intradecadal scale variability in models which require less parameterized diffusion.

3.2 Flux adjustments and their influence in coupled models

In another project, A. Fanning is currently investigating the role of flux adjustments on the transient and long-term behavior of induced climate change experiments. A version of the EMBM-TIM-OGCM has been configured for a four-basin, two-hemisphere, sector geometry model which includes a Mediterranean, Arctic, Pacific and Atlantic basin, joined at the southern extent by a cyclic circumpolar ocean. This model has been spun up to near equilibrium, and the resulting surface temperature and salinity fields were then used to spinup an ocean only model (using a restoring timescale of 50 days). At equilibrium, the resulting differences between the atmospheric fluxes (in equilibrium with the surface SST's) and those implied by the restoring boundary conditions yields a flux adjustment such that the atmospheric state of the coupled model and the oceanic state of the ocean-only model are compatible. We therefore couple these states to yield a flux adjusted model, this procedure is formally equivalent to one of the standard procedures used in coupling an atmospheric model in equilibrium with fixed SST's to an ocean model spun-up by restoring to SST and SSS (e.g., Weaver and Hughes, 1996). The flux adjusted and non-flux adjusted model are then subjected to a 4 W/m2 (linearly increasing over 75 years) net heating perturbation.

Although still preliminary, results suggest that the transient behaviour (over the first 75 years) of each model is similar, with results diverging after that point. Additional experiments to test the sensitivity of the flux corrected model's initial conditions are still being performed, and these results will be reported on at a later date.

We are also investigating the role of flux adjustments on interdecadal climate variability. The numerical simulations of Delworth et al. (1994), using the GFDL coupled model revealed interdecadal variability of the thermohaline circulation 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.

3.3 Finite element modelling

Dr. Paul Myers, partially funded through the CICS Global Oceans Grant received his PhD and has moved to undertake postdoctoral research at the University of Edinburgh in Scotland. He was working on the development of a global finite element model with specific applications to the circulation of the North Pacific and North Atlantic Oceans. The North Atlantic work was reported in earlier Progress Reports. Here I only summarize the results of the Pacific work which has appeared as Myers and Weaver (1996).

A finite element diagnostic model was used to study the circulation of the North Pacific Ocean. With the inclusion of the JEBAR term, the model produced a realistic picture of the circulation. All major currents were reproduced with the calculated transports agreeing well with observations. The three dimensional velocity structure was diagnosed from the thermal wind equation, assuming a reference velocity at the bottom. This bottom reference velocity was calculated from the Ekman, thermohaline and total transport (from the finite element model) velocities. The diagnosed velocity fields were then compared with a number of observational sections.

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 supported the suggestion of Sakamoto and Yamagata (1995) 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.

3.4 On the role of various subgrid-scale boundary layer parameterizations in coarse resolution ocean models

Amongst the numerous sub-grid-scale parameterizations necessary in an ocean general circulation model, the influence of the momentum dissipation scheme and dynamical boundary conditions has been relatively ignored compared to tracer mixing. However, the ability of the ocean to transport heat poleward may be very sensitive to such closures, since they are the only way the large-scale circulation can depart from geostrophy and thus produce noticeable vertical velocities that feed the overturning. A thermohaline circulation model has been developed for a Cartesian coordinate flat-bottomed beta-plane, based on the planetary geostrophic equations, in order to compare different parameterizations of the momentum dissipation (Laplacian, biharmonic, Rayleigh and none) and associated boundary conditions (no-slip, free-slip and no-normal-flow). It is used at coarse-resolution for a mid-latitude basin with restoring boundary conditions for the surface density and no wind-stress.

Comparison with the GFDL MOM code confirms the negligible effects of vertical viscosity and total derivatives in the momentum equations. The surface temperature fields and poleward heat transports are quite similar for the steady-states obtained using the different viscosity schemes. However, large discrepancies in the bottom water properties and the velocity field show an order one effect of these closures on the mass transports. The traditional Laplacian friction produces a more satisfying interior circulation, in better agreement with geostrophy and Sverdrup balance, but generates excessively large vertical transports along the lateral boundaries (especially upwelling in the western boundary current - the Veronis effect - and downwelling in the north-east corner). The meridional overturning is thus enhanced but drives to depth surface waters that are not as cold as the ones in the deep convection regions.

Rayleigh friction with a no-normal-flow boundary condition (a vorticity closure is used whose primary effect is to reduce vertical velocities along the boundaries by allowing horizontal recirculation) induces a more efficient thermohaline circulation with better agreement between convection regions and areas of downwelling, colder deep water, much weaker meridional overturning and Veronis effect, but higher poleward heat transport. However, this parameterization lacks physical justifications and is not as satisfying as the Laplacian closure in terms of interior geostrophic and Sverdrup balance. The analysis of the correlations between the large scale diagnostics of these models points out the Veronis effect as the major contributor to warm deep water, diffuse thermocline, large overturning but weak poleward heat transport, in agreement with Böning et al. (1995). The role of dynamical boundary conditions is more important than the interior momentum dissipation in reducing this short-cut of the thermohaline loop.

This research has either been submitted (Huck et al., 1996a) or will be submitted shortly (Huck et al., 1996b, c) for publication.

3.5 Flux Corrected Transport Algorithms and Sub-grid-scale Mixing in an OGCM

Finally Weaver and Eby (1996) have implemented a flux-corrected transport advection algorithm (Gerdes et al., 1991) into the GFDL MOM2 and compared it with traditional second order centred difference advection schemes. This technology has been passed to the CCC and may be implemented in the next generation of global ocean models.

The results from ocean model experiments conducted with isopycnal and isopycnal thickness diffusion parameterizations for subgrid scale mixing associated with mesoscale eddies were examined from a numerical standpoint. It was shown that when the mixing tensor is rotated, so that mixing is primarily along isopycnals, numerical problems may occur and non-monotonic solutions which violate the second law of thermodynamics may arise when standard centred difference advection algorithms are used. These numerical problems can be reduced or eliminated if sufficient explicit (unphysical) background horizontal diffusion is added to the mixing scheme. A more appropriate solution is the use of more sophisticated numerical advection algorithms, such as the flux-corrected transport algorithm. This choice of advection scheme adds additional mixing only where it is needed to preserve monotonicty and so retains the physically-desirable aspects of the isopycnal and isopycnal thickness diffusion parameterizations, while removing the undesirable numerical noise. The price for this improvement is a computational increase.

3.6 References

Böning, 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.

Bryan, K., 1987: Poleward buoyancy transport in the ocean and mesoscale eddies. J. Phys. Oceanogr., 16, 927-933.

Bryan, K., 1991: Poleward heat transport in the ocean. A review of a hierarchy of models of increasing resolution. Tellus, 43, 104-115.

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

Cox, M.D., 1987: An eddy resolving numerical model of the ventilated thermocline: Time dependence, J. Phys. Oceanogr., 17, 1044-1056.

Delworth, T., S. Manabe and R.S. Stouffer, 1994: Interdecadal variations of the thermohaline circulation 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.

Fanning, A.F., and A.J. Weaver, 1996a: An atmospheric energy-moisture balance model: Climatology, interpentadal climate change, and coupling to an OGCM. J. Geophys. Res., 101, 15,111-15,128.

Fanning, A.F., and A.J. Weaver, 1996b: A horizontal resolution and parameter sensitivity study of heat transport in an idealized coupled climate model J. Climate, submitted.

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 S.Z. Zhang, 1995: An interdecadal oscillation in an idealized ocean forced by constant heat flux. J. Climate, 8, 81-91.

Han, Y.J., 1984: A numerical world ocean general circulation model, Part II, A baroclinic experiment, Dyn. Atmos. Oceans 8, 141-172.

Haney, R.L., 1971: Surface thermal boundary condition for ocean circulation models. J. Phys. Oceanogr., 1, 241-248.

Huck, T., A. J. Weaver, and A. Colin de Verdiere, 1996a: The effect of momentum dissipation parameterizations in coarse-resolution thermohaline circulation models. J. Phys. Oceanogr., submitted.

Huck, T., A. Colin de Verdiere, and A. J. Weaver, 1996b: The effect of momentum dissipation parameterizations in coarse-resolution thermohaline circulation models: geostrophy, Sverdrup balance and Veronis effect. in preparation.

Huck, T., A. J. Weaver, and A. Colin de Verdiere, 1996c: Decadal variability in simplified models of the thermohaline circulation. in preparation.

McDougall, T.J., 1984: The relative roles of diapycnal and isopycnal mixing in subsurface water massconversion. J. Phys. Oceanogr., 14, 1577-1589.

Myers, P.G., and A.J. Weaver, 1996: On the circulation of the North Pacific Ocean: Climatology, seasonal cycle and interpentadal variability, Prog. Oceanogr., in press.

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

Weaver, A.J. and M. Eby, 1996: On the numerical implementation of advection schemes for use in conjunction with various mixing schemes in the GFDL ocean model. J. Phys. Oceanogr., in press.

Weaver, A.J. and T.M.C Hughes, 1996: On the incompatibility of ocean and atmosphere models and the need for flux adjustments. Climate Dynamics, 12, 141-170.

Weaver, A.J., S.M. Aura, and P.G. Myers, 1994: Interdecadal variability in an idealized model of the North Atlantic, J. Geophys. Res., 99, 12,423-12,441.
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