• Chelton, D. B., R. A. deSzoeke, M. G. Schlax, K. E. I. Naggar, and N. Siwertz, 1998: Geographical variability of the first-baroclinic Rossby radius of deformation. J. Phys. Oceanogr, 28 , 433460.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.

  • Killworth, P. D., D. B. Chelton, and R. A. De Szoeke, 1997: The speed of observed and theoretical long extratropical planetary waves. J. Phys. Oceanogr, 27 , 19461966.

    • Search Google Scholar
    • Export Citation
  • Latif, M., and T. P. Barnett, 1996: Decadal climate variability over the North Pacific and North America: Dynamics and predictability. J. Climate, 9 , 24072423.

    • Search Google Scholar
    • Export Citation
  • Merryfield, W. J., 2006: Changes to ENSO under CO2 doubling in a multimodel ensemble. J. Climate, in press.

  • Münnich, M., M. Latif, S. Venzke, and E. Maier-Reimer, 1998: Decadal oscillations in a simple coupled model. J. Climate, 11 , 33093319.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    (top) Zonally averaged phase speed of first baroclinic gravity waves corresponding to the preindustrial experiment and (bottom) its change in the 720-ppm A1B stabilization experiment.

  • View in gallery

    (top) Zonally averaged first baroclinic Rossby radius of deformation corresponding to the preindustrial experiment and (bottom) its change in the 720-ppm A1B stabilization experiment.

  • View in gallery

    (top) Zonally averaged βλ12 corresponding to the preindustrial experiment and (bottom) its change in the 720-ppm A1B stabilization experiment. Notice that some of the models show absolute changes in βλ12 that differ from what might be expected based on the corresponding changes in λ1, since , where the overbar denotes averaging.

  • View in gallery

    (top) Relative changes in zonally averaged first baroclinic Rossby radius of deformation and (bottom) its squared values.

  • View in gallery

    Zonally averaged changes in phase speed of first baroclinic gravity waves (top) in the Pacific Ocean and (bottom) in the Atlantic Ocean. The changes correspond to two time intervals, 2091–2100 and 2191–2200, relative to the preindustrial control experiment. The computations are done using the results from the GFDL−CM2.0 model, where the vertical structure in the ocean is resolved by the largest number of levels (50) and where the changes in the wave speed are representative of the model-mean response (see Fig. 1, bottom).

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Influence of Global Warming on Baroclinic Rossby Radius in the Ocean: A Model Intercomparison

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  • 1 Canadian Centre for Climate Modelling and Analysis, Meteorological Service of Canada, Victoria, British Columbia, Canada
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Abstract

Results from eight ocean–atmosphere general circulation models are used to evaluate the influence of the projected changes in the oceanic stratification on the first baroclinic Rossby radius of deformation in the ocean, associated with atmospheric CO2 increase. For each of the models, an oceanic state corresponding to the A1B stabilization experiment (with atmospheric CO2 concentration of 720 ppm) is compared to a state corresponding to the preindustrial control experiment (with atmospheric CO2 concentration of 280 ppm). In all of the models, the first baroclinic Rossby radius increases with increasing oceanic stratification in the warmer climate. There is, however, a considerable range among the models in the magnitude of the increase. At the latitudes of intense eddy activity associated with instability of western boundary currents (around 35°–40°), the increase reaches 4 km on average, or about 15% of the local baroclinic Rossby radius. Some of the models predict an increase of the baroclinic Rossby radius by more than 20% at these latitudes under the applied forcing. It is therefore suggested that in a plausible future warmer climate, the characteristic length scale of mesoscale eddies, as well as boundary currents and fronts, may increase. In addition, since the speed of long baroclinic Rossby waves is proportional to the squared baroclinic Rossby radius of deformation, the results suggest that the time scale for large-scale dynamical oceanic adjustment may decrease in the warmer climate, thereby increasing the frequency of long-term climate variability where the oceanic Rossby wave dynamics set the dominant period. Finally, the speed of equatorial Kelvin waves and Rossby waves, carrying signals along the equator, including those related to ENSO, is projected to increase.

Corresponding author address: Dr. Oleg A. Saenko, Canadian Centre for Climate Modelling and Analysis, Meteorological Service of Canada, Victoria, BC V8W 2Y2, Canada. Email: oleg.saenko@ec.gc.ca

Abstract

Results from eight ocean–atmosphere general circulation models are used to evaluate the influence of the projected changes in the oceanic stratification on the first baroclinic Rossby radius of deformation in the ocean, associated with atmospheric CO2 increase. For each of the models, an oceanic state corresponding to the A1B stabilization experiment (with atmospheric CO2 concentration of 720 ppm) is compared to a state corresponding to the preindustrial control experiment (with atmospheric CO2 concentration of 280 ppm). In all of the models, the first baroclinic Rossby radius increases with increasing oceanic stratification in the warmer climate. There is, however, a considerable range among the models in the magnitude of the increase. At the latitudes of intense eddy activity associated with instability of western boundary currents (around 35°–40°), the increase reaches 4 km on average, or about 15% of the local baroclinic Rossby radius. Some of the models predict an increase of the baroclinic Rossby radius by more than 20% at these latitudes under the applied forcing. It is therefore suggested that in a plausible future warmer climate, the characteristic length scale of mesoscale eddies, as well as boundary currents and fronts, may increase. In addition, since the speed of long baroclinic Rossby waves is proportional to the squared baroclinic Rossby radius of deformation, the results suggest that the time scale for large-scale dynamical oceanic adjustment may decrease in the warmer climate, thereby increasing the frequency of long-term climate variability where the oceanic Rossby wave dynamics set the dominant period. Finally, the speed of equatorial Kelvin waves and Rossby waves, carrying signals along the equator, including those related to ENSO, is projected to increase.

Corresponding author address: Dr. Oleg A. Saenko, Canadian Centre for Climate Modelling and Analysis, Meteorological Service of Canada, Victoria, BC V8W 2Y2, Canada. Email: oleg.saenko@ec.gc.ca

1. Introduction

The first baroclinic Rossby radius of deformation plays a fundamental role in ocean dynamics. It is a natural scale that often is associated with boundary phenomena, such as boundary currents and fronts, and with eddies (Gill 1982). In addition, the speed of long (nondispersive) baroclinic Rossby waves, which are one of the key players in the large-scale oceanic adjustment to perturbations, is proportional to the squared baroclinic Rossby radius of deformation. Outside of near-equatorial latitudes, the first baroclinic Rossby radius can be formally defined as the distance, λ1, that first baroclinic gravity waves of speed c1 propagate over time f−1 (Gill 1982):
i1520-0442-19-7-1354-e1
where f is the planetary vorticity. Values of the first baroclinic Rossby radius in the ocean vary with latitude, ranging from a few kilometers at high latitudes to greater than 100 km near the equator.

The speed of baroclinic gravity waves, and hence the baroclinic Rossby radius, is proportional to stratification (Gill 1982; see also next section). Under unperturbed climate conditions, the large-scale structure of the oceanic stratification does not change much, if averaging over a long enough period of time is applied. However, if the climate system is forced by, for example, a positive radiative forcing, the ocean, particularly the upper ocean, warms up and hence its stratification may change. It therefore seems reasonable to expect that the baroclinic Rossby radius may change with changing climate conditions. The question then is how significant could such a change be in, for example, a climate with higher CO2 level?

We address this question using results from several climate models. Since the magnitude of the change is likely to depend on the magnitude of the forcing, one would like to consider a realistic case. The purpose of this note therefore is, using a simple procedure (see next section), to evaluate whether a plausible global warming scenario could lead to noticeable changes in the first baroclinic Rossby radius of deformation in the future ocean. Here we consider a hypothetical future climate, where concentrations of greenhouse gases in the atmosphere have stabilized at the level implied by the 720-ppm stabilization experiment [Special Report on Emissions Scenarios (SRES) A1B] adopted by the Intergovernmental Panel on Climate Change (IPCC). According to this scenario, the level of CO2 in the atmosphere reaches 720 ppm by the end of the twenty-first century, which is roughly in between the other two widely discussed scenarios, B1 and A2.

2. The procedure and the data

A standard procedure for evaluating the baroclinic Rossby radii of deformation is to use a linearized quasigeostrophic potential vorticity equation. Under certain assumptions (Gill 1982), the vertical dependence can be separated from the horizontal and time dependence, leading to an eigenvalue problem of Sturm–Liouville form. For many purposes, a sufficiently accurate solution of this eigenvalue problem can be obtained by employing the so-called Wentzel–Kramers–Brillouin (WKB) method (Gill 1982; Chelton et al. 1998). Using this method, the phase speed of the first baroclinic gravity wave is
i1520-0442-19-7-1354-e2
where N is a buoyancy frequency, computed following the procedure outlined in section d of appendix B in Chelton et al. (1998); H(x, y) is the depth of the ocean. Using this procedure and data from different climate models, we first evaluate the warming-induced changes in the speed of the first baroclinic gravity waves. Then, these changes are converted into the changes in the first baroclinic Rossby radius of deformation using Eq. (1) outside of ±10° from the equator. The use of the WKB method seems to give particularly accurate results for evaluating λ1 < 100 km (see Fig. 1 in Chelton et al. 1998), as is typically found farther than about ±10° from the equator.

The data we use are from the coupled models submitted for inclusion in the IPCC's Fourth Assessment Report, archived and provided by the Program for Climate Model Diagnosis and Intercomparison (PCMDI). Two sets of data are used here. One of them, representing the hypothetical future climate, corresponds to the 720-ppm stabilization experiment (SRES A1B). The other, against which the changes in the baroclinic Rossby radius are compared, corresponds to the PCMDI preindustrial control experiment, where atmospheric CO2 was held fixed at the 280-ppm level. All quantities discussed below were computed using 3D monthly data of ocean potential temperature and salinity and then averaged over 10 yr to produce corresponding climatological distributions.

Since vertical integration in Eq. (2) is taken over the whole depth of the ocean, the term “stabilization” used by the PCMDI warrants discussion. It takes a long time for the deep ocean to stabilize. For example, the time scale for vertical mixing in the ocean is τ = H2/kν, where kν is the vertical diffusivity. Reasonable values for kν give thousands of years for τ, and a comparable time scale can be obtained by considering either the rate of isopycnal mixing or the rate of deep water production. In the 720-ppm stabilization experiment, the participating models were run for 200 yr with fixed concentration of greenhouse gases, which is not enough for the deep ocean to stabilize. Some of the models were not run for the stabilization at all, whereas some others were run for only 100 yr. Therefore, to keep the number of the models participating in this calculation relatively large, we use the data from the last decade of the first 100 yr of the SRES A1B 720-ppm stabilization experiment (corresponding to a nominal period of time between 2191 and 2200; using the data between 2181 and 2200 does not change the results). From the above discussion, however, it seems likely that the models with significantly different mixing parameters could be at different stages of stabilization after 100 yr of integration. This, as well as many other factors, may have contributed to the differences between the model results. A comprehensive discussion of all potential sources of the differences is beyond the scope here. The models are listed in Table 1.

3. Results

The speed of the first baroclinic gravity waves corresponding to the preindustrial control experiment is shown in Fig. 1 (top). In general agreement with observational estimates (Chelton et al. 1998), the models simulate values of c1 in the range of 2–3 m s−1 in low latitudes, decreasing toward higher latitudes. The reduction of c1 from low to high latitudes reflects a tendency of the oceanic stratification to decrease toward higher latitudes. An exception is the increase of c1 north of about 65°N, largely reflecting the increase of oceanic stratification poleward of 65°N associated with a strong halocline in the Arctic Ocean. The considerable differences in c1 between the models may arise from a number of factors, ranging from differences in representation of physical processes in these coupled models to adopted resolution. For example, there is a significant difference among the models in the number of vertical levels used to resolve the vertical structure of the ocean. In some of the models, up to 50% of the total number of vertical levels is used to resolve the uppermost 300 m, which is less than 10% of the mean depth of the ocean. However, since Eq. (2) assumes both a computation of vertical derivative of density and an integration of buoyancy frequency from the surface to the ocean bottom, a high vertical resolution of the whole water column is desirable.

There is general agreement between the models in that in the warmer climate, the zonally averaged speed of baroclinic gravity waves increases essentially at all latitudes (Fig. 1, bottom). However, the magnitude of the increase differs significantly between the models. On average, the largest increase of c1 is simulated in the Arctic Ocean, although the spread between the model results is also largest there. One of the models [the Meteorological Research Institute Coupled GCM (MRI−CGCM2.3.2)] shows very weak response of c1 in the northern polar latitudes. (It should be noted that Arctic Ocean is typically very poorly resolved by the current generation of global ocean–atmosphere models.) At southern high latitudes, the disagreement between the models is also large, with some of the models showing little change in c1 south of 60°S, whereas some others show a relatively large response. Between 40°S and 40°N, agreement is somewhat better in that all of the models at least show an increase of c1. The increase, however, varies significantly, from 0.2 to 0.5 m s−1, being about 0.3 m s−1 on average.

According to Eq. (1), an increase of c1 must translate into an increase of λ1. At the equator, however, the increase of c1 is by itself of particular interest. This is because equatorial Kelvin waves propagate eastward with the speed of baroclinic gravity waves, whereas the equatorial Rossby waves propagate westward with the speed that is also linearly related to the speed of baroclinic gravity waves. These waves play a fundamental role in equatorial dynamics and climate, including ENSO. Our calculations indicate that, averaged between the models the increase of c1 at the equator is 0.36 m s−1, which is 13.7% relative to the preindustrial model mean of 2.62 m s−1. This suggests that the warming of the ocean in response to the plausible increase of atmospheric CO2 may result in a nonnegligible increase in the propagation of signals along the equator, including those related to ENSO. Since these propagation speeds influence the period of ENSO, their increase may contribute to a tendency for a decreased ENSO period under increased atmospheric CO2 in these same models, described by Merryfield (2006).

The zonally averaged first baroclinic Rossby radii of deformation, corresponding to the preindustrial experiment, are shown in Fig. 2 (top). The inverse dependence of λ1 on planetary vorticity away from the equator, implied by Eq. (1), clearly dominates its latitudinal structure. Near the equator λ1 = (0.5 c1/β)1/2, where β = df /dy (Gill 1982), which gives values 220–270 km (not shown). In agreement with observational estimates (Chelton et al. 1998), the simulated Rossby radii decrease from more than 150 km in the Tropics to just a few kilometers in polar regions. All models show a local maximum of λ1 in the Arctic Ocean, associated with local maximum in c1.

The changes in the baroclinic Rossby radius are shown in Fig. 2 (bottom). As implied by the changes in c1, the baroclinic Rossby radius increases, essentially at all latitudes and in all models. The most notable absolute increase of λ1 is projected at low latitudes where values of λ1 are large so that their relative change is small. Toward the midlatitudes, however, the relative change of λ1 increases (Fig. 4, top), reaching 10%–20% at ±35°–40° of latitude in most of the models, while some of the models show a much larger increase. In the real ocean, these are the latitudes of intense generation of mesoscale eddies due to instability of western boundary currents. These eddies play an important role in the exchange of heat and other properties between the subtropical and subpolar regions. Since a characteristic horizontal scale of the eddies appears to be linked to the baroclinic Rossby radius of deformation, the climate model results suggest that the scale of these eddies, as well as the scale of boundary currents and fronts, may increase in the warmer climate. In addition, most models show a significant increase of λ1 in the Arctic Ocean (Fig. 2, bottom). This result, however, should be considered with caution, given that the Arctic Ocean is poorly resolved in these global models, as we have already noted. If this prediction were to be realized, the scale of the Arctic Ocean eddies and the width of the currents would increase accordingly.

Standard linear theory (Gill 1982) predicts that the speed of long extratropical baroclinic Rossby waves is proportional to −βλ12 [more recent developments in the theory, which bring the speed of the oceanic Rossby waves in closer agreement with satellite altimetric observations, are given in Killworth et al. (1997)]. The quantity −βλ12 and its projected change according to the models are shown in Fig. 3. The results indicate that, unless fully compensated by the changes in the background oceanic circulation, the propagation speed of baroclinic Rossby waves is likely to increase at each latitude in a warmer climate. The relative changes projected by the models in λ12 are shown in Fig. 4 (bottom). Although the spread between the models is large, most of the models predict an increase of λ12 from about 20% in the subtropics to 30%–40% at the midlatitudes, although again some of the models show a much larger increase.

Thus, according to these climate models, the time scale for large-scale dynamical oceanic adjustment is likely to decrease in the warmer climate. Furthermore, the frequency of decadal climate variability, where the oceanic Rossby wave dynamics play an important role (e.g., Latif and Barnett 1996) may increase. For example, using a simple coupled model of decadal oscillations, such as the one proposed in Münnich et al. (1998), it is straightforward to demonstrate that the 0.3 m s−1 increase of the baroclinic gravity wave speed results in the increase of the dominant decadal frequency by a factor of 1.25–1.35, depending on other parameters in that model.

Finally, to give an idea about the geographical differences and the evolution in time, Fig. 5 shows the changes in the gravity wave speed in the Pacific Ocean and in the Atlantic Ocean by the end of the twenty-first century and twenty-second century. First, it is clear that the changes may notably differ between the two oceans. Second, the oceanic stratification, as represented here by the speed of baroclinic gravity waves, and hence the baroclinic Rossby radius of deformation, will continue to increase significantly after the concentration of CO2 in the atmosphere is held fixed, which is also expected.

4. Discussion and conclusions

We have used results from eight ocean–atmosphere general circulation models to evaluate the influence of the projected changes in the oceanic stratification on the first baroclinic Rossby radius of deformation in the ocean, associated with atmospheric CO2 increase. For each of the models, an oceanic state corresponding to the A1B stabilization experiment (with final specified atmospheric CO2 concentration of 720 ppm) is compared to a state corresponding to the preindustrial control experiment (with atmospheric CO2 concentration of 280 ppm). In all the models, the first baroclinic Rossby radius increases with increasing oceanic stratification in the warmer climate. There is, however, a considerable range among the models in the magnitude of the increase. At the latitudes of intense eddy activity associated with instability of western boundary currents (around 35°–40° latitude), the increase reaches 4 km on average, or about 15% of the local baroclinic Rossby radius. Some of the models predict an increase of the baroclinic Rossby radius by more than 20% at these latitudes under the applied forcing. It is therefore suggested that in a plausible future warmer climate, the characteristic scale of mesoscale eddies, as well as boundary currents and fronts, may increase accordingly. In addition, since the speed of long baroclinic Rossby waves is proportional to the squared baroclinic Rossby radius of deformation, the results suggest that the time scale for large-scale dynamical oceanic adjustment may decrease in the warmer climate. Relative to the preindustrial climate, the squared baroclinic Rossby radius increases from about 20% in the subtropics to 30%–40% at the midlatitudes in most of the models. This, in addition to a number of oceanic implications, has a potential to affect the time scale of atmospheric extratropical variability and, in particular, the decadal climate variability where propagation of long Rossby waves from east to west across the ocean sets the dominant frequency. Finally, the speed of equatorial Kelvin waves and Rossby waves, carrying signals along the equator, including those related to ENSO, is projected to increase.

Acknowledgments

I acknowledge the international modeling groups for providing their data for analysis, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the model data, the JSC/CLIVAR Working Group on Coupled Modelling (WGCM) and their Coupled Model Intercomparison Project (CMIP) and Climate Simulation Panel for organizing the model data analysis activity, and the IPCC WG1 TSU for technical support. The IPCC Data Archive at Lawrence Livermore National Laboratory is supported by the Office of Science, U.S. Department of Energy. I am grateful to Bill Merryfield, George Boer, and Ken Denman for useful discussion and comments.

REFERENCES

  • Chelton, D. B., R. A. deSzoeke, M. G. Schlax, K. E. I. Naggar, and N. Siwertz, 1998: Geographical variability of the first-baroclinic Rossby radius of deformation. J. Phys. Oceanogr, 28 , 433460.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 662 pp.

  • Killworth, P. D., D. B. Chelton, and R. A. De Szoeke, 1997: The speed of observed and theoretical long extratropical planetary waves. J. Phys. Oceanogr, 27 , 19461966.

    • Search Google Scholar
    • Export Citation
  • Latif, M., and T. P. Barnett, 1996: Decadal climate variability over the North Pacific and North America: Dynamics and predictability. J. Climate, 9 , 24072423.

    • Search Google Scholar
    • Export Citation
  • Merryfield, W. J., 2006: Changes to ENSO under CO2 doubling in a multimodel ensemble. J. Climate, in press.

  • Münnich, M., M. Latif, S. Venzke, and E. Maier-Reimer, 1998: Decadal oscillations in a simple coupled model. J. Climate, 11 , 33093319.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

(top) Zonally averaged phase speed of first baroclinic gravity waves corresponding to the preindustrial experiment and (bottom) its change in the 720-ppm A1B stabilization experiment.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3683.1

Fig. 2.
Fig. 2.

(top) Zonally averaged first baroclinic Rossby radius of deformation corresponding to the preindustrial experiment and (bottom) its change in the 720-ppm A1B stabilization experiment.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3683.1

Fig. 3.
Fig. 3.

(top) Zonally averaged βλ12 corresponding to the preindustrial experiment and (bottom) its change in the 720-ppm A1B stabilization experiment. Notice that some of the models show absolute changes in βλ12 that differ from what might be expected based on the corresponding changes in λ1, since , where the overbar denotes averaging.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3683.1

Fig. 4.
Fig. 4.

(top) Relative changes in zonally averaged first baroclinic Rossby radius of deformation and (bottom) its squared values.

Citation: Journal of Climate 19, 7; 10.1175/JCLI3683.1

Fig. 5.
Fig. 5.

Zonally averaged changes in phase speed of first baroclinic gravity waves (top) in the Pacific Ocean and (bottom) in the Atlantic Ocean. The changes correspond to two time intervals, 2091–2100 and 2191–2200, relative to the preindustrial control experiment. The computations are done using the results from the GFDL−CM2.0 model, where the vertical structure in the ocean is resolved by the largest number of levels (50) and where the changes in the wave speed are representative of the model-mean response (see Fig. 1, bottom).

Citation: Journal of Climate 19, 7; 10.1175/JCLI3683.1

Table 1.

The climate models results that are used in this study.

Table 1.
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