A Spontaneously Generated Atmospheric General Circulation
Ben P. Kirtman and Edwin K. Schneider
Center for Ocean-Land-Atmosphere Stuides
4041 Powder Mill Road, Suite 302, Calverton, MD 20705
e-mail: kirtman @ cola.iges.org
Submitted to the Journal of the Atmospheric Sciences
A series of idealized atmospheric general circulation model (AGCM) experiments are presented. These experiments examine whether and how atmospheric deep moist convection, in the absence of meridional gradients in external forcing, interacts with the large scale flow, becoming spatially organized and yielding a coherent general circulation. In a control simulation, where the sea-surface temperature (SST) and the incident solar flux are prescribed to be independent of latitude, longitude and time, a well defined Inter-Tropical Convergence Zone (ITCZ) forms at the equator. This result suggests that the interaction between convection and the rotation of the Earth causes convection to prefer to organize at the equator. In this control simulation, the SST is not interactive, and cannot respond to the spatial variations of the heat flux into the ocean that result from the organization of the circulation. In order to examine the circulation that arises without horizontal gradients in the forcing in a physically consistent, energetically closed, model, the AGCM is coupled to a mixed layer ocean model. In this case, the ITCZ still forms at the equator even though a "reversed" pole-to-equator surface temperature gradient develops.
The SST distribution and the tropospheric circulation are very different between these two experiments, but the surface zonal mean zonal wind is quite similar. In the tropics the surface zonal wind is easterly and in the subtropics it is westerly, implying a net poleward transport of angular momentum in both simulations. Large scale zonally asymmetric convective "events" apparently produce this momentum transport by the barotropic tilted trough mechanism. The role of three dimensional zonally asymmetric motions in the momentum transport mechanism is tested in another experiment, where the AGCM is truncated to be zonally symmetric. In this case, the model enters a limit cycle where the ITCZ transits between 20oN and 20oS with a 22 month period. The motions associated with this oscillatory behavior accomplish the same poleward transport of angular momentum that the convective events produced in the zonally asymmetric model, but by a drastically different mechanism, suggesting that there may be some undiscovered general principle governing the momentum transport.
Finally, a simple argument is used to estimate the minimum modification to the uniform specified SST necessary to displace the ITCZ off the equator. A last experiment verifies this argument.
The currently accepted picture of the atmospheric general circulation is described by Lorenz (1967). The annually averaged solar heating is strongly dependent on latitude, with a maximum at the equator and a minimum at the poles. In the absence of atmospheric motions radiative-convective equilibrium (RCE) would be attained, and the differential heating would lead to a substantial pole-to-equator temperature gradient and a large associated store of zonal mean available potential energy (APE). However, the pole-to-equator RCE temperature gradient is unstable, leading to the excitation of midlatitude transient baroclinic eddies that draw energy from the zonal mean APE and transport heat poleward, reducing the temperature gradient and establishing equilibrium between the production of zonal mean APE by the external forcing and its destruction by the poleward eddy heat fluxes. These transients also transport angular momentum poleward, maintaining surface easterlies in the tropics and westerlies in the midlatitudes.
Based on this description of the general circulation, one might conclude that if there was no latitudinal variation in the solar forcing, no circulation would develop (i.e., no APE and no baroclinic eddies), and the atmosphere would be in uniform RCE everywhere. However, the solar forcing leads to vertical temperature and moisture profiles that are convectively unstable. If convection became spatially organized, then a convectively driven large scale circulation could "spontaneously" arise when the APE of the RCE state is zero. This paper shows that this situation does occur, at least in our general circulation model GCM). The circulation that develops is weak compared to the observed general circulation. However, insofar as the model is realistic, the processes found here could also be operating in the "background", overshadowed by the general circulation driven by the meridional gradients in the solar forcing.
One mechanism that would lead to a large scale spontaneous circulation is the formation of the Inter-Tropical Convergence Zone (ITCZ) preferentially at some latitude due to the interaction between convection and the rotation of the Earth. While throughout most of the tropics the time averaged precipitation exhibits a well defined ITCZ, i.e., convection is well organized, it is not clear whether or not convection will organize in an idealized environment without latitudinal gradients in SST or solar forcing. Figure 1 shows the time mean (1979-1997) zonal mean oceanic precipitation calculated from the Xie and Arkin (1996) rainfall estimates, and the zonally averaged SST over the same time period. A well defined ITCZ is situated at about 5oN, co-located with a somewhat broader SST maximum. At the equator there are relative rainfall and SST minima. In the Southern Hemisphere there is a broader and weaker rainfall maxima centered around 5oS. For the most part, the SST and rainfall extrema are co-located, but some subtle spatial shifts can be detected.
Many previous modeling studies have focused on whether the ITCZ forms at the equator or off the equator and what role the SST gradients play in the formation of the ITCZ. This issue is not the emphasis of this study. The first concern here is not whether the ITCZ forms on or off the equator, but whether convection organizes at any latitude in an idealized environment without horizontal gradients in the prescribed external forcing. Since convection is found to organize in our idealized model environment, we are then interested in how this organization interacts with the large scale flow to produce a coherent general circulation. While the focus of this study is distinct from many of the previous studies, there are elements of these earlier works that suggest that convection will in fact organize in the idealized environment.
Several studies present arguments where the SST distribution may not matter in organizing convection into an ITCZ. Charney (1971) hypothesized that the position of the ITCZ is governed by two processes: (i) Ekman pumping efficiency which goes to zero at the equator and (ii) moisture availability which increases equatorward (due to the SST gradients). The competition between these two processes predicts that the ITCZ should be close to, but not at, the equator. On the other hand, Schneider and Lindzen (1977) found a dynamical preference for the equator in the linear boundary layer mass convergence response to imposed zonally symmetric convective heating.
Holton et al. (1971) and Lindzen (1974) make zonally asymmetric arguments for convection to organize into an off equatorial ITCZ. Holton et al. (1971) argued that boundary layer convergence due to zonally propagating waves is concentrated at a critical latitude where the angular frequency equals the Coriolis frequency. The predominance of tropical easterly waves with a 4-5 day period would imply an ITCZ situated at about 6o off the equator. Lindzen (1974) invoked a wave-CISK argument to explain a maximum in convection 6-7o off the equator. (CISK stands for conditional instability of the second kind.) While in these studies the SST distribution does not explicitly enter into the calculations, the SST distribution has an implicit effect through the boundary layer moisture supply.
Waliser and Somerville (1994) also argue that there is an intrinsic property of the atmosphere, independent of the SST distribution, that drives the ITCZ to be situated off the equator. Waliser and Somerville (1994) used a Gill (1980) atmosphere model with prescribed heating to show that the maximum in low level convergence occurs when the heating is displaced between 4-12o away from the equator. They also used a zonally symmetric primitive equation model to show that the ITCZ formed off the equator even with an SST maximum on the equator. Similar to Charney (1971) and unlike Holton et al. (1971) and Lindzen (1974), the Waliser and Somerville (1994) results do not require zonal asymmetry for the formation of an off equatorial ITCZ.
There are also modeling studies that suggest that meridional SST gradients may be essential in organizing convection. Schneider and Lindzen (1976) showed that in the presence of stable stratification the tropical Ekman layer depth would remain finite, as opposed to the Charney (1971) result, and the boundary layer mass convergence forced by an Earth-like equator-to-pole RCE temperature distribution would be maximum at the equator. Lindzen and Nigam (1987) developed a simple boundary layer model to examine how low level convergence is forced by surface temperature gradients. Their model was most effective at describing the zonally asymmetric circulation. However, they applied the model to the zonally averaged circulation, and found that it reproduced the observed low level zonal mean convergence (and meridional flow), but not the zonal mean zonal flow. The maximum low level zonal mean convergence was coincident with the surface temperature maximum suggesting that the ITCZ is strongly influenced by the SST, and should form close to the SST maximum.
Goswami et al. (1984) used a zonally symmetric version of the Goddard Laboratory for Atmospheric Sciences AGCM, but with enhanced internal friction, to examine the interaction of CISK and an imposed SST in determining the position, structure and transient behavior of the ITCZ. They found that a steady ITCZ occurred over the SST maximum, but that if the SST maximum was moved after the model reached equilibrium, the ITCZ position persisted for a relatively long time (weeks to months).
Although mostly used for studies of intraseasonal variability (e.g., Kirtman, 1992), "aqua-planet" models have also been used for ITCZ studies. The "aqua-planet" model is essentially a full AGCM where all the surface grid points are sea points and the sea surface temperature is specified as independent of longitude, and, in some cases, independent of latitude. Typically, the "aqua-planet" studies have also focused on how imposed SST gradients relate to the location of the ITCZ. Hayashi and Sumi (1986) used an "aqua-planet" model, and found two ITCZs straddling the equator even though the SST maximum was on the equator. Hess et al. (1992) considered the location of the ITCZ with various convective parameterizations. Depending on the convective parameterization and the meridional distribution of the prescribed SST, a single ITCZ (on or off the equator) or double ITCZ formed, indicating a great deal of sensitivity to convective parameterization and the meridional profile of SST. Hoskins et al (1999) found that as the prescribed SST became "flatter" in the tropics the convection failed to organize and the Hadley cell disappeared. Kirtman (1992) found that the location of the ITCZ was also sensitive to the surface wind dependence in the latent heat flux.
To our knowledge, Sumi (1990) is the only "aqua-planet" study where no horizontal variations in the SST or solar forcing was prescribed. In the Sumi (1990) simulation, the organization of convection was sensitive to the rotation rate of the earth. With no rotation the convection failed to organize. When the rotation rate was half the true value the convection organized into two ITCZs straddling the equator, and when the true rotation rate was used, a single ITCZ formed along the equator.
A fundamental problem with these atmosphere-only studies is that the SST is prescribed and does not respond to variations in the surface heat flux from the atmosphere to the ocean. This means that there is an implied ocean heat transport to maintain the specified SST; otherwise, these "aqua-planet" simulation must be viewed as energetically inconsistent. Part of the intent of this paper is to re-examine the organization of convection in an "aqua-planet" model, but in this case we remove the constraint of constant SST by coupling to a mixed layer ocean model to produce an energetically consistent atmospheric general circulation.
There have been previous attempts to address the preferred location of the ITCZ in a coupled ocean-atmosphere model framework. For example, Pike (1971) found in a zonally symmetric coupled model that the ITCZ was displaced off the equator due to equatorial upwelling. Pike's (1971) calculations suggest that if the ITCZ is displaced off the equator, the induced surface easterlies at the equator results in enhanced upwelling and lowering of the SST, preventing the ITCZ from moving back to the equator. Charney et al. (1988) found similar results to Pike (1971). Xie and Philander (1994) argued that dynamic oceanic upwelling near the equator is a critical element of this mechanism, but that surface processes such as mixing and evaporation are also important. These coupled scenario suggest that understanding the preferred latitudes of the oceanic ITCZ cannot be studied in isolation from the so-called cold tongue (i.e., upwelling regions).
Many of the studies discussed above indicate substantial disagreement regarding the relationship between the location of the SST maximum and the preferred latitudes of the ITCZ. Whether an off equatorial SST maximum is required for an off equatorial ITCZ remains an open question. What role the cold tongue plays in suppressing convection also remains unclear. Moreover, it is even more unclear how the ITCZ affects the SST distribution in a coupled sense. The focus of the work presented here is distinct from much of this previous research in that we intend to understand how the organization of convection by itself leads to a coherent general circulation. We are not particularly interested with what particular latitude the convection organizes at, but rather whether it organizes at any latitude. A series of idealized uncoupled and coupled "aqua-planet" AGCM-slab mixed layer ocean model simulations are presented. These experiments are designed to understand how convection and the circulation interact to produce organized precipitation, and how this organization affects the atmospheric general circulation and the underlying SST. By coupling the AGCM to a mixed layer ocean model we are removing the constraint of constant SST, thus allowing for an energetically consistent result. However, it should be noted that the resulting circulation is without the effect of any oceanic heat transport. We are not arguing that ocean dynamics is unimportant. On the contrary, given some of the sensitivities that we find, we are suggesting the importance of ocean dynamics.
First, a control simulation is presented, where the SST and solar forcing at the top of the atmosphere are prescribed to be independent of longitude, latitude and time. The question being addressed in this simulation is: without any SST or solar forcing gradients where (if at all) does the convection organize and what is the resulting general circulation? In coupled simulations, we examine how this organization affects the SST distribution and what dynamical processes maintain the general circulation. Finally, based on understanding from the previous experiments we examine the magnitude of the influence of SST on the location of the ITCZ.
This study examines the results from a particular GCM. We do not know whether similar results would be found using any other GCM, although the results of Sumi (1990) suggest that they may.
The model used in these experiments and the experimental design are described in this section.
a. The Model
The COLA AGCM which was originally derived from the National Centers for Environmental Prediction (NCEP)(1) numerical weather prediction model (Sela, 1980) is used in the experiments described here. Versions of the AGCM has been extensively used for monsoon studies (e.g., Fennessy et al., 1994; Kirtman and Shukla, 1998) and for El-Niño Southern Oscillation (ENSO) studies (Kirtman et al., 1997; Kirtman and DeWitt, 1997; Kirtman and Zebiak, 1997). The AGCM has also been coupled to a slab mixed layer ocean model in Schneider et al. (1997) to study the influence of the tropical oceans on global climate, and in Schneider et al. (1999) to examine the climate sensitivity to upper tropospheric water vapor. Additional details regarding the AGCM can be found in Kinter et al. (1988) and DeWitt (1996). Model documentation is given in Kinter et al. (1997). The model is a global spectral model with triangular truncation at wavenumber 30. There are 18 unevenly spaced -coordinate vertical levels. The parameterization of the solar radiation is after Lacis and Hansen (1974) and terrestrial radiation follows Harshvardhan et al. (1987). The deep convection is an implementation of the Relaxed Arakawa-Schubert scheme of Moorthi and Suarez (1992) described by DeWitt (1996). The convective cloud fraction follows the scheme used by the National Center for Atmospheric Research (NCAR) in their Community Climate Model (Kiehl et al., 1994; see DeWitt and Schneider, 1997 for additional details) There is a turbulent closure scheme for the subgrid scale exchange of heat, momentum, and moisture as in Miyakoda and Sirutis (1977) and Mellor and Yamada (1982). We have examined the formulation of the model's physical parameterizations and have not found any latitude dependent empiricism - the parameterizations applied at any latitude in principle should give the same results for the same specification of values in the column. Then the only process in the model that explicitly depends on the latitude is the Coriolis effect.
In all the experiments described here the incident solar radiation at the top of the atmosphere is prescribed to be independent of latitude, longitude and time(2). The surface of the earth is assumed to be water covered and there is no surface terrain height. In some of the experiments the SST is prescribed (usually uniform in space and time), and in some experiments, the SST is determined from a slab mixed layer ocean model of constant 50 m depth.
b. Sensitivity Experiments
Four simulations are described here, all of which are designed to understand the dynamic and thermodynamic constraints that determine how convection interacts with the large scale circulation. In the first sensitivity experiment, an AGCM integration is made with prescribed SST and solar forcing. In this experiment (hereafter referred to as EXP1), both the SST and the solar forcing are invariant in latitude, longitude and time. The solar constant is 1365 W m-2 and the SST is 26 oC.
The motivation for this first experiment is to determine whether convection becomes spatially organized in the absence of SST and solar forcing gradients. We find that the interaction between rotational effects and convection leads to a convectively driven large scale circulation centered at the equator.
The results of EXP1 indicate a dynamical preference for the organization of convection at the equator. However, the resulting circulation is not energetically consistent in that the organization of convection necessarily results in meridional variations in the net heat flux into the ocean and the SST cannot respond to these variations. Therefore, the results of EXP1 can be interpreted as energetically consistent only if there is an implied oceanic heat transport and heat storage that exactly balances the meridional variations in the surface heat flux into the ocean. In order to satisfy energetic consistency explicitly and as simply as possible, the AGCM is coupled to a mixed layer ocean model. This experiment is referred to as EXP2.
Both simulations EXP1 and EXP2 maintain surface easterlies in the tropics and surface westerlies in the midlatitudes. This implies that there must be a net poleward transport of angular momentum. It is not clear from these experiments how this angular moment transport is accomplished, particularly because the meridional temperature gradients generated by the circulation in EXP1 and EXP2 are weak and not expected to support baroclinic instability. Two remaining possibilities are that the angular momentum transport is due to the zonal mean circulation or to some kind of zonally asymmetric eddies that are not related to baroclinic instability. The third sensitivity experiment (EXP3) eliminates the transport due to the zonally asymmetric eddies. EXP3 is the same as EXP2 except that the model is made to be zonally symmetric.
An interesting aspect of EXP2 is that a "reversed" pole-to-equator SST gradient develops. The coldest SST occurs at the equator. In spite of this reversed pole-to-equator SST gradient, the ITCZ remains at the equator. At first glance it appears that the circulation is somehow "thermodynamically indirect", but closer examination of the tropospheric temperature structure indicates otherwise. The organized convection modifies the lower tropospheric temperature near the equator in order to maintain a locally thermodynamically direct circulation. This effect is in competition with the meridional circulation forced by the global scale SST gradients. The question then arises: what SST distribution will suppress convection at the equator? In EXP4, we attempt to estimate the smallest change in the SST that will eliminate the equatorial ITCZ.
All the simulations are run until the model reaches equilibrium, which is about 20 years. Table 1 summarizes the four experiments presented here.
The results from the four experiments described in the previous section and in Table 1 are presented here.
a. Position of ITCZ with Uniform SST (EXP1)
The zonal mean precipitation in EXP1 as a function of latitude and time is shown in Fig. 2a, and Fig. 2b shows a snap shot of the monthly mean precipitation at month 240. Figure 2a indicates that by month 121 the model is in equilibrium with a well defined zonal mean ITCZ centered at the equator and a rainfall maximum on the order of 6-7 mm day-1. Immediately on either side of the equator there are strong descending regions with rainfall minima. There are also weak symmetric subtropical rainfall maxima of the order of 3 mm day-1at about 15o away from the equator (Fig. 2c). Throughout the ten years shown there is some variability in the rainfall, but the zonal mean ITCZ remains at the equator for the entire period. The plan view of the monthly mean precipitation (Fig. 2b) indicates that there is substantial zonal inhomogeneity in the precipitation. While the bulk of the rainfall remains within one grid point of the equator, the subtropical rainfall maxima can be detected.
Figure 2b also shows a relatively large convective center extending to the east of 300oE and south of 15oS. Off-equatorial convective events such as this can be seen in just about every monthly mean map and can appear in both hemispheres. The orientation of this convective center is consistent with a net poleward angular momentum transport, which has also been verified by an examination of the eddy momentum flux (not shown). The importance of these convective events with regard to the maintenance of the angular momentum budget is discussed in more detail later in the paper.
Since there are no meridional gradients in the forcing, the results of EXP1 suggest that there is a dynamical constraint (i.e., variation of the Coriolis force with latitude) that gives a preference for convection to organize at the equator. We have tested this hypothesis by setting the Coriolis force to zero in the model. In this case, the model is in radiative convective equilibrium and there is no latitudinal preference for the ITCZ (Fig. 2c).
The time averaged zonal mean circulation in EXP1 is shown in Figs. 3a-c. Throughout most of the upper troposphere the zonal mean zonal wind (Fig. 3a) is westerly. There are subtropical westerly jets in both hemispheres that reach their maximum amplitude at the top of the model. In the boundary layer and at the surface there are tropical easterlies and subtropical westerlies. These surface winds imply that there must be a net vertically integrated poleward transport of angular momentum. As will be shown below, this angular momentum transport appears to be accomplished by the systems associated with relatively large subtropical convective events, such as the one which can be seen in Fig. 2b.
The mean meridional circulation (Figs. 3b) is consistent with an ITCZ (or Hadley cell) centered at the equator. The descending branches of the Hadley cells are centered around 8o off the equator and there is weaker ascending motion not large enough to appear in Fig. 3b at about 15o in each hemisphere corresponding to the subtropical rainfall maximum. These secondary maxima are associated with the rising branch of weak "Ferrel" cells.
The time mean zonal mean temperature is shown in Fig. 3c (the horizontal mean temperature at each pressure level has been removed). The largest meridional gradients are in the stratosphere, and are associated with a somewhat deeper tropical tropopause. In the tropical troposphere, there is a relatively deep warm layer from the surface to about 400 mb. The subtropics are relatively cool so that the Hadley circulation seen in Fig. 3b is thermally direct even though there are no surface temperature gradients. The largest tropospheric temperature variation is at about 600 mb, and these temperature variations have a considerably larger meridional scale than the ITCZ.
The global mean surface heat flux budget in EXP1 is shown in Fig. 4a, and Fig 4b shows the mean surface heat flux as a function of latitude. Figure 4a shows that, while there is some variability in the global mean surface heat flux, no climate drift can be detected. It is also apparent from Fig. 4a that there is net surface energy imbalance of approximately 65.5 watts m-2. This imbalance does not lead to climate drift in EXP1 because the surface temperature is prescribed. However, once the model is coupled to a mixed layer ocean model this energy excess would lead to considerable warming of the SST. In order to remove the energy excess at the surface in the remaining experiments and simulate about the same global mean SST as in EXP1, we have reduced the solar constant from 1345 w m-2 to 990 w m-2. The procedure for this reduction is described in the Appendix.
The components of the surface energy budget (Fig. 4b) sum up to equal the total heat flux. In the absence of oceanic transport, relative to the global mean, there is an implied surface cooling near the equator and heating in the subtropics. The equatorial cooling is mostly due to a reduction in the short wave flux because of increased cloudiness. The long wave cooling is also reduced near the equator because of the increased clouds associated with the ITCZ. Similarly, the cooling associated with the latent heat flux in the vicinity of the ITCZ is relatively small because of the weaker surface winds. The subtropics are relatively dry and cloud free giving relatively large short wave flux. A substantial fraction of this increased short wave flux is reduced by stronger latent heat flux (via stronger surface winds) and long wave cooling effects. Both the latent heat flux and the long wave cooling effects compete with the short wave variations thereby reducing the latitudinal variations in the total heat flux. These meridional variations in the total heat flux are due to the organization of convection and the associated large scale circulation.
b. Sensitivity of ITCZ to Active Ocean Mixed Layer (EXP2)
In order to maintain the surface temperature of EXP1, (assuming global mean heat balance), meridional ocean heat transport would be required. If there were no horizontal ocean heat flux then Fig. 4b suggests that the SST would cool near the equator and warm in the subtropics. In order to obtain an energetically consistent circulation and examine how the resulting changes in the SST distribution affect the structure of the circulation and the organization of convection, we have coupled the AGCM to a mixed layer ocean model of constant 50 m depth. In the same format as Fig. 2a-b, Fig. 5a-b shows the time latitude history of the zonal mean precipitation and a snap shot of the monthly mean precipitation at month 240, respectively. As with EXP1, the maximum zonal mean rainfall is centered on the equator; however, the relative enhancement of precipitation in the ITCZ in EXP2 is smaller. While Fig. 2b and Fig. 5b are only snap shots, the comparison between these two figures does reflect the fact that there is more zonal inhomogeneity in EXP2. Large convective events in EXP2, similar to those in EXP1, can be identified that transport angular momentum poleward. Again, a detailed analysis of the vertically integrated momentum flux indicates that the transport is poleward in the regions of these convective centers.
While the ITCZ is centered at the equator in both EXP1 and EXP2, the general circulation is quite different between the two simulations. Figure 6a, for example, shows the time mean zonal mean SST which has a "reversed" pole-to-equator temperature gradient (there is no pole-to-equator temperature gradient in EXP1). The equator is about 5oC colder than the poles. The heat flux budget shown in Fig 4b suggests that colder temperatures should be expected at the equator, but the meridional structure of the SST does not mimic the total heat flux residual shown in Fig. 4b. In particular, there are no subtropical SST maxima as suggested by the heat flux residual, and there are significant SST gradients in midlatitudes.
This integrating or smoothing effect in the SST can be clearly seen by comparing Figs. 6a and 6b. Figure 6b shows the meridional structure of all the components of the surface heat flux budget in the same format as Fig. 4b. The meridional structure seen in Fig. 6b is consistent with the precipitation and circulation, but is not apparent in the zonal mean SST. In contrast to EXP1 (Fig. 4b), the total heat flux at each grid point is zero since there is energy balance and no oceanic heat transport. In both EXP1 and EXP2, the sensible heat flux is a relatively small component of the heat budget. EXP1 and EXP2 also indicate similar meridional structure with a relative minimum (maximum) in the short wave (long wave and latent heat flux) at the equator (i.e., higher cloudiness) and relative maxima (minima) in the dry descending regions. In EXP2, the incoming short wave flux is approximately balanced by 1/4 outgoing long wave flux and 3/4 latent heat flux.
The zonal mean circulation, Figs. 7a-c, also indicates that the Hadley circulation and ITCZ are centered on the equator. However, there are some marked differences in the zonal wind (Fig. 7a) and temperature (Fig. 7c) between EXP1 and EXP2. In particular, in EXP2 the upper level winds are dominated by easterlies, whereas in EXP1 the upper level winds are westerly. The easterly jets close at around 200 mb and about 20o poleward of the equator. These upper level easterlies are consistent with the atmospheric temperature following the equator-to-pole increase in surface temperature. There are also relatively weak subtropical westerlies that are trapped within the boundary layer.The mean meridional circulation in the deep tropics in EXP2 is weaker than in EXP1 (contour interval in Fig. 7c is 1/3 the contour interval in Fig. 3c), but the subtropical Ferrel cell is somewhat better defined.
Even though the ITCZ forms at the equator, the effects of the reversed surface temperature gradient are felt throughout the troposphere (Fig. 7c). The tropical tropospheric temperatures are colder than those in middle and high latitudes which suggests that the near equatorial Hadley cells are thermally indirect. However, careful examination of the meridional surface pressure gradient and temperature gradients in the lower troposphere (see Fig. 7d) indicates that the localized circulation associated with the rising branch of the Hadley cell is thermally direct. Fig. 7d indicates that in the lower tropical troposphere the temperature is colder than in the extratropics, but in the immediate vicinity of the ITCZ there is a local maximum in the temperature and a minimum in the surface pressure. It is this local lower tropospheric temperature maximum (surface pressure minimum) and the associated circulation that has become disconnected from the SST.
Returning to the zonal mean zonal wind (Fig. 7a), it is apparent that the strength of the easterlies increases with height and latitude between the equator and 20o. Increasing easterlies in upper troposphere along Hadley streamlines indicate that angular momentum balance is dominated by transient momentum flux rather than advection of angular momentum by the mean circulation (Schneider, 1984). How this transient momentum flux affects the organization of convection is examined in the next section.
c. Sensitivity ITCZ to Zonal Asymmetry (EXP3)
Both EXP1 and EXP2 have time mean zonal mean surface easterlies in the tropics and westerlies in the subtropics. This implies that there must be a net transport of angular momentum from the tropics into the subtropics. Since the surface temperature gradients in these simulations are not expected to support baroclinic instability (no gradient in EXP1 and reversed gradient in EXP2), it remains to be explained how this angular momentum transport is accomplished. Moreover, Figs 7a-b indicate that angular momentum transport in EXP2 is not accomplished by the zonal mean circulation, at least in the Hadley cell region. Both Figs. 2b and 5b suggest that there are large scale zonally asymmetric convective "events" that accomplish this transport. In EXP3 we examine the importance of the zonally asymmetric motions by repeating EXP2, but in this case the model has been truncated to be zonally symmetric.
Figures 8a-c show latitude-time cross sections of the precipitation, zonal surface wind and surface temperature in EXP3, respectively. In this case the model enters a limit cycle as the ITCZ (Fig. 8a) migrates back and forth across the equator extending into the subtropics as far as 20o. This is about the same latitude to which the zonally asymmetric convective events extended in EXP1 and EXP2. The dominant period of these oscillations is about 22 months, and can be easily detected in other fields such as the zonal wind (Fig. 8b). Similar to EXP1 and EXP2, the time mean surface zonal wind is dominated by tropical easterlies and subtropical westerlies (see Fig. 9a). For comparison, the surface zonal mean zonal wind from EXP1 and EXP2 is shown in Fig. 9a. The surface temperature (Fig. 9b) in the tropics in EXP3 is similar to EXP2 with about the same "reversed" temperature gradient.
In order to maintain surface easterlies in the tropics and surface westerlies in the subtropics in all three experiments, there must be a net poleward transport of angular momentum. In EXP1 and EXP2, this transport is accomplished by large scale zonally asymmetric convective events. Once zonally asymmetric motions (i.e. convective events) are removed from the model, transient zonally symmetric convective events accomplish a similar momentum transport. Fig. 9c shows the vertically integrated meridional flux of zonal momentum by the time mean flow (solid curve) and by the total flow (dashed curve), i.e., transients plus time mean. The flux by the time mean is relatively small and is in the wrong direction in terms of maintaining tropical easterlies and subtropical westerlies. The total flux, which is mostly due to transients, is poleward in both hemispheres. In other words, in EXP3, the ITCZ migrates back and forth across the equator providing the necessary angular momentum transport to maintain easterlies in the tropics and westerlies in the subtropics. It remains an open question as to why the model prefers to maintain similar tropical easterlies and subtropical westerlies in all the simulations.
d. Dynamic Influence of SST in Location of ITCZ (EXP4)
In the simulation with no SST gradients (EXP1) we found that convection organized at the equator and that the mean meridional circulation in the troposphere was thermally direct in that the deep tropics were warmer than the subtropics (see Fig. 3c). In EXP2, however, a reversed pole-to-equator temperature gradient developed at the surface and throughout the troposphere (see Fig. 7c), yet the ITCZ remained at the equator. Nevertheless, the low latitude circulation in EXP2 was found to be thermally direct, although the local temperature maximum at the equator was relatively small (see Fig. 7d).
The interaction between convection and rotation causes a dynamical preference for convection to organize at the equator. In turn, this organization of convection at the equator causes the tropics to cool, but does not displace the ITCZ from the equator. Conceptual models, which typically neglect this dynamical preference for the equator, would predict that the ITCZ should move towards the poles. This conceptual model where the SST maximum determines the location of convection does not apply here.
In EXP2, the effect of the SST gradient and the effect of the organization of convection are in competition in terms of the general circulation, i.e., localized temperature maximum in the equatorial lower troposphere versus equatorial SST minimum. In order for the ITCZ to remain at the equator there must be a localized surface pressure minimum there, caused by the convective warming of the atmosphere. This implies that convection at the equator could be suppressed by introducing an SST gradient that cools the atmosphere above and cancels the surface pressure minimum induced by the ITCZ. The following investigates this possibility in the model with specified SST.
In order to find this SST gradient we follow the boundary layer model of Lindzen and Nigam (1987). However, as will become apparent, the hydrostatic equation is integrated through from the surface to about 550 mb so that the concept of a boundary layer does not strictly apply. We are "inverting" the Lindzen and Nigam (1987) model to predict the SST gradients that balance the surface pressure gradients associated with organized convection at the equator. This inverted Lindzen and Nigam (1987) model is applied to the surface pressure simulated in EXP1. Then, the calculated temperature gradients are subtracted from the prescribed SST in EXP1. We are trying to find the minimum change in the SST that will cancel the surface pressure gradients associated with an ITCZ situated at the equator. If this procedure were successful, the ITCZ and associated large scale circulation would be eliminated, and the atmosphere would be in RCE.
Following Lindzen and Nigam (1987; see their equation 3), the surface pressure for a fixed boundary layer height of H0 (and boundary layer top pressure PT) can be written as
where is superscript (*) denotes the deviation from the zonal mean, Ps is the surface pressure, g is gravity, o is the density, n = 1/To, To=288 oK, is the lapse rate of 0.003 K m-1, and = 0.30. Essentially, (1) is derived by integrating the hydrostatic equation from the surface to Ho assuming temperature is linearly determined from the surface temperature Ts. Taking the zonal mean of (1) and solving for the zonal mean surface temperature gives
where the overbar denotes the zonal mean. The meridional surface temperature gradient associated with (2) can then be used to modify the prescribed SST so as to cancel the surface pressure gradients associated with an ITCZ situated at the equator found in EXP1.
Lindzen and Nigam (1987) used 3000 m (700 mb) for Ho which was intended to represent the trade inversion. Here we empirically find that the value for Ho that practically eliminates the ITCZ is about 5000 m, which corresponds to spreading the SST over the full depth of the layer in Fig. 3c that is warmed by the convection in the ITCZ. Using 3000 m for Ho produces a larger SST gradient, and produces a strong double ITCZ with a precipitation minimum at the equator.
Figure 10 shows the zonal mean surface temperature (solid curve) calculated using the results of EXP1 and (2) with Ho = 5000 m. This is the temperature that is used in EXP4. For comparison, the surface temperature corresponding to Ho= 3000 m is also shown in Fig. 10. Co-located with the ITCZ of EXP1 is a relative minimum in the implied surface temperature. In the subtropical descending regions, the surface temperature has a relative maximum. Poleward of 20o the temperature has no impact on the results.
Figure 11a shows the time mean zonal mean precipitation from EXP1 (solid curve) and EXP4 (dashed curve). For comparison, the results from EXP2 (dotted curve) and EXP3 (dot-dot dashed curve) are also shown. As was shown earlier, EXP1 has a well defined ITCZ centered at the equator, whereas EXP4 has weak double ITCZs displaced about 5o off the equator. The time mean zonal mean surface pressure (Fig. 11b) indicates that the equatorial minimum in EXP1 has been almost eliminated in EXP4.
We have tried a number of different values for H0. Increasing the boundary layer depth beyond 5000 m gives a single ITCZ centered on the equator. Decreasing the boundary layer depths gives considerably stronger double ITCZs. The value used here appears to produce the "minimum" SST gradient required to suppress convection at the equator. Based on these results we conclude that ITCZ is easily displaced from the equator by the cold tongue. In fact a temperature difference on the order of 0.2oC between the equator and 9o is enough the shift the ITCZ off the equator. This small temperature gradient is consistent in magnitude with the small local gradient observed in EXP1 (Fig. 3c) and EXP2 (Fig. 7d). This SST gradient is also similar in magnitude to the observed gradient between the equator and 9oS, but is about a factor of 4 smaller that the observed corresponding gradient in the Northern Hemisphere (see Fig. 1).
A series of idealized AGCM simulations were presented that were designed to understand how the interaction between dynamics and convection can lead to organized precipitation and a coherent general circulation without meridional gradients in the external forcing in a particular model. By experimental design we have removed the impact of land sea contrasts, latitudinal variation in the incoming solar flux and ocean dynamics. We have, however, examined how the ITCZ can affect the underlying SST through the exchange of heat fluxes at the interface of the ocean and the atmosphere. In order to do this, we have coupled the "aqua-planet" AGCM to a mixed-layer ocean model.
In the first experiment (EXP1), which can also be thought of as a control experiment, the SST was prescribed to be invariant in latitude, longitude and time. The purpose of this experiment was to examine whether convection has a preference for any particular latitude in the absence of any SST or incoming solar flux gradients. In other words, is there any purely dynamical constraint that causes the ITCZ to have a preferred latitude? The answer to this question is yes - the ITCZ forms at the equator because of the latitudinal variation of the Coriolis force. How this organization of convection produced a coherent general circulation was of particular interest here. This dynamic preference for the equator, even in the presence of a tropical minimum in SST (EXP2), has not been documented previously and contradicts the conceptual model that the organization is only driven by SST gradients.
One of the results from EXP1 was that, even though the SST was uniform in space and time, the total heat flux into the ocean had spatial structure. In particular, the heat flux into the ocean in the deep tropics was less than the heat flux in the subtropics. In order to maintain the constant SST there must be an implied heat flux. These spatial variations in the heat flux, however, may locally affect the SST which could then feed back on the organization of convection and the general circulation. In order to test this possibility, we coupled the AGCM to a mixed layer ocean model (EXP2).
In EXP2, the ITCZ also formed at the equator; however, there were significant changes in the SST and the general circulation. For instance, a rather smooth "reversed" pole-to-equator temperature gradient with the poles about 5oC warmer than the equator developed. This reversed temperature gradient was felt throughout the troposphere and the upper level zonal winds were easterly at all latitudes. A cursory examination of the atmospheric temperature suggested that the model somehow maintained a thermodynamically indirect tropical Hadley circulation with the ITCZ situated at the equator. A detailed examination of the temperature revealed that the SST effects were felt globally, but that there was a local temperature maximum (and surface pressure minimum) at the equator associated with the ITCZ. This temperature maximum was restricted to the lower troposphere, but was not seen in the SST.
While the upper level circulation in EXP1 and EXP2 differed, the surface winds were qualitatively similar. In both simulations, there were easterlies in the tropics and westerlies in the subtropics. This implies that there must be a net poleward transport of angular momentum from the tropics to the subtropics. Based on the results of EXP1 and EXP2, we speculated that this angular momentum transport was accomplished by large scale zonally asymmetric convective "events". These were observed in monthly mean maps of the precipitation and had a southwest-northeast (northwest-southeast) orientation in the Northern (Southern) Hemisphere. This particular orientation is consistent with a net poleward transport of angular momentum. However, it is also possible that the angular momentum transport was accomplished by the zonal mean meridional transport.
In order to test the importance of the zonal asymmetry in the model, we repeated EXP2 except that the model was truncated to be zonally symmetric. In this third experiment (EXP3) the circulation was dramatically different: the model enters a limit cycle where the ITCZ transits back and forth across the equator with about a 22 month period, extending as far as 20o into the subtropics. As with EXP1 and EXP2, the time mean surface winds were easterly in the tropics and westerly in the subtropics. Without the zonal asymmetry in the model, the transient displacement of the ITCZ takes on the role of the zonally asymmetric convective events by transporting angular momentum poleward. This was verified by examining the vertically integrated momentum flux. We have not explained why the model always has tropical easterlies and subtropical westerlies, and, thus requires some mechanism for poleward transport of angular momentum. Despite the similarity in the time mean surface winds among EXP1, EXP2 and EXP3, transient zonal symmetric dynamics are not the primary explanation for the momentum flux in EXP1 and EXP2. Three dimensional transient eddies must be the cause. It is not clear from these experiments what the underlying dynamics and physics of these zonally asymmetric convective events are.
Another interesting aspect of EXP2 was the apparent competition between the global scale SST gradient and the local lower tropospheric temperature maximum associated with the ITCZ. This temperature maximum is a necessary element in maintaining a thermodynamically direct circulation associated with the ITCZ. The fact that this temperature maximum was localized to the equator and quite small led us to investigate the minimum magnitude of the local SST gradients was that would cancel the pressure gradient associated with the ITCZ, and thereby suppress convection at the equator. In order to investigate this possibility, we employed a simple boundary layer model and the results of EXP1. We found that a rather small SST gradient, on the order of 0.2oC over 9o of latitude was sufficient to suppress convection at the equator. This level of accuracy in coupled general circulation models' SST simulation will likely be elusive for some time to come.
Finally it must be emphasized that, given the sensitivity of the position of the ITCZ to model parameterizations found in previous studies (e.g. Hess et al., 1993) even in the presence of nonuniform specified SST, we cannot claim any generality or applicability to nature for the results found in these experiments.
B. P. Kirtman acknowledges support from NOAA NA86GP0535. E. K. Schneider acknowledges support from NSF ATM9520579. Both authors acknowledge support from NSF ATM9321354, NOAA NA76GP0258 and NASA NAG54977.
Figure 4a shows that with prescribed globally uniform SST the AGCM simulates a net heat flux into the ocean (i.e. an imbalance) of approximately 65.5 Watts m-2. If the AGCM were coupled to the mixed layer ocean model without accounting for this imbalance the SST would warm considerably. In fact, we have made this particular simulation and found the SST to become so warm as to drive the model to be numerically unstable. In order to ameliorate this problem, we have reduced the solar constant to compensate for this global mean heat flux into the ocean.
The incident short wave flux at the top of the atmosphere in EXP1 is 431 W m-2. Approximate 44% of this incident radiation is predicted by the model to be absorbed at the sea surface, i.e., the short wave absorbed at the ground is 189W m-2. There is a net heat flux imbalance of 65.5W m-2 at the surface so that if we want to reduce the incident short wave flux at the top of the atmosphere to compensate for this imbalance we need to reduce the incident short wave flux by 65.5/0.44 = 148W m-2.
The easiest way to modify the incident short wave flux is to reduce the solar constant. The ratio of the solar constant (1365 watts m-2 ) to the incident solar flux is 3.17. This ratio is less than 4, the expected value, because we have removed all latitudinal variations in the incident solar flux. Therefore we should reduce the solar constant by 3.17*148=469 W m-2. However, since it was our intent to maintain a global mean temperature in EXP2 that was close to that prescribed in EXP1, we found, through experimentation, that this reduction of the solar constant was too strong. Ultimately, the solar constant was reduced by 375 W m-2 to 990W m-2, which led to a global mean SST of 298.8 K in EXP2 compared with 299.2 in EXP1.
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Figure1. Annual mean (1979-96) precipitation (dashed) and SST (solid).
Figure 2. (a) EXP1 time latitude cross section of the zonal mean precipitation for simulations months 121-240. Contour interval is 1 mm day-1. (b) EXP1 monthly mean precipitation for simulation month 240. Contour interval 2 mm day-1. (c) Zonal mean time mean (months 121-240) precipitation from EXP1 (solid line) and from a simulation without rotation (dashed).
Figure 3. (a) EXP1 zonal mean time mean (months 121-240) zonal wind. Contour interval is 1 m s-1. (b) EXP1 zonal mean time mean (months 121-240) stream function. Contour interval 3.0e+08 kg m3 s-1 . (c) EXP1 zonal mean time mean (months 121-240) temperature, with global mean at each pressure removed. Contour interval is 0.25oC.
Figure 4. (a) EXP1 global mean heat flux into the ocean as a function of simulation month. (b) EXP1 time mean (months 121-240) zonal mean surface heat flux components.
Figure 5. (a) EXP2 time latitude cross section of the zonal mean precipitation for simulations months 121-240. Contour interval is 1 mm day-1. (b) EXP2 monthly mean precipitation for simulation month 240. Contour interval 2 mm day-1.
Figure 6. (a) EXP2 time mean (months 121-240) zonal mean surface temperature. (b) EXP2 time mean (months 121-240) zonal mean surface heat flux components.
Figure 7. (a) EXP1 zonal mean time mean (months 121-240) zonal wind. Contour interval is 1 m s-1.(b) EXP1 zonal mean time mean (months 121-240) stream function. Contour interval 1.0e+08 kg m3 s-1 .(c) EXP1 zonal mean time mean (months 121-240) temperature. Contour interval is 0.25 oC. (d) Time mean zonal mean temperature at 900 mb (solid curve) and surface pressure (dashed curve). The global mean has been removed for both the temperature and the surface pressure.
Figure 8. (a) EXP3 zonal mean precipitation as a function of latitude and time. Contour interval is 2 mm day-1. (b) EXP3 zonal mean zonal wind as a function of latitude and time. Contour interval is 2 m s-1. (c) EXP3 zonal mean SST as a function of latitude and time. The global mean has been removed and the contour interval is 0.5 oC.
Figure 9. (a) EXP3 (solid), EXP2 (dashed) and EXP1 (dotteed) time mean (months 121-240)
zonal mean surface zonal wind. (b) Time mean zonal mean SST from EXP2 (dashed) and EXP1 (solid). (c) Vertically averaged zonal momentum flux by the total field (dashed) and by the time mean flow (solid).
Figure 10. Meridional distribution of surface temperature from EXP4 calculated using the simplified boundary layer model. The solid curve corresponds to a boundary layer depth of 5000 m and the dashed curve corresponds to a boundary layer depth of 3000 m.
Figure 11. (a) Zonal mean time mean precipitation from EXP1 (solid curve), EXP2 (dotted curve), EXP3 (dot-dot dashed curve) and EXP4 (dashed curve). (b) Zonal mean time mean surface pressure from EXP1 (solid curve) and EXP4 (dashed curve).
1. Formerly the National Meteorological Center (NMC).
2. The diurnal cycle of solar forcing remains in the model.