Dynamical Effects of Convective Momentum Transports on Global Climate Simulations

180 J O U R N A L O F C L I M A T E VOLUME 21 Dynamical Effects of Convective Momentum Transports on Global Climate Simulations XIAOLIANG SONG AND XIAOQING WU Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa GUANG JUN ZHANG Center for Atmospheric Sciences, Scripps Institution of Oceanography, La Jolla, California RAYMOND W. ARRITT Department of Agronomy, Iowa State University, Ames, Iowa (Manuscript received 11 January 2007, in final form 5 May 2007) ABSTRACT Dynamical effects of convective momentum transports (CMT) on global climate simulations are investigated using the NCAR Community Climate Model version 3 (CCM3). To isolate the dynamical effects of the CMT, an experimental setup is proposed in which all physical parameterizations except for the deep convection scheme are replaced with idealized forcing. The CMT scheme is incorporated into the convection scheme to calculate the CMT forcing, which is used to force the momentum equations, while convective temperature and moisture tendencies are not passed into the model calculations in order to remove the physical feedback between convective heating and wind fields. Excluding the response of complex physical processes, the model with the experimental setup contains a complete dynamical core and the CMT forcing. Comparison between two sets of 5-yr simulations using this idealized general circulation model (GCM) shows that the Hadley circulation is enhanced when the CMT forcing is included, in agreement with previous studies that used full GCMs. It suggests that dynamical processes make significant contributions to the total response of circulation to CMT forcing in the full GCMs. The momentum budget shows that the Coriolis force, boundary layer friction, and nonlinear interactions of velocity fields affect the responses of zonal wind field, and the adjustment of circulation follows an approximate geostrophic balance. The adjustment mechanism of meridional circulation in response to ageostrophic CMT forcing is examined. It is found that the strengthening of the Hadley circulation is an indirect response of the meridional wind to the zonal CMT forcing through the Coriolis effect, which is required for maintaining near-geostrophic balance. 1. Introduction The importance of convective momentum transport (CMT) in the atmospheric general circulation was recognized in the 1970s. Houze (1973) evaluated the momentum budget using observational data and found that the magnitude of CMT was comparable to other terms in the angular momentum budget. Using the Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE) phase III data, Stevens (1979) estimated the momentum budget of a composite Corresponding author address: Dr. Xiaoliang Song, Iowa State University, 3010 Agronomy Hall, Ames, IA 50011. E-mail: songxl@iastate.edu synoptic-scale tropical wave and found significant residuals. The residuals indicate that the cumulus-scale momentum transport is an important mechanism of momentum exchange in tropical disturbances. Numerical studies also demonstrated that realistic simulation of tropical circulation requires cumulus friction to be included in the momentum equations (Stone et al. 1974; Stevens et al. 1977). In earlier attempts to parameterize the CMT in numerical models, the horizontal momentum inside clouds was assumed to be modified only by lateral entrainment of momentum from outside the clouds (Ooyama 1971; Schneider and Lindzen 1976; Shapiro and Stevens 1980; Sui et al. 1989). Using this simple mixing-type CMT parameterization scheme, numerous DOI: 10.1175/2007JCLI1848.1 2008 American Meteorological Society

15 JANUARY 2008 S O N G E T A L. 181 studies investigated the effects of CMT in general circulation models (GCMs). Helfand (1979) found that the winter Hadley circulation was enhanced and the meridional wind field was closer to observations when cumulus friction was included in January simulations using the Goddard Laboratory for Atmospheric Sciences model. Through 15-day simulations using the European Centre for Medium-Range Weather Forecasts (ECMWF) operational forecast model, Tiedtke (1989) found that the CMT strongly affects the rotational flow but has little effect on the divergent flow. Observational, theoretical, and numerical studies in the 1980s and 1990s (e.g., LeMone 1983; Schlesinger 1984; Flatau and Stevens 1987; Moncrieff 1992; LeMone and Moncrieff 1994) further showed that the convection-induced perturbation pressure field can significantly affect the cloud momentum. Based on this finding, Zhang and Cho (1991a) and Wu and Yanai (1994) proposed more comprehensive CMT parameterization schemes that incorporate the effect of convection-induced pressure gradient. Studies using observational data and cloud-scale data produced by cloudresolving models (CRMs) showed that both the Zhang and Cho and the Wu and Yanai schemes were able to reproduce the observed and CRM-simulated apparent momentum sources (Zhang and Cho 1991b; Wu and Yanai 1994; Mapes and Wu 2001; Zhang and Wu 2003). This suggests that the two schemes can capture the essential features of convective momentum transport. Using the Zhang and Cho CMT scheme, Zhang and McFarlane (1995) investigated the effects of CMT on climate simulation in the Canadian Climate Centre (CCC) GCM. Seasonal simulations showed that by including CMT the summer Hadley circulation was enhanced and the wind field was closer to observations. For evaluating the effect on climate simulation, longterm climate statistics are more appropriate. Wu et al. (2003) conducted a 20-yr simulation in which the Zhang and Cho scheme was implemented in the National Center for Atmospheric Research Community Climate Model, version 3 (CCM3). They found that the simulation of seasonal migration of the intertropical convergence zone (ITCZ) precipitation was significantly improved when CMT was included. Preliminary analyses suggested that the improvement on precipitation resulted from the CMT-induced secondary circulation within the ascending branch of the Hadley circulation. The aforementioned studies showed that CMT has profound impacts on climate simulations. However, the mechanism through which CMT affects climate simulations is not yet clear. This is, to a large extent, due to the complex nonlinear interactions of processes in the atmosphere. Figure 1a presents a schematic illustrating FIG. 1. Sketch of the interaction between the CMT forcing and GCM for (a) standard GCM and (b) idealized GCM with experimental setup. these complex interactions. It shows that perturbations in any one of the components in the loop can affect the other components. In particular, the CMT forcing can lead to changes in wind fields, which further result in complex interactions among wind fields, temperature/ moisture fields, and convection. By altering dynamical advection or surface heat/moisture fluxes, changes in wind fields can influence temperature/moisture fields and hence convection, which in turn can affect the temperature/moisture fields through convective heating/ drying or cloud and radiation processes. By affecting geopotential height, the change in temperature will lead to an extra wind change, which in turn can induce an extra convection change and hence temperature change. In addition, both changes in convection and wind fields can affect the CMT forcing; that is, there is a convection CMT wind feedback. In general, a GCM is composed of a dynamical core and a physical parameterization suite, which respectively describe the dynamical processes (e.g., advection and pressure gradient force, etc.) and physical processes (e.g., boundary layer, gravity wave drag, convection, cloud and radiation, etc.) of the atmosphere. Thus, the effects of CMT

182 J O U R N A L O F C L I M A T E VOLUME 21 on climate simulation can be decomposed into two parts: the dynamical effects that include the response of dynamical processes and the resulting convection CMT wind feedback and the physical effects that include the response of physical processes and the resulting convection CMT wind feedback (e.g., CMTinduced wind convective heating feedback, CMT wind evaporation convection feedback, etc.). Previous studies have investigated neither of the contributions of these two types of processes to the total effects of CMT on the climate simulations, nor the response of any one type of processes to the CMT forcing in a climate model. This study will focus on one set of processes, that is, the dynamical processes, to evaluate dynamical effects of CMT on climate simulations. To understand the effect of CMT on climate simulation, it is important to evaluate the long-term statistics of the circulation response. However, it is difficult to isolate the dynamical effects of CMT in a comprehensive climate model with full physics since the effects of all the aforementioned processes are intermingled in a climate response after long-term integration. Is there an approach that not only isolates the dynamics as much as possible from the complex physical processes but also evaluates the long-term statistics of global circulation? A benchmark calculation for evaluating the dynamical cores of climate models proposed by Held and Suarez (1994) can satisfy these requirements. In their experimental setup, the physical parameterizations are replaced with simple analytic forcing functions, while the complete dynamical core is retained. Focusing on the long-term statistical properties of general circulation, this setup is particularly appropriate for investigating the dynamics in climate models. Therefore, a similar method can be applied to evaluate the dynamical effects of CMT on climate simulations. There are two more requirements for the present purpose: the model should include the CMT forcing as realistically as possible and it should include other physical processes to the minimum extent necessary. To satisfy these requirements, we propose a modified experimental setup. In this setup, all physical parameterizations in the GCM, except for the convection scheme, are replaced with the simple forcing function proposed by Held and Suarez (1994). A time-invariant water vapor field is included in the model to initiate moist convection. The CMT parameterization scheme of Zhang and Cho (1991a) is incorporated into the Zhang and McFarlane (1995) convection scheme to calculate the CMT forcing, which feeds back to the momentum equations. However, the temperature and moisture tendencies predicted from the convection scheme are not allowed to feed back to the model s thermodynamic equations so as to eliminate the thermodynamic interaction between convection and the large-scale fields. Thus, in this setup convection is controlled by the model-predicted temperature field and the prescribed moisture field. The convection scheme determines the amount of convective mass flux and other necessary quantities, which together with the model-predicted momentum fields serve as input to the momentum parameterization scheme to determine the CMT forcing. The CMT forcing feeds back to the model s momentum fields. The CCM3 with this experimental setup is referred as the idealized CCM3, which can be used to investigate dynamical effects of CMT on climate simulations. The organization of the paper is as follows. A brief description of the CMT scheme, model, and experimental design is presented in section 2. The dynamical effects of CMT on climate simulations are examined in section 3. In section 4 the momentum budgets are evaluated to understand the mechanism of CMT affecting the climate simulations. Section 5 gives the summary of results and conclusions. 2. Model, CMT scheme, and experimental design a. Model The GCM used in this study is the NCAR CCM3 (Kiehl et al. 1998). It is a global spectral model with T42 truncation (approximately 2.8 2.8 latitude longitude) in the horizontal and 18 levels in the vertical. The top of the model is at 2.9 mb. The model time step is 20 min. Deep convection is parameterized using the Zhang and McFarlane scheme (Zhang and McFarlane 1995). Detailed description of CCM3 can be found in Kiehl et al. (1998). b. Convective momentum transport scheme In this study, the Zhang and Cho (1991a) CMT parameterization scheme is implemented in the NCAR CCM3 to investigate the effects of CMT on climate simulations. The scheme incorporates a cloud model that specifies the structure of the cloud dynamical field and determines the cloud temperature to estimate the forcing terms of the governing equation for the cloudscale pressure field. The cloud mean momentum and cloud-scale horizontal pressure gradient force are obtained by solving the equation governing cloud mean momentum together with the diagnostic equation for the cloud-scale pressure field. Further details of the scheme can be found in Zhang and Cho (1991a).

15 JANUARY 2008 S O N G E T A L. 183 c. Experimental design To isolate the dynamical effects of CMT, several modifications are made in CCM3: 1) Water vapor is included in the model to initiate moist convection. However, the change of water vapor is not considered, that is, water vapor remains at its initial value, to remove the effect of water vapor change on convection. 2) The Zhang and Cho CMT parameterization scheme is incorporated into the Zhang and McFarlane convection scheme to calculate the CMT forcing, which is used to force the momentum equations. The temperature tendency due to convection is set to zero in order to remove the feedback associated with convective heating. 3) All physical parameterizations except for the deep convection scheme are replaced with simple idealized forcing. Following the suggestion of Held and Suarez (1994), diabatic heating is expressed by Newtonian relaxation of the temperature to a prescribed zonally symmetric state T eq. Boundary layer friction is expressed as Rayleigh friction. The detailed specifications are as follows: V t A V k p V, T t A T k T, p T T eq, p, T eq max 200K, 315 K 60 sin 2 10 log p p 0 cos 2 p k T k a k s k a max 0, cos p 0 700 4, p 700 k k f max 0, p 0 700, p 0 1000 mb, R c p 2 7, k f 1 day 1, k a 1 40 day 1, k s 1 4 day 1, p p 0, where p is the pressure, and R and c p represent gas constant for air and the specific heat of air at constant pressure, respectively. The A terms in the momentum and temperature equations represent advection and other dynamic forcing. The momentum damping rate k is a function of pressure, and is nonzero only in the boundary layer (p 700 mb). The temperature relaxation rate k T is about 1/40 day 1 and is increased below 700 mb to avoid the formation of unrealistic thin cold layer. The distribution of prescribed radiative equilibrium temperature T eq is shown in Fig. 2a. 4) There is no land sea contrast, no topography, and no heat or momentum flux at the surface boundary. Thus the modified model contains a complete dynamical core, idealized physics, and the CMT forcing. Since the response of complex physical processes to the CMT forcing is excluded from the idealized model (see Fig. 1b), it is particularly appropriate for investigating the dynamical effects of CMT on climate simulations. Two long-term integrations are conducted with the idealized CCM3. In the simulation referred to as IDCMT, the setup described above is used. In the simulation referred to as IDCTL, the CMT forcing is excluded from the momentum equations. The IDCTL is taken as the control run to which IDCMT is compared in order to assess the influence of the CMT. It is noted that the setup of IDCTL run is identical to that of Held and Suarez (1994). Both simulations start from 1 December with initial conditions taken from results of a previous model simulation and run for 2221 days. The zonally averaged initial specific humidity distribution on 1 December is shown in Fig. 2b. The statistics from the last 1825 days (5 yr) are used to represent the model climate. 3. Dynamical effects of CMT on climate simulations a. Climate of the IDCTL experiment The climate of the IDCTL experiment, as represented by the zonally averaged zonal wind, meridional

184 J O U R N A L O F C L I M A T E VOLUME 21 the meridional circulation shows hemispheric symmetry. The Hadley circulation lies between approximately 30 S and 30 N, with strong rising motion centered at the equator. The maximum equatorward flow associated with the Hadley circulation is located below 850 mb and the maximum poleward flow is located between 300 and 200 mb. Since temperature is relaxed to the prescribed zonally symmetric state, the temperature distribution is similar to that prescribed radiative equilibrium temperature. These features are in good agreement with those of Held and Suarez (1994). FIG. 2. Zonal average of (a) prescribed radiative equilibrium temperature (K) and (b) initial specific humidity (g kg 1 ); contour intervals are 10 K and 2 g kg 1. wind, vertical velocity, and temperature, is shown in Fig. 3. The model with simple relaxation-type physics produces a reasonably realistic zonal-mean circulation, which is similar to the observed annually averaged circulation in many aspects. In the midlatitude, westerly winds prevail throughout the troposphere with a welldefined westerly jet stream located at 250 mb near 45 latitude. Easterlies appear over the equator and near the poles, as well as in the subtropical boundary layer. The meridional wind and vertical velocity together clearly show the three-cell circulation in the meridional plane. Since the forcing is symmetric about the equator, b. CMT forcing Figures 4a,b show the zonal average of zonal and meridional CMT forcing from the IDCMT run. The CMT forcing is confined mainly to the tropics between 10 S and 10 N, where convection occurs most frequently. While the CMT forcing north of the equator is slightly larger than that to the south, it is generally symmetric about the equator. The asymmetry is due to the slightly asymmetric distribution of the humidity field (Fig. 2b), which has a peak just north of the equator, resulting in more convective instability and thus convection there. In the tropics between 10 S and 10 N, the zonal CMT forcing (Fig. 4a) shows strong positive tendency below 800 mb, which tends to reduce the easterlies in the lower tropical troposphere, and an equally strong negative tendency between 800 and 450 mb, which tends to enhance the easterlies in the middle tropical troposphere. In the upper troposphere, weak positive zonal CMT forcing appears above 450 mb over the equator and weak negative forcing appears north and south of that region. Comparing to the zonal CMT forcing, the meridional CMT forcing (Fig. 4b) is smaller in magnitude between 10 S and 10 N. It features a dipole pattern with northerly acceleration north of the equator and southerly acceleration south of the equator between 600 and 300 mb, which tends to weaken the middle part of the poleward branch of the Hadley cell, and an opposite pattern between 850 and 600 mb, which tends to strengthen the lower part of the poleward branch of the Hadley cell. Outside the region between 10 S and 10 N, the CMT tendencies for both zonal and meridional winds are comparable and very weak. To validate the CMT forcing produced by the idealized model, annually averaged CMT forcing from the full CCM3 simulation is shown in Figs. 4c,d. In general, the CMT forcing produced by the idealized model is much larger in magnitude than that from the full CCM3. The reason for larger CMT forcing in the IDCMT run is that by design the idealized model does not consume convective available potential energy, as

15 JANUARY 2008 S O N G E T A L. 185 FIG. 3. Zonal average of (a) zonal and (b) meridional wind (m s 1 ), (c) vertical velocity (mb day 1 ), and (d) temperature (K) in the IDCTL run. The contour intervals are (a) 5 m s 1, (b) 0.5 m s 1, (c) 5 mb day 1, and (d) 10 K. Negative values are shaded. convective heating and drying do not feed back to the model. As such, strong convection occurs more frequently, producing stronger time-averaged CMT forcing. In the tropics between 10 S and 10 N, the zonal CMT forcing (Fig. 4c) produced by the full CCM3 is characterized by positive values below 800 mb and negative values of roughly equal magnitude between 800 and 450 mb; and the meridional forcing (Fig. 4d) features a dipole pattern and is smaller than the zonal forcing. In general, this distribution is similar in pattern to that from the IDCMT run. This indicates that the CMT forcing produced by the idealized model is reasonable in this region. Outside the region between 10 S and 10 N, the full CCM3 still produces considerable CMT forcing in some regions; however, the CMT forcing produced by the idealized model is very weak. Since the CMT forcing is determined by convection and wind fields, both convection and wind fields in the idealized and full CCM3 simulations are examined. The results indicate that the difference in CMT forcing between the idealized run and the full CCM3 run in those regions is mainly caused by the difference in the amount of convection. The convective instability produced by the prescribed moisture field and predicted temperature field, which is relaxed to a prescribed radiative equilibrium temperature, in the idealized model is very weak in those latitudes, leading to little convection and CMT forcing. On the other hand, in the full CCM3, mainly

186 J O U R N A L O F C L I M A T E VOLUME 21 FIG. 4. Zonal annual average of (a) zonal and (b) meridional CMT forcing in the IDCMT run and (c) zonal and (d) meridional CMT forcing from 5-yr standard CCM3 simulation. Units are m s 1 day 1 and contour intervals are 2 m s 1 day 1 for (a) and (b), and 0.2 m s 1 day 1 for (c) and (d); negative values are shaded. owing to the seasonal shift of solar radiation, convection is active outside the 10 S 10 N tropical belt. Associated with it is the strong CMT forcing. Since convection in the intertropical convergence zone plays a pivotal role in driving tropical atmospheric circulation, this study will focus on effect of CMT forcing over the ITCZ on climate simulations and will not tune the prescribed moisture and reference temperature fields to get stronger CMT forcing outside the 10 S 10 N tropical belt. c. Dynamical response of large-scale circulation The dynamical response of large-scale circulation to the CMT forcing is readily identified from the zonally averaged difference of circulation between the IDCMT and IDCTL simulations (Fig. 5). The zonal wind difference (Fig. 5a) between the IDCMT and the IDCTL run is manifest. Tropical easterlies become stronger and broader above 700 mb when CMT is parameterized. Westerlies occur below 700 mb between 10 S and 10 N. The increase of westerly wind poleward of 45 N or S and decrease equatorward of that latitude implies a poleward shift of the midlatitude westerly jets. The meridional wind difference (Fig. 5b) shows that the northerlies and southerlies that lie respectively to the north and south of the equator associated with the equatorward branch of the Hadley circulation are enhanced in the IDCMT run. The southerlies and northerlies to the north and south of the equator associated with the poleward branch of the Hadley circulation are also enhanced. This indicates that the equatorward and poleward branches of the Hadley circulation are strength-

15 JANUARY 2008 S O N G E T A L. 187 FIG. 5. Zonal average of the difference of (a) zonal and (b) meridional wind (m s 1 ), (c) vertical velocity (mb day 1 ), and (d) temperature (K) between the IDCMT and IDCTL runs. Contour intervals are (a) 5 m s 1, (b) 0.5 m s 1,(c)5mb day 1, and (d) 0.5 K; negative values are shaded. ened when CMT is included. Along with the strengthening of the convergence in the Hadley cell s lower branch and divergence in its upper branch, the upward motion associated with the Hadley cell s ascending branch is enhanced and becomes more concentrated, and the downward motion associated with the Hadley cell s descending branch is enhanced and broadened (Fig. 5c). Thus meridional wind and vertical velocity together clearly show that the inclusion of CMT leads to an increase in intensity of the Hadley circulation. This result agrees with previous GCM studies that used full model physics (e.g., Helfand 1979; Zhang and McFarlane 1995; Gregory et al. 1997). Thus, the CCM3 with idealized physics captures the fundamental response of large-scale circulation to the CMT forcing, indicating that dynamical processes make significant contributions to the total response of circulation to the CMT forcing in the full GCMs. For the temperature field (Fig. 5d), there is cooling near the equator and warming in the subtropics in troposphere when the CMT is taken into account. The temperature change is generally consistent with the adiabatic heating/cooling associated with the vertical velocity change. It is noted that the circulation change due to the inclusion of the CMT forcing in the idealized GCM is much stronger than that in the full GCM, which can to a large degree be attributed to the larger CMT forcing produced by the idealized GCM. Comparing the changes in wind fields with the corresponding CMT forcing, we see that there is consider-

188 J O U R N A L O F C L I M A T E VOLUME 21 able difference between the wind response and CMT forcing, especially in the meridional direction. For instance, between 600 and 300 mb there is positive meridional CMT forcing south of the equator and negative meridional CMT forcing north of the equator, whereas the meridional wind changes in these regions are of opposite sign to the CMT forcing. This negative correlation between the wind response and the CMT forcing also occurs in the zonal wind field over the equator above 450 mb and in the lower troposphere between 10 and 20 in each hemisphere. This indicates that the wind change is not a linear response to the CMT forcing and that other processes are involved that make significant contributions to the wind response to the CMT forcing. In the next section, we will use momentum budget diagnostics to evaluate the contribution of each process that affects the momentum field. 4. Momentum budget The governing equations of the model with experimental setup can be written as du dt f u tan a 1 a cos k u F u_cmt, 1a d dt f u tan a u 1 a k F _cmt, 1b p RT p, 1c 1 u a cos 1 cos 0, a cos p 1d dt RT dt c p p k T T T eq, p, 1e where the notations are standard, and represent longitude and latitude, respectively, a is the mean radius of the earth, is the geopotential, T (1 0.608q)T is virtual temperature, f 2 sin is the Coriolis parameter, F u_cmt and F _cmt represent the zonal and meridional CMT forcing, respectively, and d dt t u a cos p a p p denotes the material derivative in pressure coordinates. To investigate the changes induced by the CMT in the zonally averaged long-term mean circulations, timeand zonal-mean equations are convenient. We define the zonal-average operator and time-average operator A 1 2 Ad, 2 0 A 1 Adt, 0 where is the average interval of time. Thus, for a long time mean ( 1825 days), Eqs. (1a) (1e) can be written as 1 a cos cos 0, p 2d f F u_cmt k u u a u u t p tan u, 2a a t f u 1 a F _cmt k a p tan uu, 2b a p R T, 2c p T t T a T p RT k c p p T T k T T eq, p. 2e

15 JANUARY 2008 S O N G E T A L. 189 The time derivative terms are negligible as the equation is averaged over the entire analysis period. This set of equations clearly shows the interconnections between the CMT forcing and the resulting changes in the zonally averaged circulation. First, the CMT forcing can only directly influence [u] and [ ]; then, the change in [ ] affects [ ] through the continuity equation (2d). The thermodynamic energy equation (2e) shows the temperature is influenced by [ ] and [ ] since T eq (, p) isa prescribed reference temperature. This indicates that the CMT forcing may affect temperature by modifying [ ]. Temperature change produces a corresponding geopotential change according to Eq. (2c), which in turn affects the meridional momentum budget Eq. (2b) through pressure gradient force term. Besides the aforementioned effects, momentum equations [Eqs. (2a) and (2b)] show that there are nonlinear interactions between the velocity fields (last three terms on the right-hand side of the equations), the Coriolis force term, and the boundary layer friction, which may also affect the final responses of the circulation. The governing equations for the control experiment (IDCTL) are the same as Eqs. (2) except that the CMT forcing terms are removed from the momentum equations. We can evaluate the contribution of each process by examining the change of each term in the momentum equations between the IDCTL and IDCMT runs. Each term in Eqs. (2a) and (2b) is first calculated using daily averaged data at each grid point, in which derivatives are calculated using centered finite differences. The results are then averaged over the final 1825 days of all integrations along each resolved latitude. Figure 6 shows the changes of each component in the zonal momentum budget between the IDCTL and IDCMT runs. In general, the zonal CMT forcing itself (Fig. 6b) is the dominant term in the momentum budget difference. The curvature term (Fig. 6f) is very small. The zonal CMT forcing provides a westerly acceleration below 800 mb and an easterly acceleration between 700 and 450 mb in the tropical troposphere, which are responsible for the zonal wind changes observed in Fig. 5a in those regions. In the tropics, boundary layer friction (Fig. 6e) and meridional advection (Fig. 6c) tend to offset the westerly acceleration induced by the CMT in the lower troposphere, and the vertical advection (Fig. 6d) tends to offset the easterly acceleration due to the CMT between 700 and 450 mb. The effects of the aforementioned terms are to reduce the response of zonal wind to the CMT forcing in those regions. In the equatorial region, meridional advection offsets the CMT forcing and produces easterly acceleration above 450 mb, while vertical advection offsets the CMT forcing and produces westerly acceleration between 800 and 700 mb. These two terms can give rise to the zonal wind changes noted in Fig. 5a in the corresponding regions, and hence explain why the zonal wind responses are different from the CMT forcing in those regions. In addition, the Coriolis force (Fig. 6a) offsets the CMT forcing and produces an easterly acceleration in the lower troposphere between 10 and 20 in each hemisphere, which accounts for the enhanced easterlies in the subtropical boundary layer. This result shows that the zonal wind change is a direct response of the zonal wind to the zonal CMT forcing and that the boundary layer friction, advection term, and Coriolis force can also significantly affect the response of the zonal wind field. The differences in the meridional momentum budget components between the IDCMT and IDCTL runs are shown in Fig. 7. The most visible changes come from the Coriolis force associated with the zonal wind change and from the pressure gradient force. The rest of the terms, including the meridional CMT forcing, are small. In the tropics, the change of the Coriolis force provides southerly acceleration south of the equator below 700 mb and northerly acceleration above, with opposite changes north of the equator. This is consistent with the meridional wind change shown in Fig. 5b. The change of pressure gradient force tends to offset the forcing induced by the change of Coriolis force. Figure 7h shows the sum of the changes in the Coriolis force and pressure gradient force. Comparing to Fig. 5b, it shows that the change of Coriolis force is responsible for the meridional wind change displayed in Fig. 5b in the tropics, and the role of pressure gradient force is to reduce the forcing associated with the Coriolis force. Since the change of the Coriolis force is associated with the zonal wind change, which in turn is a response of zonal wind to the zonal CMT forcing, it indicates that the meridional wind change is an indirect response of meridional wind to zonal CMT forcing through the Coriolis effect. Comparison of Figs. 7a and 7b shows that the change in Coriolis force approximately balances the change in pressure gradient force. This suggests that the adjustment of circulation follows an approximate geostrophic balance. As noted above, the change of pressure gradient force is induced by the temperature change, which in turn is induced by the change of meridional circulation. This indicates that, when meridional geostrophic balance is broken due to the zonal wind change in response to the ageostrophic zonal CMT disturbance, the Coriolis force anomaly will induce a change in meridional wind, which in turn will lead to a change in temperature field and hence in pressure gradient force to

190 J O U R N A L O F C L I M A T E VOLUME 21 FIG. 6. Zonal-mean change in the zonal momentum budget components [see Eq. (2a)] from the IDCTL run to IDCMT run. Units are m s 1 day 1 ; contour interval is 2 m s 1 day 1 and negative values are shaded.

15 JANUARY 2008 S O N G E T A L. 191 FIG. 7. Zonal-mean change in the meridional momentum budget components [see Eq. (2b)] from IDCTL run to IDCMT run. Units are m s 1 day 1. The contour interval is 3 m s 1 day 1 and negative values are shaded.

192 J O U R N A L O F C L I M A T E VOLUME 21 balance the Coriolis force anomaly so that the circulation can achieve a new geostrophic balance. To further evaluate this argument, an experiment is conducted in which the setup is same as the IDCTL run except that the 5-yr mean difference of the Coriolis force (fu) between the IDCMT and IDCTL runs (i.e., Fig. 7a) is added in the meridional momentum equation. The purpose is to examine the response of the meridional circulation and pressure gradient force to the change of the Coriolis force induced by the CMT forcing. The experiment is referred to as the IDFU run. Figures 8a,b show the zonally averaged difference of the meridional wind and vertical velocity between the IDFU and IDCTL simulations. Comparison of Figs. 8a,b and 5b,c shows that the difference of meridional circulation between the IDFU and IDCTL runs is almost identical to that between the IDCMT and IDCTL runs in the tropics. It demonstrates that the Coriolis force associated with the zonal wind change is the dominant forcing term in meridional momentum equation, and it actually can produce an enhanced Hadley circulation observed in the IDCMT run. This result confirms the conclusion that the meridional wind change is an indirect response of meridional wind to the zonal CMT forcing through the Coriolis effect. The zonal momentum budget equation shows that the change of meridional circulation can lead to a zonal wind change that in turn can lead to an extra Coriolis force anomaly and hence an extra pressure gradient force response. Therefore, the sum of changes in the Coriolis force and in pressure gradient force between the IDFU and IDCTL runs (Fig. 8c) is used to represent the net response of the pressure gradient force to the added Coriolis forcing. Comparing Figs. 8c and 7a shows that the net response of the pressure gradient force is approximately in balance with the added extra Coriolis forcing. This demonstrates that the change of the Coriolis force causes a change in pressure gradient force through strengthening the Hadley circulation so that circulation can achieve a new neargeostrophic balance. It suggests that when ageostrophic CMT disturbance is included, an increase in the intensity of the Hadley circulation is required through which the circulation can achieve a new near-geostrophic balance. FIG. 8. Zonal average of the difference of (a) meridional wind (m s 1 ), (b) vertical velocity (mb day 1 ), and (c) sum of the Coriolis force and pressure gradient force (m s 1 day 1 ) between the IDFU and IDCTL runs. Contour intervals are (a) 0.5 m s 1, (b) 5 mb day 1, and (c) 3 m s 1 day 1 ; negative values are shaded.

15 JANUARY 2008 S O N G E T A L. 193 5. Summary and conclusions The dynamical effects of CMT on global climate simulations are investigated using the NCAR CCM3 in this study. To isolate the dynamical effects of CMT, an experiment setup is proposed. In this setup, all physical parameterizations in the GCM except for the deep convection scheme are replaced with simple idealized forcing. The Zhang and Cho CMT scheme is incorporated into the convection scheme to calculate the CMT forcing, which is used to force the momentum equations, while the temperature and specific humidity tendencies due to convection are neglected to remove physical feedback that would obscure the diagnosis of the dynamical effects of CMT. The control simulation without the CMT produces a reasonable zonal-mean circulation. The CMT forcing produced by the idealized CCM3 is generally similar in pattern to that produced by the standard CCM3 with the same CMT scheme over the ITCZ, although having a much larger magnitude. This demonstrates that the experimental setup we proposed is useful for investigating the dynamical effects of CMT on climate simulations. Comparison of simulations with and without CMT shows that the dynamical effects of CMT on climate simulations are readily apparent. The Hadley circulation is enhanced when CMT forcing is included. This result is consistent with previous studies that used full GCMs. It suggests that the dynamical processes can make significant contributions to the total response of circulation to the CMT forcing in the full GCMs. Momentum budget analysis is conducted to understand the mechanism by which CMT affects the climate simulations. The zonal momentum budget shows that the zonal wind change is a direct response of zonal wind to the zonal CMT forcing and that the Coriolis force, boundary layer friction, and nonlinear interactions between velocity fields can also affect the response of the zonal wind to the CMT forcing. The meridional momentum budget shows that the adjustment of circulation follows an approximate geostrophic balance, and that the Coriolis force associated with the zonal wind change in response to the zonal CMT forcing is the dominant forcing term in meridional momentum equation, while the meridional CMT forcing is relatively small. This indicates that the meridional wind change is an indirect response of meridional wind to zonal CMT forcing through the Coriolis effect. The adjustment mechanism of the meridional circulation in response to the ageostrophic CMT forcing is examined. 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