Dynamical Effects of Convective Momentum Transports on

Dynamical Effects of Convective Momentum Transports on GlobalClimate 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 inves-tigated using the NCAR Community Climate Model version 3 (CCM3). To isolate the dynamical effects ofthe CMT, an experimental setup is proposed in which all physical parameterizations except for the deepconvection scheme are replaced with idealized forcing. The CMT scheme is incorporated into the convec-tion scheme to calculate the CMT forcing, which is used to force the momentum equations, while convectivetemperature and moisture tendencies are not passed into the model calculations in order to remove thephysical feedback between convective heating and wind fields. Excluding the response of complex physicalprocesses, 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 withprevious studies that used full GCMs. It suggests that dynamical processes make significant contributionsto the total response of circulation to CMT forcing in the full GCMs. The momentum budget shows that theCoriolis force, boundary layer friction, and nonlinear interactions of velocity fields affect the responses ofzonal wind field, and the adjustment of circulation follows an approximate geostrophic balance. The ad-justment mechanism of meridional circulation in response to ageostrophic CMT forcing is examined. It isfound that the strengthening of the Hadley circulation is an indirect response of the meridional wind to thezonal 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 rec-ognized in the 1970s. Houze (1973) evaluated the mo-mentum budget using observational data and foundthat the magnitude of CMT was comparable to otherterms in the angular momentum budget. Using the Glo-bal Atmospheric Research Program (GARP) AtlanticTropical Experiment (GATE) phase III data, Stevens(1979) estimated the momentum budget of a composite

synoptic-scale tropical wave and found significant re-siduals. The residuals indicate that the cumulus-scalemomentum transport is an important mechanism ofmomentum exchange in tropical disturbances. Numeri-cal studies also demonstrated that realistic simulationof tropical circulation requires cumulus friction to beincluded in the momentum equations (Stone et al. 1974;Stevens et al. 1977).

In earlier attempts to parameterize the CMT in nu-merical models, the horizontal momentum insideclouds was assumed to be modified only by lateral en-trainment of momentum from outside the clouds(Ooyama 1971; Schneider and Lindzen 1976; Shapiroand Stevens 1980; Sui et al. 1989). Using this simplemixing-type CMT parameterization scheme, numerous

Corresponding author address: Dr. Xiaoliang Song, Iowa StateUniversity, 3010 Agronomy Hall, Ames, IA 50011.E-mail: [email protected]

180 J O U R N A L O F C L I M A T E VOLUME 21

DOI: 10.1175/2007JCLI1848.1

© 2008 American Meteorological Society

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studies investigated the effects of CMT in general cir-culation models (GCMs). Helfand (1979) found thatthe winter Hadley circulation was enhanced and themeridional wind field was closer to observations whencumulus friction was included in January simulationsusing the Goddard Laboratory for Atmospheric Sci-ences model. Through 15-day simulations using the Eu-ropean Centre for Medium-Range Weather Forecasts(ECMWF) operational forecast model, Tiedtke (1989)found that the CMT strongly affects the rotational flowbut has little effect on the divergent flow.

Observational, theoretical, and numerical studies inthe 1980s and 1990s (e.g., LeMone 1983; Schlesinger1984; Flatau and Stevens 1987; Moncrieff 1992;LeMone and Moncrieff 1994) further showed that theconvection-induced perturbation pressure field can sig-nificantly affect the cloud momentum. Based on thisfinding, Zhang and Cho (1991a) and Wu and Yanai(1994) proposed more comprehensive CMT parameter-ization schemes that incorporate the effect of convec-tion-induced pressure gradient. Studies using observa-tional data and cloud-scale data produced by cloud-resolving models (CRMs) showed that both the Zhangand Cho and the Wu and Yanai schemes were able toreproduce the observed and CRM-simulated apparentmomentum sources (Zhang and Cho 1991b; Wu andYanai 1994; Mapes and Wu 2001; Zhang and Wu 2003).This suggests that the two schemes can capture the es-sential features of convective momentum transport.

Using the Zhang and Cho CMT scheme, Zhang andMcFarlane (1995) investigated the effects of CMT onclimate simulation in the Canadian Climate Centre(CCC) GCM. Seasonal simulations showed that by in-cluding CMT the summer Hadley circulation was en-hanced and the wind field was closer to observations.For evaluating the effect on climate simulation, long-term climate statistics are more appropriate. Wu et al.(2003) conducted a 20-yr simulation in which the Zhangand Cho scheme was implemented in the National Cen-ter for Atmospheric Research Community ClimateModel, version 3 (CCM3). They found that the simula-tion of seasonal migration of the intertropical conver-gence zone (ITCZ) precipitation was significantly im-proved when CMT was included. Preliminary analysessuggested that the improvement on precipitation re-sulted from the CMT-induced secondary circulationwithin the ascending branch of the Hadley circulation.

The aforementioned studies showed that CMT hasprofound impacts on climate simulations. However, themechanism through which CMT affects climate simula-tions is not yet clear. This is, to a large extent, due to thecomplex nonlinear interactions of processes in the at-mosphere. Figure 1a presents a schematic illustrating

these complex interactions. It shows that perturbationsin any one of the components in the loop can affect theother components. In particular, the CMT forcing canlead to changes in wind fields, which further result incomplex interactions among wind fields, temperature/moisture fields, and convection. By altering dynamicaladvection or surface heat/moisture fluxes, changes inwind fields can influence temperature/moisture fieldsand hence convection, which in turn can affect the tem-perature/moisture fields through convective heating/drying or cloud and radiation processes. By affectinggeopotential height, the change in temperature willlead to an extra wind change, which in turn can inducean extra convection change and hence temperaturechange. In addition, both changes in convection andwind fields can affect the CMT forcing; that is, there isa convection–CMT–wind feedback. In general, a GCMis composed of a dynamical core and a physical param-eterization suite, which respectively describe the dy-namical processes (e.g., advection and pressure gradi-ent force, etc.) and physical processes (e.g., boundarylayer, gravity wave drag, convection, cloud and radia-tion, etc.) of the atmosphere. Thus, the effects of CMT

FIG. 1. Sketch of the interaction between the CMT forcing andGCM for (a) standard GCM and (b) idealized GCM with experi-mental setup.

15 JANUARY 2008 S O N G E T A L . 181


on climate simulation can be decomposed into twoparts: the dynamical effects that include the response ofdynamical processes and the resulting convection–CMT–wind feedback and the physical effects thatinclude the response of physical processes and the re-sulting convection–CMT–wind feedback (e.g., CMT-induced wind–convective heating feedback, CMT–wind–evaporation–convection feedback, etc.). Previousstudies have investigated neither of the contributions ofthese two types of processes to the total effects of CMTon the climate simulations, nor the response of any onetype of processes to the CMT forcing in a climatemodel. This study will focus on one set of processes,that is, the dynamical processes, to evaluate dynamicaleffects of CMT on climate simulations.

To understand the effect of CMT on climate simula-tion, it is important to evaluate the long-term statisticsof the circulation response. However, it is difficult toisolate the dynamical effects of CMT in a comprehen-sive climate model with full physics since the effects ofall the aforementioned processes are intermingled in aclimate response after long-term integration. Is therean approach that not only isolates the dynamics asmuch as possible from the complex physical processesbut also evaluates the long-term statistics of global cir-culation? A benchmark calculation for evaluating thedynamical cores of climate models proposed by Heldand Suarez (1994) can satisfy these requirements. Intheir experimental setup, the physical parameteriza-tions are replaced with simple analytic forcing func-tions, while the complete dynamical core is retained.Focusing on the long-term statistical properties of gen-eral circulation, this setup is particularly appropriatefor investigating the dynamics in climate models.Therefore, a similar method can be applied to evaluatethe dynamical effects of CMT on climate simulations.There are two more requirements for the present pur-pose: the model should include the CMT forcing asrealistically as possible and it should include otherphysical processes to the minimum extent necessary. Tosatisfy these requirements, we propose a modified ex-perimental setup. In this setup, all physical parameter-izations in the GCM, except for the convection scheme,are replaced with the simple forcing function proposedby Held and Suarez (1994). A time-invariant water va-por field is included in the model to initiate moist con-vection. The CMT parameterization scheme of Zhangand Cho (1991a) is incorporated into the Zhang andMcFarlane (1995) convection scheme to calculate theCMT forcing, which feeds back to the momentumequations. However, the temperature and moisture ten-dencies predicted from the convection scheme are not

allowed to feed back to the model’s thermodynamicequations so as to eliminate the thermodynamic inter-action between convection and the large-scale fields.Thus, in this setup convection is controlled by themodel-predicted temperature field and the prescribedmoisture field. The convection scheme determines theamount of convective mass flux and other necessaryquantities, which together with the model-predictedmomentum fields serve as input to the momentum pa-rameterization scheme to determine the CMT forcing.The CMT forcing feeds back to the model’s momentumfields. The CCM3 with this experimental setup is re-ferred as the idealized CCM3, which can be used toinvestigate dynamical effects of CMT on climate simu-lations.

The organization of the paper is as follows. A briefdescription of the CMT scheme, model, and experimen-tal design is presented in section 2. The dynamical ef-fects of CMT on climate simulations are examined insection 3. In section 4 the momentum budgets areevaluated to understand the mechanism of CMT affect-ing the climate simulations. Section 5 gives the sum-mary 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 T42truncation (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 stepis 20 min. Deep convection is parameterized using theZhang and McFarlane scheme (Zhang and McFarlane1995). Detailed description of CCM3 can be found inKiehl et al. (1998).

b. Convective momentum transport scheme

In this study, the Zhang and Cho (1991a) CMT pa-rameterization scheme is implemented in the NCARCCM3 to investigate the effects of CMT on climatesimulations. The scheme incorporates a cloud modelthat specifies the structure of the cloud dynamical fieldand determines the cloud temperature to estimate theforcing terms of the governing equation for the cloud-scale pressure field. The cloud mean momentum andcloud-scale horizontal pressure gradient force are ob-tained by solving the equation governing cloud meanmomentum together with the diagnostic equation forthe cloud-scale pressure field. Further details of thescheme can be found in Zhang and Cho (1991a).



c. Experimental design

To isolate the dynamical effects of CMT, severalmodifications are made in CCM3:

1) Water vapor is included in the model to initiatemoist convection. However, the change of water va-por is not considered, that is, water vapor remains atits initial value, to remove the effect of water vaporchange on convection.

2) The Zhang and Cho CMT parameterization schemeis incorporated into the Zhang and McFarlane con-vection scheme to calculate the CMT forcing, which

is used to force the momentum equations. The tem-perature tendency due to convection is set to zero inorder to remove the feedback associated with con-vective heating.

3) All physical parameterizations except for the deepconvection scheme are replaced with simple ideal-ized forcing. Following the suggestion of Held andSuarez (1994), diabatic heating is expressed by New-tonian relaxation of the temperature to a prescribedzonally symmetric state Teq. Boundary layer frictionis expressed as Rayleigh friction. The detailed speci-fications are as follows:

�V�t

� A�V� � k��p�V,

�T

�t� A�T� � kT��, p��T � Teq��, p��,

Teq � max�200K, �315 K � 60 sin2� � 10 log� p

p0� cos2�� p

p0��,

kT � ka � �ks � ka� max�0,p � 700p0 � 700� cos4�,

k� � kf max�0,p � 700p0 � 700�,

p0 � 1000 mb, � � R�cp � 2�7,

kf � 1 day�1, ka � 1�40 day�1, ks � 1�4 day�1,

where p is the pressure, and R and cp represent gasconstant for air and the specific heat of air at con-stant pressure, respectively. The A terms in the mo-mentum and temperature equations represent ad-vection and other dynamic forcing. The momentumdamping rate k is a function of pressure, and isnonzero only in the boundary layer (p 700 mb).The temperature relaxation rate kT is about 1/40day�1 and is increased below 700 mb to avoid theformation of unrealistic thin cold layer. The distri-bution of prescribed radiative equilibrium tempera-ture Teq is shown in Fig. 2a.

4) There is no land–sea contrast, no topography, andno heat or momentum flux at the surface boundary.

Thus the modified model contains a complete dy-namical core, idealized physics, and the CMT forcing.Since the response of complex physical processes to theCMT forcing is excluded from the idealized model (seeFig. 1b), it is particularly appropriate for investigatingthe dynamical effects of CMT on climate simulations.

Two long-term integrations are conducted with the

idealized CCM3. In the simulation referred to asIDCMT, the setup described above is used. In the simu-lation referred to as IDCTL, the CMT forcing is ex-cluded from the momentum equations. The IDCTL istaken as the control run to which IDCMT is comparedin order to assess the influence of the CMT. It is notedthat the setup of IDCTL run is identical to that of Heldand Suarez (1994). Both simulations start from 1 De-cember with initial conditions taken from results of aprevious model simulation and run for 2221 days. Thezonally averaged initial specific humidity distributionon 1 December is shown in Fig. 2b. The statistics fromthe last 1825 days (5 yr) are used to represent the modelclimate.

3. Dynamical effects of CMT on climatesimulations

a. Climate of the IDCTL experiment

The climate of the IDCTL experiment, as repre-sented by the zonally averaged zonal wind, meridional



wind, vertical velocity, and temperature, is shown inFig. 3. The model with simple relaxation-type physicsproduces a reasonably realistic zonal-mean circulation,which is similar to the observed annually averaged cir-culation in many aspects. In the midlatitude, westerlywinds prevail throughout the troposphere with a well-defined westerly jet stream located at 250 mb near 45°latitude. Easterlies appear over the equator and nearthe poles, as well as in the subtropical boundary layer.The meridional wind and vertical velocity togetherclearly show the three-cell circulation in the meridionalplane. Since the forcing is symmetric about the equator,

the meridional circulation shows hemispheric symme-try. The Hadley circulation lies between approximately30°S and 30°N, with strong rising motion centered atthe equator. The maximum equatorward flow associ-ated with the Hadley circulation is located below 850mb and the maximum poleward flow is located between300 and 200 mb. Since temperature is relaxed to theprescribed zonally symmetric state, the temperaturedistribution is similar to that prescribed radiative equi-librium temperature. These features are in good agree-ment with those of Held and Suarez (1994).

b. CMT forcing

Figures 4a,b show the zonal average of zonal andmeridional CMT forcing from the IDCMT run. TheCMT forcing is confined mainly to the tropics between10°S and 10°N, where convection occurs most fre-quently. While the CMT forcing north of the equator isslightly larger than that to the south, it is generallysymmetric about the equator. The asymmetry is due tothe slightly asymmetric distribution of the humidityfield (Fig. 2b), which has a peak just north of the equa-tor, resulting in more convective instability and thusconvection there. In the tropics between 10°S and 10°N,the zonal CMT forcing (Fig. 4a) shows strong positivetendency below 800 mb, which tends to reduce the east-erlies in the lower tropical troposphere, and an equallystrong negative tendency between 800 and 450 mb,which tends to enhance the easterlies in the middletropical troposphere. In the upper troposphere, weakpositive zonal CMT forcing appears above 450 mb overthe equator and weak negative forcing appears northand south of that region. Comparing to the zonal CMTforcing, the meridional CMT forcing (Fig. 4b) is smallerin magnitude between 10°S and 10°N. It features a di-pole pattern with northerly acceleration north of theequator and southerly acceleration south of the equatorbetween 600 and 300 mb, which tends to weaken themiddle 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 pole-ward branch of the Hadley cell. Outside the region be-tween 10°S and 10°N, the CMT tendencies for bothzonal and meridional winds are comparable and veryweak.

To validate the CMT forcing produced by the ideal-ized model, annually averaged CMT forcing from thefull CCM3 simulation is shown in Figs. 4c,d. In general,the CMT forcing produced by the idealized model ismuch larger in magnitude than that from the fullCCM3. The reason for larger CMT forcing in theIDCMT run is that by design the idealized model doesnot consume convective available potential energy, as

FIG. 2. Zonal average of (a) prescribed radiative equilibriumtemperature (K) and (b) initial specific humidity (g kg�1); contourintervals are 10 K and 2 g kg�1.



convective heating and drying do not feed back to themodel. As such, strong convection occurs more fre-quently, producing stronger time-averaged CMT forc-ing. In the tropics between 10°S and 10°N, the zonalCMT forcing (Fig. 4c) produced by the full CCM3 ischaracterized by positive values below 800 mb andnegative values of roughly equal magnitude between800 and 450 mb; and the meridional forcing (Fig. 4d)features a dipole pattern and is smaller than the zonalforcing. In general, this distribution is similar in patternto that from the IDCMT run. This indicates that theCMT forcing produced by the idealized model is rea-sonable in this region. Outside the region between 10°Sand 10°N, the full CCM3 still produces considerable

CMT forcing in some regions; however, the CMT forc-ing produced by the idealized model is very weak. Sincethe CMT forcing is determined by convection and windfields, both convection and wind fields in the idealizedand full CCM3 simulations are examined. The resultsindicate that the difference in CMT forcing between theidealized run and the full CCM3 run in those regions ismainly caused by the difference in the amount of con-vection. The convective instability produced by the pre-scribed moisture field and predicted temperature field,which is relaxed to a prescribed radiative equilibriumtemperature, in the idealized model is very weak inthose latitudes, leading to little convection and CMTforcing. On the other hand, in the full CCM3, mainly

FIG. 3. Zonal average of (a) zonal and (b) meridional wind (m s�1), (c) vertical velocity (mb day�1), and (d) temperature (K) inthe 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.



owing to the seasonal shift of solar radiation, convec-tion is active outside the 10°S–10°N tropical belt. As-sociated with it is the strong CMT forcing. Since con-vection in the intertropical convergence zone plays apivotal role in driving tropical atmospheric circulation,this study will focus on effect of CMT forcing over theITCZ on climate simulations and will not tune the pre-scribed moisture and reference temperature fields toget stronger CMT forcing outside the 10°S–10°N tropi-cal belt.

c. Dynamical response of large-scale circulation

The dynamical response of large-scale circulation tothe CMT forcing is readily identified from the zonallyaveraged difference of circulation between the IDCMTand IDCTL simulations (Fig. 5). The zonal wind differ-

ence (Fig. 5a) between the IDCMT and the IDCTL runis manifest. Tropical easterlies become stronger andbroader 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 Sand decrease equatorward of that latitude implies apoleward shift of the midlatitude westerly jets. The me-ridional wind difference (Fig. 5b) shows that the north-erlies and southerlies that lie respectively to the northand south of the equator associated with the equator-ward branch of the Hadley circulation are enhanced inthe IDCMT run. The southerlies and northerlies to thenorth and south of the equator associated with the pole-ward branch of the Hadley circulation are also en-hanced. This indicates that the equatorward and pole-ward branches of the Hadley circulation are strength-

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.



ened when CMT is included. Along with thestrengthening of the convergence in the Hadley cell’slower branch and divergence in its upper branch, theupward motion associated with the Hadley cell’s as-cending branch is enhanced and becomes more concen-trated, and the downward motion associated with theHadley cell’s descending branch is enhanced andbroadened (Fig. 5c). Thus meridional wind and verticalvelocity together clearly show that the inclusion ofCMT leads to an increase in intensity of the Hadleycirculation. This result agrees with previous GCM stud-ies 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 funda-mental response of large-scale circulation to the CMT

forcing, indicating that dynamical processes make sig-nificant contributions to the total response of circula-tion to the CMT forcing in the full GCMs. For thetemperature field (Fig. 5d), there is cooling near theequator and warming in the subtropics in tropospherewhen the CMT is taken into account. The temperaturechange is generally consistent with the adiabatic heat-ing/cooling associated with the vertical velocity change.It is noted that the circulation change due to the inclu-sion of the CMT forcing in the idealized GCM is muchstronger than that in the full GCM, which can to a largedegree be attributed to the larger CMT forcing pro-duced by the idealized GCM.

Comparing the changes in wind fields with the cor-responding CMT forcing, we see that there is consider-

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) 5 mbday�1, and (d) 0.5 K; negative values are shaded.



able difference between the wind response and CMTforcing, especially in the meridional direction. For in-stance, between 600 and 300 mb there is positive me-ridional CMT forcing south of the equator and negativemeridional CMT forcing north of the equator, whereasthe meridional wind changes in these regions are ofopposite sign to the CMT forcing. This negative corre-lation between the wind response and the CMT forcingalso occurs in the zonal wind field over the equatorabove 450 mb and in the lower troposphere between10° and 20° in each hemisphere. This indicates that the

wind change is not a linear response to the CMT forcingand that other processes are involved that make signifi-cant contributions to the wind response to the CMTforcing. In the next section, we will use momentumbudget diagnostics to evaluate the contribution of eachprocess that affects the momentum field.

4. Momentum budget

The governing equations of the model with experi-mental setup can be written as

du

dt� �f � u

tan�

a �� 1

a cos�

��

�� k�u � Fu_cmt, �1a�

d�

dt� �f � u

tan�

a �u � �1a

��

�� k�� F�_cmt, �1b�

��

�p� �

RT�

p, �1c�

1a cos�

�u

��

1a cos�

�

�� cos��

��

�p� 0, �1d�

dT

dt�

RT

cpp� � �kT �T � Teq��, p��, �1e�

where the notations are standard, � and � representlongitude and latitude, respectively, a is the mean ra-dius of the earth, is the geopotential, T � (1 �0.608q)T is virtual temperature, f � 2� sin� is the Co-riolis parameter, Fu_cmt and F_cmt represent the zonaland 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, time-

and zonal-mean equations are convenient. We definethe zonal-average operator

�A� �1

2 �0

2

A d�,

and time-average operator

A �1 �0

A dt,

where � is the average interval of time. Thus, for a longtime mean (� � 1825 days), Eqs. (1a)–(1e) can be writ-ten as

��u�

�t� f �� Fu_cmt� � k� �u� � ��

a

�u

��

�u

�p �� tan�

au��, �2a�

��

�t� �f �u� �

1a

��

�� F�_cmt� � k� ��

a

��

��

��

�p �� tan�

auu�, �2b�

��

�p� �

R�T��

p, �2c�

1a cos�

�

�� cos��

��

�p� 0, �2d�

��T�

�t� ��

a

�T

�� T

�p�

RT

cpp�� kT �T� � kTTeq��, p�. �2e�



The time derivative terms are negligible as the equationis averaged over the entire analysis period. This set ofequations clearly shows the interconnections betweenthe CMT forcing and the resulting changes in the zon-ally averaged circulation. First, the CMT forcing canonly directly influence [u] and []; then, the change in[] affects [�] through the continuity equation (2d). Thethermodynamic energy equation (2e) shows the tem-perature is influenced by [] and [�] since Teq(�, p) is aprescribed reference temperature. This indicates thatthe CMT forcing may affect temperature by modifying[]. Temperature change produces a correspondinggeopotential change according to Eq. (2c), which inturn affects the meridional momentum budget Eq. (2b)through pressure gradient force term. Besides theaforementioned effects, momentum equations [Eqs.(2a) and (2b)] show that there are nonlinear interac-tions between the velocity fields (last three terms on theright-hand side of the equations), the Coriolis forceterm, and the boundary layer friction, which may alsoaffect the final responses of the circulation.

The governing equations for the control experiment(IDCTL) are the same as Eqs. (2) except that the CMTforcing terms are removed from the momentum equa-tions. We can evaluate the contribution of each processby examining the change of each term in the momen-tum equations between the IDCTL and IDCMT runs.Each term in Eqs. (2a) and (2b) is first calculated usingdaily averaged data at each grid point, in which deriva-tives are calculated using centered finite differences.The results are then averaged over the final 1825 daysof all integrations along each resolved latitude.

Figure 6 shows the changes of each component in thezonal momentum budget between the IDCTL andIDCMT runs. In general, the zonal CMT forcing itself(Fig. 6b) is the dominant term in the momentum budgetdifference. The curvature term (Fig. 6f) is very small.The zonal CMT forcing provides a westerly accelera-tion below 800 mb and an easterly acceleration between700 and 450 mb in the tropical troposphere, which areresponsible for the zonal wind changes observed in Fig.5a in those regions. In the tropics, boundary layer fric-tion (Fig. 6e) and meridional advection (Fig. 6c) tend tooffset the westerly acceleration induced by the CMT inthe lower troposphere, and the vertical advection (Fig.6d) tends to offset the easterly acceleration due to theCMT between 700 and 450 mb. The effects of the afore-mentioned terms are to reduce the response of zonalwind to the CMT forcing in those regions. In the equa-torial region, meridional advection offsets the CMTforcing and produces easterly acceleration above 450mb, while vertical advection offsets the CMT forcingand produces westerly acceleration between 800 and

700 mb. These two terms can give rise to the zonal windchanges noted in Fig. 5a in the corresponding regions,and hence explain why the zonal wind responses aredifferent from the CMT forcing in those regions. Inaddition, the Coriolis force (Fig. 6a) offsets the CMTforcing and produces an easterly acceleration in thelower troposphere between 10° and 20° in each hemi-sphere, which accounts for the enhanced easterlies inthe subtropical boundary layer. This result shows thatthe zonal wind change is a direct response of the zonalwind to the zonal CMT forcing and that the boundarylayer friction, advection term, and Coriolis force canalso significantly affect the response of the zonal windfield.

The differences in the meridional momentum budgetcomponents between the IDCMT and IDCTL runs areshown in Fig. 7. The most visible changes come fromthe Coriolis force associated with the zonal windchange and from the pressure gradient force. The restof the terms, including the meridional CMT forcing, aresmall. In the tropics, the change of the Coriolis forceprovides southerly acceleration south of the equatorbelow 700 mb and northerly acceleration above, withopposite changes north of the equator. This is consis-tent with the meridional wind change shown in Fig. 5b.The change of pressure gradient force tends to offsetthe forcing induced by the change of Coriolis force.Figure 7h shows the sum of the changes in the Coriolisforce and pressure gradient force. Comparing to Fig.5b, it shows that the change of Coriolis force is respon-sible for the meridional wind change displayed in Fig.5b in the tropics, and the role of pressure gradient forceis to reduce the forcing associated with the Coriolisforce. Since the change of the Coriolis force is associ-ated with the zonal wind change, which in turn is aresponse of zonal wind to the zonal CMT forcing, itindicates that the meridional wind change is an indirectresponse of meridional wind to zonal CMT forcingthrough the Coriolis effect.

Comparison of Figs. 7a and 7b shows that the changein Coriolis force approximately balances the change inpressure gradient force. This suggests that the adjust-ment of circulation follows an approximate geostrophicbalance. As noted above, the change of pressure gradi-ent force is induced by the temperature change, whichin turn is induced by the change of meridional circula-tion. This indicates that, when meridional geostrophicbalance is broken due to the zonal wind change in re-sponse to the ageostrophic zonal CMT disturbance, theCoriolis force anomaly will induce a change in meridi-onal wind, which in turn will lead to a change in tem-perature field and hence in pressure gradient force to



FIG. 6. Zonal-mean change in the zonal momentum budget components [see Eq. (2a)] from the IDCTL run to IDCMT run. Unitsare m s�1 day�1; contour interval is 2 m s�1 day�1 and negative values are shaded.



FIG. 7. Zonal-mean change in the meridional momentum budget components [see Eq. (2b)] from IDCTL run to IDCMT run. Unitsare m s�1 day�1. The contour interval is 3 m s�1 day�1 and negative values are shaded.



balance the Coriolis force anomaly so that the circula-tion can achieve a new geostrophic balance.

To further evaluate this argument, an experiment isconducted in which the setup is same as the IDCTL runexcept that the 5-yr mean difference of the Coriolisforce (fu) between the IDCMT and IDCTL runs (i.e.,Fig. 7a) is added in the meridional momentum equa-tion. The purpose is to examine the response of themeridional circulation and pressure gradient force tothe change of the Coriolis force induced by the CMTforcing. The experiment is referred to as the IDFU run.Figures 8a,b show the zonally averaged difference ofthe meridional wind and vertical velocity between theIDFU and IDCTL simulations. Comparison of Figs.8a,b and 5b,c shows that the difference of meridionalcirculation between the IDFU and IDCTL runs is al-most identical to that between the IDCMT and IDCTLruns in the tropics. It demonstrates that the Coriolisforce associated with the zonal wind change is the dom-inant forcing term in meridional momentum equation,and it actually can produce an enhanced Hadley circu-lation observed in the IDCMT run.

This result confirms the conclusion that the meridi-onal wind change is an indirect response of meridionalwind to the zonal CMT forcing through the Corioliseffect. The zonal momentum budget equation showsthat the change of meridional circulation can lead to azonal wind change that in turn can lead to an extraCoriolis force anomaly and hence an extra pressure gra-dient force response. Therefore, the sum of changes inthe Coriolis force and in pressure gradient force be-tween the IDFU and IDCTL runs (Fig. 8c) is used torepresent the net response of the pressure gradientforce to the added Coriolis forcing. Comparing Figs. 8cand 7a shows that the net response of the pressure gra-dient force is approximately in balance with the addedextra Coriolis forcing. This demonstrates that thechange of the Coriolis force causes a change in pressuregradient force through strengthening the Hadley circu-lation so that circulation can achieve a new near-geostrophic balance. It suggests that when ageostrophicCMT disturbance is included, an increase in the inten-sity of the Hadley circulation is required through whichthe circulation can achieve a new near-geostrophic bal-ance.

→

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 Co-riolis force and pressure gradient force (m s�1 day�1) between theIDFU and IDCTL runs. Contour intervals are (a) 0.5 m s�1, (b) 5mb day�1, and (c) 3 m s�1 day�1; negative values are shaded.



5. Summary and conclusions

The dynamical effects of CMT on global climatesimulations are investigated using the NCAR CCM3 inthis study. To isolate the dynamical effects of CMT, anexperiment setup is proposed. In this setup, all physicalparameterizations in the GCM except for the deep con-vection scheme are replaced with simple idealized forc-ing. The Zhang and Cho CMT scheme is incorporatedinto the convection scheme to calculate the CMT forc-ing, which is used to force the momentum equations,while the temperature and specific humidity tendenciesdue to convection are neglected to remove physicalfeedback that would obscure the diagnosis of the dy-namical effects of CMT. The control simulation withoutthe CMT produces a reasonable zonal-mean circula-tion. The CMT forcing produced by the idealizedCCM3 is generally similar in pattern to that producedby the standard CCM3 with the same CMT schemeover the ITCZ, although having a much larger magni-tude. This demonstrates that the experimental setup weproposed is useful for investigating the dynamical ef-fects of CMT on climate simulations.

Comparison of simulations with and without CMTshows that the dynamical effects of CMT on climatesimulations are readily apparent. The Hadley circula-tion is enhanced when CMT forcing is included. Thisresult is consistent with previous studies that used fullGCMs. It suggests that the dynamical processes canmake significant contributions to the total response ofcirculation to the CMT forcing in the full GCMs.

Momentum budget analysis is conducted to under-stand the mechanism by which CMT affects the climatesimulations. The zonal momentum budget shows thatthe zonal wind change is a direct response of zonal windto the zonal CMT forcing and that the Coriolis force,boundary layer friction, and nonlinear interactions be-tween velocity fields can also affect the response of thezonal wind to the CMT forcing. The meridional mo-mentum budget shows that the adjustment of circula-tion follows an approximate geostrophic balance, andthat the Coriolis force associated with the zonal windchange in response to the zonal CMT forcing is thedominant forcing term in meridional momentum equa-tion, while the meridional CMT forcing is relativelysmall. This indicates that the meridional wind change isan indirect response of meridional wind to zonal CMTforcing through the Coriolis effect.

The adjustment mechanism of the meridional circu-lation in response to the ageostrophic CMT forcing isexamined. When meridional geostrophic balance isbroken due to the zonal wind change in response to theageostrophic zonal CMT disturbance, the Coriolis force

anomaly will induce a change in meridional wind, whichin turn will lead to a change in temperature field andhence in pressure gradient force to balance the Coriolisforce anomaly so that the circulation can achieve a newmeridional geostrophic balance. This suggests that anincrease in the intensity of the Hadley circulation is anindirect response of meridional wind to the zonal CMTforcing through the Coriolis effect, and it is required formaintaining near-geostrophic balance.

Acknowledgments. This research was supported bythe Biological and Environmental Research Program(BER), U.S. Department of Energy, Grants DE-FG02-04ER63868 and DE-FG02-04ER63865.

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