Monsoon Dynamics with Interactive Forcing. Part I ...

Monsoon Dynamics with Interactive Forcing. Part I: Axisymmetric Studies

NIKKI C. PRIVÉ AND R. ALAN PLUMB

Program in Atmospheres, Oceans, and Climate, Massachusetts Institute of Technology, Cambridge, Massachusetts

(Manuscript received 2 August 2005, in final form 28 July 2006)

ABSTRACT

The applicability of axisymmetric theory of angular momentum conserving circulations to the large-scalesteady monsoon is studied in a general circulation model with idealized representations of continentalgeometry and simple physics. Results from an aquaplanet setup with localized subtropical forcing arecompared with a continental case. It is found that the meridional circulation that develops is close to angularmomentum conserving for cross-equatorial circulation cells, both in the aquaplanet and in the continentalcases. The equator proves to be a substantial barrier to boundary layer meridional flow; flow into thesummer hemisphere from the winter hemisphere tends to occur in the free troposphere rather than in theboundary layer. A theory is proposed to explain the location of the monsoon; assuming quasiequilibrium,the poleward boundary of the monsoon circulation is collocated with the maximum in subcloud moist staticenergy, with the monsoon rains occurring near and slightly equatorward of this maximum. The modelresults support this theory of monsoon location, and it is found that the subcloud moist static energydistribution is determined by a balance between surface forcing and advection by the large-scale flow.

1. Introduction

The classic view of the monsoon has been founded onthe existence of a strong contrast in heating betweenthe ocean and land, with the monsoon itself manifestingas an enormous sea breeze (Halley 1686). However,this depiction of monsoon dynamics fails to account forsome of the observed behaviors of the monsoon, in-cluding abrupt delayed onset and the active-breakcycle, and does not consider the impact of planetaryrotation on such a large-scale flow. An alternative viewthat considers the monsoon as a seasonal displacementof the intertropical convergence zone (ITCZ) into thesubtropics has recently gained support (e.g., Chao andChen 2001; Gadgil 2003). It is this latter view that is thefocus of this work.

The observed zonally averaged monsoon flow (notshown) depicts a global meridional circulation cell withascent in the monsoon region, outflow that crossesinto the winter hemisphere aloft, subsidence in the win-ter hemisphere Tropics, and cross-equatorial returnflow at low levels. Using a linear shallow-water model,

Gill (1980) found that a localized prescribed forcing inthe off-equatorial Tropics induces a cross-equatorialcirculation similar to the observed monsoon flow. How-ever, Held and Hou (1980), Lindzen and Hou (1988),and Plumb and Hou (1992) determined the axisymmet-ric Hadley circulation to be fundamentally nonlinear,and predicated upon the conservation of angular mo-mentum in the free troposphere. The intent of this workis to explore the validity of the nonlinear, axisymmetrictheory of the steady Hadley circulation in describingthe dynamics of the monsoon.

Held and Hou (1980) expanded upon the work ofHide (1969) and Schneider (1977) to explain the devel-opment of the annual mean Hadley cells using conceptsof angular momentum conservation. The predomi-nance of a single Hadley cell in the dynamical responseto solsticial forcing was examined by Lindzen and Hou(1988). Plumb and Hou (1992) explored the atmo-spheric response to a localized subtropical forcing in adry, axisymmetric framework and found that the criti-cal condition for the development of an angular mo-mentum conserving (AMC) meridional circulation isthe existence of an extremum of angular momentum inthe thermal equilibrium state. Emanuel (1995) showedthat assuming a moist adiabatic lapse rate, and makinguse of the Maxwell relations, the threshold may be writ-ten as

Corresponding author address: Nikki Privé, Cooperative Insti-tute for Research in the Atmosphere, NOAA/ESRL, R/GSD, 325Broadway, Boulder, CO 80305-3337.E-mail: [email protected]

VOLUME 64 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S MAY 2007

DOI: 10.1175/JAS3916.1

© 2007 American Meteorological Society 1417

JAS3916

Unauthenticated | Downloaded 11/13/21 03:45 AM UTC

�

��cos3�

sin��Ts � Tt �

�sb

�� 4�2a2 cos3� sin�,

�1�

where � is the latitude, a is the radius of the earth, � isthe angular velocity of the earth, sb is the subcloudmoist entropy, Ts is the surface temperature, and Tt isthe temperature at the tropopause. Zheng (1998) veri-fied threshold behavior in a moist axisymmetric aqua-planet model with fixed, local subtropical SST pertur-bation.

There has been interest in the application of thetheory of threshold behavior to explain certain aspectsof the monsoon. Plumb and Hou hypothesized that theabrupt onset of the monsoon might be related to thisthreshold behavior. Eltahir and Gong (1996) found thatthe subtropical meridional gradient of subcloud moistentropy was positively correlated with the strength ofthe West African monsoon.

There are several limitations to the existing nonlineartheory of the Hadley circulation. First, the work ofHeld and Hou (1980), Lindzen and Hou (1988), andPlumb and Hou (1992) is in a dry framework with anassigned distribution of radiative equilibrium tempera-ture. In these cases, the induced circulation does notaffect the forcing field, while, in the real world, theforcing is highly dependent upon the circulation. Forthe moist experiments of Emanuel (1995) and Zheng(1998), a prescribed SST perturbation was used to forcethe atmosphere, with radiative convective equilibriumtemperatures following a moist adiabat to communicatethe surface forcing throughout the troposphere. Over adry landmass forced by surface fluxes, the vertical col-umn follows close to a dry adiabat, and upper-leveltemperatures may be relatively cold even though thelower-tropospheric temperatures are high. This raisesthe question of whether strong sensible heat fluxes overan arid continent are sufficient to induce a monsoonalcirculation. Also, given the interaction possible be-tween the circulation and the forcing, the location andextent of the monsoon are not predictable from theradiative convective equilibrium state.

A second limitation is that the nonlinear theory isconcerned with the steady-state circulation, rather thanthe transient monsoon. The time scale for circulationsto reach a steady state in axisymmetric models is fre-quently quite long, on the order of hundreds of days,which is much greater than the seasonal time scale as-sociated with monsoons. Fang and Tung (1999) foundthat the abrupt increase in circulation strength ob-served when the steady forcing is shifted off of theequator was not seen when transient forcing was used.

In addition to the theory and models of the Hadley

circulation, axisymmetry has been applied specificallyto monsoon circulations, such as the work of Webster(1983) and Goswami and Shukla (1984). These twostudies focused on the intraseasonal variability of themonsoon and showed that interaction between the dy-namics of the monsoon flow and surface heat fluxessignificantly contributes to the transient behavior of themonsoon. We wish to take a similar approach as inthese seminal papers, but with a focus on the steady-state monsoon.

To address the applicability of the nonlinear axisym-metric theory of Hadley circulations to the interactivemonsoon, we wish to address the following questions:

1) How does the presence of a subtropical continentwith interactive forcing affect the monsoon circula-tion?

2) What determines the location and extent of themonsoon?

3) Is the steady monsoon circulation representative ofthe dynamics of the transient monsoon?

An axisymmetric general circulation model is used toexplore these questions.

This paper focuses on axisymmetric modeling as afirst step toward developing an understanding of thelarge-scale monsoon circulation. The observed mon-soon is strongly asymmetric, so that the applicability ofa strict axisymmetric theory is questionable. The ques-tion of asymmetry of the flow will be addressed in acompanion paper; the current work seeks to addressonly the purely axisymmetric case.

There is a wide gap in modeling the monsoon be-tween the highly idealized axisymmetric theory and fullGCM studies with realistic physics. While the axisym-metric theory is useful for developing an understandingof the basic physical mechanisms that drive and affectthe monsoon, it is unclear how the simplifications thatare involved limit the applicability to the monsoon. Onthe other hand, the wealth of feedbacks present in thefull GCM studies make diagnosis of the monsoon be-havior extremely difficult. The goal of this work is tobridge the gap between the idealized axisymmetrictheory and the more complex, interactive monsoon. Ageneral circulation model with simplified representa-tions of some physical processes and with idealized con-tinental geometry is chosen to achieve intermediatecomplexity, as described in section 2. This allows for areasonably more realistic portrayal of processes thatare suspected to be intrinsic to the monsoon, while atthe same time reducing the feedbacks to make analysismore tractable.

The first step is to characterize the Hadley responseto a steady local subtropical forcing in an aquaplanet

1418 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 64


setup. The aquaplanet cases act as a basis of compari-son for the later, more complex, cases with a subtropi-cal continent. The subtropical forcing takes the form ofan SST perturbation, the form of which is designed tomimic the presence of a landmass in order to allowdirect comparison with continental experiments. Theresults of the aquaplanet cases are described in section3, where it is found that threshold behavior of the me-ridional circulation is seen as predicted by Plumb andHou (1992) and Emanuel (1995). It is found that thestrength of the circulation weakens as the forcing isshifted poleward.

Next, a simple subtropical continent is introducedwith perpetual summer forcing, and comparison withthe aquaplanet experiments helps to determine the im-pact of continental physics on the monsoon circulation.These experiments are discussed in section 4. Thresh-old behavior of the circulation strength is not observedas clearly as in the aquaplanet cases, although the cir-culation does show a transition from local to globalextent, as predicted by the nonlinear theory. A theoryof monsoon location is introduced in section 5. Theboundary layer thermodynamics are shown to controlthe extent and location of the monsoon region such thatthe zero line of the circulation must be coincident withthe maximum in subcloud moist static energy. Over theocean, the moist static energy is closely related to thesurface temperature, while over a land surface, themoist static energy is controlled by a balance betweenadvection by the large-scale flow and surface heatfluxes.

Finally, seasonally varying forcing is implementedover the landmass to contrast with the perpetual sum-mer cases to explore the applicability of the steady so-lutions to the transient monsoon. Section 6 addressesthese experiments. The transient response approachesthe perpetual summer circulation by mid- to late sum-mer, but the early summer state is not close to thesteady result. The time scale for the transient responseis that needed for the large-scale overturning circula-tion to fold over the contours of angular momentumacross the tropical upper troposphere. The overall find-ings are discussed in section 7.

2. Model

The model used is the Massachusetts Institute ofTechnology (MIT) General Circulation Model(MITGCM), release 1.0. The MITGCM consists of adynamical core coupled to an atmospheric physicspackage; the dynamical kernel of the model is de-scribed by Marshall et al. (2004). The atmosphericMITGCM has been tested extensively against Held and

Suarez (1994), although a different atmospheric physicspackage is implemented here. The model grid spaceused is a partial sphere between 64°S and 64°N, with 40pressure levels in the vertical at 25-mb intervals. A stag-gered spherical polar grid is used with 4° latitudinalresolution. There is no orography, and the surface isassigned to the 1012.5-mb pressure level. The coeffi-cient of vertical viscosity is 10 Pa2 s�1, and an eighth-order Shapiro filter is employed to reduce horizontalnoise in the temperature, humidity, and horizontal flowfields.

Radiation and cloud physics are not included; in-stead, the atmosphere undergoes Newtonian cooling:

QNC � �NC�1 �TNC � T �, �2�

where T is the temperature at a grid point, and QNC isthe cooling rate. The time scale for cooling, �NC, is cho-sen to be 60 days; the qualitative behavior of the circu-lation was found to be similar over a range of �NC. Also,TNC � 200 K for all grid points; this profile for TNC ischosen for its simplicity in keeping with the idealizednature of the model setup.

The moist convective scheme of Emanuel (1991) isused, including the modifications of Emanuel and Živk-ovic-Rothman (1999). The convective parameters usedas part of this scheme have been optimized against ob-served data from the Tropical Ocean Global Atmo-sphere Coupled Ocean–Atmosphere Response Experi-ment (Emanuel and Živkovic-Rothman 1999). Theconvection scheme includes dry adiabatic adjustment,which is performed over regions that are unstable tounsaturated ascent. A mixed layer of momentum is in-cluded at the lowest 200 mb of the model; in this layer,horizontal velocities are homogenized over a time scaleof 500 s.

Very simple representations of ocean and land sur-faces are implemented. SSTs are prescribed over theocean, with the temperature profile fixed in time. Overland, a bucket hydrology following Manabe (1969) isused. Surface evaporation is modified by a factor B

B � �1 B � 0.75B0

B

0.75B0

B � 0.75B0

�B

�t� P � E, �3�

where B0 is an assigned bucket depth (20 cm) indicatingthe amount of moisture that can be stored per unitsurface area, B is the current moisture in the bucket perunit area, E is the evaporation rate, and P is the pre-cipitation rate. Any excess moisture gained by precipi-tation is considered to be runoff. The initial moisture

MAY 2007 P R I V É A N D P L U M B 1419


content of the buckets for each model case was assignedto be zero.

Because a Newtonian cooling scheme is used, theflux balance at the surface cannot be calculated usingradiative fluxes. Instead, the net downward flux into thesurface (THF) is prescribed as a function of latitude:

THF�� LHF�Ts � � SHF�Ts �, �4�

where � is the latitude, LHF is the latent heat flux intothe atmosphere, SHF is the sensible heat flux into theatmosphere, and Ts is the surface temperature. The sur-face temperature and heat fluxes are interdependentand calculated iteratively. Using a prescribed net radia-tive flux has the benefits of allowing direct control overthe land surface forcing and of reducing the number offeedbacks, such as cloud radiative feedbacks, in com-parison to a situation with interactive radiation. Thispermits easier diagnosis of the underlying dynamicalmechanisms, but at the cost of making the resultingflow less realistic. For example, surface temperaturesmay become very hot over a desertlike land area asthere no increase in the outgoing longwave radiationwith increased surface temperatures. Direct control ofthe land surface forcing allows the behavior of the mon-soon to be explored in parameter space by testing arange of forcing strengths.

3. Aquaplanet

The response of the atmosphere to a localized sub-tropical forcing is examined in an aquaplanet setup.These cases will form a baseline for comparison withthe continental cases. The model is spun up from restfor 200 days with SST of 302 K at all latitudes, then anSST perturbation of the form

SST�� 302 K � �T cos2�52

�� 0��,

�0 � � � ��0 � 36��

SST�� 302 K � �0, ��0 � 36�� 5�

is introduced, where T is the strength of the SST per-turbation, and �0 is the location of the SST perturba-tion (Fig. 1). The model is then integrated until an equi-librium state is reached, typically 300–1000 days. Thisform of the local SST perturbation is chosen to emulatethe presence of a continent, with an abrupt interfacebetween land and ocean in the subtropics at �0. Theuniformly warm ocean temperature profile in the equa-torial region and Southern Hemisphere is chosen toisolate the atmospheric response to the local SST per-turbation. A range of T is tested to characterize anythreshold behavior.

a. Subtropical threshold behavior

Two criteria are used to determine whether the mod-eled Hadley circulations are in agreement with the non-linear theory: 1) conservation of angular momentumacross the upper branch of the circulation cell, 2) exis-tence of threshold behavior of the circulation strengthas described by Plumb and Hou (1992) and Emanuel(1995). The ocean forcing is located at �0 � 16°N (5);this latitude is chosen as representative of a subtropicalmonsoon. The strength of the applied SST perturbation[T in (5)] is varied from 0.5 to 2.5 K.

Threshold behavior of the circulation strength isclearly observed with critical T � 1.25 K (Fig. 2).When the SST perturbation is small, the resulting cir-culation is weak, and the upper-tropospheric absolute

FIG. 2. Steady-state results as a function of subtropical SSTforcing for aquaplanet case. (top) Absolute global minimum cir-culation streamfunction strength (kg s�1). (bottom) Minimum150-hPa absolute vorticity between 6° and 64°N.

FIG. 1. Meridional SST profile (K) used in aquaplanet caseswith localized subtropical SST perturbation of magnitude Tat �0.



vorticity does not approach the critical value at zero.Above the threshold forcing, the circulation intensifiesmuch more rapidly with increased T, and the upper-level absolute vorticity is close to zero. When forcinglevels are below the threshold, the circulation is con-fined to one hemisphere and does not cross the equator(Fig. 3). Above the threshold forcing, the circulationbecomes cross-equatorial and considerably stronger(Fig. 3). In these cases, the upper-tropospheric absolutevorticity is close to zero in the circulation cell (Fig. 2),which indicates conservation of angular momentum.

b. Cross-equatorial flow

There is a tendency for cross-equatorial circulationsto jump in the lower troposphere when approaching theequator (e.g., Fig. 3). While some of the flow crosses theequator in the free troposphere, a portion of the circu-lation is confined to the Southern Hemisphere, givingthe streamfunction the appearance of two conjoinedHadley cells. This flow pattern results in a secondaryprecipitation maximum (not shown) in the SouthernHemisphere Tropics between the equator and 6°S. Themoisture content of the low-level flow is depleted dur-ing the jump as the air rises to the midtroposphere, butis replenished through large latent heat fluxes at thesurface in the Northern Hemisphere. Jumping also al-ters the streamfunction intensity. When jumping doesnot occur, the maximum streamfunction of the cross-equatorial circulation is located in the lower tropo-sphere near the equator. The initiation of jumpingeliminates the lower-tropospheric streamfunction maxi-

mum, and the circulation maximum occurs in the uppertroposphere. Double ITCZs are more common in at-mospheric models than in the observed atmosphere(Zhang 2001); however, the secondary precipitationmaximum seen in the present model results is not con-sidered to be a doubled ITCZ.

Jumping of the meridional circulation has been ad-dressed extensively by Pauluis (2001); a brief synopsis isgiven here. A pressure gradient across the equator isneeded in the mixed layer in order to allow cross-equatorial flow. When the mixed layer is thin or thepressure gradient is weak, only a limited mass flux ispossible in the mixed layer, so flow attempting to crossthe equator must rise into the free troposphere in orderto cross. In a moist atmosphere, the vertical moist sta-bility near the equator is weak, and the resulting jumpis quite deep. In the modeled case with uniform oceanSSTs, the pressure gradient across the equator is veryweak, sometimes even increasing northward, so thatcross-equatorial flow is strongly inhibited even thoughthe mixed layer is quite deep. An example of an aqua-planet case in which the flow does not jump at theequator is seen in the bottom left panel of Fig. 4, wherethe SST has a maximum at 8°N and a southward-decreasing SST gradient across the equator.

c. Latitudinal influence on circulation

A series of aquaplanet experiments are made withuniform SST and a localized boreal hemisphere SSTperturbation, which is varied in location. The form ofthe perturbation is given by (5), with �0 varied from 0°

FIG. 3. Steady-state streamfunction for aquaplanet case, 100-day time mean, SST perturbation located at �0 �16°N. Solid contours denote counterclockwise flow; dashed contours indicate clockwise flow. Note that contourinterval is 4 times greater for the figure on the right. (left) Subthreshold result for T � 1.0 K; contour interval is2.5 109 kg s�1. (right) Supercritical result for T � 2.0 K; contour interval is 1.0 1010 kg s�1.



to 26°N, and T is chosen to be 4.25 K. This high valueof T was chosen to yield cross-equatorial circulationsfor the entire range of �0 tested.

The impact of the location of the forcing on thestrength of the circulation is illustrated in Fig. 5. Themaximum streamfunction increases as �0 is movedpoleward from 0° to 6°N, although the circulation widthonly broadens slightly (not shown), with no sign ofjumping behavior. These results are in accord with thefindings of Lindzen and Hou (1988), who showed thatthe Hadley circulation strengthens as the peak forcingis moved poleward in the near equatorial region. As �0

moves from 6° to 10°N, the circulation nearly doublesin width (not shown) but decreases sharply in strengthas jumping initiates and the lower-tropospheric stream-function maximum is destroyed. As �0 is moved pole-

ward from 10° to 22°N, the circulation decreases instrength and broadens slightly. As the circulationbroadens, the easterly jet intensifies significantly, re-sulting in greater viscous effects with weakening angu-lar momentum conservation in the upper branch of thecirculation. This increased viscosity, peculiar to numeri-cal models, is hypothesized to account for the gradualweakening of the circulation as the forcing is shiftedpoleward. The �0 � 24N case is close to the local-to-global AMC transition as described by Schneider(1983), but far above the critical threshold for the ex-istence of an AMC circulation (Plumb and Hou 1992).Schneider showed that an angular momentum conserv-ing circulation forced by a �-function source undergoesa transition from a cell of regional extent to a cross-equatorial cell as the forcing is increased; the transition

FIG. 4. Steady-state streamfunction, 100-day time mean, coastline located at 16°N. Solid contours denote coun-terclockwise flow; dashed contours indicate clockwise flow. (top left) Subcritical result for THF0 � l30 W m�2 withuniform SST, and contour interval 5.0 109 kg s�1. (top right) Supercritical result for THF0 � 140 W m�2 withuniform SST, and contour interval 5.0 109 kg s�1. (bottom left) Aquaplanet case with SST maximum at 8°N andcontour interval 1.0 1010 kg s�1. (bottom right) Continental case with summer SST THF0 � 140 W m�2 andcontour interval 1.0 1010 kg s�1.



forcing needed is greater when the forcing is movedpoleward. The proximity to this transition is the likelycause of the sharp reduction in streamfunction magni-tude from �0 � 22° to 24°N. With a weaker T, thetransition to a local circulation occurs with �0 closer tothe equator.

4. Continental cases

A subtropical continent with interactive surface tem-peratures and heat fluxes is introduced. By comparingthe results of these experiments with the results fromthe aquaplanet cases, the peculiar nature of continentalforcing of the large-scale circulation can be discerned.The strength of the land surface forcing may be directlymanipulated through the total surface heat flux (4),given by

THF�� THF0 � �THF sin2�� 8�N�, �6�

where THF is 50 W m�2, and THF0 ranges from 120to 150 W m�2. This forcing profile was chosen to rep-resent a summer-mean forcing rather than a solsticialforcing. For all of these cases, the continent extendsfrom the southern coastline at 16°N poleward to themodel boundary at 64°N. For each case, the model isfirst spun up from rest for 200 days with a relativelycold continent (THF0 � 80 W m�2). The land surfaceforcing is then increased to the summer value over aperiod of 100 days, and the model is run for at least 700additional days until a steady state is reached.

a. Uniform SST

First, a series of experiments are performed whereinthe ocean is assigned uniform temperature. The onlydifference between this case and the previous aqua-planet case with localized SST perturbation at 16°N isthe replacement of the prescribed SST perturbationwith an interactive continent in the boreal hemisphere.

For the weakest continental forcing tested, THF0 �120 W m�2, no monsoon occurs and there is little pre-cipitation over the continent (not shown). The meridi-onal circulation is limited to a very weak, shallow cir-culation just along the coastline, with subsidence in themid- and upper troposphere over the continental sub-tropics.

When the land forcing is increased to 125 THF0

130 W m�2, deep moist convection commences over thesubtropical continent. Large-scale ascent occurs alongthe coastline, with a latitudinally narrow meridional cir-culation with subsidence over the tropical ocean (Fig.4). The upper-tropospheric absolute vorticity (dottedline with squares, Fig. 6) is not close to the critical valueat zero, and the deep circulation is not strongly angularmomentum conserving.

For land forcing of THF0 � 135 W m�2, the meridi-onal circulation is more global in extent, with ascentover the subtropical continent and subsidence over theSouthern Hemisphere ocean (Fig. 4). Jumping of thecirculation occurs for all cases with cross-equatorialflow, and becomes more pronounced as the land sur-face forcing increases. The upper-level tropical easterlyjet (not shown) is very strong, which is a common fea-ture in axisymmetric models. The angular momentumfield (not shown) is significantly distorted by the circu-lation, although the flow is able to cross some contoursof angular momentum in the Tropics, where there isstrong easterly shear. As the land forcing is increased,

FIG. 5. Absolute global maximum steady-state streamfunctionfor aquaplanet case, 100-day time mean, SST perturbation atNorthern Hemisphere latitude �0.

FIG. 6. Steady-state results as a function of land forcingstrength. Continent with uniformly warm ocean is represented bysolid lines with squares; continent with summer SST by dot–dashline with asterisks. (top) Absolute global minimum circulationstreamfunction strength (kg s�1). (bottom) Minimum 150-hPa ab-solute vorticity between 6° and 64°N.



the circulation broadens and the monsoon regionmoves inland, as shown in Fig. 7.

Although the strength of the meridional circulationincreases systematically with increased land surfaceforcing (dotted line with squares in Fig. 6), there is littleindication of threshold behavior. The upper-level abso-lute vorticity (Fig. 6) gradually approaches the criticalvalue at zero for THF0 � 140 W m�2, but a cross-equatorial circulation develops when the vorticity is stillsubcritical (THF0 � 135 W m�2). The threshold behav-ior (Fig. 6) may be compared with that of the aqua-planet case in Fig. 2.

b. Summer SST

The experiments with uniform SSTs help to isolatethe atmospheric response to a subtropical landmass,but the ocean forcing is far from realistic. A summer-like SST profile is implemented with subtropical conti-nent in an effort to achieve more realistic flow in theequatorial region. The SST distribution is fixed anddoes not vary with time:

SST�� SST0 � �T sin2�� 8�N�, �7�

where SST0 � 302 K and T � 28 K.First, an aquaplanet case with the summer-like SST

profile (7) is performed. In this case, the cross-equatorial winter Hadley cell dominates with a muchweaker summer cell confined to the warmer hemi-sphere poleward of the SST maximum (Fig. 4). TheHadley cells nearly conserve angular momentum. Theascent region and the precipitation maximum (notshown) are located slightly equatorward of the SSTmaximum.

When a subtropical continent is added with this sum-mer-like SST distribution, the overall meridional circu-

lation is visually similar in appearance to a simple su-perposition of the flow from the summer-like aqua-planet case (Fig. 4) and the previous continental caseswith uniform SST. Over the tropical ocean, a strongmeridional cell forms as a result of the SST distribution:ascent occurs in the boreal hemisphere near the SSTmaximum.

These results may be compared with the previouscontinental cases with uniformly warm ocean. For weakland forcing (THF0 135 W m�2), the streamfunctionover the continent is almost twice as strong in the sum-mer SST case as in the uniform SST case (dot–dash linewith asterisks in Fig. 6a), but for THF0 � 140 W m�2,the circulation is similar in intensity. The 150-mb abso-lute vorticity over the continent is near the critical valueof zero for THF0 � 135 W m�2 (dot–dash line withasterisks in Fig. 6); however, there is no sign of thresh-old behavior of the circulation strength.

c. Threshold behavior

Why does the aquaplanet case show clear thresholdbehavior while the continental case does not? There aretwo factors that contribute to this difference in behav-ior. In the aquaplanet setup, there are strong feedbacksbetween the circulation and the surface fluxes, espe-cially the latent heat flux. As the circulation intensifies,the surface winds increase, which enhances the surfaceheat fluxes and in turn strengthens the circulation; thistype of interaction has been coined the wind-inducedsurface heat exchange (WISHE) feedback (Emanuel1986). Threshold behavior might be exaggerated byWISHE, which would tend to strengthen already strongcirculations but has less impact on weak circulations.However, these feedbacks do not occur over the conti-nent given the constrained surface forcing.

Second, the location of large-scale ascent movespoleward with increased surface forcing (Fig. 7) in thecontinental case, but is nearly stationary in the aqua-planet case. As shown previously (Fig. 5), the circula-tion tends to weaken as the ascent region moves pole-ward through the subtropics; this would act to obscurethreshold behavior in the continental case.

d. Seasonal

After the land surface forcing has reached the peakstrength in the perpetual summer cases, there is a tran-sient period prior to establishment of a steady circula-tion. During this time, precipitation initiates over thecoastal continent and gradually moves poleward as themeridional circulation strengthens and broadens. Thistransient period is nearly 200 days long—considerablygreater than a seasonal time scale. It is not obvious that

FIG. 7. Location of maximum monsoon precipitation for steadymonsoon as a function of land surface forcing strength (THF0).The coastline is at �L � 16°N and there is uniform warm SST.



the nonlinear theory, which is based upon a steady-state circulation, is applicable to the highly transientmonsoon. There is a delay in onset of jumping of thecirculation during the transient period which questionsthe importance of the jumping behavior to the seasonal,transient monsoon. A series of experiments with sea-sonally varying land forcing are performed in order toinvestigate the pertinence of the steady state, perpetualsummer results to the seasonal monsoon.

To retain simplicity, the ocean SST does not vary intime and is uniformly 302 K at all latitudes. To repre-sent seasonal variation in radiative forcing, THF0 is var-ied sinusoidally in time from 80 W m�2 at winter sol-stice to the maximum summer value, with period of 365days. The summer solstice magnitude of THF0 is variedfrom 125 to 150 W m�2, as in the perpetual summercases. Although this distribution of surface forcing is farfrom realistic, it allows comparison with the previousperpetual summer experiments. Because of the unreal-istic choice of ocean surface temperatures, the resultsare not expected to be suitable for study of the dynam-ics of monsoon onset. The model is first spun up in awinter solstice regime for 200 days, then the seasonalcycle is initiated, and the model is run for five annualperiods. For all cases tested, the circulation and pre-cipitation fields quickly adjusted to the seasonal cycle,and there was very strong interannual consistency. Thelast four years of the model run were averaged to createa mean annual progression.

For land forcing of THF0 130 W m�2, the summermonsoon is weak, with a shallow capped meridionalcirculation over the subtropical continent. Little pre-cipitation occurs over the continent during the summerseason (Fig. 8). For stronger land forcing (THF0 � 140W m�2), large-scale ascent and deep convection form

over the subtropical continent during the summer (Fig.8). The precipitation maximum over the boreal tropicalocean at first weakens during spring, then shifts pole-ward onto the continent and intensifies during thecourse of the summer. At the beginning of fall, thecontinental precipitation maximum weakens abruptly,the rainfall peak then continues to migrate polewardduring the winter until it dies out the following spring.During early summer, the meridional circulation is lo-cal (Fig. 9), with ascent over the subtropical continentand subsidence over the Northern Hemisphere tropicalocean. As the summer progresses, the circulationstrengthens and broadens, with increased cross-equatorial flow (not shown). By the late summer, thecirculation is quite broad, and jumping behavior occurs,as shown in Fig. 9.

The seasonal cases show that the steady-state solu-tions are pertinent to the seasonal monsoon during latesummer only. The mean summer net surface flux be-tween 1 June and 31 August in the seasonal case isapproximately 10 W m�2 less than the solstice THF0. Inthe seasonal experiment, the THF0 130 W m�2 caseshave a mean summer THF0 125 W m�2 and do notresult in a monsoon, which is similar to the perpetualsummer results for THF0 � 125 W m�2. In the earlyand midsummer, the steady-state solution differs con-siderably from the seasonal monsoon. The meridionalcirculation associated with the monsoon during earlysummer is localized in extent, confined to the borealhemisphere. In mid-June, the circulation becomes crossequatorial and begins to fold over the contours of ab-solute angular momentum in the upper troposphere.The jumping behavior, which is a major feature of thesteady-state solutions, is not observed until mid-July inthe seasonal cases.

FIG. 8. Hovmoeller diagram of precipitation for seasonal cases, with contour interval of 2.0 mm day�1. (left)Maximum summer land forcing THF0 � 130 W m�2; (right) maximum summer land forcing THF0 � 150 W m�2.Day zero occurs at winter solstice; data are averaged over 4 yr of model integration.



5. Theory of monsoon location

What determines the location of the monsoon pre-cipitation and the size of the meridional circulationcell? Why does the monsoon tend to shift polewardwith increased land forcing? With the help of a fewassumptions, an extension of existing axisymmetrictheory can explain much of the large-scale dynamics.

Emanuel et al. (1994) have shown that under a sta-tistical equilibrium approach, the zonal wind field isclosely related to the distribution of subcloud moist en-tropy. The assumption is made that in the vicinity ofdeep convection, where there is large-scale ascent, thevertical thermodynamic profile approaches a moistadiabat. As a result, the upper-tropospheric virtualtemperature field is strongly tied to the subcloud moiststatic energy near the monsoon. The free-troposphericzonal wind field is in thermal wind balance with thedensity field,

�u

�p�

1f

�

�y, �8�

where is the specific volume and f is the Coriolisparameter. Maxwell’s equations relate the density tothe moist entropy:

��

�y�p� ��T

�p�s*

�s*�y

, �9�

where s* is the saturation moist entropy. By substitut-ing (9) into (8), and since s* is nearly constant in heightwith the assumption of a moist adiabatic lapse rate,

s* � sb �10�

�u

�p�

1f ��T

�p�s*

�sb

�y, �11�

where sb is the subcloud moist entropy. The subcloudmoist entropy is closely related to the subcloud moiststatic energy, hb, where the subscript indicates the sub-cloud value of the moist static energy h. Here

h � L�q � �cpd � rtcl�T � �1 � rt �gz �12�

�hb � Tb�sb, �13�

with L� the latent heat of vaporization, Tb the meansubcloud temperature, specific humidity q, specific heatof dry air cpd and of liquid water cl, and of total watercontent rt, and geopotential height z. Thus, the zonalwind shear can be approximated:

�u

�p�

1f ��T

�p�s*

1Tb

�hb

�y. �14�

The summer hemisphere poleward limit, or bound-ary, of the cross-equatorial meridional circulation isseen in the previous model cases to be a zero stream-function contour that is nearly vertical. Assuming a me-ridional circulation that conserves absolute angular mo-mentum in the free troposphere, the circulation bound-ary must be located in a region of zero vertical windshear. This can be seen by considering the vertical dis-tribution of momentum as the boundary is approachedfrom the monsoon region: at the boundary, there is flowinto the column only in the boundary layer and out ofthe column only in the upper troposphere, with noother sources of momentum advection. Since there isnet ascent in the monsoon region, the momentum mustbe constant throughout the vertical column in the tro-posphere. This makes the additional assumption of avertical boundary rather than a slanting boundary,which is appropriate for the boundary of the ascendingbranch of the circulation, but not for the subsidencebranch.

FIG. 9. Summer circulation for seasonal case with THF0 � 150 W m�2 and a contour interval of 5.0 109 kg s�1.(left) Early summer circulation (day 175); (right) late summer circulation (day 250). Day zero occurs at wintersolstice.



The statistical equilibrium theory (Emanuel et al.1994) may be applied to this framework in order to tiethe monsoon location to the subcloud moist static en-ergy. Let us assume a forcing region in the subtropics,which results in a localized area of high subcloud moiststatic energy. For the sake of this argument, the forcingregion is considered to be sufficiently strong to meetthe threshold criteria for creation of an angular mo-mentum conserving meridional circulation (Plumb andHou 1992; Emanuel 1995). From (14), �u/�p � 0 wheneither �T/�p or �hb/�y are zero. The vertical tempera-ture gradient is nonzero, so the zero wind shear line,and thus the circulation boundary, will occur at thelatitude at which hb is maximum or constant in latitude(�hb/�y � 0). Large-scale ascent will occur near and

equatorward of this maximum in hb, with the boundaryof the circulation coincident with the hb maximum. Theprecipitation is collocated with the large-scale ascent,so that the subcloud moist static energy distributiondetermines the location of the monsoon circulation andprecipitation.

This theory can be tested with the model. An ex-ample of a monsoonal case showing the relationshipbetween the circulation, zonal wind field, precipitation,and subcloud moist static energy is shown in Fig. 10. Inthe monsoon region, the zonal wind field is weak, withnear-zero shear as required by the theory. The locationof the poleward boundary of the monsoonal circulationcell is found to be coincident with the latitude of maxi-mum subcloud moist static energy, with the precipita-

FIG. 10. Steady-state fields for continental case with THF0 � 140 W m�2 with uniform warmocean. (top) Streamfunction, with a contour interval of 5.0 109 kg s�1, arrows indicatedirection of flow; (center top) zonal wind, with a contour interval of 10 m s�1; (center bottom)precipitation (mm day�l); (bottom) 1000-mb moist static energy (104 J).



tion peak occurring at or equatorward of this point.This correspondence between moist static energy andthe monsoon location is found to hold in all of themodeled cases with a continent. However, in some ofthe aquaplanet cases, the ascent branch of the circula-tion is not closely AMC due to numerical filtering ofthe zonal wind by the Shapiro filter; in these cases themaximum subcloud hb is located slightly equatorwardof the boundary of the meridional circulation.

What, then, determines the subcloud moist static en-ergy distribution? In radiative convective equilibriumwith this model setup, the subcloud moist static energyprofile follows that of the prescribed continental netsurface heat flux [THF(� )], although the actual valueof hb is constrained by moisture availability. In radia-tive convective equilibrium, the greatest subcloud moiststatic energy occurs where the net surface fluxes arelargest, over the coastal continent. Once the meridionalcirculation develops, the low-level flow carries air fromthe oceans, which has lower subcloud moist static en-ergy, over the coastal regions, locally reducing themoist static energy so that the maximum energy is lo-cated inland (Fig. 11). As the forcing is increased, thecirculation also intensifies, with a greater flux of lowmoist static energy air being carried onto the continentwhich must be heated by the surface forcing to bring itto the radiative convective equilibrium (RCE) energystate. The inflowing air must travel further over thelandmass while being heated from the surface to reachthe maximum subcloud moist static energy. The steadysolution is formed by a balance between the varioustendencies of subcloud moist static energy.

6. Discussion

The monsoon is considered here as a seasonal relo-cation of the ITCZ onto a subtropical landmass, and as

such, the dynamics of the Hadley circulation are fun-damental to the monsoon. The dynamics of the steadyHadley circulation have been explored in a series ofanalytic studies by Held and Hou (1980), Lindzen andHou (1988), Plumb and Hou (1992), and Emanuel(1995). However, the simple analytic theory does notconsider the effects of a subtropical landmass, whichforces the atmosphere differently from an aquaplanetor simple applied forcing, and does not account foronset or transient behavior.

The axisymmetric theory is extended to predict theextent of the meridional circulation and the location ofthe monsoon. The location of the deep ascent branch ofan AMC circulation is found to be strongly tied to thedistribution of subcloud moist static energy. Given alocal maximum of subcloud moist static energy, thepoleward boundary of the meridional circulation will becollocated with the maximum hb, and the large-scaleascent and precipitation will occur near and slightlyequatorward of the maximum. Because the circulationitself interacts strongly with the subcloud moist staticenergy distribution, this theory is diagnostic rather thanprognostic. However, the effect of various mechanismsupon the extent of the steady monsoon may be reducedto a determination of their impact upon the subcloudmoist static energy. For example, orography can affectthe subcloud moist static energy. Molnar and Emanuel(1999) have shown that the radiative-convective equi-librium surface air temperature decreases at a rate ofapproximately 2 K km�1 as the surface is raised, whichis less steep of a decline than the moist adiabatic lapserate. Assuming a moist adiabatic lapse rate, the satura-tion entropy will be greater over an elevated surfacethan over a lower surface receiving the same incomingradiation, and the subcloud moist static energy will alsobe greater.

How well do the modeled circulations conform to thetheorized requirement of collocation of the circulationboundary with the maximum of subcloud moist staticenergy? The cases with subtropical continent upholdthe theory quite well: the poleward boundary of themeridional circulation is collocated with the maximumsubcloud moist static energy, and the monsoon precipi-tation occurs slightly equatorward of this maximum.The theory holds reasonably well for the aquaplanetcases, but there are a few examples in which the bound-ary of the circulation occurs poleward of the subcloudmoist static energy maximum, and the ascendingbranch of the circulation has westerly shear with height.In these cases, the numerical filters break down angularmomentum conservation in the ascent branch of thecirculation, allowing vertical shear to develop.

The role of the land surface in forcing the monsoon

FIG. 11. Schematic diagram of subcloud moist static energy.Dashed line shows radiative convective equilibrium hb; solid lineshows hb in the presence of a large-scale circulation. As the sur-face forcing is increased, the radiative–convective equilibrium hb

also increases over the land, but not over the adjacent ocean.Poleward-flowing air from the ocean requires greater heating toreach the RCE equilibrium hb, and the hb maximum shifts inland.



circulation is revealed when the aquaplanet experi-ments are compared to the cases with subtropical con-tinent. In an aquaplanet setup with localized SST per-turbation at 16°N, the meridional circulation clearly ex-hibits threshold behavior, with a pronounced increasein the strength of the circulation for forcing above acritical magnitude. These strong circulations are nearlyAMC, with upper-tropospheric absolute vorticity closeto zero. When the SST perturbation is replaced with asubtropical continent, threshold behavior is not clearlyseen when the land forcing strength is varied. However,the meridional circulations that develop for strong landforcing appear to be angular momentum conserving,with near-zero absolute vorticity in the upper tropo-sphere.

The lack of threshold behavior in the two-dimen-sional cases with a subtropical continent in comparisonto the prominence of the behavior in the aquaplanetsituation is ascribed to a combination of factors. First,in the aquaplanet cases, there is a feedback between thecirculation strength and the surface fluxes through thesurface wind speed (WISHE). This feedback tends toaccentuate threshold behavior of the circulation strengthin the aquaplanet case. In the continental cases, the netsurface flux is prescribed, so that this feedback will notoccur, and the circulation strength is not expected toshow as strong an increase above the threshold as in theaquaplanet cases.

A second, more subtle, factor is the poleward pro-gression of the monsoon with increased forcing in thecontinental cases. A series of aquaplanet cases with var-ied location of the SST perturbation has shown that thecirculation weakens as it extends further poleward. Asthe monsoon moves poleward in the continental cases,broadening the circulation, the circulation strength isexpected to weaken somewhat, obscuring threshold be-havior. In the aquaplanet cases, the strong latent heatfluxes in the vicinity of the SST maximum act to tie thesubcloud moist energy maximum close to the SST maxi-mum; whereas in the continental cases, the constraint oflimited surface fluxes over the landmass leads to a dif-ferent balance of the subcloud moist energy budgetwhere advection plays a stronger role. As a result, thehb maximum over the continent is not necessarily col-located with the greatest surface fluxes. These resultsdiffer from the results of Webster (1983) and Goswamiand Shukla (1984), who found that feedbacks betweenthe circulation and the surface hydrology resulted in apoleward moving maximum in both latent and net heatfluxes and hence a poleward-moving monsoon.

The nonlinear theory concerns the steady-state cir-culation, but the real monsoon is a transient, seasonalphenomenon. The time scales needed to reach a steady

state in the model are quite long, especially in the two-dimensional cases. The initial adjustment period occurswhile the circulation folds over contours of constantangular momentum in the upper troposphere. In theexperiments with time-varying land forcing, the tran-sient monsoon circulation only bore a resemblance tothe steady state during the late summer period. How-ever, the ocean SST distribution used in these cases wasfar from realistic, which impacts the meridional circu-lation. In the real world, a cross-equatorial Hadley cir-culation forced by the ocean gradient exists prior to theonset of the monsoon, so that the momentum field isalready significantly rearranged when the monsoon ini-tiates. Fang and Tung (1999) found that the transientcirculation was similar in strength to the steady circu-lation for off-equatorial forcing, which supports theidea that the steady-state dynamics may be applicableto the seasonal case.

The idealized physics used in this study neglectsmany important processes which may have substantialimpacts upon the monsoon. The constraint of axisym-metry will be relaxed in Part II of this paper (Privé andPlumb 2007). The version of the MITGCM used heredoes not support orography, which may strongly influ-ence the monsoon. The model has only the simplestrepresentation of boundary layer physics, consisting ofa momentum mixed layer of fixed depth and dry adia-batic adjustment of variable depth. The land surfacehydrology is very primitive, and there is no allowancefor vegetation or other surface biosphere components.Given the importance of boundary layer thermodynam-ics to the large-scale monsoon that has been empha-sized in this study, the simplicity of the boundary layerrepresentation in the model is a serious limitation. Oneimportant process that was omitted from the model isradiation. Although the use of Newtonian coolingmakes the dynamics much more straightforward, theprescribed net radiative flux used to calculate the sur-face energy balance is not very realistic. The modelneglects feedbacks from clouds, the radiative influenceof water vapor, longwave feedbacks from the surfacetemperature, albedo and vegetative effects on radia-tion, all of which may impact the monsoon. A diurnalcycle is also not included in the model, which may im-pact the steady state.

Future work is suggested to investigate how differentphysical processes impact the subcloud moist static en-ergy and the large-scale monsoon circulation. Impor-tant processes that were neglected from the idealizedmodel used here include radiative feedbacks, oro-graphic effects, and boundary layer physics. The theorylinking the monsoon location to the subcloud moiststatic energy maximum may also be able to shed light



on transient monsoon dynamics, such as onset andbreak monsoon.

Acknowledgments. This work was supported by Na-tional Science Foundation Grant ATM-0436288; N.Privé received support from a National Science Foun-dation Graduate Research Fellowship. Thanks to KerryEmanuel, Elfatih Eltahir, John Marshall, Chris Hill,Olivier Pauluis, Jean-Michel Campin, and Ed Hill forhelpful discussions. We would also like to thank twoanonymous reviews whose helpful comments led to sig-nificant improvement of this paper.

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