1、HADLEY CIRCULATION DYNAMICSSeasonality and the Role of Continents Kerry H. Cook Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York14853-1504, U.S.A.1CONTENTS 1 Introduction 2 Definition and observations of the Hadley circulation 3 A simplified set of governing equatio
2、ns for the Hadley circulation 4 Model simulations 5 Seasonality of the Hadley circulation 6 Continental heating and the Hadley circulation 7 Summary2 1. INTRODUCTION This chapter provides 1) an introduction to Hadley cell dynamics, including a discussion of the processes that determine the circulati
3、ons climatology. 2)The physics of the seasonal oscillation of the Hadley circulation is emphasized, since this intra-annual variability provides insight into possible changes in the circulation on other, e.g., paleoclimate, time scales. 3)The role of the continents in driving the Hadley circulation
4、is also discussed. Much of the heating that ultimately drives the circulation is delivered to the atmosphere over continental surfaces through latent and sensible heat fluxes, and vertical momentum transports are also enhanced over the continents, so changes in these surfaces can modify the circulat
5、ion. 3 2. Definition and observations of the Hadley circualtion A Hadley circulation is a large-scale meridional overturning of a rot-ating atmosphere that has a heating maximum at the surface near or on the equator. The strength and geometry of the Hadley circulation can be quantified by using a st
6、ream function. Using pressure as the vertical coordinate, conservation of mass requires (1) If Equation 1 is averaged over longitude, around the entire globe, then the first term on the left-hand side (LHS) of Equation 1 is zero and a two-dimensional flow is defined. Using square brackets to denote
7、this longitudinal (zonal) average, the continuity equation is11( cos )0coscosuvaap4 (2) Equation 2 states that if v is known then is known, and vice versa. In other words, one variable can be used to fully define the two-dimensionalflow. One could use either v or as this single variable, but a more
8、physical representation of the full flow field can be generated by using a stream function. The Stokes stream function, , which is typically used to characterize the Hadley circulation, is defined by (3) v is used for practical reasons because meridional velocities are more frequently and accurately
9、 observed. Solving for and integrating from the top of the atmosphere, where it is assumed that = 0 and p = 0, yields (4) 2cosgvap02cos( ,) ( ,)papvpdpg 5cos22ag6 3. A SIMPLIFIED SET OF GOVERNING EQUATIONS FOR THE HADLEY CIRCULATIONSet of governing equations: The horizontal momentum equations; The f
10、irst law of thermodynamics; The continuity equation. The horizontal momentum equations:Newtons second law of motion (F = ma), the governing equation for motion (wind) in the atmosphere, can be written (5) To consider any variable, , on a grid that is fixed in space, such as latitudeand longitude, th
11、e Lagrangian derivative, d/dt , is converted into the Eulerian partial derivative, , by taking advection into account (6) mFdtvdadvdtt /t7 For simplicity, we choose local Cartesian coordinates with pressure as the vertical coordinate. The east/west wind, u, blows along the x axis with unit vector po
12、inting eastward, and the north/south wind, v,blows along the y axis with unit vector pointing to the north. Equation 5 can then be written in component form as (7) (8) For large-scale motion, the important forces to consider in the momentum equations are Coriolis, pressure gradient, and frictional f
13、orces (dissipation). Equations 7 and 8 becomejimFuvtuxmFvvtvy8 (9) (10) The momentum equations are further simplified for a first-order analysis of the MMC by averaging over time and longitude. The time mean,denoted below by overbars, should be thought of as an average over many years so time deriva
14、tives are negligible. The geopotential height gradient term in the zonal momentum equation is eliminated when the zonal average is taken, and Equa-tions 9 and 10 become (11) (12)xDfvxuvtuyDfuyvvtv0 pxf vvuD0 pyf uvvDy 9Each term of the simplified u-momentum equation (Eq. 11) and v-momentum equation
15、(Eq. 12) in July:Coriolis forceFrictional dissipationadvection of u-momentum935 hPa , u250 hPa , u935 hPa , v250 hPa , vCoriolis forceadvection of u-momentumCoriolis forcemeridional pressure gradient 10 The first law of thermodynamics:The full equation is (13) Equation 15 states that an air parcel c
16、an have two responses to the application of diabatic heating, J. One is a change in temperature and the other is adiabatic expansion or compression. Using the perfect gas law and Equation 6, Equation 13 is rewritten (14)Then, the climatological, zonally averaged thermodynamic equation is (15) Jdtdpd
17、tdTcvppcJSTvtT)(ppcJSTv11 Equation 15 states that an applied zonally averaged heating, ,is balanced either by the advection of cooler air, ,or by adiabatic cooling (rising air), , In the deep tropics, on large space scales, atmospheric heating is primarily balanced by rising motion, because horizont
18、al temperature gradients are weak. A longitude-height cross section of the adiabatic and diabatic heating terms in Equation 15 at 3.35N in July is shown in Figure 2-3.0pcJ0Tv0pSppcJSTv3.35N, July12A zonally averaged view of the thermodynamic balance is provided in Figure 2-4,ppcJSTv568hPa, July13 Th
19、e continuity equation:The continuity equation (Eq. 2 ) completes the set of governing equations. In local Cartesian coordinates, (16) Equations 11, 12, 15, and 16 constitute a simplified set of equations governing the MMC, and can be used to discuss how and why the Hadley circulation occurs and vari
20、es.01pva0pyv14Two driving mechanisms for the Hadley circulation derive from this structure in atmospheric heating.1.HeatingHadley Cell(Equation16)(Equation15)15Hadley Cell(Equation16)(Equation12)(Equation11)solar heating2.By its definition, the meridional geopotential height gradient at a level p is
21、 related to the average meridional temperature gradient in the atmosphere below level p:ppspTdRpln)(164. MODELSIMULATIONS Simulations with a three-dimensional climate model are used to investigate the seasonality of the Hadley circulation and the role of continents in determining climatology. The ty
22、pe of model used is a general circulation model (GCM). As in all GCMs, the governing equations are the complete, nonlinear, and time-dependent primitive equations (which were simplified in Section 3). This class of models is capable of producing a realistic representation of the Hadley circulation a
23、nd its seasonal changes, and provides information about relevant variables for which observed climatologies are not available (e.g., dissipation and diabatic heating rates). Several model simulations with different prescribed surface boundary conditions are presented.TEST1:all-ocean surface, with ob
24、served zonally uniform SSTsTEST2:One simulation has flat, featureless continents and observed zonally uniform SSTsTEST3:A simulation with realistic surface features, including topography, realistic soil moisture and surface albedo distributions, and realistic SSTs with longitudinal structure17Solid
25、lines : indicate zonallyaveraged observed SSTsdashed lines : resulting zonally averaged surface temperature from TEST2dotted lines : resulting zonally averaged surface temperature from TEST3 In test3, surface temperatures are significantly different from the surface temperature distribution in the f
26、eatureless continent case.The surface features, however, do not introduce significant differences in the MMC compared with the idealized continent simulation, primarily because the differences is temperature are largely associated with different elevations of the surface. For this reason, the analys
27、is below is focused on the simpler case (featureless continents)185. SEASONALITY OF THE HADLEYCIRCULATION The simplified set of governing equations written above can be used to provide insight into how and why the Hadley circulation changes seasonally. Examining how the terms in each equation change
28、 during the transition from equinox to solstice circulations in the GCM simulation with idealized continents (described above) explains why the summer cell weakens and the winter cell intensifies during this period. The April to July time period is chosen (Fig. 2-6), since the April circulation is n
29、eatly symmetric and the strongest winter cell occurs in July (Southern Hemisphere).19 Compared with July, the diabatic heating and vertical velocity are much closer to and more symmetric about the equator. The heating maximum is stronger in April than in July, but heating amounts are not well correl
30、ated with the circulation strength (integrated over the entire Hadley regime) in any of the GCM simulations or in the NCEP/NCAR reanalysis.April 568hPaJuly 568hPa20 Recall that dissipation depends on vertical structure in the zonal wind. Latent and sensible heating of the atmosphere diminish as wint
31、er advances.This change increases the vertical stability of the atmosphere, so the zonal wind shear becomes larger, enhancing the injection of u-momentum into the lower atmosphere and generating a larger meridional velocity.U-momentum 935hPa AprilU-momentum 935hPa JulyLatent and sensible heatingvert
32、ical stability wind shear xD v0 pxf vvuD vwinter cell enhance21v-momentum 935hPa Aprilv-momentum 935hPa Julyy f uy f u In contrast to the zonal momentum balance, the low-level meridional momentum balance does not change very much between the equinox and winter. The winter (Southern) hemisphere geopo
33、tential height gradient and Coriolis terms (Fig. 2-2c) are only slightly larger than in the autumn case (Fig. 2-8b). The most notable difference is the equatorward shift of the maxima in both terms. Since a larger zonal velocity is required to balance a given meridional geopotential height gradient
34、closer to the equator (where the Coriolis parameter, f, is smaller), this shift is consistent with the enhancement of the circulation as winter develops. fuxD v22 To understand the weakening of the Hadley circulation in the spring to summer transition, consider the Northern Hemisphere momentum balan
35、ces in Figure 2-8. In contrast to the winter hemisphere, large changes in the magnitude of the v momentum balance terms accompany the weakening of the Hadley cell (compare Northern Hemispheres in Figs. 2-2c and 2-8b). The meridional geopotential height gradient weakens by more than a factor of 4 whe
36、n the continental surfaces in the subtropics warm, and the Coriolis force weakens by a similar amount. v-momentum 935hPa Aprilv-momentum 935hPa Julyy f u0()pxxfvvuDuDvw e a k e ny 236. CONTINENTAL HEATING AND THE HADLEY CIRCULATION The Hadley circulation it is not driven by zonally uniform heating.
37、The ultimate driving force of the Hadley circulation is, of course, the solar energy flux into the climate system, and this energy is delivered into the top of the atmosphere without longitudinal structure. However, most of the solar energy that fuels the troposphere is first absorbed by the surface
38、 and converted to long-wave radiation and sensible heating that is deposited in the lower atmosphere from the surface, or converted into latent heat by evaporating water and deposited into the middle troposphere when that water condenses. After this pass through the surface, the energy distribution
39、is no longer zonally uniform.24 Surface temperature, which is closely related to sensible heat fluxes and evaporation rates, in July differs by up to 10 K at a given latitude, with significantly higher values in the western ocean basins and over land in the summer hemisphere. Precipitation is also o
40、rganized by the land/sea distribution, and varies by almost 1 order of magnitude across the tropics even in this coarse-resolution view.25all-ocean : the MMC is stronger in the winter hemisphere than in the summer hemisphere, with the up branch centered near the equator.featureless continents : the
41、winter cell becomes even stronger, and the summer cell weaker, and the center of the up branch moves farther off the equator The presence of continents is associated with a halving of the strength of the Southern Hemisphere summer cell, and the Northern Hemisphere summer cell essentially disappears.
42、 Meridional mass transport by the both winter cells approximately doubles .no continets featureless continets 26 Figure 2-11 shows the thermodynamic balance in the all-ocean case for July. Compared with the simulation with continents, shown in Figure 2-4, both the diabatic heating and vertical veloc
43、ity are located closer to the equator and are more concentrated. The maximum values are larger than in the continents case, despite the fact that the winter circulation is weaker in the absence of continents.no continet with continetpJcpS27no continet ,Julywith continet , July: 0 pyvm om entumf uvvD
44、y y f u Despite the striking intensification of the winter cell due to continents, the v-momentum balance is not very different between the two simulations in the Southern Hemisphere. Surface temperatures in the winter hemisphere are colder over land surfaces, and the surface meridional temperature
45、gradient is stronger as a result, but the cooling is confined to the surface in the vertically stable winter hemisphere(?), and even at 935 hPa the meridional temperature gradient is very similar in the two simulations.28no continet ,Julywith continet , JulyFigs.2-12a: 0 pxumomentumf vvuDFigs.2-2a T
46、he u-momentum balance in the winter (Southern) hemisphere, however, is significantly altered by the presence of continents (compare Figs. 2-2a and 2-12a). The increased roughness of the surface ( ) enhances the upward flux of u-momentum from the surface and the friction term increases. This is balan
47、ced by an increase in meridional velocity, and the Hadley circulation intensifies.xDC Vu xDxDxD f vxD29no continet ,Julywith continet , July: 0 pyvm om entumf uvvDy y f u The role of continents in flattening the meridional temperature gradient in the summer hemisphere is clearly seen in the low-leve
48、l v-momentum balance. While the simulation with continents present had essentially constant zonal-mean surface temperature in the Northern Hemisphere tropics (Fig. 2-2c), the meridional temperature gradient in the all-ocean case is appreciable, being about half the magnitude of the winter hemisphere
49、 gradient. Since the strong vertical mixing (convection) of the summer atmosphere communicates the surface temperature structure into the low and middle troposphere, the circulation can respond and the result is a stronger summer cell in the simulation with no continents.307.summaryFeatures of Hadle
50、y CirculationThermodynamic mechanism Dynamics mechanismHadley circulation is a large-scale meridional overturning of a rotating atmosphere.In the annual mean, the Hadley circulation consists of two equally strong cells, with rising air in the tropics and sinking in the subtropics.the winter hemisphe
