Eddy-driven Responses of the Hadley Cell and
Tropopause
Jacob Haqq-Misra
Department of Meteorology, The Pennsylvania State University, University Park, PA
Sukyoung Lee
Department of Meteorology, The Pennsylvania State University, University Park, PA
Dargan Frierson
Department of Atmospheric Sciences, University of Washington, Seattle, WA
1
1
Abstract
2
We present a series of dynamical states to investigate the influence
3
of eddies on the Hadley circulation and tropopause structure using an
4
idealized three-dimensional general circulation model (GCM) with gray
5
radiation and latent heat release. Beginning with the case of radiative-
6
convective equilibrium, we develop a two-dimensional state with zonally
7
symmetric flow followed by a three-dimensional state that includes mid-
8
latitude eddy fluxes. In both dry and moist cases, the contribution of
9
eddy fluxes on the general circulation is necessary to reproduce an Earth-
10
like Hadley cell. Additionally, the deepening of the tropical tropospheric
11
layer and the shape of the extratropical tropopause can be understood as
12
eddy-driven phenomena. These results suggest that the standard theory
13
for an axisymmetric Hadley circulation implicitly assumes a contribution
14
from midlatitude eddy fluxes and that eddies alone can generate a realistic
15
tropopause structure in the absence of moist convection.
2
16
1
Introduction
17
Ever since Hadley proposed a theoretical model of the trade winds in 1735, at-
18
tempts at understanding large-scale horizontal motions in the atmosphere often
19
focus on the thermally direct response as a primary mechanism, with eddy forc-
20
ing assumed to be a second order effect. Held and Hou (1980), building on work
21
by Schneider (1977), derive a dry Boussinesq approximation for the Hadley cell
22
near the inviscid limit. In their axisymmetric simulations, the authors suggest
23
that an overturning circulation analogous to a Hadley cell is constrained by the
24
conservation of angular momentum and potential temperature. The strength
25
of this overturning circulation is well below the observed mean meridional cir-
26
culation (MMC) on Earth, though, suggesting that eddy fluxes might be an
27
important influence. And indeed, the diagnostic analysis of Pfeffer (1981) finds
28
that the direct effect of eddy fluxes cause a secondary meridional circulation
29
that accounts for about 30% of the strength of the observed Hadley cell.
30
Further investigation reveals that midlatitude eddy fluxes contribute signifi-
31
cantly to maintaining the width and strength of the Hadley circulation (Becker
32
et al., 1997; Kim and Lee, 2001; Walker and Schneider, 2006) and tropopause
33
structure (Haynes et al., 2001). However, like Held and Hou (1980), all of these
34
studies force the atmosphere with Newtonian relaxation toward a temperature
35
profile that is already modified by eddy fluxes. For example, a typical relax-
36
ation profile (Held and Hou, 1980; Kim and Lee, 2001) assumes that potential
37
temperature ΘE takes the form
ΘE
1
= 1 − ∆H 3 sin2 φ − 1 + ∆V
Θ0
3
z
1
−
H
2
,
(1)
38
where Θ0 is the global mean of ΘE , φ is latitude, z is height, H is the height
39
of the rigid tropopause lid, and ∆H and ∆V are respectively the horizontal and
3
40
vertical changes in potential temperature. This temperature profile is not one of
41
radiative-equilibrium but is chosen because it generates a realistic atmospheric
42
state. However, if the structure of the atmosphere is significantly modified by
43
eddies, then the equilibrium temperature field ΘE may include some effects
44
of midlatitude eddies. By contrast, Satoh (1994) investigates axisymmetric
45
Hadley circulations in moist radiative-convective equilibrium with simple non-
46
scattering gray radiative transfer, where the magnitude of forcing depends on
47
optical depth (a function of pressure) instead of a prescribed temperature profile.
48
Caballero et al. (2008) likewise use an analytic band-semigray radiative model,
49
which incorporates wavelength dependencies and pressure broadening, in their
50
nearly-inviscid axisymmetric simulations that generally agree with Held and
51
Hou (1980).
52
In this study we investigate the explicit effect of eddies on the structure of
53
the Hadley circulation and the height of the tropopause. To accomplish this, we
54
develop a hierarchy of three dynamical states: radiative-convective equilibrium
55
(RCE), a two dimensional state (2D), and a three dimensional state (3D). We
56
initialize RCE by suppressing explicit motion including eddies and the MMC.
57
Adding in advection by overturning meridional circulation to RCE yields the 2D
58
state, which still lacks transport by eddies. The final 3D state is then obtained
59
when a 2D state is perturbed so that eddies develop. By comparing RCE, 2D,
60
and 3D cases under both dry and moist conditions, we show that midlatitude
61
eddy fluxes significantly contribute to the maintenance of the Hadley circulation
62
and tropopause structure.
63
2
64
The general circulation model (GCM) used in these calculations is described
65
thoroughly by Frierson et al. (2006). This GCM builds upon the primitive
Model Description
4
66
equation dynamical core of Held and Suarez (1994) by including latent heat
67
release. In addition, gray radiation directly forces the atmosphere, instead of
68
Newtonian relaxation to a fixed profile, and an explicit boundary layer scheme
69
replaces Rayleigh damping as surface friction. This model is still highly ide-
70
alized because the water vapor content has no effect on the radiation budget
71
and the surface is parameterized as a mixed-layer slab ocean of constant heat
72
capacity with an albedo of 0.31. For our calculations we use 25 vertical levels
73
with the sigma coordinate spacing used by Frierson et al. (2006) and a spec-
74
tral dynamical core with triangular truncation at wavenumber 42 (i.e., T42,
75
which approximately corresponds to 2.8◦ horizontal resolution). We also fix the
76
boundary layer to a depth of 1 km with a constant surface gust of 5 m s−1 . Each
77
simulation is run for a 3000 day spin-up period to reach a statistically steady
78
state. We then use the following 1000 days of model runtime in our analysis.
79
The RCE state is reached by setting v · ∇T = v · ∇v = ∇p = 0 in the
80
primitive equations so that the advection of temperature and momentum, along
81
with the pressure gradient, are zero. The model is initialized with a constant
82
temperature of 264 K at all grid points, and no perturbation is introduced into
83
the system. The resulting steady state has no zonal or meridional wind and
84
is conceptually equivalent to applying a one-dimensional radiative convective
85
model to calculate a vertical temperature profile at every surface grid point. To
86
reach the 2D state, no terms in the primitive equations are suppressed, but we
87
still refrain from perturbing any zonally asymmetric motions in the model at
88
initialization. This yields a climate state with zonally symmetric steady flow but
89
no eddy fluxes. The final 3D climate state resembles an idealized Earth climate
90
and is reached by numerically perturbing the vorticity field at initialization to
91
induce the formation of asymmetric eddies.
92
Because radiative transfer strongly destabilizes the atmosphere to convec-
5
93
tion, some convective parametrization must be used in all simulations. In the
94
dry cases, we apply convective adjustment toward a dry adiabat (Manabe et al.,
95
1965). For our moist cases, we use a simplified penetrative adjustment scheme
96
(Betts and Miller, 1986), fully described by Frierson (2007). Penetrative adjust-
97
ment schemes relax to postconvective equilibrium vertical profiles, with temper-
98
atures that follow a moist adiabat from the surface and 80% relative humidity
99
with respect to the moist adiabat, with a specified relaxation time of 2 hours.
100
These profiles are then corrected to satisfy conservation of enthalpy, and shal-
101
low convection is performed if necessary (the “shallower” scheme described in
102
Frierson (2007) is used). We initially attempted to use a moist convective ad-
103
justment scheme as a counterpart to dry convective adjustment; however, moist
104
convective adjustment proved unsuitable in producing a stable moist RCE state
105
because the lack of meridional transport in RCE causes water vapor to accumu-
106
late in the tropical troposphere. As Emanuel (1994) points out, moist convective
107
adjustment applies only within an explicitly simulated cloud layer and does not
108
adequately stabilize a large-scale model. When we adjusted toward a moist adi-
109
abat in our cloud-free simulations, water vapor formed deep saturated columns
110
in the tropics leaving the midlatitudes and polar regions unsaturated. The
111
lack of an explicit cloud scheme made the tropical atmosphere too moist and
112
caused a numerical instability to develop. Nevertheless, a simplified penetra-
113
tive adjustment scheme adequately stabilizes a large-scale model even without
114
precipitation, which makes it a suitable choice for our moist simulations.
115
3
116
A summary of the RCE/2D/3D hierarchy is given in Figure 1, which shows
117
the zonal mean potential temperature θ for all three dynamical states, with
118
dry cases along the left column and moist cases on the right. Each panel also
Results and Discussion
6
119
includes a tropopause (dark curve) defined by the World Meteorological Organi-
120
zation (WMO) with a typical lapse rate of 2 K km−1 . Dry RCE is characterized
121
by a dry adiabatic lapse rate (dθ/dp = 0) in the troposphere, while the ad-
122
dition of advection in dry 2D allows for mixing by an overturning meridional
123
circulation. The corresponding moist cases fall nearly along moist adiabats in
124
the troposphere (not shown), and tropopause heights are generally higher than
125
the dry counterparts. When eddies are included in 3D, a more realistic Hadley
126
circulation and tropopause appears. Figure 2 shows the zonal mean merid-
127
ional mass streamfunction Ψ as line contours and the zonal mean zonal wind as
128
shaded contours for the 2D and 3D states. (The RCE states have no meridional
129
circulation and no zonal wind.) The contour interval for the mass streamfunc-
130
tion is 0.1Ψmax, where the maximum value of the mass streamfunction Ψmax is
131
given in the bottom left corner of each panel. Figure 2 also includes a dark line
132
showing the tropopause. Both 3D simulations feature a characteristic double jet
133
structure with the subtropical jet at the poleward edge of the direct cell and the
134
polar front jet near the top of the indirect cell. By constructing this piecewise
135
dynamical hierarchy, we can explore the effects of baroclinic eddies on the MMC
136
and tropopause structure.
137
3.1
138
We describe the MMC with a mass streamfunction Ψ that calculates the north-
139
ward mass flux above a particular pressure level p′ as
Mean Meridional Circulation
2πa cos φ
Ψ=
g
ˆ
p′
[v] dp,
(2)
0
140
where [v] is the zonal mean meridional wind, a is the radius of Earth, and g is
141
the gravitational acceleration. This streamfunction traces out the familiar pat-
142
terns of the MMC when applied to Earth models or time-averaged observations,
7
143
showing thermally direct (i.e., Hadley) and indirect (i.e. Ferrel) circulation cells.
144
In order to clarify our conceptual argument, we can also consider the response
145
streamfunction Ψ⋆ from a diagnostic equation for nonaxisymmetric flow:
LΨ⋆ = S + Se + F.
(3)
146
Here S is the meridional gradient of diabatic heating, Se is the change in diabatic
147
heating due to eddies, and F represents eddy fluxes. The linear operator L
148
(Kim and Lee, 2001) is not a fixed operator and can vary due to changes in
149
static stability. This diagnostic streamfunction Ψ⋆ differs from the computed
150
streamfunction Ψ in equation (2), although Kim and Lee (2001) find that Ψ⋆ ≈
151
Ψ under most conditions.
152
The strength of the MMC results in part from the direct influence of eddy
153
fluxes. Although our eddy-free 2D simulations show a prominent MMC, the
154
Hadley cell strengthens by about 35% when eddies are added in 3D. This inten-
155
sification can be attributed in part to the eddy forcing term F in equation (3)
156
(Kim and Lee, 2001; Walker and Schneider, 2006) that accounts for eddy heat
157
and momentum fluxes. It is also noteworthy that the addition of water vapor
158
to our 2D and 3D simulations decreases the MMC by over a factor of 4. This
159
decrease in circulation strength follows from the increase in dry static stability
160
(as can be inferred from the θ field in Figure 1) as water enters the climate and
161
tropical convection occurs.
162
Midlatitude eddies also contribute to the width of the Hadley circulation
163
by modifying the tropical temperature gradient. The dry 2D state shows a
164
prominent MMC that extends in width to about 15◦ latitude and can be likened
165
to the dry axisymmetric simulations of Held and Hou (1980). However, our
166
dry 2D Hadley cell is notably narrower and only compares in width near their
167
inviscid limit. This difference can be attributed to the complete absence of
8
168
eddies in our 2D dynamical state, whereas the implicit effect of eddies is included
169
in the the radiative relaxation profile ΘE in equation (1) used by Held and
170
171
Hou (1980). Following from the prediction by Held and Hou (1980) that the
dry Hadley cell width ∝ ∆H gH/Ω2 , where Ω is the angular rotation rate,
172
this difference in the Hadley cell width is consistent with a smaller meridional
173
temperature gradient ∆H in the tropics (φ < 30◦ ) for our dry 2D case. When
174
we induce the formation of asymmetric eddies in dry 3D, the direct circulation
175
expands to 20◦ latitude, while a weaker indirect cell appears at 35◦ latitude
176
where surface westerly winds are present. This expansion from dry 2D to dry
177
3D is consistent with an increase in ∆H at tropical latitudes, which corresponds
178
to the indirect effect of eddies Se in equation (3).
179
The presence of Se is also evident in our moist simulations. The 20◦ lati-
180
tudinal extent of our moist 2D circulation is consistent with the closed energy
181
budget calculations in figure 6 by Satoh (1994) that use convective adjustment.
182
Comparison with the MMC in figure 1 of Satoh (1994) is misleading, though, be-
183
cause these calculations prescribe fixed surface temperatures and may implicitly
184
include contributions from eddy fluxes. Because tropical surface temperatures
185
on Earth are modified by surface winds associated with the Hadley cell, fixed
186
temperatures based on observations may not approximate a true 2D state. In
187
our moist 3D calculation, the explicit inclusion of eddies generates an expanded
188
Hadley cell out to 25◦ latitude and an indirect Ferrel cell stretching from 30◦ to
189
50◦ latitude. As in the dry simulations, this expansion of the Hadley cell occurs
190
because eddies modify the temperature structure to increase ∆H in the tropics.
191
3.2
192
We contextualize our results within the theoretical framework developed by Held
193
(1982) that considers the height of the tropopause as a balance between radiative
Height of the Tropopause
9
194
and dynamical constraints. The radiative constraint R relates the tropopause
195
height to the tropospheric and stratospheric temperatures given that lapse rate
196
in the atmosphere is in dry convective equilibrium (Held, 1982). In dry RCE
197
where baroclinic eddy fluxes and moist convection are absent, the tropopause
198
height can be written in functional form as HdRCE = f (R). The addition of
199
moisture provides a dynamical constraint Dm to the tropopause height where
200
moist convection modifies the lapse rate (Held, 1982). This effect of water vapor
201
on the moist RCE tropopause gives HmRCE = f (R, Dm ) and is illustrated in
202
our calculations as HmRCE > HdRCE in the tropics and HmRCE ≈ HdRCE in
203
the drier air poleward of 50◦ latitude.
204
The structure of the moist 2D tropopause Hm2D is similar to HmRCE every-
205
where except at low latitudes, where the MMC increases the static stability and
206
raises Hm2D in the subtropics (15◦ < φ < 30◦ ). This tropopause lifting occurs
207
from the presence of the 2D overturning circulation and can be thought of as
208
an additional dynamical contribution DΨ so that Hm2D = f (R, Dm , DΨ ). The
209
effect of DΨ is most pronounced in the tropics where the MMC is strong, but the
210
midlatitude (30◦ < φ < 60◦ ) and polar (φ > 60◦ ) tropopause also rises slightly
211
so that Hm2D ≥ HmRCE for all φ. The contribution by DΨ is shown explicitly
212
in dry 2D where the tropopause Hd2D = f (R, DΨ ) and Hd2D > HdRCE in the
213
extratropics. A slight subtropical jump in Hd2D also appears as in moist 2D
214
but with Dm = 0, which shows that DΨ modifies a state of dry RCE when an
215
overturning circulation develops.
216
Held (1982) describes a final dynamical constraint De that accounts for mix-
217
ing by eddies as the midlatitude atmosphere becomes baroclinically unstable.
218
The effects of De are seen in moist 3D where eddy fluxes lower the tropopause
219
Hm3D near 30◦ latitude and raise Hm3D toward the poles, a behavior con-
220
sistent with the finding that baroclinic waves raise (lower) tropopause heights
10
221
in the poleward (equatorward) part of a baroclinic flow channel (Egger, 1995;
222
Dell’Aquila et al., 2007). Additionally, the increase in Hm3D near φ = 25◦ ap-
223
parently results from changes to DΨ as midlatitude eddy fluxes broaden and
224
intensify the MMC. These combined radiative and dynamical effects in moist
225
3D give Hm3D = f (R, Dm , DΨ , De ), where De represents the direct effect of
226
eddies and DΨ includes indirect eddy contributions to the MMC. At the equa-
227
tor, HmRCE ≈ Hm2D ≈ Hm3D because Dm constrains the tropopause height
228
and Ψ = 0 at φ = 0◦ , while the structure of Hm3D throughout the subtropics is
229
modified by eddies. If we assume that the atmosphere evolves from RCE to 2D
230
and from 2D to 3D, then the moist 3D subtropical jump in tropopause height is
231
constrained to first order by moist convection and modified by baroclinic eddy
232
fluxes.
233
Even though moist convection is absent, the dry 3D tropopause Hd3D =
234
f (R, DΨ , De ) still shows a subtropical jump similar to Hm3D . This jump arises
235
because Hd3D > Hd2D in the tropics, which results from the influence of eddies.
236
To understand this behavior, consider the structure of potential temperature in
237
the stratosphere. The tropical stratosphere in dry 2D is warmer than dry 3D,
238
which suggests that eddy fluxes are modifying the stratospheric temperature
239
profile. These changes may be realized through the residual meridional circula-
240
tion, also known as the Brewer-Dobson circulation (Holton et al., 1995). Similar
241
tropical stratospheric cooling also occurs in moist 3D, which suggests that this
242
subtropical jump could occur even without moist convection.
243
Contrary to the situation in moist 3D where the slope of Hm3D flattens at
244
extratropical latitudes (φ > 30◦ ), it is interesting to note that the slope of Hd3D
245
increases in the extratropics. This can also be understood by considering the
246
stratospheric potential temperature. In contrast to the tropical stratosphere, the
247
polar stratosphere in 3D is warmer than 2D in both dry and moist cases, which
11
248
is again consistent with the presence of the Brewer-Dobson circulation in the 3D
249
cases. Using a tracer gas model, Mahlman et al. (1986) find that the residual
250
circulation acts to steepen isolines in the tropical stratosphere while competing
251
against the flattening effect of eddy mixing in the extratropics, which causes
252
isolines to take on a shape similar to the 3D thermal tropopause. If the change
253
in stratospheric temperature exceeds the tropospheric cooling (warming) that
254
results from the poleward sensible heat flux, then tropopause heights will rise
255
(lower) at the subtropics (poles). By comparison, the moist simulations include
256
poleward fluxes of both sensible and latent heat so that cooling (warming) at
257
the subtropics (poles) is greater in the troposphere than in dry 3D, as evident in
258
the θ field of Figure 1. If we assume that the Brewer-Dobson circulation remains
259
constant between dry and moist simulations (because the stratospheric θ values
260
are almost identical), then the tropopause height in moist 3D will flatten from
261
dry 3D in the extratropics. In a future study, we will explore the extent to
262
which the Brewer-Dobson circulation modifies stratospheric temperature in dry
263
and moist 3D.
264
4
265
The suite of dry and moist calculations presented here help to illustrate the
266
significance of baroclinic eddy fluxes on the Hadley circulation and tropopause
267
structure. In both dry and moist cases, the presence of eddy fluxes is necessary
268
to produce a Hadley circulation with a latitudinal extent resembling that of
269
Earth. Dry and moist 2D cases produce narrower and weaker Hadley cells than
270
observed. All of these characteristics are consistent with the model of Held
271
and Hou (1980). However, these calculations illustrate that the Held and Hou
272
(1980) axisymmetric state implicitly includes the contribution of midlatitude
273
eddy fluxes because the model is forced by Newtonian relaxation toward a fixed
Conclusion
12
274
temperature profile based on observations. The contribution of eddies is to
275
modify the tropical temperature gradient, thereby affecting the width of the
276
Hadley cell. A true eddy-free 2D state can therefore only be achieved by relaxing
277
toward an eddy-free profile or by using radiative forcing that does not depend
278
on a fixed state, such as gray radiative transfer.
279
The structure of the tropopause can also be understood as an eddy-driven
280
phenomenon. When moist convection is absent in dry 3D, the subtropical jump
281
in tropopause height still appears as in moist 3D. This results from greater tropi-
282
cal cooling in the stratosphere than in the troposphere. Of course, moist convec-
283
tion does contribute to the tropopause structure on Earth, but moist convection
284
may not be the only process that determines the tropical tropopause. Our calcu-
285
lations also suggest that the slope of the extratropical tropopause is determined
286
by a competition between tropospheric eddy heat fluxes and the stratospheric
287
residual circulation, which acts to steepen the extratropical tropopause in dry
288
3D and lower it in moist 3D. Although our moist calculations indicate that moist
289
convection offers a first-order constraint on the tropopause height, our dry cal-
290
culations demonstrate that eddies alone can raise the subtropical tropopause
291
almost as much. It appears that while our atmosphere is thermally forced,
292
some of its most salient features are eddy-driven.
13
293
References
294
Becker, E., G. Schmitz, and R. Geprags (1997), The feedback of midlatitude
295
waves onto the Hadley cell in a simple general circulation model, Tellus A,
296
49(2), 182-199.
297
298
Betts, A. K., and M. J. Miller (1986), A new convective adjustment scheme. Part
299
I: Observational and theoretical basis, Quart. J. Roy. Meteor. Soc, 112(473),
300
677-692.
301
302
Caballero, R., R. T. Pierrehumbert, and J. L. Mitchell (2008), Axisymmetric,
303
nearly inviscid circulations in non-condensing radiative-convective atmospheres,
304
Quart. J. Roy. Meteor. Soc, 134(634), 1269-1286.
305
306
Dell’Aquila, A., P. M. Ruti, and A. Sutera (2007), Effects of the baroclinic
307
adjustment on the tropopause in the NCEP-NCAR reanalysis, Climate Dynam-
308
ics, 28(2), 325-332.
309
310
Egger, J. (1995), Tropopause height in baroclinic channel flow, J. Atmos. Sci,
311
52(12), 2232-2241.
312
313
Emanuel, K. A. (1994), Atmospheric Convection, Oxford University Press, New
314
York.
315
316
Frierson, D. M. W. (2007), The dynamics of idealized convection schemes and
317
their effect on the zonally averaged tropical circulation, J. Atmos. Sci, 64(6),
318
1959-1976.
319
14
320
Frierson, D. M. W., I. M. Held, and P. Zurita-Gotor (2006), A gray-radiation
321
aquaplanet moist GCM. Part I: Static stability and eddy scale, J. Atmos. Sci.,
322
63(10), 2548-2566.
323
324
Hadley, G. (1735), Concerning the cause of the general trade-winds, Phil. Trans.,
325
39, 58-62.
326
327
Haynes, P., J. Scinocca, and M. Creenslade (2001), Formation and mainte-
328
nance of the extratropical tropopause by baroclinic eddies, Geophys. Res. Lett.,
329
28(22), 4179-4182.
330
331
Held, I. M. (1982), On the height of the tropopause and the static stability
332
of the troposphere, J. Atmos. Sci., 39(2), 412-417.
333
334
Held, I. M., and A. Y. Hou (1980), Nonlinear axially symmetric circulations
335
in a nearly inviscid atmosphere, J. Atmos. Sci., 37(3), 515-533.
336
337
Held, I. M., and M. J. Suarez (1994), A Proposal for the intercomparison of
338
the dynamical cores of atmospheric general circulation models, Bull. Amer.
339
Meteor. Soc, 75(10), 1825-1830.
340
341
Holton, J. R., P. H. Haynes, M. E. McIntyre, A. R. Douglass, R. B. Rood,
342
and L. Pfister (1995), Stratosphere-troposphere exchange, Rev. Geophys, 33(4),
343
403-439.
344
345
Kim, H., and S. Lee (2001), Hadley cell dynamics in a primitive equation model.
346
Part II: Nonaxisymmetric flow, J. Atmos. Sci., 58(19), 2859-2871.
15
347
348
Mahlman, J. D., H. Levy II, and W. J. Moxim (1986), Three-Dimensional
349
Simulations of Stratospheric N2O: Predictions for Other Trace Constituents,
350
J. Geophys. Res., 91.
351
352
Manabe, S., J. Smarrgorinsky, and R. F. Strickler (1965), Simulated clima-
353
tology of a general circulation model with a hydrologic cycle, Mon. Wea. Rev.,
354
93(12), 769-798.
355
356
Pfeffer, R. L. (1981), Wave-mean flow interactions in the atmosphere, J. At-
357
mos. Sci., 38(7), 1340-1359.
358
359
Satoh, M. (1994), Hadley circulations in radiative–convective equilibrium in
360
an axially symmetric atmosphere, J. Atmos. Sci., 51(13), 1947-1968.
361
362
Schneider, E. K. (1977), Axially symmetric steady-state models of the basic
363
state for instability and climate studies. Part II. Nonlinear calculations, J. At-
364
mos. Sci., 34(2), 280-296.
365
366
Walker, C. C., and T. Schneider (2006), Eddy influences on Hadley circula-
367
tions: Simulations with an idealized GCM, J. Atmos. Sci., 63(12), 3333-3350.
16
368
Figure Captions
369
Figure 1. Zonal mean potential temperature for dry and moist RCE, 2D, and
370
3D cases with a contour interval of 10 K. The dark curve indicates the height
371
of the WMO tropopause.
372
373
Figure 2. Mean meridional circulation (line contours) in 109 kg s−1 and zonal
374
mean zonal wind (shaded contours) in m s−1 for dry and moist 2D and 3D
375
cases. The maximum streamfunction Ψmax is given in the lower left corner of
376
each panel. The contour interval for the MMC in each panel is 0.1Ψmax . The
377
dark curve indicates the WMO tropopause.
17
Figure 1. Zonal mean potential temperature for dry and moist RCE, 2D, and 3D cases with a contour
interval of 10 K. The dark curve indicates the height of the WMO tropopause.
Figure 2. Mean meridional circulation (line contours) in 109 k s-1 and zonal mean zonal
wind (shaded contours) in m s-1 for dry and moist 2D and 3D cases. The maximum streamfunction Ψmax is given in the lower left corner of each panel. The contour interval for the
MMC in each panel is 0.1Ψmax. The dark curve indicates the WMO tropopause.