December 1965
~ ~~~ ~ ~
S. Manabe, J. Smagorinsky, and R. F. Strickler 769
SIMULATEDCLIMATOLOGY OF A GENERALCIRCULATIONMODEL
WITH A HYDROLOGIC CYCLE
SYUKURO MANABE, JOSEPH SMAGORINSKY, AND ROBERT F. STRICKLER
Geophysical Fluid Dynamics Laboratory, Environmental Science Services Administration, Washington, D.C.
ABSTRACT
A numerical experiment with a general circulation model with a simple hydrologic cycle is performed. The basic
framework of this model is identical with that adopted for the previous study [35] except for the incorporation of a
simplified hydrologic cycle which consists of the advection of water vapor by large-scale motion, evaporation from t.he
surface, precipitation, and a n artificial adjustment to simulate the process of moist convection. This adjustment is
performed only when the relative humidity reaches 100 percent and the lapse rate exceeds the moist adiabatic lapse
rate. The radiative flux is computed for the climatological distribution of water vapor instead of using the distri-
bution calculated by the prognostic equation of water vapor. A completely wet surface without any heat capacity
is chosen as the.lower boundary. The initial conditions consist of a completely dry and isothermal atmosphere.
A state of quasi-equilibrium is obtained as a result of the time integration of 187 days. A preliminary analysis of
the result is performed for the 40-day period from 148th day to 187th day.
According to this analysis, the hemispheric mean of the rate of precipitation is about 1.06 m./yr. which is close
to the estimate of the annual mean rainfall obtained by Budyko [5]. I n t h e Tropics rainfall exceeds evaporation and
in the subtropics the latter exceeds the former in qualitative agreement with observation. The difference betwcen
thcm, however, is too exaggerated, and an extremcly large export of water vapor from the dry subtropics into the
wet Tropics by the meridional circulation takes place. I n t h e tropospherc, relative humidity increases with dc-
creasing altitude. In the stratosphere it is very low except at the tropical tropopause, and thc mixing ratio of water
vapor is extremcly small in qualitative agreement with observation. Although water vapor is transported from thc
troposphere into the stratosphere, i t is then transported toward low lntitudca and condenses at the tropical tropopause
where the temperature is very low and the relative humidity is high.
Bmed upon a harmonic analysis of the flowfield and the surface pressure field, i t is concluded that thc cffcct
of condensation tends to increase the wave number of the tropospheric flow and surfacc prcssurc field. Also, thc
incorporation of the moist process in the model seems to incrcasc the intcnsity of meridional circulation in the
Tropics. As a result of this increase, the transport of momentum and heat by the meridional circulation in the
Tropics is much larger than that obtained from the previous study. In middle latitudes, the poleward transport
of total cnergy in thc moist-model atmosphere is less than that in the dry-model atmosphere because of the
effect of the poleward transport of latent energy or the heat of condensation.
The latitudinal distributions of radiative fluxes at the top of the atmosphere and at the earth's surface coincide
very well with those obtained by London [17] for the actual atmosphere. Bowen's ratio increases with increasing
latitude and its magnitude coincides reasonably well with that obtained by Budyko [5] or Jacobs [I l l for thc ocean
surface.
CONTENTS 8. Synoptic Manifestation- -. - __ ___ - __ ___ _- - -- --- -- ---
Abstract ______ - ____ _~_ ___ __ __ __ __ __ __ ___ __ __ __ __ 769 9. Kinetic Energy Field-" ___ ____ - __ ___ -- -. - --- -- -- ---
1. Introduction - - - - - - - - - - - - - - 770 10. Moisture Balance- - - - - - - - - - - - - - - - - - - - - - - - . - - - - - - - - -
2. Model Equations- ___ .............................. 770 A. Hemispheric Moisture Balance ______ - _- -- - --- -- -
A. Prognostic Equations .......................... 770B. Latitudinal Distribution of Moisture Balance"---
B. Lower Boundary Conditions .................... 771 C. Latitude-Height Distribution of Moisture Balance-
C. Radiative Transfer ____ _____ __ ___ - __ __ - __~__ __ - 771 D. Moisture Balance of the Stratosphere ____.-----.-
3. Condensation and Convection- - - - - - - - -
A. Non-Convective Condensation ____ __ ___ __ __ ____ 771 771 11. Energy Budget of the Earth's Surface ____________----
B. Convective Adjustment ___" __ ______ __ - __ ___ __ - 772 12. Heat Balance- __ ..................................
c. Detailed Description of the Scheme- __ __ -~ ____ 772 A. Hemispheric Heat Balance _____.______.--------
4. Initial Conditions and Time Integration ______________ 773 B. Latitudinal Distribution of Heat Balance- - - - - - - -
5. Mean Temperature Field ............................ 774 C. Latitude-Hcight Distribution of Heat Balance--. -
6. Mean Flow Field- ................................ 775 13. Allgular Momentum Balance _________________-.---. -
7.. Mean Moisture Field ............................... 776 14. Concluding Remarks __________________----.----.-. -
Appendix-Non-Convective Condensation (Iterative Method) - -
I Results of this investigation were presented at the annual joint meeting of the Amer-
ican Meteorological Societyand the AmericanGeophysical Union, Washington, D.C., Acknow'edgment""""""""""""-~~"""""- '
April 1&22, 1965. References______________________________~-----.-------
779
782
785
785
785
786
787
789
790
790
790
792
794
795
797
797
797
1 . INTRODUCTION
Two of the major objectives of this numerical experi-
ment are the simulation of the hydrologic cycle and the
investigation of its role in the general circulation of the
atmosphere. The extensive studies of the water budget
of the earth-atmosphere system (e.g., Peixoto [27] and
Budyko [5]) and the careful measurements of stratospheric
and upper tropospheric water vapor (e.g., Murgatroyd
[21], Mastenbrook [19], and Houghton [lo]) enable us t o
compare the results of our model with the features of the
hydrologic cycle in the actual atmosphere and to discuss
some of the factors essential in maintaining the moisture
distribution in the atmosphere.
In the previous study [35], we performed the integration
of a model without the hydrologic cycle. The stabilizing
effect of moist convection, however, was incorporated in
the model, i.e., the lapse rate was adjusted to the moist
adiabatic lapse rate whenever it exceeded this lapse rate.
In the present study, the effects of evaporation, condensa-
tion, advection of water vapor, and moist convection are
incorporated in the model. The basic framework of this
model is identical to the previous model except for the
hydrologic cycle. Hereafter we shalI call the previous
model the “dry general circulation model’’ and the present
model the “moist general circulation model” for con-
venience of identification. By comparing these two
models, i t is possible to discuss the effects of the meridional
transport of latent energy and condensation on the general
circulation of the atmosphere.
The basic framework of predicting large-scale precipita-
tion was first proposed by Smagorinsky and Collins [31]
and by the staff members of Tokyo University [37]. In
these studies, the so-called geostrophic approximation was
adopted and the effect of heat released by condensation
on the large-scale flowfield and temperature fieldwas
neglected. Following these studies Smagorinsky [32] has
shown that an extremely large vertical motion emerges
and the scale of upward motion decreases as a result of the
decrease of effective static stability if one incorporates the
effect of heat of condensation. According to the results
of scale-analysis, such an intense vertical motion is in-
consistent with the basic assumptions used for the geo-
strophic approximation. (See, for example, the recent
comprehensive review by Phillips [28].) Also, the geo-
strophic model is not capable of representing the flow in
low latitudes, and it completely neglects the convergence
of water into the precipitation region by the ageostrophic
wind component near the earth’s surface. Therefore, it
is necessary to use the so-called “primitive equations” for
a moist model as proposed by Smagorinsky [33].
Recent numerical studies of convect,ion performed ,by
‘Lilly [lG], Kasahara [12], and Ogura and Charney [23]
have shown that because of convective instability, intense
grid-scale convection develops exponentially in the area
where the lapse rate is unstable. Since the grid-scale
convection cqnnot be resolved by the grid itself, the
7 70 MONTHLY WEATHER REVIEW Vol. 93, No. 12
computation quickly deteriorates. Therefore, it is desir-
able to design a scheme of convection such that the grid-
scale convection does not develop. In connection with the
problem of the genesis of hurricanes, Ooyama [25], Charney
and Eliassen [7], and Ogura [22] proposed a system which
successfully controlled the abnormal growth of hurricanes
by using a concept of “balanced wind” and by cutting
the direct link between vertical motion and condensation.
Recently Kuo [14] and Leith [15] proposed rather sophis-
ticated schemes of convection for studying a similar
problem. However, further observational as well as
theoretical studies of the macroscopic behavior of moist
convection seem necessary to reach a satisfactory scheme
for treating this process. In view of our ignorance in
this matter, we used a very simple scheme of convective
adjustment depending upon both relative humidity and
the lapse rate and successfully avoided the abnormal
growth of grid-scale convection. It is hoped that the
results obtained by using this simple scheme can provide
the basis for the computation of a more exact and better
scheme of convection.
In order to avoid a sudden increase in the degrees of
freedom of the model, the climatological distribution of
water vapor instead of the distribution obtained from the
prognostic equation of water vapor is adopted for the
computation of radiative transfer only. It is our inten-
tion to eliminate this constraint in a future study.
In order to understand the role of topography and that
of the distribution of land and sea, it is desirable to per-
form first a numerical integration of the model without
these factors and to realize the importance of the missing
factors by comparing the features of the model atmosphere
with those of the actual atmosphere. Therefore, we
adopted a completely wet and flat earth’s surface without
any heat capacity instead of adopting more realistic
boundary conditions. The temperature of the earth’s
surface is determined as the balance of various thermal
components such as long-wave radiation, solar radiation,
sensible heat flux, and evaporation.
The next natural research step following this study is the
numerical integration of a model with the actual dis-
tributions of land, sea, and mountains. I t is’ expected
that the inter-comparison among the results of the two
models and the features of the actual atmosphere will
greatly improve the understanding of the role of these
factors in the general circulation of the atmosphere.
I. MODELEQUATIONS
A. PROGNOSTICEQUATIONS
The prognostic equations for temperature and the
mixing ratio of water vapor on the stereographic projec-
tion are:
December 1965 S. Manabe, J. Srnagorinsky, and R. F. Strickler 771
in the
here.
r :
C:
pRA0:
q c :
P* :
t:
X :
Y:
U:
V:
T:
Q: Q:
w :
R:
C,:
K,:
KV:
P ,.
773 :
K .*
previous paper [35], we shall not describe them
Following are the notations used in the equations.
Mixing ratio of water vapor to dry air.
Rate of change of r due to condensation.
Rate of radiative heating.
Rate of heating due to condensation and con-
Surface pressure.
Time.
Abscissa of stereographic rectangular coordinate.
Ordinate of stereographic rectangular coordinate.
Wind velocity relative to the earth in X-direction.
Wind velocity relative to the earth in Y-direction.
Temperature.
PIP,, where P is pressure.
d &/at.
dP/dt.
Gas constant of air.
Specific heat of air under constant pressure.
Horizontal mixingcoefficient as defined by equa-
Vertical mixing coefficient as defined by equation
Density of air.
Magnification factor of stereographic projection,
Rlc,.
vection.
tion (2B8) in previous paper [35].
(2Bl1) in previous paper [35].
For further explanation refer to previous paper [35].
8. LOWERBOUNDARYCONDITIONS
The temperature of the earth's surface T* is determined
such that it satisfies the requirement of the heat balance at
the earth's surface. Because of the incorporation of the
effect of evaporation, the balance equation is different
from the previous study [35]. Therefore, we shall de-
scribe it here.
If we assume that the heat capacity of the earth is
zero, the balance equation of heat is
S*+(DLR)*=~T~,+(VH),=I+(VLH),=, (2.7)
where S* and (DLR)* are the net downward solar inso-
lhtion and the downward long-wave radiation at the
earth's surface, respectively; u is the Stefan-Boltzman
constant. The sensible heat flux at the earth's surface
(V r n Q =1 is
(~H),,~=~(~).c,.QD(~).IV(~)I. (2.8)
The flux of latent energy (VLH)Q,l at the earth's surface is
(vLH),=,=p(h).L.QD(h).IV(h)l.(r,(T,)--r(h)) (2.9)
where the earth's surface is assumed to be wet every-
where, L is the latent heat of evaporation, r,(T*) is the
saturation mixing ratio of water at T*, (V(h) I is the mag-
nitude of wind velocity at height h, QD(h) is the drag
coefficient for the wind velocity at height h, Q(h) is the
Q-value at height h, and T*- T(h)/&l(h) is the approxi-
mate difference between the potential temperature of the
earth's surface and that at height h. For further illustra-
tions, refer t o previous paper [35].
C. RADIATIVETRANSFER
The methods of calculating the temperature change in
this study are described in detail by Manabe and Strickler
[18]. A brief description of the scheme is also given in the
previous paper. The distributions of gaseous absorbers
and cloud used in this study are identical with those used
in the previous work [35]. As we explained in the intro-
duction, we do not use the distribution of water vapor,
which is obtained from the prognostic equation of water
vapor, for the computation of radiative transfer. In-
stead, we use the climatological distribution of water
vapor as wellas that of carbon dioxide, and of ozone.
In short, we eliminate some part of the interaction be-
tween the hydrologic cycle and the radiative transfer.
By avoiding a sudden increase in the degrees of freedom
of the model this way, it is possible t o compa.re the present
result with the previous result [35] and t o discuss the
reasons for the differences.
3. CONDENSATION AND CONVECTION
A. NON-CONVECTIVECONDENSATION
The rate of non-convective precipitation is computed
a. If, and only if, the relative humidity reaches 1, i.e.
b. Relative humidity never exceeds 1, i.e., 100 percent.
c. The liquid water storage capacity of the atmosphere
is zero, and all the water vapor which is condensed pre-
cipitates instantaneously.
using the following assumptions.
100 percent, condensation may take place.
772 MONTHLY Vol. 93, No. 12
The amount of precipitation for each time step is a. When the lapse rate of an unsaturated layer tends to
determined so that the requirements described above are exceed the dry adiabatic lapse rate, the intensity of free
satisfied, including the release of latent heat. convection is strong enough to maintain a neutral lapse
b. The kinetic energy created by convection is dis- .B. CONVECTIVE ADJUSTMENT
rate of potential temperahre.
Two important processes which play a major role in the
general circulation of the atmosphere are the moist and
dry convection. Unfort?unately, we know very little about
the dynamical and thermodynamical aspects of the macro-
scopic behavior of moist convection. Our ignorance on
this subject does not seem to warrant the incorporation
of a very sophisticated scheme of the convective process
a.t this stage of the study of the general circulation by use
of a numerical model. Therefore, weused a simple con-
vective adjustment of temperature and water vapor as a
substitute for the actual convective process.
If one uses this scheme, moist convective condensation
takes place only when the lapse rate tends to become
super-moist-adiabatic and the relative humidity tends to
exceed 100 percent. It isweii known, however, that
convective rainfall takes place even when the large-scale
humidity is below 100 percent. Therefore, i t is obvious
that the simple adjustment process which we used here is
insufficient for simulating the macroscopic behavior of
convection in the actual atmosphere. Also, the upward
transport of momentum due to free convection, which
may not be negligible a t all, is neglected because of our
ignorance in this matter. This adjustment scheme,
however, not only prevents the abnormal growth of grid-
scale convection discussed in the introduction but also
simulates some of the essential features of free convection
in the atmosphere, Le., 1. i t prevents the appearance of
a supercritical lapse rate, and 2. as a result. i t transfers
effectively both heat and water vapor upward and causes
condensation.
We shall list the basic assumptions involved in the
(1) Dry Convective Adjustment.-The basic assumptions
process of convective adjustment.
used for the dry convective adjustment are as follows:
sipated and converted into heat, instantaneously, i.e.,
the total potential energy is invariant by this adjustment.
c. The adjustment is not applied to the logarithmic
boundary layer where forced convection predominates.
(2) Moist Convective Adjustment.-The assumptions
adopted are:
a. When the lapse rate of a saturated area tends to
exceed the moist adiabatic lapse rate, the intensity of free
convection is strong enough to maintain a neutral lapse
rate of the equivalent potential temperature.
b. The relative humidity never exceeds 1 by this
moist convective process.
c. The kinetic energy of very-small-scale eddies created
by this convection is dissipated instantaneously and
converted into heat energy.
d. All the water condensed by this moist convective
process precipitates instantaneously.
The rate of convective precipitation is determined as
the consequence of satisfying all the requirements men-
tioned above.
C. DETAILED DESCRIPTION OF THE SCHEME
The actual computations of the amount of precipitation
and the convective adjustments are performed in the
following way.
(1) Compute the changes of temperature and the
mixing ratio of water vapor for one time increment, At,
neglecting the effect of condensation.
(2) Compute the distributions of relative humidity, h,
and the lapse rate o€ temperature of the atmosphere
obtained as a result of these changes.
(3) Test the relative humidity, h, and the lapse rate,
y , in the vertical column a t each grid point. The adjust-
ment to be performed as a result of the test is indicated in
table 3C.
TABLE 3C.-Test for convective adjustment
No condensation, no convection
6 T=O 6r=0
(No adjustment)
Large-scale condensation only
dr, 6 T from r+6r=rs(T+6T, P ) (3.3)
c,QT+Ldr=O (3.4)
I
Dry convection only 1 Moist convection and large-scale condensation
I 6r=0 I I I e.(T+6T, r+dr, P)=O (3.5)
') 1 1 -g >y , 1 6r,GTfrom (3.6)
ym-moist adiabatic lapse rate. y s d r y adiabatic lapse rate.
6r-adjustment of t h e m i x i n g r a t i o of w a t e r v a p o r . h-relative humidity.
Pr, P s p r e s s u r e a t top and base of a dry or moist unstable layer containing two or more y-acceleration of gravity. 6T"adjustment of t h e t e m p e r a t u r e . r .-s a t u r a t
e.-equivalent-potential temperature @"potential temperature.
contiguous levels of the model.
~ ~~
December 1965 S. Manabe, J. Srnagorinsky, and R . F. Strickler 773
Further details of each adjustment are as follows.
a. Largescalecondensationonly.-At each saturated
level, 6r and 6T of table 3C are determined from equations
(3.3) and (3.4) using an iteration procedure (refer to the
Appendix for details). The amount of precipitation for
the entire column is computed from
b, Dry convection only.-For each dry unstable layer con-
taining n contiguous levels of the model, 6T of table 3C
can be computed a t each level by solving the n-1 equa-
tions (3.1) simultaneously with equation (3.2).
e. Moist convection and large-scalecondensation.-For
each moist unstable layer containing n contiguous levels
of the model, 6r and 6T of table 3C can be computed a t
each level by solving the n- 1 equations (3.5) simultane-
ously with the n equations (3.6) and with equation (3.7).
It is assumed that the moist adiabatic lapse rate and the
value of br,/bT at each level are unchanged by the adjust-
ment. The procedure described in a., above, is then
applied to the unadjusted levels. The total precipitation
for the column can then be computed from equation (3.8).
4. INITIALCONDITIONSANDTIMEINTEGRATION
The initial condition adopted for the present numerica
experiment is a completely calm, dry, and isothermal
atmosphere of 289' K. As we explained in the introduc-
tion, the annual mean distribution of water vapor instead
of the distribution predicted by the equation of the mixing
ratio of water is used for the computation of radiative
transfer. The total period of integration is 187 days. In
order to save computer time, the integration during the
first 50 days was performed by a drastically coarse grid,
(N=5). N is the number of grid intervals between the
pole and equator. During the next 20 days the resolu-
tion of N= 10 was adopted. After 70 days the integration
was performed by use of an (N=20) grid.
Figure 4.1 shows the time variation of both the total
potential energy and the gross static stability (refer to
Appendix I1 of previous paper) with time. The former
describes the mean temperature of the atmosphere and the
latter is the indicator of the static stability of the atmos-
phere. The discontinuities of the curves a t 50 days are
caused by the sudden change of resolution from (N=5)
grid to (N= 10) grid. According to this figure the gross
thermal structure approached a steady state at the end
of the time integration. In figure 4.2 the evolution of
the vertical distribution of temperature at 45' N. with
time is shown. In the troposphere and upper stratosphere,
where the absorption of solar radiation or heating by
convection are important, the time for arriving at
equilibrium is relatively short; whereas in the lower
stratosphere, where both the effects of solar absorption
and convection are smaller, it takes a very long time
before we reach a state of equilibrium.
FIGURE 4.1.-Variation of total potential energy and gross static
stability with time.
MB
10-
100-
300
500-
700.
850-
30
20
15
10
5
FIGURE 4.2,"Variation of the vertical distribution of temperature
of the model atmosphere with time at 45" latitude.
774 MONTHLY Vol. 93, No. 12
LPRECIPITABLE WATER
.,A/ \ ?PRECIPITATION
FIGURE 4.3.-Variation of the hemispheric mean of precipitable
water and hemispheric rates of precipitation and evaporation
with time.
Figure 4.3 shows the time variations of the hemispheric
mean value of precipitable water. In the same figure the
daily values of precipitation and evaporation are plotted
with time. It is rather surprising that the precipitable
water reached its maximum at about 40 days and started
declining again. This result may be due to the fact that
the atmosphere a t 40 days can- contain more water than
in later days of integration because the temperature of the
former is significantly higher than that of the latter. This
curve of precipitable water almost levels off at about 150
days.
An examination of figures 4.1, 4.2, and 4.3 indicates that
we reached a state sufficiently close to equilibrium except
in the stratosphere where temperature still changed slowly
with time. Therefore, we chose the last 40-day period
(from 148th day to 187th day) for our analysis. The data
are analyzed once a day and the results are averaged for
this 40-day period.
5. MEAN TEMPERATUREFIELD
In figure 5.1 the latitude-height distributions of tem-
perature that are obtained from our time integration
are compared with that of the annual mean of the tem-
perature of the actual atmosphere. In figure 5.3 a
comparison is also made on the adiabatic diagram.
According to these figures the agreement between the
computed temperature and the observed annual mean is
excellent. Since the thermal structure obtained from the
dry general circulation model is also very similar to the
observed distribution and discussed in the preceding
paper 1351, i t may be preferable to discuss the present
results in contrast with the previous results. In the lower
half of figure 5.3 the latitudinal distributions of zonal
mean temperatue a t the 500-mb. level that are obtained
from both the dry and moist general circulation models
are compared with the observed annual mean. According
to this figure, the temperature gradient in middle latitude
is smaller in the present results than in the previous
results. This improvement in the temperature gradient
is due to a modification in the distribution of heat sources
I /
"_ v \
U
FIGURE 5.1.-1n the upper and lower part, the latitude-height
distribution of temperature of the model atmosphere and that of
the acutal atmosphere (Peixoto [26], Oort [24], and Kochanski [13]),
are shown respectively.
resulting from t,he latitudinal transport of latent energy
or the condensation process. For a detailed description of
the distribution of heat of condensation refer to section 12.
The latitudinal distributions of temperature a t level 2,
(PIP, =0.074), obtained from the dry and moist general
circulation models, are compared with the annual mean
of the stratospheric temperature at the 75-mb. level in the
upper half of figure 5.3. The increase of temperature
with increasing latitude is larger and more realistic in
the present results than in the previous results. As we
discussed in the previous paper, a two-cell meridional
circulation predominates in our model stratosphere. The
tropical cell helps maintain the latitudinal increase of
temperature inlow latitudes, whereas the polar cell
tends to destroy the relatively warm area created
by the large-scale eddies in high latitudes. Accord-
ing to the comparison between the distributions of the
zonal mean of vertical motion of the moist and dry general
circulation models, the intensity of the polar cell at the
second stratospheric level is much weaker for the moist
December 1965 S. Manabe, J . Smagorinsky, and R. F. Strirkler 775
30 MB
10-
25
20
l5 1
1 C G
- I Y
- b I
W P
40 I
300-
500.
.5
700-
TEMPERATURE (DEGREES KELVIN)
KM
30
20
10
0
model than for the dry model, and the tropical cell in the
stratosphere of the moist model is almost as strong as that
of the dry model. (Refer to figure 6.3 of this paper and
figure 4B2 of previous paper.)
Therefore, the increase of stratospheric temperature with
increasing latitude is somewhat larger for the moist model
atmosphere than for the dry model atmosphere. The
temperature change due to the heat transport by the large-
scale eddies tends to decrease the latitudinal increase of
stratospheric temperature inlow latitudes (O'~35') as
figure 5D6 of the previous paper [35] shows. This
tendency is less pronounced in the moist model atmos-
phere than in the dry model atmosphere (see fig. 5D3
of previous paper and fig. 12C4 in sec. 12). This differrnce
is partly responsible for the difference in the latitudinal
increase of stratospheric temperature in the low latitudes.
For a definitive evaluation of the effect of condensation
on. the distribution of stratospheric temperature, it seems
to be necessary to wait until a quantitatively successful
simulation of the tropospheric hydrologic cycle is
accomplished.
6. MEAN FLOW FIELD
Figure 6.1 shows the latitude-height distribution of the
zonal mean of the zonal wind which emerged as a result
of the time integration. I n t h e same figure the dis-
tribution of the annual mean of zonal wind based upon
data by Buch [4], Starr and White [38], and Oort [24], and
the distributions of zonal wind during winter and summer
obtained by Kochanski [131 are shown for comparison.
The characteristic features of the present results are as
follows:
(1) The subtropical jet stream is very intense and is
located in very low latitudes (25' N.).
(2) In the stratosphere, the axis of the maximum zonal
current tilts sharply, i.e., the latitude of maximum wind
increases with increasing altitude.
(3) A very weak easterly current appears in the upper
stratosphere of the Tropics.
(4) A surface easterly current appears at about 60' N.
instead of in the polar region.
The general features of our results are closer to those of
7 76 MONTHLY WEATHER Vol. 93, No. 12
~
500 11 TLYPERATURE
210'
FIGURE 5.3-The latitudinal distribution of observed annual mean
temperature and computed temperature at different levels of the
atmosphere. The observed distributions at the 74-mb. a n d a t
the 500-mb. levels are obtained from the results of Kochanski
[13] and Peivoto [26] respectively.
the zonal wind during winter than to those of the annual
mean, though the modes of the computed distribution
deviate to the south of those of the actual winter
atmosphere.
In figure 6.2 the latitudinal distributions of the zonal
mean of the zonal wind at the stratosphere (level Ic=2,
P/P+=O.O74) which are obtained from both the dry
and moist, general circulation models, are compared with
the annual mean distribution of the actual atmosphere at
the 75-mb. level. In middle latitudes the intensity of zonal
wind obtained from our present computation is signifi-
cantly weaker than that which is obtained from the dry
general circulation model. This improvement is con-
sistent with the improvement of the temperature gradient
in middle latitudes that we discussed in section 5.
Figure 6.3 shows the latitude-height distribution of
zonal mean vertical velocity. According to our compari-
son between the present distribution and the resuIts
obtained from the integration of the dry model, the fol-
lowing features of the present results are noteworthy.
(1) The upward-mc;ving branch of the tropical cell is
very intense and narrow, and t,he downward-moving
branch in the subtropics is wide.
(2) The intensity of the cell in middle latitudes is
weaker than in the previous result.
The effects of the process of condensation on the merid-
ional circulation described above seem to be reasonable
qualitatively, but they may be exaggerated. This power-
ful tropical cell causes a large equatonvard transport of
latent energy and accordingly a very drastic tropical
rain belt, as we shall describe later. Because of the
complexity of the model, it is rather difficult to determine
the reason such an intense meridional circulation emerges.
We shall speculate on this problem later.
7. MEAN MOISTURE FIELD
Figure 7.1 shows the vertical distribution of the hemi-
spheric mean of the mixing ratio of water vapor obtained
as a result of integration. Based upon the data compiled
by Peixoto [27] by using radiosonde measurements, the
hemispheric mean values for the lower troposphere a.re
computed and plotted in the same figure. For the upper
troposphere the average mixing ratios for the latitude
range of 0"-70"N. are computed from the results obtained
by Murgatroyd [21] from aircraft measurements, and are
added to the same figure. There have been many results
which suggest the increase of water vapor with increasing
altitude in the stratosphere. After a careful examination
of his results, Mastenbrook [19] finally concluded that
the increase is due to contamination from the balloon
itself and that the stratosphere is very dry indeed. Two
of his measurements are added to the figure after slight
smoothing of his original data. The recent measure-
ments performed by Houghton [lo] using the infrared
spectrometer also suggest the existence of a dry strato-
sphere. According to this comparison, the computed
results are in reasonable agreement both in the tropo-
sphere and in the stratosphere. The formation of a dry
st*ratosphere in our model is very encouraging. We shall
examine the stratospheric water budget in section 10.
In the upper troposphere the coincidence between our
results and the distribution of the area mean of the mixing
ratio obtained by Murgatroyd is remarkable. Near the
earth's surface the computed mixing ratio is significantly
larger than the observed partly because of the assumption
of a completely wet surface. As a result of this dis-
crepancy the computed amount of precipitable wat'er is
significantly larger than the observed amount. As figure
7.2 shows, ,the computed precipitable water is as large as
the observed precipitable water for summer although the
general features of the computed latitudinal distribution
compare favorably with the observed except i n t h e
Tropics where the computed values sharply increase with
decreasing latitude.
The latitude-height distribution of relative humidity
obtained from our computation and that of the actual
atmosphere for the summer season are shown in the upper
/
December 1965 S. Manabe, J. Smagorinsky, and R. F. Strickler 777
UTITUDE LATITUDE
FIGURE 6.1.-Latitude-height distribution of the zonal mean of thc zonal mind. The cornputcd distribution and the observed annual
mean, which is obtained from the results of Buch [4], Oort [24], are shown in the upper left and lower left, respectively. The distri-
butions a t 80" W. obtained by Kochanski [13] for both January and .July are shown on the right-hand side of the figure.
40 - ,fc-""
/ I /
30 -
J .074 t
s
Y
c 3
20 - LI
,189
Y
I
10
,336
300
,664
1 I I I I I I I ,811
80 70 60 50 40 30 20 10 0 ,926 .991 0
90
LATITUDE
90 80 70' 60 50 40 30 20 10 0
FIGURE 6.2.-Latitudinal distribut,ion of the zonal mean of thc LATITUDE
zonal wind at the 2d model level (P/P*=0.074) are shown
together with that at the 75-mb. level of the actual atmosphere FIGURE 6.3.-The latitude-height distribution of vertical component
o b t a i n e d f r o m t h e r e s u l t s of Oort [24]. of wind of the model atmosphere. Units are cm./sec.
778 MONTHLY WEATHER Vol. 93, No. 12
COMPUTED
sh\
(PEIXOTO) WINTER>\
I
I
1 s
E i? Y
lod 10-5 loJ 10~3 IO-* 10-1
FIGURE 7.1.-The vertical distributions of the hemispheric mean of
the mixing ratio of water vapor for the computed and the actual
atmosphere. Data obtained by Mastenbrook [19], Murgatroyd
[21] and Peixoto [27] are used.
"
MIXING RATIO br/p OF AIR)
LATITUDE
FIGURE 7.2.-Latitudinal distributions of precipitable water (cm.)
contained in the model atmosphere and in the actual atmosphere.
Observed distributions for summer, winter, and the annual mean
are taken from the results of Peixoto [27].
and lower parts of figure 7.3, respectively. The distri-
bution of observed relative humidity in the lower tropo-
sphere was compiled by Telegadas and London [39] using
radiosonde observations, and that in the upper tropo-
sphere was constructed by Murgatroyd [21] using aircraft
observations. The reason we show the observed distri-
bution for summer is that this is the only season For which
LATITUOE
15KM
10KM
9
I
5KM
&N 7PN 6(PN 5W'N WN 3PN 2OON lOON
UTIIUDE
FIGURE 7.3.-1n the upper part of the figure, the latitude-height
distribution of relative humidity (in percent) of the model atmos-
phere is shown. I n t h e lower part is shown that of the actual
atmosphere for summer season (by Murgatroyd [21], Telegadas
and London [39]).
we have the relative humidity data of Murgatroyd [21].
There are many qualitative features which are common to
both the computed and observed atmospheres. For
example, the very dry stratosphere, the wet lower tropo-
sphere, and the dry subtropics are common. In the upper
troposphere in the Tropics, a relatively moist region emerges
in qualitative agreement with the observation by Murga-
troyd [all. This moist region is partly attributable to
stronger radiative cooling at this level. Since the data
compiled by Murgatroyd are based upon relatively few
observations (except those performed over England),
an exact quantitative compa.rison for the upper tropo-
spheric region is not justified. The distributions obtained
by Telegadas and London [39], on the other hand were
compiled from many routine radiosonde observations.
According to our comparison, the relative humidity near
the earth's surface obtained from our computation is
higher than that of the actual atmosphere. As we pointed
out, this discrepancy is partly due to the assumption of a
wet surface adopted For the present computation. How-
ever, there may be other reasons for this difference because
December 1965 S. Manabe, j. Smagorinsky, and R. F. Strickler 779
90 80 70 60 50 40 30 20 10 0
LATITUDE
FIGURE 7.4.-The latitude-height distribution of the mixing ratio
of water vapor in the model atmosphere. Units are gm./kg.
of air.
the computed humidity is about 95 percent and higher
than the mean relative humidity on the ocean surface
which is about 80 percent.
One possible reason is the shortcoming of the moist-
convective adjustment. According to the present scheme,
moist convection takes place only when the lapse rate
becomes superadiabatic and the relative humidity reaches
100 percent, whereas in t,he actual atmosphere, moist
convective condensation is usually observed when the
large-scale distribution of humidity is much less than 100
percent. Therefore, it is probable that the improvement
of the criterion for the convective adjustment would
increase the upward transport of water vapor due to the
adjustment and, accordingly, improve the distribution of
relative humidity in the model atmosphere.
Another discrepancy is the appearance of a very humid
region around the pole. This is caused by the upward
branch of meridional circulation in the polar regiou where
downward motion appears in the actual atmosphere.
Also, the latitude of the subtropical dry belt obtained
from our model is too low. Refer to figure 1OBl which
shows the latitudinal distribution of evaporation and that
of precipitation. According to this figure the latitudinal
width of the tropical rain belt is very small and con-
sequently the dry belt is also located at too low a latitude.
Finally, the latitude-height distribution of the mixing
ratio of air obtained as a result of the numerical inte-
gration is shown in figure 7.4. Aswe mentioned,
the mixing ratio is very small in the stratosphere. The
mixing ratio of the tropical tropopause is about 3 X
gm./gm. of air and increases with increasing latitude up
to 60' N. In high latitudes, the mixing ratio in the
stratosphere (k=2, P/P*=O.O74) is about 7?(10"j
gm./gm. of ail. These values are not far from those
obhined by Mastenbrook [19], Murgatroyd [21], and
Houghton [IO] in this region of the actual atmosphere.
P 9, "H = .500
%
FIGURE 8.1-Solid lines show the contour lines of the geopotential
and dashed lines show those of the temperature on the iso-
baric surface of P/z" =0.5. (175th day of integration.)
In the upper stratosphere the computed mixing ratio is
0.7-2.0X10-6 gm./gm. of air and is very dry.
8. SYNOPTICMANIFESTATION
In figure 8.1 an example of the map of the geopotential
height and temperature of the 500-mb. surface is shown,
and in figure 8.2 the map of surface pressure obta,ined
from the present experiment is compared with that ob-
tained from the dry general circulation model. According
to this figure, the scale of the pressure field obtained from
t,he moist general circulation model is significantly
smaller than that obtained from the dry general circulation
model. In other words, the heat of condensation tends to
decrease the scale of the pressure field at the earth's
surface and to increase the total number of Lows in the
hemisphere. Note the clusters of small Lows that appear
in figure 8.2. They remind us of a cyclone family in the
actual atmosphere. An increase of resolution of the
model seems to be highly desirable to resolve and describe
sufficiently the pressure distribution accompanying the
cyclone family or front.
Figure 8.3 shows the vertical distributions of the hemi-
spheric mean of the effective wave number ;ii which is
defined by the following equation
E= (Sn.dE(n))/SdE(n)
where E(n) denotes the energy spectrum. In the samc
figure, the corresponding distributions obtained from thc
dry model are shown.
780 MONTHLYWEATHERREVIEW Vol. 93, No. 12
DRY G. C. MODEL MOIST G.C. MODEL
FIGURE 8.2-Contour lines of surface pressure obtained from the moist general circulation model (175th day) and those obtained from
the dry general circulation model (259th day) are shown in the right- and left-hand side of the figure (every 5 mb.) respectively.
Dashed lines show the isotherms on the earth's surface (every 5' C.).
EFFECTIVE WAVE NUMBER - 3 4 5 6 7 8 V
.zoo -
.m -
I .wo J
FIGURE 8.3.-The vertical distributions of the hem'sphsric mean
of the effective wave number of eddies for both dry and moist
general circulation models. The distributions of the meridional
component of wind, of zonal component of wind, and of both
components are shown together.
-
6000.
E =
FE 5000- W
a W 2
4000 -
5 = 3000-
2
E 2000-
W
V
Y w
Y
W
1wo -
I I I I 1 I I I
80 70 m 50 40 30 20 10
LATITUDE
According to this comparison the wave number of the
moist model is significantly larger than that of the dry
model and increases with decreasing altitude in t,he
troposphere except very near the earth's surface. The
level of ma-dmum wave number is very close to t,he
earth's surface and is a t about the 900-mb. level. Since
the latitudinal distribution of eddy kinetic energy in the
moist model atmosphere is much larger than that of t'he
dry model atmosphere in the Tropics where the wave
number is large (see fig.. 9.3). the comDarison between the
FIGURE 8.4.-Latitudinal distributions of the pressure-weighted
vertical mean of the effective wavelength (2ra cos e/;, where e is
latitude and a the radius of the earth) for both the moist and
the dry atmosphere.
hemispheric mean wave numbers exaggerates the differ-
ence. Therefore, figure 8.4, which shows the latitudinal
distributions of the effective wavelength (=27ra cosO/Z)
for both the moist and dry model atmospheres, is made.
According to this figure the effective wavelength of the
moist atmosphere is shorter than that of the dry a-tmos-
DhereexceDt in the subtroDics and verv high latitudes v . Y I , I .I _
December 1965 S. Manabe, 1. Smagorinsky, and R. F. Strickler 781
SCALE: 4 MB/DAY
I -,, = ,034 P -
%
SCALE: 100 MB/DAY r P 5 = .126
!k
SCALE: 100 MB/DAY l- 5 = .259 !i
SCALE: 100 MB/DAY ' '
r T., - .583
"
'f
where the rate of condensation is very small. These
results show that the heat released by condensation
tends to produce small-scale motions, and is consistent
with the effect of condensation on the surface pressure
system which we described in the previous paragraph.
Figure 8.5 shows the maps of the distribution of the
vertical P-velocity (=P*.$) at P/P~=0.034,0.126,0.259,
and 0.583 at the 175th day of integration. Note that the
intervals of the isolines adopted for these maps are not the
same. According to the comparison between the distri-
bution of vertical P-velocityat P/P,=O.583 in this figure
and that of the previous study [35] (see fig. 8.5a), the
tropospheric vertical P-velocity obtained from the moist
model has much stronger and smaller centers of upward
motion in lower latitudes than does the dry model. In
middle latitudes, the difference is not so pronounced.
Figure 8.6 shows examples of the longitudinal distribution
of vertical P-velocity at 41.5" N. for both the moist and
782 MONTHLY WEATHER Vol. 9 3 , No. 12
- .583 SCALE: lOOMB/DAY P -
p*"
FIGURE 8.5a.-Isolines of vertical P-velocity (P*Q.) a t P/P* =0.583
which is transferred from figure 4C5 of previous paper [35].
dry atmospheres. This figure shows that the scale of
vertical motion obtained from the moist model issome-
what smaller than that of the dry model because of the
effect of heat released by condensation.
Figure 8.7 shows the map of relative humidity at PIP, =
0.074,0.811,0.926, and 0.991on the 175th day. Aswe
discussed in section 7, the computed relative humidity
generally increases with decreasing altitude. The vari-
ability of the tropospheric relative humidity, on the other
hand, increases with increasing altitude. The qualitative
features of this result coincide with the observed features
of relative humidity in the atmosphere, particularly over
the ocean. The relative humidity of the lowest level
(k=9, PIP, =0.991), however, is too high. In the second
stratospheric level, (k=2, PIP* = 0.074) , the relative hu-
midity is low in most of the hemisphere, but in the Tropics
it has a large variability suggesting the influence of pene-
trative convection to this level. We did not prepare a
map for the first stratospheric level (k=1, PIP* =0.009).
At this level the relative humidity is around 1 percent or
less. (See fig. 7.3.)
Since the scale of the pattern of relative humidity and
that of vertical motion in the troposphere are very small,
it is clear that the resolution adopted for our present cal-
culation is not sufficient. The increase of resolution,
therefore, could alter our result significantly.
0" 90' 180" 270" 360" 0" 90" 180" 270" 360"
LOWGITUOE LOMGITUOE
FIQURE 8.6.-Longitudinal distributions of vertical P-velocity at
various levels. Distributions on the 259th day in the dry atmos-
phere and those on the 175th day in the moist atmosphere are
shown on the left- and the right-hand side of the figure, respectively.
9. KINETICENERGYFIELD
Figure 9.1 shows the time variation of the latitudinal
distribution of zonal kinetic energy obtained from the
time integration. The maximum of the zonal kinetic
energy corresponding to the subtropical jet stream is very
large and is located a t too low a latitude (refer to fig. 6.1).
It is noteworthy that a secondary maximum of the zonal
kinetic energy appears at about 60" N. during a certain
period. This feature did not appear in the dry model
atmosphere (see fig. 4E4 of the previous paper [35]) and
reminds us of the double maximum of zonal current which
occurs in the actual atmosphere during certain periods of
winter.
The latitude-height distribution of eddy kinetic energy
obtained from the present computation is shown in figure
9.2. The level of maximum eddy kinetic energy is located
at the third model level (PlP*=O.189) as it was in the pre-
vious result and coincides with the level of the observed
maximum. This distribution, however, is quite different
from that obtained from the previous study [35]. In
figure 9.3, the latitudinal distributions of eddy kinetic
energy of both the dry and the moist general circulation
models at the 500-mb. level are compared with that of the
actual atmosphere obtained by Saltzman [30]. Based
upon this figure we may make the following comments:
1. Observed eddy kinetic energy in middle latitudes is
larger than the eddy kinetic energy obtained from either
the dry or moist model.
2 . The eddy kinetic energy in middle latitudes is smaller
for the present results than for the previous results.
December 1965 S. Manabe, 1. Smagorinsky, and R. F. Strickler 783
FIGURE 8.7.-The map distributions of the relative humidity on 175th day a t P/P*=O.O74, 0.811, 0.926 and 0.991. Dark shade, 80-100
percent; medium shade, 20-80 percent; blank area, 0-20 percent.
3. The distribution of the eddy kinetic energy obtained
from the present moist general circulation model has two
maxima; one in the middle latitudes, and the other in the
Tropics.
There are various possible reasons why in the middle
and high latitudes the eddy kinetic energy of the actual
atmosphere is larger than that obtained from our numer-
ical integration. Aswe pointed out in the previous
study [35], the lack of land and sea or mountains in our
model may be one of the reasons for this discrepancy.
According to our experience, the increase of the effective
eddy Reynolds number resulting from further increase of
resolution also increases the eddy kinetic energy. (Note
that the horizontal mixing coefficient of the model is
dependent upon the grid size.)
The reason the eddy kinetic energy obtained from the
784 MONTHLY Vol. 93, No. 12
80 -------- -. -.
"""
"""""
"""
"""""""----""------"~""""""
0 1 25 -----""
I I 1
1 50 160
QAYS
180
FIGURE 9.1.-The variation of the latitudinal distribution of zonal
kinetic energy with time. Unit is jouleom.?
.009 L .5 " 30
l k
<" ""-
"""
.e
.
90 80 70 60 50 40 30 20 10 0
LATITUDE
FIGURE 9.2.--The latitude-height distribution of eddy kinetic
energy in the model atmosphere. Unit is 10-3 joule cm.-2 mb."
moist model is smaller than that obtained from the dry
model in middle latitudes may be the difference in the
degree of baroclinic instability caused by the difference
in the vertical wind shear. According to the comparison
between the vertical eddy flux of heat in the moist model
atmosphere and that in the dry model atmosphere, the
former is significantly smaller than t.he latter in middle
latitudes. (See the upper part of fig. 5D4 of the previous
paper 1351 and the lower part of fig. 12C4 of this paper.)
This result implies that the release of potential energy in
the moist model atmosphere is smaller than that in the
dry model atmosphere in middle latitudes. Therefore,
the eddy kinetic energy of the former is smaller than that
of the latter in middle latitudes.
I20
EDDY KINETIC ENERGY AT %I MI L N E L
LATITUDE
FIGURE 9.3.-The latitudinal distributions of eddy kinetic energy
at the 5th model level (P/P*=0.5) of both the dry and moist
general circulation models and that at 500-mb. level of the actual
atmosphere obtained by Saltzman [30].
UM"
5000.0
1
FIGURE 9.4.-The latitudinal distributions of source (-V - V+)
and sink (V F) of kinetic energy in the model atmosphere.
-I3
"q
The tropical maximum of eddy kinetic energy obtained
from the present study is produced by the release of avail-
able potential energy generated by the heat released by
condensation in the Tropics. According to figure 12c4,
the potential energy is released in the Tropics as well as
in middle latitudes. Figure 9.4 shows the latitudinal
distribution of the source (-V V4) and the sink
(V * F) of kinetic energy (refer to equation 7B4 of the
previous paper [35]). In the Tropics, the magnitude and
the distribution of the source term are almost identical
to those of the sink term. In other words, this figure shows
that the kinetic energy produced in the Tropics is mostly
-x -P
-x -P
December 1965
~~~~~ ~ ~~~~~~
S. Manabe, J. Srnagorinsky, and R. F. Strickler
dissipated in the Tropics. Since the scale of tropical
eddies is relatively small, the lifetime of these eddies is
shorter than of those of the middle latitudes. This may be
why the tropical eddies dissipate before the energy is
transported elsewhere. It is rather doubtful that such a
tropical maximum of eddy kinetic energy does exist in the
actual atmosphere. According to our speculation, the
simplified scheme of convection adopted for the present
study may tend to create too much eddy available poten-
tial energy of resolvable scale because of the shortcoming
of the criterion for the onset of convection, whereas in the
actual atmosphere the heat released by condensation
creates cumulus-scale convection and the kinetic energy
of the eddies of this scale quickly dissipates instead of
producing larger-scale eddies and only occasionally large-
scale eddies such as hurricanes may be produced. Further
study of tropical convection and the actual distribution of
eddies in the Tropics is desirable before It will be possible
to engage in a thorough discussion of this subject.
I O . MOISTURE BALANCE
A. HEMISPHERICMOISTUREBALANCE
As table 10A shows, the hemispheric means of the rates
of precipitation and evaporation are about 1 m./yr. and
coincide very well with the estimate of actual rainfall
obtained by Meinardus [20] and Budyko 15, 61.
In our model, the temperature of the earth's surface is
determined by the condition of thermal equilibrium at the
earth's surface. Therefore, the rate of evaporation and
accordingly that of precipitation depend very much upon
the radiative energy reaching the earth's surface. The
successful simulation of the hemispheric mean rate of rain-
fall is the natural consequence of the successful simula-
tion of the heat regime a t the earth's surface which is dis-
cussed in section 11.
B. LATITUDINALDISTRIBUTION O F MOISTUREBALANCE
In figure 10B1, the latitudinal distributions of precipita-
tion and evaporation for our model atmosphere are com-
pared with those for the actual atmosphere estimated by
Budyko [5]. In the model atmosphere, the rainfall
exceeds evaporation in the Tropics and in the middle
latitudes, and the latter exceeds the former in the sub-
tropics. These features are in excellent qualitative agree-
ment with the observed features of the tropical rain belt,
the subtropical desert area, and the rainy region of the
middle latitudes. Quantitatively, these results are much
more exaggerated in the model atmosphere than in the
actual atmosphere. Particularly, the amount of rainfall
in the Tropics far exceeds the annual mean of the observed,
TABLE lOA.-Hernispheric water balance (from 148th dav to 187th dav)
Rate of evaporation ...................................................... 105.9cm./yr.
Rate of change of water vapor ........................................ ...- -5 cm./yr. Rate of precipitation ..__.._._.......
~
.................................... 105.4cm.lyr.
785
N 80' 60' 40' 20' 0' 20' 40' 60' 80' S ' ' 0
LATITUDE
FIGURE lOB1.-In the upper part of the figure, the latitudinal dis-
tributions of precipitation and evaporation obtained from the
model are shown, and in the lower part of the figure, observed
distributions estimated by Budyko [5] are shown.
and the width of the rain belt is very narrow. Also, the
subtropical dry area is located in too low a latitude.
In order to investigate the latitudinal distribution of
water balance, figures 10B2 and 10B3 were made. Figure
10B2. shows the latitudinal distributions of moisture
transports due to large-scale eddies, meridional circuIa-
tions, and horizontal subgrid-scale diffusion. The trans-
ports by large-scale eddies obtained by.Peisoto [27] for
the actual atmosphere are also plotted in the same fig ure.
According to this figure and figure 12B3 the excess water
produced by evaporation in the subtropics is exported to
the Tropics by the meridional circulation a n d t o t h e
middle latitudes by large-scale eddies in both the model
and the actual atmosphere. The magnitude of the south-
ward transport of water vapor due to the tropical merid-
ional circulation cell, however, is much larger than that
obtained by Peixoto [27] for the actual atmosphere because
the exaggerated subtropical desert and the extremely
sharp tropical rain belt, which emerged as a result of our
time-integration, require a large transport of water from
the subtropics into the Tropics. Figure 10B3 shows the
latitudinal distributions of various water balance compo-
nenh2 Note again that the extremely large sink of
water due to condensation in the Tropics is compensated
for by the supply of water from meridional circulation.
It is rather difficult to pin down the exact causes for the
extremely large rainfall in the Tropics a t the present
786 MONTHLY WEATHER REVIEW Vol. 93, No. 12
EDDY I
-20 I I I I I I I I I
90 80 70 M M 40 30 20 10 0
LATITUDE
FIGUBE 10B2.-The latitudinal distributions of poleward transport
of water vapor due to the large-scale eddies (EDDY) the merid-
ionalcirculation (M.C.), andsubgrid-scalediffusion (H.D.). The
annual mean of the transport by the large-scale transient eddies in
the actual atmosphere obtained by Peixoto [27] is also plotted.
-.5
- 1.0
LATITUDE
FIGURE 10B3.-The latitudinal distributions of the rate of change
of precipitable waterdue to evaporation, precipitation, large-
scale eddies (EDDY), meridional circulation, andhorizontal
mixing by subgrid-scale turbulence (H.D.).
stage of our investigation. We shall, however, list some
of the possible causes:
(1) It is well known that the latitude of the tropical
rain belt varies with season. As a result of this variation,
t.he observed maximum of the annual mean rainfall could
be less pronounced than the maximum obtained from
our model without seasonal variation.
(2) As we expla,ined in the previous paper, the dis-
tribution of the vertical mixing coefficient influences the
eccent,ricity of the meridional circulation cell and accord-
ingly the efficiency of the moisture transport due to
meridional circulation. The thinner the planetary bonnd-
ary layer is, the more efficient is the transport. The
neglect of vertical mixing of momentum due to moist
convection could exaggerate the eccentricity and increase
the supply of water vapor into the Tropics.
(3) The existence of the free-slip, insulated equatorial
wall of our model fixes the latitude of maximum con-
densation and causes a concentration of rainfall next to
this wall. It is desirable to perform the simulation of
the seasonal variation by using a model without an
equatorial wall and then to compare the amount of
rainfall with t.he observed annual rainfall.
(4) As figure 12B3 shows, ocean currents transport
heat away from the tropical region (refer to sec. 12).
Since this process is missing in the present model, ex-
cessive evaporation and accordingly excessive rainfall
may occur in the tropics of the model atmosphere.
C. LATITUDE-HEIGHTDISTRIBUTION OF MOISTUREBALANCE
In figure 10Cl the latitude-height distribution of the
northward transport of water vapor by large-scale eddies
and that by both the meridional circulation and large-
scale eddies are compared with the corresponding dis-
tributions obtained by Peixoto [27] for the actual atmos-
phere. In both the model atmosphere and the actual
atmosphere most of the moisture transport is accomplished
in the lowest 300-mb. layer of the atmosphere and the
export of water vapor from the subtropics into the
Tropics has a sharp maximum very near the earth's
surface. This sharp maximum is caused mainly by the
meridional circulation rind is much more pronounced in
our results than in Peixoto's results for the actual at-
mosphere. The eddy flus of water vapor is mostly
positive in the troposphere but is negative in the strat-
osphere where the mixing ratio of water vapor increases
with increasing latitude.
The latihde-height distributions of the vertical trans-
port of water vapor by large-scale eddies, by the meridional
circulation, and by both of these processes are shown in
figure 10C2. One interesting feature of our results is
that, the upward flux of water vapor due to large-scale
eddies has two maxima-in the Tropics and in the sub-
,tropics. The tropicaI maximum is caused by large-scale
eddies created by the release of potential energy in the
Tropics. As we discussed in section 9, it is highly
questionable that such large-scale eddies predominate in
December 1965 S. Manabe, 1. Smagorinsky, and R. F. Strickler
EDDV TRANSPORT TOTALTRANSPORT
787
.30
2o t 3
k
10 =
P Y
0
500 500
g 700 - 850 - 850 -
700-
1000 I I I I I 1000
90 80 70 60 50 40 30 20 10 0 90 80 70 60 50 40 30 20 10 0
LATITUDE LATITUOE
FIGURE lOCl.-Upper part of the figure shows the latitude-height distributions of northward transport of water vapor by the large-scale
eddies and that by both the large-scale eddies and the meridional circulation for the atmosphere. Lower part of the figure shows
the corresponding distributions for the actual atmosphere obtained by Peixoto [27]. Unit is 10l2 gm. mb." day".
the actual tropical atmosphere. Therefore, it may be
desirable to improve the scheme of simulating moist
convection in order to eliminate the excessive production
of large-scale eddies in the Tropics. In order to evaluate
the relative importance of the meridional circulation and
the large-scale eddies in transporting the moisture up-
ward, figure 10C3 was made to show t,he hemispheric
mean of the vertical transports by these processes of
the model atmosphere. From this figure, it is clear that
the meridional circulation is much less important than
large-scale eddies in transporting moisture upward. The
same is true for heat transport, .though the meridional
circulation transports heat downward as figure 5C2 of
the previous paper [35] shows.
The effects of large-scale motion described so far and
those of horizontal diffusion compensate for the net change
of water vapor caused by evaporation, condensation, and
convection as shown in figure lOC4. According to this
figure, the source region and sink region of water vapor
due to these effects are located in the lower and the upper
parts of the model troposphere, respectively. They must
be compensated mainly by the effect of large-scale eddies
as shown at the bottom of figure IOC2 and in figure 10C3.
Note the sink region of water at the level of the tropical
tropopause where the temperature is very low and relative
humidity is high. As one would expect, there are no
source or sink regions in the rest of the stratosphere be-
cause of the lack of moist convection.
D. MOISTURE BALANCE OF THESTRATOSPHERE
According to figure 1Oc3, the water vapor is transported
from the troposphere into the stratosphere mainly by the
effect of large-scale eddies. As figure 10C2 shows, the
water vapor whic.h is supplied from the troposphere is
transported toward low latitudes by both the large-scale
eddies and subgrid-scale mixing overshadowing the coun-
teracting effect of the meridional circulation in the low
latitudes. The water vapor condenses near the tropical
tropopause where the temperature is low and the humidity
is high. This condensation is the reason the relative
humidity is so lorn in the rest of the stratosphere of our
model. Figure l o l l is a schematic representation of eddy
transport of water vapor in the stratosphere. In short,
the large-scale eddies play a dominant role in transporting
the water vapor into the model stratosphere. Our result
is quite different from the meridional circulation model
proposed by Dobson [8] and that proposed by Brewer [21
for explaining the distribution of various substances in
the stratosphere.
At the 34-mb. level (k=1.5), the downward transport
of mater vapor by the large-scale eddies predominates,
and the mixing ratio of water vapor at the 9-mb. level
788 MONTHLYWEATHERREVIEW Vol. 93, No. 12
,009
TRANSPORT- M.C. t EDDY -30
.664
,926
90
.DO9
,074
Q n
I '189
,336
,500
.664
,926 .El1
,991
-m t
E X
I- S
Y
X
CI
10
0
LATITUDE
TRANSPORT - M. C. -30
TRANSPORT - URGE SCALE EDDY t 3 0
90 80 70 60 50 40 30 20 10 0
LATITUDE
FIGURE lOCZ.-The latitude-height distributions of the vcrtical
transport of water vapor by the large-scale eddies, by thc merid-
ional circulation, and by both of these two effects are shown in thc
lower, middle, and upper part of the figure, respectivcly. Units
are 1 0 -5 gm. cm.? day".
,034
,126
yp?*
'
,259
,417
,583
,741
,874
I." ,966
TRANSPORT OF WATER VAPOR (smm/cm2, day)
FIGURE lOC3.-Vertical distributions of the hemispheric mean of
vertical transport of water vapor by the meridional circulation
(M.C.), by the large-scale eddies (EDDY), and by both of these
two effects (EDDY + M.C.).
90 EO 70 60 50 40 30 20 10 0
LATITUDE
FIGURE lOC4.-Latitude-height distribution of net source of water
vapor due to evaporation, condensation, and convection. Units
are (gm. of water vaporlgm. of &)/day.
(k= 1) is significantly smaller than that at the 74-mb. level
(k=2). It is not clear whether this counter-gradient
transport is due to the truncation error of the interpolation
o f the mixing ratio, which is performed to compute the
vertical transport of water vapor, or to the genuine de-
velopment of an inverse correlation between the absolute
humidity and vertical motion. A further increase of verti-
cal resolution is necessary before we can obtain a convinc-
ing result.
December 1965
~~~ ~ ~~
S. Manabe, J. Srnagorinsky, and R. F. Strickler 789
WATER BUDGET OF THESTRATOSPHERE
-Condensation
(very cold and humid)
pole equator
FIGURE 10D.-Schematicrepresentation of watervaportransport
in the stratosphere.
11. ENERGY BUDGET OF THE EARTH'S SURFACE
Figure 11.1 shows the latitudinal distributions of various
heat balance components a t the earth's surface, i.e., the
net upward solar radiation, the net upward long-wave
radiation, and the sum of the turbulent eddy flux of
sensible heat and of latent heat. The corresponding
quantities obtained by London [17] for the actual atmos-
phere are plotted in the same figure. According to our
comparison, the coincidence between them is excellent.
In figure 11.2 the latitudinal distributions of both sen-
sible and latent heat flux from the earth's surface are
compared with those obtained by Budyko [5] for land,
sea, and the whole earth. According to this comparison,
our results lie between his results for sea and for the
whole earth. Since the relative humidity of the air over
oceans which coexist with continents should be smaller
than that of the air over the completely wet earth used
for our model, these results are reasonable. Using the
results given in figure 11.2, the latitudinal distribution of
Bowen's ratio, i.e., the ratio of sensible heat flux to latent
heat flux a t the surface, was computed and is shown in
figure 11.3. The distribution of Bowen's ratio for very
high latitudes is not computed because the latent energy
flux, which is the denominator, tends to zero, and the
sensible heat flux,which is the numerator, changes its
sign in very high latitudes. I:n the same figure, Bowen's
ratios obtained by Rudyko [5] and Jacobs [l l ] for the ocean
are added for comparison. The agreement between the
distribution of Bowen's ratio of the model atmosphere
with a wet surface and that obtained for the actual ocean
is satisfactory.
In short, the energy budget of the earth's surface of our
model is very similar to the actual budget obtained by
London [17] and the partition of the turbulent energy
transport into latent energy flux and sensible heat flux
is reasonably close to the partition taking place at the
actual ocean surface because of the assumption of the
wet surface adopted for our model.
LY/MIN
' 3 f l
FIQURE 11.1.-Latitudinal distributions of net upward solar radia-
tion (NSRFX), of net upward long-wave radiation (NRLFX),
and of upward flux of both latent and sensible heat due to turbu-
lent eddies ((VSHFX) + (VLHFX)). The corresponding dis-
tributions obtained by London[17]for the actual atmosphere
are also plotted.
4) 80 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 4)
LY/MIN. NORTH LATITUDE SOUTH
FIGURE 11.2.-Latitudinal distributions of latent and sensible heat
fluxfrom the earth to the atmosphere. The distributions, which
were obtained by Budyko [5] for land, sea, and the whole earth,
are compared with the distributions obtained from our model.
."
.4 -
s
= .3 -
c e
U J
B
0 z *2 -
m
.l-
L L 1( 80" MI' 40* 20' 0" 20" 40" MI" 80' 5
LATITUDE
FIGURE 11.3.-Latitudinal distributions of Bowen's ratio obtained
by Budyko [5] and Jacobs [l l ] are compared with that obtained
from our present results.
790 MONTHLY Vol. 93, No. 12
19. HEAT BALANCE
A. HEMISPHERICHEATBALANCE
Figure 12A shows the hemispheric mean of heat balance
of our model atmosphere and that of the actual atmosphere
obtained by London [17] and Budyko [5]. The agreement
between the two results is excellent.
B. LATITUDINALDISTRIBUTION OF HEATBALANCE
In figure 12B1 the latitudinal distribution of the
radiative fluxes a t the top of the model atmosphere are
compared with those obtained by London [17] for the
actual atmosphere. The agreement between them is
excellent. The meridional transports of energy expected
from the radiative imbalance for both dry and moist
general circulation models are given in figure 12B2.
The corresponding transports, which were obtained from
the results of Houghton [9] and London [17], are also
plotted in the same figure. The transport obtained from
the moist general circulation model'
I
is closer to the
observed transport than that from the dry model because
of the improvement in the latitudinal gradient of tem-
perature described in section 5.
In the actual earth-atmosphere system, the meridional
transport of energy required from radiative imbalance
must be accomplished by the following three processes:
(1) Northward transport of total energy (=c,T+4
+K) in the atmosphere. 4 is geopotential, and K is total
kinetic energy per unit mass.
(2) Northward transport of latent energy in the atmos-
phere.
(3) Northward tran,sport of total energy in the oceans.
Figure 12B3 shows the latitudinal distributions of these
three transports which are calculated by use of the resulk
of Houghton [9] and Budyko [5],[SI? The transport of
J The latitudinal distribution of rainfall is obtained from Budyko [ti].
NSR
MODEL ATMOSPHERE
N L R N S R
ACTUAL ATMOSPHERE
N LR
*""l I .330
i
.330 I .324
I 1 .324 i
I
I !
latent energy (2) is obtained by integrating the difference
between evaporation and precipitation with respect to
latitude. The transport of energy by the oceans (3) is
computed by integrating the thermal imbalance a t the
earth's surface. A similar computation was performed by
Bryan 131. In order to perform theseintegrations,Budyko's
data for the Northern Hemisphere and the Southern
Hemisphere are averaged. The meridional transport of
total energy in the atmosphere (1) is calculated as the
difference between the transport expected from radiative
imbalance and the net transport due to the two other
effects (2, 3). The northward transport of latent energy
which is computed by Peixoto [27] for the Northern
LY/MIN
I I I I 4a 30 20 IO 0
LATITUDE
FIGURE 12Bl.-Latitudinal distribution of net downward solar
radiation (SR) and of net upward long-wave radiation (LW R) a t
the top of the atmosphere.
14.0
13.0 HOUGHTON
12.0
t A LONDON
10.0
r-
+c .120 1 i
I I I 1
I I
+c (. 112)
i I I I
I NSR SH N S R
i i I I i
I
Unit (\y/rnin.)
FIGURE 12A.-Hemispheric mean of the heat balance of the model 'FIGURE 12B2.-Latitudinal distributions of meridional transport
(left) and actual atmosphere (right). The heat balance com- of energy expected from the radiative imbalance of the earth-
ponents of actual atmosphere are obtained by London [17] and atmosphere system. The results obtained from both dry and
Budyko [5, 61. NLR=net long-wave radiation [17]. NSR=net moist general circulation models are compared with the corre-
solar radiation [17]. SH=sensible heat flux [5]. C=heat of sponding distributions obtained by Houghton [91 and London
condensation [5]. [17] for the actual situation.
December 1965 S. Manabe, J. Smagorinsky, and R. F. Strickler 791
Hemisphere is plotted in the same figure and agrees well
with the corresponding flux estimated above.
In figure 12B4 the latitudinal distribution of the merid-
ional transport of total energy (c,T+~+K) and that of
latent energy in the model atmosphere are shown. The
energy transport in the ocean is missing because of the
assumption of a wet land surface on the earth. According
to this figure, in both the actual and model atmosphere,
an equatorward transport of latent energy by the merid-
ional circulation predominates in the low latitudes and
a poleward transport by the large-scale eddies predom-
inates in middle latitudes. The magnitude of these trans-
ports in the model atmosphere, however, is larger than in
the actual atmosphere. In order to compensste for the
large southward transport of latent heat, an extremely
large poleward transport of total energy appears in low
latit,ltdes. Both of these transports are accomplished
by the intense meridional circulation which predominates
in the low latitudes of our model atmosphere. Because
the northward transport of latent energy is by large-
scale eddies in middle latitudes? the meridional transport
of total energy (c,T+c#I+K) in middle latitudes is signs-
cantly smaller than the net energy transport expected
from radiative imbalance. In the dry model the merid-
ional transport of total energy in the atmosphere, however,
is identical with the net transport which is expected from
radiative imbalance and is shown in figure 12R2. Figure
12.0 ,
LATENTHEAT TRANSPORT
AOBIAINED BY PEIXOTO
FIGURE 12B3.-The latitudinal distribution of poleward net energy
transport of the earth-atmosphere system, which is expected from
the radiative imbalance, is shown together with the transport of
total energy (c,T+++K) and that of latent energy in the atmos-
phere, and the transport of energy by ocean currents. The estimate
of these transports was made by use of the data obtained by Budyko
[5], [6] (average of values for both hemispheres) and Houghton [9].
The meridional transport of latent energy obtained by Peixoto
[27] is plotted for comparison.
12B5 shows the comparison between the meridional trans-
port of sensible heat by large-scale eddies in the moist
atmosphere and in the dry atmosphere. The former is
significantly smaller than the latter and iscloser to the
transport obtained by Starr and White [38] for the actual
atmosphere. This is why the temperature gradient in
the middle latitudes obtained from the present model is
somewhat smaller than that obtained from the dry general
circulation model. For comparison, the latitudinal dis-
tribution of the transport of latent energy is shown in the
lower half of figure 12R5.
In figure 12B6 the latitudinal distributions of the net
thermal imbalance of the earth-atmosphere system of the
model due to radiative transfer and condensation are
compared with the corresponding imbalance in the actual
atmosphere estimated by use of the results of Budyko
[5], IS] and Houghton [9]. One of the characteristic
features of the present result is the large excess of heating
in the Tropics and the large deficit in the subtropics.
Although this feature agrees qualitatively with observa-
tion, the magnitude of the excess and the deficit are much
larger than those of the actual atmosphere. This thermal
10.0
9.0
8.0
1.0 -
TOTAL ENERGY TRANSPORT
-2 5.0 -
4.0 -
x
I I
-1.0
-5.0
-6.0
-1.0
\
\
1
\
LATENT HEAT TRANSPORT,:
\
\
\
t \ \
'1
i
I I I
FIGURE 12B4.-The net energy transport expected from the radia-
tive imbalance and the transport of total energy (c,T+qj+K) 1
and latent energy in the model atmosphere. The flux of latent
energy is computed by integrating the latitudinal distribution of
the imbalance of water.
792 MONTHLY Vol. 9 3 , No. 12
I) STARR & WHIR S E N S I B L E H E A T
5t
X
FIGURE 12B5.--In the upper part of the figure, the latitudinal
distributions of the meridional transport of sensible heat by large-
scale eddies, which are obtained from both dry and moist general
circulation models, are shown together with that resulting from
the subgrid-scale mixing (H.D.). Also, that of the sensible heat
flux obtained by Starr and White [38] for the actual atmosphere
is plotted for comparison. I n t h e lower part of the figure, the
meridional transport of latent energy in the model atmosphere
is compared with the corresponding distribution obtained by
Peixoto [27] for the actual atmosphere.
3ooc V HOUGHTON, BUDYKO
I E
MOIST 6.C. MMLL \
m 0
0
1 I I I 1 I 60 50 40 30 20 10 0
LATITUDE
FIGURE 12B6.--l'he latitudinal distributions of the net thermal
imbalance caused by the effect of condensation and radiation,
and the transport of sensible heat from the earth's surface.
Solid and dashed lines show the results of the moist and dry
general circulation models, respectively. The corresponding dis-
t,ribution for the actual atmosphere, which is computed from the
results of Budyko [5], [6] and Houghton [9], is shown by triangles.
CONDENSATION
/ i I
M.C. I
"v:"- SENSIBLEHEAT FLUX /\,
I
EDDY "-"" / i '
HORIZONTAL DIFFUSION /\
I I I """"""
*.".""".."-~-"-*~~ "*"" ""- RADIATION
-"" "" I " .""*"C.-
I I
I
I I I
L
I I I I I I I I 80 70 60 50 40 30 20 IO
LATITUDE
FIGURE 12137."The latitudinal distributions of the rate of temper-
ature change in the model atmosphere by condensation, radiation,
sensible heat flux from the earth's surface, the meridional circu-
lation (M.C.), the large-scale eddies (EDDY), and horizontal
subgrid-scale mixing (HORIZONTAL DIFFUSION).
imbalance must be compensated for by the effect of
large-scale motion. Figure 12B7 shows the latitudinal
distribution of all the heat balance components obtained
from the present results. According to this figure, the
large amount of heat released by condensation in the
Tropics is mainly compensated for by the cooling caused
by the meridional circulation. In the subtropics the
radiative cooling is compensated for by the sensible heat
flux from the earth's surface and the heating caused by
the downward branch of the meridional circulation; in
middle latitudes the radiative cooling is mainly counter-
acted by the heat of condensation; and in high latitudes it
is compensated for by the heating caused by the con-
vergence of heat transport from large-scale eddies and
heat released by condensation.
C. LATITUDE-HEIGHTDISTRIBUTION OF HEATBALANCE
The lower part of figure 12C1 shows the latitude-heighL
distribution of the rate of temperature change caused by
convection and condensation obtained from the integra-
tion of the moist general circulation model. For com-
December 1965 S. Manabe, J. Smagorinsky, and R. F. Strickler 793
FIGURE 12Cl.-In the upper part of the figure the latitude-height
distribution of the rate of the net temperature change in OC./day
caused by the sensible heat from the earth's surface and the
moist convective adjustment in the dry general circulation model.
In the lower part, that caused by the heat of condensation, the
sensible heat flux from the earth's surface, and the vertical heat
flux due to convection is shown for the moist model.
parison the latitude-height distribution of the rate of
temperature change due to moist convective adjustment
and vertical mixing obtained from integration of the dry
model is shown in the upper part of this figure. The
former has two pronounced maxima; one is located in the
Tropics, and the other in middle latitudes. On the other
hand, the latter has only one maximum near the Tropics
and the intensity of heating decreases monotonically
with increasing latitude. The height of the tropical
convective tower of the moist model atmosphere is taller
than that of the dry model atmosphere. I n the sub-
tropics, the convective activity of the moist model
atmosphere is limited to the layer close to the earth's
surface, whereas that of the dry model atmosphere
reaches high altitudes. In high latitudes, the temperature
change due to the heat of condensation in the moist model
atmosphere is larger than that of t,he dry model atmos-
phere because of the meridional transport of latent energy
from middle latitudes. The general features of the
latitude-height distribution of the rate of radiative
temperature change for the moist model are very similar
to those in the previous results. Figure 1.2C2 shows the
latitude-height distribution of long-wave radiation and of
solar radiation. Refer to the previous paper [35] and
the paper by Manabe and Strickler [IS] for a detailed
discussion of the distribution of the radiative temperature
change.
The computed distribution of the net rate of temper-
ature change due to radiation, convection, and conden-
sation are compared with a similar distribution obtained
,991 I I I I I I I I I
90 80 70 60 50 40 30 20 10 0
LATITUDE
.009
30
""p 0
0
FIGURE 12C2.-The latitude-height distribution of the rate of
temperature change in "C./day due to solar radiation and that
due to long-wave radiation are shown in the upper and lower
part of the figure, respectively.
by Albrecht [l] for the actual atmosphere in figure 12C3.
Note the net destabilizing effect of the combination of
these processes. This destabilizing effect must be com-
pensated for by the meridional circulation and the large-
scale eddies. For example, the meridional circulation is
the major counteracting factor in the subtropics, and the
large-scale eddies have a stabilizing effect in middle lat-
itudes. Figure 12c4 shows the latitude-height distri-
butions of both the northward and upward transport of
heat due to large-scale eddies. According to the compas-
ison between this figure and figures 5D3 and 5D4 of the
previous paper, the magnitudes of both vertical and
horizontal flux in middle latitudes are significantly smaller
than those obtained from the dry general circulation
model. It is noteworthy that in middle latitudes the
baroclinic activity is less for the moist model than for the
dry general circulation model. Another feature of interest
is the maximum vertical eddy flux of heat in the Tropics
which is caused by the heat of condensation. The result-
794 MONTHLYWEATHERREVIEW Vol. 93, No. 12,
- 30
4 -20 - E
-
c = Lo Y
-10 =
0
0991 90" 80' 70" 60' 50" 40" 30" 20" 10" 0" -
UTITUDE
d ,074
.-.
LATrmOE
FIQURE 12C3.-The latitude-height distribution of the net rate of
the change of temperature in OC./day d u e t o radiation, con-
vection, and condensation for the model atmosphere and the actual
atmosphere are shown in the upper and lower part of the figure.
The latter is estimated by Albrecht [I]. Heavy line is observed
tropopause.
ant release of potential energy creates a tropical maximum
of eddy kinetic energy. Refer to section 9 for a further
discussion of this result.
13. ANGULARMOMENTUM BALANCE
In figure 13.1, the latitudinal distributions of the north-
ward transport of momentum by various processes are
shown. One of the characteristic feat,ures of this result
is the large transport of momentum by the meridional
circulation in low latitudes. This result is consistent with
the very large transport of water vapor and of heat
described in sections 10 and 12.
I n figure 13.2, the latitudinal distribution of the trans-
port of angular momentum by large-scale eddies obtained
from the present computation is compared with that obtained
from our previous computation. The northward trans-
port in the actual atmosphere, as evaluated by Buch [4]
and Starr and White [38],is plotted in the same figure.
.926 4 1 ,991 I
.. .
-1
1 I I I I I 1 0
FIGURE 12C4.-Latitude-height distributions of the northward
transport of heat (1017 joule mb-1 day-1) and that of the upward
transport of heat (joule cm-2 day -1) by the large-scale eddies
are shown in the upper and lower part, respectively.
According to this figure, the actual eddy transport lies
between the results of the dry and moist computations.
As described in section 12, the heat transport by large-
scale eddies is also less for the present result than for the
previous result [35]. In short, the heat of condensation
decreases the temperature gradient and the vertical wind
shear in middle latitudes, decreases the eddy kinetic
energy in middle latitudes, and accordingly decreases the
northward fluxes of heat and momentum due to large-
scale eddies. Recently, we performed an integration of
the dry general circulation model with high resolution
(N=40). As equation (2B8) of the previous paper [351
shows, the coefficient of subgrid-scale diffusion of momen-
tum and heat is proportional to the square of the grid size
and to the absolute value of the deformation. According
to our results the effective Reynolds number seems to
increase with increasing resolution. The transport of
heat and momentum by the large-scale eddies as well as
December 1965 S. Manabe, 1. Smagorinsky, and R. F. Strickler 795
-6.01
'\ -I
FIGURE 13.l.-Latitudinal distributions of poleward transport of
angular momentum by the meridional circulation (M.C.), the
large-scale eddies (EDDY), and the horizontal subgrid-scale
mixing (HORIZONTAL DIFFUSION).
the magnitude of the eddy kinetic energy are much larger
for the (N=40) experiment than for the (N=20) experi-
LATITUDE
mente Smagorinsky and staff members [361 Performed a FIGURE 13.2.-Latitudinal distributions of the poleward transport
series of forecasting experiments using the present moist of angular momentum by the large-scale eddies in the moist
general circulation model and concluded that the increase model atmosphere and the dry model atmosphere.
of resolution from (~~2 0 ) to (~=4 0 ) greatly improved obtained by Buch [41 and Starr and White [381 are also Plotted.
%he results, especially in regwd to vertical motion and. pre-
cipitation. It is therefore desirable to perform a numeri-
cal general circulation experiment using the moist model
with high resolution (N=40).
In figure .13.3, the latitudinal distribution of surface
torque obtained from the present integration is compared
with that from the previous computation. In the same
figure, the values of the stress on the actual earth's 6.0-
surface, which were computed by Priestley [29] for both 5.0-
winter and summer, are plotted as reference. According
to this figure, the torque obtained from the present - 3.0-
integration is smaller than that of the previous study. 4
2.0-
Another notable feature in the present result is the syste- -L
matic shift of the mode of angular momentum exchange
between the earth and the atmosphere toward the low 2
latitudes. This result is consistent with the fact that the E -2.0-
width of the upward-motion branch of the tropical 3 -3.0- WINTER
meridional circulation cell in the model atmosphere is
very small.
DRY G.C. MODEL
0 SUMMER (AFlER PRIESTLEY1
-5.0 -
-6.0 -
14. CONCLUDING REMARKS 90 I 1 80 70 M I 50 I 40 I 30 I 20 I I 10
IATITUDE
model atmosphere the relative humidity is high and rainfall summer situation.
796 MONTHLY Vol. 93, No. 12
exceeds evaporation; and in the subtropics the relative
humidity is low and the evaporation is higher than precipi-
tation. The excess water vapor thus created in the
subtropics is exported to the Tropics by the meridional
circulation and to middle latitudes by the large-scale
eddies. Generally speaking, the relative humidity de-
creases with increasing altitude. In the stratosphere of
our model atmosphere the relative humidity is very low
except at the tropical tropopause and the mixing ratio of
water vapor is very small in agreement with the actual
atmosphere. The hemispheric mean of precipitation ob-
tained from our computation is 1.06 m./yr. and agrees
reasonably well with the value of 1 m./yr. estimated by
Budyko [5] and Meinardus [20] for the actual atmosphere.
At the top of the model atmosphere the latitudinal dis-
tribution of the net solar radiation and long-wave radiation
coincide very well with those estimated by London [17] for
the actual atmosphere. At the earth’s surface the latitu-
dinal distribution of the vertical turbulent flux of energy
as well as that of the radiative fluxes also agrees with the
results of London [17]. Bowen’s ratio at the wet earth’s
surface adopted for the model agrees well with that
obtained for the ocean surface by Budyko [5] and Jacobs
Dl].
Quantitatively, there are many features of the computed
hydrologic cycle which disagree with the observed features.
Both the rain belt in the Tropics and the dry belt in the
subtropics are exaggerated too much. As a result, the
southward transport of water vapor by the meridional
circulation in the Tropics is extremely large. Generally
speaking, the relative humidity of the moist layer at the
earth’s surface is too large. Therefore, the model a t -
mosphere has a significantly larger amount of precipi-
table water than the annual mean amount of the actual
atmosphere.
Unfortunately, very little is known about the hydrologic
cycle in the stratosphere because of the difficulty in
performing routine measurements. In our model, water
vapor is supplied from the troposphere into the strato-
sphere mainly by the effectof large-scale eddies. It is
then transported toward the tropical. tropopause, where
the temperature is very low and relative humidity is high,
and condenses. Because of this transport and condensa-
tion a very dry stratosphere is maintained.
There are many significant differences between the
present results and those obtained from the integration
of the dry general circulation model:
(1) The intensity of the meridional circulation in the
Tropics is larger in the present result than in the previous
result because of the effect. of moist convection in the
Tropics. Also the width of the upward motion branch of
the cell is less for the present result. Because of this
difference the meridional transport of momentum, heat,
and water vapor by the meridional circulation in the
Tropics is also very large in the present result,.Also,as
a consequence of this strong cellwe get a very strong
subtropical jet stream in the present result.
(2) In the middle latitudes the poleward transport of
total energy (c,T+++K) is significantly smaller for the
moist model than for the dry model because of the meridi-
onal transport of latent energy in the present model, and
the latitudinal temperature gradient in t.he troposphere of
middle latitudes is smaller for the former than for the
,latter. Therefore, the intensity of the zonal current in
middle latitudes obtained from the moist model is smaller
and more realistic.
(3) In the stratosphere, the latitudinal increase of
temperature obtained from the present study is somewhat
larger than that of the previous study. Accordingly, the
latitude of the maximum zonal current in the stratosphere
increases significantly with increasing altitude in qualita-
tive agreement with the features of the actual atmosphere.
(4) The heat of condensation tends to increase the wave
number of the vertical motion significantly. Accordingly,
it also increases the wave number of horizontal motion in
the troposphere and that of the surface pressure field.
(5 ) One of the characteristic features of our present
result is the tropical maximum of the eddy kinetic energy
caused by the release of eddy available potential energy.
This available potential energy is created by heat released
by convective condensation. Therefore, this tropical
maximum of eddy kinetic energy is missing in the results
of the dry model. Although this feature seems to be
highly unrealistic, further study of convection in the
Tropics is desirable before we will be able to determine how
unrealistic or realistic this feature is.
(6) The eddy kinetic energy in middle 1at.itudes is
significantly smaller for the moist model than for the dry
model. Consistent with this difference, the northward
transport of momentum and heat due to large-scale
eddies is smaller for the former than for the latter.
As we mentioned earlier (sec. 13), the results ob-
tained from the dry model wit,h high resolut’ion (N=40)
are quite different from those obtained from the dry model
with the resolution adopted for the present study (N=20).
Moreover, the release. of heat of condensation tends
to decrease the characterist,ic scale of motion, as we pointed
out earlier. Accordingly, the moist model requires higher
resolution than the, dry model. An examination of the
maps of relative humidity and those of vertical velocity
suggests that me need higher resolution to properly.repre-
sent these fields. Therefore, the present result with a
relatively coarse resolut,ion may be regarded as a pre-
liminary result before me perform the integration of the
model with higher resolution.
Another shortcoming of the model is the existence of a
free-slip insulated wall at the equator. This may be part
of the reason me get an exaggerated tropical rain belt. I t
is planned to perform an integrat,ion by use of a model
without a tropical mall.
December 1965 S. Manabe, J. Smagorinsky, and R. F. Strickler 797
As mentioned in the introduction, we computed the rate
of the temperature change due to radiation using the
climatological distribut,ion of water vapor and clouds in-
stead of the distribution obtained from the prognostic
equation of water vapor. In order to study the complete
interaction among the radiative transfer, the hydrologic
cycle, the photochemistry of ozone, and the large-scale
motion, it is necessary to eliminate this constraint and
to calculate the radiative transfer based upon the distribu-
tion of water vapor and ozone obtained from our model
itself.
APPENDIX-NON-CONVECTIVECONDENSATION
(ITERATIVEMETHOD)
As an example, we shall describe the iteration method
used in computing the non-convective condensation at
constant pressure. In our model the relative humidity h
is defined as,
h=r/r, (A-1)
Linearizing equation (3.3), and replacing 6r and 6T by Ar
and AT, respectively, we find the required change in r is
approximately:
Ar=r,(l-h)+ - AT
(3
where (dr,/bT), denotes the differentiation Gf r , wvith re-
spect to T at constant pressure. Again replaccrig. .@r
and 8T by Ar and AT, equation (3.4) may be written as
AT=-L Ar
C P
Solving (A-2) and (A-3) simultaneously, we get
(A-3)
(A-4)
ACKNOWLEDGMENT
The authors are very grateful for the assist,ance and cooperation
of many dedicated and conscientious people who made this research
possible.
We wish especially to thank Mr. J. Leith Holloway who very
capably supervised most of the programing effort of this Laboratory.
We are also grateful t.0 him for a number of useful suggestions
which contributed to the analysis and understanding of t,he results.
We are indebted to Mr. Roderick D. Graham who, having tested a
preliminary primitive-equations moist model [34], was able to point
out a t t h e beginning certain difficulties that we should expect to
encounter.
We are grateful to Dr. Kurt Spielberg of the Mathematics and
Application Branch of IBM Corporation for his participation in the
planning and writing of the original machine-language STRETCH
computer program for the moist model.
I n addition to Mr. Holloway and Mr. Graham we wish to acknowl-
edge the substantial contribution of the following present or former
members of this Laboratory: Drs. Kirk Bryan, Yoshio Kurihara,
and Kikuro Miyakoda for their useful ideas which contributed
greatly t o the course of the research; Mr. Howard H. Engelbrecht
and his very capable staff for efficiently running the programs on the
IBM STRETCH computer; Mrs. C. J. Hiland and Mrs. E. C.
Arnold for writing the extensive diagnostic programs for the inter-
pretation of the results; Mrs. Lou Ann Sangster for her very helpful
assistance with the radiation codes; Mrs. Marylin Varnadore for
efficiently making a great number of hand computations and for
her help in analyzing the results; and Mrs. J. A. Snyder and Mr. E.
W. Rayfield who assisted in the preparation of the manuscript and
the figures, respectively.
REFERENCES
1. F. Albrecht, “Untersuchungen uber den Wiirmehaushalt der
Erdatmosphiire and seine thermodynamische Bedeutung,”
Berichte des Deutschen Wetterdienstes in der U.S. Zone, vol.
17, 1950,70 pp.
2. A. W. Brewer, “Evidence for a World Circulation Provided by
the Measurements of Helium and Water Vapor Distribution
in the Stratosphere,” Quarterly Journal of the Royal Meteoro-
logical Society, vol. 75, No. 326, Oct. 1949, pp. 351-363.
3. K. Bryan, “Measurements of Meridional Heat Transport by
Ocean Currents,” Journal of Geophysical Research, vol. 67,
NO. 9, Aug. 1962, pp. 3403-3414.
4. H. S. Buch, “Hemispheric Wind Conditions During the Year
1950.” Final Report, Part 2, under Contract No. AF 19-122-
153, General Circulation Project, Department of Meteorology,
Massachusetts Institute of Technology, 1954, 126 pp.
5. M. I. Budyko, “Atlas Teplovogo Balansa Zemnogo Shara,”
Mezhduvedomstvennyi Geofizicheskii Komitet pri Prizidium,
AkademiG Nauk SSSR, GlavnaG GeofizicheskaG Observa-
hrZi imennii A. E. Voeikova, Rezul’taty, 1964.
6. M. I. Budyko, Teplovoi Balans Zemnoi Poverkhnosti, Gidro-
meteorologicheskoe izdatel’stvo, Leningrad, 1956,255 pp.
7. J. G. Charney and A. Eliassen, “On the Growth of the Hurricane
Depression,” Journal of the Atmospheric Sciences, vol. 21,
No. 1, Jan. 1964, pp. 68-75.
8. G. M. B. Dobson, “Origin and Distribution of the Polyatomic
Molecules in the Atmosphere,” Proceedings of the Royal
Society, Series A, vol. 236, No. 1205, Aug. 2, 1956, pp. 187-193.
9. H. G. Houghton, “On the Annual Heat Balance of the Northern
Hemisphere,” Journal of Meteorology, vol. 11, NO. 1, Jan.
10. J. T. Houghton, “Absorption in the Stratosphere by Some
Water-Vapor Lines in the v 2 Band,” Quarterly Journal of the
Royal Meteorological Society, vol. 89, 1963, pp. 332-338.
11. W. C. Jacobs, “The Energy Exchange Between the Sea and
Atmosphere and Some of Its Consequences,” Bulletin of the
Scripps Institution of Oceanography, vol. 6, No. 2,1951, PP.
1954, pp. 1-9.
The approximate value of (&,/dT), is computed by using
the definition of T , and the Clausius-Clapepon equation
(A-5)
where R* is the gas constant for water vapor, and e , is
the saturation vapor pressure.
(r+ Ar) and (T+ AT) are then put into equations (A-1)
and (A-4) to obtain higher order increments AT and Ar.
This cycle is repeated until h is sufficiently close t,o 1
(100 percent). The process converges very rapidly, usu-
ally requiring only one or two steps to bring h within 1
percent of saturation.
The 6r and 85” of equation (3.3) are.
6r=Ar’+Ar2f . . . +Arn
~T=AT+AT~+ . . . +ATn (-4-6)
where Ar” and ATn denote the value of Ar and AT at the
n t h 27-122.
7913 MONTHLY WE ATHERREVIEW Vol. 9 3 , No. 12
12. A. Kasahara, “A Numerical Experiment on the Development of
a Tropical Cyclone,’’ Journal o j Meteorology, vol. 18, NO. 3,
June 1961, pp. 259-282.
13. A. Kochanski, “Cross Sections of the Mean Zonal Flow and
Temperature Along 80” W.,” Journal of Meteorology, vol.
12, No. 2, Apr. 1955, pp. 95-106.
14. H. L. Kuo, “On Formation and Intensification of Tropical
Cyclones Through Latent Heat Release by Cumulus Convec-
tion,” Journal of the Atmospheric Sciences, vol. 22, No. 1, 1965,
15. C. E. Leith, “Convection in a Six-Level Model Atmosphere,”
Contract W-7405-eng-48, Lawrence Radiation Laboratory,
University of California, Livermore, Calif., 1965.
16. D. K. Lilly, “On the Numerical Simulation of Buoyant Con-
vection,” Tellus, vol. 14, No. 2, May 1962, pp. 148-172.
17, J. London, “A Study of the Atmospheric Heat Balance,”
Final Report on Contract AF 19(122)-165 (AFCRC-TR-57-
287), Department of Meteorology and Oceanography,
New York University, 1957, 99 pp.
18. S. Manabe and R. F. Strickler, “On the Thermal Equilibrium
of the Atmosphere with a Convective Adjustment,” Journal
of the Atmospheric Sciences, vol. 21, No. 4, July 1964, pp.
19. H. J. Mastenbrook, “Frost-Point Hygrometer Measurements
in the Stratosphere and the Problem of Moisture Contami-
nation,” Humidity and Moisture (editor-in-chief A. WexIer) ,
vol. 2 Applications (edited by E. J . Amdur), Reinhold Pub-
lishing Gorp., New York, 1963, pp. 480-485.
20. W. Meinardus, “Eine neue Niederschlagkarte der Erde,”
Petermann’s Geographische Mitteilungen, vol. 80, 1934, pp. 1-4.
21. R. J. Murgatroyd, “Some Recent Measurements by Aircraft
of Humidity up to 50,000 feet in the Tropics and Their
Relationship to Meridional Circulation,” Proceedings of the
Symposium on Atmospheric: Ozone, Oxford, IUGG Monograph
NO. 3, Paris, 1959, 30 pp.
22. Y. Ogura, “Frictionally Controlled, Thermally Driven Circula-
tions in a Circular Vortex with Application to Tropical
Cyclones,” Journal of the Atmospheric Sciences, vol. 21, NO. 6,
Nov. 1964, pp.’610-621.
23. Y . Ogura and 5 . G. Charney, “A Numerical Model of Thermal
Convection in the Atmosphere,,’ Proceedings of the Inter-
national Symposium on Numerical Weather Prediction, Tokyo,
1960, Meteorological Society of Japan, Tokyo, 1962, pp.
24. A. H. Oort, “On the Energetics of the Mean and Eddy Circula-
tions in the Lower Stratosphere,” Tellus, vol. 16, No. 4, 1964,
25. K. Ooyama, “A Dynamic Model for the Study of Tropical
Cyclone Developments,” Department of Meteorology and
Oceanography, New York University, 1963, 26 pp.
26. J. P. Peixoto, “Hemispheric Temperature Conditions During
pp. 40-63.
361-385.
431-452.
pp. 309-327.
the Year 1950,” Scientific Report No. 4, Contract AF 19
(604)-2242, Department of Meteorology, Massachusetts
Institute of Technology, 1960, 142 pp.
27. J. P. Peixoto, “Hemispheric Humidity Conditions During the
Year 1950,” Scientijic Report No. 3, Contract AF 19(604)-
6108, Department of Meteorology, Massachusetts Institute
of Technology, 1958, 211 pp.
28. N. A. Phillips, “Geostrophic Motion,” Reviews of Geophysics,
vol. 1, No. 2, May 1963, pp. 123-176.
29. C. H. B. Priestley, “A Survey of the Stress Between the Ocean
and Atmosphere,” Australian Journal of Scienli$c Research,
series A, vol. 4, No. 3, Sept. 1951, pp, 315-328.
30. B. Saltzman, “Spectral Statistics of the Wind at 500 mb,”
J O U ~Q ~ of the Atmospheric Sciences, vol. 19, No. 2, Mar.
1962, pp. 195406.
31. J. Smagorinsky and G. 0. Collins, “On the Numerical Pre-
diction of Precipitation,” Monthly Weather Review, vol. 83,
No. 3, Mar. 1955, pp. 53-68.
32. J. Smagorinsky, “On the Inclusion of Moist Adiabatic Proc-
esses in Numerical Prediction Models,” Berichte des Deut-
schen Wetlerdienstes, Band 5, Nr. 38,1956, pp. 82-90.
33. J. Smagorinsky, “On the Dynamical Prediction of Large-
Scale Condensation by Numerical Methods,” “Physics of
Precipitation”, Geophysical Monographs, No. 5, American
Geophysical Union, 1960, pp. 71-78.
34. J. Smagorinsky, “A Primitive Equation Model Including
Condensation Processes,” Proceedings of the lnternational
Symposium on Numerical Weather Prediction in Tokyo, 1980,
Meteorological Society of Japan, Mar. 1962, p. 555.
35. J. Smagorinsky, S. Manabe, and J. L. Holloway, “Numericd
Results From a Nine-Level General Circulation Model of
the Atmosphere,” Monthly Weather Review, vol. 93, No. 12,
Dec. 1965, pp. 727-768.
36. J . Smagorinsky and Staff Members, “Prediction Experiments
with a General Circulation Model,” Proceedings of the Inter-
national Sgmposium on Dynamics of Large-Scale Processes in
the Atmosphere (I A M A P I WMO), Moscow, USSR, 1965.
37. Staff Members of Tokyo University, “The Quantitative Fore-
cast of Precipitation with the Numerical Prediction Method,”
Journal of Meteorological Societ4 of Japan, Series 2, vol. 33,
38. V. P. Starr and R. M. White, “Balance Requirements of the
General Circulation,” Final Report, Part I, Contract AF
19(122)-153, Department of Meteorology, Mmsachusetts
Institute of Technology, 1954, pp. 186-242.
39. K. Telegadas and J. London, “A Physical Model of the Northern
Hemisphere Troposphere for Winter and Summer,” Scien-
tific Report No. I, Contract AF 19(122)-165, Research Di-
vision, College of Engineering, New York University, 1954,
55 PP.
NO. 5, 1955, pp. 25-36.
[Received August 16, 1965; rewised October 28, 19651