Monthly Weather Review
VOLUME 99, NUMBER 5
MAY 1971
UDC 551.589:651.613.1:561.511.33:556.1(1W)
SIMULATION OF CLIMATE BY A GLOBAL GENERAL CIRCULATION MODEL
1. Hydrologic Cycle and Heat Balance
J. LEITH HOLLOWAY, JR., and SYUKURO MANABE
Geophysical Fluid Dynamics Laboratory, NOAA, Princeton, N.J.
ABSTRACT
The primitive equations of motion in spherical coordinates are integrated with respect to time on global grids
with mean horizontal resolutions of 500 and 250 km. There are nine levels in the models from 80 m to 28 km above the
ground. The models have realistic continents with smoothed topography and an ocean surface with February water
temperatures prescribed. The insolation is for a Northern Hemisphere winter. In addition to wind, temperature,
pressure, and water vapor, the models simulate precipitation, evaporation, soil moisture, snow depth, and runoff.
The models were run long enough beyond a state of quasi-equilibrium for meaningful statistics to be obtained. Time
means of meteorological and hydrological quantities computed by the models compare favorably with observed
climatic means. For example, the thermal structure of the model atmosphere is very similar to that of the actual
atmosphere except in the Northern Hemisphere stratosphere; and the simulated distributions of the major arid
regions over continents and the distributions of the rain belts, both in the Tropics and in middle latitudes, are success-
fully simulated by the models described in this paper. The increase in the horizontal computational resolution
improved the distributions of mean surface pressure and precipitation rate in particular.
CONTENTS 1. INTRODUCTION
335
336
336
337
338
338
339
340
342
343
343
344
346
348
349
355
355
357
360
360
361
362
The first objective of general circulation modeling
experiments is the simulation of climate on a continental,
hemispheric, or global scale. Once this initial goal has been
achieved to a reasonable degree of faithfulness to reality,
the more interesting and enlightening goal can be pursued,
which is the use of these models for studying the physical
mechanisms that create and maintain climate. This is
accomplished by controlled experiments in which some
of the defining parameters of the model are changed while
others are kept constant. In this way, meteorology may
become an empirical science in a manner similar to the
field of experimental chemistry where different substances
are mixed in a laboratory to learn about various chemical
reactions. Modifications can be made to the model that
could never even be considered as remotely feasible in
nature [e.g., the removal of mountain ranges (Mintx 1968
and Kasahara and Washington 1969) or the elimination of
ocean currents (Manabe and Bryan 1969)I. Furthermore,
Appendix A-computational techniques- - - - - - - - - - - - - - - - - -
A. Time integration ______________________________
B. Revised pressure gradient formulation--- - - - - - - - - -
C . Revised vertical pressure-velocity equation- - - - - - -
D. Shortcomings of the Kurihara grid-..---_---_-----
Appendix B-some results from the high-resolution model- -
Appendix C-derivation of the smoothed topography- - - - - -
Acknowledgments- __ - - - - - - - - - - - - - - _ - - - - - - - - - - - -
References- - - - - - - - - - - - - - -
363
363
363
363
364
364 cost of research into 367
369
369
proposed methods for climate modification can be tested
in atmospheric models without the tremendous expense
and risk involved in testing them in the red atmosphere.
Some ideas can be disposed of as useless even without the
for making their applica-
tion inexpensive enough to be feasible. Finally, theories
involving inadvertent modification of weather by human - - - - - - - - - - - - - - - - -
335
3 36 MONTHLY WEATHER REVIEW VOl. 99, No. 5
activity can be tested in general circulation models with
greater certainty than by means of statistical studies of
atmospheric data spanning the period over which the
amount of the particular human activity changed
significantly.
Following the pioneering simulations of basic features
of the general circulation of the atmosphere by Phillips
(1956) and Smagorinsky (1963), various attempts have
been made to simulate the global distribution of climate.
One important contribution toward this objective was
made by Mintz and Arakawa (Mintz 1968) who con-
structed a general circulation model of the atmosphere
with realistic topography and sea-surface temperatures
as lower boundary conditions and successfully simulated
the essential features of the global distribution of surface
pressure. Their model, however, does not include a
hydrologic cycle that strongly controls the atmospheric
circulation. On the other hand, Leith (1965) and Washing-
ton and Kasahara (1970) incorporated into their models
the effects of condensation, but these models do not take
into consideration one of the most important climatic
processes (viz, the water balance of the earth's surface).
Previous to this study, attempts have been made to
incorporate moist processes into general circulation models
of the atmosphere a t the Geophysical Fluid Dynamics
Laboratory (GFDL) of NOAA. For example, Manabe et
al. (1965) constructed a hemispheric model in which the
effects of both evaporation and precipitation were taken
into consideration. By using this model, they were success-
ful in simulating some of the features of the hydrologic
cycle such as the tropical rain belt, the subtropical dry
belt, and the rain belt of middle latitudes (see also Manabe
and Smagorinsky 1967). Their model was, however, highly
simplified, having neither land-sea contrast nor mountains.
Instead, it had a flat moist surface with no heat capacity,
which can be perhaps visualized as a very shallow swamp.
Following this preliminary study, Manabe (1969) incor-
porated a computation scheme of ground hydrology into a
general circulation model with idealized continents and
oceanic areas in a limited domain. His success in simulat-
ing some of the fundamental features of the hydrologic
cycle, despite the extreme idealization of the geography
and of the computation scheme of hydrology, encouraged
us to attempt this present study of the numerical simula-
tion of the hydrologic cycle on a global scale.
For making a global atmospheric model, it is necessary
to design a grid system that covers the whole globe. Such a
grid system was proposed by Kurihara (1965). Using this
system, Kurihara and Holloway (1967) successfully per-
formed a numerical time integration of a global model
without moist processes and laid the foundation for the
present study .
The models described in this paper, therefore, represent
the most advanced stage in a series of atmospheric models
developed at GFDL during the last 14 yr. The evolution
of these models can be traced by referring to some pre-
vious papers by the GFDL staff. For the benefit of the
reader who does not wish to make such an extensive litera-
1 Smagorinsky 1963, Manabe and Strickler 1964, Smagorinsky et al. 1965, Manabe et al.
1965, Manabe and Wetherald 1967, Kurihara and Holloway 1967, Manabs 1969
ture search, we are presenting in the next section a
moderately detailed description of the current models.
In the remainder of this paper, we shall describe the
results obtained from time integrations of these models
with respect to simulating the global distributions of cli-
mate and hydrologic elements. Since it is not reasonable to
cover all aspects of our results in one paper, special
emphasis is placed here on the discussion of the balance of
heat and water in the earth-atmosphere system of the
model. The general circulation and energetics of disturb-
ances in the model Tropics have already been discussed by
Manabe et al. (1970b). A detailed discussion of the model's
flow field and the effects of mountains (Manabe and Hollo-
way 1971) will be published. A synopsis of some of the
hydrologic results, as they pertain to climate modification,
has been presented in Manabe and Holloway (1970a).
Some of these results, applying to the future development
of hydrologic models, were presented in Manabe and
Holloway (1970b).
2. DESCRIPTION OF THE MODEL
A. EQUATIONS OF MOTION
In deriving the equations of motion, we adopted the
so-called "u coordinate" system in which the pressure,
normalized by surface pressure, is chosen as the vertical
coordinate (Phillips 1957). Making the hydrostatic as-
sumption, we may write the momentum equations on a
spherical surface as
a - at (p*u) = --Ddu) +(f+y u) p*v
and
where u and v are the eastward and northward components
of the wind, respectively; p,, surface pressure; u, pressure
normalized by surface pressure; T, temperature; 4, geo-
potential height; e, latitude; A, longitude; a, radius of the
earth;f, the Coriolis parameter; R, the gas constant for
air; and and "F are the frictional forces due to subgrid
scale mixing in the horizontal and vertical directions, re-
spectively (see section 2E for details of these frictional
terms). The three-dimensional divergence operator D3( )
is defined by
(3)
where a denotes the individual change of normalized pres-
sure u, and
May 1971 j. Leith Holloway, jr. and Syukuro Manabe
The continuity equation may be written as
337
- aP* =-03(1).
at (5)
Integration of eq (5 ) with respect to u yields the following
prognostic equation for surface pressure:
The vertical u and p velocities can be obtained from the
diagnostic relations
and
The vertical p velocity, w , is necessary for computing the
adiabatic heating (or cooling) term in the thermodynamic
equation. It was found that the use of the finite-difference
representation of eq (8) caused serious computational
difficulties. Therefore, the form of eq (8) is somewhat
modified for the actual computation (see appendix A for
further details of this modification).
The geopotential height can be obtained by integrating
the following hydrostatic equation with respect to o:
!x-- RT
ao- (9)
(note that the equation of state for a perfect gas is used
for deriving this equation). The prognostic equation of
temperature (Le., the thermodynamic equation) is de-
scribed in subsection 2C.
e. FINITE-DIFFERENCE GRID SYSTEM
The model equations are integrated with respect to
time by a finite-difference scheme based on the so-called
“box” method. The grid system used for the model
is identical to that used by Kurihara and Holloway
(1967) with the exception that the two, circular polar
points have been eliminated by annexation to the sur-
rounding four boxes which become pie-shaped in the
process. There are 2,304 grid points at the centers of
2,304 boxes covering the globe. One octant of the grid is
shown in figure 1. The rectangles surrounding the grid
points represent plan views of rectangular parallelepipeds
(or simply boxes) centered on the grid points. Notice
that the boxes a t one latitude are staggered with respect
to those at adjacent latitudes. There are 24 grid points
between the Poles and the Equator and 96 points around
the Equator. The north-south grid distance is 417 km
everywhere; and in the east-west direction, the spacing
varies from 417 km at the Equator to 650 km near the
Poles.
I n the box method, the nonlinear components of the
tendencies of pressure, wind, temperature, and humidity
are functions of the flux divergence of mass, momentum,
FIGURE 1.-Diagram of one octant of the low resolution (N24)
computational grid. Map projection is not conformal.
heat, and water vapor computed at each box. The result-
ing computed tendencies are extrapolated in time by the
so-called “leapfrog” method. For further details on the
method of time integration of the model equations, see
appendix A for a discussion of several finite-difference
problems that had to be solved to integrate the model
experiment successfully.
The model has nine unevenly spaced levels in the
vertical from the lowest at about an 80-m height up to a
top level at approximately 28 km above the ground. As
pointed out in the previous subsection, the o coordinate
system is used to facilitate the incorporation of mountains
into the model. In this u system, the levels are surfaces
of constant ratio of pressure to surface pressure. A tabula-
tion of the u levels and their approximate elevations
above the surface points at sea level is shown in table 1
in which data are included for half levels interspersed
between the nine integer levels of the model. The vertical
u velocity is defined at these half levels. The derivation of
the smoothed topography used in these model experiments
is described in appendix C.
TABLE 1.-The u levels and their approximate elevations above the
surface points at sea level
Level O=PlP* Hright (m)
0. 5 0.00000000 rr,
1.0 .01594441 27,900
1.5 .04334139 21,370
2.0 .07ooMMo 18,330
2.5 .11305591 15,290
3.0 .16500000 12,890
3.5 .24081005 10,500
4.0 .31500000 8680
4.5 .41204675 6860
5.0 .50000000 M30
5.5 .60672726 4010
6.0 .685woao 3060
6.5 .77337055 2110
7.0 .835MMoo 1490
7.5 .90154066 860
ao . wM)o 520
8. 5 .980looOo 170
9.0 .990000M) 80
9. 5 1.000000M) 0
3 38 MONTHLY WEATHER REVIEW Vol. 99, No. 5
C. THERMODYNAMICS AND RADIATION
The model’s temperature tendency equation based on
the thermodynamic equation is
where c p is the specific heat of air under constant pressure
and *F, represents the contribution of the horizontal
subgrid scale mixing discussed in subsection 2E. The
first term on the right-hand side of eq (10) computes the
warming or cooling resulting from the large scale three-
dimensional flux divergence of heat. The second term
gives the adiabatic temperature change produced by
large-scale vertical motion. The third and fourth terms
represept the heating (or cooling) by condensation or
convective processes and by radiation, respectively.
The scheme for computing the convective temperature
changes consists of a so-called “moist convective’’ adjust-
ment and a “dry convective” adjustment. Since the former
is described in the following subsection, we shall describe
only the latter here. The dry convective adjustment is
performed if the lapse rate given by the other terms in
the thermodynamic equation is super dry-adiabatic. The
lapse rete is adjusted to the dry-adiabatic lapse rate so
as to simulate the effects of strong mixing by dry con-
vection in the free3 atmosphere. This adjustment is
performed in’ the model in such a way that the sum of
potential and internal energies are conserved.
The scheme for computing the radiative heating and
cooling is identical to that described by Manabe and
Strickler (1964) and Manabe and Wetherald (1967). It
was incorporated, for example, in the GFDL stereographic
models described in Smagorinsky et al. (1965) and Manabe
et al. (1965). The computation scheme consists of two
parts (via, a part for longwave radiation and one for
solar radiation). The principles of computing the flux of
longwave radiation are not very different from those
adopted for constructing a so-called “radiation” diagram
such as the one proposed by Yamamoto (1952). (Stone
and Manabe 1968 compared the flux of longwave radiation
obtained by this method with those obtained by various
methods proposed by other authors.)
The insolation at the top of the atmosphere is for a
Northern Hemisphere winter and did not change during
the entire time integration of the model. For simplicity,
the diurnal variation of solar radiation is eliminated by
use of the effective mean zenith angle for each latitude.
The gaseous absorbers, taken into consideration for the
computation of both solar and terrestrial radiation, are
water vapor, carbon dioxide, and ozone. I n addition, the
effects of clouds are incorporated into the scheme. As in
previous GFDE models, the distribution of mixing ratie
computed by the prognostic equation of water vapor is
not used for the computation of radiative transfer. In-
stead, we used the climatic distributions of water vapor
in the troposphere for the months of December, January,
and February, which are determined by a method based
upon studies by Telegadas and London (1954) and by
Murgatroyd (1960). The mixing ratio of the upper tropo-
sphere is assumed to be smoothly connected to the strato-
spheric value of a mixing ratio of 3 X g water vapor/g
air, as suggested by Mastenbrook (1965). The distribution
of ozone is determined from ozone measurements by
Hering and Borden (1965). Their total amounts am
normalized in such a way that they coincide with the dis-
tributions compiled by London (1962) who used extensive
measurements of total ozone by means of a Dobson spec-
trometer. For the computation of the radiative transfer,
the distributions of both water vapor and ozone are speci-
fied to be functions of latitude and height but not of longi-
tude. On the other hand, the mixing ratio of carbon dioxide
is assumed to have a constant value of 0.0456 percent by
weight everywhere. Clouds are classified into three cate-
gories (viz, high, middle, and low clouds, including
cumuliform). The distribution of these clouds in January
is determined by use of the table of cloud amount com-
piled by London (1957).
The distribution of albedo over oceanic surfaces and
for the snow-free surfaces of the continents is specified
by referring to the distributions of albedo compiled by
Posey and Clapp (1964). The albedos of the grid points
where snow cover is computed are determined by a method
based on a study by Kung et a1. (1964). According to their
results, the surface albedo is a function of snow depth
because exposed patches not covered by snow decrease
in both size and number as the snow depth increases.
Figure 3 of their paper shows that the difference between
the albedo of bare soil and that of a snow-covered surface
is approximately proportional to the square root of the
snow depth if the snow depth is less than 10 cm. When the
snow depth exceeds 10 cm, the value of the surface albedo
becomes almost independent of snow depth. Based on
their results, the following formulas were derived for
computing the albedo of snowv-covered surfaces :
and A=Ab+(Sw)1/2. (A8-Ab), if S,<l cm, (11)
A=A,, if Sw>l cm, (12)
where Ab and A, are the albedos of bare soil and of deep
snow, respectively, and A is the albedo of the earth’s
surface covered by snow of water equivalent S,, assumed
here to be one-tenth of the snow depth. For our com-
putations, A, is assumed to be 0.60. Poleward of latitude
75O, however, the albedo over land and pack ice is assumed
to be 0.75 everywhere, as suggested by the results of Kung
et al. (1964).
D. MOlSB PROCESSES
The tendency equation used for predicting mixing
ratios in the model is
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 3 39
The first term in eq (13) gives the contribution t o the
mixing ratio change, resulting from the three-dimensional
flux divergence of water vapor. The second term stands
for the effects of moist convective adjustment and con-
densation. The third and fourth terms represent the con-
tributions of the horizontal and vertical subgrid scale
mixing, respectively. These last two terms are discussed
further in subsection 2E. If in the numerical evaluation of
this equation truncation error causes a negative mixing
ratio at any layer, this erroneous value is set to zero.
Whenever possible, moisture is borrowed from adjacent
layers in the column to make up this deficit of water
vapor in such a way as to satisfy the water balance over
the entire domain.
One of the most serious difficulties in designing a
numerical model of the general circulation is in the
parameterization of moist convection. Since we know
very little about the interaction of small-scale convection
with the large-scale fields of motion, we adopted an
extremely simple system for simulating the effect of
moist convection on the macroscopic behavior of the
atmosphere. Despite its simplicity, this system qualita-
tively possesses at least some of the essential characteristics
of moist convection in the actual atmosphere. The basic
assumptions adopted for this system of moist convection
are :
1. If air is saturated and the lapse rate is super moist-adiabatic,
free convection is strong enough to make the equivalent potential
temperature uniform and the relative humidity saturated in the
convective layer.
2. The sum of potential, internal, and latent energy is conserved
during the convective adjustment.
The net effect of this moist convection scheme in the
model is to neutralize the lapse rate, release the heat of
condensation, and transfer heat frnni the lower t o the
upper layers.
More specifically, the tendency equations for tempera-
ture and mixing ratio are first evaluated without the
convective adjustment terms, and the resulting tendencies
are extrapolated in time to obtain tentative values of
temperature and mixing ratio at the next time step. If
the combination of these temperatures and mixing ratios
a t two or more adjacent levels defines a super moist-
adiabatic lapse rate in the presence of saturated or
supersaturated air, free convection of sufficient intensity
is assumed t o take place to produce a uniform equivalent
potential temperature and a saturated humidity in the
layers associated with these levels in the model. Excess
moisture is condensed, and the integral of this condensa-
tion over the entire column of air above a grid point is
counted as the precipitation amount. For each moist
unstable layer containing n contiguous levels of the
model, the n temperature and n mixing ratio corrections
are determined from the solution of 2 n simultaneous
equations derived from n saturation mixing ratio versus
temperature relations, n- 1 neutral moist lapse rate
conditions, and one integral energy conservation require-
ment based on assumption (2 ). Further details of the
moist convective scheme may be found in Manabe et al.
(1965).
If the tentative lapse rate is not super moist-adiabatic,
condensation will still be forecast to occur in the model
atmosphere whenever and wherever the tentative mixing
ratio exceeds the saturation value. At each supersaturated
level, incremental changes of temperature and mixing
ratio are determined from the simultaneous solution of a
pair of equations by an iterative method. For simplicity
in the computation scheme, all condensation resulting from
this procedure is assumed to fall out of the atmosphere
immediately, and no condensation goes into clouds or
evaporates while falling through drier lower layers. Dif-
ferentiation between rain or snow depends upon the tem-
perature at a height of about 350 m. This height is selected
subjectively by reference to a survey article by Penn
(1957). If the temperature at this level is freezing or
below, snow is forecast; otherwise, rain is predicted.
E. SUBGRID SCALE VERTICAL AND HORIZONTAL MIXING
The formulation of the vertical mixing of momentum
used in this work is identical to that described by Smagor-
insky et al. (1965). The frictional force produced by this
vertical mixing of momentum is computed by
where p and g are the density of air and the acceleration
of gravity, respectively. The components of the vector
VF are FA and vFO appearing in eq (1) and (2). The stress
on a horizontal surface v~ is computed by
(15)
where the coefficient of vertical diffusion, K ", is based on
the mixing length hypothesis, namely,
The mixing length 1 is assumed to increase linearly with
respect to height up to 75 m and then to decrease linearly
with height to 2.5 km where it becomes zero. Therefore,
no subgrid scale vertical mixing is assumed to occur above
2.5 km. The value of 1 at 75 m is assumed to be 30 m (this
implies that the Kdrmhn constant is equal to 0.4 below
75 m). The equation for computing the stress at the lower
boundary is presented in subsection 2F.
The vertical diffusion of mixing ratio in this model is
the same as described by Manabe et al. (1965). The
change in mixing ratio, resulting from small-scale vertical
340 MONTHLY WEATHER REVIEW Vol. 99, No. 5
mixing, is given by
P* aw vF,=- - P a2
where
For computational stability, the vertical diffusion equa-
tions are solved implicitly by a method described by
Richtmyer (1957).
No attempt is made to incorporate a vertical diffusion
of heat other than to compute the sensible heat flux a t the
surface of the earth. Since we incorporated the vertical
mixing of momentum and mixing ratio, this mechanism
for vertical mixing of heat should have been incorporated
into the model for consistency. However, the effects of the
dry and moist convective adjustments are so large in
most areas that the omission of this type of mixing does
not make a significant difference. It is, therefore, felt that
the dry and moist convective adjustments provide the
model with adequate small-scale vertical mixing of heat.
The formulation of the horizontal subgrid scale mixing
is an adaptation of the scheme used by Smagorinsky et al.
(1965). According to Smagorinsky (1963), the rates of
change of the east-west and north-south momentum,
resulting from the horizontal stresses appearing in eq (1)
and (2), are comput,ed as
(19)
and
where +A, rig, roX, and roo denote the stress tensors re-
sulting from mixing along constant u surfaces. Ignoring
the density variation on a constant u surface and assuming
the hydrostatic relationship, we can express the stress
tensors by
(21) +A=- 7 eo- -pp,&DT
and
rM=r@A=p*KHDs (22)
where the tension and shearing rates of strain, respectively,
are defined as
and
+--- - . a ae a ( COS e 1 ‘-a COS sax D -
The assumption of an inertial subrange yields the follow-
ing relation by dimensional analysis :
KH= I: ID I (25)
where 1D1=(D~+D~)1/2 and I , is a characteristic length
corresponding to the scale that defines the exchange coef-
ficient. This length is assumed to be defined as
where the parameter k, related to the KBrmhn constant is
assigned the value 0.2 in this paper. I n the above relation,
6, is the grid distance in the appropriate direction. For the
computations of the rates of strain on the northern and
southern grid box interfaces, 6, is aAB; on the’eastern and
western interfaces, &=a cos BAA where AB and AX are the
increments of latitude and longitude, respectively, on the
grid system. The performance of the nonlinear viscosity
described here was extensively discussed by Manabe et al.
(1970~).
For preventing excessive mixing of heat and moisture
along mountain slopes, we assume that these properties are
mixed on isobaric instead of on u surfaces.2 The approxi-
mate equation for computing the contribution of hori-
zontal mixing to the change of temperature or mixing
ratio of water vapor is
where a stands for either temperature or mixing ratio. For
a more general form of this equation, refer to Kurihara
and Holloway (1967). In the derivation of eq (27), the
more general form of the equation is simplified by the drop-
ping of less important terms for economy in computation.
We feel that this approximation does not cause serious error
except near steep mountain slopes.
For computational stability, these horizontal mixing
computations are performed by using the so-called “for-
ward time differencing’’ method.
F. BOUNDARY CONDITIONS AT THE EARTH’S SURFACE
The surface stress in the model (r *) is computed by
(a*) =-P(h)Co(h)IV(h)IV(h) (2% 1
where CD(h) is the drag coefficient applicable to minds at
height h and is defined as
C,(h) = { ko[loge(hz;)]-q2 (29)
and where p(h) is density, V(h) is the velocity at height
h, and k, is the Etirmtin constant. The roughness param-
eter zo is assumed to be 1 cm, and h is choscn to be equal
to the height of the lowest prognostic level. The surface
stress thus computed constitutes the lower boundary
condition for the computation of the Reynolds stress
resulting from vertical mixing.
2 Momentum is not mixed on isobaric surfaces, which is inconsistent with the mixing
formulation used here for heat and moisture. However, the difference between results
computed by mixing momentum on constant u instead of on constant pressure surfaces
is thought to be small.
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 341
FIGURE 2.-Polar stereographic maps of the prescribed February sea-surface temperatures for the model in the Northern (left) and Southern
(right) 'Hemispheres. The areas of pack ice are shaded with slashed lines, and the continental areas are shaded with dots; units, OK.
Similarly, the heat flux (,,H)* a t the surface of the earth
for either land or sea is given by the relation
(v -K )* =c p p (h ) c ~(h ) I V(h) I { T*- T(h) [~(h)l-"'") (30 1
where T* is the surface temperature. For insuring that a
minimum amount of heat is exchanged between the
earth's surface and the lowest level of the model atmos-
phere, the wind speed I V(h) I used in eq (30) is not allowed
to be less than 1 m/s.
The flux of latent energy (.LH)* from the ocean is
obtained from
(,L.H)*=LE (31 1
E=P(h)CD(h>I V(h)ltrAT*)--r(h)l (32)
and
where L is the latent heat of evaporation, E is the rate of
evaporation, and r,(T*) is the saturation mixing ratio of
water vapor over water at the surface temperature. Over
land, E is computed from eq (32) only when the land sur-
face is sufficiently wet. The formula for estimating the
rate of evaporation from a drier surface is discussed in the
following subsection. The heat and moisture fluxes at the
earth's surface constitute the lower boundary conditions
for the computation of the vertical mixing of heat and
moisture.
Over land, the temperature of the earth's surface T* is
determined in such a way that it satisfies the require-
ments of aaurface heat balance. If we assume that the
heat capacity of the land surface is zero (ie., no heat con-
duction into the soil), the equation of the heat balance
requirement is
where S* and (DLR)* are the net downward insolation
and the net downward longwave radiation at the earth's
surface, respectively, and asB is the Stefan-Boltzmann
constant. Since the diurnal variation of insolation is elim-
inated in the model, we assume that it is therefore justifi-
able to neglect heat conduction into the soil. Equation
(33) is solved with respect to T* numerically. Once T* is
determined, it is then possible to compute the upward flux
of both sensible and latent heat from eq (30-32).
Over pack ice, the term Qfce representing heat conduc-
tion into or out of the ice is added to the right-hand side
of eq (33) ; thus
&ice=kl-'( T*-271.2OK) (34)
where k is the thermal conductivity of ice (assumed to be
5 X cal . s-'. cm-I "C-' in this study) and I is the ice
thickness taken to be 2 m in the ice-covered area specified
in figure 2. We considered 2 m as a representative thickness
of sea ice in the Arctic (in the Southern Hemisphere sum-
mer, sea ice is of negligible extent around the Antarctic).
The temperature of the sea water below the pack ice is
assumed to be 271.2"K. If the solution to this heat bal-
ance equation results in a value of T* above freezing, this
value is set back to freezing with the implicit assumption
that the excess heat is used for melting pack ice.
The surface temperature over the oceans is prescribed
342 MONTHLY WE
as the climatic mean February values determined from
U.S. Hydrographic Office (1944) data. See figure 2 for a
map of these prescribed sea temperatures.
C. GROUND HYDROLOGY
One essential part of the hydrologic cycle of the earth-
atmosphere system is the storage of water in the ground
or on top of the surface as snow. I n the design of the
scheme for computing the ground hydrology, we desired
to make this procedure very simple for two reasons:
1. For ease in interpretation of the results, i t is advisable to try
a rather simple scheme before using a very sophisticated one.
2. These computations have to be performed a t a great number
of grid points, which dictates that the most efficient method must
be used, lest the hydrologic calculations take an inordinate amount
of computer time.
The procedure incorporated into the model is highly ide-
alized and is the same as used by Manabe (1969). The
reader should refer to this reference for more details of
this system and for some of the justifications for our
simplifying assumptions.
The maximum amount of water that can be stored in
the ground is called the field capacity of the soil of a
particular area. The field capacity of soil, of course, de-
pends upon a number of characteristics of the ground
surface and thus varies considerably throughout the world,
the domain of this global general circulation model. For
the utmost simplicity in our first attempt to model the
ground hydrology on a global scale, we have set the field
capacity of the soil to 15 cm over all land areas. Most of
the time, the actual soil moisture a t a given point falls
short of the field capacity of the soil in that area,. I n the
model, a budget of soil moisture is kept at each land grid
point. Over all land points, the soil moisture was initially
set t o its full capacity of 15 cm. Changes in soil moisture
are computed as the residual of contributions from proc-
esses that increase soil moisture (ie., rainfall and snow-
melt) and those that decrease it (i.e., evaporation and
runoff). Runoff is predicted a t a grid point only if a fore-
cast change in soil moisture would result in a water depth
exceeding the field capacity. Implicit in this procedure is
the assumption that the rate of infiltration of water into
the soil is always greater than the sum of the rainfall and
snowmelt rates, as long as the field capacity of the soil is
not exceeded. Any moisture above 15 cm is thus computed
as runoff at the grid point where this occurs. Runoff is
assumed to flow‘directly to the sea via rivers without
affecting the soil moisture at any other point.
The effect of soil moisture on evaporation is incorporated
into the model by a simple scheme used by Budyko (1956).
When the soil does not contain a sufficient amount of
water, the amount of evaporation is smaller than the value
obtained from eq (32), which gives the evaporation from
the sea or a perfectly wet surface. Equation (32) thus
gives an upper limit for evaporation over a land surface.
This upper limit is termed “evaporability” or “potential
ATHER REVIEW Vol. 99, No. 5
evaporation.” If the soil moisture is greater than a certain
critical percentage (75 in this study) of the maximum soil
capacity, evaporation is assumed to equal evaporability.
Otherwise, evaporation from land is computed to be
linearly proportional to soil moisture up to this critical
value. Over snow or ice, the sublimation also equals
evaporability; but in the computation of the latter, r,(T*)
is the saturation mixing ratio of water vapor over ice
instead of over water in eq (32), and L is now the latent
heat of sublimation in eq (31).
The equation for the prediction of the water equivalent
depth of snow S is
(35)
where S , is the rate of snowfall, Me is the rate of snowmelt,
and E is the sublimation rate. The snowmelt rate may be
calculated from a heat balance condition at the snow-
covered surface as
or Me=EJ;l, if Ex>O (36) .I
Me=O, i f ExlO
where L, is the latent heat of fusion and E,! the rate of
excess heat energy made available for melting snow, is
computed from
with T* held constant a t freezing [see eq (30) for (Jl), and eq (31) for (vLH)*].
After the snow disappears by melting or sublimation,
moisture again evaporates from the soil surface. Therefore,
it is necessary to keep track of soil moisture even when the
ground is covered by snow. We must know the water-
holding capacity of snow to do this. The water-holding
capacity of snow depends on the snow depth and density
and on many other complicating factors, and it ranges
from 2 to 5 percent of the weight of the snow according
to a study by Qerdel (1954). For simplicity, we shall
assume that the moisture-holding capacity of snow is
zero. If the soil moisture below a snow cover is less than
the field capacity, the rate of increase in soil moisture
there equals the sum of the rainfall and snowmelt rates,
and the runoff rate is zero. If the soil moisture below the
snow equals the field capacity, its value remains at that
level, and the runoff is taken to be the sum of the rainfall
and snowmelt. Because of the possible effects of freezing,
melting, and sublimation of soil moisture, the actual
processes could be more complicated than those idealized
conditions assumed to occur in our model. Nevertheless,
we feel that the scheme described here for computing soil
moisture, snowmelt, and runoff represents the elementary
features of the hydrologic phenomena at the ground
surf ace.
J. Leith Holloway, Jr. and Syukuro Manabe
-
- 25
- 20
23-
220 I -
-15 z
230 -IO$
- i
242 25 26
27 28
29
0 Is’ 3 0 45’ 60” 75‘ 90’5 75’ 60’ 45’ 30’ Is’
LAlllUDE ”
343
FIQURE 3.--Latitude-height distribution of the ~e a n zonally averaged temperature computed by the N24 model compared with the mean
observed distribution for December through February derived by Newell et al. (1969); units, OK.
3. SIMULATION OF CLIMATE BY THE MODEL
The low resolution (N24) model was started from zonally
averaged data from a previous model. In general circula-
tion model experiments, about 100 days must be in-
tegrated before quasi-equilibrium is reached. As a result
of a number of model changes in stream, more than 200
days were required for equilibrium in this model experi-
ment. A total of 341 days was integrated in time. A
period of 70 days was averaged for the hydrologic means
and another 40-day period was used for the wind and
temperature means. Unless otherwise stated, d l results
presented in this section are for the N24 grid model. See
appendix B for a discussion of the high-resolution (N48)
model run.
A. TEMPERATURE
Figure 3 shows a 40-day mean latitude-height distribu-
tion of the zonally averaged temperature computed by
the model compared with the mean observed distribution
for the Northern Hemisphere winter. The zonal mean
observed temperatures and zonal winds presented in this
paper are derived by Newell et al. (1969) for the months
of December through February.
I n general, the atmospheric temperature distribution
computed by the model is similar to the observed ex-
cept in high latitudes of the winter hemisphere. In
the Northern Hemisphere troposphere, high-latitude
temperatures are several degrees lower than the observed
values, due in part to the perpetual winter there. For
example, the temperature of the Arctic is about 10°K
too low. This effect in turn pushes the snowiline south-
ward. Since the presence of snow increases the albedo
above what is normal without snow and the heating of
the ground surface by solar radiation is consequently
decreased, the extreme winter conditions in the Northern
Hemisphere are self-perpetuating by positive feedback
and tend to propagate southward.
I n the summer stratosphere of the model, the warm
Antarctic is simulated successfully. Therefore, the tem-
perature in the lower stratosphere of the model in the
Southern Hemisphere increases with latitude, but this
increase is not as large 8s in the real atmosphere. As the
results of Manabe and Hunt (1968) indicate, this dis-
crepancy with observation is probably attributable t o
low vertical resolution in the tropical stratosphere, which
smoothes out and thus raises the minimum temperature
at the equatorial tropopause. They were able to simulate
a sharp tropical tropopause in a time integration of a
hemispheric general circulation model, having 18 vertical
finite-difference levels, double the number in our model.
I n the Northern (winter) Hemisphere of the model, the
temperature of the lower stratosphere is too low in higher
latitudes. It has, nevertheless, a maximum in middle
latitudes, in qualitative agreement with features of the
actual atmosphere. I n section 7, the heat balance of the
lower stratosphere is analyzed to determine how the
thermal structure of the model stratosphere is maintained.
- I n figure 4, the observed global distribution of surface
ambient air temperature over the entire earth during
January is compared with the values of surface tempera-
344 MONTHLY WEATHER REVIEW VOI. 99, No. 5
FIGURE 4.-Global distribution of mean temperatures computed in the N24 model experiment for the lowest prognostic level (at a height of
about 80 m) compared with the distribution of observed mean surface ambient temperature for January; units, OM. These maps and
all those of this type that follow are drawn on a modified elliptical map projection. The dots on the observed map and on later ones
outline highland areas.
tures computed by the model experiment for the lowest
prognostic level. I n the Northern Hemisphere, the
observed temperatures are from Crutcher and Meserve
(1970); and in the Southern Hemisphere, from Taljaard
et al. (1969). I n the Northern Hemisphere, the conti-
nental temperatures created in the model experiment
are somewhat lower than normal because of extensive
snow cover extending to low latitudes, attributed to the
perpetual winter in this hemisphere. This results in a
large temperature contrast between land and sea (e.g.,
off the east coast of Asia) because the sea-surface temper-
atures are specified as the climatic values.
I n the Southern Hemisphere, surface temperatures
computed by the model are very high over Australia and
the southern halves of South America and Africa. These
temperatures result from the dry soil and produce low
relative humidities and low pressures over these regions
as described in subsections 3C and 3D.
B. WIND AND MERIDIONAL CIRCULATION
Figure 5 shows the time-mean computed and observed
latitude-height distributions of the zonally averaged
zonal component of the wind with easterly winds (nega-
tive values) shaded. The axes of the computed tropo-
J. Leith Holloway, Jr. and Syukuro Manabe 345 May 1971
16
a E 70
= 2
315
500
685
LATITUDE
0'5
LATITUDE
FIQURE 5.-Latitude-height distributions of the time-mean zonally averaged zonal component of the wind with easterly winds (negative
values) shaded; units, m/s. The observed data are derived for December through February by Newel1 et al. (1969).
spheric jet streams in the model occur too close to the
Equator by about 6" t o 10' as compared with the observed
jets in both hemispheres. However, their heights are about
correct; and the maximum wind speeds of both jets are
very well simulated by the model. The computed wind
speeds in the stratospheric polar night jet and in the
easterly wind belt in the tropical stratosphere are much
too strong. Furthermore, the location of the polar night
jet in the model is nearly 20' too far south.
Preliminary results from a time integration of an
1 I-level global model, incorporating a seasonal variation
of solar radiation, show a markedly reduced intensity of
the easterlies in the stratosphere of the model Tropics.
Therefore, it is possible that the strong easterlies in the
model stratosphere result from the assumption of 8
perpetual January or from the lack of a seasonal variation.
The reawn for the very strong jet in the winter strato-
sphere of the model is not clear to the authors.
Figure 6 shows the stream function of the mean merid-
ional circulation computed from the time-mean meridional
and vertical velocities given by the model. For comparison,
on this same figure is shown the stream function of the
Northern Hemisphere meridional circulation, computed
by Oort and Rasmusson (1970) from observed winds for
five Januaries (note that the streamlines in this figure are
drawn at logarithmic intervals).
The Northern (or winter) Hemisphere Hadley cell is
considerably larger and stronger than the corresponding
direct cell in the Southern Hemisphere, and actually it
straddles the Equator and crowds the weak Southern
Hemisphere Hadley cell to the south. This asymmetry of
the meridional circulation is caused by the asymmetries in
the insolation and in the sea-surface temperatures. The
intensities of the computed and observed northern Hadley
circulations agree quite well, the centers being about
200 x 10'2 g/s.
The strong northern Hadley circulation creates intense
cross-equatorial flow at two levels [viz, a very shallow but
strong boundary layer flow southward into the intertrop-
ical convergence zone (ITCZ), located at about latitude
I O O S in the model, and-a strong return flow just below the
equatorial tropopause]. This meridional circulation in the
Tropics supplies latent heat to the ITCZ a t low levels
and exports heat energy from the ITCZ in the upper
troposphere. This subject is discussed in more detail in
section 6. [See eq (39) for the definition of heat energy.]
Manabe et al. (1970b) show that the heat of condensation is
responsible for the remarkable intensity of the Hadley cell.
Agreement is also good for the locations and intensities
of the Northern Hemisphere Ferrel and polar cells in the
troposphere. The agreement between the two meridional
circulations deteriorates toward the north, both because
the model has certain deficiencies near the Poles (e.g., too
high surface pressure) and because the observed stream
function is least accurately estimated in the Arctic.
In the model stratosphere, a two-cell meridional circula-
tion predominates; however, it is not evident in the stream
function for the actual stratosphere shown in the lower
346 MONTHLY WEATHER REVIEW Vol. 99, No. 5
I O
COMPUTED
LATITUDE
25
20
1 I5 p
IO p
t c I
I
5
1 OBSERVED t
25
LATITUDE
FIGURE B.-Stream functions of the mean meridional circulation; units, 1012 g/s.
half of figure 6. One should note that the observed stream
functions are least accurate in the stratosphere because of
the inaccuracy of the wind measurements. Teweles (1965)
and Mijrakoda (1963) computed the distribution of vertical
trelocity by use of the so-called "adiabatic" method and
by the w equation, respectively. Both of their results
clearly indicate a two-cell meridional circulation in the
winter stratosphere.
C. SEA-LEVEL PRESSURE
The mean sea level pressure for the N24 model is plotted
in figure 7 versus latitude and compared with the ob-
served pressure curve derived for the Northern Hemi-
sphere winter by Mintz (1968). The surface pressure over
land is reduced to sea level by
where p s , is the sea-level pressure; TgJ the temperature of
the lowest prognostic level; z*, the height of the land sw-
face above sea level; and y, the lapse rate, assumed to be
6"K/km everywhere.
An unfortunate characteristic of the general circulation
models used in this study is that they create much higher
than normal sea-level pressures in polar regions (fig. 7).
The mechanism producing these high polar pressures is
1050
FIGURE 7.-Zonal mean sea level pressures observed in the actual
atmosphere (solid line) and computed by the low resolution
(N24) model (dashed line) and by the high resolution (N48) model
(dotted line).
probably a combination of several factors, some of which
are unique to the type of grid system used for these models;
two of these factors are:
1. The assumption of a perpetual Northern Hemisphere winter
insolation produces extreme cold over the polar region and excessive
snow cover over the entire winter hemisphere. The resultant cold
dome of air covering the north polar region favors the development
of high pressure there.
2. As discussed in appendix A, subsection D, our models probably
have a systematic bias in generating higher than normal pressures in
polar regions.
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 347
FIQURE 8.-Mean global sea-level pressure computed by the low resolution (N24) model and observed in the actual atmosphere; units, mb.
The computed meridional profile exhibits minima in
the sea-level pressure in the Tropics and in the mid-latitude
storm belts and high pressure at subtropical latitudes and
in polar regions. However, these features of the computed
distribution are shifted systematically toward the Equator
from their counterparts in the observed profile. Further-
more, the intensities of the high-pressure belts in the model
subtropics are too weak. Another failing of this model is
the lack of a strong pressure gradient from latitudes 45' to
65's which results in the model not properly simulating
the location and strength of high-latitude surface wester-
lies in the Southern Hemisphere. The exact reasons for
these unrealistic features of the model simulation are not
determined; but they are partly related to the loss of com-
putational accuracy, resulting from the coarseness and
irregularities of the grid system mentioned above, as evi-
denced by the fact that a doubling of the resolution of the
finite-difference grid greatly improves the zonal pressure
distribution. In contrast to the low-resolution results, the
mean zonal pressure of the high-resolution model exhibits
a poleward shift of the pressure patterns, a reduction of the
high polar pressures, and an intensification of the sub-
tropical Highs and the middle latitude low-pressure belts
(see appendix B for further details).
The two-dimensional global distribution of sea-level
pressure is compared in figure 8 with the observed January
mean global sea-level pressure compiled by Crutcher and
Meserve (1970) in the Northern Hemisphere and by Tal-
348 MONTHLY WEATHER REVIEW Vol. 99, No. 5
16
s
70-
Ly
u
IA 2
F165-
315-
500 -
685-
1
9:&i
990 90
I ! I
"N 75" 60' 45' 3 0 15" a 15' 3 0 4 9 60' 75'
LATITUDE
- 25
- 2 0
t
-102
-15 p d
E
I
-5
-1
90 'S
FIGURE 9.-Zonal mean latitude-height distribution of relative humidity from the low resolution (N24) model experiment. Relative
humidities greater than 40 percent are shaded; those greater than 80 percent are indicated by darker shading.
15KN
c lOKM
!?
T
5KM
I
5 KM
n
BOON 700N 60°N 5PN 4ODN 30°N ZWN 100N 0' 10's
LATITUDE
FIGURE IO.-Eatitude-height distribution of the zonal mean ob-
served relative humidity for the summer season based on data
from Telegadas and London (1954) in the lower troposphere and
Murgatroyd (1959) in the upper troposphere.
jaard et al. (1969) in the Southern Hemisphere. This map
shows that, in the Northern Hemisphere, the model simu-
lates a well-developed Aleutian Low but an underdeveloped
Icelandic Low. On the computed pressure map, the Sibe-
rian High tends to merge into the highly exaggerated polar
High. I n the Southern Hemisphere, subtropical Highs form
west of the three major continents (viz, Africa, Australia,
and South America), in agreement with features of the
observed distribution. .However, the strengths of these
Highs fail to attain climatic levels. Low-pressure centers
develop over these Southern Hemisphere continents as a
result of high surface temperatures (see subsection 3A).
The low-pressure belt along the periphery of the Antarc-
tic is simulated in the model experiment in qualitative
agreement with observation, but it is not deep enough and
is at too low a latitude. This feature of the Southern Hemi-
sphere pressure distribution accounts for the lack of strong
westerlies in high southern latitudes of the model
experiment.
The distribution of sea-level pressure is markedly im-
proved by the increase in resolution of the horizontal
finite differences. For example, in the high-resolution model
experiment, the strengths of subtropical Righs are en-
hanced significantly; and the Siberian High is clearly sep-
arated from the polar High because of the markedly
decreased north polar pressures. See appendix B for details
concerning this improvement.
D. HUMlDliTV
The zonal mean latitude-height distribution of relative
humidity from the low-resolution model experiment is
presented in figure 9. The latitude-height distribution of
mean observed relative humidity for the summer season
is shown in figure 10, borrowed from the paper by Manabe
et al. (1965). A comparison between these two figures
shows that the mean computed relative humidity near
the surface is too high at all latitudes compared with
observation. In agreement with features of the actual
atmosphere, the model stratosphere, in contrast, is very
dry except a t very high latitudes of the Northern (winter)
Hemisphere. There are mid-latitude wet zones in both
hemispheres. The dry zones in the subtropics, resulting
from the descending motion in the poleward legs of the
Hadley cells, seem to extend downward from the dry
stratosphere aloft and spread into the mid-troposphere of
the Tropics, in agreement with observed data. In the
Tropics, the vertical motion is very strong in the mid-
troposphere. The very dry air produced by this down-
ward motion may be responsible for lowering the zonal
mean relative humidity in the mid-troposphere.
In figure 11, the mean surface relative humidity com-
puted by the model experiment is compared with the mean
global distribution for January, derived by Ss&va-Kov&ts
(1938). Over the oceans, the computed surface humidity
exceeds the observed values by 10 to 20 percent. The
reason for this is not obvious. However, realistically low
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 349
FIGURE 11.-Global mean relative humidities; areas of relative humidity below 60 percent are dotted; those above 90 percent are shaded by
slashed lines on the computed map, and those above 85 percent are shaded on the observed map. Over the Antarctic, the observed data
are missing.
values of relative humidity are correctly computed by
the model for the arid regions of the world. For example,
dry air is computed by the model near the ground over
the Sahara, Australia, southwestern United States, and
India during this season. Dry areas are also simulated
in the southern parts of South America and South Africa,
although in these areas the computed dry belts are
somewhat too wide. As pointed out above, the surface
temperatures of most of these dry regions are very high.
4. WATER BALANCE
In this section, we shall present global maps of the dis-
tributions of various hydrologic variables computed by
the low resolution (N24) model experiment and compare
these with climatic data.
Figure 12 shows a comparison between the computed
mean precipitation rate and the observed rate derived
from data for December, January, and February by Moller
(1951). In this figure, areas with computed or observed
350 MONTHLY WEATHER REVIEW Vol. 99, No. 5
FIQURE 12.-Mean precipitation rate computed by the low resolution (N24) model compared with the estimated observed rate (Moller 1951).
precipitation rates in excess of 0.5 cmlday are shaded by
diagonal lines, and dry regions with rates of precipitation
lower than 0.1 cmlday are dotted. The computed distri-
bution of precipitation exhibits a tropical rain belt,
subtropical dry belts, middle-latitude moist regions, and
polar dry zones that correspond rather well in location
and intensity to the observed distributions.
From the eastern Indian Ocean eastward to the central
Pacific Ocean, the computed tropical rain belt runs along
the Equator OT slightly to the south, in agreement with
observation during this Northern Hemisphere winter
season. This belt dips southward in the Amazon Valley
in South America and toward Madagascar in the western
Indian Ocean and swings northward in southern Africa,
in good agreement with observed rainfall patterns.
The tropical rain belt splits into two legs in the eastern
Pacific Ocean. The computed southern leg is not as
well-developed as observed, and the northern leg straddles
the Equator rather than being centered at about 5" to
10°N, as occurs in the real atmosphere. This latter dis-
crepancy with observation can probably be attributed t o
the lack of a distinct minimum in the sea-surface tempera-
ture centered on the Equator, which occurs in nature but
unfortunately is not very pronounced in the U.S. 1EIydr0-
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 351
graphic Office (1944) data used for this model experiment.
The cooler sea water actually observed at the Equator
tends to suppress the genesis and development of tropical
disturbances [e.g., see the results of the model experiment
by Manabe and Bryan (1969)l. Thus, the observed rainfall
maximum is shifted slightly northward t o where the sea
is warmer.
The location of the subtropical dry belt in the Southern
Hemisphere in the model atmosphere agrees well with
observation. The areas of minimum precipitation in this
belt are off the west coasts of the continents where the
oceanic anticyclones are located and the outflow from them
predominates. The East Coasts are relatively wet, in
agreement with the observed distribution of precipita-
tion and with a similar model experiment by Manabe
(1969). Dry air flowing out of subtropical anticyclones
west of Africa and Australia causes the low precipitation
rates and resulting deserts in the southwestern regions of
these continents. %The dry air flows more than halfway
across Australia but is confined to the West Coast of
South America. The reason for this difference is that,
in South America, the very high Andes Mountain Range
extending north-south along the entire continent just
east of the West Coast effectively blocks the dry air from
spreading eastward; but there are no such high and
extensive mountains in the western part of Australia.
The precipitation patterns computed from a model
without mountains confirm this theory by exhibiting a
dry area across the entire southern part of South America.
This phenomenon was discussed in Manabe and Hollo-
wa.y (1970a, 1970b). In fact, the computed distribution of
precipitation given in figure 12 shows a greater eastward
extension of the dry area in South America than is actually
observed. As discussed in appendix C, this can be attrib-
uted t o the smoothing of the model’s topography that
reduced the maximum height of the Andes far below the
true elevations of these mountains. The Andes being
rather narrow in the east-west direction are particularly
susceptible t o height reduction by space smoothing.
The Northern Hemisphere subtropical dry belt is well
simulated by the model in location and magnitude of
precipitation values. The extreme dryness of the Sahara
Desert is well simulated by the model. The joining of the
subtropical dry belt with the polar dry zone over North
America is suggested but not completely realized by the
N24 model results. However, in the precipitation dis-
tribution computed by the high resolution (N48) model,
these two dry zones are joined in agreement with climatic
data (see appendix B for further details).
The computed mid-latitude wet belt in the Southern
Hemisphere is continuous around the entire globe, in
agreement with observation, except in southern Argentina
where the observed wet belt is slightly interrupted by the
Andes. I n the Northern Hemisphere, however, the wet
zone in middle latitudes, computed by the model, is
broken into cells by the mountains on the continents. This
topographic effect is not as pronounced in the model as in
nature because of the smootjlness of the topography used
in the model computations. The shallowness of the dry
break in the middle of the North American Continent has
been mentioned above. This northern middle-latitude moist
belt is characterized by areas of high precipitation rate off
the east coasts of the continents, in agreement with ob-
servation. The wet area, created off the northwestern coast
of the United States, is centered too far south, which is no
doubt related to the equatorward shift of surface-pressure
patterns, as discussed in the previous section. Finally, for
some unknown reason, precipitation rates over Europe are
substantially above climatic values and those simulated by
the high-resolution model run (see fig. 32 in appendix B).
In figure 13, the global distribution of evaporation rate
computed by the model is compared with the evaporation
rate distribution compiled by Budyko (1963). I n the
oceanic regions, the computed evaporation is significantly
less than the rate estimated by Budyko, particularly in
the subtropics. This discrepancy is, no doubt., related to the
fact that the relative humidity is generally too high near
the surface of the model oceans, as pointed out in the pre-
ceding section. Naturally, such high surface humidities
tend to lower the general level of evaporation from the
ocean surface. Although the rates of evaporation of the
model have local maxima in the subtropical regions of both
hemispheres in qualitative agreement with features of
Budyko’s distribution, the local maxima are too small and
are located too close to the Equator. I n the preceding sec-
tion, it is pointed out that the oceanic anticyclones of the
low resolution (N24) model are also located too close to the
Equator. Since the oceanic anticyclones produce outflow of
very dry air over the ocean surface, they tend to enhance
evaporation. Accordingly, the discrepancy between the
observed and computed locations of the subtropical anti-
cyclones seems to be partially responsible for the unrealis-
tic distribution of evaporation mentioned above. I n middle
latitudes, evaporation from the oceanic surfaces of the
model is most rapid off the east coasts of the Eurasian and
the North American Continents, in excellent agreement
with features of Budyko’s distribution. In t.hese areas, cold
continental air with low absolute humidity flows out over
the warm oceanic surfaces, which creates large air-sea
temperature differences and enhances evaporation.
In continental regions, agreement between the model’s
distribution and Budyko’s is better. For example, the
model computes a very low rate of evaporation in deserts
such as the Sahara, southwestern Africa, and southern
South America, in good agreement with Budyko’s distri-
bution. In high northern latitudes and in the Antarctic,
the evaporation rate of the model is very small. In fact,
in a few northern latitude areas, the evaporation rate is
even slightly negative, which indicates frost formation.
The effective reflection of solar radiation by snow or
pack ice leaves little energy available for sublimation in
these areas.
421361 0-71-2
352 MONTHLY WEATHER REVIEW Vol. 99, No. :5
FIQIJRE 13.-Global distribution of evaporation rate computed by the N24 resolution model and the same rate derived by Budyko (1963)
from observed data.
Figure 14 depicts the computed soil moisture on the
model continents. Dry areas having less than 0.5 cm of
soil moisture are dotted; and wet regions, where the soil
moisture is greater than 5 cm in depth, a.re indicated by
slashed shading. The snowline, shown a s a dashed line,
appears too far south on all Northern Hemisphere conti-
nents because of perpetual winter. The arid regions of the
earth, having little soil moisture, are well simulated by
the model. For example, the Sahara, the desert in Western
Australia, and the arid region of southwestern Africa are
well represented by the computed soil moisture distribu-
tion. These are areas of little precipitation as observed in
nature and as simulated by the model (fig. 12). On
figure 14, India appears as a desert. Recall, however, that
the season of this model experiment is a perpetual January,
which is the time of- the winter monsoon in India when
there is little or no rain in this country. If this experiment
had incorporated a seasonal variation of insolation, rain-
fall would have occurred in India during the summer
season, and desert conditions would not have become
established here. The desert area of the southwestern
United States is shifted southward into Mexico. This is
certainly related t o the extensive snow cover to the north
as well as to the equatorward shift of pressure pstterns,
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 353
FIGURE 14.-Computed soil moisture on the N24 resolution model continents.
0.25 -
20 -
.I5 -
s
FIGURE 15.-Zonal mean distributions of various snow balance
components. The envelope of curves is the snowfall rate; sub-
tracting from this is the snowmelt rate (shaded by slashed lines).
The sublimation rate is subtracted from the remainder but is left
unshaded. The net snow accumulation rate is dotted.
discussed in the previous section. The computed areas of
deep soil moisture amounts coincide with regions of
tropical rain forests (viz, tropical Africa, the Amazon
River Basin, and the Indonesian Islands).
Large areas of the continents of the Northern Hemi-
sphere of the model are snow covered. Figure 15, which
shows the zonal mean distributions of various snow
balance components on the continents, indicates that
snow accumulates significantly north of 45"N with a
maximum around 55"N. As pointed out, the extensive
accumulation of snow cover results chiefly from the
assumption of a perpetual January insolation. In view of
the lack of a seasonal varia.tion in the model insolation, we
felt that the distribution of soil moisture beneath the
snow cover is not meaningful. Therefore, it is not shown
in figure 14. According to figure 15, the latitude of the
maximum rate of snowfall does not coincide with the
latitude of the maximum rate of snow accumulation be-
cause of the effect of snowmelt. In the Northern Hemi-
sphere, the rate of snowmelt is at a maximum around
45'N; and in the Southern Hemisphere, i t is a t a maxi-
mum at the periphery of the Antarctic Continent. As will
be indicated in the following paragraph, the snowmelt
contributes very significantly to the runoff in the Northern
Hemisphere of the model.
Figure 16 depicts the distribution of runoff computed
on the model continents. White areas indicate no runoff,
and slashed shading indicates regions with runoff greater
than 0.1 cmlday. For the most part, these areas corre-
spond well with the watersheds of some of the earth's
major rivers (e.g., the Amazon in South America; the
Congo, the Zambezi, and the source of the Nile in Africa;
and the rivers in eastern and western United States).
According to the comparison between the distribution of
runoff rate and that of snowmelt rate shown in figure 17,
the areas of major runoff in the Northern Hemisphere of
the model correspond very well with those of snowmelt, in-
dicating the significant contribution of snowmelt to runoff
in these areas. This comparison also indicates that the
excessive runoff in the western part of the Eurasian Con-
tinent results mainly from the excessive snowmelt taking
place there, This snowmelt occurred during the early part
of the averaging period and is responsible for a rapid
decrease in snow depth there.
Evaporation from the earth's surface represents a
source of water vapor in the atmosphere, and precipita-
tion, on the other hand, is a sink for atmospheric water.
The distributions of these two meteorological phenonema
point out the locations of major sources and sinks of
354 MONTHLY WEATHER REVIEW VOl. 99, No. 5
0 NONE
0 to 1 cm/doy (Contours at .05 cm/da
> I cm/doy (Contours at 2, 5, and 10 cm/day
FIQURE 16.-Distribution of runoff computed for the model continents.
FIQURE 17.-Computed global distribution of mean snowmelt rate during the 70-day period of averaging of the N24 model experiment.
atmospheric water vapor. Figure 18 shows the model’s
zonally averaged evaporation and precipitation for the
whole earth, continental areas, and oceans as a function
of latitude. This figure shows that the major source of
water vapor is over the subtropical oceans of the Northern
(or winter) Hemisphere where precipitation is suppressed
by the general downward motion and the evaporation
from the earth’s surface is enhmced by high sea-surface
temperatures. The major sink of atmospheric water vapor
is in the ITCZ, especially over land where orography
enhances the already in tense tropical precipitation rates.
Secondary sinks are evident in middle-latitude rain belts,
particularly in the continental region of the Northern
Hemisphere.
At points where the curves for precipitation and evapo-
ration diverge are areas of deficiencies or excesses of
moisture that must be compensated by transport from
other areas. For example, the net excess of water vapor
I .I I . I . .,,,,,
1 CONTINENT i OCEAN
,601
n
CONTINENT
.60 -
- PRECIFITATION
.so -
.40 -
.30 -
OCEAN
.M) -
S O -
.40 -
FIQURE 18.-Latitudinal distributions of the rates of precipitation
and evaporation (in cm/day) .
added to the atmosphere in the northern oceanic sub-
t.ropics must be transported to the Tropics or to the
mid-latitude storm belt where precipitation exceeds
evaporation. On the other hand, subtropical continental
areas have low values of both evaporation and precipita-
tion so that net advection of water vapor into or out of
these areas is very small. The resultant transport of
latent energy by the advection of water vapor in the
model atmosphere is discussed in section 6.
5. HEAT BALANCE
A. HEAT BALANCE OF THE EARTH-ATMOSPHERE SYSTEM
The heat balance of the earth-atmosphere system is
determined by the net radiative flux a t the top of the
atmosphere. In table 2, the global mean values of radiative
fluxes of the model atmosphere are compared with those
TABLE 2.--F~uzes of radiation at the top of the atmosphere (in ly/min)
gind of radiation vonder Haar Deo., Jan., Feb. Model Jan.
Incident solar
Net downward solar
Net upward terrestrial
0.61 0.61
.36 .32
.32 .30
May 1971 1. Leith Holloway, Jr. and Syukuro Manabe 355
of the actual atmosphere estimated by vonder Haar
(1969) for the period from December to February. It
should be pointed out that the results of vonder Haar
are based on recent observations from meteorological
satellites. This table indicates that both the net downward
flux of solar radiation and the net upward flux of longwave
radiation at the top of the model atmosphere are signifi-
cantly less than those at the top of the actual atmosphere,
as estimated- by vender Haar. - The- differenoe in the
magnitude of the net solar radiation is chiefly due to the
difference in planetary albedo between the model and the
actual atmosphere. According to our computation, the
planetary albedo of the model atmosphere is approxi-
mately 0.37, which is larger than the albedo of the actual
atmosphere, as observed from meteorological satellit&
(0.31). One of the reasons for this discrepancy is the
excessive snow cover of high reflectivity in the Northern
Hemisphere of the model, which has been mentioned in
preceding sections. However, there may be other reasons
for this discrepancy. As vonder Haar indicated, the
planetary albedo obtained from satellite observations is
approximately 5 percent less than the theoretical estimate
by London (1957). Since the distribution of clouds and
their optical properties (used in this study) are very
similar to those adopted by London, it is probable that
our cloud properties suffer from the same deficiencies as
London’s and thus may also be significantly different
from reality.
Fortunately, an error in the planetary albedo may not
result in an extremely unrealistic climate in this study
because the distribution of sea-surface temperature is
specified as a lower boundary condition. However, a
several percent difference in planetary albedo may
markedly alter the climate of a joint ocean-atmosphere
model in which the sea-surface temperature is determined
as the results of the interaction between the oceanic and
the atmospheric parts of the model (see Manabe and
Bryan 1969). Therefore, it seems to be very important to
identify the causes of this discrepancy by repeating the
heat balance study of London with the improved data.
The latitudinal distributions of the zonal mean values
of the net radiation fluxes a t the top of the model atmos-
phere are shown in figure 19. For comparison, the cor-
responding quantities estimated by vonder Haar (1969)
for the actual atmosphere are also plotted in this same
figure. As pointed out, fluxes of both solar and terrestrial
radiation of the model are significantly less than the
356 MONTHLY WEATHER REVIEW Vol. 99, No. 5
,401
.oo , -/%
c 90°N 80 70 60 50 40 30 20 10 0" 10 20 30 40 50 60 70 80 9 0 °S
LATITUDE
FIGURE 19.-Latitudinal distributions of the zonal mean values
of the net downward solar radiation and the upward longwave
radiation a t the top of the model atmosphere (in ly/min).
observed values, particularly at low latitudes where
London's cloud distributions may be inaccurate. Careful
re-examination of the cloud distribution by means of
satellite data are highly desirable. The general features
of the model distribution, however, agree well with the
observed distribution.
For depicting the horixont,al distribution of the radiative
imbalance, the global distribution of the flux of net
downward radiation at the top of the model atmosphere
is shown in the upper half of figure 20. The distribution of
the corresponding quantity in the actual atmosphere,
as estimated by vonder Haar (1969) from satellites, is
added for comparison to the lower half of this figure. The
general features of the two distributions agree well with
each other, although the model distribution lacks some of
the longitudinal variations in the net flux, which are
COMPUTED
FIGURE 20.-Global distribution of the flux of downward radiation [ = (net downward solar radiation) - (net upward terrestrial radiation)]
at the top of the a,tmosphere.
May 1971 1. Leith Hdloway, j r . and Syukuro Matrabe
-.30
0.40-1 " I ' " " " " " " ' t
LATENT HEAT FLUX
: ; ~; ;; ; I I ;
I J LONGWAVE RADIATION \ D I
.oo .-' , , , , , , , , , , , , , , c 90iN sb 7b LO 50 40 30 20 IO On IO 20 30 40 50 60 70 80 90'5
LATITUDE
FIQURE 21.-Latitudinal distribution of the zonal mean values of
the net downward solar radiation and the net upward longwave
radiation a t the surface of the model earth (in Ig/min).
evident in the vonder Haar distribution (note that the
cloud distribution assumed for the computation of radia-
tive transfer lacks a longitudinal variation). The net flux
of the model is, nevertheless, significantly smaller than the
observed flux at low latitudes, particularly in the sub-
tropics of the Southern Hemisphere, as pointed out in the
preceding paragraph.
B. HEAT BALANCE OF THE EARTH'S SURFACE
The heat fluxes contributing to the heat balance at
the surface of the model earth are the fluxes of solar and
terrestrial radiation, the turbulent fluxes of sensible and
latent heat into the atmosphere, and the heat flux to the
interior of the ocean. In this subsection, we shall examine
the distribution of these fluxes. According to figure 21
showing the latitudinal distribution of the radiative
fluxes at the surface of the model earth, the net downward
flux of solar radiation is much larger than the net upward
flux of terrestrial radiation except at high latitudes of the
Northern Hemisphere where the flux of solar radiation is
very small. The corresponding quantities at the surface
of the actual earth in the Northern Hemisphere, estimated
by London (1957), are also plotted for comparison in
this figure where July Northern Hemisphere values are
used for the Southern Hemisphere summer (January).
The agreement between the radiation fluxes computed by
the model and those estimated by London from observed
data appear, in general, to be very close.
Figure 22 is presented Lo show how the heat gain
resulting from the net downward flux of radiation
[= (downward flux of solar radiation) - (upward flux of
longwave radiation)] is compensated by the other heat
balance components mentioned above. The distributions
on the continents and those on the oceans are shown
separately for detailed examination.
On the model continents, because of the assumption of
a zero heat capacity of the ground surface, the heat gain
from the net downward radiation is exactly compensated
by the heat loss, which is due to the upward fluxes of sen-
sible and latent heat. In the Tropics and in middle latitudes
of the model where soil moisture is relatively large as a
result of the excess of precipitation over evaporation, the
latent heat flux is chiefly responsible for removing heat
'
CONTINENT a OCEAN
.20.
-.IO -
-20 -
CONTINENT a OCEAN
NET RADIATION
HEAT FLUX FROM THE OCEAN
CONTINENT
2o t
-
.IO/
NET RADIATION .
//,
LATENT HEAT FLUX
-.20
t
* NET RADIATION
357
5
FIGURE 22.-Latitudinal distributions of the zonal mean values of
various heat balance components a t the surface of the model
earth (in Iy/min). Thin solid line indicates the heat flux from
the interior to the surface of the ocean.
from the ground surface. On the other hand, sensible heat
flux plays a major role in the removal of heat from the
ground surface of the model subtropics where soil moisture
is small because of meager precipitation. In short, sensible
and latent heat fluxes supplement each other in removing
heat from the ground surface of the model.
Over the model oceans, the sensible heat flux is much
smaller than the latent heat flux except at very high lati-
tudes. In general, the Bowen ratio, whichis the ratio of sensi-
ble heat flux to latent heat flux, increases with increasing
latitude, in agreement with the features of the energy ex-
change over the actual oceans. Over ocean surfaces
(different from the case of a land surf ace), the heat loss due
to both sensible and latent heat fluxes does not necessariIy
compensate for the heat gained by net downward radia-
tion. The imbalance among these components constitutes
the heat sources and sinks for the model oceans. As figure
22 indicates, the model oceans gain heat in the Southern
358 MONTHLY WEATHER REVIEW Vol. 99, No. 5
FIGURE 23.-Global distribution of net downwaxd radiation at the earth’s surface. The net downward radiation is defined as the difference
between the net downward solar radiation and the net upward longwave radiation.
(summer) Hemisphere and lose heat in the Northern
(winter) Hemisphere.
Thus far, we have discussed the latitudinal distribu-
tions of various heat balance components at the earth’s
surface. Next, we shall briefly describe the global distribu-
tions of these components. The global distributions of net
downward flux of radiation and of net upward flux of sen-
sible heat at the surface of the model earth are shown in
the upper halves of figures 23 and 24, respectively. The
distributions of the corresponding quantities at the surface
of the actual earth, estimated by Budyko (1963), are added
to the lower halves of these figures for comparison. Another
heat balance component (i.e., latent heat flux at the surface
of the model earth) may be inferred from figure 13 which
shows the globaI distribution of the evaporation rate.
According to figure 23, the general features of the dis-
tributions of the net downward flux of radiation at the
surface of the model earth are quite similar to those of
Budyko’s distribution. For example, the net downward
radiational flux of the model is maximum in the subtropics
of the Southern Hemisphere except over the continents
where the net downward flux is very small because of the
high temperatures of the ground surface. This flux is nega-
tive in high latitudes of the Northern Hemisphere, in
agreement with the same features of Budyko’s distribution.
On the other hand, there are significant differences between
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 3 59
FIQURE 24.-Global distribution of net upward flux of sensible heat at the earth’s surface.
the two flux distributions. In general, the net downward
radiation flux of the model has a more zonal distribution
than the flux of the actual atmosphere, probably a result
of the lack of a zonal variation in cloudiness. Furthermore,
the net flux of the model is significantly less than the flux
estimated by Budyko in the subtropics of the Southern
Hemisphere. Again, it is highly probable that the inac-
curracy of cloudiness in the model is responsible for this
discrepancy. Statistical studies of cloud data obtained from
meteorological satellites are required to verify these
speculations.
In general, the distribution of the sensible heat flux of
the model (upper half of fig. 24) is much less zonal than
that of the net downward radiation. In the Southern
(summer) Hemisphere and in the lower latitudes of the
Northern Hemisphere, the sensible heat flux of the model
is relatively large over the continents, particularly over
arid regions such as the Sahara Desert, the Australian
Desert, Mexico, and India. In these areas, the magnitude
of the latent heat flux is small because of insu5cient soil
moisture; and a large amount of sensible heat flux is
required to compensate for the large values of net down-
ward radiation. Over the continents in middle and high
latitudes of the Northern Hemisphere, the sensible heat
flux of the model has 1~ small negative value as a result
of the temperature inversion at these latitudes. Since most
360 MONTHLY WEATHER REVIEW VOl. 99, No. 5
O.3OJ " " " ' " ' ' ' ' ' I ' L
HEATENERGY ' 20-
SENSIBLE HEAT
__*_r__..---*--
__lr -Cr_-
------- RAOlAllON
-.20,, , , , , , , , , , , , , , , ,
~ ~
90°N80 70 60 50 40 30 20 10 O' 10 20 30 40 50 MI 70 80 90's
WON 80 70 60 50 40 30 20 10 Oo 10 20 30 40 50 60 70 80 90'5
FIGURE 25.-Latitudinal distributions of the zonal mean values LATITUDE
of various heat balance components in the atmosphere (in ly/min).
FIGURE 26.-Latitudinal distributions of the northward transport
of energy (X cal/day).
of the weak insolation reaching the surface here is reflected
by snow cover, the magnitudes o€ all heat balance compo-
nents are very small over the model continents. Over the
oceanic regions of the Northern Hemisphere, the sensible
heat flux of the model is very large off the east coasts of the
continents where the outflow of cold continental air over
warm ocean currents takes place. These features of the
model distributions are in excellent agreement with those
of Budyko's distribution shown in the lower half of figure
24. This agreement suggests that the computation schemes
for the heat and water balance at the continental surfaces
of the model are working properly, despite the extreme
idealization of the various processes involved.
C. HEAT BALANCE OF THE MODEL ATMOSPHERE
The components of the heat balance in the a.tmosphere
are the net radiation, the heat of condensation, and the
supply of sensible heat from the earth's surface to the
atmosphere. Figure 25 shows the latitudinal distribu-
tions of the zonal mean values of these heat balance
components in the model atmosphere. According to this
figure, radiation has a cooling effect at all latitudes of the
model; and the other two components of the heat balance
already mentioned have a heating effect and tend to com-
pensate for the radiative cooling. The imbalance among the
three components is indicated by a solid line identified as
"net." In the model atmosphere, large values of net heat-
ing occur in the Tropics of the Southern Hemisphere where
the heat of condensation released by the tropical rain belt
is very large. On the other hand, a great deal of net cooling
takes place in the subtropics of the Northern Hemisphere
and in high latitudes where the heat of condensation is
practically negligible. The latitudinal distribution of the
heat imbalance described here is such that the cells of
meridional circulation are intensified, particularly the
cross-equatorial Hadley cell, as discussed in subsection 3B.
6. MERIDIONAL ENERGY TRANSPORT
The latitudinal distributions of the imbalances in the
water vapor and heat budgets in the model atmosphere,
described in sections 4 and 5 should be compensated by
the meridional transports of water vapor and heat energy
by the atmospheric circulation. Figure 26 shows the dis-
tributions of the northward transports of heat energy,
latent energy, and total energy required for compensating
the imbalance in the heat and water vapor budgets of
the model atmosphere. I n this paper, heat energy, latent
energy, and total energy are defined as
(39)
(latent energy) = Lr, (40)
(heat energy)= c,T + 4,
and
(total energy)= c,T + 4 + Lr (41)
where c, is the specific heat of air under constant pressure,
is geopotential height, r is the mixing ratio of water
vapor, and L is the latent heat of condensation. In this
definition of total energy, the kinetic energy (being rela-
tively small) is neglected.
In section 4, it is demonstrated that the subtropics of
the Northern Hemisphere constitute a source of moisture
for the model atmosphere because the rate of evaporation
far exceeds the precipitation rate there. Figure 26 indicates
that the northern subtropics export great amounts of
moisture both northward and sourthward. A major part
of this southward flux of latent energy crosses the Equator
and feeds the tropical rain belt in the Southern Hemi-
sphere of the model. The tropical rain belt in turn con-
verts latent energy into heat energy through the condensa-
tion process and exports a great deal of heat energy back
to the Northern Hemisphere. The direction of net cross-
equatorial transport of total energy [(latent energy) + (heat energy)] is northward (i.e., from the summer to the
winter hemisphere). However, the magnitude of this net
transport is rather small because the transport of latent
energy and that of heat energy have comparable mag-
nitudes but opposite directions. In summary, the tropical
rain belt in the Southern (summer) Hemisphere is chiefly
maintained through the interhemispheric exchanges of
heat and latent energies.
~~
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 361
According to figure 18, which shows the latitudinal
distributions of the rates of precipitation and evaporation,
precipitation exceeds evaporation in middle latitudes.
That is, the model atmosphere loses water vapor in middle
latitudes and has to import moisture from elsewhere.
Figure 26 indicates that middle latitudes receive moisture
from lower latitudes and export great amounts of heat
energy toward higher latitudes.
Figure 27 is presented to illustrate how this energy is
transported poleward in the model atmosphere. In this
figure, the northward transports of both heat and latent
energy are subdivided into three parts &e., transports
by meridional circulation, large-scale eddies, and subgrid
f i MERIDIONAL CIRCULATION 141 HFATENERGY (cpT++l
10
-2 SUBGRID
-4
A SCALE MIXING
LATENT ENERGY (Lr) t
SCALE MIXING
5
LATITUDE
FIGURE 27.-Latitudinal distributions of the northward transport
of energy (X 10 l8 cal/day) by the meridional circulation, large-
scale eddies, and subgrid scale mixing. The transport values in
the actual atmosphere, estimated by Oort and Rasmusson (1970)
for January, are plotted by open circles (eddy) and by
triangles (meridional circulation).
scale mixing). According to this figure, the cross-equatorial
transports of both heat and latent energy are essentially
accomplished by the meridional circulation (viz, by the
interhemispheric Hadley cell described in section 3).
In the model subtropics, the poleward transport of
latent energy by the large-scale eddies is significant. In
middle latitudes, the poleward transports of both heat
and latent energy are chiefly accomplished by large-scale
eddies. For comparison, the northward transports in the
actual atmosphere, which were obtained by Oort and
Rasmusson (1970) for the Northern Hemisphere, are
plotted in figure 27. The features of the observed distribu-
tion are quite similar to those of the model. Finally, it
should be pointed out that the poleward transport of
energy by subgrid scale mixing is practically negligible.
7. STRATOSPHERIC HEAT BALANCE
As pointed out in subsection 3A, the zonal mean
temperature of the lower stratosphere of the model
increases with increasing latitude in the Southern
(summer) Hemisphere and is at a maximum in the
Antarctic. In the Northern (winter) Hemisphere, it has
a maximum value in middle latitudes. These features
of the model stratosphere are in excellent qualitative
agreement with those of the actual atmosphere. There-
fore, it seems appropriate to discuss how the temperature
distribution is maintained in the model stratosphere.
Figure 28 shows the latitude-height distribution of
heat transport by the large-scale eddies and indicates
that the large-scale eddies transport heat poleward in
the model stratosphere in both hemispheres. The com-
parison between the latitudinal distribution of eddy
transport and that of zonal mean temperature in the
lower stratosphere of the model (see fig. 3) reveals that
heat is transported against the horizontal temperature
gradient in most of the lower stratosphere except in the
higher latitudes of the Northern Hemisphere. Such a
countergradient flux of heat in the lower stratosphere
was first discovered by White (1954). This counter-
gradient flux plays a key role in creating the temperature
FIGURE 28.-Latitude-height distribution of the northward transport of heat by the large-scale eddies in the model atmosphere; units,
1017 J mb-1- day-1.
361 MONTHLY WEATHER REVIEW Vol. 99, No. 5
1.1
9 -
1.4 -
1.3.
1.2 -
1.0 -
-
RADIATION
1
I !
+'O1
\i ,' !;
+1.51 I , I I 'L*/, , , , , , , , , , , , 1
90'N BO 70 60 50 40 30 20 IO 0 IO 20 30 40 50 60 70 80 90'5
MTITUDE
FIGURE 29.-Upper half, mean rates of temperature change by
radiation, meridional circulation, large-scale eddies, and sub-
grid scale horizontal diffusion at the 70-mb level of the model
as a function of latitude; lower half, the latitudinal distributions
of zonal mean temperature and zonal mean vertical p velocity
at the 70-mb level.
distribution in the model stratosphere of the summer as
well as of the winter hemisphere.
For illustrating how the heat balance of the model
stratosphere is maintained, the rates of temperature
change by radiation, meridional circulation, large-scale
eddies, and subgrid scale eddies at the 70-mb level are
shown in figure 29 as a function of latitude. (Because of
interpolation error in the analysis computation, the sum
of all contributions in fig. 29 does not vanish exactly.) The
latitudinal distributions of zonal mean temperature and
zonal mean vertical p velocity a t the 70-mb level are also
added to the lower part of figure 29 for convenience in the
discu~sion.~ I n the tropical stratosphere of the model, the
adiabatic cooling in the upward-moving branch of the
meridional circulation tends to lower the temperature and
is responsible for the temperature minimum there. I n
middle latitudes of the Northern Hemisphere, the adiabatic
8 As pointed out in section 3, the latitudinal distributions of various quantities in the
model atmosphere are shifted systematlcally toward the Equator from their observed
counterparts. Therefore, one should keep this bias in mind when examining these results.
heating in the downward-moving branch of the meridional
circulation raises the temperature and is the chief cause
of the temperature maximum a t these latitudes. I n both
hemispheres of the model, the poleward eddy transport of
heat, discussed in the preceding section, removes heat
from lower latitudes, supplies heat to high latitudes, and
tends to increase the temperature with increasing latitude.
Although the effects of the meridional circulation and the
large-scale eddies tend to compensate each other, the net
contribution of these two dynamical effects is to create
the existing temperature gradient in the lower stratosphere
of the model. On the other hand, the radiative effect tends
to destroy the temperature gradient generated by these
two dynamical effects. The distributions of heat balance
components in the Northern Hemisphere of the model are
in excellent qualitative agreement with those obtained by
Manabe and Hunt (1968) from their 18-level model.
8. CONCLUDING REMAR
I n this study, it is shown that the global model of the
atmosphere that we have developed is capable of simulat-
ing, at least qualitatively, some of the major features of
the hydrologic cycle and of the global climatic patterns
during January. For example, the tropical rain belt, the
rniddle-latitude rain belt, the areas of large runoff rate,
and major arid regions (such as the Sahara and Australian
Deserts) are successfully simulated. The horizontal dis-
tributions of the net downward radiation and the upward
fluxes of sensible and latent heat a t the surface of the model
continents are very similar to those of the corresponding
quantities obtained by Budyko (1963). The latitudinal
distributions of the poleward transports of heat and latent
energies in the model atmosphere also compare favorably
with thoqe in the actual atmosphere, as estimated by Oort
and Rasmusson (1970). It is noteworthy that the massive,
interhemispheric Hadley cell predominates in the model
Tropics and transports heat energy and latent energy in
opposite directions across the model Equator. This cell
supplies latent energy to the tropical rain belt of the model
a.nd removes the heat energy released by condensation.
I n the lower stratosphere of the model, except at high
northern latitudes, the temperature increases with increas-
ing latitude, in agreement with features of the actual
stratosphere. The effect of the countergradient heat
transport by the large-scale eddies, combined with the
effect of the adiabatic temperature change due to the
meridional circulation, is responsible for this temperature
gradient in the summer as well as in the winter hemisphere
of the model. The effects of radiative transfer tend to
destroy this temperature gradient.
There are various indications that the global model
used for this study has a systematic bias toward develop-
ing excessively high pressure in polar regions. Furthermore,
the model tends to overpredict the relative humidity
near the earth's surface. The development of a model free
of such biases seems to be essential for the satisfactory
simulation of climate.
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 363
It is suggested that the perpetual January insolation,
assumed for this study, is partly responsible for the un-
realistically low temperatures in the Arctic. A natural
extension of this study would be a simulation of the sea-
sonal variation of climate by a model incorporating the
effects of the seasonal variation of insolation.
One of the probable future applications of mathe-
matical models of climate is in the evaluation of the
possibility of climatic change caused by human activity.
For example, it is important to know how the increase
in carbon dioxide content in the atmosphere, resulting
from fossil fuel combustion, affects the climate. Since
climatic change often causes changes in oceanic tempera-
tures, which in turn affect the climate, one cannot predict
the global change of climate by using a model with a
given distribution of sea-surface temperatures. It is,
therefore, desirable to combine a mathematical model
of the atmosphere with an ocean model, such as the
one developed by Bryan and Cox (1967), t o create a
joint ocean-atmosphere model. I n such a model, the sea-
surface temperatures are deterJmined as a result of coupling
between the model ocean and the model atmosphere.
Recently, Manabe and Bryan (1969) constructed such a
joint model with highly idealized topography. The con-
struction of a joint ocean-atmosphere model with realistic
topography is a next major goal of our research.
APPENDIX A-COMPUTATIONAL TECHNIQUES
A. TIME INTEGRATION
The time step for the integration of the low-resolution
grid (N24) model is 400 s, and that for the high-resolution
grid (N48) is 300 s. Experimentation shows that the high-
resolution model remains stable with a 300-s time step as
well as with one of 200 s or half the N24 value. Therefore,
the longer time step is used to save computer time.
For preventing the growth of a computational mode,
the wind, temperature, humidity, and pressure fields at
three consecutive time steps are averaged once every 53
time steps by the weights 0.25, 0.5, and 0.25. After such a
smoothing time step, one noncentral time extrapolation
is performed before the normal leapfrog time integration
is restarted.
As an additional precaution, the high-resolution (N48)
model time integration is performed by a so-called “Euler
backward” scheme proposed by Matsuno (1966) for 12
time steps out of every 288 or every simulation day [see
Manabe et al. (1970~) for further details on this sys-
tem]. This procedure is done to prevent the development
of high-frequency gravity waves that tend to appear in
high-resolu tion model experiments. During this procedure,
the time-step length is left unchanged.
8. REVISED PRESSURE GRADIENT FORMULATION
Equations (1) and (2) contain two terms for evaluating
the pressure gradient (i.e., a derivative of geopotential on
the u surfaces and a surface pressure gradient term, which
corrects the u surface geopotential gradient to one on
constant pressure surfaces). The pressure gradient cor-
rection term is adequate for models without mountains;
but in models with realistic topography, the two-term
pressure gradient evaluation permits large truncation
error and is responsible for a checkerboard pattern in the
surface-pressure field. This truncation error is markedly
reduced by use of a single pressure-gradient term, as
suggested by Sangster and Smagorinsky (Smagorinsky
et al. 1967). In the east-west direction, this single term is
This term is evaluated on a. constant pressure surface
defined by a given u level at the central grid point. This
pressure is obtained by the product of surface pressure at
this point and the given u value. Geopotentials at all
surrounding grid points involved in the gradient compu-
tation are computed by a build-up from the surface to the
specified constant pressure surfaces. When constant pres-
sure surfaces fall below the earth’s surface at a grid point,
geopotentials are estimated under the assumption of a
locally-representative effective temperature of air be-
tween the u =l level and the specified pressure level. A
similar form of this single-gradient term can be derived in
the north-south direction.
C. REVISED VERTICAL PRESSURE-VELOCITY EQUATION
The original version of the vertical p-velocity eq (8)
generates large irregularities in the field of vertical motion
and thereby adversely affects the temperature field in the
stratosphere where the static stability is very high. Such
irregularities propagate downward through the pressure
interaction term and generate irregularities in the tropo-
sphere. The field of surface pressure p* has small-scale
patterns because of the uneven topography. Therefore,
the advection term of surface pressure on the right-hand
side of eq (8) generates intense small-scale vertical motions.
Miyakoda (1967) pointed out that this difficulty can be
avoided by use of an alternate form of the equation of w,
originally suggested by Smagorinsky (1962). This form of
the equation does not involve the horizontal advection of
surface pressure. The new vertical p-velocity formulation
derived below was incorporated into the model as soon as
this model deficiency was discovered. It was put into the
model between the averaging period for the hydrologic
means and the period of averaging for the zonal wind
fields, and it was used for the entire high-resolution time
integration.
The vertical p-velocity equation is derived from the
vertical u-velocity & and the definitions of w and u as
follows:
and P=fJP* (42)
w=-. dP
at (43)
364 MONTHLY WE
Therefore,
aa dP* w=p* -+a - a t a t
(44)
Equation (44) is equivalent to eq (8). In the a coordinate
system, the continuity equation may be written as
apx=-p* a; --v,* (p*V).
aa at (45)
Substituting the surface pressure tendency of eq (45)
into eq (44), we obtain
where
du +a(u COS e )
a COS eax a COS eae * v,. V=
(46)
(47)
D. SHORTCOMINGS OF THE KURIHARA GRID
The Eurihara computational grid used for the models
described in this paper was developed a t GFDL to allow
the hydrodynamical equations to be integrated over the
entire globe without horizon tal boundaries. It provides
reasonably uniform resolution in all directions and over
the entire domain. However, the finite-diff erence solutions
to the equations solved on this grid suffer from some
deficiencies of the grid, which we shall point out in this
subsection.
Recently, Rao and Umscheid (1969) carried out a
series of test computations on a barotropic model solved
on the Kurihara grid system. Their results reveal that the
model tends to develop an area of high pressure around
the Pole, unless they chose a very high computational
resolution. A similar bias is evident when we compare
results from a baroclinic model, using the Kurihara grid
(Eurihara and Holloway 1967), with those from a similar
model, having a rectangular array of comparable grid size
(Smagorinsky et al. 1965).
As known, finite-diff erence approximations computed
on the Kurihara giid are accurate only to the first order,
whereas those computed on regular grids have second-
order accuracy. This results in lowering the effective
resolution of the Eurihara grid somewhat below that of a
regular grid having the same mean grid spacing. It is
very probable that the excessive polar High described in
subsection 3C is partly due to the poor accuracy of the
computation on an irregular grid. This speculation is
substantiated by figure 7, which indicates a significant
lowering of polar pressures resulting from the increase in
computational resolution. The magnitude of the pressure
decrease, however, is far from sufficient. It is likely that
the truncation error of the finite-diff erence computation
ATHER REVIEW VOl. 99, No. 5
is particularly large in the polar region where the curvature
of the curvilinear coordinate (Le., latitude circles) is a t 8
maximum.
Finally, Shuman (1970) showed an example of large
truncation errors arising from a bite-difference computa-
tion in a polar region. I t is related to the manner in which
wind vectors are averaged in the application of the box
method to this grid. The vector components of the wind,
on the interfaces between pairs of boxes, are computed
as the arithmetic means of the components a t the centers
of the boxes that meet at these interfaces. This computa-
tion is done without regard to the slight differences in
the directions of the unit vectors, located a t the adjacent
grid points involved. This approximation used in averaging
vector components is most inaccurate near the Poles
where the directions of the unit vectors change most
rapidly from one box to the next. As pointed out by
Dey (1969) , this approximation creates fictitious hori-
zontal convergence upwind of the Pole and false divergence
downwind of the Pole when air flows across the Pole.
The fact that these patterns of convergence and divergence
are not centered on the Bole suggests that there is no
connection between this finite-difference error and the
high-pressure phenomenon at the Poles.
However, despite these finite-diff erence inaccuracies
inherent in the Kurihara grid, we were able to time
integrate our model over the entire globe successfully for
several hundred simulation days. Apparently, the errors
near the Poles are not serious enough to degrade the
results of the atmospheric simulation appreciably in
middle and low latitudes, especially at high resolution.
One method for reducing the various fhite-difference
errors described above is to increase the resolution of the
grid on which the computations are' performed. Partly
for this reason, the resolution of the grid was doubled
and the model experiment described in this paper was
repeated. Some of the results of this high-resolution-
model experiment are presented in appendix B.
APPENDIX B-SOME RESULTS
FROM THE HIGH-RESOLUTION MODEL
Manabe et al. (1970a) demonstrated that the results
from a hemispheric general circulation model are markedly
improved by reducing the mean grid spacing from 500
to 250 km. Therefore, we decided to integrate the model
equations on a finer horizontal grid network for as many
simulation days as practical, considering the enormous
amount of computer time required for these high-resolu-
tion calculations. The Univac 1108 electronic computer4
requires about 27 hr of real time to integrate a 24-€ IT
atmospheric simulation a t high resolution. There are 9,216
grid points in the high-resolution model with 48 grid
points between the Poles and the Equator and 192
around the Equator. The grid distances vary from 208
4 Mention of a commercial product does not constitute an endorsement.
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 365
lANOhlH€ RdHEMISbH€ R€ l I I I I ' ' I ' I ' ' I ' I I ' I I I I I ' ' GLOBAL
0.120- SOUlHfRN HEMISPHEE
,110 -
.loo -
,
I
,030 I I I J I I I I I I I I I I I I I I I I ~~~~~~~~I I
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
2.0 -
- 248 g
w LI
-2
- 247
\I
\r'
1.8 l f i I I 1 1 I ' I I 1 I 1 1 l I I I I I I ' I I I I I I I I I I l f
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 40 50 52 54 56 58 60 62 64 66 68 70
FIGURE 30.-Time variations of (upper graph) the global and hemispheric means of the eddy kinetic energy in the N48 model experiment
and of (lower graph) the global means of temperature (solid line) and precipitable water (dashed line). The time in days is along the
abscissa.
to 325 km. Hereafter, this grid will be called N48, and the
low-resolution grid, N24. Results from the N48 model
experiment are compared with those of the N24 experiment
in this appendix whenever the increase in resolution made
a significant change in the model simulations. The deriva-
tion of the high-resolution smoothed topography is
described in appendix C.
The data fields from the N24 model at simulation day
302 are linearly interpolated to the N48 grid as input for
the high-resolution model experiment. The N48 model is
time integrated for 70 days beyond this initial time. Figure
30 shows the time variations of the hemispheric and
global mean values of the eddy kinetic energy and the
time series of the global means of the temperature and
precipitable water during this 70-day period. Obviously,
it would have been desirable to extend the integration for
a longer period of time to approach more closely a state of
quasi-equilibrium. However, the experiment is terminated
on the 70th day because of the enormous amount of
machine time required for integrating each simulation
day of this high-resolution model. Various quantities,
shown in this appendix, represent the average state of
the 36 days inclusively from the 35th to the 70th model
day. Because of the great variability of precipitation and
other hydrologic quantities, it would have been desirable
to time average over a longer period. Unfortunately, the
shortage of computer time limited the averaging period
so that the lack of a stable mean offsets some of the gain
in accuracy obtained by the high-resolution computation.
The zonal mean sea level pressure, averaged over the
36-day period at the end of the N48 model experiment,
appears in figure 7 presented in section 3. The latitudes
and intensities of the pressure maxima in the northern
and southern subtropics are significantly improved by
the increase in the horizontal resolution of the finite
differencing. The latitudes of the low-pressure minima in
middle latitudes are closer to the Poles and to the ob-
served locations in the N48 results than in the pressure
distribution simulated by the N24 model experiment. In
both hemispheres, the mean observed minima are at
about 68" latitude. In the Northern Hemisphere, the N48
model simulates a low-pressure trough at about 5S0N,
whereas the N24 trough is as far south as 48"N. In the
Southern Hemisphere, the discrepancy is even greater;
but again, the low-pressure trough is situated closer to
the observed location in the high-resolution-model experi-
366 MONTHLY WEATHER REVIEW V O I . 99, No. 5
FIGURE 31.-Global distribution of mean sea level pressure during the 36-day averaging period for the N48 resolution model experiment;
units, mb.
ment. The computed polar pressures are far above normal
in the N48 model experiment; but in the Northern
Hemisphere, they are, nevertheless, considerably closer
to observed values than those of the N24 resolution
results. In summary, the increase in the horizontal com-
putational resolution produces a poleward shift of the
sea-level pressure patterns coupled with an increase in the
amplitude of the meridional variation of pressure in middle
and low latitudes.
Figure 31 presents a map of the global distribution of
the mean sea level pressure during the 36-day averaging
period for the N48 resolution model experiment. This
figure should be compared with the mean observed
sea-level pressure distribution and that obtained by the
N24 model, both of which are shown in figure 8.
In the Northern Hemisphere, the increase in the hori-
zontal resolution on the whole improves the simulation
of the centers ,bf high and low pressure over what is
obtained at lower resolution. For example, the pressures
a t the Pole are reduced to values much closer to climatic
means. The Siberian High is much better developed in
the N48 results and is now practically detached from the
polar High. The reduction in the excessively high, north
polar pressure decreases the fictitiously strong pressure
gradient to the north of the Aleutian Low seen on the
N24 map. As a result, the Aleutian Low itself is moved
northward for a closer agreement with the mean observed
sea-level pressure in this area. Unfortunately, the Ice-
landic Low is not improved in the high-resolution
integra tion.
The subtropical high-pressure belt in figure 31 is much
more clearly defined in both the Northernd an Southern
Hemispheres than at the N24 resolution. I n the Southern
Hemisphere, the Lows in the middle-latitude storm belt
are located farther south, in better agreement with
observations. Furthermore, the pressure difference be-
tween the subtropical Highs and the middle-latitude
Lows is greater. This improvement in turn improves the
simulation of the surface westerlies in high southern
latitudes.
The mean precipitation rate computed by the W48
resolution model is shown in figure 32. This figure should
be compared with the observed precipitation rate pre-
sented in the lower half of figure 12. On the whole, the
high-resolution precipitation simulations are considerably
better than the N24 computations although the N48
results tend to be less smooth, in part, because the aver-
aging period is half as long as that for the lowresolution
mean.
I n the Northern Hemisphere, the middle-latitude
precipitation belt is simulated better at high resolution
than at low. The improvement probably can be attributed
as much to the more accurate topography as to the
generally better simulation of the dynamics of the atmos-
phere provided by the finer computational grid. The
centers of high precipitation rate over the oceans and
extending into the continents .are interspersed with drier
areas centered on the continents. I n agreement with the
climatic data, these areas of low precipitation rate,
computed by the N48 model on the continents, extend
from the subtropical dry belt t o the polar regions of low
precipitation. The dry areas in Asia and in North America
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 367
0 0
FIGURE 32.-Mean global precipitation rates computed by the high resolution (N48) model experiment.
are wider in the N48 model results, in better agreement
with observation.
In the Tropics, the rain belt obtained by the high-
resolution model is narrower than in the N24 experiment.
Partly because of the relatively short averaging period,
some roughness appears in the rainfall patterns. The high-
resolution rainfall distribution lacks the spur of high
rainfall, which appears in the observed map and even in
the N24 results, extending from the central equatorial
Pacific toward southern South America.
In the Southern Hemisphere, the regions of low pre-
cipitation rate over the subtropical oceans do not extend
as far inland on the West Coasts of southwestern Africa
and southern South America as in the N24 experiment, in
good agreement with observation. This improvement in
simulation is, no doubt, attributable to the higher moun-
tains in the high-resolution model. These taller mountains
are more effective in blocking dry air from flowing out of
the dry anticyclones, situated off the west coasts of
Africa and South America. As pointed out earlier, the
N48 topography is less smooth and higher, especially in
regions of narrow mountain ranges such as the Andes,
than the topography used in the N24 model experiment
(see appendix C).
In both hemispheres, the computed middle-latitude
belts of maximum precipitation rate are slightly more
intense and are located at somewhat higher latitudes in
the N48 results than in those of the low-resolution ex-
periment. These positions correspond more closely to
their observed latitudes and strengths. This improvement
is correlated with the more realistic pressure distribution
a t these latitudes.
421-3161 0-7il--3
APPENDIX C-DERIVATION
OF THE SMOOTHED TOPOGRAPHY
The topography used in the N24 model experiment is
shown in figure 33. The basic data for the mountain
heights came from a computer tape produced by the
Scripps Institution of Oceanography (Smith et al. 1966).
For the N24 grid, these Scripps data are interpolated to
the Kurihara grid and smoothed by the repeated applica-
tion of the following space smoothing function:
where zo is the raw unsmoothed height at the central grid
point, z r is the height at the surrounding grid point i,
wi is a weighting factor proportional to the length of the
interface between the box i and the central box (nor-
malized so as to make the sum of the weights equal to
one-half), and z is the resulting smoothed height. The
summation is over all N surrounding contiguous boxes in
the grid.
Three applications of this smoothing function give the
desired degree of smoothing. It is, of course, necessary to
smooth the topography until the scale of variations in land
height matches the resolution of the grid. The Scripps data
contain ocean-bottom topography as negative values in
addition to positive land-height values. All data are used;
and when a negative smoothed height results at a grid
point which had been above sea level in the input data,
the original shoreline is restored (i.e., the height is rede-
fined as a positive 1 m).
368 MONTHLY WEATHER REVIEW Vol. 99, No. 5
90'
FIGURE 33.-Polar stereographic maps of the continental boundaries and mountain heights in the Northern (left) and Southern (right)
Hemispheres of the N24 (upper) and N48 (lower) resolution grids. Areas with elevations > 1 km are shaded with slashed lines and those
> 3 km with checkered lines.
The topography for the high resolution (N48) model is
derived slightly differently from that for the N24 grid.
The interpolation and smoothing are performed in one
operation by weighting data on the Scripps grid network
(in most areas spa.ced every degree of latitude and longi-
tude) by a function of the great circle distance from the
location of the Scripps data to the particular Eurihara
grid point for which the smoothed terrain height is being
computed. The weighting function is a two-dimensional
normal curve truncated a t a radius of 200 km, at which
distance the weight is 13.5 percent of that at the origin.
The computation of a typical smoothed height involves
an average of about 12 Scripps data points. The restora-
tion of the continental shorelines after smoothing is done
by a method similar to that used for the N24 grid (i.e.,
the land or sea status of a grid point is determined by the
May 1971 J. Leith Holloway, Jr. and Syukuro Manabe 369
land-sea status of the nearest Scripps data point). Mathe-
matical eroding of the coasts is reduced by halving the
ocean depths before smoothing the combined land-ocean-
bottom topography. The resolutions of the N24 and N48
grid networks are illustrated by the degree of smoothing
and simplication of the continental outlines of the N24
maps in sections 3 and 4 and of the N48 maps in appendix
B. Maps of the N48 topography are shown in the lower
half of figure 33. Notice that the Rocky Mountains in
North America and the Andes in South America are some-
what taller and more narrow on the high-resolution grid.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the many useful suggestions
provided by Dr. Y. Kurihara for improving the model and enabling
us t o carry out a successful integration. We wish to express our
appreciation to Dr. J. Smagorinsky for his encouragement and
valuable support and to Dr. K. Miyakoda for his very valuable
advice for solving some of our computational difficulties. We are
indebted to Mr. R . Wetherald for programming the computations
of the hydrologic scheme in the model. We also wish to thank Mrs.
W. Carlton who wrote a substantial part of the computer programs
for the model and the analysis computation. Finally, we are greatly
indebted to all of the members of the GFDL staff who assisted with
the preparation of the manuscript and figures and in particular to
Mr. L. Dimmick.
REFERENCES
Bryan, Kirk, and Cox, hfichael D., “A Numerical Investigation of
the Oceanic General Circulation,” Tellus, Vol. 19, No. 1, Stock-
holm, Sweden, Feb. 1967, pp. 54-80.
Budyko, M. I., TeplovoI balans ZemnoZ Poverkhnosti (Heat Balance
of the Earth’s Surface), Gidrometeorologicheskoe Izdatel’stvo,
Leningrad, U.S.S.R., 1956, 254 pp.
Budyko, M. I. (Editor), Atlas Teplovogo Balansa Zemnogo Shara
(Guide t o the Atlas of the Heat Balance of the Earth), Gidro-
meteoizdat, MOSCOW, U.S.S.R., 1963, 69 pp.
Crutcher, Harold L., and Meserve, J. M., “Selected Level Heights,
Temperatures and Dew Points for the Northern Hemisphere,”
NAVAIR 50-1C-52, U.S. Naval Weather Service, Washington,
D.C., Jan. 1970, 8 pp. and numerous charts.
Dey, Clifford H., “A Note on Global Forecasting With the Kurihara
Grid,” Monthly Weather Review, Vol. 97, No. 8, Aug. 1969, pp.
Gerdel, Robert Wallace, “The Transmission of Water Through
Snow,” Transactions of the American Geophysical Union, Vol. 35,
No. 3, June 1954, pp. 475-485.
Hering, Wayne S., and Borden, Thomas R., Jr., “Mean Distribu-
tions of Ozone Density Over North America, 1963-1964,” Environ-
mental Research Papers, No. 162, U.S. Air Force Cambridge
Research Laboratories, Hanscom Field, Mass., Dec. 1965, 19 pp.
Kasahara, Akira, and Washington, Warren M., “Thermal and
Dynamical Effects of Orography on the General Circulation of
the Atmosphere,” Proceedings of the W M O /I UGG Symposium on
Numerical Weather Prediction, Tokyo, Japan, November 86-
December 4 , 1968, Japan Meteorological Agency, Tokyo, Mar.
Kung, Ernest C., Bryson, Reid A., and Lenschow, Donald H.,
“Study of a Continental Surface Albedo on the Basis of Flight
Measurements and Structure of the Earth’s Surface Cover Over
North America,” Monthly Weather Review, Vol. 92, No. 12, Dec.
Kurihara, Yoshio, “Numerical Integration of the Primitive Equa-
tions on a Spherical Grid,” Monthly Weather Review, Vol. 93, No.
7, July 1965, pp. 399-415.
597-601.
1969, pp. IV-47-IV-56.
1964, pp. 543-564.
Kurihara, Yoshio, and Holloway, J. Leith, Jr., “Numerical Integra-
tion of a Nine-Level Global Primitive Equations Model Formu-
lated by the Box Method,” Monthly Weather Review, Vol. 95, No.
Leith, Cecil E., “Numerical Simulation of the Earth’s Atmosphere,”
Methods in Computational Physics, Volume 4. Applications in
Hydrodynamics, Academic Press, New York, N.Y., 1965, 385 pp.
(see pp. 1-28).
London, Julius, “A Study of the Atmospheric Heat Balance,” Final
Report, Contract No. AF19(122)-165, Department of Meteorol-
ogy and Oceanography, New York University, N.Y., July 1957,
99 PP- London, Julius, “Mesospheric Dynamics: Part 111. The Distribution
of Total Ozone in the Northern Hemisphere,” Final Report, Con-
tract No. AFlg(604)-5492, Department of Meteorology and
Oceanography, New York University, N.Y., May 1962, pp. 68-
108.
Manabe, Syukuro, “Climate and the Ocean Circulation: I. The
Atmospheric Circulation and the Hydrology of the Earth’s Sur-
face,” Monthly Weather Review, Vol. 97, No. 11, Nov. 1969, pp.
739-774.
Manabe, Syukuro, and Bryan, Kirk, “Climate Calculations With a
Combined Ocean-Atmosphere Model,’’ Journal of the Atmos-
pheric Sciences, Vol. 26, No. 4, July 1969, pp. 786-789.
Manabe, Syukuro, and Holloway, J. Leith, Jr., “Climate Modifi-
cation and a Mathematical Model of Atmospheric Circulation,”
A Century of Weather Progress, American Meteorological Society,
Boston, Mass., 1970a, pp. 157-164.
Manabe, Syukuro, and Holloway, J. Leith, Jr., “Simulation of the
Hydrologic Cycle of the Global Atmospheric Circulation by a
Mathematical Model,” Proceedings of the Reading, England,
Symposium, July 15-23, 1970, IASH-UNESCO Publication No.
92, International Association of Scientific Hydrology, Gentbrugge,
Belgium, July 1970b, pp. 387-400.
Manabe, Syukuro, and Holloway, J. Leith, Jr., “Simulation of
Climate by a Global General Circulation Model: 11. Effect of
Mountains,” U.S. Department of Commerce, Geophysical Fluid
Dynamics Laboratory, Princeton, N.J., 1971 (unpublished
study).
Manabe, Syukuro, Holloway, J. Leith, Jr., and Stone, Hugh M.,
“Tropical Circulation in a Time Integration of a Global Model
of the Atmosphere,” Journal of the Atmospheric Sciences, Vol. 27,
Manabe, Syukuro, and Hunt, Barrie G., “Experiments With a
Stratospheric General Circulation Model: I. Radiative and
Dynamic Aspects,” Monthly Weather Review, Vol. 96, No. 8,
Manabe, Syukuro, and Smagorinsky, Joseph, “Simulated Clima-
tology of a General Circulation Model With a Hydrologic Cycle:
11. Analysis of the Tropical Atmosphere,” Monthly Weather
Review, Vol. 95, No. 4, Apr. 1967, pp. 155-169.
Manabe, Syukuro, Smagorinsky, Joseph, Holloway, J. Leith, Jr.,
and Stone, Hugh M., “Simulated Climatology of a General
Circulation Model With a Hydrologic Cycle: 111. Effects of
Increased Horizontal Computational Resolution,” Monthly
Weather Review, Vol. 98, No. 3, Mar. 1970a, pp. 175-212.
Manabe, Syukuro, Smagorinsky, Joseph, and Strickler, Robert F.,
“Simulated Climatology of a General Circulation Model With a
Hydrologic Cycle,” Monthly Weather Review, Vol. 93, No. 12,
Dec. 1965, pp. 769-798.
Manabe, Syukuro, and Strickler, Robert F., “Thermal Equilibrium
of the Atmosphere With a Convective Adjustment,” Journal of
the Atmospheric Sciences, Vol. 21, No. 4, July 1964, pp. 361-385.
Manabe, Syukuro, and Wetherald, Richard T., “Thermal Equi-
librium of the Atmosphere With a Given Distribution of Relative
Humidity,” Journal of the Atmospheric Sciences, Vol. 24, -No. 3,
May 1967, pp. 241-259.
8, Aug. 1967, pp. 509-530.
NO. 4, July 1970b, pp. 580-613.
Aug. 1968, pp. 477-502.
3 70 MONTHLY WEATHER REVIEW Vol. 99, No. 5
Mastenbrook, H. J., “Frost-Point Hygrometer Measurements in the
Stratosphere and the Problem of Moisture Contamination,”
Humidity and Moisture-Measurement and Control in Science and
Industry, Volume 2: Applications, Reinhold Publishing Gorp.,
New York, N.Y., 1965, pp. 480-485.
Matsuno, Taroh, “Numerical Integrations of Primitive Equations
by Use of a Simulated Backward Difference Method,” Journal
of the Meteorological Society of Japan, Vol. 44, NO. 1, Tokyo,
Feb. 1966, pp. 76-84.
Mintz, Yale, “Very Long-Term Global Integration of the Primitive
Equations of Atmospheric Motion: An Experiment in Climate
Simulation,” Meteorological Monographs, Vol. 8, No. 30, American
Meteorological Society, Boston, Mass., Feb. 1968, pp. 20-36.
Miyakoda, Kikuro, “Some Characteristic Features of Winter
Circulation in the Troposphere and the Lower Stratosphere,”
Technical Report No. 14, Contract No. NSF-GP-471, Depart-
ment of the Geophysical Sciences, University of Chicago, Ill.,
Dec. 1963, 93 pp.
Miyakoda, Kikuro, Geophysical Fluid Dynamics Laboratory,
NOAA, Princeton, N.J., 1967 (personal communication).
Moller, Fritz, “Vierteljahrskarten des Niederschlags fur die Ganze
Erde” (Quarterly Charts of Rainfall for the Whole Earth),
Petermanns Geographische Mitteilungen, Vol. 95, No. 1, Justus
Perthes, Gotha, East Germany, 1951, pp. 1-7.
Murgatroyd, R. J., “Some Recent Measurements by Aircraft of
Humidity up to 50,000 Feet in the Tropics and Their Relation-
ship to Meridional Circulation,” Proceedings of the Symposium on
Atmospheric Ozone, Oxford, England, July 80-85, 1969, IGGU,
Paris, France, 1960, 30 pp.
Newell, R. E., Vincent, D. G., Dopplick, T. G., Ferruzza, D., and
Kidson, J. W., “The Energy Balance of the Global Atmosphere,”
The Global Circulation of the Atmosphere, American Meteorologi-
cal Society, Boston, Mass., 1969, pp. 42-90.
Oort, Abraham H., and Rasmusson, Eugene M., “On the Annual
Variation of the Monthly Mean Meridional Circulation,” Monthly
Weather Review, Vol. 98, No. 6, June 1970, pp. 423-442.
Penn, Samuel, “The Prediction of Snow vs. Rain,” Forecasting
Guide No. 2, U.S. Weather Bureau, Washington, D.C., Nov.
1957, 29 pp.
Phillips, Norman A., “The General Circulation of the Atmosphere:
A Numerical Experiment,” Quarterly Journal of the Royal Mete-
orological Society, Vol. 82, No. 352, London, England, Apr. 1956,
Phillips, Norman A., “A Coordinate System Having Some Special
Advantages for Numerical Forecasting,” Journal of Meteorology
Vol. 14, No. 2, Apr. 1957, pp. 184-185.
Posey, Julian W., and Clapp, Philip F., “Global Distribution of
Normal Surface Albedo,”. Geojisica International, Vol. 4, No. 1,
Mexico City, D. F., Mexico, 1964, pp. 33-48.
pp. 123-164.
Shuman, Frederick G., “On Certain Truncation Errors Associated
With Spherical Coordinates,” Journal of Applied Meteorology,
Vol. 9, No. 4, Aug. 1970, pp. 564-570.
Smagorinsky, Joseph, Geophysical Fluid Dynamics Laboratory,
NOAA, Princeton, N.J., 1962 (personal communication).
Smagorinsky, Joseph, “General Circulation Experiments With the
Primitive Equations : I. The Basic Experiment,’’ Monthlu Weather
Review, Vol. 91, No. 3, Mar. 1963, pp. 99-164.
Smagorinsky, Joseph, Manabe, Syukuro, and Holloway, J. Leith,
Jr., “Numerical Results From a Nine-Level General Circulation
Model of the Atmosphere,” Monthly Weather Review, Vol. 93,
No. 12, Dec. 1965, pp. 727-768.
Smagorinsky, Joseph, Strickler, Robert F., Sangster, W. E.,
Manabe, Syukuro, Holloway, J. Leith, Jr., and Hembree, G. D.,
“Prediction Experiments With a General Circulation Model,”
Proceedings of the International Symposium on Dynamics of Large-
Scale Processes in the Atmosphere, Moscow, U.S.S.R., June 2$30,
1965, Izdatel’stvo “Nauka,” Moscow, 1967, pp. 70-134.
Smith, S. M., Menard, H. W., and Sharman, G. F., “World-Wide
Ocean Depths and Continental Elevations Averaged for Areas
Approximating One Degree Squares of Latitude and Longitude,”
S.I.O. Reference Report 65-8, Scripps Institution of Oceanog-
raphy, La Jolla, Calif., Mar. 1966, 14 pp.
Stone, Hugh M., and Manabe, Syukuro, “Comparison Among
Various Numerical Models Designed for Computing Infrared
Cooling,” Monthly Weather Review, Vol. 96, No. 10, Oct. 1$6$,
SzBva-KovBts, J6zsef, “Verteilung der Luftfeuchtigkeit auf die
Erde” (Distribution of the Humidity of the Air Over the Earth),
Annalen der Hydrographie und Maritimen Meteorologie, Vol. 66,
No. 8, Ernest Siegfried Mittler & Sohn, Berlin, Germany, 1938,
Taljaard, J. J., van Loon, H., Crutcher, H. L., and Jenne, R. L.,
“Climate of the Upper Air: Part 1. Southern Hemisphere,
Volume 1. Temperatures, Dew Points, and Heights a t Selected
Pressure Levels,” NAVA I R 50-1C-55, U.S. Naval Weather
Service, Washington, D.C., Sept. 1969, 6 pp. plus 134 figures.
Telegadas, Kosta, and London, Julius, “A .Physical Model of the
Northern Hemisphere Troposphere for Winter and Summer,”
Scientijic Report No. 1, Contract No. AF19(122)-165, College
of Engineering, New York University, N.Y., Feb. 1954, 55 pp.
Teweles, Sidney, “The Energy Balance of the Stratosphere,”
WMO Technical Note No. 70, World Meteorological Organiza-
U.S. Hydrographic Office, “World Atlas of Sea Surface Tempera-
tures, Second Edition,” H.O. Publication No. 225, Washington,
D.C., 1944, 48 maps.
vonder Haar, T. H., ‘Tariations of the Earth’s Radiation Budget,”
Ph. D. thesis, University of Wisconsin, Madison, 1969, 118 pp.
Washington, Warren M., and Kasahara, Akira, “A January Simu-
lation Experiment With the Two-Layer Version of the NCAR
Global Circulation Model,” Monthlv Weather Review. Vol. 98.
pp. 735-741.
pp. 373-378.
tion, Geneva, Switzerland, 1965, pp. 107-122.
Rao, M. Sanker, and Umscheid, Ludwig,. Jr., “Tests of the Effect
of Grid Resolution in a Global Prediction Model,” Monthly
Weather .. Review, Vol. 97, No. 9, Sept. 1969, pp. 659-664.
Proble’ms,” Interscience Tra& in Pure and Applied Mathematics
No. 4, Interscience Publishers, Inc., New York, N.Y., 1957,
238 pp. (see pp. 101-104).
NO. 8, Aug. 1970, pp. 559-580.
White, Robert M., “The Counter-Gradient Flux of Sensible Heat
in the Lower Stratosphere,” Tellus, Vol. 6, No. 2, Stockholm,
Yamamoto, G., “On a Radiation Chart,” Science Reports, Geo-
physics, Ser. 5, Vol. 4, No. 1, Tohoku University, Sendai, Japan,
June 1952, pp. 9-23.
Richtmyer, Robert D., ‘‘Difference Methods for Initial-Value Sweden, May 1954, PP. 177-179.
[Received July 21, 1970; rewised November 24, 19701