UDC 551.576.1:551.558.1:j51.515.51(213)
Cumulus Convection and larger Scale Circulations
II. Cumulus and Mesoscale Interactions
RAUL ERLANDO LOPEZ 1-Department of Atmospheric Science, Colorado State University,
Fort Collins, Colo.
ABSTRACT-This paper (part 11) is the, second of two
papers dealing with cumulus and broader scale flow
interaction. The first (part I) is a companion paper that
deals with this topic from broad-scale considerations. The
second (part 11) deals with this topic from the cumulus
scale point of view.
A numerical model of individual convective clouds has
been used to investigate the effects of a typical population
of cumulus clouds on the large-scale features of a tropical
disturbance or cloud cluster. The typical cloud population
has been determined from U.S. Navy aircraft recon-
naissance radar data in the tropical Atlantic Ocean.
This study shows that the detrainment of cloud mass
from the population produces net cooling of the air around
the clouds. This occurs because the cooling produced by
the evaporation of the detrained cloud liquid water over-
compensates for the detrainment of sensible heat excess.
A heat and moisture budget for a steady-state tropical
cloud cluster has been computed using the typical cloud
population. A mass budget of the cluster reveals that the
vertical circulation required to explain typically observed
rainfall rates has a magnitude many times larger than
the synoptic mass circulation. The synoptic scale vertical
mass circulation is, in fact, a small residual between both
the much larger upward mass transport by the clouds
and the downward mass transport induced in the cloud-
free region around the clouds.
1. INTRODUCTION
Parameterization of the effects of cumulus convection
on larger scale circulations is perhaps one of the most
important current problems in meteorology. To attack
this problem, we should first investigate three aspects of
cumulus convection :
1. The behavior of individual clouds.
2. The size distribution of clouds present in different convective
3. The role of cumulus clouds in the heat and moisture budget
systems.
of different cloud systems.
Corresponding to the first aspect, a new numerical model
of individual cumulus clouds has been developed by the
author (L6pez 1973-designated as paper A).2 The model
has been designed with the specific purpose of simulating
those aspects of cumulus convection that are important
to the cloud-environment interaction processes. In the
present paper, the second aspect of cumulus convection
will be explored by applying the results of the numerical
cloud model in paper A to radar data representative of
tropical cloud clusters. The resulting typical cloud popu-
lation in turn is used to investigate the third aspect by
performing a heat and moisture budget of a mean tropical
disturbance or cloud c l u ~t e r .~ The main objective here
is to ascertain the mechanisms by which cumulus clouds
I Now at the Institute of Tropical Meteorology, Department of Physics, The University
2 This model was first presented in the form of a project report (LBpez 1972).
3 The terms “tropical disturbance” and “cloud cluster“ are used interchangeably in
of Puerto Rico, Rio Piedras, Puerto Rico
this paper. For a more precise definition, refer to figure 3 in part I by Gray (1973).
impart heat to their environment for the maintenance of
the energy budget of tropical disturbances.
The statement that cumulus convection produces the
energy necessary for hurricane development is generally
accepted; however, the mechanism by which cumulus
clouds impart their energy to their environment is im-
perfectly understood. Also generally accepted is the con-
cept that the frictionally induced vertical velocity at the
top of the boundary layer produces a flux of low-level
air that rises in cumulus towers. As condensation takes
place, the temperature of these ascending currents will be
higher than the environment. This excess enthalpy is then
assumed to be imparted to the surrounding clear air by
the detrainment process.
The excess sensible heat that a cloud parcel has at a
given time, however, is not available to the environment
in its entirety. Most of it is converted into potential
energy as the warmer parcel continues to rise. Only a
fraction of this heat is given directly to the environment
when part of the cloud mass is detrained to the exterior.
This exportation of sensible heat from the cloud, however,
is counteracted by the simultaneous cooling produced by
the evaporation of the detrained cloud wa.ter. The net
result of the detrainment of cloud mass may even result
in the cooling of the cloud’s environment.
Another way in which cumulus clouds interact with
their environment is by generating local mass sources
and sinks by virtue of their large upward mass transport.
As a result, a cloud produced convergence-divergence
field is imposed on the environment. A compensatory
downward transport of mass will be induced in the cloud-
free regions. With the usually stable stratification of the
856 1 Vol. 101, No, 12 / Monthly Weather Review
Tropics, .considerable compressional warming can result
from the descending branch of the convective circulation.
The investigations presented in this paper are directed
toward a better understanding of the magnitude and
relative importance of each of these two cumulus-induced
processes in the maintenance of the energetics ’of tropical
disturbances.
2. CLOUD MODEL
The model used in these investigations is Lagrangian,
time dependent, one dimensional, and parametric. (For a
detailed description, see L6pez 1973.) The Lagrangian
scheme works as follows: A cloud in the model is started
by generating a series of boundary-layer parcels that go
up one after the other through cloud base during a given
forcing period. Each of these parcels is followed in time in
a Lagrangian way. Thus at a given moment, a cloud
consists of a vertical stack of parcels that were generated
at cloud base at different times. The equations of motion,
thermodynamics, water substance, and mass continuity
are solved for each of the parcels at every time step. These
different cloud parcels axe not isolated; instead, they are
allowed to interact with one another by means of a vertical
exchange of mass and rain particles. This treatment is
capable of simulating vertical profiles of temperature,
moisture, liquid water content, and vertical velocity for
the entire depth of the cloud.
The model is Time dependent; thus the entire depth of
the cloud is simulated throughout its complete life cycle
of growth, maturity, and decay. Each of the cloud parcels
is followed in time until it is incorporated into the en-
vironment, at the time when it has no liquid water present
and its vertical velocity is of the same order of magnitude
as the environment’s turbulence intensity.
Although the formulation of the model is basically
one dimensional, the clouds are assumed to consist of two
interacting axisymmetrical regions-a protected core and
an exposed surrounding shell. Mixing with the environ-
ment thus proceeds in two steps-environment to shell
and shell to core. In addition to this turbulent mixing
between shell and core, mass is exchanged between the
two by means of siibcloud-scale circulations inside the
cumuli. This is modeled in the following way. The shell
and the cap of the cloud slow down because of their more
direct mixing with the environment. This generates
vertical velocity shears across the cloud. We assumed that
shears result in an internal circulation of the cloud that is
parameterized in terms of a Hill’s vortex model. Because
of this vortex circulation, mass from the core moves out
and down, feeding mass into the shell. Eventually, the
cloud turns itself inside out (the old core being exposed)
while the cloud mass that was the shell before becomes the
new core, and sa on. The radii of the core and shell parcels
are part of the predicted variables, which (of course) vary
with both time and height; thus the cloud’s profile is
known at every time step.
The mixing between cloud and environment is param-
eterized in the model in terms of the turbulence intensity
of the interior and exterior of the cloud. I n this way, the
entrainment and detrainment rates are not proportional
to the cloud scale (or mean) vertical velocity of the cloud;
instead, t,hey are proportional tc: the root-mean-square
(rms) of the velocity fluctuations inside and outside the
cloud. By doing this, we avoid the commonly used but
physically invalid assumption of similarity. Additional
equations have been introduced in the model to predict
the turbulence level of the different cloud parcels at all
times.
I n general, all these improvements allow a more realistic
representation of the dynamics of cumulus clouds and of
the total rainfall produced by the individual convective
elements than has been heretofore possible with other
one-dimensional parametric models. The present model
has been developed to serve as a tool in the investigation
of the interaction of cumulus convection with the large- .
scale circulations. For this reason, the model has been
designed to be much simpler and less time consuming than
existing two-dimensional hydrodynamic models of cumulus
clouds.
3. EFFECTS OF CLOUDS ON ENVIRONMENT
Cloud Detrainment
As a cloud grows and decays, some of its mass is given
off to the environment by the process of detrainment. In
this way, excess sensible heat, liquid water, and water
vapor are exported to the surrounding air. The magnitude
of these transports depends on the rate of mass detrain-
ment and on the thermodynamic properties of the cloud;
thus the rate a t which a layer of an individual cloud gives
off excess sensible heat can be expressed as
ds? __- dmd. at -cP(T’-T’‘) - at
Here, the prime refers to the cloud, the double prime to
the environment; dm,/dt is the detrainment rate for the
cloud layer; and 9 represents sensible heat. Similarly, the
rates a t which cloud air, excess water vapor, and liquid
water are-given to the environment by a cloud segment
can be written as
(2) dm, am,
at at -=-,
am, I / am,, -=(x;-x, ) - dt at
and
(3)
(4)
I n these expressions, x refers to the mixing ratio of water
vapor; Qcl, the cloud.liquid water content; and m, and m,,
the mass of water vapor and liquid water, respectively.
Now consider a group of active cumulus clouds. Assume
this field of clouds is surrounded by a large vertical
cylinder of radius R, which extends from the surface to the
December1973 1 L6pez 1 857
during its growing stage. Thus N f , the number of clouds
of type i, can now be obtained as
Total mass available from subcloud layer
mass used by cloud i during its growing stage Na=
HORIZONTAL SECTION
Volume V
Mass m or
Ocean surface
(9) Nf=-= Ami
ami
FIQURE 1.-Geometrical model for the computations of the effect of
cumulus clouds on the surrounding environment.
level of the tropopause. This cylinder is divided into
horizontal layers of height, Az, and mass, m (fig. 1). The
rate a t which a layer of this enclosing cylinder receives
excess sensible heat from the clouds can be obtained by
adding the excess heating rates produced by each of the
cloud segments contained in the layer. Thus (1) becomes
cloud segments in the layer
(5)
The total excess heating of the cylinder layer during a
long period of time, At, can be obtained by integrating
eq (5) with respect to time. Thus
21
A 9 =N ,l C ,(T ’ --T ’ ’ )~~ d t dt
where N , is the total number of clouds of type i that
existed during the time interval, At, and T~ is the lifetime
of cloud type i. We have assumed that At>>ri. N t is
dependent on the total low-level mass available to form
clouds of type i and on the amount of subcloud-layer mass
that a cloud of type i uses during its growth period. The
mass channeled into clouds of type i from the subcloud
layer during the time interval At is given by
Equations similar to (6) can be readily derived for the
increase in air mass, excess water vapor, and liquid water
produced by the process of detrainment for a layer of the
cylinder surrounding the clouds. These equations have
the form:
dm
d t Am,=N, (a’-d‘)--ddt+. . -7
(12)
The net change in temperature due to detrainment
alone for a section of the enclosing cylinder is produced
by the combined effect of the direct detrainment of
sensible heat and the evaporation of the liquid water
detrained from the clouds at the same time. Thus the
rate of temperature change of the layer by detrainment
alone can be expressed as
A !!- Amw (13) AT -=
At (m+Am,)c, At (m+Am,)c, .A t
where L is latent heat. Similarly, the rate of moisture
alteration due to detrainment is
Ami = -aiV eVap0B?rR2At In these formulas, m is the mass of the layer of the en-
closing cylinder and is defined as (7)
where V*Vo is the subcloud-layer convergence into the
clouds of the disturbance ; p o , the density of the subcloud
layer; B, the height of cloud base; R, the radius of the
cylinder enclosing the disturbance; and at, the fraction of
the total mass convergence going into clouds of type i.
The subclofid-layer mass used up by a cloud of type i
during its growing stage is given by
where r0, wo, and t o are the radius, velocity, and duration
of the updraft through cloud base, feeding the clouds
Evaluation of Net Heating and
Moisture Alterations
Before eq (13) and (14) can be evaluated using the
cloud model of paper A, the subcloud-layer convergence
into the clouds, V V,, and the distribution of cloud
types, ai, must be specified as external conditions. Al-
though the radius of the enclosing cylinder and the
averaging time interval At enter into the numerator of
eq (9), these quantities do not have to be specified in
85% / Vol. 101, No. 12 / Monthly Weather Review
the final evaluation of the heating and moisture-alteration
rates [see eq (13)-(15)l.
The frequency distribution of the different cloud types,
q, will be obtained from radar data representative of
tropical cloud clusters presented in the next section. If all
the cumulus within the cluster had to be sustained by the
synoptic convergence of only 3-5 X lo-* s-l, then low-level
mass requirements would permit only -1/500 to ljl000 of
the cluster area to be occupied by such clouds (L6pez 1968,
Williams and Gray 1973). The actual convergence of mass
into the clouds of a disturbance (or cloud cluster), however,
is probably several times larger than these values. The
downdrafts generated by cloud growth and evaporation of
rain will obscure the true value of the low-level mass con-
vergence available for cloud formation (Riehl and Malkus
1958, Gray 1973). If the rain-producing efficiency of the
cloud population of a disturbance is known, an estimate of
the actual low-level convergence into the clouds (V V,)
could be obtained from the associated rainfall data. In the
case of the cumulonimbus simulatedin paper A, for example,
the total rain produced was 240 acre-ft (3.0X loll g of water)
while the total mass of subcloud-layer air flowing into
the cloud throughout its growing stage was 6m=5.6X1013
g [eq (S)]. On the other hand, Williams and Gray (1973)
calculated a mean rainfall of 2.5 cm/day for tropical cloud
clusters over a 4 O latitude square area. This corresponds
to a total mass of water of 2.5 A g/day where A is the
area of the disturbance or cloud cluster. This means that
a total of N=2.5 A!3.0X1011 cumulonimbi of the type
simulated in paper A would be needed to provide the
observed daily rainfall if only that type of cloud is assumed
to be present in the disturbance. The total mass of sub-
cloud-layer air needed for the growth of those clouds in
1 day would be then N6m. This amount of low-level mass
must be supplied to these particular clouds in 1 day to
account for the typically observed rainfall rates. Thus
from eq (7),
Am= --V-V,poBAAt=NSm
where At is an interval of 1 day. The equivalent low-level
convergence into the clouds of the cluster can now be
evaluated as
The towering and small cumulus simulated in paper A
would similarly require convergences of 5.8X
and 1.6X10-3s-1 if the cloud population of the disturbance
was composed of only clouds of their type.
These convergences are much larger than the synopti-
cally evaluated ones. The actual magnitude of the con-
vergence of mass into the growing clouds, however, hinges
on the rain-producing efficiency of the convective system
(i.e., how muah subcloud moisture is needed to produce
1 g of rain mater) and the mean rainfall rate over the
area of the disturbance. The more efficient precipitator
a cloud is, the less convergence of water vapor is needed
to produce the same amount of rain. In the case of our
simulated cumulonimbus, the efficiency is 40 percent,
which would put this cloud in the category of "efficient",
and thus put the computed convergence values on the
conservative side. Similarly, a rainfall rate of 2.5 cm/day
for a tropical disturbance is not large. Thus a mass con-
vergence into the sub-cloud layer of 10-4s-1 does not
seem unrealistic. For illustration, this last figure will
be used in the computation of the heating and moisture-
alteration rates for the typical cloud population.
If the observationally evaluated synoptic convergences
of to lo-%-' are real, most of the large mass required
for the growth of clouds, as computed above, must come
from subsynoptic sources (viz, the compensatory sub-
sidence induced around the individual growing clouds).
This extra vertical exchange may be very significant in
the momentum and heat budget of tropical cloud clusters.
Convergence-Divergence Pattern
Induced by Clouds
The vertical transport of mass by individual clouds
produces local mass sources and sinks that are reflected
on the environment as regions of horizontal divergence
and convergence. At any particular level, the magnitude
of this horizontal divergence field will depend on the
change of mass of the individual clouds present a t that
location. In turn, the rate at which the mass of a layer of
an individual cloud changes is determined by the internal
vertical advection of mass and by the mass gained and
lost through entrainment and, detrainment. Thus
""=(e) dt dt Advection
(16) dm
+ (%)Entrainment-(x)De trainment'
Now consider a group of clouds surrounded by the
same control volume used before. The combined change
in mass experienced by all the cloud segments contained
in a layer of the enclosing cylinder can be expressedas
dm= E. dt allcloud 6 t segments in the layer
By integrating eq (17) over a long period of time, At,
the total mass change experienced by the clouds can be
expressed as
where the different symbols have the same meaning as
before.
The divergence due t,o the cloud's vertical mass trans-
port in the layer of the cylinder during a large period
December1973 f L6pez 1 859
of time, At, can now be expressed as
where m is given by eq (15). If the values of Am, m, and
N i from eq (18), (15), and (9) are introduced in eq (19),
the expression for the horizontal divergence of the layer
due to the clouds becomes
X[cYIJ*' 0 2 d t +a 2 1 $ d t +a 3 r 2 dt+ . . .]. (20)
Equation (20) will be evaluated by using the cloud
model of paper' A to compute the geometry and the
entrainment and detrainment rates of different cloud
types, The cloud distribution and the value of the
subcloud-layer mass convergence will be the same as
those that will be used to evaluate the corresponding
heating and moisture alteration rates [eq (13) and (14)].
4. MODEL CLOUD POPULATION
Radar Information
A realistic assessment of the role of convection in
the heat and moisture budgets of tropical storms should
take into consideration the type of cumulus population
present in the disturbance. The combined effect of all
the convective elements depends on the proportion in
which the different cloud types are present. For example,
if most of the low-level moisture convergence is channeled
into small cumuli, only a fraction of the storm's latent
heat input can be realized as sensible heat. Not only is
the magnitude of the latent heat release dependent on
the cloud population but also its distribution with
height. Although cumulus convection is of utmost im-
portance to the energetics of disturbances, very little
effort has been devoted to investigating the types of
clouds present in tropical cloud clusters. Holle (1968)
has performed some studies on tropical oceanic cloud
populations. He, however, did not intend to answer the
question of what are the different types and relative
frequencies of cumulus clouds present in a disturbance
at a given time.
During the 1968 Barbados Meteorological Experiment,
the author flew with the Navy's Weather Reconnaissance
Squadron Four into about a dozen tropical cloud clusters
in the West Indies region. The scope of the 10 cm (APS 23)
airborne radar was photographed on every other scan.
From these automatic picture sequences, the lifetimes of
the new individual echoes that appear on the scope every 5
min have been estimated. Groups of individual echoes
have not been considered. Very large echoes are probably
composed of several individual cells, and their lifetimes
would not be representative of individual convective
elements. We felt that, by considering only individual
860 / Vol. 101, No. 12 / Monthly Weather Review
' O r
LIFETIME irnin)
FIGURE 2.-Frequency distribution of echo lifetimes.
isolated echoes, we could obtain a frequency distribution
of echo duration representative of the entire population of
convective elements, whether they appear singly or in
clusters. The histogram of Figure 2 was constructed from
more than 600 such individual echoes. This echo lifetime
distribution is typical of all the disturbances encountered.
Several different stratifications of the data were tried (e.g.,
cloud cover amount, surface pressure, latitude, range, and
time of day) with no significant departure from the form
of the overall average distribution.
The average echo lifetime for all the data is 14.5 min.
This value is smaller than the average of 32 min for hurri-
canes obtained by Senn et al. (1959) and 35 min obtained
by Senn and Stevens (1965). They, however, did not con-
sider echoes of short duration (5 10 min). On the cther
hand, McIntyre (1956) has found 17 min to be the average
for hurricane cumuli by tracing echoes that lasted from
4.5 to 46 min. Nevertheless, these previous studies and the
present one agree that both hurricanes and tropical cloud
clusters contain many more short-lived echoes than long-
lived ones. A similar conclusion can also be derived from
echo lifetime distributions obtained for middle latitudes
for both winter and summer storms (Blackmer 1956,
Battan 1953).
One reasonably can assume that the long-lived echoes
are generally wider and taller than the short-lived ones
(Battan 1953, Senn and Stevens 1965). The present data
do not allow us to measure accurately the horizontal and
vertical sizes corresponding to the different lifetime
categories. The available evidence, however, suggests
that the longer lived echoes are indeed generally wider and
taller than the short-lived ones. This evidence would tend
to indicate that the cloud populations of tropical dis-
turbances are composed of a majority of small cumuli,
some towering cumuli, and a few cumulonimbus towers.
Thus a large portion of the latent heat contained in the
low-level moisture input is not realized as sensible heat
because condensation in clouds of small vertical extent is
severely limited. This fact must be taken into consideration
16 -
12 - - E
I --
r
e,
w = 8 -
5 I
4
4 -
I I I 1 I I I
0 IO 20 30 40 50 60
RADAR ECHO OURATION imln)
FIGURE 3.-Relationship between radar echo duration and the
maximum height attained by clouds simulated with the numerical
model of paper A (L6pez 1973) by assuming different initial
conditions. The arrows identify the three typical clouds described
in paper A.
if the effect of cumulus convection on tropical cloud cluster
energetics is to be properly evaluated.
Cloud Population From Radar and
Numerical Model Data
Although few in number, there are some clouds in
figure 2 that produce echoes of very long duration (50-90
min). One or two of such long-lived echoes were detected
in each of the disturbances considered in this study. To
produce these persistent echoes, one probably needs a
local source of low-level mass of long duration. With the
numerical cloud model, we have been able to produce
radar echoes lasting 40 to 50 min by maintaining an
8-km-wide updraft through cloud base for 40 min, with a
peak speed of 5 m/s. To visualize such a persistent low-
level mass flux is difficult unless one postulates the
existence of a strong mesoscale organization of the sub-
cloud layer. When considering echoes of long duration, we
.are probably dealing with cloud systems that have orga-
nized the planetary boundary layer so that it can provide
a constant source of low-level mass for the close re-
formation of individual convective cells of a shorter
lifespan. The simulation of such a mesoscale cloud system
is beyond the scope of the cloud model used in this study.
Thus we will assume that the effect on the environment of
a cloud having a 60-min radar echo is equivalent to the
effect produced by two clouds having a 30-min echo;
similarly, a 90-min echo cloud will be represented by three
30-min echo clouds, and so on.
Using the results of the cloud model developed in paper
A, we can obtain some information about the distribution
of cloud sizes corresponding to the echo lifetime distribu-
tion of figure 2. Thus figure 3 has been prepared from the
results of the numerical model by plotting the radar echo
duration versus the maximum height att,ained by clouds
of different initial conditions. For this diagram, we
SUECLOUD-LAYER MASS INPUT (units of IO"P)
FIGURE 4.-Relationship between radar echo duration and the total
subcloud-layer mass input for clouds simulated with the numerical
model of paper A by assuming different initial configurations.
The arrows identify the typical clouds described in paper A.
assumed that the minimum reflectivity, 2, detected by
the radar corresponds to 30 dB (10 Log,, 2). The close
correlation between maximum cloud height and echo
duration (fig. 3) indicates that clouds exhibiting long-lived
echoes penetrate high into the troposphere. The maximum
height obtained by a cloud, however, is not a good repre-
sentation of its overall size-clouds with small initial radii
can rise to high altitudes providing that the initial forcing
is intense and of long duration. On the other hand, the
total mass of subcloud-layer air flowing into a cloud during
its growing stage is a better indication of the overall size
of a convective element. Figure 4 shows the duration of
the radar echo as a function of the total subcloud-layer
mass input for clouds of different initial configuration; for
facility of presentation, the abscissa has been plotted on a
logarithmic scale. Values of 0.4-2.2 krn have been used for
the initial radius, 5-20 min for the growth period, and
2.5-5.5 m/s for the maximum updraft velocity through
cloud base. Clouds having radar echoes lasting more than
40 min have been composed of two or three clouds with
shorter lived echoes. A good correlation exists between
echo duration and the amount of mass necessary for cloud
growth. Note that there is a rapid decrease in echo duration
with decreasing mass input for the smaller clouds (those
utilizing 0.1X1013 g do not produce detectable radar
echoes). In comparison, clouds having very long radar
echoes require large amounts of subcloud-layer mass
to grow.
Using the curve of figure 4 and the radar information
in figure 2, we developed a typical cloud population for
trade wind tropical disturbances. This population is
shown in figure 5 as the frequency distribution of classes
of clouds having different amounts of subcloud-layer
mass inputs during their growth stages. The class inter-
vals of the distribution of echo duration (fig. 2) have
December1973 1 Upez 1 861
t I 50 c I
IO
001 0 2 0 4 0 6 0 8 J 2 4 6 8 1 2 4 6 8 1 0 20
SUBCLOUD- LAYER MASS INPUT [units Of l0”p 1
FIGURE 5.-Typical cloud population for the trade-wind tropical
cloud cluster shown as a frequency distribution of classes of clouds
using different amounts of subcloud-layer mass during their
growth stages. The mass-input classes correspond to the echo
lifetime classes of figure 2. The arrows identify the three typical
clouds described in paper A.
been translated in terms of subcloud layer mass-input
classes using the relationship between lifetime and mass-
input given by figure 4. From this diagram, one can see
that the majority of the clouds in a tropical disturbance
are small, processing individually only a very small
amount of subcloud-layer air. The few large clouds, on
the other hand, process a large amount of subcloud-layer
mass during their growth stages. The relative importance
of the collective effect of the clouds in each category can
be obtained by computing from figure 5 the mass used
by each class as a fraction of the total subcloud-layer
mass utilized by all clouds in the population. The results
of this computation are portrayed in figure 6. The large
arrow indicates the median of the frequency distribution
Le., 50 percent of the clouds in the population use more
and 50 percent of the clouds in the population use less
subcloud-layer mass than the median cloud type. Note
also that the largest 50 percent of all the clouds process
approximately the same amount of low-level mass as
the smallest 50 percent. Although less important individ-
ually, the small clouds (because of their large numbers)
have as much participation in the vertical mass and
energy transports out of the boundary layer as the larger
but less frequent cloud cells.
The cr, of eq (11), (12), and (20) are the ordinate of figure 6
ii.e., the fraction of the total low-level mass convergence
going into the different classes of clouds). Using these
values of at, we can evaluate the combined effect of the
typical cloud population from these equations. A repre-
sentative cloud from each of the classes of figure 6 has
been used. The characteristics and defining parameters
of each of these clouds are listed in table 1. For each
type of cloud, the corresponding radar echo lifetime class
is listed together with the actual echo duration; radius,
duration, and peak speed of the generating impulse;
maximum height attained; accumulated rain; percent of
total subcloud-layer mass used by the cloud class; and
subcloud-layer mass used by the typical cloud. Notice
that clouds having echoes lasting 45 min or more have
862 / Vol. 101, No. 12 ./ Monthly Weather Review
SUBCLOUD-LAYER MASS INPUT (unili 01 10”~)
FIGURE 6.-Mass used by different classes of clouds as a fraction of
the total subcloud-layer mass available for cloud formation.
The cloud classes are expressed in terms of the subcloud-layer
mass used in their growth stages. The classes correspond to the
echo lifetime classes of figure 2. The large arrow indicates the
median of the distribution.
been assumed to consist of two or three cells of shorter
echo duration.
We emphasize at this point that the purpose in de-
veloping this typical cloud population is to obtain an
order of magnitude estimate of the effects of an ensemble
of different types of cumuli on the atmosphere of a dis-
turbance. The limitations imposed by the quality of the
radar data, the accuracy of the numerical model, and the
assumptions about the structure of large embedded cloud
systems do not warrant the use of this derived cumulus
population for detailed energy balances of tropical storms.
With these restrictions in mind, the typical cloud popu-
lation will now be used to compute the alteration rate
of temperature, moisture, and mass produced on the
synoptic scale of a tropical cloud cluster as the result
of sustained cumulus convection.
5. INTERACTION OF A MODEL CLOUD
POPULATION WITH SYNOPTIC FEATURES
OF A TYPICAL TROPICAL DISTURBANCE
The model cloud population described in section 4 will
now be used to investigate the interaction of an ensemble
of cumulus clouds with the synoptic flow features of a
tropical cloud cluster. The interaction between cloud and
synoptic scales takes place in two reciprocal directions.
First, the large-scale synoptic flow and t8he static stability
of a disturbance determine the different types of cumulus
clouds that will be produced and the numbers in which
they will be present. Second, once the cloud population
is established, the large-scale fields of temperature,
moisture, and momentum will be altered and controlled
by the collective influence of the individual clouds.
The first type of interaction has been tacitly incorpo-
rated in the characterization of the model cloud popula-
tion: Here, the types of clouds present and their relative
frequencies were obtained from radar observations;
TABLE 1.-Characteristics of the typical clouds of a tropical disturbance
Radar Actual
class duration
Class echo radar ro TO wo Max. Accum. ai ami number duration echo height rain
(fin)
5 4.0
10 9.5
15 16.0
20 20.0
25 25.5
30 26.0
35 26.5
40 36.5
45 46. 0
50 52.5
55 52.5
60 62.5
65 62.5
70 73.0
75 73.0
80 82.5
85 82.5
90 88.5
(m) (d n ) (mis) (m) (acre- (%) (1013g) ft)
500 5 2.5 2,032 0.05 2.30 0.044
466 10 2.5 2,645 .13 1.28 .076
924 10 2 .5 5,352 1.44 2.30 .297
1,000 20 2 .5 6,759 5.35 5.05 .696
1,833 15 2.5 10,111 30.66 8.16 1.754
2,247 20 2 .5 12,347 80.72 11.08 3.514
2,000 20 5.5 14,115 240.14 12.17 5,568
2,ooO 20 5.5 14,115 240.14 7.06 5.568
2,247 20 2.5 12,347 86.07 8.91 4.210
1,000 20 2.5 6,759
2,000 20 5 .5 14,115 241.58 8.88 5.865
924 10 2 .5 5,352
2,000 20 5 .5 14,115 241.58 7.67 5.865
924 10 2 .5 5,352
2,000 20 5 .5 14,115 320.86 4.70 9.082
2,247 20 2.5 12,347
2,000 20 5.5 14,115 320.86 4.70 9.082
2,247 20 2.5 12,347
2,000 20 5.5 14,115 480.28 3.11 11.136
2,000 20 5 .5 14,115
2,000 20 5 .5 14,115 480.28 4.59 11.136
2,000 20 5 .5 14,115
2,000 20 5.5 14,115 326.21 3.74 9.778
2,247 20 2.5 12,347
1,000 20 2.5 6,759
2,000 20 5.5 14,115 326.21 2.13 9.778
2,247 20 2.5 12,347
1,000 20 2.5 6,759
2,WO 20 5 .5 14,115 401.58 1.48 12.596
2,247 20 2.5 12,347
2,247 20 2.5 12,347
whereas their actual numbers and characteristics were
determined from the typically observed rainfall rate and
the vertical distribution of temperature and moisture of a
tropical disturbance. The numerical cloud model served
as the linking agent that combined all of these observations
into a coherent model of the cloud population that is
determined by the large-scale flow.
The second type of interaction (that by which the
clouds modulate and alter the synoptic scale) now will be
explored further by computing a heat and moisture
budget for a typical tropical disturbance.
One of the most interesting features of tropical dis-
turbances is the fact that, despite the copious amounts
of rain produced in a day, the majority of the storms
travel for hundreds of miles over the oceans without
apparent change in intensity. Williams and Gray (1973)
have considered a sample of 1,257 individual satellite-
observed trade-wind clusters over the Pacific Ocean.
Of these, 537 were classified as conservative, 166 developed
into tropical storms or typhoons, and the rest were either
in the formative or dying stages. While the conservative
clusters were tracked in the satellite pictures for 12-18' of
longitude, no appreciable tropospheric warming or surface-
pressure falls were detected even though the rainfall was
computed as 2.5 cm/day. Thus the typical tropical
disturbance can be considered as constituting a quasi-
steady state system. I n the following, only the con-
servative steady-state cloud clusters will be considered.
Interaction of a Steady-State Cloud Cluster
as a Whole With the Environment
Since the steady-state condition implies that the total
moisture content of the entire system must stay constant,
the same amount of water that precipitates out of the
clouds of such a disturbance must be brought in from the
outside in the form of evaporation from the ocean surface
and by Iow- and middle-level synoptic water-vapor
convergence. Conversely, the heat released by the con-
densation of this rainwater must be exported to the exterior
of the cluster if the steady-state balance is to be met. The
mechanism by which this is accomplished, however, is not
direct. First, the latent heat of condensation is converted
into potential energy insomuch as air from lower levels is
lifted up and carried aloft inside the clouds. Because of
this vertical mass transport, a convergence zone is pro-
duced at the top of the disturbance that generates an
outflow region at high levels. Finally, potential energy is
exported to the outside as mass leaves the disturbance.
Under steady-state conditions, the potential energy
advected from the disturbance plus the long-wave
radiational losses must be equal to the energy released
through the condensation of rainwater.
The mass that leaves the disturbance at its outflow
layer must be compensated by a region of convergent
inflow farther down. Actually, Williams and Gray (1973)
have found mass convergence into the conservative
clusters all the way from the surface to 400 mb. Further-
more, this low- and middle-level convergence brings into
the disturbance the water vapor necessary to establish
the observed net rainfall rates. Accordingly, the water-
vapor convergence into the conservative clusters was
found by Williams and Gray to be equivalent to a rainfall
rate of 2 cm/day. Forty-three percent of this moisture
convergence occurred below 900 mb while 57 percent was
found to come from convergence in the layer between 900
and 400 mb.
In general, we can view the steady-state tropical
cluster (on the whole) as a system that takes in the latent
heat contained in the low and middle level water-vapor
convergence, converts this latent heat into potential
energy, and (after subtracting the net long-wave radia-
tional losses) exports potential energy to the environment
at the layer of divergent mass outflow. With these heat-,
water-, and mass-balance restrictions imposed on the
cluster as a whole, the different effects (detrainment and
subsidence) of the individual clouds on the cluster's
atmosphere should cancel one another so that no change in
the mean vertical profiles of temperature and moisture
should be apparent.
Divergence Pattern Induced by the
Model Cloud Population
Figure 7 portrays the vertical profile of divergence
imposed on the environment surrounding the cumulus
cloud population of figure 5. This profile was computed
from eq (20). A low-level convergence into the clouds of
December1973 J h6pez J 863
529-411 0 - 74 - 4
DIVERGENCE (uita of IO%-’)
FIGURE 7.-Vertical profile of divergence imposed on a tropical
cloud cluster by the upward mass transport performed by the
cloud population of figure 5, assuming a low-level convergence of
10-4s-1.
10-4s-1 has been assumed. As noted before, this high
convergence is necessary to explain a production of about
2.5 cm of rain per day over the disturbance region. The
convergence and divergence produced in the region
surrounding the clouds is concentrated at very low and
very high altitudes while, in the intervening regions, the
effect is much smaller. The convergence at very low levels
is the reflection of the mass-sink that results from the con-
tinuous ascent of low-level air into the base of the growing
clouds. As these growing clouds penetrate through the
environment, the surrounding air is pushed aside and local
mass sources are produced along the path of the ascending
currents. However, as the source of low-level air is gradual-
ly cut off for some clouds and while the tops of the clouds
are still bouyant, local mass sinks are induced in the
environment as a result of the shrinking radius of the
stretched cloud stems. These two effects tend to cancel
among clouds of different growth stages and sizes so that,
in the mean, no marked convergence or divergence is
observed throughout most of the cloud layer. The cloud
air penetrating high altitudes, however, accumulates
continually at the equilibrium level of the high clouds.
Consequently, a region of high horizontal divergence is
induced in the environment at about 12 km. The large
clouds show an anvil at this location. The large convergence
at about, 13-14 km results from the fast subsidence of
negatively buoyant cloud air that has overshot the
equilibrium position and captured surrounding air par-
ticles. A large amount of entrained environmental air is
brought down from higher levels together with the
descending cloud mass. This sinking motion tends to
further emphasize the large divergence of mass at about
12 km. This large divergence region has also been observed
by Williams and Gray (1973), Reed and Recker (1971),
and Yanai et al. (1973). To explore the implications of this
effect on the vertical transport of horizontal momentum
as well as on the dynamics of severe storms under vertical
wind shear would be interesting.
The divergence field that results from the growth of the
clouds will induce a downward flow of mass around the
clouds to compensate for their upward mass transport.
In this descending branch of the convective circulation,
potential energy is converted into sensible heat, and the
temperature of the environment is raised. The resultant
warming, however, will be compensated by the cooling
produced from the evaporation of detrained cloud water
and by the cooling resulting from long-wave radiational
loses.
The divergence profile presented in this section is not
to be compared with the synoptic profiles that have been
obtained for tropical disturbances by Williams and Gray
(1973) and by Reed and Recker (1971). The present pro-
file is a result of the upward mass transport of the clouds
alone and does not include the effect of the downward
sinking motion that will be induced in the clear areas
around the clouds. The difference between the upward
and downward mass transports produces the large-scale
divergence profiles reflected in the synoptic data. The
problem of the compensatory sinking motions in the clear
areas around the clouds and the net divergence profile
produced will be considered in this section.
Interaction of the Model Cloud Population
With the Disturbance’s Atmosphere
In computing a heat and water budget for the interior
of the disturbance, the principal feature to be considered
is the compensatory descending current that will be
induced in the cloud-free region around the convective
element as a result of the divergence-convergence pattern
established by the clouds. The resulting dry adiabatic
compression will release sensible heat to the environment
(dTsubsidence). This heating Will be compensated by cooling
due to evaporation of cloud liquid-water (dTdetrslnment)
and by long-wave radiational loses (dTrdlatlon). The sink-
ing motion will also result in the drying of the cloud-free
regions (dxgUb8ldenCe). This Will similarly be compensated
by the detrainment of water vapor and liquid water from
the different types of clouds present (dXdetrslnment). The
advection of environmental mass into the disturbance’s
atmosphere is another source of heat (d Tadvectlon) and
moisture (dXs4v,ct,on) that should be included in the heat
and water budgets.
We can express the change in temperature of a hori-
zontal slab of the cloud cluster’s atmosphere in a quan-
titative form as
The change in temperature due to subsidence can in turn
864 / Vol. 101, No. 12 / Monthly Weather Review
RATE OF TEMPERATURE CHANGE PC/doyl
FIGURE &-Vertical profiles of the different heating terms of the
heat budget of a steady-state tropical cloud cluster.
be written as
where dTJdz is the lapse rate of the cluster; gJc,, the dry
adiabatic lapse rate; W,, the vertical velocity of the
cloud-free regions within the disturbance; and dt, a small
interval of time. The vertical velocity W, can be ob-
tained from the vertical integration of the divergence
profile presented in figure 7 after provision is made for
the advection of mass in and out of the disturbance by
the synoptic divergence profile. The radiation term has
been obtained from tropical data presented by Cox
(1969). His infrared cooling profile for low-, middle-, and
high-cloud conditions was believed adequate for the rep-
resentation of the long-wave radiation processes in a
tropical cloud cluster. The corresponding short-wave
warming profile was computed for similar cloudiness
structures using the radiation model described in Manabe
and Strickler (1964).
The change in temperature due to advection of en-
vironmental air into the disturbance can be expressed as
d T a d v e c t ion= (Tenvlronment- T d l Rturbance) ' - (23) m
where dmad is the amount of mass advected into the
disturbance during a small interval of time dt and m is
the mass of a layer of the cluster. This advected mass can
be evaluated from the convergence 'profile obtained by
Williams and Gray (1973) for conservative cloud clusters.
The changes in temperature due to detrainment from the
clouds can be obtained from eq (13).
The change in the mixing ratio of water vapor of a
horizontal layer or slab of the disturbance can also be
- n E
P
a W
2 v)
W
a n
FIGURE B.-Same as figure 8 except this is for the moisture budget.
expressed in the form
dX=dXeubsldence + d X s d v e c t l o n + dXdetralnment* ( 24 )
The contribution due to subsidence is
where dX/dz is the vertical gradient of niixing ratio in
the cloud cluster's atmosphere and the other terms have
the same meaning as in eq (22). The change in mixing
ratio due to advection becomes
(26) m dX%dvect Lon= (Xen~ironment-Xdlsturbance)
Similarly, the water-vapor contribution of the detrain-
ment from the clouds can be obtained from eq (14).
Results of the Heat and Moisture Budget
Equations (21) and (24) have been integrated for a
period of 24 hr in time steps of 15 min. Every 15 min, the
change in temperature and moisture of 500-m-thick layers
of the disturbance were found, and new temperature and
mixing ratio profiles were computed. These new values
were used to evaluate the new changes, and so on. Figures
8 and 9 portray the accumulated effect of each of the terms
of eq (21) and (24) for the time interval of 1 day. The final
temperature profile was within 0.2OC of the initial (en-
vironmental) temperature while the mixing ratio profile
was within 0.1 g/kg of the initial values.
The values with height of the different terms of the
heat budget of the disturbance are shown in figure 8. A
mean tropospheric cooling of l.O°C is experienced during a
day due to radiational losses (dotted line). This cooling is
December1973 1 Ldpez 1 865
compensated by the much larger warming produced by
the induced sinking motion (dashed line). This sinking
produces a mean warming of 7.5'C/day, the largest
warming being experienced in the lower half of the dis-
turbance's atmosphere (18'C). Notice that, as a result of
the induced ascent at high levels, a local cooling of about
5'C results a t about 200 mb. The net effect of detrainment
on the disturbance is a mean cooling of 6.1'6. Note how
the subsidence warming is modulated by the cooling due to
detrainment. This close adjustment is a result of the de-
pendence of the subsidence-warming term on the differ-
ence between the dry adiabatic lapse rate and actual
lapse rate of the disturbance [eq (2 2 )]. As the detrainment
cooling changes the lapse rate of the disturbance, the
sinking warming changes in the opposite sense. As a
result, there is a tendency in the long run for a close com-
pensation of both effects. The effect of advection of
environmental air is small compared to any of the other
terms (approx. -0.lOC).
Considering the different terms of the humidity budget
(fig. 9), one can see that there is a good balance between
the subsidence and detrainment effects while the advec-
tion of environmental air contributes very little to the
total moisture budget. The dryness produced by the
subsidence of cloud-free air is balanced closely by the
detrainment of water vapor and cloud liquid water at all
levels. This close adjustment is a result of the dependence
of the detrainment term on the difference between the
mixing ratio of the cloud and that of the disturbance. As a
result, there is a tendency for the clouds in the long run t o
compensate exactly for the dryness produced by subsidence.
clouds in the energetics of a tropical disturbance, we must
consider both the ascending and descending branches of
the cumulus convection circulation. The effect of the
ascending branch (upward mass transport inside the
clouds) is t o cool the disturbance and increase the mois-
ture of the disturbance by the process of detrainment and
to induce a compensatory sinking motion around the
clouds. The effect of the induced descending branch of the
convective circulation around the clouds is t o warm the
disturbance by converting potential energy into sensible
hetit and to decrease the humidity of the air around the
clouds by bringing down upper air of lower water vapor
content.
two branches of the convective circulation and of radiation
balance one another so that the temperature and moisture
profiles remain nearly constant in time. From the point
of view of the total disturbance, the heat liberated in the
condensation of the 2 or 3 cm of rain per day is used to
compensate for the radiational losses, and the rest is
exported as potential energy to the general tropical circula-
tion.
I These results show that to explain the role of cumulus
I
I I In the quasi-steady state disturbance, the effects of the
I
Direct sensible temperature decreases, around and
after cumulus convection has taken place, have been
866 / Wol. BOP, No. 12 / Monthly Weather Review
reported by Kininmonth (1970) from data of the VEM-
HEX project of 1969. Further evidence of the direct
cooling action of cumulus clouds is the lower troposphere
low temperatures found in tropical disturbances and
waves of the easterlies (Riehl 1945). In part I, Gray
(1973) has discussed other evidences of direct cumulus
cooling. In the study of 1,000 Pacific trade-wind cloud
clusters, Williams and Gray (1973) found no appreciable
tropospheric warming or surface-pressure falls even
through the rainfall was very large. Their average cloud
cluster precipitation was computed to be 2.5 cm/day for
a 4' latitude square area. The 1500 cal.cm-2.day-1
liberated through the condensation of this rainfall resulted
in no tropospheric warming even though the ventilation
of the storms was small. Recent computations by Gray
(1973) also indicate that it is impossible to explain the
tropospheric sensible temperature balance around the
globe without invoking a direct cloud sensible cooling
that averages about two-thirds of the net tropospheric
radiational cooling.
Cooling Bower Hypothesis
The results of the computations performed in this
section indicate that, by itself, detrainment from active
cumuli produces a net cooling of the air in which the
clouds are embedded. The evaporation of detrained liquid
water overcompensates for any direct detrainment of
sensible heat from the clouds. Even in the case of vigorous
cumulonimbi with temperature excesses of 5' and 6'C,
enough liquid water is present to produce a net cooling
effect on the environment. If the results of the computa-
tions presented here are verified, the classical view of
cumulus clouds providing heat to the environment through
direct diffusion (Riehl and Malkus 1958) must be revised.
It appears that, as a result of detrainment alone (direct
diffusion of cloud mass), cumulus clouds act as cooling
towers instead of performing the often hypothesized
warming role (Ooyama 1963, Charney and Eliassen 1964,
Qgura 1964, Ruo 1965, Rosenthal 1970). This point of
view .has also been expressed by Gray (1973).
Figure 10 portrays the different components of the
vertical mass circulation present in a steady-state dis-
turbance. Curve A (solid line) represents the mean upward
mass transport that the model cloud population must
perform to produce a rainfall rate of 2.5 cm/day. This
means that the mass transport by the clouds establishes
the divergence profile shown in figure 7. Curve B (dash-
dot line) represents the upward mass transport resulting
from the synoptic divergence profile of Williams and
Gray (1973). The difference bet.ween the required (curve
A) and the synoptic (curve B) upward mass transport
must be compensated locally inside the disturbance by a
downward mass transport in the clear regions between
clouds. This downward mass circulation is portrayed in
curve C (dotted line). This sinking motion releases
I
‘t c
> ‘.
I I
I I
-2-2
Sinking Motion
Induced bsld~
The Disturbance
Sinking Inducea \
:-&-- in the Clear &reo
I the
I Mrturbance
I
Down UP W (mb/doy)
FIGURE 10.-Different components of the vertical mass circulation present in a steady-state cloud cluster.
sensible heat to the disturbance’s atmosphere, as noted
previously. The compensation for the remaining upward
mass circulation (the synoptic contribution) occurs outside
the disturbance. Adding this downward-outside contri-
bution to curve C, we obtain the total downward branch
of the mass circulation of the disturbance (curve D).
For illustration, we assumed that the subsidence occurring
outside takes place over an area equal to that of the
disturbance.
Role of Recycling in Generation
of Individual Cumulus Elements
The general st,ability of the cloud cluster lower layers
and the need for a lifting mechanism to initiate parcel
condensation until free convection is obtained are gen-
erally accepted. Over the ocean, these conditions require
the application of substantial mechanical forcing to
initiate buoyant elements. As discussed by L6pez (1973),
t o generate cumulus over the oceans without cloud base
vertical velocities of 1-5 m/s is impossible. This is equiva-
lent to having local convergences during the cloud’s
growing stages of about 3-6X10-3s-1. These values are
1,000-2,000 times larger than the synoptic convergence.
Even if the active cumulus take up only 1 percent of the
cluster area, these convergences are 10-20 times larger
than that specified by synoptic convergence. The only
way the extra convergence under the cluster cumulus
can occur is by a large mass recycling mechanism, which
is 10-20 times greater than the synoptic mass convergence.
The recycling dry and moist downdraft air that pene-
trates into the boundary layer from upper lev€-, is
believed to be the primary mass source for cloud parcel
initiation. Were the cluster cumulus to be initiated or
forced only by the synoptic convergence of 3-5x 10-%11,
then low-level mass requirements would permit only
about l /l ,O O O of the cluster area to be occupied by parcel
ascent if all the mass sent into cumulonimbi (or only
about 1/500 of the area) is occupied by all towering
cumulus or by all cumulus parcel ascent. The radar data
presented in this paper show that t’he areas of the cluster
occupied by active cumulus clouds are typically 10-20
times larger than these amounts. The fundamental
requirement of large up-and-down mass recycling 10-20
times larger than the mean vertical mass flow a t cloud
base is clearly evident, given the typical cloud cluster
synoptic convergences and stable lapse rate conditions.
Developing Cloud Clusters
The preceding computations apply to the case of a
steady-state tropical disturbance [i.e ., a system that ex-
ports a t high altitudes (in the form of potential energy)
the latent heat advected into it at low and middle levels].
This type of dsturbance represents the typical cloud
cluster that travels for several days over the oceans with
no appreciable change in intensity. The heat liberated
in the condensation of the 2 or 3 cm of rain produced in a
day is exported as potential energy to the general tropical
circulation in which the cloud cluster is embedded, after
provision is made for the disturbance’s own radiational
losses.
December1973 1 L6pez 1 867
2 -
3 -
B 4 -
g 5 -
2 6 -
3
w
7 - ClRCULATlON
B -
9 -
IO -600 -400 -m
-9
- IO
- CUMUWS MODEL
(LOPEZ)
* * * *. BROAD-SCALE MODEL
(GRAY1
DOWN-DRY
UP W (mb/&y) DOWN
FIGURE 11.-Comparison of the cloud cluster vertical circulation as
determined in this paper and with similar values obtained by
Gray (1973).
The response of the large-scale flow to the energy ex-
portation of a disturbance, however, can result in drastic
changes in the synoptic features of the region. This is the
case of hurricane development. The interaction between a
disturbance and the surrounding flow can be viewed in the
following way: A tropical disturbance as a whole takes in
environmental mass a t low and middle levels and exports
mass a t high altitudes. A compensatory sinking motion
is induced in the air surrounding the disturbance t o
satisfy the synoptic upward mass transport of the dis-
turbance as a whole. In this way, the potential energy
produced by the cloud cluster as a whole is converted
into sensible energy outside the cluster. The degree of the
resultant warming depends, however, on the scale on
which the compensatory sinking occurs. If the subsidence
takes place over a broad region, a slight warming is ex-
perienced, which is probably used to compensate for the
radiational cooling of the area. If the compensatory sub-
sidence occurs over a small region near the disturbance,
however, enough compressional warming could take place
to explain hurricane development. I n fact, Oliver and
Anderson (1969) have found from satellite observations
that the majority of hurricanes form around a circulation
center that develops in the clear urea ahead of the con-
vective region. The study of the large-scale flow features
leading to a concentrated compensatory descending
current is beyond the scope of this investigation. There
are reasons to believe, however, that the broadscale
flow a t the level of the disturbance’s outflow (approx.
200 mb) might be the controlling factor. Thus if the wind
pattern at that level allows the outflow from the disturb-
ance to be spread over a broad region, only gentle sub-
sidence and warming will occur. However, if the upper
air wind pattern restricts the outflow, strong local sub-
sidence and considerable warming might develop near
the disturbance. The convective activity would then
organize itself around the resulting warm core low-pressure
- CUMULUS MOML
LOPEZ)
I I I I I 1 I I I 1 I
-16 -12 -8 -4 0 4 8 I2 16 20
RATE OF TEMPERATURE CHANGE (OC/doy)
FIGURE 12.-Comparison of each model’s subsidence warming and
evaporation cooling.
region. Further studies along these lines could provide
considerable insight into the physics of hurricane develop-
ment from weak tropical disturbances.
6. COMPARISON OF THE BUDGETS COMPUTED
IN THIS PAPER WITH SIMILAR BUDGETS
COMPUTED FROM SYNOPTIC DATA ALONE
In part I, Gray (1973) has discussed the heat and
moisture budgets and vertical circulation of the mean ,
tropical cloud cluster of the Pacific. His computations were
based entirely on composited synoptic data without any
cumulus scale information. His results will now be com-
pared with the budgets and vertical circulation obtained
in this paper, which were based on detailed knowledge of
individual cumulus clouds of different types and em-
pirically derived cumulus populations.
Figures 11, 12, and 13 show the comparison of the two
methods with regard to their local vertical circulations,
heat budgets, and moisture budgets, respectively. One
can clearly see how well these models agreed in specifying
the required mass, energy, and wa.ter-vapor budgets. This
lends consistency and credibility to the results of each
approach. This inward meshing of the dynamics from
opposite scales of consideration should always be a
desirable goal for ultimately verifying cumulus broader
scale interaction models.
These two computations were done independently.
The two methods used are very different from each other
since they reflect two completely different approaches to
the study of cumulus larger scale interactions. The fact
that the end results of the computations agree so well,
868 1 Vol. 101, No. 12 1 Monthly Weather Review
0.5
I
i
2
-3
-4 3
-5 2
-7 E
W a
-6 3 fn
-e
-9
- IO
cf\ ..
*.
CUMULUS MODEL
(LOPEZ)
BROAD-SCALE
MODEL
(GRAY)
..
-16 -12 -8 -4 0 4 8 12 16
9 . kg-’.&y-.‘
FIGURE 13.-Comparison of each model’s water-vapor budget.
despite the varying methodologies, is strong evidence for
the correctness of both treatments.
7. SUMMARY
A numerical model of individual cumulus clouds has
been used in this section to investigate the effects of cumu-
lus convection on the large-scale features of tropical
disturbances or cloud clusters. A cloud population charac-
teristic of ‘tropical cloud clusters has been determined from
radar and synoptic observations. With the help of the
numerical cloud model, the effects of the typical ensemble
of cumuli have been calculated. One major effect consists
of the detrainment of cloud mass, which will cause a direct
transport of excess sensible heat as well as cooling of the
surrounding clear air as a result of the evaporation of the
detrained cloud liquid water. The net effect was found to
be one of cooling as the evaporation overcompensates for
the detrainment of excess sensible heat. In this regard,
cumulus clouds should be considered as a basic cooling
tower as opposed to a hot tower concept. The other
effect produced by the typical population is the induction
of a descending motion in the environment to compensate
for the upward mass transport of the clouds. The induced
. subsidence will result in the warming and drying of the
environment.
Using all of this information, we computed a heat and
moisture budget for a steady-state tropical disturbance.
Under steady-state assumptions, the heat liberated from
the condensation of rainwater is exported to the environ-
ment in the form of potential energy at the level of the
disturbance’s outflow. At the same time, the water
vapor necessary to produce the rainfall is imported into
the disturbance in the form of a low- and middle-level
mass convergence. Inside the disturbance, the warming
resulting from the sinking motion is compensated by the
net cooling resulting from detrainment plus the cooling
resulting from infrared radiational losses. Similarly, the
dryness resulting from the subsidence is compensated by
the detrainment of water vapor and liquid water €rom
the clouds.
The convergence of mass at low and middle levels
into the disturbance as a whole and the high-altitude
outflow of massfrom the disturbance will, in turn, induce
a descending motion in the clear air surrounding the
storm. The warming will be large or small depending on
the scale a t which the subsidence occurs. Under favorable
situations, the warming could be large enough to produce
hydrostatically the low pressures needed for the organi-
zation of a tropical disturbance into a full-fledged hurri-
cane. The present numerical model of cumulus clouds
has proven to be useful in investigating the interaction
of cumuli witlh the large-scale features of tropical dis-
turbances, and future investigations using this tool are
expected to result in the clarification of the problem of
formation of hurricanes from a weaker disturbance and
in the maintenance of the tropical general circulation.
ACKNOWLEDGMENTS
The author wishes to express his sincere gratitude to William M.
Gray under whose guidance this investigation was performed.
His kind criticism and encouragement are very much appreciated.
Special thanks are due to Edward Bussel, Barbara Brumit, and
Larry Kovacic who helped with the programming, manuscript typ-
ing, and drafting.
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