the dissipation of scattered and broken cloud

351.5'76.11

'THE DISSIPATION OF SCATTERED AND BROKEN CLOUD*

By E. WENDELL HEWSON, M . A . , Ph.D., F.R.S.C

(Manuscript receircd .\pYil 20, 1948)

SUMMARY Shaw's early work on the dissipation of scattered and broken

cloud is outlined and the loss of heat by cloud resulting from terrestrial radiation is indicated. The process of cloud dissipation is described and various criteria are given.

The implications of these concepts in evaluating the significance of the slice method for studying cumulus clouds are then considered.

A method of calculating the time required for a specified system of scattered and broken cloud to dissipate as a result of radiational cooling is described and the assumptions involved are discussed. The influence of the turbulent transfer of heat and water vapour under various conditions is indicated in a general manner and the effect of the absorption of solar radiation by the cloud is evaluated.

Widespread vertical motion of the atmosphere may have a marked influence on cloud dissipation, depending on whether ascent or subsidence of the whole air mass is occurring. A method of calculating the amount of subsidence required to cause a given system of cloud to dissipate is described. For a particular case, the effects of ascent of the air mass and of radiation are combined, and useful criteria thereby obtained.

I . I N T R O ~ U C T I O N The various atmospheric processes which lead to the formation

of cloud have been studied extensively in past years. Rather less attention has been paid to those processes by which clouds dissipate, although the latter a re equally fundamental and significant. Early in the present century W. N. (later Sir Napier) Shaw (1902) described, in a paper entitled " La lune mange les nuages-a note on the thermal relations of floating clouds ", one type of physical process which would account for the dissipation of certain types of clouds. A few writers have described Shaw's treatment of this problem, but by and large his contribution has received little attention. Shaw ascribed the dissipation of individual cloud elements under certain conditions to what may be termed " warming through cooling ", a process by which the temperature of a mass of cloud increases as the end result o f an initial small fall in the temperature of the cloud. The initial cooling occurs as the result ot the net loss of heat by the cloud by terrestrial radiation. In his * This paper was read before the Canadian Branch of the Royal

Meteorological Society a t Toronto, Ontario, on February 13, 1942, hut not submitted for publication during the war years. Several additions are incorporated in the present paper, more particularly the material in Section 9. It is published by permission of the Controller, Meteorological Division, Air Services Branch, Depqrtment of Transport, Canada.

243

244 E. W. HEWSON

paper Shaw described apparatus by which this " warming through cooling " could be demonstrated in the laboratory. The present paper represents an attempt to develop and amplity the meteorological implications of Shawls basic contribution.

2. THE HEAT LOSS OF CLOUDS BY TERRESTRIAL RADIATION

I t is essential for present purposes to be able to compute the rate of loss of heat of a given cloud by terrestrial radiation. One of several methods may be used, depending on the degree of accuracy desired.

I t was shown by Hewson and Longley (1944) that : Net loss of heat by cloud=yr(TT4 - TS4 + TB4)

where y a t ordinary tropospheric temperatures has the value 0.35 (approximately 1 / 3 ) ; (r is Stefan's constant (8 .14 x 1 0 - l ~ cals. cm.? min.-' deg.-4) ; and TT, T,, and T , are the temperatures a t the top and base of the cloud and at the surface of the earth, respectively. These authors also showed that, under the average temperature conditions prevailing in middle latitudes, clouds below a height of 7 km. always undergo a net loss of heat by terrestrial radiation.

If a more accurate value of the net loss of heat by a cloud is required, the radiation chart developed by Elsasser (1942) may be used. . is will be shown later, the effect of solar radiation on the cloud is small, but it may be included if necessary.

3 . TERRESTRIAL RADIATION AND CLOL'D DISSIPATION

Let us first denote, following Brunt (19-3~)~ the total water content (vapour + liquid + ice) of the cloud in grams per kilogram of dry air by the symbol [. Thus we may write

where I, y , and s are the numbers of grams of water vapour, liquid water, and ice, respectively, per kilogram of dry air. I t will be noted that x is the mixing ratio as customarily defined. In addition, we will take the value of f a t the mean pressure of the cloud as representatihe of that for the cloud as a whole.

[ = x + y + z

T -

FIG. l.--Thr dissipation of cloiid rcwllin:: from its descent alnnp !he envircmnwnt curve i r i a b-eriea of MI- barie aiid riatiirated adiabatic steps.

THE DISSIPATION OF SCATTERED AN11 BICOKEN CLOUD 245

Figure I gives a portion of a tephigram, with the curve A B C representing the variation of temperature with pressure obtained from a portion of a sounding in the troposphere. Cloud of limited horizontal dimensions extends through the pressure interval D to F , with its mean pressure a t E . The total water content of the cloud, represented by that a t E , is ,$; the saturation mixing ratio line with the value ,$ is shown by a heavy broken line, and is referred to a s the ,$-line. Next consider the effect of terrestrial radiation on the cloud, representing for our immediate purposes the initial condition of the cloud a s a whole by that a t E . It is assumed that other cloud forming or dissipating processes are absent. First the cloud cools slightly a t constant pressure as a result of terrestrial radiation, so that the point representing the cloud moves from E to G. At G, the cloud is cooler and therefore denser than its environment, and a s a result it subsides. Since water or ice particles are present to maintain saturation during the adiabatic heating, the temperature of the cloud increases at the saturated adiabatic rate, the point moving from G to H . At H the cloud is again in equilibrium with its environment and its descent ceases. The mean pressure and temperature of the cloud are now those at H . It will be noted that the cloud is now warmer than it was initially, the temperature a t H being greater than that at E ; hence Shaw’s “ warming through cooling ”. In addition, some of the liquid water or ice has evaporated, and the proportion of liquid or solid to vapour in the cloud has decreased. The process is repeated. Continued radiational cooling causes the mean temperature of the cloud to drop a t constant pressure from H to J, after which it increases to K , and the process continues in a succession of alternate isobaric and satuated adiabatic steps. The isobaric cooling proceeds slowly, but the subsequent subsidence is much more rapid. In the atmosphere such pronounced steps are unlikely to occur; rather the cloud descends along the environment curve in a series of infinitesimal isobaric and saturated adiabatic steps.

During the descent the mass of liquid water or ice per unit mass of dry air decreases and the mass of water vapour increases as the cloud particles evaporate. As the cloud approaches the pressure a t which the &line intersects the environment curve, at B , it becomes more and more tenuous. Finally at B the cloud disappears completely, for the mass of water initially present in all states in the cloud is just suflicient a t B to saturate the air which earlier constituted the cloud. Thus during the descent from E to B ( y + s ) = ( E - x) grams of liquid water and ice per kilogram of dry air, where x, y and z are the initial values, have evaporated.

I t will be apparent from the foregoing discussion why the process described is limited to smaller cloud elements. Since the cloud subsides through its environment, there must be vertical convergence and hence horizontal divergence of the air below the cloud and vertical divergence and hence horizontal convergence above. Wi th a very extensive layer of unbroken cloud it is doubtful whether compensating air currents of sufficient magnitude to permit the subsidence of the cloud would be set up. Even if some subsidence occurred, its effect would tend to be counteracted by the fact that the cloud loses heat by terrestrial radiation a t its top but gains heat

,

246 E. 1%‘. HEWSON

a t its base. Thus additional condensation occurs just above the cloud top, whereas the cloud elements a t the base evaporate, perhaps resulting on some occasions in a slight net increase in the height of the cloud as a whole. Wi th smaller cloud elements the subsidence i5 sufficiently rapid to render the above effect negligible in comparison.

4. CRITERIA FOR CLOUD DISSIPATION

do or do not dissipate, it is desirable to specify several quantities: In order to describe in detail the conditions under which clouds

a = the lapse rate of temperature of the environment below the cloud.

I?’ = the saturated adiabatic lapse rate. P ” = t h e lapse rate of dew point of adiabatically ascending

All thrsr quantities a re given on the tephigram or similar thermu- dynamic diagrams. The saturated adiabats are readily idrntified ; since the dew point of adiabatically ascending unsaturated air moves along the saturation humidity mixing ratio lines on such thermodynamic diagrams, these lines give the value of I”’.

The behaviour of cloud elements when the lapse rate of the environment below the cloud lies within certain limits will now be indicated. tt<F”. T h e cloud descends slowly, its density increases, a i d if

does not dissipate. An environment curve in which the lapse rate of temperature

below the cloud is less than I?” is shown in Fig. 2. The heavy broken line is the (-line for the cloud. A s radiational cooling proceeds, the cloud descends by a series of isobaric and saturated adiabatic steps, a s described previously. This is not an example of “ warming through cooling ”, however, since there is a slight inversion of temperature, i.e., z is slightly negative, and as a result the cloud cools a s i t descends. If the lapse rate remains as shown for a long enough time, and if other cloud forming or dissipating processes do not interfere, the cloud will descend to the surface.

unsaturatrd air (14’ C. per km.).

T -

FIG. 2.-Descent of rlaud when a<17“; it does not dissipate and it! liquid water o r icr confrut

increases.

T - - r

PIG. 3.-Descent of cloud when a=r”, it does not dissipate, its liquid water content being

cunslant.

THE DISSIPATION OF SCATTERED AND BROKEN CLOUD 247

Furthermore, during the descent there is a continuous condensation of water vapour so that the proportion by mass of liquid water or ice to water vapour increases. Thus the density of the cloud increases as it descends; by density we mean here the mass of liquid water or ice per unit mass of dry air, not per unit volume.

The cloud descends slowly. I t requires appreciable time for the isobaric cooling to produce even a small decrease in temperature, but the ensuing subsidence occurs almost instantaneously. Thus the rate of descent of the cloud depends on the magnitude of the height interval through which the cloud subsides after a specified isobaric temperature decrease has occurred ; the magnitude of the height interval decreases as the lapse rate decreases. Thus it will be apparent that the descent shown in Fig. I is more rapid than that in Fig. 2, since the saturated adiabatic descent for the same isobaric temperature decrease is greater in the former case. ~<1”‘. The cloud descends slowly, its densi ty remains coilstarit,

and it does n o t dissipate. In Fig. 3 the lapse rate of temperature of the environment below

the cloud is equal to the lapse rate of dew point of adiabatically ascending unsaturated air. Thus the environment curve below the cloud lies parallel to the saturation humidity mixing ratio lines, and hence to the (-line for the cloud. Since a>o, “ warming through cooling ” occurs, If other factors permit, the cloud will in time descend to the earth’s surface. There is neither condensation nor evaporation within the cloud a s it descends, so that the density of liquid water or ice does not change.

1 - T - FIG. 4.-Descent of cloud when I’’>a>T”: since thc environment curve does not intersect FIG. 5 . - l k ~ e n t Of cloud whell T‘>a> 1”’; the &line below blie cloud, the density of liquid since the environmmt curve intersects the water in the cloud decreases but the rloud do:,s [-line below the cloud, the cloud dissipates.

not dimipat?.

The cloud descends slowly, more slowly than that in Fig. I , but less slowly than the cloud in Fig. 2. a > Y . There are two main subdivisions of lapse rates of the environment in this category. Any given lapse rate is classified according to whether

it lies between the limits set by the lapse rate of dew point and the saturated adiabatic lapse rate, i .e., whether r’>a>F”; or

it is greater than the saturated adiabatic lapse rate, i.e., whether =>I”.

(i)

(ii)

248 E. W. HEWSON

( i ) F‘>r)L”’. In this and the other subdivision the behaviour of the cloud depends not only on the lapse rate of the environment below the cloud, but also on the value of for the cloud. Two cases arise : ( a ) If the [-line does izot intersect the envirotzmertt curve at some position below the initial cloud level, the density of the cloud decreases, but the cloud does not dissipate completely. ‘This situation is illustrated in Fig. 4. The density of the liquid water or ice in the cloud decreases as it descends.

Since the lapse rate of the environment below the cloud is greater than in the two previous cases, the cloud descends mure rapidly. If the atmospheric conditions do not change during the descent, the cloud will reach the surface. ( b ) I f the [-line intersects the environment curz’e at some position below the initial cloud level, f h e density of the cloud decreases during descent, and the cloud dissipates completely. The (-line intersects the environment curve below the cloud in the case shown in Fig. 5 . The cloud descends at about the same rate as that discussed in ( a ) ; it dissipates completely at the level specified by the intersection of the &line and the environment curve. Since this is the same situation as that described in detail in section 3 and illustrated by Fig. I , it is unnecessary to go into further detail.

T - + PIC;. 6.-D~scent of cloud when a>l“; since the saturated adiabat tlrrounh the cloud does not intersect the &line the cloud does not

dissipAte.

T -

FIO. 7.-Descent of thud when a > P ; since the sitturated rtdiahat through the cloud intPrswcta

the E-line, the cloud dimipates.

( i i) a>l”. There are two cases in this category, depending on whether or not the &line intersects the saturated adiabat through the mean pressure and temperature of the cloud in its initial position. ( a ) If the @line does not intersect the saturated adiabat through the mean pressure and temperature of the cloud in its initial position, the cloud descends rapidly, its density decreasing, but the cloud does not dissipate completely. In Fig. 6 the lapse rate of the environment below the cloud lies between the dry and saturated adiabatic lapse rates. In this situation the processes involved are quite different from those discussed previously. Because the lapse rate of the environment is greater than the saturated adiabatic lapsf, rate, the cloud, warming a t the saturated adiabatic rate a s it descends, never reaches equilibrium with its environment, since its

T H E DISSIPATION OF SCATTERED AND BROKEN CLOUD 249

density throughout its descent is always greater than that of the surrounding air. In this case it is not necessary to invoke terrestrial radiation to account for the descent of the cloud, although it may play a part ; any small perturbation of the cloud which increases its density relative to that of the surrounding air acts as a trigger which sets off the essential instability of the cloud considered as a unit.

I t will be apparent that the cloud descends rapidly, since it acquires energy from the environment, energy which is in part converted into kinetic energy of descent. The liquid water or ice content of the cloud must of necessity decrease as the cloud particles evaporate to maintain saturation. Because the &line and the saturated adiabat do not intersect, ?c approaches but does not become equal to E, Le., the liquid water or ice content 6 - x decreases but does not become zero, so that the cloud does not dissipate. ( b ) If t he [-line intersects t h e saturated adiabat t h r o u g h the m e a n pressure and temperature of t h e cloud in i ts initial posit ion, t h e cloud descends rapidly, i t s densi ty decreasing, and t h e cloud dissipates at t h e level specified by the intersection of t h e &line and the saturated adiahat. The above relationship between the &line and the saturated adiabat is illustrated in Fig. 7. As before, the cloud descends rapidly, its density decreasing in the process. At the intersection of the two curves, x = [ , i.e., the liquid water or ice content - x of the cloud becomes zero and the cloud has dissipated completely by the time it reaches that level. In this situation the cloud dissipates rapidly.

Although in Figs. 6 and 7 the lapse rate of the environment is shown as less than the dry adiabatic lapse rate, the same considerations hold when 'it is greater. The only difference is that the cloud will descend even more rapidly, since the difference in air density between cloud and environment is greater than in the cases shown in Figs. 6 and 7.

I t will be noted that a general principle emerges from the above discussion. Other things being equal, the rate of descent of the cloud increasos as the lapse rate of the environment below increases, but with a discontinuity a t the point where a=I" . As this point is passed and greater lapse rates are encountered, the speed of descent of the cloud increases greatly, as the schematic diagram given in Fig. 8 indicates. Thereafter the increase in rate of descent is proportionately less. The broken curve in Fig. 8 shows schematically the corresponding variation of the time required for the cloud to dissipate in those cases where [ - x is small enough to permit dissipation to occur; the curve starts slightly to the right of the co-ordinate marked F", since the cloud will only dissipate by this process when r>I'".

5 . CLOUD DISSIP4TION A N D THE SLICE METHOD

Since the process of dissipation described above presumably applies to cumulus clouds after their phase of active growth has finished, as well a s to other types of clouds, it may be of interest to discuss the implications of these ideas when applied to instability criteria.

250 E. W. HEWSON

9. Bjerknes (1938) introduced the concept that in studying the development of cumulus cloud it is insufficient to consider only the rising air in the individual clouds themselves ; the subsidence between the clouds required by considerations of continuity has an important effect in modifying the environment. Thus it is necessary to consider a horizontal slice of the atmosphere rather than an individual parcel of air. S. Petterssen (1939) extended Bjerknes' treatment of the problem. N . R. Beers (1945) used the circulation theorem in a further discussion. The question is discussed by Sir Charles Normand (1946), who points out that the subsidence of the air need not occur between the individual cloud elements. He mentions two other alternatives. The first is that suggested by H. Koschmieder (1g40), to the effect that a whole system of clouds must be considered together and the descent of air may occur in a distant portion of the larger system. Thus there need not be subsiding air beside individual clouds. The second is that subsiding currents occur in the clouds themselves. Normand mentions specifically the evidence for strong downdrafts in cumulonimbus clouds.

I I I I I

( - l ine T - F

Lopse rate a+

E'io. &-Schematic representation of the varia- PIG. 9.--Thc formation and subsequent tioii of speed of desccnt of cloud and of time dissipation of cumulus humilis cloud. required for dissipation with lapse rate below

the cloud.

The considerations presented below are a variation of Normand's point concerning descending currents in the clouds themselves. The slice method as usually described postulates that there is rising air in all the individual cloud elements and subsiding air between them. However, Figs. 6 and 7 serve to emphasize the fact that a cloud may, considered as a unit, be in unstable equilibrium, and that the realization of that instability occurs only when the cloud undergoes a downward impulse; it is clear from Figs. 6 and 7 that the cloud element is in stable equilibrium for upward impulses. That a parcel of air may be unstable for an upward impulse is generally recognized ; the fact that it may be stable for an upward impulse but unstable for a downward impulse has not received the same attention.

Let u s now consider the formation and dissipation of cumulus humilis cloud, as indicated in Fig. 9. The curve A B C represents the lapse rate of the environment, with a superadiabatic lapse rate in the lower layers, from A to B . A parcel of air near the surface, at A , receives an upward impulse and rises dry-adiabatically to D , a t which level it becomes saturated. Saturated adiabatic ascent occurs from D to E . I t is assumed that turbulent frictional retardation during the whole ascent prevents the air from rising beyond E. Initially, then, the cloud element extends from L) to E ,

T H E DISSIPATION O F SCATTERED AND BROKEN CLOUD 251

with a saturated adiabatic lapse rate throughout. Since the air comprising the cloud became saturated at D , the &line for the cloud is the saturation mixing ratio line through D . As a result of the turbulent transfer of heat between cloud and environment, the lapse rate in the cloud conforms more closely to that of the environment. Kadiational cooling of the cloud commences as soon as it has formed, but its effect is secondary during the period of development. A s soon as growth has finished, descent along the environment curve as a result of radiational cooling commences, as indicated in F ig . 9. As will be shown later, if daytime conditions are considered, the gain of heat by the cloud by the absorption of solar radiation is less than the loss by terrestrial radiation, and there is a net loss of heat, so that the foregoing analysis still applies. The cloud descends along the environment curve to B , then warms a t the saturated adiabatic rate until the intersection with the ,$-line at F is reached, a t which level the cloud has completely dissipated. The air a t F which originally comprised the cloud, being colder and therefore denser than its environment, continues to descend, but now dry adiabatically, and reaches the surface a t G.

For the purposes of illustration the above degcription involves some over-simplification. The fact that little subsidence of the base of cumulus humilis cloud is observed does not invalidate the argument. I t is obvious from the figure that the liquid water or ice content of the top of the cloud is substantially greater than that of its base. As a result, as the cloud descends the water or ice near its base evaporates before that near the top does, and the net effect is a gradual lowering of the top of the cloud, but without much lowering of the base. In some instances it may not require radiational cooling to initiate the process ; a downward impulse acting on the cloud may perhaps be sufficient. I t is not claimed that the above process explains the dissipation of cumulus clouds under all circumstances. I t is possible to visualize a lapse rate distribution below the cloud which would require some other method of dissipation for the cloud. However, it is probable that in a good proportion of cases the process of dissipation is that described above. The effect of the turbulent transfer of water vapour from the cloud to its environment will be mentioned later.

There are several observations which support the above hypothesis about the life cycle of cumulus humilis clouds. Sailplane pilots report that active thermals are capped by cumulus clouds which a re growing, and which have the firm, solid, swelling appearance characteristic of the earlier stages of development. On the other hand, they shun cumulus clouds which have the ill-defined and wispy appearance characteristic of the dying phase, for they have found from experience that they cannot climb below these. Furthermore, some experienced pilots have reported the presence of definite down- currents below cumulus clouds of the latter type. Extensive investigations of vertical air currents in curnulonimbus clouds have been made during the course of the Thunderstorm Project in the United States; these studies, described by Byers and Braham (1948), show that up-currents are prevalent in the growing stage but that down-currents predominate in the final phase of cumulonimbus clouds.

252 E. W. HEWSON

The second point is the observation that, in the experience of the author, individual elements of cumulus huniilis cloud do not, after commencing to decay, subsequently redevelop a s a result of a fresh infusion of rising air from below. In other words, the bubbles of air which have risen to form new clouds become manifest as such in the clear portions of the sky, but not where a dissipating cloud already exists. There may be more than one explanation for this, but the most probable explanation would seem to be that down- currents below the dissipating cloud prevent the ascent of a fresh bubble of air from below.

Wi th these points in mind, we may now proceed to consider their significance in connection with the basic assumptions on which the slice method rests. We win take in succession three stages in the development of a field of cumulus: early afternoon; mid- afternoon : and late afternoon.

lO.--Vertical cnrrcnts in and near curntilus hiiinili6 cloud and how they w r y during the afternoon.

( i ) Early afternoon. As the insolation increases the lapse rate in the lower layers during the day, cumulus may start to develop during the late morning. If S O , by early afternoon thc sky will usually be partly clouded. The lapse rate and the associated instability in the lowcr layers are still increasing, and although some cumulus a rc in the dying stag'r, a preponderance of the cloud is of the growing and active type. I n the former there will be down-currents ; in the latter, up currents, as suggested in Fig. 10 (a ) . Because of the preponder- ancc of growing clouds [in Fig. 10 (a), four growing as against two dccaying] , there is a small residual subsidence between the cloud elements, as indicated by the small arrows between clouds. (ii) Mzd-afternoon. By mid-afternoon thc Inpse rate and instability in the lower layers havc reached their greatest magnitude, and the cloud amount has reached its maximum for the conditions prevailing. As indicated in Fig. 10 ( h ) , growing and decaying clouds are now equal in number (four of each) over the same area. Since the descent of air in the dying clouds is equal, or ~ e r y nearly w, to thr ascrnt ot air in the developing clouds, there is little or no

T H E DISSIPATION OF SCATTERED AND BROKEN CLOUD 253

vertical motion between, as indicated by the absence of arrows between clouds. (iii) Late afternoon. By this time the lapse rate and instability are decreasing, as is the cloud amount, and there is a preponderance of decaying clouds (two growing and four decaying), as indicated in Fig. 10 (c). As a result, there is a small residual ascent of air between cloud elements.

When cumulus cloud development and dissipation are considered on the above basis, it would appear that vertical motions between clouds are of secondary importance only. In addition, this analysis suggests that, contrary to the slice approach which as presented assumes descending motion between clouds, the small residual vertical motion is a t one time upward, a t another time downward. The above conclusions are of course predicated on the assumption that a large number of cloud elements are considered together, so that the problem can be viewed statistically. Even if the downward transport of air in dying clouds is not exactly equal t o the upward transport in growing clouds, the principle suggested is nevertheless still valid.

6. COMPUTATION ?F TIME REQUIRED FOR DISSIPATION

By an extension of the foregoing concepts it is possible to compute the time interval required for a specified cloud to dissipate when subject t o the conditions assumed. In order t o make the computation it is only necessary to assume that the cloud dissipates as the end product of two main steps, the first isobaric and the second saturated adiabatic, rather than by a series of infinitesimal steps. This is equivalent to holding the cloud a t constant pressure until it has cooled sufficiently so that on release it subsides saturated adiabatically in a single step to the level at which complete dissipation occurs, i .e . , to the level a t which the ,$-line intersects the environment curve below the cloud. A numerical example will serve to illustrate the procedure.

A sounding of the atmosphere reveals the vertical temperature distribution shown in Fig. 1 1 . Broken cloud extends initially from 740 rnb. to 680 mb., so that its mean pressure is 710 mb. The temperature a t the cloud top (TT) is 4" C.; that a t the cloud base (TB) is 7' C. The surface temperature (T,) is 15' C. The saturation mixing ratio a t the mean temperature (5.5' C.) and the mean pressure (710 mb.) of the cloud, denoted by A , is 8.0 gm. per kgm. of dry air. Now assume that there is 1.0 gm. of liquid water per kgm. of dry air in the cloud; there will be no ice present with the cloud temperatures above oo C.

,$=x+y+z=8.o+ r.o+o=g.o gm. per kgm. The (-line with this value is shown in Fig. 11 by a heavy broken line. I t intersects the environment curve below the cloud a t a pressure of 800 mb. and a temperature of g o C., a t B ; the subsiding cloud therefore dissipates completely at 800 mb. The temperature to which the cloud must cool a t constant pressure if it is to subside subsequently in one saturated adiabatic step and then dissipate completely is that specified by the intersection, a t C, of the isobar through A and the saturated adiabat through B . The temperature a t C is 4' C. The amount of isobaric cooling AT of the cloud, i .e . , of cooling from A to C, is given by 5.5 - 4 = 1.5' C. As the cloud

Thus

254 E. W. HEWSON

cools from A to C, its liquid water content increases as water vapour condenses. At A the saturation mixing ratio is 8.0 gm. per kgm. ; at C it is 7.2 gm. per kgm. Therefore the amount of water vapour which has condensed as the cloud cools from A to C is

Ax=S.o- 7.2=0.8 x I O - ~ gm. per kgm.

0 I0 2 0

“CI

PIG. 11.-The computation of the time required for

dissipation.

If the cloud, at C, is then releascd, it descends saturated adiabatically to B , deriving energy from the environment during this stage. Since this descent occurs rapidly in comparison with the time taken €or the cloud to cool isobarically from A to C, the time required for dissipation is then effectively that required for the isobaric cooling of the cloud from A to C to occur. The method of computing the latter is described in the next paragraph.

Let u s now consider the process as it affects a vertical column of the cloud, of cross section I cm.%, and extending from top to base, i . e . , through a pressure interval Ap of 60 nib. The mass of air in this column is given by

m = A p ~ g = 6 0 x 1 0 ~ / 9 ~ 8 x 1 0 ~ = 6 1 grn. where g is the acceleration of gravity. As shown in section 2 , the vertical column of cloud loses heat by terrestrial radiation. The consequent rate of cooling is retarded, however, as a result of the release of latent heat of vaporization L as water vapour condenses ; this latent heat is effectively heat supplied to the column during the process. Denoting the specific heat of dry air a t constant pressure by c,, the decrease in heat content of the column in time t is given

Heat lost by terrestrial radiation-heat supplied by condensation = decrease in heat content.

by

Ar(TT4 - TS4 + TB4)t - mLAx =,rnc+T 0.35 x 8.14 x 10-”(277~ - 2884+28~4)t - 61 x 592 x 0.8 x I O - ~

=61 x 0.24 x 1.5 t =350 min.=6 hours

Thus the cloud dissipates in approximately 6 hours.


I t will be noted that in the above computation neither the decrease in heat content of the liquid water nor of the water vapour component of the cloud has been taken into account. Computation readily shows, however, that both these quantities are negligible in comparison with the decrease in heat content of the dry air component.

A further point concerning the computation also arises. Isobaric cooling of the cloud from A to C and then saturated adiabatic descent from C to B are not precisely equivalent to subsidence of the cloud along the environment curve from A to B . In the former case the cloud derives energy from the environment during the descent from C to B , of amount proportional to the area A B C , whereas in the latter case when the cloud descends by small steps the corresponding area is very small, in fact, effectively zero. Calculation shows that the error introduced in this way in the computed time interval for dissipation is also negligibly small, being less than I per cent.

In computing the loss of heat of the cloud by terrestrial radiation, the initial temperatures of the top and base of the cloud have been used. Since the cloud subsides along the environment curve from A t o B , it might be considered preferable to take mean values for the descent. However, the error introduced by using the initial values is very small and thus negligible in comparison with the other uncertainties involved in the method.

The temperature scale on the tephigram is linear, and the isobars on it are very nearly straight lines. Thus it follows that the sum of the small isobaric temperature decreases postulated in the step by step process of descent along A B will be very nearly equal to the value of A?’ obtained by taking the temperature difference between A and C . However, there is more uncertainty involved in obtaining the value for Ax in a similar manner. As the tephigram shows, the variation of the saturation mixing ratio is non-linear along a n isobar and the sum of the small isobaric decreases in mixing ratio which occur during the descent of the cloud along AB will not be exactly equal to the value of Ax found by taking the difference in saturation mixing ratio between A and C. The value of Ax obtained in this way will be an underestimate, so that the computed time for dissipation will also be an underestimate. The error involved will not be large, however, amounting to about 3 or 4 per cent in the example considered in this section.

7. TIME INTERVAL FOR DISSIPATION WITH A COMBINATION OF

Although a simple vertical temperature distribution was chosen for Fig. 1 1 for the purposes of illustration, the method of computation described in the preceding section works equally well with a more complicated distribution. Two typical cases a re shown in Fig. 12 .

In the first of these, Fig. 12 (a), the lapse rate near the surface is greater than that above. The dissipation process is as follows: the cloud, represented in its initial position by point A , subsides in a series of steps from A t o B ; further radiative cooling or a

LAPSE RATES

256 E. W. HEWSON

downward-acting impulse permits the realization of its instability for downward motion at B , and it descends saturated adiabatically to D , at which level it dissipates. The time required for dissipation may be determined by calculating the time needed for the cloud to cool isobarically from A to C, by the method given in the preceding section. That computation gives the time necessary for descent from A to B ; since the descent from B to D occurs relatively rapidly, the time needed for this stage is negligible, so that the time required for dissipation may be taken a s the time for isobaric cooling from A to C.

(0) (bl

FJ(:. lZ.--c’loud dc.%int arid dissip;ifioii wi!h coxnplcn 1ap.w rn im below :, (a) two main

pliases; ( b ) three main pliasrs.

For the situation illustrated in Fig. 1 2 ( b ) two separate calculations are required. The cloud descends from A to B in the same time interval calculated for it t o cool isobarically from A to C. Between B and L) the cloud, being denser than its environment, descends rapidly along the saturated adiabat, and comes into equilibrium with the environment a t D . Thereafter, as the cloud loses heat by terrestrial radiation, it subsides along the environment curve until reaching the pressure a t which the ,$-line intersects the environment curve, a t E , where it dissipates. The time required for this final stage is the same as that for isobaric cooling from D to F , which may be calculated. Since the time for descent from B to D is small and may be neglected, the total time required for dissipation is given by the sum of the times for descent from A to B and from D to E.

The time rrquired for dissipation with any combination of lapse rates may be computed in a similar manner. The same method permits the calculation of the rate of descent of the cloud when a < P , irrespective of whether or not the cloud will dissipate.

8. FURTHER FACTORS REQUIRING CONSIDERATION

There are a number of points that come to mind regarding the foregoing treatment, and which merit discussion. For example, it may be objected that one rarely observes broken clouds descending to the earth’s surface in the manner suggested in Figs. 2 , 3, 4 and 6.

Considering Fig-s. 2 and 3 first, a computation of the rate of descent of the cloud in each case shows that it requires as much as 24 or 36 hours for the cloud to reach the surface. Only under unusual conditions would the lapse rate remain constant, o r nearly so, and


cloud forming or other cloud dissipating factors remain absent during such a lengthy period of time which extends over the whole daily cycle. Thus the cloud may descend somewhat, but in general other factors will make their influence felt before the process has gone very far.

In Fig. 4 a re indicated the conditions in which cloud is most likely to descend to the surface to become fog. However, for this to occur, the cloud would in all probability have to be initially quite low. At first glance one might assume that, when the lapse rate below the cloud is only slightly less than the saturated adiabatic lapse rate, a higher cloud might descend to the surface. However, owing to the fact that I”>>I”’ except at high temperatures (as shown by the relatively large angle between saturated adiabats and saturation mixing ratio lines on the tephigram), such a cloud under those conditions must have a very high liquid water content if it is to reach the surface. For example, the cloud shown in Fig. 11 has a liquid water content of I gm. per kgm. of dry air which is 0.9 gm. per m.3. Recent measurements of the liquid water content of various types of clouds by Houghton and Radford (1938), Lacey (1940), Diem (1942), Langmuir (1944), Tolefson (1944), and Brock (1947) indicate that even this is a relatively high value which is not often encountered in middle latitudes, except in clouds from which precipitation is occurring, and such precipitating clouds a re obviously not amenable to the analysis presented in preceding sections. A cloud with the same mean pressure as that assumed, 710 mb., and the same ,$-value, 9 gm. per kgm., would have to contain about three times as much liquid water, i .e. , about 3 gm. per kgm. of dry air, if it is t o subside to the surface within a few hours. Non-precipitating clouds with such large water contents must be very rare, except perhaps in the tropics. There, even higher liquid water contents would be required to permit middle cloud to subside to the surface.

The rapid descent to the surface of the cloud illustrated in Fig. 6 is not likely to occur, for the same reason, since an abnormally high water content for the cloud must be assumed. The more probable occurrence is shown in Fig. 5 , in which a lower water content of the cloud is presumed.

Further consideration of the water content of clouds in relation to the processes described and discussion of other points not yet raised are desirable.

(a ) Liquid W a f e r Contents of Clouds It will be apparent that the degree of usefulness of the methods

described depends on an accurate knowledge of the liquid water content of any given cloud. Although some recent measurements of this quantity have been referred to above, and earlier measurements are also available-see Kohler (1927)-0ur knowledge of the water contents of clouds is far from adequate for our present purposes. The following limitations of the available data should be kept in mind: the number of clouds whose water contents have been measured is few ; many of those studied may not be represen- tative of clouds in the free atmosphere since many of the cloud samples were taken at mountain stations ; finally, the accuracy of

258 E. W. HEWSON

some of the determinations is open to question. Wi th a sufficient number of accurate measurements available it would be possible to specify the mean value 2nd range of values of water contents of the various types of clouds for a range of pressures and temperatures. However, the data a re so few and some of them are of such doubtful accuracy that the author has not felt it worthwhile at the present time to attempt such a tabulation. I t is obvious that a full investigation of the physical properties of clouds is needed, not only for studies of cloud dissipation, but also for studies of artificially-induced precipitation, icing on aircraft, etc. Finally, there is one further possibility of estimating water contents which should be mentioned. If the water vapour content of the air which has subsequently risen to form cloud is known, and precipitation from or evaporation of the cloud has not occurred, it 7 s possible that a reasonably accurate estimate of the &value could be made. Such a n approach might well give sufficiently accurate values for cumulus humilis clouds. However, turbulent mixing may be significant during the period of growth as well as during the process of dissipation, and must be taken into account.

( b ) Turbulence Computation suggests that the turbulent transfer of heat between

cloud and environment is always negligible. The turbulent loss of water vapour by the cloud is also negligible when the lapse rate and hence the coefficient of eddy diffusivity are small.

With larger lapse rates the eddy coefficient is considerably greater and the loss of water vapour by the cloud becomes appreciable. Using a value of the eddy coefficient characteristic for highly turbulent air flow, computation shows that the loss of water vapour may be sufficiently rapid to halve the time required for dissipation as calculated by the method given in section 6. Tha t the effect of turbulence on cumulus clouds must be considerable under the highly turbulent conditions in which they form and dissipate is shown by the observation by Poulter (1938) that within certain limits the fraction of the sky covered by cumulus clouds is proportional to the initial relative humidity of the layer in which they form. The effect of the turbulent transfer of water vapour from cloud to environment is, of course, to reduce the vapour pressure near the edge of the cloud and thus maintain a vapour pressure gradient around individual cloud droplets which causes them to evaporate. Thus it is the water (or ice) component of E which decreases ; on the tephigram this decrease appears a s a progressive shifting to the ,$-line to lower saturation mixing ratio values.

The evaporation of cloud droplets occurring as a result of the removal of water vapour from the cloud by turbulent processes introduces a n additional factor. The evaporation process involves a cooling of the cloud, greatest near its edge, which augments the cooling due to terrestrial radiation, and thus tends to increase the rate of descent of the cloud, and to further reduce the time required for its complete dissipation.

(c) Solar Radiation The effect of the absorption of solar radiation by a cloud is

found without undue difficulty. According to the theoretical

THE DISSIPATION OF SCATTERED ANI) BROKEN CLOUD 259

investigation by Hewson (1g43), the absorption by a cloud of the limited vertical thickness to which the present methods apply is likely to be a t most 5 per cent of the radiation incident on the cloud; usually the percentage absorption will be less. Taking a high value for the solar radiation incident on the cloud in order to obtain an upper limit to the magnitude of the effect, we will assume that the incident solar radiation is I cal. per cm.2 per min. If 5 per cent is absorbed, a t the end of time t in minutes the heat absorbed is 0.05t cal. per cm.2 In section 6 the heat lost by terrestrial radiation in time t in the example given (shown by the first term on the left of the equation) is o.Igt cal. per cm.2 If the heat gained from the sun is included, the net loss by radiation becomes (0.15 -o.og)t= o.Iot cal. per cm.2 The effect of the solar radiation is thus to increase the time required for dissipation from 6 hours to 84 hours. Such an increase is about the maximum possible ; usually the increase is much less, perhaps amounting to half a n hour.

( d ) Absence of Other Cloud Producing or Dissipating Factors A further point is the difficulty of determining whether or not

other effects are present. Fo r example, if it is desired to forecast the behaviour of cumulus clouds in the late afternoon, the possible influence of the advection of cooler air in the lower layers should not be overlooked. If there is a horizontal temperature gradient present and cooler air flows in over a still relatively warm ground surface, cumulus clouds may continue to form, and they may not dissipate until after a longer interval of time has elapsed than would be anticipated from the consideration alone of the principles put forth above. And again, if there is a general subsidence of the air over a region, cloud will tend to dissipate as a result ; if there is ascending motion, the cloud may tend to develop rather than dissipate. These latter cases are of sufficient interest to warrant a separate treatment, which is given in the next section.

9. THE EFFECT OF WIDESPREAD VERTICAL MOTION OF THE ATMOSPHERE O N CLOUD DISSIPATION

The effect of vertical motion depends, of course, on whether there is widespread subsidence or widespread ascent of the air in question.

(u) Widespread subsidence At first sight, it might appear that the rate of descent of

scattered and broken cloud in a subsiding atmosphere is the same as that of the subsiding air in which the cloud exists, neglecting, of course, the effect of the loss of heat by the cloud by terrestrial radiation a s described earlier. However, since the environment subsides a t the dry adiabatic rate whereas the cloud subsides a t the saturated adiabatic rate, such is not the case. I t will be apparent tha t widespread subsidence results in an increased rate of dissipation of cloud of this type, but it is not so obvious that the amount of the increase varies greatly depending on whether the lapse rate of the environment is less than or greater than the saturated adiabatic lapse rate. Neglecting, for the moment then, the effect of radiational heat losses by the cloud, we will now consider these two cases in turn.

260 E. W. HEWSON

a<I”. The process involved is readily seen with the aid of a thermodynamic diagram. On the tephigram shown in Fig 13 (a ) , A $ , represents the initial vertical distribution of temperature in an air mass ; broken cloud is present, with a mean pressure of 700 mb., a mean temperature of slightly over I I O C., and a total water content in all states of 15% gm. per kgm. of dry air a s represented by the <-line. In order to clarify the discussion we will consider the behaviour of the cloud a s the air mass subsides through the relatively large unit intervals of pressure of 20 mb. Thus in the first step the air mass subsides dry-adiabatically from its initial position A,$, on the tephigram to the position A , B , , the pressure of each particle of air of the column increasing by 2 0 mb. during the process. A 5 this happens the clear air initially surrounding the cloud at C warms dry-adiabatically, the point representing it on the tephigram moving horizontally from C to D through a pressure interval of 2 0 mb. Initially the cloud subsides a t the same rate a s its environment, but since it warms not a t the dry adiabatic rate but a t the saturated adiabatic rate, it soon becomes cooler and therefore denser than its environment, and it commences to subside more rapidly than the latter, deriving energy from it. Thus by the time the whole a i r mass has subsided through a pressure interval of 2 0 mb., from position A , B , to position A , B , , and the initial environment of the cloud has descended through the same interval, from C to D, the cloud has subsided saturated-adiabatically from C to E and thence to F , or through a pressure interval of sj mb. according to the tephigram.

m W 0 D

5 I0 20 25 5 I0 pcl 20 25

w iQ1

Fib. 13-Descent and dissipation of cloud in a sub siding air mn&s ((L) the physical basis of the process,

( b ) the simplilied procedure

At F , the cloud is again in equilibrium with its environment, the temperature and thus the density of both being now the same, so that both are descending a t the same rate. In the next step the process is repeated. The air mass subsides through a further pressure interval of 2 0 mb., from A , B , to A $ , , the new environment of the cloud subsiding from F to G. As before, however, the cloud descending and warming at the saturated adiabatic rate soon becomes denser than the surrounding air and subsides more rapidly than the


air mass a s a whole, reaching equilibrium with the latter a t a lower level, at H . In the final step the air mass descends from A,B, to A,B,, the immediate environment of the cloud a t H moving from H to ] while the cloud itself subsides from H to K . However, a t K the saturation mixing ratio is equal to the f-value of the cloud, so that the latter will have evaporated completely by the time it reaches that level.

Thus the cloud descends from 700 mb. to 850 mb., or through an interval of 150 mb., while the air mass subsides by 60 mb. only during the same period of time. For clarity of illustration the steps chosen were large ones ; in the atmosphere one would anticipate that the steps actually occurring would be much smaller and more numerous than the three indicated in Fig. 13 ( a ) .

I t is unnecessary to go through the complicated process shown in Fig. 13 ( a ) in order to determine how much subsidence of the air mass is necessary to cause the cloud to dissipate completely. Fig. 13 ( b ) shows the same vertical temperature distribution and the same cloud as found initially. To obtain the required air mass subsidence, proceed down the saturated adiabat through C to its intersection with the (-line a t K . Then draw a dry adiabat through K to intersect the original curve A o B o a t L. The pressure interval between L and K , 60 mb., is the amount of subsidence required to permit complete dissipation of the cloud.

By carrying out the above simple procedure for cloud with various initial pressures, temperatures, and liquid water contents, and with various initial lapse rates below, the following facts emerge.

(i) Lapse R a t e below Cloud. For small or negative lapse rates, the air mass must subside nearly as far a s the cloud to cause its complete dissipation. The difference between the two amounts of subsidence decreases a s the lapse rate decreases, becoming very small with marked inversions. On the other hand, as the lapse rate approaches the saturated adiabatic, the difference becomes progressively greater. With lapse rates only slightly less than the saturated adiabatic, the air mass may have to subside only one- tenth as far a s the cloud to cause its complete dissipation.

Initial Pressure, Temperature, and Liquid W a t e r Content of Cloud. The lapse rates being equal, little subsidence of the air mass is necessary to cause cloutl to dissipate when its initial pressure or liquid water content is low or when its initial temperature is high ; greater subsidence is required when the initial pressure or liquid water content is high or the initial temperature is low.

The effect of subsidence on cloud dissipation in comparison with that of radiational cooling is readily evaluated. Let us determine the time required for dissipation of the cloud represented in Fig. 1 1

undcr the influence of subsidence, radiational cooling being neglected. The saturated adiabat through A (710 nib.) intersects the E-line at D (760 mb.) ; the cloud thus descends through a pressure interval of 50 mb. before dissipating completely. The cloud thus dissipates at a higher level with subsidence alone than with radiational cooling . alone, the descent required with the latter assumption being from A to B , which is through a pressure interval of 90 mb. The dry adiabat through D intersects the air mass temperature curie at E , at a pressure of about 7 5 2 mb. Thus a

(ii)

262 E. W. HEWSON

subsidence of the air mass of 8 mb. only is sufficient to cause the cloud to descend 50 mb. and to dissipate completely. If we assume that the air mass subsides at the rate of I mb. per hour, which is a small rate of subsidence, the cloud will have dissipated completely a t the end of 8 hours. This figure is comparable with the time of 6 hours calculated for dissipation under the influence of radiational cooling alone. Wi th greater rates of subsidence the time required is correspondingly less.

I t will be apparent from the foregoing that in a subsiding air mass the time required for cloud dissipation will be less and often substantially less than that computed for a horizontally moving air mass as in section 6. The attempt to combine the effect of radiational heat losses by the cloud and that of subsidence of the air mass leads to additional complexities ; the author has not succeeded in combining them in a manner which produces a con- venient method of calculating the time required for dissipation when both processes a re in operation.

When the lapse rate below but not above the cloud is greater than the saturated adiabatic rate, the behaviour of the cloud is similar to that suggested in Fig. 7. The cloud is unstable for downward-acting impulses, and will descend and dissipate so rapidly that any accompanying subsidence of the air mass is of no significance.

If the lapse rate both above and below the cloud is of this type, then the cloud will grow if given an upward impulse, and will descend rapidly and perhaps dissipate if given a downward impulse. The behaviour of the cloud is thus indeterminate. The small effects of both the subsidence of the air mass and the radiational heat losses by the cloud are to make its descent and perhaps complete dissipation slightly more probable.

+I".

( h ) Widespread Ascent The effect of widespread ascent of the air is to offset that of

radiational heat losses, so that the cloud may grow rather than dissipate. The magnitude of the influence of ascent of the air mass depends on whether the lapse rate is less than o r greater than the saturated adiabatic rate.

Let us consider an air mass which is initially nearly isothermal in the vertical, as represented by curve A $ , in Fig. 14 (a ) . The total moisture content of the cloud is shown by the t-line, and its mean pressure, a t C, is initially 850 mb. As with descending motion, we consider the ascent of the air mass in three units of 20 mb. each, and assume that the relative humidity of t he environment is initially sufficiently low that it remains unsaturated throughout the ascent. As the air mass rises, the initial environment of the cloud ascends dry adiabatically through a pressure interval of 20 mb., from C to D . At first the cloud rises at the same rate as the air mass, but since it cools at the saturated adiabatic rate it soon becomes warmer and therefore less dense than its environment, and it begins to rise more rapidly than its environment, deriving energy from the latter during the process. Thus by the time the initial environment has risen from C to D the cloud has risen from C through E to F , a t which level it is in equilibrium

a<r".


with its new environment. The process is repeated in the next step; the new environment ascends dry adiabatically through a second 2 0 mb. pressure interval from F to G, while during the same time the cloud rises along the saturated adiabat from F to H . In the final step the environment rises through a further 20 mb. interval, from H to 1, and the cloud rises from H to K , at which point the pressure is 700 mb. Thus the cloud has risen through a pressure interval of 150 mb. while the air mass has risen through an interval of only 60 mb.

In the atmosphere the steps will, of course, be smaller and more numerous than suggested by Fig. 14 (a). The density of the cloud increases during the ascent; a t K its liquid water content is more than twice as great as it was initially, a t C.

m m m 0 -

5 I0 15 20 25 5 10 15 2 0 25 T “CI T L*CI

FIG. 14.-Ascent of cloud in an ascending air mass : (a) the physical features involved; ( b ) the simplified

procedure.

As Fig. 14 ( b ) shows, the amount of ascent of the air mass required to cause a specified ascent of the cloud is readily obtained. Suppose that we wish to know through what pressure interval the air mass must rise to produce an ascent of the cloud through Ijo mb. From C, proceed along the saturated adiabat through a pressure interval of 150 mb., reaching K a t 700 mb., and thence g o dry-adiabatically from K to the intersection with the initial air mass temperature curve A,B, at L. The pressure interval between K and L, 60 mb., is the required value.

W e may also determine whether the cloud will ascend o r descend when it exists in an ascending air mass and when radiational heat losses by the cloud are taken into account. For a given cloud there is a certain rate of ascent of the air mass which permits the cloud to cool at constant pressure. That certain rate of ascent is the one which permits the cloud, as it cools by terrestria1 radiation, to remain continuously a t the temperature of its environment as the surrounding air mass rises past it. Under such circumstances there are no buoyant forces acting on the cloud. In terms of Fig. 14 ( b ) , that condition is fulfilled when the air mass rises through a pressure interval of 60 mb. during the same period of time that the cloud cools at constant pressure from C to M , M being the intersection of the isobar through C with the air mass

264 E. 1%’. HEWYON

temperature curve A , B , after the air mass has risen 60 mb., from A,B, t o A,B,.

’l‘he time required for the cloud to cool at constant pressure from C to A4 may be computed in prccisely the same manner as in section 6. For the calculation of the radiational heat loss take the cloud a t its mean temperature during the cooling, a t N , so that

take the surface temperature T , to be the same, 15 .5 ’ C. At C the temperature is 18.3’ C., and the saturation mixing ratio is 15-6 gm. per kgm. ; a t hl the corresponding values a re 12.8” C. and 10.9 gm. per kgm. Thus AT=5-5‘ C . and Ax=4.7 gm. per kgm. The cloud extends through a pressure interval of 40 nib., so that the mass in a column o f cross section I cm.2 is 41 gm. Solving the equation given in ,section 6, we find that the time required for the cloud to cool at constant pressure from C to M is 14 hours. Thus

ascends through a pressure interval of 60 nib. in a period of 14 hours, or a t the rate of 4 mb. per hour, the cloud will cool but will remain at the same pressure, i.e., at practically the same height. If the rate of ascent of the air mass is greater than this critical value, the cloud will ascend; if less, the cloud will descend. This critical value changes with the lapse rate, being greater for lapse rates near the saturated adiabatic. Fo r such lapse rates, and especially a t lower temperatures where the saturated adiabatic lapse rate is relatively large, the critical value may be more than twice a s great as the value computed above. The effect of the turbulent transfer of water vapour will be to hasten the cooling of the cloud, since the evaporation of cloud particles near the periphery will cause atltfitional cooling of this portion of the cloud.

Even although the rate of ascent of the air mass shown in Fig. 14 ( b ) may be less than the critical 4 mb. per hour, so that the cloud descends, it will not dissipate, since u<T”’. Only if Y > a > r ” is there any possibility of complete dissipation, and that event is likely only if the initial liquid water content of the cloud is small and the rate of ascent of the air mass is considerably less than the critical value.

When the lapse rate below the cloud is greater than the saturated adiabatic rate and that above is less, the cloud is unstable for downward impulses, and the tendency is for it to descend rapidly and dissipate as in Fig. 7. On the other hand, a n upward impulse might cause sonic slight upward growth of the cloud. The ascent of the air mass is gencrally so small during the time intervztl involved that it has little eft‘ect.

With saturated adiabatic lapse rates both above and below the cloud it is unstable, moving. upward for an upward impulse or downward for ;t downward irnpulsc. The bchaviour of thc cloud is thus indeterminate. The small effect of the ascent o f the air niass favours ascent and growth of the cloud; that of radiational heat losses fa\-ours descent and dissipation.

7’ T- -?’ B- --I 5.5’ C. Since the air mass is nearly isothermal, we may

a > I ” .

10. ACKNOWLEDGMENTS ’l‘he author wishes to acknowledge his indebtedness 10 a

First and foremost, he wishes to acknow- number of individuals.


ledge his debt to Professor D. Brunt, under whom he studied for several years; it was during Professor Brunt's lectures that his attention was first drawn to Sir Napier Shaw's basic work on cloud dissipation, and his interest aroused in the physical problems involved. His own students contributed to no small degree; their keenness and interest helped to bring into sharper focus the various physical aspects of the problem. Finally, he acknowledges the assistance of Dr. F. Loewe who was kind enough to draw to his attention several papers containing information on the liquid water content of clouds.

REFERENCE s Beers, N. R. 1945

Bjerknes, J . 1938 Brock. .G. W. 1947

Brunt, D. 1939

Byers, H. R. and 1948

Diem, H. 1942 Elsasser, W. M. 1942

Hewson, E. W. and 1944 R. W. Longley

Houghton, H. G. 1938 and W. H. Radford

Kiihler, H. 1927 Koschmieder, H. 1940 Lacey, J . K. 1940 Langmuir, I. 1944

R. R. Braham, Jr .

Hewson, E. W. 1943

Normand, 1916

Petterssen, S. 1939 Poulter, R . M. 1938 Shaw, 1%'. N. 1902 Tolefson, H. €3. 1944

Sir Charles

Handbook of Meteorology. New York (McGraw-

Quart. J . R . Met. SOC., London, 64, p. 325. Trans. Amer. SOC. Mech. Eng., New York, 69, p.

769.

Hill), p. 693.

Physical and Dynamical Meteorology, Cambridge,

J . Amer. Met. Soc., Lancaster, Pa., 5, p. 71.

Ann. Hydrogl., Berlin, 70, p. 142. Harv. Met. Stud., Milton, Mass., No. 6. Quart. J. R. Met. S O C . , London, 69, p. 47. Meteorology, Theoretical and Applied, John

Pap. Phys. Oceanogr. Met., Cambridge, Mass., 6,

(Univ. Press), 2nd Ed. , p. 85.

Wiley & Sons, New York, p. 82.

Nn A _. Geofys. Publ., Oslo, 5, No. 1 . Wiss. Abh. Heichamst Wetterd., Berlin, VIII, 3. Bull. Amer. Met, SOC., Milton, Mass., 21, p. 357. Gen. Elect. Rep., Schenectady, N.Y., Parts I and

Quart. J . R . Met. SOC., London, 72, p. 145.

Geofys. Publ. , Oslo, 12, No. 9. Ouart 1. R. Met. Soc.. London, 64, p. 277.

11.

Tbabid.,.$S, p. 95. Washington, N.A.C.A., Gust. Res. Proj., Bull.

No, 9, R.B., L4E17, xc-35.

the dissipation of scattered and broken cloud

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