Q. 1. R. Meteorol. SOC. (1991), 117, pp. 243-255 551 574.12: 551.558.1

Growth of droplets in cloud edge downdraughts

By PETER JONAS Pure und Applied Phyyics Department, UMIST, Munchester

(Received 2 May 1990. Revised 6 August 1990)

SUMMARY Thermodynamic analysis of aircraft observations of the downdraughts at the edges of small maritime

cumulus clouds is used to obtain estimates of the rate of entrainment of cloudy air into the downdraughts. The entrainment rates are around 10.‘ to lO-’s-’. A simple entraining parcel model is used to investigate the fate of droplets entrained at this rate into such downdraughts. It is shown that the majority of small droplets evaporate totally, resulting in a subsaturation in the downdraught of less than I%, except close to cloud top or cloud base. However, a few droplets which contain large soluble nuclei continue to grow, or undergo only a small amount of evaporation, during their descent. The limited evaporation ensures that some droplets undergoing a cycle of ascent and descent will grow even without net ascent. The largest droplets a t some levels are therefore to be found in the downdraughts although the droplet concentration and liquid water content are much lower than in the cloud at the same level. The calculated growth and the thermodynamic properties of the downdraughts are in good agreement with observations of small maritime cumulus.

1. INTRODUCTION

The growth of droplets in warm cumulus clouds a few kilometres deep has attracted considerable attention. The early observations of droplet spectra averaged over horizontal distances of tens or hundreds of metres showed that they were wider than expected on the basis of growth by condensation on a spectrum of nuclei and that the dispersion of the spectrum increased with height above cloud base (e.g. Warner 1969b). The largest droplets were larger than expected on the basis of growth by condensation alone, Observations also show that variations from the average spectrum are present at all levels in these clouds (e.g. Squires 1958a; Paluch 1986; Meischner and Bogel 1988). Although the clouds are turbulent, it was shown by Bartlett and Jonas (1972) that this did not significantly affect the results of calculations of the growth of a population of drops by condensation and therefore the observations cannot be explained by the effects of turbulent mixing within the cloud.

The observed features of the droplet spectra are now generally believed to be a consequence of the effects of entrainment of air from the environment into the clouds although doubt exists as to the detailed mechanisms. Entrainment of subsaturated air is also demonstrated by observations that the average liquid water content is significantly sub-adiabatic (Warner 1969a) and that the clouds often contain substantial regions of relatively dry subsiding air (Squires 1958b).

Recent workers (e.g. Paluch 1986; Choularton et al. 1986; Bower and Choularton 1988) have suggested that the broadening of the spectrum and the rapid growth of a small number of the droplets in clouds are results of “inhomogeneous mixing” (Baker et af. 1980). This mechanism represents the entrainment of subsaturated air from outside the cloud as a series of events, each of which results in total evaporation of some droplets, followed by mixing of the depopulated but saturated air through the cloud. This reduces the droplet concentration but introduces fresh nuclei; these may not be activated during later stages in the cloud development. The remaining drops then eiperience an increased supersaturation during their subsequent growth due to the reduced droplet concentration.

An alternative mechanism was earlier proposed by Mason and Jonas (1974) who suggested that large droplets from earlier decaying clouds, or from decaying regions in the same cloud, might become entrained into the active region of a cloud. This

243

244 P. R. JONAS

re-entrainment would increase the lifetime of some larger droplets, and hence increase their growth, while the re-entrainment of smaller droplets would broaden the spectrum. Such a process is consistent with the common observation that cumulus clouds grow as a succession of turrets rising through the less active parts of the cloud. Recently Roesner et al. (1990) have suggested that entrainment of water from less vigorous regions in a cloud could lead to the gradual increase in the vigour of a cloud and its eventual ability to penetrate through a capping inversion. Telford and Chai (1980, 1983), while criticising some aspects of this model, suggested that droplets entrained into penetrative down- draughts might be forced to undergo several cycles of descent and ascent during which growth was possible.

Although entrainment is seen as crucial to the development of cumulus and to the growth of droplets, there have been few attempts to study the structure of the entraining clouds and in particular the regions close to cloud boundaries where entrainment occurs. Thermodynamic analysis by Paluch (1979), and others, has suggested that the entrainment of air occurs at cloud top. It is impossible, however, to discriminate with certainty between cloud top and cloud edge entrainment by thermodynamic analysis alone since the cloud top passes through a range of levels during active growth and because air may be forced to descend outside the cloud before it is entrained through the edges.

Observations by Jonas (1990) show that many moderate cumulus clouds are sur- rounded by a shell of subsiding air and that deeper clouds showed a greater likelihood of having entrained air originally from levels above the top of mature clouds. It was suggested that this shell could be either a result of mixing between a cloud and the surrounding dry air leading to evaporative cooling and descent in the outer regions of the cloud, or a dynamical consequence of the ascent of the thermal leading to descent of subsaturated air initially above the top of the rising thermal. Such dynamically forced motion was observed in laboratory experiments by Woodward (1959) in which forcing of the downdraught by evaporative effects was impossible. It was also suggested by Jonas that some droplets entrained into this forced downdraught might not evaporate rapidly enough to compensate for their earlier growth in the interior of the cloud. This could explain his observations that some of the cloud edge downdraughts contained the largest droplets found at a particular level.

In this paper the observations of maritime cumulus are briefly described. Thermo- dynamic analysis is then used to estimate the rate of entrainment of cloudy air into the downdraughts at the edges of the clouds. Calculations are also presented of the expected change of the droplet spectrum in downdraughts under several assumptions concerning their forcing. The calculations are carried out for a range of conditions which encompass the range of observations and the results are shown to be consistent with observations of low concentrations of large droplets in the downdraughts together with low values of the liquid water content.

2. OBSERVATIONS

Detailed observations of cumulus structure have been reported by Jonas (1990) and only the salient features will be repeated here.

The observations were of warm maritime cumulus clouds less than 4 km deep formed under conditions with only weak wind shear. These were sampled along straight and level paths and the vertical velocity records showed that many such clouds were accompanied by narrow regions of descending air on either side. The regions of descent immediately adjacent to the cloud were typically 100 to 200m wide with descent at 1 to 3ms- ' . The descent speed was comparable with the maximum updraughts inside the clouds.

DROPLET GROWTH IN DOWNDRAUGHTS 245

Several examples of droplet spectra were presented by Jonas (1990). In some situations, especially in active clouds, the largest droplets in the downdraughts at the cloud edges were around 1 pm larger than in the cloud interior at the same level, as can be seen in Fig. 1, although the liquid water content was much lower than in the cloud. Adjacent to decaying clouds however, the droplets in the downdraughts were smaller than in the cloud while the liquid water content was also very low. Thermodynamic analysis was used to identify the origin of the air in the downdraughts. It was shown that the air originated in the cloud free regions above the observation level and often near the level of the cloud top. The example presented by Jonas (1990) showed evidence of little mixing between the downdraught and the cloudy air at lower levels. Subsequently, analysis of a number of cases has enabled the rate of entrainment of cloudy air into the downdraught to be estimated.

I

0 5 10 15 20 25

Droplet radius (p)

Figure 1. Droplet spectra observed in the downdraughts at the edges of an active cumulus cloud (symbols) and the average spectrum in the cloud interior at the same level. Redrawn from Fig. 9 of Jonas (1990).

Thermodynamic analysis is ambiguous but the observations are consistent with the hypothesis that the downdraught is composed of dry air from close to, or slightly above, the level of cloud top which has undergone variable amounts of mixing with air from within the cloud. The fact that the cloudy air is itself a mixture of air from many levels including air from below cloud base (Paluch 1979) makes it impossible to specify the level where the entrainment occurs but the observations presented in Fig. 2(a) are consistent with a small amount of entrainment of cloudy air into the downdraught although there is no evidence of entrainment in the example shown in Fig. 2(b).

In order to estimate the rate of entrainment between the downdraught and the cloud, it was assumed that the mixing could be approximated by entrainment of air from one level. Cases were examined where cloud penetrations were made at two or more levels including roughly mid-level and also close to cloud top. It was assumed that the downdraught thermodynamic properties measured at the lower of these levels were a result of mixing between air from just above cloud top with air from the cloud at the upper observation level. The time available for mixing was estimated from the height difference between the lower observation level and cloud top together with the down- draught velocity at the upper observation level. The estimates of entrainment rate for a number of clouds are shown in Table 1 where it appears that the entrainment rate is

246 P. R. JONAS

(a) d.4

3.0 -

25 -

2.0 -

1.5-

3.5

3.0 -

25 -

2.0 -

1.5-

286 287 288 209

Potmtd t v h (K)

286 287 288 289

Potmtid terrperotue (K)

Figure 2 . Total water content plotted against wet equivalent potential temperature for two cumulus observed within two hours. The solid line is the environment sounding with crosses indicating height at 50mb intervals from 950 to 700mb and solid squares indicating cloud base and top. (a) An example of an entraining downdraught around a cloud 2.1 krn deep. Open squares are individual measurements in the cloud edge downdraught at 1.3 km and squares with crosses are in-cloud points at 2.0km within 200 rn of cloud edge. The thick line indicates possible mixing between environment air at cloud top level and cloudy air to produce the observed downdraught properties. (b) A non-entraining downdraught. As (a) except that the observations are

at 1.4 and 2.1 km.

typically in the range to lo-* s-'. No account has been taken of possible entrainment between the downdraught and the surrounding, relatively quiescent, dry air. The cal- culations are for a range of conditions of cloud development which was assessed sub- jectively from the visual appearance of the cloud prior to the aircraft penetrations and from the velocity and humidity profiles across the cloud. Decaying clouds were characterised by low mean liquid water contents and in-cloud downdraughts which are comparable in magnitude to the updraughts.

DROPLET GROWTH IN DOWNDRAUGHTS 241

TABLE 1. CALCULATION OF THE RATE OF ENTRAINMENT OF CLOUDY AIR INTO THE DOWNDRAUGHT.

2.1 2.0 1.3 0.66 2.4 2.3 1.2 0.65 3.1 3.0 1.5 >10 3.3 3.2 1.5 6 3.4 3.2 1.8 0.89 3.8 3.7 1.8 0.45 3.9 3.1 1.9 2 4.1 4.0 2.1 0.84 4.2 4.0 2.1 0.1

2.3 2.6 1.8 2.7 2.1 3.1 2.4 2.9 2.8

0.0022 0.0014

0.009 0.0015 0.0007 0.0024 0.0012 0.0001

>0.01

htop = cloud top height; h,,, h,, = upper, lower observation height; fen, = fraction of downdraught air entrained from h,, to produce air at hol; V,, = downdraught velocity at hou; rmlx = entrainment rate calculated using rmlX = f,,,. Vou/(h,?,,-ho,). Cloud types M, A and T are respectively mature and active clouds and rapidly growing cloud turrets.

In order to explain the presence of droplets within the downdraughts, a simple model was developed of the evolution of the droplet spectrum following entrainment and making use of the entrainment rates estimated above. The model also predicts the thermodynamic properties of the downdraught air. The objective of this work is to identify those processes which are crucial to the formation of the large droplets rather than to describe the detailed structure of a particular cloud.

3 . MODEL DESCRIPTION

In the present calculations, a cloud edge downdraught was treated as a parcel of air which entrains air, water vapour and droplets from a cloud at a constant rate while descending due to its lack of buoyancy or due to some, unspecified, external forcing. The thermodynamic equations given by, for example, Mason and Jonas (1974), were solved to obtain the temperature and vapour mixing ratio in the downdraught while the changes in the droplet spectrum were calculated using the full droplet growth equations. Growth by condensation alone was included. While the effect of coalescence would have been to produce droplets of radius 100 pm in the cloud in concentrations of lo2 kg-' (Jonas and Mason 1974) the small number of such droplets entrained into the down- draught region would not significantly affect the changes in the population of the small droplets by condensation or evaporation.

The downdraught was assumed to be adjacent to, and to entrain air from, a moderate cumulus cloud. The cloud properties were calculated using the model of Mason and Jonas (1974) with a typical maritime condensation nucleus spectrum, modified to give a droplet concentration of around 100 mg-', and the properties at 100 m height intervals were tabulated. A linear interpolation was used for calculating the properties of air entrained into the downdraught. As Roesner et a/. (1990) point out, a cloud which is formed by a succession of thermals rising through the remnants of an earlier cloud can gradually erode an inversion so that a model of such a developing cloud does not give a well defined cloud top height. In accordance with the aim of the present work the cloud model was only used to provide a consistent set of cloud properties, in particular the updraught, supersaturation and droplet spectrum. The Mason and Jonas (1974) model was therefore run with two successive thermals to provide the model cloud properties; with the prescribed environmental conditions this gave a cloud similar in vigour to those

248 P. R. JONAS

observed. It should be noted that during the cloud development, lateral entrainment was assumed. This is inconsistent with the existence of a shell of subsiding air surrounding the cloud, which implies that much of the air entrained into the cloud will have originated from the level of the cloud top. However, in tests where the entrained air was assumed to have descended from 2.5 km above cloud base there was little significant difference in the cloud development,

In some calculations the vertical velocity of the downdraught was held constant, to simulate a downdraught forced by the motion of the cloud. In other calculations the velocity was determined by the buoyancy of the descending air with respect to the quiescent air outside the cloud. This is a simple representation of those downdraughts where the forcing is small. A third set of calculations in which the buoyancy was determined with respect to the cloud and where the initial downward velocity was small represents tht: penetrative downdraughts often observed in cumulus. Mason and Jonas (1982) showed how such penetrative downdraught regions might be forced to ascend after having reached the bottom of their descent. In the present work the calculations were terminated at the base of the descent since the objective was to study behaviour in the downdraught rather than the subsequent fate of the droplets. A comparison between the different cases enabled the behaviour in the different downdraughts to be identified.

It should be emphasised that the model cannot give a complete description of the microphysical and dynamical structure of a downdraught, and therefore cannot be used to reproduce observations. In particular, there is no dynamical or microphysical feedback from the downdraught to the developing cloud. As noted above, such feedback will alter the origin of the air entrained into the cloud, while re-entrainment of large droplets from the downdraught may influence the development of the cloud droplet spectrum. While the present model is adequate for identifying relevant microphysical processes, it is not suitable for studying the detailed dynamics of the cloud and downdraught regions.

The downdraught in all cases was assumed initially to have the thermodynamic properties of the dry air at the level of the cloud top; these were identical with those used in the calculation of the growing cloud. In particular, the initial relative humidity in the downdraught was 85%. The downdraught initially contained no liquid water. Although the air contained a similar nucleus population to that entering the cloud at its base, this is not critical to the development of the droplet spectrum since the downdraught remains subsaturated.

The calculations of the deve!opment of the droplet spectrum in the downdraught and the vertical variation of the thermodynamic properties were carried out for a number of assumed entrainment rates based on the values determined from the field observations. A single set of cloud properties was used which was a reasonable approximation to the cloud properties observed on many occasions. These were for a cloud about 2.8 km deep with a cloud base at 900mb and 5 "C. The temperature in the cloud decreased linearly with height from 5.6 "C at the cloud base to - 16 "C at cloud top. The liquid water content increased steadily to a maximum of 1.1 g kg-' at cloud top (see Figure 7 ) . The droplet concentration in the upper regions of the cloud was around 100mg-' which agrees well with those reported by Jonas (1990).

4. RESULTS

Since the main feature in the observations is the presence of large droplets in the downdraughts, the calculated droplet spectra were processed to give the variation of the largest droplets as a function of height. Results for two assumed entrainment rates, representative of those observed, are shown in Fig. 3. These were obtained for a fixed

DROPLET GROWTH IN DOWNDRAUGHTS 249

I I sb 0; 1.0 1(5 2.0 2k 3.0

Height above doud bose (h)

Figure 3. Radius of the largest droplets in the model cloud (solid line) and in a downdraught at cloud edge with a constant speed of 2ms-I. The spectra in the downdraught were calculated assuming entrainment rates

of ~ x ~ O - ~ S - ' ( x ) and lO-'s-' (+).

downdraught speed of 2 m s-l, again representative of the observations. The radius of the largest droplets in the model cloud is also shown. At the largest entrainment rate, droplets 2pm larger than in the cloud are predicted to be found in the downdraught at some levels. With an entrainment rate of 10-'s-' the downdraught remained sub- saturated, indeed the relative humidity decreased from its initial value of 85%, and no droplets remained in the downdraught. The critical entrainment rate below which the downdraught humidity decreased varied slightly with temperature and velocity but was in the range 5 X

Since the entrainment is continuous, the largest droplets in the downdraught cannot be smaller than largest droplets in the cloud at the same level, unless evaporation is instantaneous. Near the top of the cloud the downdraught is significantly subsaturated due to the limited entrainment of water into it, as can be seen in Fig. 4. At these levels the maximum radius is the same in the downdraught as in the cloud at the same level. However, as the downdraught reaches lower levels the subsaturation decreases due to the entrainment and evaporation of droplets. The evaporation of some of the droplets entrained into the downdraught at these levels is however sufficiently slow that droplets descending in the downdraught to a lower level may be larger than those in the cloud at the same level, as suggested by Jonas (1990).

The calculated concentration of the large droplets is, however, often very low, less than 103kg-'. Droplets in concentrations less than about l0'kg-l are unlikely to be detected in a passage through a 100m wide downdraught because of the small cross sectional area of the volume sampled by high frequency optical probes. Figure 5 shows the calculated concentration of droplets larger than the maximum radius in the cloud at the same level as a function of height. It can be seen that observable concentrations of large droplets are only expected over a limited range of heights and for entrainment rates greater than 5 x lop3 s-'. Detailed spectra, for example Fig. 6, also show that for sufficiently large entrainment rates, greater than 5 x s-l, the concentration of large drops may be high enough for them to be detected. In the example shown the number of droplets in the downdraught, larger than those in the cloud, exceeds lo4 kg-' between

to 3 X lo-' s-'.

250 P. R. JONAS

8.0 0.5 1.0 1.5 20 25 3.0

Height above doud base (b)

Figure 4. Variation with height above cloud base of the subsaturation in downdraughts with constant speed 2ms-I for entrainment rates of 5 x lo-’ ( x ) and lO-*s I (+).

b.0 0.5 1.0 1.5 2.0 2.5 3.0

Height above doud bose (h)

Figure 5 . Variation with height above cloud base of the number of droplets in the entraining downdraught larger than any of those in the cloud at the same level. Calculations are with entrainment rates of 5 X 1W3 ( X )

and 10 z b - l (+).

heights of 1.8 and 2.2km. The calculated difference between the radius in the down- draught and in the cloud has a maximum value of 3pm at 1.1 km above cloud base.

At lower levels the evaporation of droplets entrained into the downdraught increases as the subsaturation again increases because of the reduced rate of liquid entrainment from low levels in the cloud. The increase in evaporation rate results in the limited life of all droplets in the downdraught which consequently, at low levels, again contains no droplets larger than in the cloud at the same height (Fig. 3).

The results of the calculations for forced downdraughts therefore reproduce several of the features of the observed spectra in downdraughts at cloud edge. Low concentrations of droplets up to 3pm larger than those in the adjacent cloud may be found in the downdraughts over a limited range of heights provided that the entrainment into the

DROPLET GROWTH IN DOWNDRAUGHTS

2c 25 1

'0 5 10 15 20 25

Droplet m d k (p)

Figure 6 . Calculated droplet spectra 1.8km above cloud base for a downdraught of 2 m s ~ ' . Assumed entrainment rates are Sx lo-' (x) and lO-*s-l (+) while the solid curve is the in-cloud spectrum. Respective values of the droplet concentration and liquid water mixing ratio are 29, 49 and 101 mg-' and 0.54, 0.77 and

0.96g kg-I.

X

1 .o I

Height above doud base (h)

Figure 7. As Fig. 3 except showing the variation of the liquid water mixing ratio with height above cloud base in the cloud and in the entraining downdraughts.

downdraught is sufficiently rapid. Despite the presence of large droplets in the down- draughts, the calculated liquid water content is smaller than in the cloud due to the evaporation of small droplets, as can be seen in Fig. 7. The calculated liquid water content is in reasonable agreement with the observations of Jonas (1990), suggesting that, despite the simplicity of the model and the assumptions made in deriving values for the entrainment rates, the important mechanisms have been included. Although results are presented here only for one downdraught speed, they are supported by other calculations for constant speeds in the range 1.0 to 3.5111s-'. In general, increasing the downdraught speed increases the size difference between the downdraught and the cloud but reduces the concentration of large droplets.

252 P. R. JONAS

Calculations were made in which changes in the downdraught velocity were deter- mined by its buoyancy with respect to the cloud-free air although the initial speed was 2 m s-’. The results (not shown) are very similar to those with a prescribed downdraught velocity. In these cases the downdraught velocity was generally increased by the evap- orative cooling but the change in the size of the largest drops in the downdraught at any level was less than 0.5 pm. It appears therefore that provided the downdraught is initially driven by forcing due to the ascent of the cloud, giving large downdraughts at the cloud top, the subsequent changes in velocity do not significantly affect the behaviour of drops entrained into the downdraught.

However, when the calculations were repeated with the buoyancy determined with respect to the cloud and a small value for the initial downdraught speed, a rough approximation to the conditions under which penetrative downdraughts are initiated and sustained, very different results were obtained. The profiles of the downdraught velocity were similar to those obtained by Jonas and Mason (1982) and showed that downdraughts initiated by evaporative cooling at cloud top were capable of penetrating deeply even into active clouds. The evaporation of entrained droplets was almost complete due to the time available for evaporation when compared with the cloud edge downdraughts. This results in there being no large droplets in the penetrative downdraughts.

This hypothesis is supported by calculations in which although the buoyancy was calculated with respect to the cloud, the initial velocity was 2 m s-’. This is the same as that used for the cloud edge downdraught calculations but is unrealistically high for the initial downdraught in a parcel of air entrained at cloud top; such air is essentially at rest and achieves its downward velocity only as a result of evaporative cooling. In this artificial case, the higher speed resulted in less evaporation. The size of the largest droplets obtained using the high initial speed is shown in Fig. 8. Near cloud top the behaviour is very similar to that near the top of the cloud edge downdraught. At lower levels, where the downdraught velocity is determined more by buoyancy than by the initial conditions, the droplet evaporation more closely resembles that in the penetrative downdraught and large drops are not observed.

Figure 8. As Fig. 3 except that although the downdraught has an initial speed of 2ms-’ , changes in speed are subsequently determined in response to buoyancy with respect to the cloud.

DROPLET GROWTH IN DOWNDRAUGHTS 253

-10

-11

-12

-13-

5. DISCUSSION

The calculations described above suggest that it is possible for some droplets entrained, together with saturated air, from a cloud into a downdraught, to evaporate sufficiently slowly that on reaching a lower level they are still larger than the largest drops at that level in the cloud. Whether or not this occurs depends on the balance between the rate of entrainment of liquid water and the evaporation as the air becomes subsaturated due to the descent. The conditions under which such growth is possible are now considered in detail.

A drop containing a soluble nucleus may evaporate only slowly, or even continue to grow in subsaturated air provided it is smaller than the equilibrium radius given by the Kohler curve (Mason 1957). In order that droplets may achieve net growth during a cycle of ascent and descent, as for example droplets growing in an active cloud and then entrained into a downdraught, it is necessary that the growth rate, with respect to height, in the updraught exceeds the magnitude of the evaporation rate in the downdraught. The net growth depends on the effective supersaturation, which is the average supersaturation weighted by the reciprocal of the velocity. Typical conditions in the growing cloud are a supersaturation of 0.1-0.2% in an updraught of 0.5-2 m s-' compared with asubsaturation of 0.4% in a downdraught of 2 m s-' when the entrainment rate is s-'. This gives an effective supersaturation for drops cycling between 2.5 and 3.5 km above cloud base of -0.015%. In a similar downdraught where the entrainment rate is a factor of two smaller, the subsaturation is typically 0.6% and the effective supersaturation is -0.09%. Figure 9 shows the critical nucleus mass (sodium chloride nuclei are assumed) which, if exceeded in droplets of the radius shown, will result in net growth in an ascent-descent cycle assuming the typical effective supersaturations indicated above. The critical mass is calculated for values of temperature and pressure typical of those in the small cumulus but is insensitive to the exact values.

It can be seen from Fig. 9 that drops of radius around 20pm will grow in a cycle of ascent and descent under conditions representative of those calculated for an entrainment

-

-

-

I -0.09

I I I I 5 10 15 20 25

-1 41,

D r e t radius (p) Figure 9. Calculated critical mass of a sodium chloride nucleus as a function of droplet radius. If a droplet has a nucleus larger than the critical mass, net growth is possible in an ascent-descent cycle. The calculations are for effective supersaturations of -0.09 and -0.015% as described in the text to represent typical cycles

with entrainment into the downdraught at, respectively, 5x and lO-'s-'.

254 P. R. JONAS

rate of 10-*s-' provided they contain a nucleus larger than about 1O-"g. In contrast, drops of this size will only grow under the lower entrainment rate conditions if they contain nuclei larger than 8 x lo-" g. In the numerical calculations, these are present at a concentration which is an order of magnitude smaller than that of nuclei larger than lo-" g. This explains why large drops are predicted to occur at lower concentrations as the entrainment rate is decreased.

In maritime clouds, nuclei larger than lo-'' g are often present in concentrations of around 3 x lo3 kg-' (Mason 19.57). The majority of droplets in these medium cumulus are smaller than 1.5 pm with nuclei smaller than 10-" g so that these will evaporate in a downdraught even if entrainment into the downdraught is high. Much of the cloud water content is in the small droplets and their evaporation into the downdraught may be sufficient to prevent large subsaturations arising and permit growth of the droplets on the small number of larger nuclei, if the entrainment rate is high enough. Although the number of large droplets observed will depend on the conditions in the cloud and in the downdraught, it is expected that the concentration of large droplets will exceed 3 x 10'kg-l if the entrainment rate into the downdraught is in excess of 5 x 10-3s-'. It appears therefore that the condensation nucleus spectrum, together with the rate of entrainment into the downdraught which prevents the subsaturation becoming too large, plays a crucial role in the existence of large droplets in the downdraught at cloud edge.

In the case of penetrative downdraughts, the initial velocity is reduced and the critical mass is greatly increased, reducing the number of droplets which can grow in the ascent-descent cycle. It is possible that in some situations droplets may be found in the penetrative downdraughts which are larger than in the cloud at the same level but these have not, apparently, been observed.

6. CONCLUSIONS

The results presented here show that mixing between a cloud and the downdraught which surrounds it occurs with a typical rate of to 10-2s-'. A small number of droplets entrained into the downdraught undergo growth in an ascent-descent cycle if they contain a sufficiently large nucleus and if the entrainment is sufficiently rapid to maintain only a small subsaturation. This may lead to observable concentrations of droplets in the downdraught which are 1 to 2pm larger than in the adjacent cloud. This calculated growth is comparable with the observations of Jonas (1990) in small maritime cumulus clouds. Such growth is less likely to occur in penetrative downdraughts where the initial velocity is small or in rapidly growing cloud turrets where there is little entrainment of cloudy air into the downdraught. It remains to be seen whether these findings are specific to maritime clouds since they depend on the presence of a small number of large soluble nuclei. There appear to be no reports of similar observations in continental cumulus clouds despite the large number of observations of these clouds, for example during CCOPE.

Large droplets may be re-entrained from the downdraught into the body of the cloud, broadening the spectrum. Whether this is a significant factor in the rapid growth of a small number of drops cannot be determined without detailed observations of the mixing between a cloud and the downdraught and of the airflow within and around the cloud. This problem may also be clarified by detailed numerical modelling of the entrainment at the boundaries of clouds and of the flow around a growing cloud.

The persistence of droplets within the downdraught complicates estimation of the vertical fluxes of water and latent heat within a cloud and its surroundings. The cloud can be envisaged to consist of four regions; the main rising body of the cloud, penetrative

DROPLET GROWTH IN DOWNDRAUGHTS 255

downdraught regions which are subsaturated and contain no liquid water, slightly sub- saturated cloud edge domdraughts which contain droplets and the slowly subsiding, subsaturated, environment. Parametrization of the average fluxes due to an ensemble of cumulus must take account of the fluxes in each region. The present work only provides limited information since turbulent fluxes were not measured. However, in a typical example, the flux of liquid water in the cloud edge downdraught was about 10% of that in the cloud interior since the low water content was compensated by the large area of the downdraught region and the high velocity. Experiments are presently being carried out to clarify the contribution of the various regions to the cloud fluxes and these will be published in due course.

Baker, M. B., Corbin, R. G. and Latham, J.

Bartlett, J . T. and Jonas, P. R.

Bower, K. N. and Choularton, T. W.

Choularton, T. W., Consterdine, I . E. , Gardiner, B. A, , Gay, M. J., Hill, M. K., Latham, J . and Stromberg, I. M.

Jonas, P. R.

Jonas, P. R. and Mason, B. J .

Mason, B. J. Mason, B. J. and Jonas, P. R.

Meischner, P. and Bogel, W.

Paluch, I . R.

Roesner, S., Flossmann, A. I . and Pruppacher, H. R.

Squires, P.

Telford, J . W. and Chai, S. K.

Warner, J

Woodward. B

1980

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1988

1986

1990

1974

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1957 1974

1988

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1985a

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1969a

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