Clouds with turbulence; the role of entrainment

ATMOSPHERIC RESEARCH ELSEVIER

AtmosphericResearch 40 (1996) 261-282

Clouds with turbulence; the role of entrainment J.W. Telford Atmospheric Sciences Center, Desert Research Institute, Reno, NV 89506, USA

Accepted 10 March 1995

Abstract Cloud physics has grown up with concentrated efforts focused on compartmentalized topics in the subject, where researchers have studied specific problems with little regard to other areas. The developing understanding of turbulent entrainment and the understanding that turbulence is best described in the atmosphere by circulating self-contained entities, which are often buoyant and carry fluid from one level to another, has led to a unifying picture of clouds wherein all clouds and convective processes can be seen as one phenomenon in which various conditions decide the final form. The microphysical processes are described and the controlling effects of entity type entrainment mixing are shown to provide an explanation for many of the observations. The inadequacy of most computer calculations in providing viable models is pointed out. The need for self-consistent conceptual structures as a basis for adequate models is stressed. Improved instruments for remote sensing and aircraft measurements, along with the present conceptual developments and computational capabilities, suggest that adequate models of clouds may be soon developed.

1. Introduction

The progression of research in cloud physics has shown that different aspects of such studies - - the cloud condensation nuclei, growth of cloud drops by coalescence, the development of ice in clouds, thunderstorm electrification and the dynamical explanation of how air parcels move from one place to another - - have all tended to proceed in isolation from each other. The original basic questions of how a cloud develops and then forms precipitation have been lost in the pursuit of details which are largely of the researchers' own creation. Thus, for example, supersaturation in the air between the cloud drops is often offered as the key to the explanation of droplet growth because it originally demanded so much effort, whereas it is only an intermediate derived variable. Once the drops are formed the pressure change in the rising air determines the amount 0169-8095/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0169-8095(95)00038-0

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of water released, and the drop size is determined from the number of drops absorbing the water. The studies of turbulent processes in clouds have now shown that many of these concerns are side issues, since turbulent effects provide qualitative explanations for most of the questions about microphysics posed thirty years ago without calling on the extraordinary details which so often remain the subject of intense and continuing study. This is particularly true of numerical modeling. Examples of new results coming out of such work seem to be singularly concerned with problems of their own making, and unrelated to the real world; the problems of "turbulent closure" come to mind. Modeling of marine stratus clouds depends largely on assertions chosen for their ease of application in numerical and conceptual development, and which appeal uncritically to earlier use for justification. The process seems to proceed in a glow of virtual reality where the proponents gather together to fend off any logical analysis based on the data (e.g., Chen and Cotton, 1987; see Telford, 1992) and to contribute to large observational efforts, plans which cleverly exclude any crucial tests, such as "Does the assumed radiation from the cloud tops actually cool them ?" The basis for this assertion will be discussed below. It is very unfortunate and deleterious to the subject that in some quarters "cloud dynamics" has come to imply computer programs rather than the relevant observations. If computer programs are to be developed which are of some use in addressing practical problems of interest to society, such as global change estimation, the computer codes must be based on concepts which are vigorously tested until they represent the real world and nothing else. This paper presents the development of cloud physics as the author has seen and understood it. This development has necessarily followed the progress of our understanding of air motion in clouds and in their surroundings. The discussion shows how the study of turbulence has produced a unified explanation for most of the questions posed earlier during the development of the subject. These studies show promise of continuing to provide qualitative, and eventually quantitative, explanations of cloud formation, precipitation development and cloud lifetimes and dissipation.

2. The problems of cloud physics It is clear that to produce a cloud a moist parcel of air must rise until the falling pressure cools it to saturation. Then drops form and, as the air continues to rise, the drops grow until stable air is reached or the updraft entrains so much dry air that all the drops evaporate and growth stops. After forty years of intensive study it is not yet known how to calculate updraft velocities to match the observations, or how long the cloud top entrainment must continue to dilute the cloud so as to evaporate all the drops and create the downshear side of the cloud, or how long the cloud will last. There is as yet no trustworthy procedure for determining the lifetime of a small cumulus cloud, although calculations abound and new explanations are being considered. Here the turbulence concepts play a role which current modeling approaches strenuously attempt to ignore, possibly because computer advocates are confused by the measurements and feel that the efforts they put into the computations deserve recognition.

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This discussion refers mostly to fair weather cumulus clouds. These were the clouds chosen for the first studies because they are very visible, invite aircraft penetration, occur frequently, have a finite life cycle and easily allow comparison of temperature, vertical velocity, etc., measured in the cloud relative to that measured in the surrounding air.

The first aspect observed regarding such clouds was the liquid water content which was measured at different heights in the cloud. The liquid water mixing ratio was found to be much less than expected for the thermodynamic water release in an undiluted parcel rising from cloud base. There are nearly undiluted parcels near cloud base but, near cloud top, the liquid water mixing ratio diminishes to about 20% of that to be expected when an undiluted parcel rises from the base to the same level (Warner, 1955; Warner and Squires, 1958). Across the cloud perpendicular to the shear direction the liquid water mixing ratio is roughly constant and there is no difference between the edges and the center (Warner, 1955), showing conclusively that the subsaturated air is not entering the cloud and mixing across it from the sides. The shear is defined here as between subcloud flow and the mid cloud levels; the upshear direction is upwind when the wind increases with height and there is no change in direction. This observed distribution of liquid water is inconsistent with a typical model in which cloudy air rises in the middle and descends at the edges, being diluted by entraining subsaturated air through its sides. The data are also inconsistent with any flow into the center of the base, as is sometimes suggested both by the computer models and buoyant blobs in water tanks. Since the cloud is observed to be more diluted near its top, it is clear that the subsaturated air is mixed in down from the top surface and progressively penetrates deeper and deeper. Additional observations clarify what happens whenever such a cloud forms. First the liquid water mixing ratio is higher on the upshear growing side and decreases to about half this value on reaching the downshear edge (Mossop, 1985; Rogers et al., 1985). Thus, the upshear edge is less diluted since it is there that the new growth first forms. As the cloudy columns are further surrounded in front (upshear) by new cloud, the new upshear edges remain the least diluted. As the cloud columns age they entrain subsaturated air from above and pass through the center of the cloud until they are diluted and cooled to the point where the column subsides and totally evaporates, so establishing the downshear edge. This description explains earlier observations that the cloudy outline moves through the air in the upwind direction (Malkus, 1949). It was observed that there is very little motion relative to the cloud in the clear subsaturated air just beyond the cloud boundaries at mid level (Telford and Wagner, 1974), so the air is not being pushed aside to allow the cloud to pass, as would occur around a rigid shell like a dirigible. The cloud outline moves in the embedding air mass by the creation of new cloud on the upshear side by vertical growth, and the evaporation of the older, diluted cloud columns on the downshear side, which forms the other edge that follows along. There is no effective vertical motion in the surrounding clear air because it follows the wet adiabat in its sounding, which is very stable for parcels not containing cloud water. In this original observation the conclusion was strengthened by the fact that the shear direction and the cloud movement through the surrounding air were both across

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wind, which makes explanations suggesting the wind is blowing around the cloud rather implausible. The compensating downward flow probably follows a slight divergence all around the growing cloud with a very slow subsidence over a large area. Other observations, such as that of the large area of disturbed turbulent air surrounding the downshear side of such clouds, first reported by Ackerman (1958), confirm that the attached region of evaporated former cloud is often about as large as the cloud itself. It remains in place after its cloudy content has evaporated, following the diluting cycle in which the cloudy columns cross the cloud from where they began on the upshear edge. Detailed measurements (Telford and Wagner, 1980) show that the area beyond the downshear edge remains disturbed in all three components of velocity, temperature and moisture. The upshear edge is often observed to be extremely sharp, with less than a meter in the transition from undisturbed subsaturated air ahead to that within the cloud itself. Clouds frequently grow in the modified air remaining after previous clouds have evaporated, as thermodynamic analysis shows (Telford and Chai, 1993c). Thus there are probably occasions when the air in front of the cloud differs from that some distance away although this air has not ever been part of the same cloud, showing that some care is needed in interpreting such measurements. The dynamics of small cumulus clouds is well established by observations, indicating that the role being played by turbulence entities totally dominates any other circulating flow except for the feeding updraft which creates the new supply of cloud. Circulation can only be modeled correctly to give useful results when the up and down internal motion of the turbules is included. None of the current models give a useful description of real clouds, that I can recall, and it is clear that cloud dynamics is not a computer exercise, as yet, despite books claiming it is. The cloud scale overturning coming out of the computers is largely fictitious. The argument that a model is useful because it represents some aspect of a problem which is not understood, appears to me to be particularly pernicious. If all known aspects are misrepresented it is likely that all are false. The inadequacy of cloud models was discussed by Telford (1975a), and the same inadequacies still apply. For example the role of turbulence in carrying drier air from the cloud top downwards deep through the cloud clearly cannot be simulated by gradient diffusion since, with the same turbulence, the equally dry air from the vertical sides has negligible effect horizontally across shear. Similady, the water distribution observed (increasing dilution with height and towards the downshear side, but no increase in the dilution at the edges or in the middle) cannot be reproduced by representing a cloud as a single large vortex ring, which many numerical models produce. Furthermore, in the water tank the surroundings have neutral stability, and no shear or latent heat release, and cannot reproduce the large Reynold's Numbers needed to fully represent the turbulent motion found in the atmosphere. The motion in water tank experiments, which produces such vortex rings, cannot provide realistic conditions and so such experiments demonstrate little directly about real clouds. The vortex ring itself does not simulate a typical cloud. A cloud appears to encompass many small vortex rings carrying drier air down from on top. To a large extent observations of marine stratus clouds have provided most of the information on the nature of the turbulent structures active in clouds. There the lower

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turbulent intensity allows the organization to be more clearly recognized. Here, again, computer calculations based on the general flow equations have not provided much similarity to observations. It is wise to distinguish between models which are conceptual structures crafted to explain facts, and calculations whose purpose seems to be to include only simple, numerically amenable assumptions or idealizations and to remain unhampered by all but the minimum contact with the real world. The earlier location of a parcel in time and space can often be deduced as a result of changes in the cloud droplet spectra, whereas without cloud there is little that can be said about the history of a parcel. The droplet spectra and liquid water mixing ratio provide the keys to interpreting the transport resulting from the descending turbules which dilute all clouds. The resulting observed cloud droplet spectra (Telford and Wagner, 1981) also provides an adequate explanation for a number of conclusions about cloud condensation nuclei, the role of giant nuclei, and the condensation process, which are used to explain the onset of coalescence.

3. Cloud microphysics Twenty years ago the principal problems in cloud physics were associated with the formation of warm rain. Ice forming processes posed questions which were less clearly focused because of the fascination with the crystal shapes and the many intriguing questions which could be asked about this mysterious phenomenon. The crucial effects of ice multiplication are now well described and although the explanation is still far from totally clear, the role of turbulence may well be the key to understanding the ice development process (Hobbs and Rangno, 1985; Telford et al., 1987), as well as other aspects of clouds. In any case, attempts to explain the microphysical development of ice in clouds without the turbulent elements descending from cloud tops and the returning vertical counterflows seem unlikely to ever be successful. Such vertical circulation is essential to the explanation of the final cloud evaporation and other observations, as already discussed. The problems associated with warm rain formation and coalescence growth were seen to be a result of the following: (1) Coalescence depends on falling drops actually coming into contact with one another; but the collection efficiency is almost zero for collecting drops with diameters less than 36 /xm (Hocking, 1959). (2) Condensation theory and laboratory experiments produce droplet spectra in which the drops come closer and closer together in diameter as more water is released and the droplets grow larger (Howell, 1949; Squires, 1952a,b). (3) Typical continental cloud condensation nuclei concentrations range from 200 to 2000 drops/rag. Much confusion arises because the usual measure of drop concentration is drops/cc, but this concentration changes as the pressure and volume of the parcels change without the drop numbers changing. Commonly a cloud has about 1 g / k g of liquid water. With such drop numbers the drop's diameters lie between 10 and 22 /~m, and so never become large enough to exceed the Hocking limit. Hence the collection efficiency remains effectively zero. The narrow theoretical droplet size spectrum also

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inhibits coalescence because, without a wide spread in sizes, the difference in relative fall speeds needed for coalescing collisions does not occur often enough. Actual cloud droplet spectra are extremely broad and bigger drops appear than could ever be accounted for in this way (Telford et al., 1984; Rogers et al., 1985). Warm rain is widely observed (Bowen, 1950; Battan, 1963), so the following postulates were pursued in order to find an explanation. (a) There are giant nuclei in the air and these grow to much larger sizes than the other drops by condensation, which allows them to continue to grow by coalescence (Blanchard and Woodcock, 1957; Woodcock, 1950, 1952). (b) The condensation process involves the water molecules bouncing back from the water drop surface, and the air molecules do not immediately acquire the temperature of the drop on contact as they bounce back. Thus there is a jump in both water vapor pressure and temperature at the drop surface which changes the growth process. These effects are described in terms of "accommodation" coefficients. (c) The drops acquire an electric charge which increases the collection rate so coalescence becomes effective. (d) The shear in the turbulence pushes drops together so that many more come into contact and coalesce. An alternative idea is that micro-vortex circulations concentrate the drops in small regions, and so coalescence gets a rapid start to form the few larger drops needed. (e) The stochastics of drop encounters was shown to result in the formation of a very few larger droplets which could continue growth to raindrop sizes in much less than the average time (Telford, 1955), but this concept could not overcome the lack of coalescence between the small drop sizes resulting from the condensation calculation. An additional aspect of the problem was that cloud condensation nuclei observed over the continents were found in much greater numerical concentrations than over the sea. This became confused with the fact that, over North America, most rain forms in clouds where temperatures fall below freezing and probably involve the ice process, implying that coalescence rain is too rare to be important. The explanation of all these concerns seems to directly stem from what is now known of the turbulent motion in clouds. At present no other explanations are adequate, and most other ideas involve speculation where definitive new questions cannot be formulated or answered. The result of the turbulent recycling up to and down from cloud top is seen to both spread the droplet spectra and also generate larger drops (Telford and Chai, 1980; Telford et al., 1984), so coalescence will always start if entrainment continues long enough, regardless of the cloud condensation nuclei spectra or concentration. Continental clouds however tend to entrain faster because most of them originate over a wanner surface than the sea. Hence they develop more active entrainment because the driving force is increased due to a larger decrease in wet bulb potential temperature at their tops, for a similar airmass, because these clouds are warmer. Thus they have shorter lifetimes, if they do not grow to thunderstorm size, than marine cumulus clouds and hence sustain fewer vertical cycles which enable growth of big drops. Being warmer they also tend to rise higher and so become colder and form ice earlier in their lives (Telford et al., 1987) which leads to precipitation and evaporation before liquid drop coalescence processes develop. The effects of heating over land can

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be confirmed by satellite observations of lightning, which show few occurrences over the oceans and high concentrations over the continents, with a drift towards the East due to prevailing winds. There are few lightning observations near the West Coast of the USA but storms are seen out to sea from the East Coast.

4. Some analytical comments All these ideas for the enhancement of drop growth without specific consideration of turbulence fell short of providing an explanation for the observed data. Giant nuclei no doubt occur, but there is little evidence that they are always present in the numbers needed to provide one per raindrop. The accommodation coefficients make some difference, but have not been shown to produce the large spread in droplet diameters observed, or the large drops needed for coalescence. Droplets become charged because of the random distribution of ionic charges in the air but the estimated charge is less than about 50 electrons (Gunn, 1955). Measurements have shown that this small charge has a negligible effect on coalescenge (Telford et al., 1955; Telford and Thorndike, 1961). The small scale turbulence (Saffman and Turner, 1956) shear was never a serious contender because the turbulent intensity required was vastly in excess of anything observed or possible in terms of the buoyant energy released in cloud. The micro-vortex effect has not been worked out to my knowledge. As mentioned, the stochastics of coalescence was interesting but the collection efficiencies for the drop sizes available were still too small for the process to get started. All of these attempts to find an explanation for coalescence rain formation carefully avoided any realistic attempts to represent the complexities of the turbulent dynamics in the cloud. Peculiar approximations were pursued, such as assuming that subsaturated exterior air mixes instantaneously across the whole cloud at each height (Mason and Chien, 1962), and assuming that the cloud is a spherical biob with no difference in pressure between top and bottom, so mixing could be assumed to ensure that there was no difference in droplet spectra between the middle of the cloud, where they were calculated, and the top and the bottom. Nor, in this simulation, was there any change in the liquid water mixing ratio from one height to another (Mason and Jonas, 1974; Jonas and Mason, 1982; see Telford and Chai, 1983). Smooth monotonic updrafts remain a feature of many models, such as electric charge separation theories, and recently four review papers represented the current state of cloud physics as an extension of the investigations just described (in the Squires Memorial volume of JAM, Beard and Ochs, 1993; Blyth, 1993; Hudson, 1993; Saunders, 1993) with little mention of how entrainment affects cloud microphysics or the role of turbulent entities. While it is clear that unifying approximations are a part of all physical theories, such hypothetical structures need to be tested in the real world. The strength of a conjecture is not that it allows some particular approach to be worked out in the arithmetic but that, when it is worked out, it gives a realistic and useful result. The observed droplet spectra in cumulus clouds have long been known to be extremely broad with a few big drops exceeding 30 /zm in diameter and this is now explained as a result of turbulence as manifest in Entity Type Entrainment Mixing (ETEM, Telford and Chai, 1980; Telford

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and Wagner, 1981), but this has received little attention as the other recent reviews show, the assumption apparently being that one of the favored approaches must give, eventually, a useful answer, even if there are currently some uncomfortable facts.

5. Marine stratus clouds

When it became apparent that the albedo of marine stratus clouds was an important factor in the heat balance of the earth, interest grew in studying the low level stratus clouds over the oceans. It quickly became apparent that, while these clouds may not have the direct applicability to precipitation formation over land that is attributed to cumulus clouds, they are the key to the water cycle wherein much of the water substance reenters the atmosphere. Hence they are also important in any attempts at forecasting beyond a few days. In addition, the developing ability to measure vertical velocity and temperature from aircraft, without an immediate reference in adjacent still air a minute or two before or after in the flight, removed the concern that good measurements could not be obtained in other than cumulus clouds. The advent of the Forward Scattering Spectrometer Probe enabled droplet sizes to be measured at 10 times per second. In many circumstances there are sufficient drops measured to give good statistics at the largest drop sizes using one-second averages. The low turbulence in marine stratus clouds, with the concomitant low entrainment rate, long life and the clearly discernable structure consistent with isolated turbules, immediately revealed characteristics applicable to all clouds and a common basis for understanding turbulence. In cumulus clouds the shorter lifetime and the high entrainment rate which produces such a turbulent jumble obscures many features. Although it has long been known that cumulus cloud interiors are characterized internally by abrupt transitions in vertical velocity, water content and drop spectra, interpreting these as descending internal turbules was not easy to show or without critics. Measurements showed that the drop size spectra were totally changed by the entrainment of subsaturated air at the cloud tops. In the Pacific Ocean off the West Coast of North America near San Francisco, there are persistent stratus clouds with soundings in which the cloud top has risen until it has reached a level where it and the overlying air have the same wet bulb potential temperature (more strictly, the moist potential temperature, see Telford and Chai, 1993b), but since the relative humidity above is only about 30%, there is an associated inversion temperature increase of 10 to 20°C. The overlying air also has a constant wet bulb potential temperature for a considerable distance above, the result of earlier conditioning by clouds upstream (Chai and Telford, 1983; Telford and Chai, 1984; Telford and Keck, 1988). Thus, mixtures of cloud and subsaturated air from just above have the same or less density than the surrounding cloud and so cannot subside into the cloud, and so entrainment stops. Then the warm overlying air loses heat to the cooler cloud by radiative exchange and cools until this metastable state, as seen in the measurements (Rogers and Telford, 1986), starts spawning more turbules. These isolated turbules are frequently clearly seen in such clouds in the liquid water traces, but they are barely resolved in horizontal dimension

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with the equipment used (10-40 m across, Rogers and Telford, 1986). They are also evident in the fact that liquid water at cloud base is frequently missing, evaporated by the drier turbules which come to rest there. The active mechanism is clearly evident in these clouds, whereas in cumulus clouds the enormous clutter from the continual stream of descending and rising turbules obscures this structure. The entrainment in marine stratus clouds is seen to be intermittent. The metastable generation of turbules relaxes the instability until further radiative cooling regenerates instability by further cooling of the subsaturated air above. Regions of active and currently inactive entraining cloud have been found twenty kilometers apart (Telford and Wagner, 1981). The most startling effect of the entraining turbules is however seen in the droplet spectra. If we examine the concentrations of the largest drops which contain 5% of the liquid water, we find a very small diameter spread from parcel to parcel at cloud top. Nearer the cloud base adjacent cloud parcels have large variations in the diameters of these biggest drops, as well as in the liquid water mixing ratio and drop concentrations. Such data are seen in Fig. 1. The biggest drops are found in the most dilute parcels (Telford and Wagner, 1981), which have made the greatest number of cycles to the cloud top where dilution occurs. The explanation is given below.

6. Turbulent stirring due to radiation at cloud tops There is a question as to whether thermal radiative heat loss at the tops of layer clouds can produce downward convection and turbulent transfer in the cloud. The conventional view is that marine stratus and fog form as a result of thermal radiative cooling from the top surface of the cloud which mixes the air and brings up moisture from the surface. This idea seems to have developed because Petterssen (1938) and Leipper (1948) explained fog development over cooler water to be a consequence of downward convection driven by thermal radiative cooling in the air above the surface or from the drops, once condensation starts. However, aircraft observations show that convection from the sea continues below cloud base under stratus cloud when cooler water is encountered, with the cloud having a higher absolute potential temperature than the surface. Thus there can be no cloud top cooling stirring the air. The cloud base is observed to build down towards the surface even though the cloud is not cooled by radiation or by any other phenomenon (Rogers and Telford, 1986). The cause of the upward moisture transfer is the convection driven by water vapor and the occasional saturated patches of air leaving the sea surface. The moisture transfers upwards without producing any temperature changes when the temperature stability is less than the wet adiabat (Telford, 1992). Recently fog was observed from an aircraft over the cooler in-shore water west of San Francisco (Telford and Chai, 1993a). There was virtually no vertical motion observed above the noise level of the instruments in this fog, which had no overlying cloud to inhibit heat loss, so here also there was no vertical transfer of heat for any reason, including radiative cooling from above. On reaching warmer water further offshore, the resulting convective turbulence stirred in subsaturated air from above and

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Fig. 1. The diameter of the largest drops is shown as a function of altitude during the climb of an aircraft penetrating a marine stratus cloud layer. At the lower levels, parcels with smaller drops are thoroughly interspersed with parcels containing drops approaching the largest size needed for the commencement of coalescence growth, which removes such drops from the cloud. The smaller drops occur in the least diluted parcels of new cloud where the drop numbers are high, while the largest drops occur in diluted cloud which has cycled up to and down from cloud top. The drop concentrations tend to be in proportion to the liquid water content at each level, suggesting that the average drop size is roughly constant from parcel to parcel. In the lower half of the cloud the diluted parcels are cooler. This is fig. 6a from Telford and Wagner (1981).

the fog became small convective clouds, rising from the surface and soon totally dissipating. While these data show radiative cooling was not active, other observations seem to support radiative cooling as an active ingredient to fog formation over water. Cases where the measured air temperature in fog was less than the surface temperature have been reported. Little can be learned from those measurements over land or near the shore, since the heating and cooling of the land creates transitory conditions where advection so complicates the picture that unambiguous interpretation is difficult. However, Pili6 et al. (1979) describe shipboard measurements where the ship entered fog and the sea surface temperature increased but the measured air temperature decreased. The obvious question is whether the thermometer and the surrounding structure were shielded from the sun before the ship entered the fog, so the temperature change could not have been a consequence of the sudden chill on the ship as the sun was cut off. In

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particular no mention is made of the entrainment at fog top which adds drier air and normally controls the events possible at the surface, and no measurements of water vapor mixing ratio or detailed wind structure are given. Thus the paper does not provide adequate descriptions relating to the accompanying circumstances which could enable some of these points to be discussed. In addition, no reasons are given as to why some cases gave the fog temperature as the same as the water. Why was the radiative cooling not also active in these cases? The presence of higher cloud cannot be assumed from the paper. There is a paragraph which illustrates the problem of understanding their observations. " F r o m the temperature data it is apparent that upwind of the fog heat was being transferred from the relatively warm clear air to the cold surface. Within the fog, however, heat was being transferred from the warmer surface water to the cooler air. The cooling of the air and lifting of the inversion off the surface, therefore, cannot have been a result of transfer of heat to the surface. Since the fog was repeatedly observed attached to the warm water and since cold advection was not observed, the cooling of the foggy air must have been due to radiation to the sky from condensed liquid water." It is not clear how the transfer of heat to the surface would lift the inversion off the surface. Since in other cases reported the air is not cooled in the fog, the inversion is not regularly the result of any such temperature decrease. The observations of fog forming where the warm water is encountered are certainly very interesting and can be contrasted to the observations of Taylor (1917) that in every case where he observed fog formation the air was flowing from a warmer to a cooler sea surface. However it seems that for the top of the fog to rise, the subsaturated air initially above must have become saturated by being entrained into the fog so the foggy air below could replace it, probably assisted by turbulent stirring due to the convection driven by the warmer surface water. The mixtures of the foggy air with air above would need to be cooled to sink, so as to maintain saturated drop filled air up to the inversior,. This cooling would normally occur from the evaporation of the drops if the air above had a lower wet bulb potential temperature, which would necessarily be so unless the overlying air were almost saturated. Alternatively, heating from below due to the warmer water could well produce all the stirring needed without any assistance from radiation. However, without entrainment, no explanation is offered as to how cooling the top of the fog by radiation could cool the subsaturated air above it so the inversion could rise. There is no such problem with entrainment, but lacking temperature and mixing ratio measurements above and below the inversion, if one is present, no consistent conclusion is possible. Since the air was subsaturated upstream over the cooler water the evaporation there should have added water vapor to the air, but no fog formed so it must have been mixing through a sufficient depth to keep it below saturation. Initially, on encountering the warmer water, the surface air would be heated and convect and mix more, not less, so it is difficult to see how, without fog already present, radiation could form fog to begin with, so as to be consistent with the vague explanation given. An effect not considered is the transfer of momentum up from the sea into the air

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over the warmer water and the blocking of the airflow this engenders. Such a micro-front might develop a closed circulation which becomes saturated. Without accurate wind measurements accompanying these data little consistent can be deduced. These data are less than conclusive proof that radiative cooling plays the role attributed to it. To establish that radiative cooling actually occurs in these circumstances, as distinct from the cases observed higher up from aircraft where such cooling does not occur, would require much more careful and complete measurements and an adequate explanation.

7. Turbules In the entraining turbules, the initially cooled subsaturated air at first totally evaporates all the drops entrained from the adjacent cloud. Since the interior of the turbule is well mixed, all drops grow under the same conditions. The fully developed turbules are probably Hill's spherical vortices, as first described by a potential flow solution for a moving fluid sphere by Hill (1894; see Lamb, 1945). These were studied in water tank experiments (Scorer, 1957; Turner, 1973), with salty solutions to generate negative buoyancy. Although they are turbulent, the average flow lines follow the potential flow streamlines (Saunders, see Turner's book, 1973, fig. 6.13). This is because the rate of change of average momentum along a streamline is determined by the local average pressure gradient when the turbulence is small in scale. Taking averages in this way does not seem to effectively describe the nonlinear relationships with the across stream momentum flux due to shear, when the turbulence and the shear stress are formulated as intermediaries to balance the pressure gradient. A solution describing the three dimensional flow applicable to cloud turbules has been formulated by Telford (1988) using the entrainment theory. Similarly turbules are also a common component of stratified two-dimensional flows studied in the laboratory, and have been observed at sea (Voropayev and Afanasyev, 1994). The entity type entrainment mixing (ETEM) process proceeds in four stages. Firstly, the turbulent entity forms where subsaturated air and cloud mix at cloud top. The cooling due to evaporation starts a descending vortex in which the air soon becomes saturated as the entraining drops enter and are well mixed throughout the interior subsaturated air. Then, in the second stage, the drops which continue to enter the turbule after it has become saturated do not evaporate at all and so do not change size, but there are drastic changes in number concentrations from parcel to parcel. Once the parcels start to descend the drop sizes decrease, although in fog this descent may be too small to have much effect. An outstanding example was documented in an offshore wind west of the coast near San Francisco (Telford and Chai, 1993a). The average drop diameters in the fog were almost the same for every parcel, whereas the number concentrations changed randomly from parcel to parcel by 100 to 1 or so, as seen in Fig. 2. If the drop diameters were a result of the variations in cloud condensation nuclei (CCN) concentrations, then such an outcome is not possible. Fewer drops would mean that such drops would grow larger, because all drops are clearly formed in a similar process which

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Fig. 2. The droplet spectra are compared over warm and cool water. The fog began convectingafter reaching the warmer water beyond the coastal upwelling, and became diluted. The drop concentrationover the warm water decreased to about 10% of the maximum in fog, and some parcels had average drop size diameters above 20/xm. The fog converted to small cumulus clouds, and the base rose as the dilution proceeded, and the tops penetrated through the inversion and soon the cloud totally evaporated. In the equilibrium fog over the cooler water the entrainmentof dry air stopped after the fog formed near the coast. There was no turbulencein the fog and the average drop size was almost constant. The initial stage in ETEM (entity type entrainment mixing) leads us to expect equal sized drops with varying concentrations.This is fig. 6 from Telford and Chai (1993a).

initially releases about the same liquid water. This regularity in the size of the drops is no longer seen once convection and vertical cycling start over the warmer water further out to sea (Fig. 2). The third stage occurs when the parcel of drops descends in a stratus or cumulus cloud. These drops evaporate to much smaller sizes than they were at the same pressure when they were in undiluted parcels on the way up. This occurs because the same amount of water has to evaporate from fewer drops to keep the air saturated. Continual entrainment of larger undiluted drops from the surrounding cloud during the parcel descent adds a supply of larger drops, so a wide range in drop diameters develops, as shown in Fig. 3, in total contrast to the calculated droplet spectra using non-entrainment condensation theory, which produces a very narrow distribution. Following the descent, which leaves a parcel with all sizes of smaller drops including a few recently entrained larger ones, a fourth stage may occur. The parcel may be forced to rise by the backflow necessary to accommodate newer descending parcels. This new ascent results in the few biggest drops acquiring a disproportionate fraction of the new water released as the pressure again decreases (Telford and Chai, 1980). Hence drops are formed which are much bigger than any formed originally, just as though giant nuclei were present. Fig. 4 shows the result of calculations of repeated vertical cycling. With the longer life resulting from the cooler cumulus clouds over the sea, which reduces the entrainment rate, several vertical cycles can occur. This results in clouds

J. W. Telford / Atmospheric Research 40 (1996) 261-282

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Fig. 3. These are observed cloud drop size spectra from a cumulus cloud (fig. 2 from Telford et al., 1984). These spectra in no way resemble the narrow distributions calculated for condensationdrop growth without ETEM. The ETEM process spreads the narrow drop size spectrum which results from undiluted condensation in an updraft, and also generates some drops larger than can be produced directly, which may then start the coalescence growth process.

with fewer drops but more larger ones, which leads to rain regardless of the nuclei population from which they start. Thus the distinction between marine and continental cloud condensation nuclei (CCN) populations does not appear to be important. The apparent tendency for non-freezing marine cumulus clouds to rain more often than similar ones over land is a result of differences in the turbulent entrainment cycling

J. W. Tel/brd / Atrnospheric Research 40 (1996) 261-282

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resulting f r o m surface heating in c o n v e c t i v e conditions o v e r land, not the nuclei c o m p o s i t i o n , size or concentration.

8. M a r i n e s t r a t u s a n d c u m u l u s c l o u d s All the p r e c e d i n g ideas are an o u t c o m e o f the observational and c o n c e p t u a l studies of turbulence. The p r e s e n c e o f liquid water m a k e s little difference in the density o f the air

276

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and hence has no effect on the turbulence after it has formed, whether it is in clear air or cloud. The activity in cumulus clouds stems from the same physical phenomena that occur in marine stratus clouds. There is no justification for separating such studies, which allows data to be ignored and work to continue on theories which clearly violate the evidence. To repeat, a theory is not much use if it is clearly wrong, even if it appears to answer some question which has not yet been resolved. Most computer models to date appear to have this problem since they fail to reproduce the droplet spectra, and we have yet to see a discovery coming from such computer programs. The usual marine boundary layer cloud models offer no answers about cloud droplet spectra, and there is no hope of them ever doing so since they eliminate the existence of the turbules which control the process. The same applies to cumulus programs. Furthermore, models based on computer programs formulated to exclude the main driving mechanism bringing water up from the seas lose all contact with reality. As described by Telford (1992) water vapor and the occasional patches of saturated air below cloud maintain vapor transport without heat transfer in a wide range of circumstances: below cloud and also in clear air where no clouds are present, whenever the lapse rate becomes less stable than the wet adiabat. This can occur at night, for example, at an inversion which has been smoothed out in temperature contrast due to radiative exchange but still maintains the water vapor mixing ratio contrast (author's personal observations at STORM-FEST, Kansas City, MO, February, 1992, using NCAR King Air aircraft system). Once again, the mechanism is transport by turbulent entities. Many attempts to simplify the calculation of turbulence effects are based on averaging fluctuating quantities so the flow is uniform and hence can be derived as an outcome of simple differential equations. This basis for understanding is at fault, however, in the context of atmospheric flow and, indeed, with any phenomena with non-linear governing equations. The whole idea that a rate specification is always a good starting point is not realistic. To expect to find the position of an automobile, for example, by recording compass and speedometer readings is unrealistic. Writing down these variables once a minute would be hopelessly inadequate in city traffic. Why not look outside? Similarly it does not seem sensible to write computer programs which generate temperature as a function of height in layer clouds from postulates about turbulent transport by uniform heat fluxes, which we then try to measure, when we know that turbulence gives different temperatures and vertical velocities every few centimeters, and fluxes which vary in time and position. Worse yet, trying to restrict the collection of data to that which can be processed to yield something that corresponds to the calculation leaves little room for sympathy. Since the temperature structure is fairly clearly defined, why not measure it every half hour or so and look for causes to explain these data? The developing understanding of the structure of turbulence illustrates how to avoid this type of mistake, which presently dominates much thinking. Thus the entrainment theory applies to the surface boundary layer (Telford and Presley, 1978; Telford, 1981, surface roughness; Telford, 1982, von Karman's constant; Telford, 1988, spherical vortex flow), plume convection (Telford, 1966, 1970, 1972, 1975b) and cumulus clouds, all which are examples of the same structure of turbulence, which unites these areas of research.

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277

The influence of turbulent structures on droplet spectra has been observed as the major factor controlling the microphysics of cumulus clouds. The effects of mixing cloudy and subsaturated air were first formulated as a statistical phenomenon in terms of time constants for the turbulent blending as compared to the evaporation of the droplets into the subdividing tiny parcels of subsaturated air (Baker and Latham, 1979, 1982; Baker et al., 1980, 1984). However, this approach failed to resolve the problem because a descending parcel results in reduced droplet diameters, which is the same net result as that due to homogeneous mixing. Even if non-homogeneous mixing is the active mechanism, it has the same effect. Attempts to elaborate this approach, both by observations and conceptually, soon lead to the entity type entrainment mixing (ETEM) idea (Telford and Wagner, 1981; Telford and Chai, 1980, 1993a,c). Recently examination of this approach in more detail resulted in the conclusion that the details associated with homogeneous and heterogeneous mixing give the same results, because the cloud drops falling at their terminal velocities fall in and out of the tiny subsaturated parcels just before the end of the blending process (Telford et al., 1993). Thus the drops share the evaporation even before the saturated and subsaturated air finally mix. The result is always the same as for homogeneous mixing wherein all drops decrease in diameter. The evidence is that concentrations decrease but droplet diameters do not (Telford and Chai, 1993a; Telford et al., 1993). Thus the ETEM process remains as the only viable process. Observations in cumulus clouds show that the droplet spectra broaden at successive positions in the cloud as the observing aircraft penetrates from the upshear side. Often the droplet spectra have a number concentration peak apparent at diameters smaller than the main larger peak, as illustrated in Fig. 5. The concentrations decrease further into the cloud where a few larger drops can then be seen (Rogers et al., 1985). This is consistent with the progress of the ETEM process as simulated by Telford and Chai (1980). However, since several cycles are needed to develop big enough drops to start coalescence, the onset of the ice process frequently terminates the ETEM activity in those clouds with a substantial fraction of their volume above the freezing level but with a base warmer than freezing in temperature (Telford et al., 1987). The ice seems to develop in the older downshear side of the cloud, so vertical mixing seems to be important in this case also. The observations of Hobbs and Rangno (1985; see Telford et al., 1987) show that if the cloud tops are not colder than - 15°C, so that the cloud tops are not cold enough to flood the ~loud with ice particles, then rapid ice development, which frequently occurs and is referred to as ice multiplication, requires that the cloud base is warmer than freezing (Telford et al., 1987). The ice particles descending in parcels towards cloud base need to reach temperatures above freezing so they can start to melt inside the cloud. Thus many of the fragments which this partial melting produces can survive and be carried up again. Once the ice process starts, precipitation begins and the cloud rapidly dissipates. Similarly, the turbulence appears to correlate with electric charging in clouds (Christian et al., 1980). Wagner and Telford (1981) have attempted to show how this might be explained by the motion of the turbules. The concentration of negative charge at about - 10 to - 15°C was suggested as the level where the descending icy turbules could become surrounded by the rising, unfrozen lower cloud parcels, which latter

J. W. Telford / Atmospheric Research 40 (1996) 261-282

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would often be denser because their latent heat of freezing had not yet been released. This would produce an increase in buoyancy in the descending turbules with their negative charges and perhaps stop their descent so the cloud accumulates a negative charge near this level. It is generally observed that the interiors of cumulus clouds show rapid transitions

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from parcel to parcel on a horizontal penetration, no doubt the result of freshly descending turbules.

9. Summary The perception of the role of turbulence in clouds has changed from an inconvenient abstraction which could be dismissed as irrelevant, to the prime mechanism affecting their development. The progress in this understanding has come from the improvement in instrumentation and the observational planning following from this. While the phenomenon of turbulence was recognized a hundred years ago in attempts to explain the rapid mixing it produced, with ideas such as Reynold's fluxes and mixing length theories, these ideas were essentially analogs to the molecular diffusion process. As more accurate, rapid and airborne measurements became available, such ideas were shown to be totally inadequate and of little value. The difficulties in developing solutions to the steady state fluid flow equations tended to obscure their inadequacy in handling the small scale intermittent organized structures which dominate turbulent transport, as well as the need to accurately represent the effects of rapid fluctuations characteristic of turbulence. However, many of the present computer simulations are sufficiently at variance with the observations to demonstrate these inadequacies beyond any doubt. Modem observing instrumentation and data processing and analysis technology (particularly the modern personal computers and their enormous software support developed for other purposes, new remote sensing techniques, and satellite observation platforms) make it clear that the new intellectual basis resulting from conceptual progress in the description of turbulence can offer the opportunity to develop new, accurate cloud models, provided that the view that the failed modeling efforts have exhausted the intellectual potential of the subject is not allowed to prevail. New observational efforts aimed at directly testing ideas such as those presented here, to obtain direct evidence for or against these conclusions, would be extremely valuable in advancing cloud physics to the point where our knowledge of clouds can be applied effectively to global change and other societal problems.

Acknowledgements The drive to explore all aspects of the cloud microphysical problems by the many researchers involved and whose papers are not referred to here, or whose papers have not been seen in this review as part of the present mainstream, has played the critical role in providing a basis for anyone seeking adequate explanations. Only by exploring the complete range of phenomena can some ideas be seen to survive as more acceptable than others. Figs. 2, 3 and 5 are reproduced from previous articles by this author in the Journal of Atmospheric Sciences published by the American Meteorological Society. The various research papers reported here were largely funded by the National Science Foundation, and this paper was written with the support of Grant ATM-9311752.

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