A new aspect of condensation theory

This paper examines the effects of the mixing of dry air into a cloud top from the point of view of the droplet spectra. It is shown theoretically that the resulting cycling of the air up and down in the cloud, as seems to be the essential mechanism by which cumuli have been diluted to their observed liquid water mixing ratio, can double the largest drop radius and generate cloud parcels containing drops of all sizes up to this maximum. These changes in the droplet distribution with size occur by a process which is not greatly influenced by the cloud condensation nuclei or the details of droplet growth since maritime like spectra can develop in continental type cumuli. It shows that large numbers of cloud condensation nuclei should not have much effect in inhibiting the rainforming process by reducing coalescence growth. On the contrary, the controlling parameters which determine precipitation efficiency and times seem to be those which control the mixing.     

A comparative study on the growth of cloud drops by condensation using an air parcel model with and without entrainment

During a study of the growth of cloud drops by condensation the evolution of cloud drop size spectra with height above cloud base was determined for maritime aerosols, and for continental aerosols containing aerosol particles of mixed composition. Air parcel models were used in which the parcel was either completely closed to mass and heat transfer (strictly adiabatic models), or open to heat transfer and to partial or complete mass transfer (entrainment models). It was found that adiabatic models and models which consider the entraining of air devoid of aerosol particles predict drop size distributions which are considerably narrower than those observed in non-precipitating cumulus clouds, and have only a single maximum. On the other hand, relative broad drop size distributions and distributions with a double maximum — as they are observed in atmospheric clouds — are predicted if the entrainment of both air and aerosol particles are considered in the condensation model. Our results support the findings ofWarner (1973) which were obtained for a purely maritime aerosol.     

Do Cloud Properties in a Puerto Rican Tropical Montane Cloud Forest Depend on Occurrence of Long-Range Transported African Dust?

We investigated cloud properties of warm clouds in a tropical montane cloud forest at Pico del Este (1,051 m a.s.l.) in the northeastern part of Puerto Rico to address the question of whether cloud properties in the Caribbean could potentially be affected by African dust transported across the Atlantic Ocean. We analyzed data collected during 12 days in July 2011. Cloud droplet size spectra were measured using the FM-100 fog droplet spectrometer that measured droplet size distributions in the range from 2 to 49 µm, primarily during fog events. The droplet size spectra revealed a bimodal structure, with the first peak (D < 6 µm) being more pronounced in terms of droplet number concentrations, whereas the second peak (10 µm < D < 20 µm) was found to be the one relevant for total liquid water content (LWC) of the cloud. We identified three major clusters of characteristic droplet size spectra by means of hierarchical clustering. All clusters differed significantly from each other in droplet number concentration ( \(N_{\rm tot}\) ), effective diameter (ED), and median volume diameter (MVD). For the cluster comprising the largest droplets and the lowest droplet number concentrations, we found evidence of inhomogeneous mixing in the cloud. Contrastingly, the other two clusters revealed microphysical behavior, which could be expected under homogeneous mixing conditions. For those conditions, an increase in cloud condensation nuclei—e.g., from processed African dust transported to the site—is supposed to lead to an increased droplet concentration. In fact, one of these two clusters showed a clear shift of cloud droplet size spectra towards smaller droplet diameters. Since this cluster occurred during periods with strong evidence for the presence of long-range transported African dust, we hypothesize a link between the observed dust episodes and cloud characteristics in the Caribbean at our site, which is similar to the anthropogenic aerosol indirect effect.     

On the hydrodynamic behavior of supercooled water drops interacting with columnar ice crystals

A numerical evaluation of the complete Navier-Stokes equations of motion for steady-state, incompressible flow past an infinite circular cylinder is given in terms of the stream function, vorticity, and pressure distribution past such bodies. A method is described which allows use of these flow characteristics: (1) to approximate the characteristics of air flow past hexagonal columnar ice crystals falling under gravity at terminal velocity in air, (2) to compute the trajectory of supercooled cloud drops relative to such ice crystals, and (3) to determine the efficiency with which short columnar ice crystals and needle shaped ice crystals collide with supercooled cloud drops. It is found that for all columnar type ice crystals riming is negligible if the cloud drop size is less than 5 m, and that for riming to commence short columnar crystals must have diameters larger than 50 m, while needle crystals must have diameters larger than 40 m. It is further shown that the collision efficiency cut-offs at the small drop radius and at the large drop radius end of the collision efficiency diagram can be explained on the basis of the cloud drop trajectories for these drop size ranges.     

The Influence of the Acoustic-electric Coalescence on Phase and Mass Transfer of Supercooled Drops

The objective of this work is to study the influence of electrical discharge on the evolution of the cloud droplet spectra using a 1-D cloud model. It is shown that droplet motion and the electrical effects produced by lightning may cause a rapid and effective droplet coalescence process, with noticeably more phase transfer from liquid toward frozen water. As a measure of the drop spectra changes, we investigated variations of the radar reflectivity factor and the mass-weighted mean diameters at five temperature levels (0, −5, −10, −15, and −20C) with 15 combinations of the initial conditions. The model simulations suggest that about where the lightning occurred, after a few seconds, the initial unimodal spectra of supercooled water drops can be transferred to the bimodal spectra of unfrozen and frozen water drops. The number of newly created frozen drops is a few orders less than unfrozen water drops, but can still be very important for further transformations due to gravitational coagulation and other microphysical processes, e.g. glaciation. The results indicate that the procedure established to describe processes related to the electrical discharge and droplet spectra transformations can be used within a 3-D mesoscale model. It is concluded that the outcome can be also used to explain some of the physical characteristics inferred from polarimetric radar observations.     

Size distribution models of fog and cloud droplets and their volume extinction coefficients at visible and infrared wavelengths

Based on the average variability of the skewness with respect to the droplet mode radius, a wide set of mean size-distribution models is presented in terms of the modified gamma function for fog and stratified cloud droplets. These models appear appropriate for giving reliable size-distribution curves relative to the various formation stages of the droplet population both in fogs and in stratus and stratocumulus clouds.The corresponding volume extinction coefficient has been computed at various wavelengths from 0.4 to 17 m using Van de Hulst's (1957) approximation multiplied by Deirmendjian's (1960) correction factors. This set of theoretical extinction data has been compared with experimental extinction measurements performed in atmospheres characterized by a marked thermal inversion for describing the evolutionary features of the water droplet size distribution within the whole ground layer.     

Characteristics of cloud drop spectra in tropical warm clouds

Characteristics of cloud drop spectra were studied using 400 samples obtained from 120 warm cumulus clouds formed during the summer monsoon season.The total concentration of cloud drops (N _T) varied from 384 to 884 cm^–3 and the maximum concentration was observed in the layer below the cloud-top. The width of the drop spectrum was broader in the cloud-base region and in the region below the cloud-top. The spectrum was multimodal at all levels except in the cloud-top region where it was unimodal. The concentration of drops with diameter greater than 50 m (N _L) varied from 0.0 to 0.674 cm^–3.N _L was larger in the cloud-base region.N _L decreased with height up to the middle level and thereafter showed an increase. In the cloud-top region no large drops were present. The computed values of the liquid water varied between 0.132 and 0.536 g m^–3 and the mean volume diameter (MVD) varied between 8.1 and 12.0 m. The LWC and MVD showed a decrease with height except in the middle region of the cloud where the values were higher than the adjacent levels. The dispersion of the cloud drops was lower (0.65) in the cloud-top region and higher (1.01) in the cloud-base region.The observed cloud microphysical characteristics were attributed to vertical mixing in clouds induced by the cloud-top gravity oscillations (buoyancy oscillations) generated by the intensification of turbulent eddies due to the buoyant production of energy by the microscale-fractional-condensation (MFC) in turbulent eddies.     

Impact–entrainment relationship in a saltating cloud

The problem of impact–entrainment relationship is one of the central issues in understanding saltation, a primary aeolian transport mode. By using particle dynamic analyser measurement technology the movement of saltating particles at the very near‐surface level (1 mm above the bed) was detected. The impacting and entrained particles in the same impact–entrainment process were identified and the speeds, angle with respect to the horizontal, and energy of the impacting and entrained sand cloud were analysed. It was revealed that both the speed and angle of impacting and entrained particles vary widely. The probability distribution of the speed of impacting and entrained particles in the saltating cloud is best described by a Weibull distribution function. The mean impact speed is generally greater than the mean lift‐off speed except for the 0·1–0·2 mm sand whose entrainment is significantly influenced by air drag. Both the impact and lift‐off angles range from 0° to 180°. The mean lift‐off angles range from 39° to 94° while the mean impact angles range from 40° to 78°, much greater than those previously reported. The greater mean lift‐off and especially the mean impact angles are attributed to mid‐air collisions at the very low height, which are difficult to detect by conventional high‐speed photography and are generally ignored in the existing theoretical simulation models. The proportion of backward‐impacting particles also evidences the mid‐air collisions. The impact energy is generally greater than the entrainment energy except for the 0·1–0·2 mm sand. There exists a reasonably good correlation of the mean speed, angle and energy between the impacting and entrained cloud in the impact–entrainment process. The results presented in this paper deserve to be considered in modelling saltation. Copyright © 2002 John Wiley & Sons, Ltd.     

Some effects of intra-red radiation on the dynamics of the atmospheric boundary layer

An approximate infra-red radiation scheme, employing essentially the cooling to space approximation, is included in a one-dimensional model of the atmospheric boundary layer. The approximate scheme is found not to produce significant errors in the behaviour of the dynamical model when integrated over a few hours. Radiative cooling is shown to be important in the development of a clear well-mixed layer which is capped by an essentially dry region; in particular, convetive instability is induced and this enhances the rate of entrainment of dry air. The development of fog is found to require sound models of both radiative transfer and turbulent diffusion.     

Lagrangian motion of air parcels in the stratosphere in the presence of planetary waves

Development of thoughts on tracer transport mechanisms in the stratosphere which lead to new approaches to two-dimensional modeling of the tracer problem is reviewed.Three-dimensional motions of individual air parcels affected by a planetary wave are investigated theoretically, treating a steady, upward propagating wave in a uniform flow. It is shown that trajectories of air parcels are of elliptical form when projected onto the meridional plane and that they have no mean meridional or vertical motion, even though the usual zonal Eulerian-mean vertical motion exists. The origin of the difference between the mean air parcel motion and the Eulerian-mean motion is discussed.On the basis of the knowledge of air parcel motion, two approaches to two-dimensional modeling are considered. The generalized Lagrangian mean motion (quasi-zonal weighted mean taken over a meandering material tube), recently introduced by Andrews and McIntyre, is identical with the mean motion of an air parcel in a steady state. Such a mean meridional circulation may be used for advecting a tracer in the meridional plane in a two-dimensional model. The transport effect is represented solely by the advection and an eddy transport does not appear in this scheme, to a first approximation.The finding that trajectories of air parcels are elliptical necessitates a reexamination of the Reed-German eddy diffusivity currently used in two-dimensional chemical-dynamical models. By applying a mixing length type hypothesis, we derive an eddy diffusivity formula for use in Eulerian-mean calculations, which, in the case of a conservative tracer is dominated by an anti-symmetric tensor. The eddy transport due to this anti-symmetric tensor diffusivity is of advective type (not diffusive) and has the effect of taking the Stoke drift effect into account, when used in the usual Eulerian-mean formulation.     

The coalescence of water drops II. The coalescence problem and coalescence efficiency

By the use of the model of approaching drops (Arbel and Levin, 1977) the coalescence efficiencies of drops are computed. It is found that for interactions of drops at their terminal velocities the coalescence depends both on the size of the large drop and on the size ratio of the interacting drops in agreement with the experimental results of Whelpdale and List (1971) and Levin and Machnes (1977).The results were found to be sensitive to the assumption of the drops deformation and to the critical separation distance. This distance is defined as the distance at which the drops begin to merge. The variations of the coalescence efficiency with these parameters is discussed.Appendix: List of symbols D distance between the deformed surfaces of the drops - D _o initial value ofD - D _s stop distance, the distance at which the impact velocity vanishes - D _c critical coalescence distance - E collection efficiency - E ₁ collision efficiency - E ₂ coalescence efficiency - E _2R coalescence efficiency for collisions with stationary targets - F _c centrifugal force - p ratio of the radii of the interacting drops - r _o initial distance between drops' centers - R _L radius of larger drop - R _s radius of smaller drop - R _D radius of deformation - v approach velocity of two deformed surfaces - v _o initial value ofv - V _i impact velocity (given negative sign when drops approach each other) - V _c critical impact velocity - W _i velocity of the smaller drop at infinity for it to reachD _o with velocityv _o - x _i impact distance, the distance between the trajectories of the two drops - x _c critical impact distance for coalescence -  average critical impact distance for coalescence - X _c critical impact distance for collisions - coefficient of deformation given in equation 1 - _i impact angle defined byWhelpdale andList (1971) given also inArbel andLevin (1977) - coefficient of deformation given in equation 2 - viscosity of air - _i impact angle used inArbel andLevin (1977) and here - _c critical angle for coalescence - average critical angle for coalescence On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The 1982 eruptions of El Chichon volcano,Mexico (3): Physical properties of pyroclastic surges

Two major pyroclastic surges generated during the 4 April 1982 eruption of El Chichon devastated an area of 153 km² with a quasi-radial distribution around the volcano. The hot surge clouds carbonized wood throughout their extent and were too hot to allow accretionary lapilli formation by vapor condensation. Field evidence indicates voidage fraction of 0.99 in the surge cloud with extensive entrainment of air. Thermal calculations indicate that heat content of pyroclasts can heat entrained air and maintain high temperatures in the surge cloud. The dominant bed form of the surge deposits are sand waves shaped in dune forms with vertical form index of 10–20, characterized by stoss-side erosion and lee-side deposition of 1–10 cm reversely graded laminae. A systematic decrease in maximum lithic diameter with distance from source is accompanied by decrease in wavelength and amplitude. Modal analysis indicates fractionation of glass and pumice from the surge cloud relative to crystals, resulting in loss of at least 10%–25% of the cloud mass due to winnowing out of fines during surge emplacement. Greatest fractionation from the –1.0–0.0– grain sizes reflects relatively lower pumice particle density in this range and segregation in the formative stages of the surge cloud. Extensive pumice rounding indicates abrasion during bed-load transport. Flow of pyroclastic debris in the turbulent surge cloud was by combination of bed-load and suspended-load transport. The surges are viewed as expanding pyroclastic gravity flows, which entrain and mix with air during transport. The balance between sedimentation at the base of the surge cloud and expansion due to entrainment of air contributed to low cloud density and internal turbulence, which persisted to the distal edge of the surge zone.     

A comparison of concentrations of fission products,radon 222, and cloud condensation nuclei over the North Atlantic

The concentrations of airborne fission products were observed to be air mass dependent during a cruise of the USNSHayes from Norfolk, Va to Athens, Greece in May–June 1977. Minimum concentrations of fission products, radon, and CCN (cloud condensation nuclei) were measured in maritime air which had previously transited northern North America. Higher fission products, radon, and CCN concentrations were measured in recent, continental air traceable to mid North America or central Europe. These data are consistent with either entrainment by strong winds of previously precipitated fission products (the continental effect) or greater transfer of fission products from the stratosphere to low levels by tropospheric folding.     

Characteristics of Cloud Drop Spectra at Different Levels and with Respect to Cloud Thickness

--Measurements on drop size spectra were made in cumulus clouds over Pune (inland) region on many days during the summer monsoon seasons. In this paper, the measurements in non-raining cumulus clouds made in the years 1984, 1985 and 1986 at different levels and for different cloud thickness have been studied. In general, the drop size spectra broadened with height and the concentration of drops with diameter > 50 wm (N_L), mean volume diameter (MVD), liquid water content (LWC) and dispersion increased with height while the concentration of drops with diameter < 20 wm (N_S) and the total concentration of drops (N_T) decreased with height. The average drop size distributions were unimodal at the lower levels while they were bimodal at the higher levels. High water contents were confined to drops in the size range 5-25 wm at both higher and lower levels. The average drop size spectra were broader and N_L, LWC, MVD and dispersion greater while N_T and N_S smaller for thicker clouds (range of vertical extent 1.1-2.1 km) as compared to those for thinner clouds (range of vertical extent 0.3-1.1 km). Water contents for the drops > 28 wm were higher while those for the drops > 28 wm lower in thicker clouds than in thinner clouds. The average drop size distributions were bimodal in the former case, while they were unimodal in the other case.     

On some measurements of the condensation of different vapors upon Aitken condensation nuclei

No final theory on the activity of Aitken nuclei has been established yet. In particular the supersaturation is not known for the Aitken nuclei to grow into droplets, f.e. according toF. Volz only nuclei of radius >0.1 can cause condensation under atmospheric conditions. On the other hand according toH. G. Müller condensation over the continents has to occur at the Aitken nuclei since precipitation washes out the other nuclei.This uncertainty becomes obvious in the interpretation of the experimental results.Chr. Junge found that the necessary activation supersaturation of a continental Aitken aerosol and of artificial aerosols of the same size of nuclei lies between 2 and 20%, 10% being sufficient for the main fraction of nuclei to grow.In contrastW. Wieland was able to activate in a mixing cloud chamber a big portion, if not all, of the nuclei of a continental aerosol at supersaturations below 1.5%. Some of our own results, obtained with the same technic, agree with this. At supersaturations below 0.8% at least half of the Aitken nuclei present are activated. To obtain the same result with benzene and acetone we found, that benzene required a slightly smaller, and acetone a somewhat bigger supersaturation.However later experiments revealed a considerable effect of the geometry of the mixing cloud chamber upon the results. Since the physics of the chamber has not been fully explored the method was abandoned. Instead the principle of cooling by adiabatic expansion was used. An expansion apparatus based on the principle of a fotoelectric nucleus counter was developed allowing us to measure with two cathode ray oscillographs the pressure and simultaneously the change of intensity of a lightbeam due to the scattering on the forming cloud as a function of time. The length of the lightbeam could be chosen between 60 and 200 cm. The overpressure before the expansion was always 180 mm of mercury. The ratio of expansion rates was 12.53060 at the beginning of the expansion. The slowest rate was about 6 seconds, corresponding to a rate of ascent of 210 m/s at the beginning of the expansion. Smaller rates could not be obtained because of heat transfer at the chamber walls.The present work has been performed for the Eidgenössische Kommission zum Studium der Hagelbildung und der Hagelabwehr (Switzerland) at the research station Osservatorio Ticinese Locarno-Monti della Centrale Meteorologica Svizzera     

Experimental evaluation of the coalescence efficiencies of colliding water drops

The coalescence of water drops of sizes comparable to rain drops (200–2500 m diameter) was investigated. The method used provided a good separation between collision and coalescence effects. The result suggests a dependence of the coalescence efficiency on both the size of the large drop and the ratio of the radii of the interacting drops (p-ratio). The coalescence was observed to rapidly decrease due to bouncing and partial coalescence as the angle of impact increased from head-on to grazing angle. However, some bouncing was observed at very low impact angles.The results of the coalescence efficiency were fitted with an empirical equation for use in numerical models of cloud growth and precipitation development.On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A numerical determination of the effect of electric fields and charges on the efficiency with which cloud drops and small raindrops collide with aerosol particles

Summary Numerical calculations were carried out to determine the effect of a vertical electric field on the efficiency with which electrically charged or uncharged cloud drops and small raindrops of diameters ranging from 84 m to 1.248 mm collide with electrically charged or uncharged particles of density 2 gm/cm³ and diameters between 1 and 20 m. For this purpose, numerical flow fields about spheres of Reynolds numbers ranging from 1 to 400 were used to integrate the trajectory of the particle relative to the drop, and the force between two conducting spheres was used to represent the electrostatic force on the particle. The effect of thunderstorm strength electric charges and field on the collision efficiency was found to be highly significant for the smaller collector drops, and declined to insignificance for the largest collector drop.     

Simulation of the size distribution and erosivity of raindrops and throughfall drops

This paper presents a model that simulates the size distribution and erosivity of raindrops and throughfall drops. It utilizes existing models of rainfall drop size distribution and fall velocity and combines them with newly collated evidence of throughfall drop size distributions. A sensitivity analysis reveals that the model is sensitive to parameters that are easily measured or estimated: rainfall intensity, the mean volume drop diameter of the intercepted throughfall, canopy cover, and canopy height. The results of the model may be used at two levels. Firstly, to calculate specifically the size and fall velocity of individual drops, parameters that are needed in studies examining the response of soil surfaces to forces applied by rainfall. Secondly, to produce erosivity indices, based on rainfall intensity but which take account of the effects of a vegetation canopy. The paper shows that while the kinetic energy of rainfall (E(0), J mm^?1 m^?2) may be calculated from an equation of the familiar form: the kinetic energy of throughfall under any canopy may be calculated by combining this equation with another that relates the energy of drops under a 100 per cent canopy cover (E(100)) and the canopy height: .     

On mixing processes in cumulus clouds

An examination is made of the hypothesis that internal cloud properties are determined by the mixing of dry air from above the cloud top and cloud base air in such a way that the mixture is neutrally buoyant with respect to the clear air environment at each level. It is concluded that the resulting mixture is much drier than is actually observed. Comments are made about observed cloud properties which need to be taken into account in any model of the mixing process.     

The coalescence of water drops I. A theoretical model of approaching drops

The approach of two water drops in the absence of air flow around them is theoretically investigated. By assuming deformation criteria it is possible to solve the equation of motion of the drops under the influence of a variety of forces. These forces include the viscous force exerted by the air between the two deformed surfaces, the London-Van Der Waals forces and the force of gravity. It is found that the viscous forces dominate over the whole distance of the interaction. The equations have analytical solutions when a head-on approach is considered and when the deformation of the drops is assumed constant during the interaction. The equations were solved numerically for other deformation criteria and for non head-on approaches.The results of the present model are used in the following paper to compute the coalescence efficiencies of water drops. The model is primarily applicable to situations in which the large drop is stationary and the small one approaches it from below. However, it could also be used for interaction between freely falling drops as long as their relative velocities exceed about 13 cm/sec.Appendix: List of symbols C constant of the motion - D distance between the deformed surfaces of the drops - D _o initial value ofD - D _m the value at which the viscous force is maximum - D _N normalized distance - D _s the distance at which the velocity of approach vanishes - F _c centrifugal force - F _g force due to gravity - F _N normalized viscous force - F _LV force due to London-Van der Waals effect - F _R radial component of the force - F _V viscous force - F _t tangential component of the force - g acceleration due to gravity - M _L mass of large drop - m _s mass of small drop - p ratio of radii of interacting drops - R radius of an arbitrary drop - r distance between the centers of mass of the two drops - R _D radius of deformation - R _L radius of larger drop - R _s radius of smaller drop - t time - u defined in equation 20 — has the meaning of kinetic energy - v relative velocity of the deformed surfaces - v ₀ initial value ofv - V ₀ initial relative velocity of the centers of the drops - V _c critical impact velocity - V _i impact velocity - V _N ,v _n normalized velocity - V _t tangential component of the velocity - W _i velocity of the small drop at infinity for it to reach the pointD ₀ at velocityV ₀ - x instantaneous impact distance -  average critical impact distance for coalescence - x ₀ initial value of the impact distance - x _c critical impact distance for coalescence - coefficient of deformation - _i impact angle according toWhelpdale andList (1971) - coefficient of deformation - viscosity - surface tension - F _s sum of forces acting on the small drop - F _L sum of forces acting on the large drop - time constant - _R Rayleigh's oscillation period On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.