Clouds drop size distributions

K2. Keily, D. P., Measurement of drop size distribution and liquid water content in natural clouds, Dept, of Meteorol., Mass. Inst, of Tech., Contr. No. AF19(628)-259, NASA Rept. No. N64-30005 (1964). 

Reaction of dissolved gases in clouds occurs by the sequence gas-phase diffusion, interfacial mass transport, and concurrent aqueous-phase diffusion and reaction. Information required for evaluation of rates of such reactions includes fundamental data such as equilibrium constants, gas solubilities, kinetic rate laws, including dependence on pH and catalysts or inhibitors, diffusion coefficients, and mass-accommodation coefficients, and situational data such as pH and concentrations of reagents and other species influencing reaction rates, liquid-water content, drop size distribution, insolation, temperature, etc. Rate evaluations indicate that aqueous-phase oxidation of S(IV) by H2O2 and O3 can be important for representative conditions. No important aqueous-phase reactions of nitrogen species have been identified. Examination of microscale mass-transport rates indicates that mass transport only rarely limits the rate of in-cloud reaction for representative conditions. Field measurements and studies of reaction kinetics in authentic precipitation samples are consistent with rate evaluations. 

The net enhancement factor for a droplet consisting of pure water can be as much as 1.6 (Madronich, 1987). Calculations by Ruggaber et al. (1997) suggest that the actinic flux inside cloud drops with a typical size distribution and dissolved particulate matter is more than a factor of two greater than in the cloud interstitial air. This effect of enhanced actinic flux inside droplets may be quite important for aqueous-phase photochemistry in fogs and clouds. 

Effect of aerosol particles on cloud drop number concentrations and size distributions Clouds and fogs are characterized by their droplet size distribution as well as their liquid water content. Fog droplets typically have radii in the range from a few /an to 30-40 /an and liquid water contents in the range of 0.05-0.1 g m" Clouds generally have droplet radii from 5 /an up to 100 /im, with typical liquid water contents of 0.05-2.5 gin"5 (e.g., see Stephens, 1978, 1979). For a description of cloud types, mechanisms of formation, and characteristics, see Wallace and Hobbs (1977), Pruppacher (1986), Cotton and Anthes (1989), Heyms-field (1993), and Pruppacher and Klett (1997). 

The size distributions of the particles in cloud samples from three coral surface bursts and one silicate surface burst were determined by optical and electron microscopy. These distributions were approximately lognormal below about 3/x, but followed an inverse power law between 3 and ca. 60 or 70p. The exponent was not determined unequivocally, but it has a value between 3 and 4.5. Above 70fi the size frequency curve drops off rather sharply as a result of particles having been lost from the cloud by sedimentation. The effect of sedimentation was investigated theoretically. Correction factors to the size distribution were calculated as a function of particle size, and theoretical cutoff sizes were determined. The correction to the size frequency curve is less than 5% below about 70but it rises rather rapidly above this size. The corrections allow the correlation of the experimentally determined size distributions of the samples with those of the clouds, assuming cloud homogeneity. 

Mounting of the cloud water collectors on the aircraft is a critical issue because flow-field effects can easily distort the size distribution of drops. If at all possible, the collector should be mounted on a pylon so that the collector is in the free airstream. Substantially greater efficiencies can be achieved if the collector is mounted with a forward inclination of about 12° to 15° relative to a perpendicular from the aircraft longitudinal centerline. This kind of mounting accounts for the nose-up attitude at which most aircraft fly under cruise conditions and also provides a component of the airstream to drive impacted cloud droplets down the rod into the collection vessel, minimizing losses due to blow-off (28). 

Evaporation Module. Evaporation can significantly alter the aerosol size distribution as the spray cloud descends from the aircraft release height to deposit on the ground. The net effect of evaporation, because of reductions in the drop size and thus a decrease in gravitational settling velocity, is to decrease deposition near the source and increase the downwind drift of spray drops or vapor. The FSCBG model has two options that can be used to account for the evaporation of material. 

Junge and McLaren (1971) have studied the effect that the presence of insoluble material has on the capacity of aerosol particles to serve as cloud condensation nuclei. Using Eq. (7-25) they calculated the supersaturation needed for an aerosol particle to grow to the critical radius at the peak of the Kohler curve, from where spontaneous formation of cloud drops becomes feasible. The results are shown in Fig. 7-8. They indicate that the difference is less than a factor of two in radius for particles whose soluble fraction is greater than e =0.1. The majority of particles can be assumed to meet this condition (see Fig. 7-19). By assuming particle size distributions similar to those of Fig. 7-1 for continental and maritime background aerosols, Junge and McLaren also calculated cloud nuclei spectra as a function of critical supersaturation and compared them with observational data. These results are shown in Fig. 7-8b. We shall not discuss the data in detail. The results make clear, however, that the presence of insoluble matter in aerosol particles does not seriously reduce their capacity to act as cloud condensation nuclei. 

Fig. 8-7. Washout coefficients according to Slinn and Hales (1971) are shown in curves A and B (left-hand scale). They are based on rain drop size spectra of Zimin (1964) with r,max = 0.2 and 1 mm, respectively, and a precipitation rate of 10 mm/h (10 kg/m2 h). Curve C represents the first term and curves D and E the second term in the bracket of Eq. (8-6) in nonintegrated form (right-hand scale applies). These latter three curves are based on the mass-size distribution for the rural continental aerosol in Fig. 7-3. Curve C was calculated with eA(r2)=l for r2>0.5 ra and eA < I for r2<0.5(im, decreasing linearly toward zero at r2 = 0.06 p.m. This leads to eA = 0.8. Curves D and E were obtained by using the washout coefficients of curves A and B, respectively. Note that below-cloud scavenging (curves D and E) affect only giant particles, whereas nucleation scavenging (curve C) incorporates also submicrometer particles.

For a given environment and given entrainment rate e, we need one more equation to close the system, namely, an equation describing the liquid water mixing ratio wL of the drop population. This liquid water content can be calculated if the droplet size distribution is known, such as a simple integral over the distribution. We thus need to derive differential equations for the droplet diameter rate of change dDp/dt. These equations will link the cloud dynamics discussed here with the cloud microphysics discussed in the following sections. 

The CCN behavior of ambient particles can be measured by drawing an air sample into an instrument in which the particles are subjected to a known supersaturation, a so-called CCN counter (Nenes et al. 2001). If the size distribution and chemical composition of the ambient particles are simultaneously measured, then the measured CCN behavior can be compared to that predicted by Kohler theory on the basis of their size and composition. Such a comparison can be termed a CCN closure, that is, an assessment of the extent to which measured CCN activation can be predicted theoretically [see, for example, VanReken et al. (2003), Ghan et al. (2006), and Rissman et al. (2006)]. The next level of evaluation is an aerosol-cloud drop closure, in which a cloud parcel model, which predicts cloud drop concentration using observed ambient aerosol concentration, size distribution, cloud updraft velocity, and thermodynamic state, is evaluated against direct airborne measurements of cloud droplet number concentration as a function of altitude above cloud base. The predicted activation behavior can also be evaluated by independent measurements by a CCN instrument on board the aircraft. Such an aerosol-cloud drop closure was carried out by Conant et al. (2004) for warm cumulus clouds in Florida. 

Minimum droplet diameters are a few micrometers, where large droplets exceed 100 /xm. In general, droplet spectra are wider for orographic clouds, less wide for stratus, and rather narrow for cumulus cloud types. Continental cumuli drop sizes range only from a few micrometers to around 20 /um in diameter. Frequency distributions of the mean cloud droplet size for various cloud types are shown in Figure 15.30. 

Gases like HNO3, NH3, and SO2 can be removed from interstitial cloud air by dissolution into cloud drops. For a droplet size distribution N(Dp), the local rate of removal of an irreversibly soluble gas like HNO3 with a concentration Q is given by (20.26) as... 

It is seen that the diffusion flux into the droplet depends strongly from the droplet radius smaller droplets under otherwise constant conditions will have a larger gas uptake than larger drops. Eq. (4.296) represents the flux into a single droplet, with the dimension mass per droplet volume and time, e.g. mol s . To gain the mean flux into a droplet in a cloud we must integrate the single droplet flux over all droplets (N (r) - droplet size distribution) ... 

The mean size of droplet represents a single value that characterizes the whole spray distribution. This value, together with the size distribution, defines the spray characteristics. Many papers have appeared on the subject of drop size prediction. The so-called Sauter mean diameter seems to be the most suitable mean value to characterize the droplet cloud together with the size distribution. This is defined as the ratio of the total droplet volume to the total droplet surface [23] that is. 

---