Andrew Glen Summary 3 - Cloud Microphysics

Condensation & Coalescence: There are 2 main precipitation processes, Coalescence which is known as a ‘warm’ cloud process and the Bergeron Findeisen process which is often known as a ‘cold’ process. Coalescence is a process which is independent of temperature but is exclusive to temperatures above 0˚C, and therefore has no involvement from ice. Battan (1953) describes how pre-1947 (Thunderstorm Project) most observed ‘warm’ cloud precipitation events had occurred over oceans. But the 1947 Thunderstorm Project data set shed light on the formation of precipitation in continental convective clouds by ‘warm’ rain processes. The Thunderstorm Project data set was collected during the summer of 1947 near Wilmington, Ohio using a modified 3-cm vertical scanning radar. The study by Battan (1953) discusses the observation of coalescence by looking at first echo studies, and identifying the level of the first formation of precipitation, and the thickness of the cloud. The radar observations can be interpreted in terms of drop size which can then be related to the initiation of precipitation. Several assumptions are used to develop this method; the main source of error can be associated with the assumption that all drops are the same size, but is not essential when vertical development is dealt with. The use of the vertical scanning radar allows the growth of the colloids to be observed as the first echo, the colloids then rapidly form droplets of the order of 100µm diameter, which are efficient coalescence elements. Figure 1 shows an example of a growth curve from the first echo study, Battan (1953). The plot shows the cloud development over time, the +8˚C curve indicates the cloud top temperature, which ascends over time. The +13˚C curve indicates the cloud base, which descends over time. It can be seen that the cloud always remains below the 0˚C altitude and therefore never experiences freezing.

Figure 1. Example of cloud growth from a first echo study. Battan (1953)

When considering ‘warm’ rain processes there are 2 main methods of droplet growth, condensation and coalescence. Condensation occurs first and is the condensing of liquid water onto a soluble particle known as a condensation nuclei (CN). This condensational growth can only occur in environments that are above saturation, and can be modeled by the Köhler curve. The Köhler curve is the relationship between the radius of a particle and the supersaturation of the environment while balancing the effects of vapour pressure and chemical composition known as the curvature and solution terms respectively. If a droplet can grow larger than the critical radius, which is the radius at peak supersaturation, then the droplets growth can be maintained as long as there is sufficient vapour around the population of CCN. Condensation droplets are typically between 1µm and 10µm, the process of condensation can take a fraction of a second at high supersaturations, but a droplet cannot grow large enough to precipitate by this process alone. The supersaturation is affected by condensation of vapour onto droplets, which decreases the supersaturation and an increase in supersaturation by maintaining an updraft. The rate of change of supersaturation is defined in equation 1.

dS dz dw =Q − Q Equation 1 dt1 dt 2 dt

Where: S is the supersaturation w is the mixing ratio of the liquid water condensate Q1 and Q 2 are constants

There is a fundamental step between the Köhler curve and equation 1. The Köhler curve is calculated and describes the conditions for a single CCN droplet, whereas equation 1 represents a population of active CCN droplets. This is where coalescence takes over with drop to drop interactions of several condensation droplets. As condensation droplets grow, a size distribution occurs with a small amount of CN droplets larger than the mode size of the distribution. These larger droplets are what initiate coalescence growth, by having slightly higher terminal velocities they can collide with CN droplets of modal and smaller sizes within an air mass. Coalescence becomes efficient as soon as a few droplets become bigger than 40µm in diameter, Brenguier & Chaumat (2001). There are several parameters of influence for the coalescence process, drop shape, fall velocity, size distribution, electric charge, aerodynamic forces and turbulence. Typical fall velocities of drops can be seen in figure 2 from Beard (1976) and it can be seen that terminal velocity is a function of pressure due to an inverse relationship to air density.

Figure 2. Drop terminal velocities as a function of drop diameter and ambient pressure. (Beard 1976)

The collisions occur as the larger droplets fall faster and sweep out smaller CN droplets in their path. However not all droplets in the cylinder of air below the collector drop are swept out, due to droplets which can pass by the collector drop because they have little momentum and are forced to follow the stream lines around the collector drop, this is known as the collision efficiency, E c. The volume swept out can therefore be calculated by equation 2: +2π − = ERrC ( )( Vv ) Volume swept out Equation 2

Where: R and r are the radii of the droplets, large and small respectively V and v are the velocities of the droplets, large and small respectively

There is also the coalescence efficiency Es, which is how likely 2 drops will merge and is affected by charge, size, oscillation and how well the viscous air between the 2 drops surfaces is removed. The collection efficiency E E, is defined as the product of the coalescence efficiency and the collisional efficiency as seen in equation 3.

× = EC E S E E Equation 3

Figure 3 shows contours of collection efficiency as a function of the collector droplet radii (R) and collected droplet radii (r), as it shows the optimal collection efficiency is a R~100µm and r~10µm and decreases dramatically as the collected droplet radius (r) decreases, whereas if the collector droplet radius (R) increases the efficiency has less of a decrease. Coalescence doesn’t always end up in growth of a droplet, break up can occur spontaneously or due to the collision. The break up could result in a number of smaller drops, or the apparent identities that went into the initial collision.

Figure 3. Contours of semi empirical collection efficiency E E as a function of large (R) and small (r) droplet radii. Beard & Ochs (1993)

Modeling Condensation & Coalescence: Various models have been devised to simulate how droplet growth occurs from condensation and coalescence. Scott (1968) uses a stochastic analytical solution for coalescence growth without including condensation or cloud dynamics. This method of modeling has a number of flaws as it can only resolve specialized and non realistic efficiency formulas. Figure 4 shows the distribution of water content with respect to droplet size from the analytical model, initialized from a Gaussian distribution. The figure shows that initially there is a high concentration of water at relatively small sizes, then as time progresses the distribution shifts to larger sized droplets, and the distribution broadens as larger droplets coalesce with the smaller droplets.

Figure 4. The distribution of water content with respect to droplet size, over a period of 1600 seconds. Scott (1968)

A model was developed by Berry & Reinhardt (1974) to add a new concept to process of cloud droplet development. This process is known as large hydrometeor self collection and joins the 3 other methods of development, auto conversion, accretion and breakup. The model uses a density function proportional to a concentration of droplets in each size bin over a volume of cloud to represent the droplet distribution. Figure 5 shows how an initial bimodal distribution, of 2 distinct sizes develops over time and allows for the study of impact of the presence of larger droplets. The variance of the distribution, specifically the larger sized tail is what dictates how fast coalescence growth will occur. As the figure shows the spectrum on the left, the spectrum with a mode of 10µm decreases in amplitude as time progresses, and increases in radius slightly. However the spectrum on the right, the larger sized spectrum, grows in amplitude and width as time progresses. Together this indicates that the initial peak at large sizes coalesces with the 10µm droplets to create a larger droplet, which can in turn sweep out more smaller droplets to create a bimodal distribution weighted heavily at large sizes. The results from Berry & Reinhardt (1974) also show that even a small distribution of droplets at a large size have a significant effect in the growth of droplets, and that the wider the spectrum of large sizes in the distribution the faster the growth will occur. In the atmosphere a bimodal distribution is rarely seen, but a unimodal distribution with a few large sizes is enough to accelerate growth.

Figure 5. Time evolution of the initial droplet spectra composed of 0.8gm -3 with a mode radius of 10µm, and 0.2gm -3 at a radius of 50µm. Berry & Reinhardt (1974)

Yum & Hudson (2004) used an adiabatic condensational growth model to show that the broadness of cloud droplet spectra in adiabatic cloud parcels is significantly dependent on cloud supersaturation. With the model showing that the rate of narrowing is slower when cloud supersaturation is lower, this gives a broader spectrum for continental clouds or weaker updrafts. However typical observations oppose this finding with cleaner clouds generally having a broader spectrum. This disagreement between model and observations could be due to differences in the moisture content of an adiabatic model and that of the measured environment, also errors in measurements from the Fast-Forward Scattering Probe (FSSP) and CCN instruments and averaging of non-linear processes. The paper neglects to cover some important variables which may have a large impact on the results, such as giant and ultra giant aerosol particles, turbulence and finally the condensation coefficient which is very difficult to measure. Turbulence causes an inhomogeneous distribution of aerosol particles in the cloud as they experience a centrifugal effect, this will lead to growth rates increasing in areas of high drop density and therefore providing a broadening effect, Shaw et al (1998). It is expected that the effect of giant and ultra giant aerosols will cause the largest error. Brenguier & Chaumat (2001) used similar results collected by a FSSP during the Small Cumulus Microphysics Study (1995) and compared data that showed a narrow droplet spectra to a narrow spectrum predicted under the same conditions by a condensational growth model. It was found that the measured narrow spectra showed characteristics close to adiabatic model, with LWC values slightly below the adiabatic value. However the spectra measured using the FSSP are still broader than the model derived spectra.

Giant & Ultra Giant Aerosol: Giant and ultra giant aerosol, particles >5µm radius have very low concentrations in the atmosphere. The particles have a short lifetime as they are susceptible to impacting and settling out, which makes observation and measurement difficult. Observed concentrations of giant cloud condensation nuclei (GCCN) over the ocean were found to be between 10 -4 and 10 -2 cm -3, Feingold et al (1999). These nuclei have a significant effect in moving a non- precipitating stratocumulus into a precipitating state. GCCN do not have an influential effect on drizzle formation in a stratocumulus cloud when the relative concentration of CCN is low, this is due to drizzle already being active as there is a low concentration of CCN which therefore creates relatively large drizzle droplets. At high CCN concentrations the GCCN have a noticeable effect as drizzle development is slow. This is represented in figure 6 which shows the time taken for 10% of the LWC to be transferred to drizzle droplets, as it can be seen in figure 6c that the difference between a and b is very small at low concentrations. Figure 6b shows that at low LWC the GCCN allow for higher concentrations of CCN to turn into drizzle in a shorter time.

Figure 6. Contours of time (min) required for 10% of the LWC to be transferred to drizzle (drops with r > 20µm) through the collection process as a function of initial drop number N 0 and LWC, (a) no GCCN, (b) 10 -3 GCCN cm -3, (c) percentage difference between (a) and (b).

In figure 6a and b the time it takes for the conversion is approximately 17 minutes at an LWC of 0.5gm -3 and a concentration of 40cm -3 but for figure 6a at the same LWC it takes 120 minutes for a concentration of 300cm -3. However for figure 6b at LWC of 0.5gm -3 and a concentration of 300cm -3 it takes approximately 70 minutes.

Updrafts & Entrainment: Updrafts and entrainment occur within clouds and have a strong influence on what ‘type’ of air is in a cloud and where the air originated. The fact that updrafts and downdrafts occur gives an indication that mixing occurs within the cloud with air from below and above the cloud level. The vertical motions within the cloud are inhomogeneous in the horizontal, vertical and in time, making modeling very complex. There are 3 main ways that vertical motion can be modeled, jets, bubbles and plumes, but the jet and bubble term are widely used and a fusion of the two is believed to be the main forcing for convective updrafts. The jet is formed by injecting positively buoyant air in from a surface point and observing how it rises and expands, with this movement mixing and entrainment at the side of the jet also occurs as the air around it is disturbed and tries to equilibrate. The bubble model is a buoyant parcel which has no connection to the surface, the bubble rises and expands with internal overturning motion in a toroidal pattern. The overturning allows for mixing with the ambient air. Penetrative downdrafts are also important in cloud dynamics and for mixing of air parcels, Warner (1977) discusses there affect and the rate at which they can form, on the order of 10 minutes. Penetrative downdrafts are caused by mixing and entrainment at the top of a cloud which brings in dryer air which mixes with the cloudy air, evaporating water vapour as it tries to maintain the saturated vapour pressure and therefore cools the surrounding area. As the air cools it its density increases and the parcel becomes negatively buoyant, Squires (1958). Paluch (1979) created a way of determine the penetrative downdraft in a cloud from measured variables and an environmental sounding. The diagrams he created use wet equivalent potential temperature and mixing ratio, which are conserved throughout cloud. Mixed air parcels in the cloud can therefore be identified by measuring their quantities of the above variables which should have the linear average values for the variables from the dry air parcel and the cloudy parcel. This method gives support to penetrative downdrafts, but also allows mixing from any side of the cloud to be identified. Mixing within clouds can either occur homogeneously or inhomogeneously. Homogeneous mixing involves all drops experiencing the same process, as if the dry and moist air parcels are instantly mixed together, so evaporation occurs simultaneously for all droplets. Inhomogeneous mixing allows the droplets in the edge of the moist parcel to interact with the dry parcel first, thus only the dry/moist interface of droplets will experience evaporation. This therefore means the size distribution for inhomogeneously mixed parcels will remain the same, but with a reduced concentration. As opposed to the homogeneously mixed parcel which will have a reduction in size and concentration as evaporation takes place.

Parameterization Precipitation from clouds can also be parameterized so that a simplified relationship between the amount of water available in the cloud for precipitation, the liquid water content and the drop concentration can be formed. Kessler (1969) proposed the first parameterization as shown in equation 4:

dM = k(m − a) Equation 4 dt

Where: M is the precipitable water content m is the cloud water content k is the autoconversion rate a is the autoconversion threshold

This parameterization is very simplistic and only deals with the mass of water and no size resolution of droplets, so is only applicable for a highly monodispersed distribution. The linear relationship has an autoconversion threshold to cross otherwise no precipitation will form. Kessler assumed that the rate of autoconversion increases with cloud water content but is zero for some values below the threshold, Ghosh & Jonas (1998).

Another parameterization is by Berry (1968) and is .

dM m 2 = Equation 5 dt .0 0366N 60 5( + b ) mDb

Where: M is the precipitable water content m is the cloud water content Nb is the droplet number density at the cloud base Db is the droplet relative dispersion at cloud base, and is shown in equation 6. σ D = a Equation 6 b a

Where: σa is the standard deviation of the droplet radii ā is the mean.

This scheme includes a droplet number density function and dispersion function at cloud base, allowing for the initial distribution to effect how the precipitation is produced. A different autoconversion rate is predicted for maritime and continental clouds, typically for -3 -3 maritime clouds N b ~ 50cm , D b ~ 0.366 and for continental clouds N b ~ 2000cm , D b ~ 0.146, Ghosh & Jonas (1998).

Conclusion: The ‘warm’ rain process involves major mechanisms in cloud maintenance, with precipitation events reducing the clouds liquid water content. Precipitation events are highly dependent on the rate of condensation and coalescence that occurs, which depends on the amount of CCN available in the cloud. Beard & Ochs 1993 found that the growth of a few cloud droplets (1 per 10L) be coalescence with smaller droplets would explain the development of warm rain in 15-30 min. The CCN distribution is affected by location of the cloud, maritime or continental and the internal processes of the cloud. Overall cloud microphysics is a complex interactive problem that needs exploring. References:

Beard, K. V., 1976, Terminal velocity and shape of cloud and precipitation drops aloft, J.Atmos.Sci., 33 , 851-864.

Beard, K. V., & Ochs., H. T., 1992, Warm rain initiation: An overview of microphysical mechanisms, J.Appl.Meteorol., 32 , 608-625.

Berry, E. X., & Reinhardt, R. L., 1974, An analysis of cloud drop growth by collection: Part 1. Double distributions, J.Atmos.Sci., 31 , 1814-1824.

Brenguier, J. L., & Chaumat, L., 2001, Droplet spectra broadening in cumulus clouds. Part I: Broadening in adiabatic cores, J.Atmos.Sci, 58 , 628-641.

Feingold, G., Cotton, W. R., Kreidenweis, S. M., Davis, J. T., 1999, The impact of giant cloud condensation nuclei on drizzle formation in stratocumulus: Implications for cloud radiative properties, J.Atmos.Sci, 56 , 4100-4117.

Ghosh, S., & Jonas, P. R., 1998, On the application of the classic Kessler and Berry schemes in large eddy simulation models with a particular emphasis on cloud autoconversion, the onset time of precipitation and droplet evaporation, Ann.Geophysica, 16 , 628-637.

Kessler, E., 1969, On the distribution and continuity of water substance on atmospheric circulation, Meteorological Monograms, 10 , 84

Paluch, I. R., 1979, The entrainment mechanism in Colorado cumuli, J.Atmos.Sci , 36 , 2467- 2478

Shaw, R. A., Reade, W. C., Collins, L. R., Verlinde, J., 1998, Preferential concentration of cloud droplets by turbulence: Effects on early evolution of cumulus cloud droplet spectra, J.Atmos.Sci , 55 , 1965-1976.

Squires, P., 1958, Penetrative downdrafts in cumuli, Tellus , 3, 381-389.

Warner, J., 1977, Time variation of updraft and water content in small cumulus clouds, J.Atmos.Sci , 34 , 1306-1312.

Yum, S. S., & Hudson, J. G., Adiabatic predictions and observations of cloud droplet spectral broadness, Atmospheric Research, 73 , 203-223.