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Cloud Microphysics Condensation & Coalescence

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Cloud Microphysics Condensation & Coalescence 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.
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