Kyoko Taniguchi Warm Rain Process The Warm Rain Process .

ATSC5210Kyoko TaniguchiWarm Rain ProcessThe warm rain process refers to the precipitation formation from warm clouds, whichinvolves no ice phase through the whole process. Therefore, the entire cloud is below thefreezing height all the time, unless cloud droplets are supercooled, so they remain in the liquidphase below the freezing temperature. This process is commonly observed in, but not limited to,tropical regions because of high moisture content. In fact, such a process has been reported invarious places (Fig. 1).Figure 1: Warm rain reported locations (dots) and area (shaded) (Alpert, 1955). Notice thatwarm rain is extended to outside of tropics.The warm rain process consists mainly of three steps; the activation of nuclei,condensational growth, and collectional growth. The first two steps are generally described withthe Köhler curve (Fig.2). The number and size of the activated nuclei are defined by the criticalsize (rc) on the curve. rc depends on supersaturation (S 1) and the droplet size spectrum. Atthe region of nuclei smaller than rc, condensation growth causes the supersaturationdisequilibrium, so that evaporation is promoted to regain the equilibrium. As a result, the dropletsize goes back to the original size. On the other hand, at the region of r rc, condensation alsocauses disequilibrium, but more condensation occurs to achieve the equilibrium. Accordingly,those activated nuclei grow spontaneously in theory. However, more than one growing droplettriggers competition of water vapor. In general, the mean size of droplets decreases as thenumber of the activated nuclei increases. Twomey proposed approximation analytical solutionof the maximum supersaturation and the mean droplet size with the power law assumption, whilewholeof both the suprsaturation curve and the size distribution spectrum can be calculated basedon the environmental conditions without approximation in models nowadays. In models,impacts of the environmental conditions, e.g. initial size distribution of CCN, updraft etc., to theevolution of the droplet spectrum can be examined. For instance, stronger updraft enhance theCCN activation.1

Figure 2: Köhler curve with (solid line) and without (dashed line) HNO3 (Kokkola et al, 2003).The peak radii and corresponding saturation ratio, i.e. critical radii (rc), and critical saturationratio (Sc), change with initial conditions.When condensation grows droplets large enough, they start falling due to the gravity pull.While they fall, they experience air resistance. The air resistance depends on the shape and sizeof the droplet, air motion, as well as height. The shape of falling drops have flattened rather thanspherical bottom due to the air pressure for r 200µm. Falling drops also have oscillation sincethey are not solid. In addition, air density decrease with height, so the aerodynamic effect ondrops becomes complicated. The equilibrium between these forces introduces the constantfalling velocity, the terminal velocity. To reach the ground, i.e. to be precipitation, terminalvelocity needs to exceed the updraft. The terminal velocity is a function of the ratio of surfacearea and mass. The general trend can be obtained with some simplification such as sphericalassumption (Fig3). As a rule, larger drops fall faster than smallers.The velocity difference causes collision of droplets. Two main results are expected fromthe collision; break-up and coalescence. The key dividing factors are contact angles, drop sizes,oscillation, electric charges and air viscosity. The possibilities are expressed by the coalescenceefficiency (Es) defined as the number of coalescences divided by the number of the collision.However, not all droplets on the cylindrical pass of larger droplet would collide due to theaerodynamic effect around the droplets; so the radius of the collision pass is smaller than theactual radius of the larger droplet. In addition, droplets may not collide even within the collisionpass because air trapped between the droplets acts as cushion, so the droplets do not touch eachother. The colliding possibility is expressed by the collision efficiency (Ec), defined as thenumber of collisions divided by the number of droplets in the volume swept out. The product ofthese two efficiencies indicates collection efficiency, which is related to the collectional growthof droplets. Hence, an accurate determination of Es and Ec is fundamental to estimate warm rainprocess precipitation. Based on the measurement, model and experimental data, Beard and Ochs(1984) developed the collision efficiency as a function of the droplet sizes (Fig.4). Scott2

examined coalescence growth through time with various droplet size spectra (1968). In hisresults, smaller droplets decrease with time, but do not disappear completely while larger dropconcentration increases. Therefore, the spectrum becomes wider and lower through time. Berryand Reinhardt investigated the formation of large drops using an initial bimodal size spectrumand found three principal collection steps: autovonversion, accretion, and large hydrometeor selfcollection (1974a). They also observed the same result using an initial unimodal size spectrum(Berry and Reinhardt, 1974b). They published these results along with a mathematicalexplanation (Berry and Reinhardt, 1974c) in a series of papers. Their studies indicate the natureof droplet growth; larger drop formation is preferable and the development rate depends on theshape of the initial spectrum.Figure 3: Terminal velocity at five pressurelevels in a summer atmosphere as functionof equivalent spherical diameter and thestandard curve for sea level, 1013mb(Beard, 1976).Figure 4: Semiempirical collectionefficiency as a function of large (R) andsmall (r) droplet radii (Beard and Ochs,1984)Those steps are certainly fundamental steps, but the real warm rain process containscomplications. Comparison studies of observation and theoretical model show significantdisagreements, e.g. the time length of the whole process. The instrumental uncertaintiesare always responsible for some disagreement, yet they do not provide an entirelysatisfactory explanation. In fact, the whole process takes more than hours according totheoretical calculation while observation data indicate a process occurring within 30minutes. The disagreements may be explained in several ways.One of the explanations is the presence of giant particles. In general, theatmospheric particles are classified into three classes based on size: small for r 0.1µm,large for 0.1 r 1µm, and giant for r 1µm. Especially for r 10µm, some people usethe term ultragiant. The origin of the giant or ultragiant CCN varies, and their existencesare recognized over various locations. Their concentration differs with time and space, butthe standard CCN distribution is exponentially decaying, so that they are relatively rarecompared to smaller size CCN. Measuring the giant CCN is challenging due to low3

concentration since the normal size CCN detection has hard time as well. The first echostudy is one of the useful methods and has been known for a long time. Although themethod is more actively employed to capture the warm rain process (e.g. Battan, 1953)because the strong reflectivity of water comparing to ice, this method can indicate thr giantparticles existence based on the fact that droplets with giant CCN have strong reflectivityon radar even in the early stage of cloud development because of their size. The impacts oftheir existence are crucial. Feingold et al capture that effect of ultragiant CCN on thecollection efficiency (1999). At the higher liquid water content (LWC) with low particledensity, the collection occur rapidly, so no difference can be seen, while ultragiant CCNexpedite collection at the lower LWC and higher particle density due to the Esimprovement. This effect is regardless of particle solvability.Another explanation is turbulence. Unlike the atmospheric molecules, aerosolparticles are inhomogeneously distributed because of the various densities of aerosols. Asclearly shown in Fig. 5 turbulence redistributes aerosols into the so-called preferentialconcentration, with lower particle density at stronger vorticity (Shaw et al, 1998). Thedegree of preferential concentration depends on the characteristics of both particles andturbulence, such as size. Therefore, droplet distribution within a cloud is highlyheterogeneous, which introduces various saturation state (S) locally, i.e. growth ratedeparts locally. Also, the temporally and spatially inconsistent distribution allows nucleiactivation and condensational growth above the cloud base, and total collection efficiencyincreases. This turbulence promotion on droplet growth is vital at the early evolution stageand the effect is proportional to the strength of turbulence (Riewer and Wexler, 2005),which can be measured with eddy dissipation rate.Figure 5: Results of Direct Numerical Simulation. (a) Random particle distribution(initial) and (b) particle distribution after several eddy turnover times (Shaw et al, 1998).Note that turbulence redistributed particles highly heterogeneously.In calculation of models, assumptions are always employed. The most universalassumption is adiabatic process. In the adiabatic process, the system does not interact with4

its surrounding, so some properties, such as total LWC and potential temperature in thiscase, are conserved. Unlike this assumption, observations indicate a non-adiabatic processand the degree of the adiabaticity decreases with the height from the cloud base (Brenguierand Chaumat, 2001; Cotton, 1975) shown in Fig.6. However, mixing with surrounding airreduces LWC, as well as Es, and decelerates the warm rain process as a result. In fact,warm rain associated with LWC 1.0g m-3 (Cotton, 1972). Therefore, mixing is anoteworthy process in the warm rain process.Figure 6: Observations data with height from cloud base (Cotton, 1975). Note that none ofthe observational values are adiabatic value, Q/Qa 1.0Figure 7: Calculated dropletconcentration as function of radius inhomogeneous (a) and inhomogeneousmixing (b). The Solid lines indicate theideal mixing at constant altitude with 15 C (Plauch and Knight, 1984).When the clear (S 1) and the cloudy (S 1) air meet, there are two extreme waysof mixing; homogeneous mixing and inhomogeneous mixing (Paluch and Knight, 1984).5