Lecture 11: Growth of Cloud Droplet in Warm Clouds Wallace and Hobbs Section 6.4

Processes for Cloud Droplet Growth How does this happen?? By: condensation collision/coalescence ice-crystal process today

Condensation & Collision Water Droplet Growth Condensation & Collision Condensational growth: diffusion of vapor to droplet Collisional growth: collision and coalescence (accretion, coagulation) between droplets PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

Water Droplet Growth - Collisions Droplets collide and coalesce (accrete, merge, coagulate) with other droplets. Collisions require different fall velocities between small and large droplets (ignoring turbulence and other non-gravitational forcing). Diffusional growth gives narrow size distribution. Turns out that it’s a highly non-linear process, only need 1 in 105 drops with r ~ 20 µm to get process rolling. How to get size differences? One possibility - mixing.   Homogeneous Mixing: time scale of drop evaporation/equilibrium much longer relative to mixing process. All drops quickly exposed to “entrained” dry air, and evaporate and reach a new equilibrium together. Dilution broadens small droplet spectrum, but can’t create large droplets. Inhomogeneous Mixing: time scale of drop evaporation/equilibrium much shorter than relative to turbulent mixing process. Small sub-volumes of cloud air have different levels of dilution. Reduction of droplet sizes in some sub-volumes, little change in others. Fig. from Bill Olsen PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

After a water droplet forms, it continues to grow by added condensation or sublimation directly onto the particle. This is the slower of the two methods and usually results in drizzle or very light rain or snow. Cloud particles collide and merge into a larger drop in the more rapid growth process.

Water Droplet Growth - Collisions Droplets collide and coalesce (accrete, merge, coagulate) with other droplets. Collisions governed primarily by different fall velocities between small and large droplets (ignoring turbulence and other non-gravitational forcing). Collisions enhanced as droplets grow and differential fall velocities increase. Not necessarily a very efficient process (requires relatively long times for large precipitation size drops to form). Rain drops are those large enough to fall out and survive trip to the ground without evaporating in lower/dryer layers of the atmosphere. concept Fig. from Bill Olsen PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

Collision/Coalescence Collision/Coalescence - cloud droplet growth by collision this is a dominant process for precipitation formation in warm clouds (tops warmer than about -15°C) some cloud droplets will grow large enough and will start to fall in the cloud -->> since the bigger drops fall faster than the smaller drops, they will "collect" the smaller drops - the bigger drop grows droplet fall speed is called its terminal velocity need droplets of different sizes for this process to really work Q: what determines the droplets fall speed relative to the ground??

Droplet Fall Speeds and Droplet Growth Q: what determines the droplets fall speed relative to the ground?? A: droplet size and updraft strength --> given a growing cu with an updraft strength of 4 ms-1: if the particle terminal velocity is -2 ms-1, the particles fall speed is: ANSWER if the particle terminal velocity is -4 ms-1, the particles fall speed is: ANSWER if the particle terminal velocity is -6 ms-1, the particles fall speed is: 2ms-2 0ms-1 2ms-1 downward

Life cycle of a droplet Growth by collision the drop initially forms in the updraft of the cloud near cloud base it grows in size by collisions since Vg = w + Vt Vg = ground relative fall speed of the drop w = updraft velocity Vt = drop's terminal velocity then the drop will begin to fall when Vt > w

Factors promoting growth by collision/coalescence Different drop sizes thicker clouds stronger updrafts consider a shallow stratus deck....

Droplet Growth in a Shallow Stratus Deck Often, drops will evaporate from shallow stratus before reaching the ground or you may get drizzle if they are large enough

QUESTION FOR THOUGHT: 1.  Why is a warm, tropical cumulus cloud more likely to produce precipitation than a cold, stratus cloud? 2.  Clouds that form over water are usually more efficient in producing precipitation than clouds that form over land. Why?

Water Droplet Growth - Collisional Growth Continuum collection: VT(R) R VT(r) (increases w/R, vs. condensation where dR/dt ~ 1/R) PHYS 622 - Clouds, spring ‘04, lect.4, Platnick PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

Water Droplet Growth - Collisional Growth Integrating over size distribution of small droplets, r, and keeping R+r terms : PHYS 622 - Clouds, spring ‘04, lect.4, Platnick PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

Water Droplet Growth - Collisional Growth Accounting for collection efficiency, E(R,r): If small droplet too small or too far center of collector drop, then capture won’t occur. • E is small for very small r/R, independent of R. • E increases with r/R up to r/R ~ 0.6 • For r/R > 0.6, difference is drop terminal velocities is very small. –drop interaction takes a long time, flow fields interact strongly and droplet can be deflected. –droplet falling behind collector drop can get drawn into the wake of the collector; “wake capture” can lead to E > 1 for r/R ≈ 1. PHYS 622 - Clouds, spring ‘04, lect.4, Platnick PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

Water Droplet Growth - Collisional Growth Collection Efficiency, E(R,r): ? ? R&Y, p. 130 PHYS 622 - Clouds, spring ‘04, lect.4, Platnick PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

Water Droplet Growth - Collisional Growth VT(R) VT(r) Terminal Velocity of Drops/Droplets: • differences in fall speed lead to conditions for capture. • terminal velocity condition: constant fall velocity VT where r is the drop radius rL is the density of liquid water g is the acceleration of gravity m is the dynamic viscosity is the Reynolds’ number. u is the drop velocity (relative to air) CD is the drag coefficient FD FG B. Olsen µ = dynamic viscosity of fluid PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

Water Droplet Growth - Collisional Growth Terminal Velocity Regimes: Low Re; Stokes’ Law: r < 30 mm High Re: 0.6 mm < r < 2 mm Intermediate Re: 40 mm < r < 0.6 mm k1 = 1.19 x 106 cm-1 s-1 B. Olsen PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

PHYS 622 - Clouds, spring ‘04, lect.4, Platnick air parcel droplets R&Y, p. 132-133 collector drop • Fig. 8.4: collision/coalescence process starts out slowly, but VT and E increase rapidly with drop size, and soon collision/coalescence outpaces condensation growth. • Fig. 8.6: – with increasing updraft speed, collector ascends to higher altitudes, and emerges as a larger raindrop. – see at higher altitudes, smaller drops; lower altitudes, larger drops. From Bill Olsen. PHYS 622 - Clouds, spring ‘04, lect.4, Platnick

Precipitation Growth in Cold Clouds - Warm versus Cold Clouds Our previous discussion regarding droplet growth by condensation and collisions is valid for warm clouds: warm clouds - have tops warmer than about 0°C comprised entirely of water

Collision Efficiency

Water Droplet Growth - Collisional Growth Approach: We begin with a continuum approach (small droplets are uniformly distributed, such that any volume of air - no matter how small - has a proportional amount of liquid water. A full stochastic equation is necessary for proper modeling (accounts for probabilities associated with the “fortunate few” large drops that dominate growth). Neither approach accounts for cloud inhomogeneities (regions of larger LWC) that appear important in “warm cloud” rain formation. PHYS 622 - Clouds, spring ‘04, lect.4, Platnick PHYS 622 - Clouds, spring ‘04, lect.4, Platnick