A very brief discourse on cloud microphysics ATM

A very brief discourse on cloud microphysics ATM 419 Spring 2016 Fovell 1

Condensed water species • • • Cloud droplets (qc) Rain drops (qr) Ice crystals (qi) Snow aggregates (qs) Graupel particles (qg) Hail (qh) 2

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Particle size distribution • Marshall and Palmer (1948) collected raindrops and plotted their frequency (number of drops ND) vs. drop diameter (D) and found an exponential relationship • N 0 is the intercept • l is the slope • qx is the area beneath the curve 6

Particle size distributions • exponential distribution (at left) • gamma distribution • log-normal distribution Moments • single moment (predict slope or intercept) • double moment (predict slope AND intercept or number concentration separately) At left: a single-moment distribution that fixes intercept, so slope varies inversely with total condensate mass 7

Collision and collection • the slope determines the average particle size • average particle size determines fall speed (along with density), and collision frequency with other particles. • results in accretion (see below) 8

Purdue-Lin scheme (originating at South Dakota) mp_scheme = 2 is based on Lin et al. (1983) • cloud water (free-floating) • cloud ice (free-floating) • snow (slowly falling) • rain (quickly falling) • graupel OR hail (moderately or very quickly falling), depending on particle size distribution configuration [Most schemes follow this one, somewhat or very closely] 9

Purdue-Lin • Exponential distributions are assumed for rain, snow and graupel The slopes are a function of particle density (rx) and mixing ratio (ls) 10

• Intercept is fixed, so as mixing ratio increases, total mass AND average particle size become larger • Fallspeeds increase as particle size increases • Fallspeeds also increase as air density decreases (i. e. , higher altitude) owing to less drag 11

A ‘typical’ particle interaction: RACS (rain accreting snow, producing graupel) - Each rain particle has a size-dependent fallspeed. Integrating over all diameters yields the mass-weighted average particle fallspeed UR - Ditto for each snow crystal, yielding US - The absolute difference is the encounter speed - The rest of equation comes from integrating over both size distributions - The end result benefits graupel or hail 12

• Production rates depend on many factors, such as encounter velocity, collision and collection efficiencies, relative particle sizes, particle concentrations (i. e. , size distribution assumptions), etc. . • There an enormous number of model “knobs” in a microphysics scheme, many or most of which have no true known value • Most microphysics schemes differ with respect to these assumptions. 13

Fovell and Ogura (1988) 14

Fovell et al. (2016) 15

Bu et al. (2014) Fovell et al. (2016) 16