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Water in the atmosphere Water content of air mass water vapour Mass mixing ratio, x mass dry air ~ 10gkg1 1% Saturated vapour pressure, equilibrium over flat surface Rate of evaporation = rate of condensation svp is a function of T only Saturated vapour pressure Condensation vapour pressure Relative Humidity, R.H. 100% svp at same T Condensation when R.H.≥100% R.H. can increase by (i) increasing x, (ii) cooling air Cooling damp air • • • • • • Radiation loss Ascent (of air mass) Descent, through inversion Advection, over cool region Influx of cold dry air Convection radiation fog hill fog/cloud, fronts steam fog advection fog, har Arctic sea smoke cumulus clouds Warm Rain Process • • • • • Saturation Nucleation Growth by condensation Growth by accretion Rainfall Nucleation s.v.p. over curved surface > s.v.p. over flat surface svp r 1 2 1.2 109 exp 1 svp r RT r w For typical molecule, r~0.6nm, would need RH=740% (SS=640%) In atmosphere maximum SS observed is ~1% Condensation must be on particles with r~100nm Radius Name Conc. (cm-3) SS < 0.1 µm Aitken nuclei 10,000 1% 0.1 - 1 µm large nuclei 100 0.1% > 1 µm giant nuclei 1 0.01% Nucleation Hygroscopic nuclei Fewer water molecules in surface so lower evaporation rate svp r 1.2 109 Bm 1 3 svp r r Kohler curves Sizes of droplets Growth by Condensation To grow by dr require this much water dm w dV w 4 r 2 dr r dr dr 1 dm dt w 4 r 2 dt dr F D p 2 dt w 4 r wr Mass flux of water vapour diffusing through shell of radius n dm dp 2 F 4 n D dt dn Same flux through every shell, so integrate to find Δp r F dn F 1 p dp 2 4 D n 4 D r r Vapour pressure at droplet = svp (T) Vapour pressure in cloud = svp * RH p pcloud pdrop surface svp RH 1 svp SS dr D svp SS 1 dt w r Growth by condensation Terminal velocity of drops For laminar flow, at terminal velocity drag force=weight mg 6 rv 3 4 mg 3 r w g v 6 r 6 r v 2 w g 2 r 9 Growth by Collision/Accretion dm r1 r2 dt Continuous collection model v v w E 2 1 dr1 w 4 r r1 r2 dt 2 1 1 dr1 xs air E v1 dt 4w dr1 r1 dt collection efficiency v v x For large drops (>40µm) v1 r1 2{r1+r2} l 2 if r1 r2 and v1 v2 r2 v2 2 relative volume swept out per unit time r1 v1 liquid water content of cloud 2 s air E Arial view of convection cells Cloud streets