G. McFiggans et al. Aerosol effects on warm cloud activation 2597 1.004 1 1.002 1001 50nmNH小28O4 097 200 nm(NH ).so 20m:A H2so4 50% insol 200 nm NacL. 50% insol 0.95 0° Droplet Diameter um Fig 3. Activation curves for a range of dry diameter of salt((NH4)2SO4-solid, NaCI-dashed) particles (red, green and blue curves)and for 200 nm particles containing 50% by mass insoluble core(magenta) reached. As more particles activate and grow, they will com- altitude with the maximum just above cloud base. Numer- te for available water vapour. The water supersaturation ous implementations of simple adiabatic cloud parcel mod- will continue to rise above cloud base but will slow as grow- els exist which describe heat transfer and mass transfer of g droplets scavenge the water vapour and relatively fewer water vapour between an adiabatically cooling air parcel and additional (smaller) aerosol particles will activate. When the aerosol/droplet population based on fundamental thermo- supersaturation sources and sinks balance, the peak super- dynamic principles(see Howell, 1949, Mordy, 1959, Prup- saturation is reached - usually within a few 10s of metres pacher and Klett, 1997; Seinfeld and Pandis, 1998 above cloud base. Following this point, the growing droplet Figure 4 demonstrates the predicted behaviour of an ide- population will lead to a reduction in supersaturation. No alised lognormal(NH4) SO4 aerosol population with height new particles will activate and the most recently activated above cloud base at an updraught velocity of 0.5 ms-using droplets may evaporate. Some particles will not have suf- such a model. It clearly shows how the droplets activated ficient time to reach their critical radius even though their from the larger classes of aerosol continue to grow above critical supersaturation is reached. This results from water the supersaturation maximum at the expense of the smaller vapour scavenging by the larger droplets reducing supersatu- classes of activated particle which evaporate to below their ration to below the critical value of the smaller particles be- critical radius. The model uses the form of the Kohler equa- fore sufficient water vapour can condense(such kinetic limi- tion shown in Eq(1) tations are discussed further in Sect. 4). Only particles reach- Given this behaviour, it can be seen that both the number ing a certain size will survive and grow. Some of the largest of particles in a given size range and the gradient of the dis- particles may not actually activate, but may be large enough tribution in certain critical size ranges will determine its acti- to be considered as droplets since even at their subcritical vation behaviour moving into supersaturation. The Twomey sizes they will often be greater than 10 or 20 microns in ra-(1959)analytical solution to this problem dius, deplete water vapour, and even act as collector drops A pseudosteady-state or quasi-equilibrium is eventually =c(100s)ands=/4(7,P)m232)l/+ reached for a constant updraught velocity where the decrease kB(3/2,k/2) in saturation ratio by condensation to the droplet population and the increase in saturation ratio owing to the updraught where c is proportional to the CCN concentration at 1%su- maintains a broadly constant supersaturation with increasing persaturation, w is the updraught velocity, k is the slope parameter of the CCN size spectrum and N is the number www.atmos-chem-phys.net/6/2593/20 Atmos. Chem. Phys., 6, 2593-2649, 2006G. McFiggans et al.: Aerosol effects on warm cloud activation 2597 10−1 100 101 102 0.95 0.96 0.97 0.98 0.99 10−1 100 101 102 1 1.001 1.002 1.003 1.004 1.005 Droplet Diameter µm Saturation Ratio 50 nm (NH4 ) 2 SO4 50 nm NaCl 100 nm (NH4 ) 2 SO4 100 nm NaCl 200 nm (NH4 ) 2 SO4 200 nm NaCl 200 nm (NH4 ) 2 SO4 , 50% insol 200 nm NaCl, 50% insol Fig. 3. Activation curves for a range of dry diameter of salt ((NH4)2SO4 – solid, NaCl – dashed) particles (red, green and blue curves) and for 200 nm particles containing 50% by mass insoluble core (magenta). reached. As more particles activate and grow, they will com￾pete for available water vapour. The water supersaturation will continue to rise above cloud base but will slow as grow￾ing droplets scavenge the water vapour and relatively fewer additional (smaller) aerosol particles will activate. When supersaturation sources and sinks balance, the peak super￾saturation is reached - usually within a few 10’s of metres above cloud base. Following this point, the growing droplet population will lead to a reduction in supersaturation. No new particles will activate and the most recently activated droplets may evaporate. Some particles will not have suf- ficient time to reach their critical radius even though their critical supersaturation is reached. This results from water vapour scavenging by the larger droplets reducing supersatu￾ration to below the critical value of the smaller particles be￾fore sufficient water vapour can condense (such kinetic limi￾tations are discussed further in Sect. 4). Only particles reach￾ing a certain size will survive and grow. Some of the largest particles may not actually activate, but may be large enough to be considered as droplets since even at their subcritical sizes they will often be greater than 10 or 20 microns in ra￾dius, deplete water vapour, and even act as collector drops. A pseudo “steady-state” or quasi-equilibrium is eventually reached for a constant updraught velocity where the decrease in saturation ratio by condensation to the droplet population and the increase in saturation ratio owing to the updraught maintains a broadly constant supersaturation with increasing altitude with the maximum just above cloud base. Numer￾ous implementations of simple adiabatic cloud parcel mod￾els exist which describe heat transfer and mass transfer of water vapour between an adiabatically cooling air parcel and the aerosol/droplet population based on fundamental thermo￾dynamic principles (see Howell, 1949; Mordy, 1959; Prup￾pacher and Klett, 1997; Seinfeld and Pandis, 1998). Figure 4 demonstrates the predicted behaviour of an ide￾alised lognormal (NH4)2SO4 aerosol population with height above cloud base at an updraught velocity of 0.5 ms−1 using such a model. It clearly shows how the droplets activated from the larger classes of aerosol continue to grow above the supersaturation maximum at the expense of the smaller classes of activated particle which evaporate to below their critical radius. The model uses the form of the Kohler equa- ¨ tion shown in Eq. (1). Given this behaviour, it can be seen that both the number of particles in a given size range and the gradient of the dis￾tribution in certain critical size ranges will determine its acti￾vation behaviour moving into supersaturation. The Twomey (1959) analytical solution to this problem: N = c(100 + S ∗ ) k and S ∗ = A(T , P )w3/2 ckβ(3/2, k/2) !1/(k+2) (7) where c is proportional to the CCN concentration at 1% su￾persaturation, w is the updraught velocity, k is the slope parameter of the CCN size spectrum and N is the number www.atmos-chem-phys.net/6/2593/2006/ Atmos. Chem. Phys., 6, 2593–2649, 2006