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Cloud Microphysics Cloud microphysics Claudia Emde Meteorological Institute, LMU, Munich, Germany WS 2011/2012 Growth Precipitation Cloud modification Overview of cloud physics lecture Atmospheric thermodynamics gas laws, hydrostatic equation 1st law of thermodynamics moisture parameters adiabatic / pseudoadiabatic processes stability criteria / cloud formation Microphysics of warm clouds nucleation of water vapor by condensation growth of cloud droplets in warm clouds (condensation, fall speed of droplets, collection, coalescence) formation of rain, stochastical coalescence Microphysics of cold clouds homogeneous, heterogeneous, and contact nucleation concentration of ice particles in clouds crystal growth (from vapor phase, riming, aggregation) formation of precipitation, cloud modification Observation of cloud microphysical properties Parameterization of clouds in climate and NWP models Cloud microphysics December 15, 2011 2 / 30 Growth Precipitation Cloud modification Growth from the vapor phase in mixed-phase clouds mixed-phase cloud is dominated by super-cooled droplets air is close to saturated w.r.t. liquid water air is supersaturated w.r.t. ice Example ◦ T=-10 C, RHl ≈ 100%, RHi ≈ 110% ◦ T=-20 C, RHl ≈ 100%, RHi ≈ 121% )much greater supersaturations than in warm clouds In mixed-phase clouds, ice particles grow from vapor phase much more rapidly than droplets. Cloud microphysics December 15, 2011 3 / 30 Growth Precipitation Cloud modification Mass growth rate of an ice crystal diffusional growth of ice crystal similar to growth of droplet by condensation more complicated, mainly because ice crystals are not spherical )points of equal water vapor do not lie on a sphere centered on crystal dM = 4πCD (ρ (1) − ρ ) dt v vc Cloud microphysics December 15, 2011 4 / 30 P732951-Ch06.qxd 9/12/05 7:44 PM Page 240 240 Cloud Microphysics determined by the size and shape of the conductor. saturated vapor pressures over water and ice is a maxi- For a sphere, mum near this temperature. Consequently, ice crystals growing by vapor deposition in mixed clouds increase Ϫ Њ C ϭ ␲ in mass most rapidly at temperatures around 14 C. ␧ 4 r 0 The majority of ice particles in clouds are irregu- lar in shape (sometimes referred to as “junk” ice). ␧ ϫ where 0 is the permittivity of free space (8.85 This may be due, in part, to ice enhancement. 10Ϫ12 C 2 NϪ1 mϪ2). Combining the last two expres- However, laboratory studies show that under appro- sions, the mass growth rate of a spherical ice crystal priate conditions ice crystals that grow from the is given by vapor phase can assume a variety of regular shapes (or habits) that are either plate-like or column-like. The simplest plate-like crystals are plane hexagonal dM ϭ DC ␳ ϱ Ϫ ␳ ␧ [ v( ) vc] (6.36) dt 0 plates (Fig. 6.40a), and the simplest column-like Equation (6.36) is quite general and can be applied (a) to an arbitrarily shaped crystal of capacity C. Provided that the vapor pressure corresponding to ␳ ϱ v( ) is not too much greater than the saturation vapor pressure esi over a plane surface of ice, and the ice crystal is not too small, (6.36) can be written as (b) dM ϭ C ␧ GiSi (6.37) dt 0 where Si is the supersaturation (as a fraction) with ϱ Ϫ ͞ respect to ice, [e( ) esi] esi, and ϭ ␳ ϱ (c) Gi D v( ) (6.38) The variation of GiSi with temperature for the case of an ice crystal growing in air saturated with water is shown in Fig. 6.39. The product G S attains a Growth Precipitationi i Cloud modification maximum value at about Ϫ14 ЊC, which is due mainlyMass to the growthfact that the rate difference of an between ice crystal the (d) 4 ) 1 – 3 m 1 – Approximate form: (e) kg s 9 2 – dM = 4πCG S dt i i (10 i S i 1 G Maximum growth rate at about -14◦C 0 0 –10 –20 –30 –40 Fig. 6.40 Ice crystals grown from the vapor phase: (a) hexa- Temperature (°C) gonal plates, (b) column, (c) dendrite, and (d) sector plate. Figure from Wallace and Hobbs Fig. 6.39 Variation of GiSi [see Eq. (6.37)] with temperature [Photographs courtesy of Cloud and Aerosol Research Group, for an ice crystal growing in a water-saturated environment at University of Washington.] (e) Bullet rosette. [Photograph a total pressure of 1000 hPa. Cloud microphysics courtesy of DecemberA. Heymsfield.] 15, 2011 5 / 30 P732951-Ch03.qxd 9/12/05 7:41 PM Page 81 3.5 Water Vapor in Air 81 3.3 Can Air Be Saturated with Water Vapor?26 It is common to use phrases such as “the air is sat- cules between its liquid and vapor phases is urated with water vapor,”“the air can hold no (essentially) independent of the presence of air. more water vapor,” and “warm air can hold more Strictly speaking, the pressure exerted by water water vapor than cold air.” These phrases, which vapor that is in equilibrium with water at a given suggest that air absorbs water vapor, rather like a temperature is referred more appropriately to as sponge, are misleading. We have seen that the equilibrium vapor pressure rather than saturation total pressure exerted by a mixture of gases is vapor pressure at that temperature. However, the equal to the sum of the pressures that each gas latter term, and the terms “unsaturated air” and would exert if it alone occupied the total volume “saturated air,” provide a convenient shorthand of the mixture of gases (Dalton’s law of partial and are so deeply rooted that they will appear in pressures). Hence, the exchange of water mole- this book. to a plane surface of pure water at temperature T, and depend only on temperature. The variations with Ϫ the pressure es that is then exerted by the water vapor temperature of es and es esi are shown in Fig. 3.9, Ϫ is called the saturation vapor pressure over a plane where it can be seen that the magnitude of es esi surface of pure water at temperature T. reaches a peak value at about Ϫ12 °C. It follows Similarly, if the water in Fig. 3.8 were replaced by a Growththat if an ice particle is in water-saturatedPrecipitation air it will Cloud modification plane surface of pure ice at temperature T and the grow due to the deposition of water vapor upon it. rate of condensation of water vapor were equal to MassIn Section growth6.5.3 it is shown rate thatof this anphenomenon ice crystal the rate of evaporation of the ice, the pressure esi exerted by the water vapor would be the saturation vapor pressure over a plane surface of pure ice at T. Because, at any given temperature, the rate of evapo- 60 Ͼ ration from ice is less than from water, es(T) esi(T). The rate at which water molecules evaporate 50 from either water or ice increases with increasing 27 temperature. Consequently, both es and esi increase 40 Maximum growth rate at about with increasing temperature, and their magnitudes ◦ over pure water (hPa) -14 C s 0.28 e 30 0.24 ) es–esi difference between saturated · · · · · · 0.20 pressures over water and ice is · T, e · ·T, e s· · · · 20 0.16 maximal at this temperature · · · · · · es · · · (hPa) · · · 0.12 si · · e )ice crystals grow most rapidly · · · – · · · · 10 0.08 s · e Water Water 0.04 Saturation vapor pressure 0 0 (a) Unsaturated (b) Saturated –50 –40 –30 –20 –10 0 10 20 30 40 Temperature (°C) Fig. 3.8 A box (a) unsaturated and (b) saturated with respect to a plane surface of pure water at temperature T. Dots repre- Fig.Figure 3.9 fromVariations Wallace and Hobbswith temperature of the saturation (i.e., sent water molecules. Lengths of the arrows represent the equilibrium) vapor pressure es over a plane surface of pure relative rates of evaporation and condensation. The saturated Cloudwater microphysics (red line, scale at left) and the difference between es December 15, 2011 6 / 30 (i.e., equilibrium) vapor pressure over a plane surface of pure and the saturation vapor pressure over a plane surface of ice water at temperature T is es as indicated in (b). esi (blue line, scale at right). 26 For further discussion of this and some other common misconceptions related to meteorology see C. F. Bohren’s Clouds in a Glass of Beer, Wiley and Sons, New York, 1987. 27 As a rough rule of thumb, it is useful to bear in mind that the saturation vapor pressure roughly doubles for a 10 °C increase in temperature. Growth Precipitation Cloud modification Ice crystal shapes ice crystals in natural clouds have mostly irregular shapes partly due to ice enhancement under appropriate conditions, ice crystals that grow from vapor phase can have a variety of regular shapes/habits (e.g. plate-like, column-like) Figure from Libbrecht 2005 Cloud microphysics December 15, 2011 7 / 30 Growth Precipitation Cloud modification Morphology diagram Figure from Libbrecht 2005 Cloud microphysics December 15, 2011 8 / 30 P732951-Ch06.qxd 9/12/05 7:44 PM Page 241 6.5 Microphysics of Cold Clouds 241 Table 6.1 Variations in the basic habits of ice crystals with temperaturea Supersaturationb, c Between ice and Near to or greater than Temperature (ЊC) Basic habit water saturation water saturation 0 to Ϫ2.5 Plate-like Hexagonal plates Dendrites Ϫ1 to Ϫ2 ЊC Ϫ3 Transition Equiaxed Equiaxed Ϫ3.5 to Ϫ7.5 Column-like Columns Needles Ϫ4 to Ϫ6 ЊC Hollow columns Ϫ6 to Ϫ8 ЊC Ϫ8.5 Transition Equiaxed Equiaxed Ϫ9 to Ϫ40 Plate-like Plates and multiple habitsd Scrolls and sector plates Ϫ9 to Ϫ12 ЊC Dendrites Ϫ12 to Ϫ16 ЊC Sector plates Ϫ16 to Ϫ20 ЊC Ϫ40 to Ϫ60 Column-like Solid column rosettes below Ϫ41 ЊC Hollow column rosettes below Ϫ41 ЊC a From information provided by J.
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