Presentation on theme: "4/29/20151 PHYS-575/CSI-655 Introduction to Atmospheric Physics and Chemistry Lecture Notes #6 Cloud Microphysics – Part 2 Overview of Clouds 1. Nucleation."— Presentation transcript:
4/29/20151 PHYS-575/CSI-655 Introduction to Atmospheric Physics and Chemistry Lecture Notes #6 Cloud Microphysics – Part 2 Overview of Clouds 1. Nucleation of Water Vapor 2. Warm Clouds 3. Water Content and Entrainment 4. Droplet Growth (Warm Clouds) 5. Microphysics of Cold Clouds 6. Artificial Modification of Clouds 7. Thunderstorm Electrification 8. Cloud and Precipitation Chemistry
4/29/20152 Cloud Condensation Nuclei (CCN) CCN are pre-existing atmospheric particles that come from a large variety of sources: Dust Volcanoes Factory smoke Fires and soot Sea Salt Di-methyl Sulfate (Phytoplankton) Abundance ranges from 10 3 -10 5 per cubic centimeter, larger over continents and urban areas. Two Types: Hydrophilic/Hydroscopic: water sticks readily Hydrophobic: repels water http://apollo.lsc.vsc.edu/classes/met130/notes/chapter6/ccn.html
4/29/20153 Aerosol Particle Sizes – Bi-modal Distributions http://www.defra.gov.uk/environment/airquality/aqs/air_measure/images/02.gif A bi-modal distribution of particle - Number density - Surface area (per unit volume) - Mass (per unit volume) All suggest that at least two kinds of processes are responsible for growth of aerosol particles from a small initial nucleus (drop embryo) to the final raindrop. Initially, a drop must be large enough to be stable before condensation can increase its size. But if the stable critical size is reached, then diffusion of water to the droplet will cause growth.
4/29/20154 4. Growth of Cloud Droplets (Warm Clouds) Stable droplets grow by both diffusion and coagulation. Diffusion growth requires that the latent energy release be conducted away from the droplet, otherwise the droplet will heat up and evaporate. So diffusion of mass inward must be balanced by outward diffusion of energy.
4/29/20155 Growth by Condensation - Continued Consider the radial flow of condensable gas across a spherical surface of radius x, centered upon the growing particle. The flux (cm -2 s -1 ) of particles across this surface is given by Fick’s (1 st ) Diffusion Law: Where D is the diffusion coefficient, and ρ v is the vapor density (or other condensable). The total inward flux is given by: The particle will grow due to this inward flow of particles at a rate: Integrate from the surface of the particle of radius r to infinity.
4/29/20156 Growth by Condensation - Continued Mass of particle of radius r: where ρ l = liquid density Ideal Gas Law for Vapor
4/29/20157 Growth by Condensation - Continued S = Supersaturation of the Vapor (expressed as a fraction) where
4/29/20158 Growth by Condensation - Continued For fixed values of G l and the super-saturation ratio S, dr/dt is inversely proportional to the radius of the growing drop. So the droplets grow by condensation initially increase in radius very rapidly, but their rate of growth diminishes with time. Growth by condensation alone is far to slow to produce raindrops in warm clouds.
4/29/20159 Growth by Condensation - Continued Growth by condensation alone is far to slow to produce raindrops in warm clouds.
4/29/201510 Growth rates starting from a range of initial nuclei sizes.
4/29/201511 Cloud Droplet size by Condensation vs. Observation Red: Observed Blue: Theory
4/29/201513 Terminal Fall Speeds of Water Droplets in Air Stoke’s Law: The viscous force on a falling particle of radius r is: The forces on a spherical drop of radius r, volume V’ and density ρ’ falling downward in background air of density ρ is: Gravity (down) = ρ’ V’ g Buoyancy (up) = ρ V’ g Drag Force (up)= F drag In steady balance: which gives: Where η is the viscosity of air. V is the fall (terminal) velocity.
4/29/201514 Terminal Fall Speeds of Water Droplets in Air Stokes’ Law: For cases where ρ’ (liquid) >> ρ (air), we can write: For example, at 1013 hPa, 20 o C: r = 10 μm v = 0.3 cm s -1 r = 20 μm v = 1.2 cm s -1 For r < 5 μm, the calculated v is generally about 10% accurate r > 5 μm, the v calculated with the above expression is an overestimate, because at those sizes the drops become non-spherical and the drag becomes much larger than that given by Stoke’s Law.
4/29/201515 Coagulation Growth: Collision and Coalescence Consider a collector drop of radius r 1 falling faster and overtaking a smaller drop of radius r 2. As they approach, the smaller drop will tend to follow a stream- line around the larger drop and thereby avoid collision.
4/29/201516 Coagulation Growth: Collision and Coalescence We define a Collision Efficiency E such that:
4/29/201517 Collision Coalescence Not all droplets that collide actually coalesce. This is due to a thin layer of air that can become trapped between the two drops and which causes the drops to bounce off of each other. This is similar to the bounce of water drops across a plane surface of water if they are incident at a shallow angle. But at a steep enough angle of collision the droplets will coalesce. Define Coalescence Efficiency = E’ Collection Efficiency E c = E E’
4/29/201518 Coagulation Growth: The Continuous Collection Model The rate of increase in the mass M of the collector drop due to collisions: Where w l is the LWC (Liquid Water Content) in kg m -3 of the cloud droplets which have radius r 2 and mass density ρ l. Droplet Mass: Assuming ν 1 >>v 2, and E c =E, then
4/29/201519 Coagulation Growth: The Continuous Collection Model Because: (1)v 1 increases with r (2)E increases with r Then dr 1 /dt increases with r. Droplet growth is an accelerating process. The larger they are, the faster they fall, and thus the faster they grow.
4/29/201520 Coagulation Growth: The Continuous Collection Model with Updraft w = updraft velocity. h = height above reference level Then: Assuming v 1 >>v 2, E c = E: r H = radius of collector drop at height H above reference level where radius is r o : If we assume w l is independent of h:
4/29/201521 Warm Precipitation Steps in the formation of raindrops: (1)Nucleation (2)Diffusive growth of drop embryo by molecular diffusion of water molecules to the nucleus. (3) Droplets fall, larger drops fall faster than small drops, leading to collisions and coalescence. (4) Thus the largest drops grow the fastest, and eventually fall to the ground. Homogeneous Nucleation: Cloud Condensation Nuclei (CCN) form from highly supersaturated water vapor that by chance form stable groupings of molecules. Heterogeneous Nucleation: Droplets grow on pre-existing nuclei, such as dust, salt, soot, ions, or other small solid particles.
4/29/201522 Statistical Distribution of Drop Sizes Particle Growth Models
4/29/201523 5. Microphysics of Cold Clouds If a cloud extends above (in altitude) the 0 o C level it is called a cold cloud. Water drops that exist in atmospheric temperatures < 0 o C are referred to as super-cooled droplets. A mixed cloud contains both liquid water droplets and ice particles. A cloud that contains only ice particles is said to be glaciated. A super-cooled droplet is unstable. For freezing to occur, enough molecules must come together to form a stable ice nucleus. Homogeneous nucleation: pure ice Heterogeneous nucleation: a freezing nucleus must be present.
4/29/201524 Ice Nucleation Laboratory measurements of condensation-freezing and deposition on a wide range of materials, the onset of ice nucleation occurs at higher temperatures under water-supersaturated conditions (so condensation-freezing is possible) than under water-subsaturated conditions.
4/29/201525 Ice Nucleus Concentrations Ice nucleus concentrations tend to be higher in the northern than southern hemispheres. However, ice nucleus concentrations can vary by several orders of magnitude over a few hours. On average, the number N of ice nuclei per liter of air active at temperature T tends to follow the empirical relationship ln N = a(T 1 – T) Where T 1 is the temperature at which one ice nucleus per liter is active. Thus the concentration of ice nuclei increases by a factor of 10 for ever 4 o C decrease in temperature. In urban air, the total concentration of aerosol is on the order of 10 8 liter -1 and only about one particle in 10 8 acts as an ice nucleus at -20 o C.
4/29/201529 Ice Multiplication or Ice Enhancements Ice crystals are fragile and fracture when they collide producing numerous ice “splinters.” When a supercooled droplet freezes in isolation it does so in two distinct stages: (1)First, almost instantaneously, a fine mesh of ice shoots through the droplet and freezes just enough water to raise the temperature to 0 o C. (2) More slowly, an ice shell forms over the surface and then thickens towards the middle. As the water freezes it expands and causes stresses that shatter the shell, throwing off numerous small ice splinters.
4/29/201530 Ice Development in Cumuliform Clouds
4/29/201531 Growth of Ice Particles http://www.cs.wisc.edu/~yoh/cellular/images/snowflakes.jpg http://www.its.caltech.edu/~atomic/snowcrystals/class/w040123b025.jpg
4/29/201532 A Guide to Snowflakes http://www.its.caltech.edu/~atomic/snowcrystals/class/class.htm