Precipitation  Hydrometer: Any product of condensation or sublimation of atmospheric water vapor, whether formed in the free atmosphere or at the earth’s surface, or blown by wind from the earth’s surface: cloud, haze, fog, mist, drizzle, rain, ice pellets, hail, snow, snow grains, ice crystals, virga, blowing spray, dew, frost, glaze, etc.  Precipitation: Liquid water or ice that falls to the earth’s surface.

 Virga: Liquid water or ice that falls towards but does not reach the earth’s surface.  Aerosols: Small, suspended particles in the atmosphere. Haze, smoke, fogs, dust, pollen grains, etc. Note: Clouds are usually not considered aerosols.

Processes that control the growth of precipitation.  1. Nucleation: Any process by which the phase change of a substance to a more condensed state (such as condensation, deposition, and freezing) is initiated about a particle (nucleus) or at a certain locus, or place. l Condensation nuclei, freezing nuclei.  2. Diffusion: Transport of a property through a medium. For precipitation growth, it is the movement of water vapor molecules toward an existing hydrometer.

 3. Collision: Two hydrometers striking each other and combining to form a larger hydrometer.

Nucleation  Of liquid droplets. l Homogeneous: Occurring in clean air, no impurities. Practically impossible. l Heterogeneous: Involves impurities in air. l Cloud Condensation Nuclei (CCN): A particle, either liquid or solid, upon which condensation of water vapor begins in the atmosphere.

 Number of CCNs of various sizes in the atmosphere.

 The smaller the size of the CCN, the greater the typical number found in the air. The number per unit volume, for nuclei greater than 0.2  m, can be related to the radius of the CCN by: where, n = number per volume, R = radius of particle, c = a constant dependant on total concentration of particles.

Curvature Effect  A curved liquid water surface (pure water droplet) requires more water molecules in vapor state around it to achieve saturation (balance) than a flat water surface.  If the air were saturated (with respect to a flat water surface), it would be unsaturated with respect to a curved surface and the droplet would evaporate until a saturated state (with respect to its curved surface) existed.

 The smaller the droplet, the greater the supersaturation (with respect to a flat surface) is required to keep the droplet from evaporating.

Solute Effect  Once an impurity, such as a salt particle, replaces a water molecule in the lattice structure of the droplet, the equilibrium vapor pressure (number of water vapor molecules required to surround the droplet to maintain equilibrium) decreases.  Therefore, the water droplet can maintain itself at a lower vapor pressure and grow when the vapor pressure increases.

 Assume an unsaturated volume of air contains cloud condensation nuclei of varying sizes.  The volume begins to cool and the relative humidity increases.  When the RH reaches near 78%, condensation begins on the majority of nuclei.  As the air cools further, RH increases. The CCNs containing the most salts grow fastest. They require the lowest vapor pressure to maintain equilibrium.

 As RH approaches 100%, the curvature effect becomes negligible for the larger nuclei but remains appreciable for smaller droplets.  As droplets grow, they remove water vapor from the air, which decreases RH.  But, continued cooling increases RH.  When particles are small, the cannot condense water vapor very rapidly.  As they grow larger, they become more efficient in removing water vapor.

 Eventually, water vapor is removed at the same rate it is being produced.  The smaller droplets are less efficient at removing vapor, due to curvature effect, and may actually decrease.  The larger droplets will continue to grow to become cloud droplets because the curvature effect is negligible.

Kohler Equation  Combination of Curvature and Solute Effect.  Ratio of actual saturation vapor pressure (in equilibrium over a solution with a curved surface), to vapor pressure over a flat pure water surface.

 Where, T = absolute temperature ( o K), R = drop radius (  m), i = number of ions per molecule in solution, m s = mass of solute in the droplet, M s = molecular weight of solute, c 1 = o K  m, c 2 = 4.3 X  m 3 g -1

Critical Radius, pg. 161  Peak of the Kohler curve for a particular CCN. For a particular RH, l at larger radii, droplet will grow; l at smaller radii, droplet will shrink. l If RH becomes greater than the peak of the Kohler curve, the droplets can grow unimpeded.

 Location of peak changes with solute mass changes. l For larger droplets, critical radius peak is at lower RH.

 Left of the peak on Kohler curve: l Small CNN grow into small droplets that stop growing at equilibrium state of humidity, temperature and solute. l Called haze droplets. l Can exist at RH < 100% l Aerosol swelling - e.g., wet haze droplets and smog.

 Right of the peak on Kohler curve: l CNNs are activated. l Continue to grow as long as water vapor is available. l Become cloud droplets.

 The radius of the droplet where the critical point occurs (i.e., whether it will grow- be activated or reach equilibrium and remain small) is given by: where: i (number of ions per molecule in solution) M s (molecular weight of solute) from table 8-1 T in o K

 The supersaturation fraction at this critical peak is given by: where: i (number of ions per molecule in solution) M s (molecular weight of solute) from table 8-1 T in o K m s = mass of solute in the droplet

Activated Nuclei  Those nuclei to the right of the Kohler peak can continue to grow as long as there is water vapor to condense onto the droplet.  The number density (number of activated cloud condensation nuclei per cubic meter) is approximately: where:  S is the supersaturation (eq. 8.3a)

 The number is small compared to the total number of particles in the air.  The distance between cloud droplets is given by:

Nucleation of Ice Crystals  Processes that aid in freezing of liquid water droplets: l Homogeneous freezing: When temperatures approach -40 o C, liquid water spontaneously freezes. Deposition nucleation: Water vapor deposits directly on ice crystals. Unlikely on particles of 0.1  m or less. l Immersion nucleation: Occurs for liquid droplets which contain an ice nucleus. Freezes when reaches a critical temperature below 0 o C, dependent on the size of the drop. See equation 8.8

 Condensation freezing: Occurs when the nuclei is more attractive as a condensation nuclei than as a deposition nuclei. Water condenses on the nucleus and immediately freezes.  Contact freezing: Supercooled liquid water droplet strikes an ice crystal and freezes on the ice crystal.  Ice Nuclei are substances with molecular structures similar to ice. Notice Table 8.2 and the temperatures at which certain ice nucleation processes can begin with various ice nuclei.

Droplet Growth by Diffusion (condensation and deposition)  Using eq. 8.9, the typical droplet size would have a radius of  m; typical cloud droplet sizes. Typical precipitation drops range from 500  m to 2000  m.  Some other process rather than just diffusion must be occurring to cause them to grow to precipitation size.

For Ice Crystal Growth by Diffusion  The type of ice crystal produced (habit) is dependant on the temperature and supersaturation existing at the time of formation. See figure 8.6  1-D crystals tend to gain mass faster than 2-D or 3-D

Wegener-Bergeron-Findeisen Process  At temperatures below 0 o C, the equilibrium vapor pressure over liquid water is greater than over an ice crystal.  Therefore, in a cloud of mixed liquid droplets and ice crystals, the ice crystal will tend to gain water molecules at the expense of the liquid droplet.  If relatively few ice crystals are present, they can grow large enough to precipitate by this process.  If they pass through air warmer than 0 o C, they can melt and arrive at the ground as rain.

Collision and Collection (Coalescence)  Only process for making precipitation size droplets in warm clouds.  As droplets fall, those with greater mass fall fastest and can collide with slower falling droplets. The droplet can thus grow by this method.  Droplets blown upward by updrafts can also collide and coalesce.  Not all colliding droplets coalesce. Apparently a charge difference on the droplets aids in coalescence.

Fall rate of droplets  Cloud droplets, aerosols R<40  m: where: k 1 = -1.19x10 8 /ms  Droplets R = 500 to 1000  m: where: k 2 = -220 m 1/2 /s  Drops R = 20 to 2,500  m: where the density correction factor, c, is: R o = 2500  m, R 1 = 1000  m, w 0 = 12 m/s

Precipitable Water  Depth of water resulting from all water (vapor, liquid, solid) precipitating from a column of unit cross-sectional area extending between two levels.  Total precipitable water extends the column from the surface to the “top of the atmosphere”.

 g = -9.8 m/s 2   liq = 1000 kg/m 3  Rainfall amounts at any particular location can be much greater than indicated because airflow advects moisture into the column during the precipitation process.  Pressure must be converted to base units.  r T must be in kg/kg.

Rainfall estimates by Radar  Z = radar reflectivity factor = the measure of the efficiency of a radar target in intercepting and returning radar energy.  Z is dependant on the size, shape, aspect, and the dielectric properties of the surface of the target.  It includes not only reflection, but also scattering and diffraction.

 For hydrometers, it is dependant on drop-size distribution, number of particles per unit volume, physical state of hydrometers (ice or water), shapes of the individual elements of the group, if asymmetrical, their aspect to the radar.  One simplified expression is: where: D = droplet diameter, V = volume.  This is a meteorologically defined expression relating to droplet sizes.

 A more complex, but accurate expression is: where, N(D) = number concentration of size D droplets per volume interval: where:  is mean droplet size  N o is number of particles per unit volume.

 A radar expression is given as: The radar reflectivity factor, Z, is usually expressed in terms of decibels where:

Z-RR (rainfall rate)  A unique relationship between Z and RR does not actually exist (has not been determined).  Stull uses: where, c = mm/hr  National Weather Service Doppler radars use the following as an average expression for various forms of expected precipitation: R is in mm/hr

 For drizzle: For thunderstorms: For snow: For hail: varies from:

 Problems:  N1 (b, d, f), N2(b, d, f), N5 (c, h), N7 (c, h), N9 (d, e), N10, N11 (d, f, h), N16, N18 ( a, c, d, f), N21 (a), N23.  SHOW ALL EQUATIONS USED AND CALCULATIONS