Jon Ahlquist 10 5 2006 Chapter 7 Precipitation The size of cloud droplets and raindrops Increased saturation vapor pressure around a curved surface curvature effect Terminal velocity of droplets of various sizes Growth of cloud droplets to rain drops by collisioncoalescence Formation of ice in the atmosphere Growth of ice crystals via the ice crystal process Rain from ice Ice different shapes at different temperatures Measuring precipitation How Do Cloud Droplets Grow p 164 Formation of raindrops from cloud droplets is complex Typical condensation nucleus 0 2 micrometers Typical cloud droplet 20 micrometers Typical rain droplet 2000 micrometers 2 mm See fig 7 1 p 164 Rain droplet radius is about 100 times greater than cloud droplet radius so volume is about 100x100x100 1 million times greater How can cloud droplets become raindrops with a million times the volume in a few tens of minutes We ll see they grow not by continued condensation but by many small droplets merging to form a rain drop First we ll consider small droplets Saturation around a cloud droplet Compare the number of neighboring molecules for a molecule on a flat surface versus the number of neighbors when the surface is curved Figure below not in textbook Precipitation p 164 column 1 Is it ever too cold to snow No but little snow when it is very cold for 2 reasons Capacity for water vapor is small at low temperatures so even saturated air can condense little moisture Coldest temperatures occur when skies are clear Clouds are greenhouse blankets Is it ever too warm to snow Snow flakes possible with surface temperature at 50 F See p 177 Precipitation any form of water solid or liquid that falls from a cloud and reaches the ground including rain drizzle sleet snow snow grains snow pellets ice pellets and hail Precip types on pp 174 184 Saturation around a cloud droplet Curvature effect water evaporates more easily from a tiny droplet than from a flat surface because a molecule on the surface of a droplet has fewer neighboring water molecules in the liquid to hold it See next slide Thus saturation vapor pressure is higher around tiny cloud droplets than over pan of water Note the larger number of water molecules shown in red around the droplet than above the flat water surface The difference is exaggerated Fig 7 2 p 165 Red balls indicate water vapor molecules More exist around curved cloud droplet than over flat surface at saturation Saturation around a droplet p 165 Saturation vapor pressure is largest for smallest droplets Droplets 1 m or larger behave almost like flat surface Fig 7 3 p 165 Light blue circle represents water molecule on surface Light blue rectangle represents water with a flat surface MET1010 Intro to the Atmosphere Extra neighbors for flat surface Tiny spherical water droplet if relative humidity is above saturation vapor pressure line va po rp res su re ab ov e if relative humidity is below saturation vapor pressure line Sa t 1 Jon Ahlquist 10 5 2006 Wettable vs unwettable hydrophobic condensation nuclei Imagine wettable and unwettable condensation nuclei side by side Suppose that roughly the same amount of water condenses on each one Condensation on unwettable nucleus has small diameter Condensation on wettable nucleus has large diameter Some substances like salt NaCl are hygroscopic i e water can condense on them at less than 100 relative humidity Here is why When water condenses onto hygroscopic material the hygroscopic material dissolves forming a solution like salt water The molecules in the solution like salt ions Na and Cl bind closely with water inhibiting evaporation Known as solute effect Curvature effect which raises humidity needed for condensation and solute effect which lowers humidity needed for condensation roughly cancel each other Most condensation in the air occurs around 100 relative humidity Terminal velocity of a person Condensation drop on unwettable nucleus has small diameter High sat vapor pressure more evap Condensation spreads over entire wettable nucleus large diam Lower sat vapor pressure less evap Solute Effect p 165 column 1 Therefore In the troposphere the terminal velocity of a person without a parachute is about 100 mph In 1960 US Air Force Capt Joseph Kittinger jumped out of a balloon at 102 000 feet with parachute Because air is so thin at that altitude he reached about 600 mph before his parachute slowed him See http hypertextbook com facts JianHuang shtml In 1972 a DC 9 over Czechoslovakia exploded at 33 360 feet from a Croat terrorist bomb Yugoslav stewardess Vesna Vulovic strapped in her seat survived the plane s fall onto a snow covered mountainside She was the only survivor She fractured skull broke 3 vertebra both legs was in coma for 3 days temporarily paralyzed from waist down but made full recovery MET1010 Intro to the Atmosphere Condensation on a large diameter wettable nucleus evaporates less easily than from a tiny droplet on an unwettable hydrophobic nucleus because of less curvature Analogy to cultured pearls Cultured pearls are made by inserting a spherical seed made from shell into an oyster The seed is almost as big as the desired pearl The oyster does not have to deposit much onto the seed to produce what appears to be a large pearl If water condenses onto a large wettable condensation nucleus it appears to be a large droplet which does not evaporate as easily because its surface is flatter How fast does a water droplet fall Terminal velocity p 166 Terminal velocity maximum speed of falling body Force of gravity downward balances air resistance up drops fall faster than smaller drops Terminal velocity Table 7 1 p 166 Larger Condensation nucleus 0 2 um essentially 0 m s droplet 20 um 0 01 m s 1 cm s Small rain droplet 1 mm 4 m s Cloud Similar principle for things that rise buoyantly e g a weather balloon rises at its terminal velocity Its upward buoyancy force is balanced by air resistance so it rises at a steady rate Forming a rain drop in a cloud without ice Falling droplets collide pp 166 167 Larger droplets fall faster and collide with smaller droplets If there is big difference between size of falling droplet and droplet it nears small droplet may be swept to the side not collide Just as not every bug in front of your car hits the windshield A few of the droplets that are swept to the side swirl back in the big droplet s wake hit it on the back Example Of 100 droplets in the path of a bigger droplet 80 may hit it directly and 20 are
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