Snowfall

Snowfall is associated with colder climates and regions where people are accustomed to accumulation.  Even though there may be freezing temperatures at high altitudes, it is not uncommon for snow to fall and change its phase from solid to liquid before reaching the ground.

Water droplets and ice crystals forming in clouds are subjected to gravitational forces and fall, however the particles are small enough that they do not fall fast.  Clouds maintain altitudes from air currents, temperatures, densities, and pressures.  Precipitation occurs when particles collide and form bonds.  This creates larger and larger particles until they descend.  Snowfall will often transform from a solid state to a gaseous state, known as sublimation, and back to a solid state several times on its way to the ground.

Snow can also change its pattern several times on its way to the ground.  Patterns can change from columns to plates to crystals, and back.  Snow continually changes its pattern because atmospheric conditions change from the formation phase of snow until it reaches the ground.

This rimmed snowflake is evidence of the collisions made by snowflakes on their path to the ground.  It is riddled with rime, or ice crystals, that form when the snow collides and bonds to water particles on its path through the air.

The path a snow particle takes to the ground can be simple or complex.  A simple path would be a particle that is formed and falls in a straight vertical line with a constant velocity to the ground.  A complex path would be snow that is formed and follows an inconsistent path in the vertical and horizontal direction while undergoing accelerations and decelerations.   (Though after considering the real world probability of occurrence, the simple path is probably more complex and unique than a seemingly randomly altering path.)

The best snowfall to consider is the most simple, which is snow that falls at a constant velocity from an initial height to a final height to the ground.  Kinematics can produce the time taken for a particle to move from a cloud at ten thousand feet to the ground, at a constant velocity of one foot per second.

t = (d/v), where t = time, d = distance, and v = velocity.

We get 10,000 seconds, or under three hours, for a particle to fall from the cloud to the ground.  This is reasonable given that “a snow crystal can spend a few minutes to five or six hours in the air.”8  Given the time a particle can spend in the air, it’s possible for a particle to travel great horizontal distances with velocity in the horizontal direction.  It is safe to conclude that it is possible for a snowflake to reach the ground after all clouds have passed and the sky has become clear.

The velocity of a snowflake is determined through F = ma = D - Fg.  This is where F = force, m = mass of the snowflake, a = acceleration of the snowflake, D = the drag acting on the snowflake and Fg = the gravitational force.  We can find the terminal velocity of a snowflake when the acceleration of the snowflake becomes zero.  We then get D = Fg.  The drag is known by

D = (1/2)CρAv2 , where C = drag coefficient, ρ =
the density of air, A = the cross section of the snowflake.  “v” will be the terminal velocity.9

Physics and energy explain the transformations undergone by snow in the cloud, during its fall, and on the ground.  The particles gain gravitational potential energy as they increase in altitude and mass.  When snow falls, the gravitational energy is transformed into kinetic energy and thermal energy.  This describes sublimation during free fall.  Energy is not just transformed into thermal energy but it is also transformed by other forces from interactions with its environment.  Snow has to collide enough times to maintain a large enough mass and to possess enough energy to reach the ground.  The accumulation of snow begins a new interaction with the environment.

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