Continuing last week's discussion, I now mention modification of the wet-bulb process considering melting and sublimation (change from solid to gas phase). Examination of the phase diagram of water :

indicates that sublimation is impossible for temperatures > .01 °C (32.02 °F). All melting occurs very near 0 °C (32 °F). Because supercooled water is common in our atmosphere, both sublimation and evaporation occur if temperatures are less than that, though supercooled water is very rare with temps < -40 °C (or °F). Saturation vapor pressure is shown on the diagram for specific temperatures along the evaporation and sublimation curves. An approximate relation for evaporation was provided last week :

Es = 6.112 e(17.67 T/(243.5 + T))    [1]

An approximate relation for sublimation (from Atmospheric Thermodynamics) is :

Es = 10(10.55 - 2667/Tk)    [2]

Last week's discussion dealt more with ideality and definitions than reality. Sure...we can define a wet-bulb process, dew point, and relative humidity, but how relevant is such for each real process considered ? Why does a person typically feel much cooler after exiting a swimming pool than after being soaked with sweat after strenuous exercise during a hot day ? You'll probably say 'the pool water was cooler', so the person's body is cooler to begin with. Yes, and each contains impurities (as does rain). During the (ideal) wet-bulb process, temperature on the wet-bulb begins as ambient air temperature (hopefully). Thus, using the wet-bulb equation :

Rw,R dR = - Tw,T (Cpd + R Cpv)/Lv dT    [3]

I could justify using averages between ambient and wet-bulb temperatures for R & L_v :

R = Rw + ((Cpd + R~ Cpv)/Lv)(Tw - T)    [4]

Our atmosphere is much more complicated. Similarly as for the swimming example, temperature of precipitation falling from clouds is often much less than air it is falling thru. Thus, when meteorologists use the wet-bulb temperature for estimating air temperature during rain, such is approximate. Observed temperature is often a few °C less - mainly because of cold downdrafts associated with precipitation, but also because the cold precipitation cools air via conduction, and because of the wet-bulb process. Considering the wet-bulb process only, latent heat transfer occurs at the temperature of precipitation. Thus, L_v is larger than for the ideal wet-bulb process, causing R_w - R to be less; meaning wet-bulb temperature is less. Such a difference is very small, typically only hundredths of a °C though. Using the example from last week, we may consider a 'wet-bulb process' because of precipitation rather than a psychrometer. Supposing precipitation temperature is 14.0 °C, [4] becomes :

.007791 = Rw + (1006.3 + R~(719.3))/2467600)(Tw -25.0)

My main reason for this discussion though is frozen precipitation, which includes snow. The real process for this is much different than ideal also. Snow falls from clouds, sometimes initially with a temperature significantly < 0 °C. Thus, sublimation can initially occur. It then may fall thru air with temperature > 0 °C. If air surrounding a snowflake is > 0 °C, melting must occur, but if not, then sublimation can continue. Such modeling has been done to great detail. Using the wet-bulb equation last week, I tabulated maximum temperatures for which wet-bulb temperature is 0 °C. This week I include melting also. For simplification, I consider melting and evaporation independently. During melting,

Cpd dT = - Lf dR    [5]

dT = - (333700)(.004249)/1006.0 = - 1.41

The new table is :

 P (mb)    T (°C)    T (°F)
 1050      10.20      50.4
 1000      10.71      51.3
  950      11.28      52.3
  900      11.90      53.4
  800      13.40      56.1
  700      15.32      59.6
  600      17.88      64.2