Extra Credit #5: Tucson Relative Humidity; Due Mar. 29, 2000

The figure in the lower left hand column the hand-out on Monday, Mar.
20, 2000 illustrates how the saturation mixing ratio changes with air
temperature.  The table on the right hand side contains the same data.
Use this table to make a graph on your own like the one on the left
hand side.  Then, for two days, obtain the air temperature and dew
point temperature from any source for Tucson in the morning, about noon
and in the late afternoon.  Using this data and the plot you made,
calculate the relative humidity at each of the three times.  The
example below should help in the steps of the calculations.

Example:
At 2:18 on Tuesday, Oct. 19, 1999 the air temperature was 30 C and the
dew point was -3 C.  The equation for relative humidity is 
RH = actual mixing ratio/saturation mixing ratio * 100%

The saturation mixing ratio depends upon the air temperature and
the plot we made shows how they are related.  Looking at the plot we
see that for an air temperature of 30 C, there would be 26.5
grams of water vapor per kilogram of air if it was saturated.  So,
saturation mixing ratio(T=30 C)=26.5 g/kg.

The dew point is the temperature to which the air must be cooled in
order to start forming dew and thus achieve saturation with the current
amount of water vapor.  In other words, if the air temperature was
equal to the dew point, the air would be saturated.  So, we can also
use the plot we made to estimate the actual amount of water in the air
or the actual mixing ratio if we know the dew point.  Using the dew
point temperature of -3 C, we see from the plot that the air would have
about 3.0 grams of water per kilogram of air if the air was saturated
at a temperature of 26 F.  So, the second piece of the puzzle is actual
mixing ratio = 3.0 g/kg.

Now we can compute the RH for this time.

RH = actual mixing ratio/saturation mixing ratio * 100%
   = (3.0 g/kg)/(26.5 g/kg) * 100%
   = 11 %