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Geography 1001
Continuing Education
Name____________________________
Exercise 5
Humidity and Adiabatic Processes
Humidity. (see text Section 6.2) The amount of water vapor in the air is referred to as
humidity. The amount of water vapor that the air is capable of holding at any given time
is largely dependent on the temperature of the air. The following table shows the water
vapor capacity for air at various temperatures. As air temperature increases, air’s
capacity to hold water vapor also increases.
Temperature (°C)
0
5
10
15
20
25
30
Water Vapor Capacity (g/kg)
4.0
5.0
7.5
10.0
15.0
20.0
27.5
Specific humidity is the actual amount of water vapor in the air at a given time, stated in
grams/kg. Relative humidity is stated as a percent, and indicates the amount of water
vapor in the air compared to the air’s water vapor capacity.
The simple formula given below states the relationship between relative and specific
humidity:
Relative humidity = (specific humidity/water vapor capacity) * 100
Using this formula, and the information provided in the table above, answer the
following questions (show calculations):
1. Suppose that the air temperature is 15.0 °C, and the relative humidity is 50%.
a) What is the specific humidity? ______________________
b) If the air temperature falls to 10.0 °C without changing the specific humidity,
what would the relative humidity be?
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2. Assuming an air parcel has a specific humidity of 15.0 g/kg, what is the relative
humidity if the air temperature is 25°C?
3. What temperature would the air in question 2 need to be lowered to in order to
attain 100% relative humidity?
Adiabatic Cooling and Heating. (See text pp. Section 6.3.) If a parcel of air is forced to
ascend in altitude, it will expand with the lessened air pressure, and it will cool because
of the decrease in the number of molecular collisions between air molecules.
Alternatively, if the air parcel is forced to descend in altitude, it will be compressed with
the increasing air pressure, and it will warm because of the increased number of
molecular collisions. This is known as adiabatic cooling and heating. Upon lifting, the
air may cool to its dew point. If so, the air has reached 100% relative humidity and
therefore condensation occurs, clouds form, and with sufficient condensation some
form of precipitation will result.
If air is forced to rise but has not cooled to its dew point temperature, the air will cool at
a constant rate of about 10°C/1000m (5.5°F/1000 ft). This is known as the dry adiabatic
rate (DAR). If the rising air cools to its dew point temperature, condensation
commences; the air will continue to cool as it rises, but at a rate of about 6°C/1000m
(3.2°F/1000 ft). This is known as the moist adiabatic rate (MAR). The MAR is less than
the DAR because latent heat is released into the air during condensation.
If the air stops its forced ascent, adiabatic cooling will also cease, and there would be no
further condensation. If the air were forced to descend (e.g., on the leeward side of a
mountain range), the air would heat adiabatically at the dry adiabatic lapse rate of
10°C/1000m.
It is important not to confuse adiabatic cooling with the environmental lapse rate (ELR).
The environmental lapse rate is simply the decrease in temperature with altitude
through stratified air (air that is neither rising or descending) at a particular place and
time. For adiabatic cooling or heating to occur, air must be forced to rise or sink,
respectively.
Summary:
DAR = 10°C/1000m
MAR = 6°C/1000m
ELR varies depending on place and time. In the example below we will use 4.5°C/1000m
2
4. Figure 1 illustrates air that is being forced to rise as it crosses over a mountain
range. Assume that as the air rises and cools that it does not cool enough to
reach its dew point. Upon reaching the summit, the air is forced to descend
down the leeward side of the range.
Figure 1
Stratified Air
Rising Air
a) On Figure 1: Based on the adiabatic rates given on page 2, and assuming an
environmental lapse rate (ELR) of 4.5°C/1000m, calculate and fill in the
temperature (in °C) for the elevations shown for both the rising air, the
nearby stratified air, and for air that has descended on the leeward side of
the mountains
b) Figure 1: How does the temperature of the rising air at the summit compare
with the temperature of the adjacent stratified air at the same elevation?
Why is this so?
c) Figure 1: How does the temperature on the windward side at the base of the
mountain compare with the same elevation on the leeward side? Why is this
so?
Figure 2 shows air being forced to rise over the same mountain, except that the air does
cool to its dew point at 1300m, condensation occurs, and clouds form (note that
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precipitation is falling from the base of the clouds). The air continues its forced ascent
to the top of the summit and is then forced to descend on the leeward side.
Figure 2
Rising Air
5. Answer the following questions based on the Figure 2 diagram:
a) Calculate and fill in the temperatures (in °C) for the elevations indicated in
Figure 2.
b) At what temperature did the air reach its dew point (i.e., condensation
level)?
c) At the elevation where the dew point is reached and condensation begins,
what is the:
relative humidity? __________________%
approximate specific humidity? _______________g/kg
(estimate using the table from pg. 1)
d) At the summit, what is the approximate specific humidity?
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e) As the air crosses the summit and starts to descend on the leeward side,
cooling ceases and adiabatic warming begins. Relative humidity drops below
100% and condensation ceases. Assuming that no additional water vapor is
added or subtracted to the air as it descends, determine what the humidity
conditions are at the base of the mountain on the leeward side.
approximate specific humidity? ______________g/kg
relative humidity? ______________%
f) In terms of latent heat, briefly explain why the air is warmer at the base of
the leeward side of the range than it is at the same elevation on the
windward side of the range.
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