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Comparing Humidity by Altitude
Name: Charles
Status: N/A
Age: N/A
Location: N/A
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Date: N/A
Question:
Is there a way to compare humidity at a given
temperature at 5,000 feet with that at sea level?
Replies:
It depends on HOW you want to compare it. Weathermen generally
report "relative humidity," which is the partial pressure of water
vapor in the air divided by the maximum possible value at that
temperature. That maximum value depends only on the air temperature
and not on pressure or altitude, so 80% humidity at 5000 feet means
exactly the same partial pressure of water vapor as 80% humidity at
sea level for the same temperature.
That does not mean, however, that if a parcel of air at 80% humidity
at sea level were lifted to 5,000 feet its relative humidity would
remain at 80%. First of all, its total pressure would drop, so the
partial pressure of water vapor would be less than at sea level for
exactly the same mixture of air and water! Additionally, the
temperature would drop as well, because the air parcel will expand,
and the energy of expanding comes at the expense of thermal
energy. (Another way to think of this is that the potential energy
of the air increases when it rises, so conservation of energy
requires that its kinetic - that is, thermal - energy decreases by
the same amount.) Lowering the air temperature increases its
relative humidity for the same partial pressure of water vapor. In
general, the relative humidity of a parcel of air will increase as
the air rises, because the temperature effect outweighs the vapor
pressure effect.
A commonly reported humidity measure that depends only on the
partial pressure of water vapor is the dew point. If air masses at
sea level and 5,000 feet have the same dew point, they have the same
partial pressure of water vapor. Again, however, that does not mean
that a given mass of air holds the same amount of water vapor in
both cases, even if their temperatures are equal.
A sensible comparison of the humidity of two air masses would be the
ratio of water vapor pressure to air pressure, or the ratio of water
vapor mass to air mass. Meteorologists refer to this quantity as
the mixing ratio. It's hard to find mixing ratio measurements
unless you can find primary weather measurements (not usually
reported in newspapers). If you know the actual atmospheric
pressures at sea level and 5,000 feet (you can generally look this
up in a table; variations caused by weather conditions are really
tiny) and the relative humidities at both locations, AND if the air
temperature is the same in both places, then the relative humidity
divided by the air pressure is proportional to the mixing
ratio. The location with the highest ratio has the more water per
air. If the temperatures aren't the same, you could in principle
convert dew points to partial water vapor pressures and hence to
mixing ratios, but you'd need the table for converting dew points to
partial vapor pressures.
A nice tool for calculating and converting between these and other
measures of humidity can be found at
http://www.cactus2000.de/uk/unit/masshum.shtml
http://www.cactus2000.de/uk/unit/masshum.shtml.
Richard Barrans
Charles,
For a constant temperature, but a difference in air pressure,
the vapor pressure (absolute humidity) at 5,000 feet will be
lower than at the surface, simply because the air pressure is
lower (the partial pressure of all molecules would be less).
However, the saturation vapor pressure (which is dependent
solely on temperature) at 5,000 feet will be the
same as at the surface, if the temperature at the surface
and 5,000 feet is the same.
Relative humidity is the ratio of vapor pressure to saturation
vapor pressure. In the situation that you describe, the
relative humidity would be less at 5,000 feet than at the surface,
because the vapor pressure is less at 5,000 feet.
David R. Cook
Climate Research Section
Environmental Science Division
Argonne National Laboratory
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Update: June 2012
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