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Name: Charles
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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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