# Measures of Water Vapor

Water vapor is a gas. Its presence in the atmosphere can be expressed in a number of ways.

Mixing ratio (or specific humidity) -- a measure of the amount of water vapor in terms of the number of grams of water vapor in a kilogram parcel of dry air. The conventional unit is g/kg.

There is a relationship between dew point temperature and water vapor that can be established experimentally or computationally. The approximate computational/experimental results are summarized in the table below, which shows the amount of water vapor held in a kilogram air parcel having various dew point temperatures. You don't have to know these amounts, but do need to consider the implications. The nature of the information in this table relates to a common rule of thumb, namely that "warm air can 'hold' more water vapor than cold air, at a given pressure". Maps of dew point temperature, then, indirectly give us information about the amount of water vapor actually present at a given level.

There is also a relationship between dew point temperature and precipitable water. The general nature of the relationship in both cases is that the dew point temperature is directly proportional to the amount of water vapor present in the atmosphere.

 Air Parcel Dew Point Temperature (oC) Air Parcel Dew Point Temperature (oF) Amount of Water Vapor (g) in a dry Air Parcel (kg) 0 32 4 10 ~50 8 20 ~68 16 30 ~86 32

Precipitable Water -- the total atmospheric water vapor contained in a vertical column of air of unit cross-sectional area extending between the ground and the top of the troposphere, commonly expressed in terms of the height to which that water substance would stand if completely condensed and collected in a vessel of the same unit cross section. The conventional unit is cm or inches.

Vapor pressure -- a measure of the amount of water vapor as a function of its contribution to the total atmospheric pressure. This contribution is the partial pressure of water vapor. The conventional unit is millibars or kilopascals.

## Relative Humidity

One interesting and extremely useful property of the dew point temperature is that it will always be an indication of the actual amount of water vapor present in each kilogram air parcel. For example, if the actual temperature is 20C and the dew point is 0C, then we know that the air would have to be cooled 20C in order for condensation to occur.

This brings up an interesting concept. Suppose we know that the temperature is 30C (86F) but the dew point temperature is 20C (68F). Then we know that if we could somehow increase the amount of water vapor in that air parcel to potentially what would be present if the dew point temperature were 30C (86F), then it would have a mixing ratio of 32 g/kg. In fact, we could view the table above as a table showing the MAXIMUM amount of water vapor an air parcel could have.

So, in this example, in which the temperature is 30C and the dew point is 20C, we could say that the air parcel holds 16/32 or 0.5 or 50% of the amount of water vapor it would hold if the dew point temperature for this case were raised to the maximum possible (which is the actual temperature, never higher). When the temperature and dew point temperature are the same, meteorologists refer to this as a "saturated" state.

Meteorologists call this the "relative humidity" and the formula for it is:

Relative Humidity (RH) =( Mixing Ratio/Saturation Mixing Ratio) X 100

where RH is expressed as a percentage, mixing ratio is obtained from a table like the one above and is set by the dew point temperature, and saturation mixing ratio is obtained from a table like the one above and is set by the actual temperature. By the way, the mixing ratios in the right hand column in the table below are liberally rounded and are not exact values. Also, this table only works approximately at 1000 mb, since mixing ratios vary strongly with pressure.

 Air Parcel Dew Point Temperature (oC) Amount of Water Vapor (g) in a dry Air Parcel (kg) 0 4 5 6 10 8 15 12 20 16 25 24 30 32 35 48

We'll examine this concept in more detail in a class demonstration. But the table is useful. For example, suppose the temperature is 25C and the dew point is 10C. This dew point temperature corresponds to the actual mixing ratio of 8 g/kg, while the actual temperature corresponds to the maximum amount of water vapor that an air parcel of that temperature could hold, which is 24 g/kg. Using the formula above, then the RH = (8/24) X 100, or 33%. In other words, for these conditions, the air parcel holds about 1/3 of the water vapor it would hold at saturation. To prove that, just keep the dew point temperature constant, and assume that some process cools the air to 10C, the same as the dew point. Then the RH = 8/8 X 100 or 100%.

The diagram below is based upon an incorrect concept (the air parcel does not change size, nor is the water vapor clumped in one area). But the diagram tries to express the concept by showing the water vapor determined by experiment for a given dew point staying constant, but the "capacity" of the air parcel to contain more water vapor indicated by the size of the yellow parcel. At an RH of 100% meteorologists say that the atmosphere is "saturated" and water vapor molecules to condense as water droplets, evidenced by the formation of a cloud at the level where this is occurring.