## Section4.1Measuring and reporting water content

NOAA Jetstream: https://www.weather.gov/jetstream/hydro

The H$$_{2}$$O abundance is spatially and temporally variable and Earth's clouds are made of ice and/or liquid water. As an abundant and condensible (as a solid or liquid) species, the behavior of H$$_{2}$$O is of central importance for energy transfer, weather, and surface climate. Water vapor is also the dominant greenhouse gas in the Earth's atmosphere.

It is important to note that water vapor exists in the atmosphere as a molecular gas, just like N$$_2\text{,}$$ O$$_2\text{,}$$ and CO$$_2\text{.}$$ A common misconception is to think of water vapor in the atmosphere as tiny suspended liquid droplets. This misconception is understandable, given that water does readily change between different phases (solid, liquid, and gas), and can precipitate out of the gas to form droplets. To repeat: water vapor exists in the atmosphere as a molecular gas, just like N$$_2\text{,}$$ O$$_2\text{,}$$ and CO$$_2\text{.}$$

There are a number of different ways of expressing the water content of the atmosphere:

• mixing ratio (specific humidity): mass of water relative to the mass of all other molecules in given volume of air (for example, grams water vapor per kilogram dry air)

• absolute humidity: mass of water per unit volume of air (for example, grams of water vapor per cubic volume of air)

• vapor pressure: the pressure exerted by water vapor molecules in the air, expressed in units of pressure (mb or inches Hg)

• saturation vapor pressure: vapor pressure exerted by water vapor in equilibrium with liquid water (pressure exerted at saturation); expressed in units of pressure (mb or inches Hg). At equilibrium saturation, the rate of evaporation equals the rate of condensation.

• relative humidity: a measure of how close the water vapor pressure in the air is to the saturation vapor pressure at that temperature. Relative humidity = (actual vapor pressure)/(saturation vapor pressure)x100%

• dewpoint: the temperature to which air must be cooled to become saturated. The dew point is a measure of the actual water vapor content of the air

Another common misconception (or perception) is that humid air is "heavier" than dry air. In fact, for a given volume humid air weighs less than dry air (and will thus tend to be more buoyant). As we shall see, this behavior plays an important role in cloud formation and convective storm systems.

If temperature is 81 F (36.13 mbar vapor pressure) and dewpoint is 70 F (25.04 mbar vapor pressure), what is the relative humidity? Answer.
Note that the dewpoint temperature indicates the "actual" water abundance: the water vapor pressure is 25.04 mbar. However, air at 81 F has a water vapor pressure of 36.13 mbar (in other words, that is how much water air can "hold" before condensation occurs). We can therefore calculate the relative humidity by the expression: $$\phi=\frac{25.04}{36.13}\times100=69\%$$
Assuming the same air as Example 4.1.1 and a surface pressure of 1 bar (1000 mbar), what is the absolute humidity of water? Answer.
By comparing the water vapor pressure to the total pressure (25.04/1000), we see that water molecules make up about 2.5% of the air. From the ideal gas law (PV=nRT), we can estimate that air contains about 40 moles of gas per cubic meter. So per cubic meter of air, there is $$2.5\% \times 40 = 1$$ mole of water. Because 1 mole of water has a mass of 18 grams, this also gives us the absolute humidity: 18 g H$$_2$$O / m$$^3\text{.}$$
Assuming the same air as Example 4.1.1 what is the specific humidity of water? Note that dry air has an average molecular weight of 29 grams per mole. Answer.
As indicated in the answer to Example 4.1.3, each cubic meter of air contains about 40 moles of gas, and we also found that there is 1 mole of water per cubic meter. So we have 39 moles of "dry" air per cubic meter. The weight of this air is $$39 \textrm{ moles} \times 29 \textrm{ grams/mol}=1131 \textrm{ g}\text{.}$$ In other words, there is about 1.13 kg of dry air and 18 g of water vapor per cubic meter. So the specific humidity is $$18 \textrm{ g}/ 1.13 \textrm{ kg} = 15.9$$ grams of water per kilogram of dry air.

Throughout ENVR 202, we will typically adopt the approach of using the saturation vapor pressure for considerations of humidity and condensation. As we will see, there are a number of practical advantages to this approach:

• the water content (in mbar) can be readily found from the dewpoint temperature, which is widely reported by weather stations and in forecasts

• comparison of the saturation vapor pressure at the dewpoint with that of the current air temperature provides one of the simplest methods for calculating relative humidity

• the consideration of the saturation vapor pressure can be used to determine the lifting condensation level (the altitude at which clouds will begin to form)