Relative humidity

The relative humidity is the percentage of saturation of a specific volume of air at a specific temperature. The relative humidity of air depends on the temperature and the pressure of the air volume of interest. As the unit of relative humidity is percent it ranges between 0 (the air is completely dry) and 100% (the air is saturated).

Thus the mathematical definition is:  RH = 100 * E(Td) / E(T), with:

  RH =  relative humidity [%];

  E (Td) = saturation vapour pressure at dew point temperature Td (usually in g/(m^3));

  E (T) = saturation vapour pressure at (actual) air temperature T (usually in g/(m^3)).

The relative humidity describes how much water is carried by the air, and is an important factor to determine the development of clouds and precipitation

Relative humidity: ice clouds

Relative humidity is generally defined with respect to liquid water. In the higher atmosphere most clouds are only consisting of ice, making the traditional concept of relative humidity with respect to water inadequate for detecting cloud development.

The relative humidity with respect to ice indicates when air moisture freezes onto ice crystals, thus making ice clouds. As an example, at a typical temperature of -40° C at the 200 hPa level, a relative humidity of 70% (with respect to water), is already more than 100% relative humidity with respect to ice, indicating rapid development of ice clouds.You can use the relative humidity (ice clouds) whenever you are looking for ice clouds at high altitude flight levels or at lower levels down to the surface level, if the temperatures are cold enough that some ice crystals are present in the air. This temperature is theoretically 0 degrees or colder, but especially in non arctic climates or over snow/ice free surfaces colder temperatures than 0 degrees are necessary to form the initial ice crystals. 

Dew point

The dew point is the point at which dew starts to form on solid surfaces (that is for example the drops on grass that appear early in the morning). By definition it is the air temperature at which a specific volume of air (that has a constant pressure) condenses water vapour into liquid water at the same rate as it evaporates. This also means that the vapour pressure is equal to the saturation vapour pressure. If the relative humidity is 100%, the dew point temperature is the same as the air temperature and thus the air is saturated. If the temperature decreases, but the amount of water vapour stays constant, water will start to condensate. This condensed water is called dew as soon as it forms on a solid surface. Although the dew point is a temperature, it is still counted as part of the different humidity measures, which is why it was added to this page.

The dew point temperature calculation is based on the Magnus-Formula:

Magnus formula

T = air temperature [°C] ; E(T) = pressure [hPa] ; Td = dew point temperature [°C]

  for T > 0 °C: c1=6.1078;  c2=17.08085; c3=234.175
  for T < 0 °C: c1=6.1078;  c2=17.84362; c3=245.425

which after a few changes becomes:

dew point formula

Dew point deficit

The dew point deficit shows the difference between the actual air temperature and the dew point temperature. This difference cannot be negative as the dew point can't be greater than the actual air temperature.