The Relationship between Relative Humidity and the Dewpoint Temperature in Moist Air: A Simple Conversion and Applications

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The relative humidity (RH) and the dewpoint temperature (td) are two widely used indicators of the amount of moisture in air. The exact conversion from RH to td, as well as highly accurate approximations, are too complex to be done easily without the help of a calculator or computer. However, there is a very simple rule of thumb that can be very useful for approximating the conversion for moist air (RH > 50%), which does not appear to be widely known by the meteorological community: td decreases by about 1°C for every 5% decrease in RH (starting at td= t, the dry bulb temperature, when RH = 100%). This article examines the mathematical basis and accuracy of this and other relationships between the dewpoint and relative humidity. Several useful applications of the simple conversion are presented, in particular the computation of the cumulus cloud-base level (or lifting condensation level) as zLCL >> (20 + t/5)(100 – RH), where zLCL is in meters when t is in degrees Celcius and RH in percent. Finally, a historical perspective is given with anecdotes about some of the early work in this field.

Junior Research Group, Department of Atmospheric Chemistry, Max Planck Institute for Chemistry, Mainz, Germany

Publisher’s Note: This article was amended to correct an error in the value for coefficient A1 at the bottom of page 226. The correct value for coefficient A1 is 17.625.

CORRESPONDING AUTHOR: Mark G. Lawrence, Max Planck Institute for Chemistry, Junior Research Group, Department of Atmospheric Chemistry, Postfach 3060, 55020 Mainz, Germany, E-mail: lawrence@mpch-mainz.mpg.de

The relative humidity (RH) and the dewpoint temperature (td) are two widely used indicators of the amount of moisture in air. The exact conversion from RH to td, as well as highly accurate approximations, are too complex to be done easily without the help of a calculator or computer. However, there is a very simple rule of thumb that can be very useful for approximating the conversion for moist air (RH > 50%), which does not appear to be widely known by the meteorological community: td decreases by about 1°C for every 5% decrease in RH (starting at td= t, the dry bulb temperature, when RH = 100%). This article examines the mathematical basis and accuracy of this and other relationships between the dewpoint and relative humidity. Several useful applications of the simple conversion are presented, in particular the computation of the cumulus cloud-base level (or lifting condensation level) as zLCL >> (20 + t/5)(100 – RH), where zLCL is in meters when t is in degrees Celcius and RH in percent. Finally, a historical perspective is given with anecdotes about some of the early work in this field.

Junior Research Group, Department of Atmospheric Chemistry, Max Planck Institute for Chemistry, Mainz, Germany

Publisher’s Note: This article was amended to correct an error in the value for coefficient A1 at the bottom of page 226. The correct value for coefficient A1 is 17.625.

CORRESPONDING AUTHOR: Mark G. Lawrence, Max Planck Institute for Chemistry, Junior Research Group, Department of Atmospheric Chemistry, Postfach 3060, 55020 Mainz, Germany, E-mail: lawrence@mpch-mainz.mpg.de
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