The probability distribution of relative humidity in the lower troposphere

Water vapour in the lower troposphere plays a major role in the energy balance at the Earth's surface through modifying radiative and latent heat fluxes. Here we develop an analytic model for the probability density function (PDF) of relative humidity in the lower troposphere based on the advection-condensation paradigm. Our theory represents a significant advance on previous work by describing the continuous vertical structure of the PDF throughout the lower troposphere, including the sub-cloud layer. The PDF depends on only three parameters: the decay scale of saturation specific humidity with height, the near-surface relative humidity, and the strength of the mean vertical (synoptic) motion at a given location. The theoretical PDFs closely match those derived from the ERA5 reanalysis at both global and regional scales. Our theory thus provides a basis to understand the distribution of tropospheric water vapour better in current and future climates.