Modified Relative Humidity Based on the Johnson's S_B Distribution Function

Abstract

A new atmospheric humidity variable called the modified relative humidity (MRH) is proposed based on properties of the Johnson's S_B distribution function. The frequency distribution of MRH can be roughly approximated by the normal distribution, while other variables such as relative humidity and the water vapor mixing ratio cannot. This characteristic suggests that MRH is convenient for statistical variable controls such as data assimilation and climatological grid data controls. Super-saturation and negative water vapor states induced by positive and negative humidity increments are avoided by using MRH. Three types of MRH, Types-I, -II, and -III, were examined. Type-III, with three fixed parameters, was the best function for approximating to the normal distribution. However, Types-I and -II, each with two fixed parameters, were beneficial for stable statistical humidity variable estimations.