Determining precipitable water vapour from upper-air temperature, pressure and geopotential height

Radiosonde measurements of relative humidity (RH) are the main source of uncertainty in precipitable water vapour (PWV) calculation from pressure, temperature, and RH/dewpoint (PTU) data. This paper presents a formula expressing PWV in terms of pressure and temperature as functions of geopotential height (GPH), thereby allowing the PWV to be determined: (1) without any moisture-related calculations other than those involved in measuring GPH (in radiosondes with a pressor sensor) or pressure (otherwise); (2) without relying on humidity measurements by using Global Positioning System (GPS)-based GPH according to the gravity field, provided that pressure is directly measured. The numerical instability associated with random data errors or deviations from hydrostatic equilibrium makes the second approach unfeasible on short time scales, revealing discrepancies between the PTU- and GPS-based GPHs; however, the estimation of long-term average PWV above a location is not hindered. The estimation of PWV without humidity data was tested using high-resolution data from 62 upper-air stations operated by the NOAA National Weather Service. The seasonal mean {DJF, MAM, JJA, SON} PWV from the surface to 300 hPa calculated from PT and GPS data over the period 2016-2018, after rejecting individual estimates inconsistent with the 0%-100% RH range, showed a mean bias error of {-0.1, +0.1, -1.4, -0.9} kg center dot m-2 relative to the PTU-based values across the stations, and a RMSE ranging from 2.4 (DJF) to 3.2 (JJA) kg center dot m-2. By restricting the analysis to observations with above-average matching between the PTU- and GPS-based GPH, the bias magnitude and RMSE reduced respectively to less than 0.5 and 1 kg center dot m-2 in all seasons. The results indicate that evaluating the long-term agreement between the two PWV calculation methods at different sites could be useful in detecting systematic observation errors in GPS radiosonde systems using a pressure sensor. Radiosonde observations remain a reliable basis for measuring precipitable water vapour (PWV) and evaluating competing remote sensing techniques with better geographic coverage or temporal resolution. Humidity measurements represent a source of uncertainty in radiosonde-based estimation. The method developed here does not rely on humidity data when applied to Global Positioning System (GPS) radiosondes with a pressure sensor, making it possible to estimate average PWV. By highlighting long-term inconsistencies between the GPS altitude and the hypsometric equation, it proves useful to detect radiosonde biases.image