Modeling the Slant Wet Delays From One GPS Receiver as a Series Expansion With Respect to Time and Space: Theory and an Example of Application for the Tahiti Island

Abstract

Traditionally, the modeling of the water vapor contents of the atmosphere is done through the estimation of precipitable water (PW)—the integrated value of the mass of water vapor over a vertical column expressed in millimeter equivalent height. This modeling method is justified by the fact that, to a high degree of approximation, the atmosphere can be seen as the stacking of horizontal layers, including water vapor, over distances larger than the height of the tropopause. Nevertheless, the cycle of the water vapor, the most prevalent of the greenhouse gases in the atmosphere, has a highly turbulent regime both in time and in space that the variations in PW cannot fully embrace. In this article, we explore the modeling method, as a series expansion in time and space, of the slant wet delays (SWDs) from one GPS receiver, as an extension of the usual modeling in zenith wet delays (ZWDs) and then PW values. In the first part, we assess, from a metrological point of view, the derivation of the SWDs computed from GPS carrier phase measurements, in the case of a very humid location, the tropical island of Tahiti, for a typical sample over the wet and dry seasons. In the second part, we introduce the series expansion of the SWDs, as seen from one GPS receiver, in terms of trigonometric functions of time and spherical harmonics of elevation and azimuth. This allows us to infer time and space correlations for the SWDs that are unreachable through the modeling of ZWD values alones. In a third part, to show that our approach also includes the zenith case, we make a comparison between the modeled SWDs in the zenith direction with wind velocities from a ground weather station and radiosonde soundings (RSs). The three main conclusions from our data case are: first, the SWDs are correlated in time by about four days, and in space, with an angular correlation distance of about 20°, both for the dry and wet seasons; second, the postfit residuals are almost uncorrelated with the SWDs from a temporal and spatial point of view, but with a diurnal component; third, there is a weak correlation between the SWDs and wind velocity, the pattern depends on the season.