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.

Assessment of the Accuracy of the Saastamoinen Model and VMF1/VMF3 Mapping Functions with Respect to Ray-Tracing from Radiosonde Data in the Framework of GNSS Meteorology

“…The mapping function concept was first derived for astronomy and positioning applications [9], considering integrated quantities along the radio ray path. This approach needs to be extended to take into account both dry and wet variations in refractivity along the ray path caused by the turbulent atmosphere [55] to meet the requirements of modern applications such as GNSS meteorology and data assimilation in numerical weather models. The Saastamoinen ZHD model assumes atmospheric hydrostatic equilibrium, while the mapping function assumes an azimuthal isotropous atmosphere with smooth variation over time.…”

Beyond Mapping Functions and Gradients

“…Eq. ( 1) is sufficient by itself to model these slant (extra) delays, as evidenced by tomography applications and the statistical analysis of these delays [69]. The zenithal total delays have proven to have a physical meaning, as they are related to the modeling of PW through an a priori model of the "dry" atmosphere and a proportional correspondence to zenithal wet delays.…”

“…(1)? The response is a careful yes [69]. Strictly speaking, a mapping function defines, from the point of view of differential geometry, a time-evolving coordinate chart that is a non-orthogonal system of coordinates made of the refracted elevation at ground level, the length along the bended ray, and the azimuth.…”

Multi-Year Variations in Atmospheric Water Vapor in the Baikal Natural Territory According to GPS Observations

“…It is known that water vapor is the most significant greenhouse gas in the atmosphere [3], and its changes can serve as an indicator of cloud formation and precipitation. One significant feature is that variations in moisture content can be caused by other external factors of temperature change (for example, due to a sharp change in the content of other greenhouse gases).…”

“…One significant feature is that variations in moisture content can be caused by other external factors of temperature change (for example, due to a sharp change in the content of other greenhouse gases). The works [3][4][5][6][7][8] show the relationship between changes in the mass of vertically integrated water vapor (IWV) and changes in temperature. It has been found that an increase of the temperature of 1 K leads to an increase in IWV of about 5-7%.…”