An investigation of three dimensional ray tracing method efficiency in precise point positioning by tropospheric delay correction

Earth's atmosphere has a series of layers, each with its own specific traits. Moving upward from ground level, these layers are named the troposphere, stratosphere, mesosphere, thermosphere and exosphere. The exosphere gradually fades away into the realm of interplanetary space. The troposphere is the lowest layer of our atmosphere. Starting at ground level, it extends upward to about 10 km above sea level. Humans live in the troposphere layer, and nearly all weather occurs in this layer and affects their activities. Ninety nine percent of the water vapor in the atmosphere is found in the troposphere; therefore most clouds appear in this layer. Air pressure and temperature drops in the troposphere with height. The tropospheric path delay is one the main error sources in Global Navigation Satellite System (GNSS) such as Global Positioning System (GPS) observations and reduces the accuracy of GNSS point positioning. Accurate estimation of tropospheric path delay in GNSS signals is necessary for positioning and also its meteorological applications. The tropospheric delay is divided into the dry (hydrostatic) and wet (non-hydrostatic) parts. The dry tropospheric delay depends on the pressure variations between satellite and station on the Earth’s surface and can be determined accurately using experimental models. The wet delay can be determined by subtracting the dry delay from the total GPS derived delay. In this paper the efficiency of 3D ray tracing in increasing the accuracy of point positioning is investigated. The 3D ray tracing technique based on Eikonal equation is the strongest and newest ray tracing method. These equations are solved in order to get the ray path and the optical path length. The Eikonal equation itself is the solution of the so-called Helmholtz equation with respect to electro-magnetic waves. In this method the ray paths are not limited to a certain azimuthally fixed vertical plane. In 2D methods the ray paths are forced to stay within a vertical plane of constant azimuth. European Center for Medium Range Weather Forecasting (ECMWF) is currently publishing ERA-I, a global reanalysis of the meteorological data. This reanalysis provides values of several meteorological parameters on a global gride ∼75 km. The vertical stratification is described on 37 pressure levels. Tropospheric corrections were calculated using 3D ray tracing, 2D ray tracing and Saastamoinen methods in Tabriz and Abarkuh stations using ERA-I meteorological parameters. These corrections were applied to the GPS observations and the stations coordinate were computed. Furthermore, these stations coordinates were determined twice using Bernese GPS processing software, one time the tropospheric delay was not canceled from observations and second time it was considered as unknown parameter and evaluated with stations coordinates. The result of this process was considered as a reference to evaluate the three prescribed correction methods. These comparisons indicate that the correction computed from 3D ray tracing is more efficient than that of 2D ray tracing and Saastamoinen model corrections. Also the correction amount in Tabriz station is meaningful with respect to Abarkuh station, which can be attributed to small variations of water vapor in Abarkuh station.