IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 44, NO. 10, OCTOBER 2006 2927 Water Vapor Tomography Using GPS Phase Observations: Simulation Results Tobias Nilsson and Lubomir Gradinarsky Abstract—Global positioning system (GPS) tropospheric to- mography normally requires that the slant wet delays between the GPS satellites and the ground receivers are estimated with high accuracy, which may be difficult given the presence of a number of error sources. This paper presents an alternative ap- proach, namely to estimate the three-dimensional structure of the atmospheric water vapor directly from raw GPS phase observa- tions. The method is tested in a number of simulations, where the impact of network size, the possible horizontal and vertical resolutions, the observation noise, and the inclusion of additional global navigation satellite systems were studied. The simulation results indicate that the refractivity field can be obtained with an accuracy of ∼20% or better up to around 4 km with a height resolution of 1 km provided that a sufficient number of receivers and satellites is available. Index Terms—Global positioning system (GPS), humidity, Kalman filtering, meteorology, simulation, terrestrial atmosphere, tomography. I. I NTRODUCTION T HE GLOBAL positioning system (GPS) is a useful tool for retrieving the total amount of integrated water vapor in the atmosphere [1]–[3]. Using a local network of GPS receivers, it is also possible to estimate the three-dimensional (3-D) structure of the wet refractivity of the atmosphere. This is done by using tomographic methods. These have been success- fully applied to retrieve the electron content in the ionosphere [4]. For the troposphere, several different methods have been developed [5]–[11]. The application of GPS for tomographic retrieval of the water vapor distribution in the troposphere requires that the slant wet delays, i.e., the delay of the GPS signals in the atmosphere due to water vapor between each satellite and each receiver, are es- timated from the GPS phase data recorded by the receivers. To retrieve the 3-D structure of the wet refractivity, the troposphere is divided into a finite number of boxes (normally called voxels, finite volume pixels) where the refractivity is assumed to be constant. By doing this discretization, the slant wet delays can be described as linear combinations of the refractivities of the voxels; hence the refractivity field can be obtained by solving a linear system of equations. Manuscript received May 3, 2005; revised December 20, 2005. This work was supported by the Swedish National Space Board. T. Nilsson is with the Onsala Space Observatory, 439 92 Onsala, Sweden (e-mail: tobias@oso.chalmers.se). L. Gradinarsky is with the Sensor Technology, Astra-Zeneca R&D, 431 86 Mölndal, Sweden, and also with the Onsala Space Observatory, 439 92 Onsala, Sweden (e-mail: lbg@oso.chalmers.se). Digital Object Identifier 10.1109/TGRS.2006.877755 To retrieve the slant wet delays from the GPS data, the delays are modeled as functions of a number of unknown parameters. Normally, a slant wet delay is modeled as being a function of a zenith wet delay and a gradient [5]. This model is then used in GPS data processing, where the model parameters are estimated along with other unknowns contributing to the signal delays. The residuals of the processing are then considered to contain the unmodeled part of the slant wet delays. Hence, slant wet delays can be obtained by adding the residuals to the slant wet delays calculated from the retrieved zenith wet delays and gradients. However, it is not obvious that the retrieved slant wet delays will be accurate enough. The parts of the delays due to water vapor not modeled by the zenith delays and the gradients might be absorbed in the estimation of other unknown parameters in the GPS processing, like clock errors. Even for ideal conditions, the slant wet delays retrieved in this way may not be very accurate [12]. Hence, some of the information about the 3-D structure of the wet refractivity contained in the slant wet delays may be lost in this process. Consequently, the refractivity field retrieved using these slant wet delays in GPS tomography may contain unacceptable errors. In this paper, a new method to retrieve the 3-D structure of the water vapor is presented. Instead of using one model for the slant wet delays in GPS processing and then applying another model to retrieve the wet refractivity field, we apply the voxel discretization of the wet refractivity field already in the GPS processing step. Hence, slant wet delays are described as linear combinations of the refractivities of voxels in GPS processing. This has the advantage that any error arising from the modeling of slant wet delays in terms of zenith delays and gradients will disappear. Another advantage is that the number of steps required to obtain the wet refractivity field is reduced. The disadvantage is of course that there are many parameters that need to be estimated in the processing. It can be shown that apart from the refractivity of the voxels, the parameters needed to be estimated will be errors in the satellite and the receiver clocks. However, the clock errors need to be estimated (alternatively removed using differencing methods) anyway, and there are no reasons why the effect of clock error esti- mation should be less if it is done in the first step before the tomographic estimation of refractivities. Also, the number of additional parameters needed to be estimated will be small compared to the number of observations if there are many satellites and receivers available. Given N satellites and M receivers, there will be N ∗ M observations at each epoch and N + M clock errors to be estimated, and if N and M are large, 0196-2892/$20.00 © 2006 IEEE