Local tomography troposphere model over mountains area Witold Rohm ⁎, Jaroslaw Bosy Institute of Geodesy and Geoinformatics Wroclaw University of Environmental and Life Sciences Grunwaldzka 53, 50-357 Wroclaw, Poland article info abstract Article history: Received 28 August 2008 Accepted 17 March 2009 The term GNSS meteorology refers to the utilization of the Global Navigation Satellite System's (GNSS) radio signals to derive information about the state of the troposphere. GNSS tomography allows to resolve the spatial structure and temporal behavior of the tropospheric water vapor. This paper presents the verification of GNSS tomography over dense local GNSS network. The paper addresses the problem of obtaining a stable tomographic solution from an ill-conditioned system of linear equations. The main interests are in suitable horizontal and vertical resolution in given conditions. Here the Moore–Penrose pseudo inverse of variance–covariance matrix is used. The minimum constraints solution is obtained with no additional assumptions. The results are validated with the help of simulated weather conditions. Three various scenarios are tested. As general output of this paper the optimal model construction scheme is presented with possible further improvements. The verification of the tomography model based on the local GPS KARKONOSZE, situated in the Karkonosze mountains area in Poland. © 2009 Elsevier B.V. All rights reserved. Keywords: GNSS meteorology Tomography Troposphere delay 1. Introduction The GNSS meteorology has reached a point, where there is a need to develop methods not only to compute Integrated Water Vapour over the GNSS receiver, but also to investigate the water vapor distribution in space and time (4D resolu- tion). The method, which makes it possible to obtain the 3D picture of any medium and in particularly the lower tropo- sphere is tomography. The GNSS tomography is an innovative remote sensing technique which works under all weather con- ditions with a high temporal resolution (Bender and Raabe, 2007). The mathematical fundamentals date back to beginning of the XX century when Radon has developed his transform. The first application of his theorem was medical tomograph constructed in the fifties. While the number of applications has been growing including: geodynamics, gas tracing, medi- cine, ionosphere and finally the troposphere, the principles stayed untouched. To obtain the data about the distribution of the investigated quantity the model space has to be divided into closed volumes with assumed constant value. The ray path has to be retrieved to obtain the distance the ray travels inside each voxel. The inversion of the system of equations linking the distance in each voxel with the observed integrated delay gives the required quantity. The tomography models has been investigated by Flores (1999), who proposed the discretization of the model space into voxels and additional horizontal and vertical smoothing equa- tions, also (Hirahara, 2000) with same discretization techniques but different inverse solution. The others, like Shrestha (2003) and Hoyle (2005) investigated the division into horizontal layers exclusively. There has been also attempts to construct the tomog- raphy models for atmospheric turbulence researches (Nilsson, 2008). The main issues in tomography models concern two areas: the model space construction, setting boundary conditions and in consequence inversion of the equations system. In case of Hirahara (2000) it was kind of diagonal dumping matrix in which variance has been limited to some theoretical extend. Referring to Flores (1999) there are some additional vertical, horizontal and boundary conditions plus assumed drift rate. The influence of applying drift rate may produce smoothing result on obtained quantities. In this paper there are only vertical constraints – additional equations assuming that the refractivity inside layer is constant during integration Atmospheric Research 93 (2009) 777–783 ⁎ Corresponding author. Tel.: +48 71 320 19 52; fax: +48 71 320 56 17. E-mail addresses: witold.rohm@up.wroc.pl (W. Rohm), jaroslaw.bosy@up.wroc.pl (J. Bosy). 0169-8095/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.atmosres.2009.03.013 Contents lists available at ScienceDirect Atmospheric Research journal homepage: www.elsevier.com/locate/atmos