Combination of Radio Occultation data in 3D and 4D functional model tomography for retrieving the wet refractivity indices

Document Type : Research Article


1 Ph.D. Student, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

2 Assistant Professor, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran

3 Associate Professor, Department of Surveying and Geomatics Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran


Atmospheric wet refractivity indices, which are dependent on the water vapor, are one of the most important parameters for analyzing climate change in an area. Wet refractivity indices can be estimated from Radiosonde stations measurement or calculated from numerical meteorological models. But due to low temporal and spatial resolution of radiosonde stations and severe variations of water vapor in the lower levels of Atmosphere, today’s numerical meteorological models provide low accuracy for atmospheric parameters. But nowadays, by growing number of stations that can use global positioning satellite measurements, atmospheric parameter can be estimated via remote sensing measurements in wide temporal and spatial resolutions. Wet refractivity indices cause delay in GPS measurement signals thus this delay have information about distribution of wet refractivity indices in atmosphere. By the use of global positioning satellites that can estimate atmospheric wet delay and tomography method, wet refractivity indices can be estimated. One of the growing methods for measuring the atmosphere parameters is the radio occultation technique. By increasing the number of low earth orbit satellites that carry GNSS receiver, this technique can provide observation in all of the globe, which its observations are obtained directly from the type of atmosphere parameters. The aim of this study is to use a combination of RO and GPS observation in 3D and 4D atmospheric tomography. But since tomography problem are ill-posed because of the poor distribution of GPS observations in network, a functional model has been implemented to estimate the wet refractivity indices from of the atmospheric tomography problem. By expanding tomography’s unknowns to base functions coefficients, the number of unknowns will be decreased and problem will become well-posed and unknowns can be estimated from inverse problem. In the three-dimensional functional model, combination of spherical cap harmonics and empirical orthogonal functions have been used to solve the inverse problem. Spherical cap harmonics are used to represent the wet refractivity indices in horizontal distribution and empirical orthogonal functions are used for the vertical distribution of the unknown coefficients. Eventually, the B-spline is used to represent the four-dimensional functional model and the dependence of coefficients to the time. After implementing 3D and 4D functional models, the relative weight of RO data with comparison to GPS data has been calculated using variance component method. The US region of California has been selected as the study network due to its high tectonic importance and the large number of GPS stations. The results in two considered tomography epochs have been validated with radiosonde station data in the network and also have been compared with ERA5 reanalysis data. Comparison of the profiles obtained from tomography and the ERA5 data profiles with the radiosonde wet refractivity indices shows that the results obtained from the functional model tomography are better than those of the ERA5 data. The results of the combination illustrate that using RO data in both 3D and 4D models, the RMSE has been decreased and showed improvement of about 7 to 10 percent compared to uncombined tomographic models. Also, it is seen that using RO data in the 4D model has higher accuracy compared to the 3D model due to the use of a time-dependent functional model that increases the functional model's accuracy.


Main Subjects

Adavi, Z. and Mashhadi-Hossainali, M., 2014, 4D tomographic reconstruction of the tropospheric wet refractivity using the concept of virtual reference station, case study: northwest of Iran. Meteorology and Atmospheric Physics 126, 193-205.
Al-Fanek, O. J. S., 2013, Ionospheric imaging for Canadian polar regions. University of Calgary.
Alizadeh, M., 2013, Multi-Dimensional modeling of the ionospheric parameters, using space geodetic techniques. Techn. Univ. Wien.
Alizadeh, M., Schuh, H., Todorova, S. and Schmidt, M., 2011, Global ionosphere maps of VTEC from GNSS, satellite altimetry, and Formosat-3/COSMIC data. Journal of Geodesy 85, 975–987.
Aster, R., Borchers, B. and Thurber, C., 2005, Parameter estimation and inverse problems: Elsevier Academic. Borchers, CH Thurber–Elsevier-Academic Press, New York, London.
Bender, M., Dick, G., Ge, M., Deng, Z., Wickert, J., Kahle, H., Raabe, A. and Tetzlaff, G., 2011, Development of a GNSS water vapour tomography system using algebraic reconstruction techniques. Advances in Space Research 47, 1704-1720.
Bender, M., Dick, G., Heise, S., Zus, F., Deng, Z., Shangguan, M., Ramatschi, M. and Wickert, J., 2013, GNSS Water Vapor Tomography.
Bender, M. and Raabe, A., 2007, Preconditions to ground based GPS water vapour tomography. Annales geophysicae. pp. 1727-1734.
Bevis, M., Businger, S., Herring, T. A., Rocken, C., Anthes, R. A. and Ware, R. H., 1992, GPS meteorology: Remote sensing of atmospheric water vapor using the Global Positioning System. Journal of Geophysical Research: Atmospheres 97, 15787-15801.
Bjornsson, H. and Venegas, S., 1997, A manual for EOF and SVD analyses of climatic data. CCGCR Report 97, 112-134.
Böhm, J., Heinkelmann, R. and Schuh, H., 2007, Short note: a global model of pressure and temperature for geodetic applications. Journal of Geodesy 81, 679-683.
Böhm, J., Niell, A., Tregoning, P. and Schuh, H., 2006, Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data. Geophysical Research Letters 33.
Champollion, C., Masson, F., Bouin, M.-N., Walpersdorf, A., Doerflinger, E., Bock, O. and Van Baelen, J., 2005, GPS water vapour tomography: preliminary results from the ESCOMPTE field experiment. Atmospheric research 74, 253-274.
Chen, P., Yao, Y. and Yao, W., 2017, Global ionosphere maps based on GNSS, satellite altimetry, radio occultation and DORIS. GPS solutions 21, 639-650.
Dettmering, D., Schmidt, M., Heinkelmann, R. and Seitz, M., 2011, Combination of different space-geodetic observations for regional ionosphere modeling. Journal of Geodesy 85, 989-998.
Farzaneh, S. and Forootan, E., 2018, Reconstructing Regional Ionospheric Electron Density: A Combined Spherical Slepian Function and Empirical Orthogonal Function Approach. Surveys in Geophysics 39, 289-309.
Flores, A., Ruffini, G. and Rius, A., 2000, 4D tropospheric tomography using GPS slant wet delays. Annales Geophysicae. Springer, 223-234.
Forootan, E., 2014, Statistical signal decomposition techniques for analyzing time-variable satellite gravimetry data. Universitäts-und Landesbibliothek Bonn.
Haines, G., 1985, Spherical cap harmonic analysis. Journal of Geophysical Research: Solid Earth 90, 12563-12574.
Haji-Aghajany, S. and Amerian, Y, 2017, Three dimensional ray tracing technique for tropospheric water vapor tomography using GPS measurements. Journal of Atmospheric and Solar-Terrestrial Physics 164, 81-88.
Haji-Aghajany, S., Amerian, Y. and Verhagen, S., 2020a, B-spline function-based approach for GPS tropospheric tomography. GPS Solutions 24, 1-12.
Haji-Aghajany, S., Amerian, Y., Verhagen, S., Rohm, W. and Ma, H, 2020b, An optimal troposphere tomography technique using the WRF model outputs and topography of the area. Remote Sensing 12, 1442.
Hansen, P. C., 1998, Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion. SIAM.
Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz‐Sabater, J., Nicolas, J., Peubey, C., Radu, R. and Schepers, D., 2020, The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society 146, 1999-2049.
Hirahara, K., 2000, Local GPS tropospheric tomography. Earth, planets and space 52, 935-939.
Koch, K.-R. and Kusche, J., 2002, Regularization of geopotential determination from satellite data by variance components. Journal of Geodesy 76, 259-268.
Limberger, M., 2015, Ionosphere modeling from GPS radio occultations and complementary data based on B-splines. Technische Universität München.
Liu, Z., 2004, Ionosphere tomographic modeling and applications using Global Positioning System (GPS) measurements.
Razin, M. R. G. and Voosoghi, B., 2017, Regional ionosphere modeling using spherical cap harmonics and empirical orthogonal functions over Iran. Acta Geodaetica et Geophysica 52, 19-33.
Recommendation, I., 453-9, 2001, The radio refractive index: its formula and refractivity data. Recommendations and Reports of the ITU-R 8, 618-7.
Schmidt, M., Dettmering, D., Mößmer, M., Wang, Y. and Zhang, J., 2011, Comparison of spherical harmonic and B spline models for the vertical total electron content. Radio Science 46.
Schumaker, L. L. and Traas, C., 1991, Fitting scattered data on spherelike surfaces using tensor products of trigonometric and polynomial splines. Numerische Mathematik 60, 133-144.
Sharifi, M.A., Sam-Khaniani, A., Joghataei, M., Schmidt, T., Masoumi, S. and Wickert, J., 2013, Tropopause analysis over the Iranian region using GPS radio occultation data. Advances in Space Research 52, 1700-1707.
Subirana, J. S., Hernandez-Pajares, M. and Zornoza, J.e.M.J., 2013, GNSS Data Processing: Fundamentals and Algorithms. European Space Agency.
Xia, P., Cai, C. and Liu, Z., 2013, GNSS troposphere tomography based on two-step reconstructions using GPS observations and COSMIC profiles. Annales geophysicae. Copernicus GmbH (Copernicus Publications) on behalf of the European Geosciences Union (EGU).
Xu, X., Luo, J. and Shi, C., 2009, Comparison of COSMIC radio occultation refractivity profiles with radiosonde measurements. Advances in Atmospheric Sciences 26, 1137–1145.
Zhao, Q., Yao, Y. and Yao, W, 2018, Troposphere water vapour tomography: A horizontal parameterised approach. Remote Sensing 10, 1241.