Efficiency of the adaptive neuro-fuzzy inference system in tropospheric slant water vapor modeling

Document Type : Research Article


Assistant Professor, Department of Geoscience Engineering, Faculty of surveying, Arak University of Technology, Arak, Iran


The passage of satellite signals through the atmosphere with variable nature of its troposphere will have a significant delay in the movement of these signals. This effect is commonly known as tropospheric delay. It can be divided into wet and dry components. The dry component is usually modeled using devices that measure air pressure. Unlike the dry component, the wet component of tropospheric refraction cannot be modeled using air pressure measuring devices. This component depends on the water vapor (WV) and moisture content of the troposphere. The WV is one of the key parameters in climate system analysis and a major factor in atmospheric events. Using the observations of local and regional GNSS networks, it is possible to estimate the slant tropospheric delay (STD) and subsequently, the slant wet delay (SWD) for each line of sight between the receiver and the satellite. The SWD observations are used to model horizontal and vertical WV variations in the upper atmosphere of the study network. This is done with a tomography technique. In tomography, the horizontal variations of tropospheric wet refractivity are modeled with the polynomial in degree and rank of 2 with latitude and longitude as variables. Also, altitude variations are modeled in the form of discrete layers with constant heights.
The main innovation of this paper is in estimating the tropospheric parameters for each line of sight between the receiver and the satellite by the adaptive neuro-fuzzy inference system (ANFIS). The SWD obtained from GPS observations for the different signals at each station is compared with the SWD generated by the ANFIS (SWDGPS-SWDANFIS). The square of the difference between these two values is introduced as the cost function in the ANFIS. By calculating the value of the cost function at each step, the weights associated with the ANFIS network are corrected by the back-propagation (BP) method. In the next step, using the estimated wet refractivity, the value of slant water vapor (SWV) is calculated. To evaluate, GPS observations from 27-31 October 2011 and Tabriz radiosonde observations are used. For a more detailed evaluation, 2 test stations are selected and ANFIS zenith wet delays (ZWDANFIS) are compared with the ZWDGPS. Observations of test stations are not used in modeling step. In order to further examine the accuracy of the proposed method, the results of this study have been compared with the results of voxel-based tomography (TomoVoxel) method and troposphere tomography using artificial neural network (TomoANN). Also, relative error, mean square error (RMSE), standard deviation, and correlation coefficient were used to evaluate the results. At the Tabriz Radiosonde station, the correlation coefficient for the ANFIS, TomoVoxel and TomoANN have been calculated as 0.9131, 0.8863 and 0.9006, respectively. The minimum relative error for the TomoANFIS, TomoANN and TomoVoxel are 8.31%, 8.55% and 8.71%, respectively. Also, the maximum RMSE for three models is 0.9718, 1.0281 and 1.2346 mm/km, respectively. The results of this paper indicate the very high capability of the TomoANFIS model in showing the temporal and spatial variations of SWV. This method can be used to discuss the behavior of the atmosphere in real time and near to real time applications.


Main Subjects

موسوی، ز.، خرمی، ف.، نانکلی، ح.ر.، جمور، یحیی.، 1386، تعیین مقدار بخارآب موجود در جو با استفاده از تخمین تأخیر وردسپهری سیگنال‌های جی‌پی‌اس در شبکه ژئودینامیک سراسری ایران، همایش ژئوماتیک 1386.
Adavi, Z. and Mashhadi hossainali, M., 2014, 4D-Tomographic Reconstruction of the Tropospheric Wet Refractivity Using the Concept of Virtual Reference Station, Case Study: North West of Iran. Meteorology and Atmospheric Physics, 126 (3-4), 193-205.
Adavi, Z. and Mashhadi hossainali, M., 2015, 4D-tomographic reconstruction of water vapor using the hybrid regularization technique with application to the North West of Iran. Advances in Space Research 55 (7), 1845-1854.
Aster, R., Borchers, B. and Thurber, C., 2003, Parameter estimation and inverse problems, vol 90. Elsevier Academic Press, USA.
Bevis, M., Businger, S., Herring, T., Rocken, C. and Ware, RH., 1992, GPS metrology: remote sensing of atmospheric water vapor using the global positioning system. J Geophys Res 97(D14), 15787–15801.
Benevides, P., Catalao, J., Nico, G. and Miranda, P., 2018, 4D wet refractivity estimation in the atmosphere using GNSS tomography initialized by radiosonde and AIRS measurements: results from a 1-week intensive campaign. GPS Solutions 91(2018): 22:91.
Bosy, J., Rohm, W. and Sierny, J., 2010, The concept of the near real time atmosphere model based on the GPS and the meteorological data from the ASG-EUPOS reference stations. Acta Geodyn Geomater 7:253–261.
Chen, B. and Liu, Z., 2014, Voxel-optimized regional water vapor tomography and comparison with radiosonde and numerical weather model. Journal of Geodesy 88(7): 691–703.
Davis, JL., Herring, TA., Shapiro, II., Rogers, EE. and Elgered, G., 1985, Geodesy by radio interferometry: effects of atmospheric modeling errors on estimates of baseline length. Radio Sci 20(6), 1593–1607.
Dach, R., Hugentobler, U., Fridez, P. and Meindl, M., 2007, Bernese GPS Software Version 5.0. Astronomical Institute, University of Bern, Bern.
Emardson, TR., Elgered, G. and Johansson, JM., 1998, Three months of continuous monitoring of atmospheric water vapor with a network of Global Positioning System receivers. J Geophys Res 103:1807–1820.
Ghaffari Razin, M.R. and Voosoghi, B., 2020, Estimation of tropospheric wet refractivity using tomography method and artificial neural networks in Iranian case study. GPS Solutions 24(3), 1-14.
Haji Aghajany, S. and Amerian, Y., 2017a, three dimensional ray tracing technique for tropospheric water vapor tomography using GPS measurements. Journal of Atmospheric and Solar-Terrestrial Physics, 164 (2017), 81-88.
Haji Aghajany, S. and Amerian, Y., 2017b, Comparing the Efficiency of Radiosonde and ERA-Interim Meteorological Data in Precise Point Positioning Tropospheric Delay Correction Using Three Dimensional Ray Tracing Method. JGST; 7 (3), 127-138.
Haji Aghajany, S., Amerian, Y. and Verhagen, S., 2020, B-spline function-based approach for GPS tropospheric tomography. GPS Solutions 24(3), 1-12.
Jang, J.S., 1993, ANFIS: adaptive-network-based fuzzy inference system. IEEE transactions on systems, man, and cybernetics. 23(3), 665-685. 10.1109/21.256541.
Mars, P., Chen, J.R. and Nambiar, R., 1996, Learning Algorithms: Theory and Applications in Signal Processing, Control and Communications. CRC Press, Boca Raton, Florida.
Rahimi, H., Nafisi, V. and Asgari, J., 2013, Tropospheric Delay estimation using constrained ray-tracing method based on surface meteorological parameters and Numerical Weather Models. JGST, 3 (2), 15-26.
Seeber, G., 2003, Satellite Geodesy, Foundations, Methods and Application, Walter de Gruyter, Berlin and New York, 531.
Saastamoinen, J., 1973, Contributions to the theory of atmospheric refraction. Part II: refraction corrections in satellite geodesy. Bull.Geod, 107, 13-34.
Skone, S. and Hoyle, V., 2005, Troposphere Modeling in a Regional GPS Network, Journal of Global Positioning Systems,  4(1-2), 230-239.
Sadeghi, E., Mashhadi Hossainali, M. and Etemadfard, H., 2014, Determining precipitable water in the atmosphere of Iran based on GPS zenith tropospheric delays. Annals of geophysics 57.
Wilgan, K., Hurter, F., Geiger, A., Rohm, W. and Bosy, J., 2017, Tropospheric refractivity and zenith path delays from least-squares collocation of meteorological and GNSS data. Journal of Geodesy 91(2), 117–134.
Yao, Y. and Zhao, Q., 2016, A novel optimized approach of voxel division for water vapor tomography. Meteorol. Atmos. Phys. 2016, 129, 57–70.
Zhao, Q., Zhang, K., Yao, Y. and Li, X., 2019, A new troposphere tomography algorithm with a truncation factor model (TFM) for GNSS networks. GPS Solutions 23(3), 23:64.
Zadeh, L. A., 1965, Fuzzy sets. Information and control. 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X.