Institute of Geophysics, University of TehranJournal of the Earth and Space Physics2538-371X49120230522Estimation of precipitable water vapor (PWV) using generalized regression neural network (GRNN) and comparison against tomography, ECMWF, Saastamoinen, GPT3 and ANN modelsEstimation of precipitable water vapor (PWV) using generalized regression neural network (GRNN) and comparison against tomography, ECMWF, Saastamoinen, GPT3 and ANN models2432648924110.22059/jesphys.2022.342130.1007425FASeyyed Reza Ghaffari-RazinCorresponding Author, Department of Surveying Engineering, Faculty of Geoscience Engineering, Arak University of Technology, Arak, Iran. E-mail: mr.ghafari@arakut.ac.ir0000-0002-5579-5889Reza Davari MajdDepartment of Surveying Engineering, Faculty of Civil Engineering, Islamic Azad University of Khoy, Khoy, Iran. E-mail: rdavarymajd@trn.ui.ac.ir0000-0001-7213-7119Navid HooshangiDepartment of Surveying Engineering, Faculty of Geoscience Engineering, Arak University of Technology, Arak, Iran. E-mail: hooshangi@arakut.ac.ir0000-0001-9929-8908Journal Article20220528Precipitable water vapor (PWV) is a key parameter in meteorological studies and forecasting of atmospheric events such as rain and flood. Due to the spatial limitations of GPS and meteorological stations, as well as observational discontinuities in the time domain, PWV modeling is of great importance. Obtaining PWV using direct measurements and water vapor measuring devices is a difficult task. The best way to get information on PWV variations indirectly is to use GNSS measurements. The GNSS meteorological technique can provide continuous and almost instantaneous observations of the amount of PWV around a GNSS station. Research has shown that the accuracy of weather forecasts can be improved using GNSS-dependent techniques. Models based on GNSS observations for estimating PWV are known as tropospheric analytical models. The tomographic model is one of the most famous and widely used tropospheric models. There are limitations such as a large number of unknown parameters, rank deficiency of design matrix and the inevitability of using regularization methods, assuming the amount of water vapor inside each voxel is constant and also, the need for initial amounts of water vapor inside the voxels in the voxel-based tomography (VBT) method. Such limitations have led researchers to use machine learning methods to estimate the spatio-temporal variation of PWV. <br />In this paper, the spatio-temporal modeling of PWV is suggested using the generalized regression neural network (GRNN) model. The GRNN model is a type of artificial neural network (ANN) that uses radial basis functions (RBF) as an activity function in the hidden layer. As a result, its accuracy is higher than the ANN model. Eight parameters of longitude, latitude and height of GPS station, day of year (DOY), time (min.), relative humidity (RH), temperature (T) and pressure (P) are considered as inputs of GRNN and ANN models and the PWVs corresponding to these eight parameters are the outputs. After the training step, to evaluate the GRNN and ANN models, the observations of two GPS networks are used. In the GPS network of north-west of Iran, observations of 23 GPS stations in the period of 300 to 314 (winter season) from 2011 have been used. For the central Alborz GPS network, observations of 11 stations at the period of 162 to 176 (summer season) in 2016 are also used. Results obtained from GRNN and ANN models in two interior control stations, one exterior control station (outside the GPS network territory) and also in Tabriz and Tehran radiosonde stations are compared and evaluated with the results of VBT, ECMWF, Saastamoinen and GPT3 models. The statistical parameters of root mean square error (RMSE), relative error and correlation coefficient (R) are used to evaluate the accuracy of the models. At the north-west GPS network, the averaged RMSE values of GRNN, ANN, VBT, ECMWF, Saastamoinen and GPT3 models in the two interior control stations are calculated as 2.14, 2.57, 3.32, 3.36, 6.31 and 4.35 mm, respectively. For the central Alborz GPS network, the averaged RMSE of two interior control stations are computed as 2.01, 2.42, 3.24, 3.26, 6.00 and 4.06 mm, respectively. For the exterior control station, the GRNN model has less error than the ANN, VBT and Saastamoinen models, but more than the ECMWF and GPT3 model. The results of this paper show that the GRNN model has a very high accuracy compared to other analytical and empirical models of the troposphere. This model has the ability to show the spatio-temporal variations of precipitable water vapor with high accuracy at the GPS network territory and; it can considered as an alternative for the other analytical and empirical models.Precipitable water vapor (PWV) is a key parameter in meteorological studies and forecasting of atmospheric events such as rain and flood. Due to the spatial limitations of GPS and meteorological stations, as well as observational discontinuities in the time domain, PWV modeling is of great importance. Obtaining PWV using direct measurements and water vapor measuring devices is a difficult task. The best way to get information on PWV variations indirectly is to use GNSS measurements. The GNSS meteorological technique can provide continuous and almost instantaneous observations of the amount of PWV around a GNSS station. Research has shown that the accuracy of weather forecasts can be improved using GNSS-dependent techniques. Models based on GNSS observations for estimating PWV are known as tropospheric analytical models. The tomographic model is one of the most famous and widely used tropospheric models. There are limitations such as a large number of unknown parameters, rank deficiency of design matrix and the inevitability of using regularization methods, assuming the amount of water vapor inside each voxel is constant and also, the need for initial amounts of water vapor inside the voxels in the voxel-based tomography (VBT) method. Such limitations have led researchers to use machine learning methods to estimate the spatio-temporal variation of PWV. <br />In this paper, the spatio-temporal modeling of PWV is suggested using the generalized regression neural network (GRNN) model. The GRNN model is a type of artificial neural network (ANN) that uses radial basis functions (RBF) as an activity function in the hidden layer. As a result, its accuracy is higher than the ANN model. Eight parameters of longitude, latitude and height of GPS station, day of year (DOY), time (min.), relative humidity (RH), temperature (T) and pressure (P) are considered as inputs of GRNN and ANN models and the PWVs corresponding to these eight parameters are the outputs. After the training step, to evaluate the GRNN and ANN models, the observations of two GPS networks are used. In the GPS network of north-west of Iran, observations of 23 GPS stations in the period of 300 to 314 (winter season) from 2011 have been used. For the central Alborz GPS network, observations of 11 stations at the period of 162 to 176 (summer season) in 2016 are also used. Results obtained from GRNN and ANN models in two interior control stations, one exterior control station (outside the GPS network territory) and also in Tabriz and Tehran radiosonde stations are compared and evaluated with the results of VBT, ECMWF, Saastamoinen and GPT3 models. The statistical parameters of root mean square error (RMSE), relative error and correlation coefficient (R) are used to evaluate the accuracy of the models. At the north-west GPS network, the averaged RMSE values of GRNN, ANN, VBT, ECMWF, Saastamoinen and GPT3 models in the two interior control stations are calculated as 2.14, 2.57, 3.32, 3.36, 6.31 and 4.35 mm, respectively. For the central Alborz GPS network, the averaged RMSE of two interior control stations are computed as 2.01, 2.42, 3.24, 3.26, 6.00 and 4.06 mm, respectively. For the exterior control station, the GRNN model has less error than the ANN, VBT and Saastamoinen models, but more than the ECMWF and GPT3 model. The results of this paper show that the GRNN model has a very high accuracy compared to other analytical and empirical models of the troposphere. This model has the ability to show the spatio-temporal variations of precipitable water vapor with high accuracy at the GPS network territory and; it can considered as an alternative for the other analytical and empirical models.https://jesphys.ut.ac.ir/article_89241_571db1df874b19b4c30f57c1543342eb.pdf