Extended Abstract
Introduction
The Earth's atmosphere (atmosphere) is divided into concentric layers with different chemical and physical properties. To study wave propagation, two layers called the troposphere and ionosphere are considered. The troposphere is the lowest part of the Earth's atmosphere and extends from the Earth's surface to about 40 kilometers above it. In this layer, wave propagation is mainly dependent on water vapor and temperature. Unlike the ionosphere, the troposphere is not a dispersive medium for GPS signals (seeber, 2003). As a result, the propagation of waves in this layer of the atmosphere does not depend on the frequency of the signals. The delay caused by the troposphere can be divided into two parts of hydrostatic delay and wet delay. The hydrostatic component of the tropospheric delay is due to the dry gases in this layer. In contrast, the wet component of tropospheric refraction is caused by water vapor (WV) in the troposphere. The study of atmospheric water vapor is important in two ways: First, short-term climate change is highly dependent on the amount of atmospheric water vapor. Water vapor has temporal and spatial variations that affect the climate of different regions. Second, long-term climate variation is reflected in the amount of water vapor. Obtaining water vapor using direct measurements and water vapor measuring devices is a difficult task. Radiosonde and radiometers are used to directly measure atmospheric water vapor, but the use of these devices will have problems and limitations, for example, the maintenance cost of these devices is expensive and also these devices do not have a suitable station cover. The best way to get information about water vapor changes indirectly is to use GPS measurements. GPS meteorological technology can provide continuous and almost instantaneous observations of the amount of water vapor around a GPS station.
Estimation of precipitable water vapor (PWV) and water vapor density using voxel-based tomography method has disadvantages. The coefficient matrix of tomography method has a rank deficiency. Initial value of water vapor must be available to eliminate it. Also, the amount of WV inside each voxel is considered constant, if this parameter has many spatial and temporal variations. In this method, the number of unknowns is very high and it is computationally difficult to estimate (Haji Aghajany et al., 2020). To overcome these limitations, this paper presents the idea of using learning-based models. To do this, in this paper, 3 models of artificial neural networks (ANNs), adaptive neuro-fuzzy inference system (ANFIS) and support vector regression model (SVR) have been used.
 
Materials and Methods
Due to the availability of a complete set of observations of GPS stations, radiosonde and meteorological stations in the north-west of Iran, the study and evaluation of the proposed models of the paper is done in this area. Observations of 23 GPS stations were prepared in 2011 for days of year 300 to 305 by the national cartographic center (NCC) of Iran. Out of 23 stations, observations of 21 stations are used to training of models and observations of the KLBR and GGSH stations are used to test the results of the models. In the first step, the observations of 21 GPS stations that are for training are processed in Bernese GPS software (Dach et al., 2007) and the total delay of the troposphere in the zenith direction (ZTD) is calculated. It should be noted that for every 15 minutes, a value for ZTD is calculated using the observations of each station. In the second step, the zenith hydrostatic delay (ZHD) is calculated. By subtracting ZHD from ZTD, zenith wet delay (ZWD) are obtained. ZWD values are converted to PWV values. The obtained PWV values are considered as the optimal output of all three models ANN, ANFIS and SVR. Also, the input observations of all three models will be the latitude and longitude values of each GPS station, day of the year and time.
 
Results and Discussion
After the training and achievement of the minimum cost function value for all three models, the PWV value is estimated by the trained models and compared at the location of the radiosonde station as well as the test stations. The mean correlation coefficient for the three models ANN, ANFIS and SVR in 6 days was 0.85, 0.88 and 0.89, respectively. Also, the average RMSE of the three models in these 6 days was to 2.17, 1.90 and 1.77 mm, respectively. The results of comparing the statistical indices of correlation coefficient and RMSE of the three models at the location of the radiosonde station show that the SVR model has a higher accuracy than the other two models. The average relative error of ANN, ANFIS and SVR models in KLBR test station was 14.52%, 11.67% and 10.24%, respectively. Also, the average relative error of all three models in the GGSH test station was calculated to be 13.91%, 12.48% and 10.96%, respectively. The results obtained from the two test stations show that the relative error of the SVR model is less than the other two models in both test stations.
 
Conclusion
The results of this paper showed that learning-based models have a very high capability and accuracy in estimating temporal and spatial variations in the amount of precipitable water vapor. Also, the analyzes showed that the SVR model is more accurate than the two models ANN and ANFIS. By estimating the exact amount of PWV, the amount of surface precipitation can be predicted. The results of this paper can be used to generate an instantaneous surface precipitation warning system if the GPS station data is available online.