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

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 (SWD_GPS-SWD_ANFIS). 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 (ZWD_ANFIS) are compared with the ZWD_GPS. 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 (Tomo_Voxel) method and troposphere tomography using artificial neural network (Tomo_ANN). 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, Tomo_Voxel and Tomo_ANN have been calculated as 0.9131, 0.8863 and 0.9006, respectively. The minimum relative error for the Tomo_ANFIS, Tomo_ANN and Tomo_Voxel 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 Tomo_ANFIS 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.