## 1 Introduction  
The modeling of troposphere wet delay in real-time applications is more difficult than that of the hydrostatic part due to the fast spatio-temporal variation of water vapor. The tropospheric delays are calculated by integrating the refractivity along the signal path and mapped in the zenith direction with various mapping functions [1; 2]. Numerous atmospheric models have been developed to determine tropospheric delay from the 1960s to the present. The most commonly used models are [PERSON] [3], [PERSON] [4], [PERSON] [5], [PERSON] [6], [PERSON] et al. [7], and [PERSON] and [PERSON] models [8]. These models generally use the temperature, pressure, water vapor pressure, station altitude, and latitude to calculate tropospheric delay. The zenith hydrostatic delay (ZHD) can be determined within a millimeter accuracy by empirical models [4]. These models achieve deviations of up to about 20% in determining wet delay [7]. The error in the zenith direction for the [PERSON] model is approximately 0.2 mm for hydrostatic delay and 30 mm for wet delay [9]. The determination of zenith wet delay (ZWD) with a high spatial resolution is an important issue in meteorological estimation studies, as well as real-time positioning based on Global Navigation Satellite System (GNSS) observations [10]. In the last decade, Continuously Operating Reference Station (CORS) networks have been established in many countries. The Real Time Kinematic (RTK) method's positioning accuracy depends on the inter-station distances of the GNSS networks. The troposphere delay error reaches a few cm at distance of 70 km and above between the reference stations [11]. In addition, tropospheric delay can cause errors in the height component up to several cm for RTK positioning [12]. The error increases when the regional meteorological conditions notably change, and differences up to 3-4 cm may occur, depending on the season. The wet delay for any location can be accurately estimated with an effective interpolation method by using the surrounding GNSS station observations. In this way, a sufficient resolution and accuracy for meteorological forecasts can be achieved. Therefore, tropospheric error interpolation becomes more important, especially for sparse GNSS networks [13]. Spatial interpolation of the tropospheric wet delay is a difficult issue due to the rapid spatial variations of water vapor in the troposphere. Furthermore, the complexity of the physical structure of the atmosphere adversely affects interpolation methods designed without using meteorological parameters. Although different methods (IDW: Inverse Distance Weighted, LIM: Linear Interpolation Method, OK: Ordinary Kriging, etc.) have been presented for tropospheric interpolation in GNSS networks, it can be said that zenith wet delay interpolation is still a challenging issue, especially when inter-station distances increase [11]. Therefore, the incorporation of meteorological parameters into the advanced models, such as the artificial neural network model, may enhance the interpolation performance. The tropospheric delay for GNSS signals has been defined by mathematical models based on the relative humidity, pressure, and temperature meteorological parameters in various studies [2; 4; 7; 8; 9]. On the other hand, ZWD caused by water vapor also depends on the weighted mean temperature of the troposphere. Therefore, the pressure, temperature, weighted mean temperature, and water vapor pressure were used as the input in the artificial neural network (ANN) model for spatial ZWD interpolation in the study. In this context, modeling and interpolation of the troposphere delay is of great importance for the field of GNSS meteorology, which has become an important field of research. Nowadays, artificial neural networks have become a frequently used effective method for estimating meteorological parameters. Moreover, ANN is a powerful nonlinear approach in dealing with complicated problems, such as meteorological forecasts and tropospheric estimation studies.