# A New Zenith Tropospheric Delay Grid Product for Real-Time PPP Applications over China
## 1 Introduction  
In GNSS data processing, in order to avoid the rank defect issue, slant tropospheric delays along the signal paths between visible satellites and the receiver are usually mapped into the zenith direction (i.e., zenith total delay or ZTD) with a mapping function. ZTD can be divided into zenith hydrostatic delay (ZHD) and zenith non-hydrostatic delay which is always named as zenith wet delay (ZWD). ZHD, which accounts for about 90% of the ZTD, can be precisely calculated on the bases of models given the observed meteorological parameters. ZWD or the correction to _a priori_ ZWD which will assimilate ZTD residual errors, however, usually needs to be estimated in the data processing because of the complex variations of water vapor in both time and space. There are some empirical tropospheric delay estimation models, among which Hopfield model [1] and Saastamoinen model [2] are most commonly used. These two models can provide _a priori_ ZTD with accuracies of decimeters to sub-decimeters when precise meteorological parameters are available. Great efforts have also been made to develop new _a priori_ models with good performances even without precise meteorological measurements, such as the UNB models which were initially developed for users of the Wide Area Augmentation System (WAAS). In North America, the bias of ZTD derived from UNB3 is 2.0 cm and decreases to \(-0.5\) cm for UNB3m [3, 4]. The deviations of ZTDderived from UNB3m, however, can reach 6.1 cm in high altitude regions [5]. The EGNOS model, which is a simplified version of UNB3, can provide ZTD with equivalent accuracy compared to the meteorological-parameter-based Hopfield or Saastamoinen model [6]. [PERSON] et al. developed a new global tropospheric zenith delay model (IGGtrop) based on the NCEP reanalysis data. According to their assessment using 125 International GNSS Service (IGS) stations, the mean bias and Root Mean Square (RMS) of ZTD are about 0.8 and 4.0 cm, respectively [7; 8]. [PERSON] et al. analyzed the temporal and spatial variations of ZTD based on Global Geodetic Observing System (GGOS) atmosphere data and built the GZTD model using spherical harmonic function. Compared to IGGtrop, GZTD has equivalent accuracies but less model parameters [9]. A wide range of mapping functions has also been developed in the past. There are mainly two kinds of mapping functions. The first one is the so-called empirical mapping function which only needs the epoch time and stations approximate coordinates as inputs, such as the Niell Mapping Function (NMF) [10], the Global Mapping Function (GMF) [11] and mapping functions derived from Global Pressure and Temperature 2 (GPT2/GPT2w) [12; 13]. These mapping functions were developed based on historical radiosondes or reanalysis products, which do not need external data in geodetic data processing. The second kind of mapping functions, such as Isobaric Mapping Functions (IMF) [14] and Vienna Mapping Functions (VMF1) [15], are derived from the operational analysis fields of numerical weather models at the epoch of the observations. They are theoretically more accurate than empirical mapping functions, but they rely on external data source. Due to the strong correlation between ZTD and the vertical position, Precise Point Positioning (PPP) processing usually needs several tens of minutes to separate these two parameters for convergence, which significantly limits its real-time applications. The convergence time is much longer for users only using Chinese BeiDou Navigation Satellite System (BDS) due to the current satellite constellation, namely most of the satellites are geostationary satellites (GEO) and inclined geostationary satellites (IGSO) with slow changes of geometry relative to ground users. If the accurate _a priori_ ZTD are available, ZTD can be fixed or strongly constrained in PPP processing and the convergence can be efficiently accelerated [16; 17].