# Assessment of ZTD Derived from COSMIC Occultation Data with ECWMF, Radiosondes, and GNSS
## 2 Materials and Methods
### ZTDs from Ground-Based GNSS-ZTD  
Ground-based GNSS-ZTD observation data are from the International GNSS Service (IGS) products [27], and named ZPD files, which contain the total zenith tropospheric delay, the north-south and east-west gradient components of the delay, and the root mean square error. The meteorological parameters (such as the air pressure (hPa), temperature (K), and relative humidity (%)) are obtained from the IGS stations in Rinex format. It is difficult to continuously measure from radiosonde due to its high cost and disposable equipment, but observations from ground based GNSS can provide continuous observations throughout the year. The Saastamoinen model is read as [4; 28]:  
\[\rm{ZTD}=0.002277\frac{P_{0}+\Big{(}0.05+\frac{1255}{T_{0}+273.15}\Big{)}e}{f( \varphi,H)}, \tag{2}\]  
\[\rm{f}(\varphi,H)=1-0.0026\cos 2\varphi-0.00028H, \tag{3}\]  
where ZTD, e are the zenith troposphere delay (m) and wet pressure (mbar), respectively; \(\rm{P_{0},T_{0},\varphi,H}\) are the dry atmospheric pressure (hPa), temperature (K), and geographic latitude (degree), altitude (km) at the GPS receiver, respectively. f (\(\varphi\), H) is the vertical total mass center of the atmosphere, and only related to latitude and altitude. The ZTD derived from ground-based GNSS data of IGS is corrected to the lowest tangent point height of the matched occultation data by the press-height formula, and the corrected ZTD data with the bottom height \(\rm{H_{occ}}\) of occultation event can be obtained, which are named gnsZTD. Since the meteorological observation data of GNSS stations can only provide the surface temperature and pressure and relative humidity, but not the profile with temperature, humidity, and pressure along the height, it is difficult to obtain accurate ZTD changes from \(\rm{H_{occ}}\) to the ground. For 40% of the detection depth of COSMIC-1 is less 1 km, we assume that the temperature gradient of this part is fixed:  
\[\rm{T(h)=T_{0}-L(h-H)}, \tag{4}\]  
in which L is temperature laps rate, 6.5 (K\(\cdot\)km\({}^{-1}\) ), and T\({}_{0}\), H are referenced to the above explanations. In turn, the temperature at a special height h can be expressed with the temperature at the GPS receiver from ground-based observation or ECWMF model. Then, based on the pressure formula read as:  
\[\rm{\frac{\partial P}{\partial h}=\frac{Pg}{R_{d}T(h)}}, \tag{5}\]  
the pressure \(\rm{P_{occ}}\) at \(\rm{H_{occ}}\) can be obtained by integration from ground to \(\rm{H_{occ}}\). In (5), g is the gravity coefficient; \(\rm{R_{d}}\) is 287 (\(\cdot\)kg\({}^{-1}\cdot\)K\({}^{-1}\) ). Finally, the pressure at \(\rm{H_{occ}}\) is used to obtain occzTD via (2) with the assumption that the ZTD at \(\rm{H_{occ}}\) has the same proportional coefficient to P\({}_{\rm occ}\) as the ground ZTD to its pressure. Equation (5) with the height correction of hydrostatic delay is applied, since the atmPrf file only provides dry temperature and dry pressure. Bottom-down corrections introduce errors into the corrected ZTD if the humidity is provided by the ECMWF, and there is an increased reliance on ECMWF for atmPrf in applications when the height is below the atmPrf's bottom. We will try to correct the height deviation of the occultation base with other data in the future. Since the bottom heights of atmPrf, echPrf, and sonPrf are all the bottom height of the atmosphere profile from the occultation data, we corrected the ground-based ZTD data to this height based on the above correction formula. Therefore, we unified the ZTD obtained in different ways into the same height range for comparison. However, not every IGS station provides meteorological observations, not to mention complete meteorological observations throughout the day. Moreover, there is no guarantee that the temporal resolution of the meteorological observation data at each station is the same.