**1. Introduction**

The use of global navigation satellite systems (GNSSs) is essential in a variety of fields that require precise location and time information, including aviation (e.g., Sabatini et al. [1]), transportation (e.g, Kubo et al. [2]), search and rescue services (e.g, Molina et al. [3]), agriculture (e.g., Kahveci et al. [4]), and maritime operations (e.g., Ostolaza et al. [5]). Additionally, remote sensing of atmospheric constituents with the exploitation of GNSS signals is nowadays a well-established and widely applied approach, which is referred to as GNSS meteorology [6]. The methodology is based on the fact that the radio signals transmitted from the satellites to the receivers on the ground are delayed when propagating through the troposphere due to the presence of dry gases and water vapor [7]. Advanced GNSS processing techniques produce various tropospheric products that are used in several meteorological applications, including nowcasting and numerical weather prediction (NWP) [8–11],

as well as weather monitoring, including extreme events [12–14]. Special meteorological interest derives from the near-real time (NRT) ZTDs, which are estimated based on raw GNSS observations. The ZTD is a standard GNSS product expressing the total signal delay in the zenith direction above a receiver [6,15]. This vertical lag contains information on the total columnar amount of water vapor [16].

In Europe, collaborative scientific efforts over the past two decades substantially contributed to the development of networks and analysis centers collecting and processing, respectively, GNSS data to compute tropospheric delays. The establishment of the European GNSS water vapor program (E-GVAP; [17]) in 2005 allowed for the operational distribution of NRT ZTD estimates to the meteorological community [6]. This service encouraged the implementation of precipitation forecast impact studies involving the assimilation of NRT ZTD observations into NWP models. Poli et al. [18] found an improvement in the prediction of precipitation patterns over France during spring and summer when assimilating ZTD data into a global four-dimensional variational (4D-var) assimilation and forecasting system. Positive impacts of ZTD data assimilation on precipitation forecasts of convective-scale systems over France were also demonstrated by Yan et al. [19,20], using the three-dimensional variational (3D-var) assimilation systems of AROME, ALADIN, and Meso-NH (Mesoscale Non-Hydrostatic) atmospheric models. Eresmaa et al. [21] positively evaluated the application of a bias correction algorithm in the ZTD observations prior to assimilating them into the 3D-var/HIRLAM (HIgh Resolution Limited Area Model) modeling system. In addition, their study showed mixed results (positive/negative) concerning the impact of ZTD assimilation on the predicted precipitation, which were dependent on the forecast lead-time. Similarly, Bennitt and Jupp [22], and Schwitalla et al. [23], who performed numerical experiments over Europe with the United Kingdom (UK) Meteorological Office 3D and 4D-var model, and the 3D-var/WRF model, respectively, found no clear impact of ZTD assimilation on precipitation forecasts. Bennitt and Jupp [22] further showed that 4D-var assimilation does not lead to better forecasts compared to the assimilation under the 3D-var system. Boniface et al. [24] identified that the impact of ZTD assimilation in AROME model depends on the rainfall synoptic conditions, while Arriola et al. [16] highlighted the importance of ZTD observations processing before the assimilation application. More recent studies focused on investigating different observational bias correction methods and on estimating spatiotemporal correlations of observations errors for application on ZTD data used for data assimilation [25–27].

The literature review shows that improvements in the precipitation forecast skill may be gained by assimilating ZTD observations into NWP models. However, regional studies using the WRF modeling system are relatively rare (e.g., Rohm et al. [28]), while no research focusing on Greece has ever been conducted. The present study aims to fill this knowledge gap by examining the impact of GNSS ZTD data assimilation on the precipitation forecast skill of the 3D-var/WRF model. For that reason, four dry and three wet period heavy precipitation events, observed in 2018 over Greece, were selected to examine the model's performance under different meteorological conditions. Prior to assimilation, an integrated method was employed to process the ZTD observations in order to review their quality, correct their systematic errors with respect to the model, and finally, to use those that fulfilled specific selection criteria. The results of the numerical experiments are compared against precipitation observations obtained from the network of surface meteorological stations operated by NOA [29]. The applied model configuration is based on NOA's operational weather forecasting system in order to assess the GNSS ZTD data assimilation capacity in terms of supporting real-time weather prediction applications.
