Data Pre-Processing

The accuracy of the NRT ZTDs, derived from the AUTh GNSS network, was examined by comparing the data against high-quality reference ZTD data provided by EPN. Based on the availability of the EPN weekly combined ZTD solutions, the validation was performed over the AUT1 station (Figure 1b) using concurrent data of the 2018 dataset. Following previous studies [60–62], the accuracy of the ZTD observations was defined as the standard deviation of the difference between the AUT1 and EPN ZTDs. The analysis resulted in an accuracy of 7.6 mm, which is between the optimal (5 mm) and

target (10 mm) accuracy value according to the E-GVAP standards for NRT ZTDs used in the NWP models [63]. This outcome was a strong indication that the accuracy of the AUTh GNSS ZTD data was sufficient to assimilate them into the WRF modeling system.

Further, the observations in the 3D-var system are considered to have unbiased errors with respect to the WRF model. To meet this assumption, a statistical bias correction was applied to the ZTD data for each studied precipitation episode. More specifically, the differences between the observed and modeled ZTDs were computed for each GNSS receiver during a 10 day period prior to each event using the WRF simulations conducted for the model background errors covariance matrix specification (see Section 2.2.1). Then, the corrections were estimated as the mean values of the ZTD differences and they were subtracted from the ZTD observations that were lined up for data assimilation. Even though this method provides statistical corrections, this is a standard bias correction approach for ZTD data that proved to be successful in reducing the observations-model divergences and capturing the systematic errors between the ZTD observations and model forecasts [16,18–25,28]. The last stage of the ZTD data pre-processing included a selection algorithm based on the following conditions: (a) The formal ZTD error to be lower than the standard deviation of the difference between the observed and modeled ZTD, (b) the ZTD difference between observations and model output to be lower than five times the ZTD formal error, and (c) the difference between the receiver height and the model's orography to be below 100 m. Similar criteria have been applied in previous studies [19–25]. Based on data availability and the above selection algorithm, the number of GNSS reference stations used per event ranged from 48 to 56. The assimilated ZTD observations had the same range, since assimilation was performed once (at 0000 UTC or 0600 UTC) during the conducted experiments. The locations of the 55 stations used for the event of 27 November 2019 are shown in Figure 1b, demonstrating a sufficient and homogeneous spatial coverage of the Greek territory.
