## 4 Discussion  
### Landslide Motion and Rainfall Pattern  
There are many publications concerning rainfall triggers for landslides for the areas of central and southern Europe (e.g., [65; 66; 67]). The most common parameters used for rainfall threshold definition is intensity (of both antecedent cumulated rainfall and event rainfall) and duration [67]. The effect of the antecedent rainfall depends heavily on the hydrological conductivity of the landslide mass, and only rainfall events with a large amount of precipitation are considered capable of triggering the increase of deformation rate of deep-seated landslides. The authors of [68] noted in their case that the time lag \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Time Period of** & **Displacement Rates** & **Displacement Rates B** & **Total Rainfall (mm)** & **Time Lag between Rainfall Peak** \\
**Time Series** & **A (mm/yr)** & **(mm/yr)** & **(Kate Vilasis Station)** & **and InSAR Time Series (Days)** \\ \hline
6 September 2016– & 14.8 & 20.8 & 712 & 17.6 \\
28 May 2017 & 14.8 & 20.8 & 712 & 17.6 \\ \hline
19 September 2017– & & & & \\
23 April 2018 & 16.6 & 92.6 & 1041 & 12 \\ \hline
9 October 2019– & & & & \\
6 May 2020 & 19.1 & 26.6 & 704 & 11 \\ \hline
24 September 2020– & & & & \\
31 May 2021 & 30.0 & 99.8 & 935 & 12 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Displacement rate A corresponds to the linear displacement rate of the Krini landslide (descending orbit) before the maximum seasonal rainfall is reached, and linear displacement rate B corresponds to the displacement rate following the rainfall peak (see Figure 11 for trendlines). The total rainfall corresponds to the total rain during each time period. The displacement rate A & B values of the last line (period 2020–2021) refers to the ascending orbit data. for peak precipitation and peak deformation rate may be up to 20 days, while [65] found a 12-day relation. Since proximal rainfall data is available for Achaia (Figure 1), we examined the correlation between the rainfall patterns and the seasonal movement of the Krini landslide because for this landslide the displacement rate is well constrained by the co-located GNSS station (Figure 9 and Figure S10). For this purpose, we used a signal processing method, the cross correlation [69]. We used this approach to convert our data to signal and compare them, so that we could determine if a time delay (time lag) exists between the maximum peaks of the time series of rainfall and of InSAR, respectively. The cross-correlation technique is used to measure the similarity of two time series as a function of the displacement of one relative to the other and to detect correlations among these two series [70]. We applied this technique to the daily rainfall dataset, which could play an important role in the movement of a landslide and to the InSAR time series. We used the InSAR time series of the descending track due to the completeness of its dataset during the period 2016-2020 rather than the time series from the ascending track (Figure 4). First, we resampled and interpolated the daily rainfall data to fit it to the time span of the InSAR time series. Because it was complete, we selected the data from the meteorological station Kato Vlassia (Figure 1a) and then performed the correlation for motions (displacements) of the Krini landslide. We applied the cross correlation to the two time series, especially to three subperiods (see boxes in Figure 10). These time periods consisted of three sets of eight months of observations that had complete datasets. We selected to work with three separate time periods because our InSAR time series contains network gaps (Figure 4) which correspond to gaps in the time series. We used the following time periods: 6 September 2016-28 May 2017, 19 September 2017-23 April 2018 and 9 October 2019-6 May 2020. We calculated the displacement rate before and after the changes of the displacements through fitting the trendline to the data (Table 2).