## 3 Results  
### Observed Correlation of Rainfall, GNSS-IWV, and CAPE at the GNSS Station Locations  
#### 3.1.1 Rainfall, GNSS-IWV, and CAPE Characteristics at the GNSS-IWV  
In this study, we aim to decipher the influence of both GNSS-IWV and CAPE on extreme-rainfall events. We use the 90 th percentile of daily mean rainfall to characterize extreme rainfall. The corresponding 90 th percentiles for the stations TUCU and CATA are 22 mm/day and 20 mm/day, respectively. The median value of daily mean rainfall is 3.1 mm/day for TUCU and 2.8 mm/day for CATA, respectively. We first show that each station (TUCU and CATA) in the eastern central Andes has a different rainfall distribution.  
We rely on a two-sample Kolmogorov-Smirnov (KS) test to compare the distribution of rainfall at both stations during 2008-2013 due to data availability for CATA station. Based on the test result the hypothesis that rainfall in both stations are from the same continuous distribution is rejected. Therefore, we accept the alternative hypothesis that each station has a different rainfall distribution. The \(p\)-value (\(p\) = 4%) confirms the difference between both distributions at the 5% level. Similarly, the KS test for the comparison of IWV data shows that they are drawn from different distributions.  
Similar to a previous work [48], our analysis suggests that the rainfall and GNSS-IWV distributions are best fitted by a lognormal distribution. The estimated parameters \(\mu\) and \(\sigma\) reveal different values for each station that underline their different climatic environments.  
The density function of the lognormal distribution is defined as follows [49]:  
\[f(y)=\frac{1}{\sigma y\sqrt{2\pi}}\exp\Biggl{(}\left[\frac{-(logy-\mu)^{2}}{2 \sigma^{2}}\right]\Biggr{)} \tag{11}\]  
where the logarithm of \(y\) has a normal distribution. \(\mu\) is the mean of logarithmic values, and \(\sigma\) is the standard deviation of logarithmic values.  
We note that the tail of the rainfall distribution can be described by a power law starting at \(x_{min}\) = 12.9 and with the estimated exponent \(\alpha\) = 2.5 for TUCU station and \(x_{min}\) = 28 and the estimated exponent \(\alpha\) = 2.9 for CATA station (Figure 2A). In order to compare both stations, we show the exceedance probabilities of the binned rainfall and GNSS-IWV data (Figure 2).  
Based on the approach described by [PERSON] [50], we fit the power-law distribution to CAPE data using a maximum likelihood estimator. Relying on the goodness-of-fit parameter, we observe that a power law is a plausible hypothesis for the CAPE data. (Figure 3A,B). In order to homogenize the number of observations of CAPE, as there  
Figure 2: Logarithmically binned rainfall data (**A**) and GNSS-IWV (**B**) for TUCU station (blue dots) and for CATA station (red dots). The fitting parameters of the lognormal distribution (see Equation (11)) show the differences between two stations (2008–2013). Note that the tail of the distribution exhibits power-law behaviour starting at \(x_{min}=12.9\) and with the estimated exponent \(\alpha=2.5\) for the TUCU station and \(x_{min}=28\) and the estimated exponent \(\alpha=2.9\) for the CATA station.  
are many more observations at lower magnitudes as shown in (Figure 3A,B), we use a logarithmic binning of CAPE.