# Hydrological Drought Frequency Analysis in Water Management Using Univariate Distributions
## 3 Case Study  
The presented case study consists in the determination of minimum annual flows, drought durations and annual volume deficits on the Prigor River, Romania, using the proposed methodology.  
The Prigor River is the left tributary of the Nera River, and it is located in the south-western part of Romania, as shown in Figure 4.  
The main morphometric characteristics of the river are presented in Table 2[38].  
In the section of the hydrometric station, the drainage area is 141 km\({}^{2}\) and the average altitude is 729 m. The minimum 1-day data are presented in Table 3.  
There are 31 annual observed data for low flows, with the values of the main statistical indicators presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & \\ \hline \multirow{2}{*}{**Low Flows**} & \(\mu\) & \(\sigma\) & \(C_{v}\) & \(C_{s}\) & \(C_{k}\) & \(L_{1}\) & \(L_{2}\) & \(L_{3}\) & \(L_{4}\) & \(\tau_{2}\) & \(\tau_{3}\) & \(\tau_{4}\) \\ \cline{2-11}  & **[m\({}^{3}\)/s]** & **[m\({}^{3}\)/s]** & [-] & [-] & [-] & [m\({}^{3}\)/s] & [m\({}^{3}\)/s] & [m\({}^{3}\)/s] & [-] & [-] & [-] & [-] \\ \hline \multirow{2}{*}{\(1\)-day} & minimum & \multirow{2}{*}{0.335} & 0.157 & 0.469 & 1.359 & 4.593 & 0.335 & 0.084 & 0.026 & 0.013 & 0.251 & 0.307 & 0.152 \\  & & & & & & & & & & & & \\ \hline \hline \end{tabular} Where \(\mu,\sigma,C_{v},C_{s},C_{k},L_{1},L_{2},L_{3},L_{4},\tau_{2},\tau_{3},\tau_{4}\) represent the mean, the standard deviation, the coefficient of variation, the skewness, the kurtosis, the four L-complet of variation, the L-skewness, and the L-kurtosis, respectively P.  
\end{table}
Table 4: The statistical indicators of the data series.  
Figure 4: The Prigor River location—Prigor hydrometric station.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Length** & **Average** & **Sinusity** & **Average** & **Drainage** \\
**[km]** & **Stream Slope [\%]** & **Coefficient [-]** & **Altitude, [m]** & **Area, [km\({}^{2}\)]** \\ \hline
33 & 22 & 1.83 & 713 & 153 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The morphometric characteristics.  
For parameter estimation with L-moments, the data series must be in ascending order for the calculation of natural estimators, the respective L-moments.  
In this case study, for low-flow frequency analysis with MOM, a coefficient of 3 was chosen for the choice skewness, to reflect the perennial/ephemeral character of the river. It can be seen from Figure 5 that the predominant droughts are in the summer, and in the winter period, the important droughts appear only in 2012, 2013 being the driest year as well. The droughts of 2012 and 2013 are predominantly in the summer period, having the highest magnitude in those years.  
The deficit volumes calculated for the thresholds of 95% are presented in Table 5. The analysis was also conducted for other thresholds, such as 90% and 80%.  
The drought durations determined for the thresholds of 95% are presented in Table 6. The analysis was also conducted for other thresholds, such as 90% and 80%.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & & \multicolumn{8}{c}{**95\% Threshold**} \\ \hline  & & **1990** & **1991** & **1992** & **1993** & **1994** & **1995** & **1996** & **1997** & **1998** & **1999** & **2000** \\ \hline D & [days/year] & 23 & 0.0 & 23 & 2.0 & 54 & 0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 2.0 \\  & 2001 & 2002 & **2003** & **2004** & **2005** & **2006** & **2007** & **2008** & **2009** & **2010** & **2011** \\ \cline{3-12} D & [days/year] & 1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 59 & 0.0 & 0.0 & 34 \\  & **2012** & **2013** & **2014** & **2015** & **2016** & **2017** & **2018** & **2019** & **2020** & & \\ \cline{3-12} D & [days/year] & 59 & 39 & 0.0 & 35 & 0.0 & 67 & 33 & 27 & 0.0 & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: The annual drought durations.  
Figure 5: Water deficit graph for the Prigor River for the WMO reference period.