# Hydrological Drought Frequency Analysis in Water Management Using Univariate Distributions
## 5 Conclusions  
This article presents hydrological drought analysis using frequency analysis. Considering the complexity of this hydrological phenomenon, it is necessary to establish well-founded criteria regarding the analysis of minimum flows, deficit volumes and drought durations. Thus, this article presents the necessary criteria regarding the frequency analysis of minimum annual flows, the establishment of drought thresholds based on the duration curve of the average daily flows, as well as the deficit volumes and drought durations corresponding to the thresholds. A preferred analysis in hydrology is the use of average monthly flows, which often do not reflect the phenomenon of drought. In this article, the analysis with time series moving averages for 7 and 30 days is proposed [7]. The methodology provides the necessary mathematical support for frequency analysis of hydrological drought for the elaboration of a norm in Romania. Mathematical support in statistical analysis is useful, because the use of software (EasyFit, HEC-SSP,... ) without knowledge of mathematical foundations often leads to superficial analyses with negative consequences in water management. The case study consisted of hydrological drought analysis for the Prigor River. The frequency analysis was performed using eight probability distributions, their parameters being estimated with two of the most used parameter estimation methods in the analysis of extreme phenomena in hydrology. All the mathematical characteristics necessary for the application of the eight analyzed distributions, for the method of ordinary moments and the method of linear moments are presented. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Distribution**} & \multicolumn{3}{c}{**Methods of Parameter Estimation**} \\ \cline{2-3}  & \multicolumn{2}{c}{**L-moments**} \\ \cline{2-3}  & **RME** & **RME** & **RAE** \\ \hline  & 95\% threshold & \\ \hline LN3 & 0.2118 & 0.7498 \\ \hline PE3 & 0.2119 & 0.7498 \\ \hline W3 & 0.2121 & 0.7497 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Distribution performance values for annual drought durations. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Distribution**} & \multicolumn{6}{c}{**Methods of Parameter Estimation**} & \multirow{2}{*}{**Observed Data**} \\ \cline{2-3}  & \multicolumn{2}{c}{**MOM**} & \multicolumn{3}{c}{**L-moments**} & \multirow{2}{*}{**0.307**} & \multirow{2}{*}{0.152} \\ \cline{2-3} \cline{5-8}  & **RME** & **RAE** & & & & & \\ \cline{2-3}  & LN3 & 0.0169 & 0.0577 & 0.0087 & 0.0342 & & 0.197 & & \\ \hline PE3 & 0.0114 & 0.0431 & 0.0057 & 0.0257 & & 0.159 & & \\ \hline IPV & 0.0187 & 0.0632 & 0.0102 & 0.0392 & & 0.212 & 0.307 & 0.152 \\ \hline WH3 & 0.0124 & 0.0573 & 0.0096 & 0.0444 & & 0.083 & & \\ \hline FL3 & 0.0141 & 0.0495 & 0.0066 & 0.0306 & & 0.186 & & \\ \hline W3 & 0.0087 & 0.03567 & 0.0056 & 0.0254 & & 0.155 & & \\ \hline WK5 & 0.0058 & 0.0273 & 0.0055 & 0.0253 & & 0.152 & & \\ \hline L5 & 0.0110 & 0.0401 & 0.0056 & 0.0256 & & 0.152 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Distribution performance values for minimum annual flows. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Distribution**} & \multicolumn{3}{c}{**Methods of Parameter Estimation**} \\ \cline{2-3}  & \multicolumn{2}{c}{**L-moments**} \\ \cline{2-3}  & \multicolumn{2}{c}{**RME**} & **RAE** \\ \hline  & 95\% threshold & \\ \hline LN3 & 0.2118 & 0.7498 \\ \hline PE3 & 0.2119 & 0.7498 \\ \hline W3 & 0.2121 & 0.7497 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Distribution performance values for annual deficit volumes. For ease of application of these distributions, parameter approximations were made for MOM and L-moments. For confidence interval calculation using Chow's relation [37], Appendix A presents the frequency factor of distributions analyzed for both parameter estimation methods. A criterion for choosing distributions for L-moments analysis is the variance of \(\tau_{3}-\tau_{4}\).