# Hydrological Drought Frequency Analysis in Water Management Using Univariate Distributions
## 2 Methodology  
The data analysis period must be at least the World Meteorological Organization (WMO) reference period [17]. In general, low flow frequency analysis is performed for values of the minimum annual flows (AM), the values being the minimum flows recorded in one day of a year [3; 10]. In water management, data on the water deficit is of more interest, being a series of minimum 7-day low flows or minimum 30-day low flows, both of which are moving-average daily annual discharges. The 7-day time period eliminates the effect of daily fluctuations [3], being useful for run-of-river facilities, and the 30-day time period is useful for dams with water reservoirs. The analysis was performed for the three variables, namely minimum 1-day low flows, minimum 7-day low flows, and minimum 30-day low flows. These values are obtained from the chronological series of daily flows observed over the entire analysis period, by selecting minimum 1-day low flows, minimum 7-day-moving-average low flows, and minimum 30-day-moving-average low flows. Figure 1 shows the duration curves used in establishing the thresholds that define hydrological drought. These values represent the magnitude of the drought, but a drought is defined as an extended period of dryness, so in addition to the magnitude presented, the duration is also necessary [3; 6]. The duration is obtained using thresholds that define the drought period. These thresholds are obtained from the duration curve of average daily flows. Usual values of thresholds are 80%, 90% and 95% of the duration curve [6]. With the help  
Figure 1: Duration curves for Prigor river. of these thresholds, the cumulative annual drought durations and annual volumes can be determined (Figure 2). The duration curve of average daily flows can be approximated with a polynomial having logarithmic terms of the duration (d) and flow (\(k=\) Q/Q\({}_{\rm m}\)) as follows:  
\[k(d)=\sum_{i=1}^{n_{p}+1}C_{i}\cdot\ln(d)^{i-1} \tag{1}\]  
\[D(k)=\exp\left(\sum_{j=1}^{n_{k}+1}C_{j}\cdot k^{j-1}\right) \tag{2}\]  
If the duration curve is tabulated, cubic spline interpolation can also be used. The determination of the volumes for the thresholds (80%, 90% and 95%) is achieved by the annual summation of the threshold differences and time series (of daily average flows, 7-day moving average, 30-day moving average). Figure 2 shows how to determine the drought volume for the time series of average daily flows corresponding to the Q\({}_{80\%}\) threshold. The duration is determined by the annual summation of the days that have values of the chronological series lower than the established thresholds. A problem with extreme drought events is the much longer duration of low flow compared to the duration of other extreme values, such as floods. Moreover, if in floods there is a form of the flood that can be simplified (flood hydrograph), in droughs, a valid hydrograph cannot be obtained for these types of events; only recession curves are obtained (lack of precipitation). The complexity of the drought phenomenon compared to other hydrological phenomena is noticeable; it requires various types of analyses. In this article, only frequency analysis will be analyzed for minimum annual flows, durations and annual deficit volumes. The analysis is carried out according to Figure 3.  
For the study of hydrological drought, the time series of average daily flows and annual minimum flows are used. The chronological series of moving averages (7-day moving average, 30-day moving average) are obtained from the time series of daily average flows through moving averaging. Figure 2: Determining drought volumes and durations for the Q\({}_{80\%}\) threshold. From the time series of average daily flows, the duration curve of average daily flows is obtained by descending ordering. The thresholds for hydrological drought analysis (80%, 90%, 95%) are extracted from the duration curve of average daily flows.