## 3 Materials and Methods
### Drought Hydrographs  
Drought hydrographs visually denote streamflow declines, thereby indicating the minimum streamflow values recorded for the corresponding river. These graphs are constructed using datasets collected at specific measurement points, e.g., a limnigraphic station, and are plotted on a chart where the vertical axis represents streamflow and the horizontal axis represents time. These graphical representations facilitate the identification of hydrological drought duration.  
In the construction of drought hydrographs based on streamflow data in rivers, the methodological guidelines applied in flood hydrograph generation are used. This involves graphically and numerically determining the duration of the flood and its peak flow, which represents the maximum flow of the flood. From this and with methodological adjustments, annual values of minimum flows (\(Q_{V}\)) in m\({}^{3}\)/s and drought durations in days are established. With these identified data, statistical probability distribution methods are then applied for estimation [16].  
Comprehending drought hydrographs is essential for efficiently managing available water resources during different seasons. This understanding aids in anticipating water scarcity and implementing mitigation measures to meet human needs in the anticipated extreme event. Figure 4 presents the components to describe a drought hydrograph, where \(Q_{V}\) is the valley streamflow (the minimum value recorded in the dataset for the year under study); \(V_{S}\) represents a volume under the \(q_{v}(t)\) curve; \(q_{V}(t)\) is the curve function described by the drought hydrograph; and \(Q_{Reference}\) corresponds to the maximum value streamflow rate of the drought hydrograph.  
Figure 3: Observed dataset dispersion regarding the standard deviation.  
When elaborating the drought hydrographs from Figure 5, the authors considered the datasets from 1972 to 2021 provided by the Monteria Automatic station. This involved numerically identifying minimum streamflow values, \(Q_{V}\), and delimiting the extremes of the hydrograph, including the onset of the descent, the minimum zone, and the rise of the observed streamflows in the river. The hydrometric information available at the Monteria Automatic station enables the creation of the graphs shown in Figure 5, highlighting depressions in the river's instantaneous streamflows. Figure 11 presents the total annual drought hydrographs recorded at the Monteria Automatic station.  
Figure 4: Standard drought hydrograph.  
Figure 5: Annual drought hydrograph recorded at the Monteria Automatic station from 1972 to 2021. (**a,b**) Before the hydroelectric power plant enters operation. (**c,d**) After the hydroelectric power plant enters operation.  
Each hydrogen represents the maximum drought experienced in the study year, providing insight into the multiannual minimum streamflow or valley streamflow, \(Q_{V}\) (m\({}^{3}\)/s), as well as the duration of each dry event in the Sinu River basin.  
The minimum streamflow for the entire dataset occurred in 1988 with a streamflow of 37.50 m\({}^{3}\)/s, and the maximum minimum streamflow was 160.00 m\({}^{3}\)/s, with an average minimum streamflow of 86.22 m\({}^{3}\)/s. Concerning durations, there is a minimum drought duration of 6 days in 2010 and a maximum drought duration of 95 days in 1983.  
Overall, maximum droughts occurred during the period when the hydroelectric plant was not in operation, while the minimum duration of drought occurred when it was operational.  
Time durations were computed considering the drought hydrographs, as shown in Table 2. The periods of 1970-1999 and 2020-2021 were identified in order to neglect and consider the effects produced by the Hydropower Plant Urra I, respectively.