Page - 572 - in Book of Full Papers - Symposium Hydro Engineering

where, 𝐷 𝐼 is the difference in inflows, 𝐼 𝑂 is the observed inflow, 𝐶 𝐷 𝐼 is the cumulative difference in inflows, and 𝜎 ( ) is standard deviation. However, when calculating 𝐶 𝐷 𝐼 in “Eq. [3],” the upper limit on 𝐶 𝐷 𝐼 has to be considered because a considerable amount of inflows that cannot store at the reservoir are not associated with the future water use. In order to determine a threshold, this study calculated “Eq. [3] and [4]” repeatedly with changing the threshold and then conducted Receiver Operating Characteristics (ROC) analysis. ROC analysis is commonly used in verification of weather forecast, but it is also used in verification of drought indices compared with actual drought cases. This study set ROC model as “Table 1” ROC analysis is separated observed value and prediction value. In this study, the observed value is defined as ‘Water supply’ and the prediction value is defined as ‘DIDI’ in “Table 1” If an actual event occurs and an event predicted in the forecast result, it is expressed as ‘Hit (H).’ Whereas, if an actual event occurs and an event did not predict in the forecast result, it is expressed as ‘Missing (M).’ If an actual event does not occur and an event predicted in the forecast result, it is expressed as ‘False (F).’ On the other hands, if an actual event does not occur and an event did not predict in the forecast result, it is expressed as ‘Negative hit (N).’ Table 1 ROC classification model Water supply Reduction Normal DIDI Drought Hit (H) False (F) Normal Missing (M) Negative Hit (N) The ‘Water supply’ in “Table 1” means that water supply is reduced or normal when dam operation is simulated using the water supply adjustment criteria and historical inflow data. ‘Drought’ in “Table 1” means that DIDI is less than zero and ‘Normal’ of DIDI means that DIDI is equal to or greater than zero. H, F, M, and N with various thresholds can be calculated using ROC classification model in “Table 1.” Then ‘Hit rate (HR)’ and ‘False Alarm Rate (FAR)’ can be estimated by “Eq. [5] and [6].” 𝐻 𝑅 = 𝐻 /(𝐻 + 𝑀 ) [5] 𝐹 𝐴 𝑅 = 𝐹 /(𝐹 + 𝑁 ) [6] Finally, ROC score has to be calculated to evaluate results of ROC analysis quantitatively. ROC score, which indicates how well the drought index can reproduce actual water shortage, is calculated as the area shown in “Fig. 1.” The procedure for calculating the DIDI described above is shown in “Fig. 2,” and the optimal DIDI is the DIDI to which the threshold value having the maximum ROC score is applied. 572