Estimation of Reservoir Volumes at Drafts of 40% - 90%: Drought Magnitude Method Applied on Monthly River Flows from Canadian Prairies

The draft ratios for sizing the reservoirs can vary within a wide range (40% - 90% of the mean annual flow, MAF), depending upon the demands for water by various users, and environmental and ecological considerations. The reservoir volumes based on the drought magnitude (DM) method were assessed at aforesaid draft ratios using monthly-standardized hydrological index (SHI) sequences of 10 Canadian rivers located in the Canadian prairies and northwestern Ontario. These rivers are typified by a high level of persistence lag-1 autocorrelation, ρ1m ≥ 0.50 and up to 0.94) and coefficient of variation (cvo) in the range of 0.42 to 1.48. The moving average (MA) smoothing of monthly SHI sequences formed the basis of the DM method for estimating reservoir volumes. The truncation or cutoff level in the SHI sequences was found as SHIx [=(α - 1)μo/σo], [(α - 1)μo/σmax], or [(α - 1)μo/σav], where α (=0.40 to 0.90) is the draft ratio i.e. proportion of the MAF, μo and σo are the overall mean and standard deviation of the monthly flows, σmax is the maximum value of standard deviations and σav the average of 12 monthly values. The failure probability levels (PF) were fixed at 5%, 2.5% and 0% (corresponding reliability of 95%, 97.5% and 100%). The study revealed that the coefficient of variation is the most important parameter that influences the reservoir size while the role of lag-1 autocorrelation (ρ1m) appears more pronounced at high draft ratios, α such as 0.90, 0.80 and 0.70 in increasing the reservoir size. The DM based method can be regarded as an alternative to Behavior analysis for sizing reservoirs at the desired probability of failure or reliability level.

Compatibility of Drought Magnitude Based Method with SPA for Assessing Reservoir Volume: Analysis Using Canadian River Flows

The traditional sequent peak algorithm (SPA) was used to assess the reservoir volume (VR) for comparison with deficit volume, DT, (subscript T representing the return period) obtained from the drought magnitude (DM) based method with draft level set at the mean annual flow on 15 rivers across Canada. At the annual scale, the SPA based estimates are larger, on an average of nearly 70%, compared to the DM based estimates. To ramp up the DM based estimates to be in parity with SPA based values, the analysis was conducted through the counting and the analytical procedures involving only the annual SHI (standardized hydrological index, i.e. standardized values of annual flows) sequences. It was found that MA2 or MA3 (moving average of 2 or 3 consecutive values) of SHI sequences was required to match the counted values of DT to VR. Further, the inclusion of mean, as well as the variance of the drought intensity in the analytical procedure, with the aforesaid smoothing led DT comparable to VR. The distinctive point in the DM based method is that no assumption is necessary such as the reservoir being full at the beginning of the analysis—as it is the case with the SPA.