3.3 Verification of the Existing WH System
The arbitrary design parameters of the existing WH system are verified with the results of the hydrological analysis.
We assume a Poisson distribution with a parameter for the number of flash flood events occurring in a rainy season; the probability that flash flood events occur times in a rainy season is equal to . The parameter is equal to the mean as well as to the variance. As presented in subsection 3.1, flash flood events occurred 4, 4, 2, 2, and 3 times in the rainy seasons 2014-2015, 2015-2016, 2016-2017, 2017-2018, and 2018-2019, respectively. The sample mean of these numbers of occurrence is 3.0, and their unbiased sample variance is 1.0. The K-S test to examine their goodness-of-fit to the Poisson distribution with parameter results in the significance level to justify the fitting.
Firstly, the reservoir capacity of the desalination plant, which is 300 m3, is discussed. The CDF of the fitted LN3 to the total runoff volume is equal to 0.46770 at = 300 m3. The probability that the reservoir in an empty state cannot be filled up with a single flash flood event in a rainy season is evaluated as = 0.20253 = 1/4.9375, implying that this likely happens once in five years. Indeed, a carry-over operation is implemented in the existing WH system to reduce the risk of shortage in the freshwater from the desalination plant.
Secondly, the maximum runoff discharge is discussed to evaluate the performance of the spillway. The CDF of the fitted GEV to is equal to 0.97063 at the design = 1,000 L/s and to 0.98690 at the historical = 1,816 L/s. The probabilities that the maximum runoff discharge exceeds those in a rainy season are evaluated as = 0.084351 ≈ 1/12 and = 0.038546 ≈ 1/26, respectively. As there is no substantial human activity in the downstream area of the WH system, that return period of 12 years might be acceptable. The historical event with that = 1,816 L/s on April 13, 2016, did not damage the hydraulic structures and the observation system. On the other hand, the Japanese guideline recommends that the design flood discharges for spillways of WH irrigation dams should be of 200 years return period with the safety factor 1.2 (Rural Development Bureau 2015). The maximum runoff discharge achieving the 200 years return period is estimated at 8,302 L/s, using the fitted GEV. This value implies that, according to the Froude number similitude, the spillway must be (8,3021.2/1,000)2/5 ≈ 2.508 times larger than the existing one if based on that guideline.