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.