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Table 1. Primary data of the rainfall depth D (mm) at the observation system during the period from October 2014 through July 2019
Maximum
Mean
Minimum
AUG
0.06
0.02
0.00
SEP
1.09
0.33
0.00
OCT
27.47
8.29
0.03
NOV
10.51
4.94
0.47
DEC
21.11
8.87
1.20
JAN
29.35
13.56
1.53
FEB
26.27
23.06
15.07
MAR
29.21
11.71
0.17
APR
23.79
12.73
1.65
MAY
4.60
1.00
0.00
JUN
0.89
0.24
0.00
JUL
0.16
0.04
0.00
Annual
109.98
84.82
63.39
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Table 2. Observed rainfall-runoff events with total runoff volume more than 100 m3
Date
12DEC2014
11JAN2015
14JAN2015
26OCT2015
09JAN2016
13APR2016
16FEB2017
10MAR2017
17FEB2018
26APR2018
07FEB2019
25MAR2019
25MAR2019
Start
19:15
01:15
22:52
08:08
02:39
15:32
10:46
21:33
07:48
16:58
05:41
01:30
09:59
End
04:38+
08:32
03:18+
10:42
04:36
16:40
20:34
01:14+
09:53
04:55+
11:27
03:58
12:03
T (min)
564
390
267
155
118
69
589
222
126
718
347
149
125
Do (mm)
13.81
8.52
8.59
10.28
6.79
8.47
16.97
10.85
6.38
23.40
6.00
8.86
3.36
Da (mm)
12.0
10.5
8.4
7.8
2.7
3.4
10.4
5.4
4.4
14.7
6.0
6.0
3.6
V (m3)
307.49
289.23
309.39
593.02
191.19
917.84
323.32
316.78
290.12
865.60
174.38
365.69
135.90
Qmax (L/s)
66
54
93
243
141
1816
87
153
169
283
55
263
55
C (%)
1.99
3.03
3.22
5.15
2.51
9.68
1.70
2.61
4.06
3.30
2.59
3.69
3.61
TV[Q] (L/s)
519
621
339
803
358
6655
349
593
550
971
304
642
220
MV[Q] (L/s)
31
10
11
118
56
1156
18
48
120
51
15
66
14
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Table 3. Results of correlation analysis among the eight random variables
Pearson’s correlation coefficients
T (min)
Spearman's rank correlation
coefficients
T (min)
Do (mm)
Da (mm)
V (m3)
Qmax (L/s)
C (%)
TV[Q] (L/s)
MV[Q] (L/s)
0.833
0.916
0.154
−0.325
−0.511
−0.283
−0.366
0.827
0.548
−0.023
−0.203
−0.021
−0.099
0.286
−0.295
−0.379
−0.254
−0.345
0.730
0.691
0.717
0.667
0.925
0.994
0.992
0.912
0.926
Do (mm)
0.678
Da (mm)
0.909
0.716
V (m3)
0.157
0.673
0.288
Qmax (L/s)
−0.222
0.355
−0.109
0.814
C (%)
−0.460
−0.200
−0.246
0.433
0.604
TV[Q] (L/s)
0.004
0.448
0.181
0.790
0.754
0.561
MV[Q] (L/s)
−0.419
0.101
−0.338
0.571
0.834
0.571
0.993
0.642
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Table 4. Results of probability distribution fitting with maximum likelihood estimation
Distribution
Lognormal
with three
parameters
(LN3)
Generalized
extreme
value
(GEV)
Parameter
T (min)
Do (mm)
Da (mm)
V (m3)
Qmax (L/s)
C (%)
TV[Q] (L/s)
MV[Q] (L/s)
µLN3
5.16301
2.20939
1.70731
5.41270
2.81730
0.596690
5.70378
2.88152
σ LN3
0.916120
0.471100
0.594090
0.786280
4.58172
0.711930
1.28020
2.33610
ξ LN3
42.1510
−0.009210
0.832810
89.6068
54.0000
1.27461
200.213
9.81461
DE
0.144846
0.138071
0.130864
0.210453
0.251232
0.140335
0.153611
0.164577
inf α
0.947908
0.965321
0.979172
0.612377
0.384731
0.959986
0.918896
0.872911
− log L
84.4264
37.3833
33.8718
85.6856
73.6632
21.7861
95.8066
66.9363
µGEV
182.314
7.78439
5.55130
264.926
79.4597
2.73008
406.419
22.4402
σ GEV
118.253
3.42315
2.70683
124.834
61.2649
0.934180
210.007
21.3527
ξ GEV
0.470720
0.109170
0.0759941
0.344930
2.31550
0.282070
0.690560
1.45587
DE
0.182691
0.135505
0.137564
0.206040
0.248055
0.125288
0.146506
0.143037
inf α
0.778415
0.970789
0.966450
0.639151
0.400545
0.986860
0.942972
0.952986
− log L
84.9072
37.3475
34.1111
85.8357
78.3715
21.7335
95.3514
67.9867
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Table 5. Results of probability distribution fitting with maximum goodness-of-fit estimation
Distribution
Lognormal
with three
parameters
(LN3)
Generalized
extreme
value
(GEV)
Parameter
T (min)
Do (mm)
Da (mm)
V (m3)
Qmax (L/s)
C (%)
TV[Q] (L/s)
MV[Q] (L/s)
µLN3
4.91581
1.84277
1.86760
5.43546
4.46005
0.812416
6.23104
3.52357
σ LN3
1.16979
0.457032
0.608888
0.511063
1.19553
0.430577
0.586062
1.39746
ξ LN3
68.8622
2.62107
0.0104740
87.3835
33.8576
0.831299
6.80639
3.67047
DE
0.114420
0.125828
0.0891584
0.170383
0.111443
0.0932289
0.121203
0.112188
inf α
0.995679
0.986221
0.999949
0.844769
0.997004
0.999865
0.991026
0.996707
− log L
94.6349
43.9408
34.2804
88.7423
79.9660
23.1412
69.5114
µGEV
170.239
8.02932
5.28000
281.316
103.336
2.78526
425.485
31.6440
σ GEV
127.638
2.44079
3.18422
94.0019
77.0699
0.840122
249.585
34.9721
ξ GEV
0.230487
0.0699960
0.186238
0.130905
0.112806
0.107889
0.0519790
0.0106120
DE
0.138085
0.125888
0.0904005
0.169084
0.143217
0.0937528
0.117581
0.154496
inf α
0.965291
0.986148
0.999930
0.851266
0.952494
0.999848
0.993825
0.915568
− log L
85.4008
39.6504
34.6077
88.0383
85.9461
22.3367
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Table 6. Verification of the reservoir capacity of the desalination plant
Distribution
F(300)
Pres (300)
1 Pres (300)
LN3 with MLE
0.467704
0.202526
4.93764
GEV with MLE
0.465437
0.201153
4.97134
LN3 with MGE
0.440914
0.186886
5.35086
GEV with MGE
0.439624
0.186164
5.37161
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Table 7. Verification of the spillway capacity
Distribution
F(1000)
F(1816)
Pspill (1000)
Pspill (1816)
1 Pspill (1000) 1 Pspill (1816)
LN3 with MLE
0.810749
0.845283
0.433202
0.371332
2.30839
2.69301
GEV with MLE
0.807924
0.849523
0.437985
0.363283
2.28318
2.75267
LN3 with MGE
0.978234
0.994308
0.063211
0.016930
15.8201
59.0657
GEV with MGE
0.999408
0.999985
0.001775
0.000044
563.359
22563.5
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Table 8. Contrasting MLE and MGE in terms of the spillway capacity design
Distribution
Q200
( Q200 × 1.2/1,000)2/5
LN3 with MLE
11547793
45.3599
GEV with MLE
71124056
93.8597
LN3 with MGE
2921
1.65166
GEV with MGE
825
0.996213
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Figure 1. Photo of the gorge in the barren catchment area
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rR
ee
rP
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Figure 2. Photo of the observation system including VAISALA WXT536 weather transmitter and SR50A
acoustic distance sensor for measurement of runoff discharge
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Figure 3. Photographs taken during the flash flood event on April 13, 2016, with an interval of 1 hour
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Figure 4. Comparison of the observed total runoff depths with the estimations by the SCS runoff curve
number method
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Figure 5. Empirical and fitted probability distributions for the duration
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Figure 6. Empirical and fitted probability distributions for total rainfall depth at the observation system
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Figure 7. Empirical and fitted probability distributions for total rainfall depth at the auxiliary raingauge
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Figure 8. Empirical and fitted probability distributions for total runoff volume
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Figure 9. Empirical and fitted probability distributions for maximum runoff discharge
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Figure 10. Empirical and fitted probability distributions for bulk runoff coefficient
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Figure 11. Empirical and fitted probability distributions for total variation in runoff discharge
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Figure 12. Empirical and fitted probability distributions for maximum variation in runoff discharge
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