Geoscience Reference
In-Depth Information
Table 6.3
Annual maximum series for the Wye (1971-97) sorted using the Weibull
and Gringorten position plotting formulae
Rank
X
F(X) Weibull
F(X) Gringorten
P(X)
T(X)
1
11.17
0.03
0.02
0.97
1.04
2
13.45
0.07
0.05
0.93
1.07
3
14.53
0.10
0.09
0.90
1.12
4
14.72
0.14
0.12
0.86
1.16
5
16.19
0.17
0.16
0.83
1.21
6
16.19
0.21
0.19
0.79
1.26
7
16.58
0.24
0.23
0.76
1.32
8
17.57
0.28
0.26
0.72
1.38
9
18.09
0.31
0.29
0.69
1.45
10
18.25
0.34
0.33
0.66
1.53
11
18.75
0.38
0.36
0.62
1.61
12
18.79
0.41
0.40
0.59
1.71
13
20.01
0.45
0.43
0.55
1.81
14
20.22
0.48
0.47
0.52
1.93
15
21.10
0.52
0.50
0.48
2.07
16
21.75
0.55
0.53
0.45
2.23
17
21.84
0.59
0.57
0.41
2.42
18
22.64
0.62
0.60
0.38
2.64
19
23.28
0.66
0.64
0.34
2.90
20
23.36
0.69
0.67
0.31
3.22
21
23.37
0.72
0.71
0.28
3.63
22
23.46
0.76
0.74
0.24
4.14
23
23.60
0.79
0.77
0.21
4.83
24
24.23
0.83
0.81
0.17
5.80
25
25.19
0.86
0.84
0.14
7.25
26
27.68
0.90
0.88
0.10
9.67
27
29.15
0.93
0.91
0.07
14.50
28
48.87
0.97
0.95
0.03
29.00
Table 6.4
Values required for the Gumbel formula, derived from the Wye data set in
Table 6.3
Mean (
¯
)
Standard deviation (
σ
Q
)
a value
b value
21.21
6.91
18.11
0.19
Applying the method of moments and Gumbel
formula to the data give some interesting results.
The values used in the formula are shown below
and can be easily computed. When the formula is
applied to find the flow values for an average
recurrence interval of fifty years it is calculated as
39.1 m
3
/s. This is less than the largest flow during
the record which under the Weibull formula has
an average recurrence interval of twenty-seven
years. This discrepancy is due to the method of
moments formula treating the highest flow as an
extreme outlier. If we invert the formula we can
calculate that a flood with a flow of 48.87 m
3
/s (the
largest on record) has an average recurrence
interval of around three hundred years.
