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Using the regional equation
Qest
1940 m'ls, as in Example I
Combining these estimates from the record and regional
equation, using a weighting factor of 0.5 for both (see section
5.2.2), gives
a = 0.5x1435+0.5x194O
1688 m',/s
(b) As N< 10, the regional curve should still be applied to
estimate Q,oo. The curve ordinate is unchanged at
Q,oolQ : 2.89
(c) Combining the estimates of Q and Q,oolQ results in
Q,oo 1688 x 2.89
= 4878 m!/s
(d) In obtaining the standard error of estimate, the RHS
terms in Equation 3.25 changed from Example I are
E(Q) = 1688 m3,/s
and the variance of Q estimated from the flood record is
given by
E(Q)
and
var(Q)
1704 m'ls
(cu.Q)'
N
= (0.54 x 1704)' = 6.048 x 10.
t4
Therefore, from Equation 3.25
var(Qroo) l1M' x 0.522 + 2.89' x 6.048 x l0'
= 2.021 x 106
Thus
Se(Q'oo) : (2.021 x106)v,
1422 m3/s which is 2590 of Q,oo
5.4.4 Example 4: N:21
(a) As in Example 3, Q can be estimated directly from the
annual series.
var(Qo6) - (Cn'Qou')'
2t
N
i]r
where C" :
The Cn for the 0.54 from
2l years of record is 0.43, which compares
Figure 4.12
well with the regional estimate of C" : 9.54
Thus
var(Qo6) : (0.54 x
(b) Since T ) 5N and N > 20, frequency analyses may be
1435)' : 2.002 x l0'
performed on the annual series using two- and three-parameter
distributions. The EVI distribution fitted by the
3
The variance
maximum
of
likelihood method gives
Q estimated from
a good fit to the data
the regional equation is
the
and yields
same as in Example l, i.e.,
var(QesJ = 3.410x105
Q'oo
: 4l7O m'/s
and an approximate standard error of estimate of 800 m',/s.
From Equation 4.10, the variance of the combined estimate (This
of Q is
standard error is based on a formula used by NERC
(1975, p. 170), assuming Cu : 0.54).
l:l+l
(c) The corresponding estimate using the regional curve is
var(Q) var(Qo') var(Q.r¡) 2.002 x l0r Q,oo 1665x2.89:4812m3/s
and the associated standard error of estimate is obtained
+
from Equation 3.25 as
3.410 x l0r
var(Q,oo) 1665' x 0.522 + 2.8g'z x
(0'54 x 1665)'z
so that var(Q) = 1.261 x 105
2l
Hence from Equation
1.769 x loó
3.25
so that
var(Qroo) 1688' 0.522 + 2.89'? x 1.261 x 105
: 2.541 x Se(Q'oo) 1330 m3,/s which is 2490 of
106
Q,oo
and
Se(Q,oo) = (2.541 x l0ó)/z
1594 m!/s, which is 2890 of Q,oo
5.4.5 Results Summary
Table 5.2 summarises the estimates of Q and Q'oo obtained
in the four examples using the RFE method.
5.4.3 Example 3: N: 14
The reduction in the standard error of estimate in Table
(a) As N > N"( = 3), Q can be estimated directly from the 5.2 with increase in record length illustrates the value of increasing
lengths of flood record. In Example 4, a second
annual series.
Hence
estimate of Q,oo : 4l7O m'ls (by frequency analysis of the
l4
2l years ofrecord) is available and a designer would choose
a = I a weighted mean of the two.
I ei =1704m',/s
It will be seen that the estimate of Q in the second example,
obtained by combining the estimates from the re-
14 i-: I
gional equation and the three years of record, is closer to
(b) Applying the regional curve produces
the Q estimate using the full flood record than that in Example
3 which is based on 14 years and, as a consequence,
Q'oo :1704 x2.89
= 4925 m3/s
the corresponding Q,oo estimate is also closer to the Qroo
estimate determined from the full record. Although this
may be a chance result it does emphasise that even a short
(c) The new RHS terms in Equation 3.25 are
flood record is useful.
Water & soil technical publication no. 20 (1982)
81
a
2t
= I )- Qi:1665m'/s