(a) The annual maxima for the River Warleggan at Trengoffe during the water years 1969 – 80 are shown below. Using only these data, the Gringorten equation (13.4) and log-probability paper, determine Q5, Q20 and Q100. Are these values significantly different from those in Example 13.6a? (b) Repeat

Question

(a) The annual maxima for the River Warleggan at Trengoffe during the water years 1969 – 80 are shown below. Using only these data, the Gringorten equation (13.4) and log-probability paper, determine [latex]Q_{5}, Q_{20} and Q_{100}[/latex]. Are these values significantly different from those in Example 13.6a? (b) Repeat the above analysis but this time using the full 1969 – 94 record from Table 13.7 and below. What do you deduce about the importance of a long record? (c) Calculate the values of QMED obtained from the 1969–80 data below and the full 1969 – 94 record. What are the percentage differences compared to the 8.077 m³/s value in Table 13.7? (d) Using all of the 1969 – 94 data, calculate the values of [latex]Q_{T}[/latex]/QMED and y so they can be combined with the data in Table 13.8.

[latex] ext { Gringorten: } \quad P=\frac{r - 0.44}{N + 0.12}[/latex] (13.4)

[latex]\begin{array}{llcccr} ext { Water year } & { ext { Date }} & Q\left( m ^3 / s ight) & ext { Water year } & { ext { Date }} & Q\left( m ^3 / s ight) \ 1969 & ext { 17 Jan } 1970 & 14.869 & 1975 & ext { 29 Jan } 1976 & 13.907 \ 1970 & ext { 12 Jan } 1971 & 6.107 & 1976 & ext { 3 Feb 1977 } & 3.047 \ 1971 & ext { 30 Nov } 1971 & 8.493 & 1977 & ext { 9 Dec } 1977 & 10.085 \ 1972 & ext { 6 Aug } 1973 & 8.493 & 1978 & ext { 22 Dec } 1978 & 5.167 \ 1973 & ext { 15 Nov } 1973 & 15.519 & 1979 & ext { 27 Dec 1979 } & 23.914 \ 1974 & ext { 13 Nov } 1974 & 12.973 & 1980 & ext { 16 Nov 1980 } & 7.494 \end{array} [/latex]

Accepted Answer

(a) The ranked data are shown in Table STQ13.4a, along with the P % values calculated from equation (13.4). The data are plotted as Fig. STQ13.4a. The [latex] Q_T [/latex] values equivalent to P = 20%, 5% and 1% give [latex]Q_{5}, Q_{20} and Q_{100}[/latex] = 15.2 m³/s, 24.0 m³/s and 36.0 m³/s respectively. Example 13.6 gave much lower values (11.8 m³/s, 17.3 m³/s, 23.8 m³/s).

(b) Repeating the above analysis but using all 26 years of record results in Table STQ13.4b and Fig. STQ13.4b. The data show less scatter and plot easier. This time [latex]Q_{5}, Q_{20} and Q_{100}[/latex] = 13.0 m³/s, 19.6 m³/s and 28.0 m³/s. These are between the two values obtained from the short records. It may be surmised that the 1969–80 record contains larger flood peaks than the other (see the values of QMED below). This is not unexpected: weather often fluctuates in cycles, such as a sequence of wetter than average years. A long record averages these fluctuations out and is more reliable.

(c) Using the 1969 – 80 record in Table STQ13.4a, QMED = (10.085 + 8.493)/2 = 9.289 m³/s.

From the 1981 – 94 record in Table 13.7, QMED = 8.077 m³/s.

Using the full 1969 – 94 record in Table STQ13.4b, QMED = (8.629 + 8.493)/2 = 8.561 m³/s.

This confirms the statement above that the first part of the record contained larger floods, and again illustrates the need for a long record. The largest percentage difference is 100 × (9.289 - 8.077)/8.077 = 15%. The other difference is 6%.

(d) The values are listed in Table STQ13.4b. They are included in Fig. 13.9b in the text.

Table 13.7 River Warleggan at Trengoffe – recorded data and annual maximum frequency analysis [Data from the FEH CD-ROM courtesy of the Institute of Hydrology, Wallingford] QMED = (8.629 + 7.525)/2 = 8.077 m³/s.
$\underline{Recorded data}$			$\underline{Prior to development, ranked data and \% probability}$				$\underline{Post development}$
Water year	Date	Q m³/s	Rank r	Water year	$Q_{T}$ m³/s	p% Eqn (13.4)	1.35 $Q_{T}$ m³/s
1981	20 Dec 1981	17.914	1	1981	17.914	3.97	24.184
1982	6 Nov 1982	10.085	2	1992	13.843	11.05	18.688
1983	19 Dec 1983	4.651	3	1985	12.973	18.13	17.514
1984	27 Jan 1985	5.673	4	1982	10.085	25.21	13.615
1985	24 Aug 1986	12.973	5	1986	9.813	32.29	13.248
1986	10 Dec 1986	9.813	6	1987	9.543	39.38	12.883
1987	1 Feb 1988	9.543	7	1988	8.629	46.46	11.649
1988	24 Feb 1989	8.629	8	1994	7.525	53.54	10.159
1989	14 Feb 1990	6.239	9	1993	7.074	60.62	9.55
1990	1 Jan 1991	4.936	10	1989	6.239	67.71	8.423
1991	31 Oct 1991	3.807	11	1984	5.673	74.79	7.659
1992	18 Dec 1992	13.843	12	1990	4.936	81.87	6.664
1993	24 Jan 1994	7.074	13	1983	4.651	88.95	6.279
1994	27 Jan 1995	7.525	14	1991	3.807	96.03	5.139

Table 13.8 St Neot at Craigshill Wood, Cornwall – recorded data and growth curve [Data courtesy of the Institute of Hydrology, Wallingford] QMED = (8.712 + 7.996)/2 = 8.354 m³/s.
Recorded data			Ranked data for QMED and growth curve
Water year	Date	Q m³/s	Water year	$Q_{T}$ m³/s	Rank r	$Q_{T}$ /QMED	y Eqn (13.5)
1971	29 Nov 1971	8.712	1979	21.081	1	2.52	3.051
1972	6 Aug 1973	5.319	1981	14.372	2	1.72	1.982
1973	17 Sep 1974	13.094	1973	13.094	3	1.57	1.439
1974	13 Nov 1974	10.823	1974	10.823	4	1.30	1.056
1975	29 Jan 1976	7.996	1982	9.352	5	1.12	0.751
1976	14 Oct 1976	5.832	1971	8.712	6	1.04	0.488
1977	9 Dec 1977	7.699	1975	7.996	7	0.96	0.249
1978	23 Dec 1978	6.009	1977	7.699	8	0.92	0.023
1979	27 Dec 1979	21.081	1980	7.504	9	0.90	– 0.203
1980	9 Mar 1981	7.504	1978	6.009	10	0.72	– 0.441
1981	19 Dec 1981	14.372	1976	5.832	11	0.70	– 0.718
1982	5 Nov 1982	9.352	1972	5.319	12	0.64	– 1.123

Table STQ13.4b
Water year	$Q_{T}$	Rank r	P %	$Q_{T}$ /QMED	y
1979	23.914	1	2.14	2.793	3.832
1981	17.914	2	5.97	2.093	2.787
1973	15.519	3	9.8	1.813	2.272
1969	14.869	4	13.63	1.737	1.921
1975	13.907	5	17.46	1.624	1.651
1992	13.843	6	21.29	1.617	1.43
1974	12.973	7	25.11	1.515	1.241
1985	12.973	–	–	–	–
1977	10.085	9	32.77	1.178	0.924
1982	10.085	–	–	–	–
1986	9.813	11	40.43	1.146	0.658
1987	9.543	12	44.26	1.115	0.537
1988	8.629	13	48.09	1.008	0.422
1971	8.493	14	51.91	0.992	0.312
1972	8.493	–	–	–	–
1994	7.525	16	59.57	0.879	0.099
1980	7.494	17	63.40	0.875	– 0.005
1993	7.074	18	67.23	0.826	– 0.109
1989	6.239	19	71.06	0.729	– 0.215
1970	6.107	20	74.89	0.713	– 0.323
1984	5.673	21	78.71	0.663	– 0.436
1978	5.167	22	82.54	0.604	– 0.557
1990	4.936	23	86.37	0.577	– 0.69
1983	4.561	24	90.20	0.543	– 0.843
1991	3.807	25	94.03	0.445	– 1.036
1976	3.047	26	97.86	0.356	– 1.346

Question 13.SQ.4: (a) The annual maxima for the River Warleggan at Trengoffe d......

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