Question

2 (a) The following data are annual maximum flood discharges for a river recorded over a 10 year period YearDischarge (m3s-1 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 80 76 58 112 96 59 179 75 129 42 The return period may be determined from the Gringorten Formula R- (n + 0.12) (m 0.44) (i)Using a logarithmic scale for return period and linear scale for discharge, plot these data and estimate the 80-year return period flood discharge (7 marks) (ii) Comment on the advisability of determining the 80-year return period event by this method; outline a method that may be preferable (3 marks) For a 124 km2 ungauged river catchment, the triangular Unit Hydrograph (UH) for 10 mm effective rain in 2-hours has a time-to-peak Toof 6 hours and a time base Tb of 16 hours. Calculate the flood hydrograph generated by a 6-hour storm giving 9 mm, 19 mm and 14 mm of effective rain in the three 2-hour periods. The baseflow may be taken as 5 m3s-1. (10 marks) (b)

Answer 1

(a) (i)

• Arrange the discharge data in decreasing order, assign them ranks, and find out the return periods for each discharge using the Gringorten formula and tabulate the results as shown below.

Discharge	Rank 'm'	Return Period 'R'
			179	1	18.07
129	2	6.49
112	3	3.95
96	4	2.84
80	5	2.22
76	6	1.82
75	7	1.54
59	8	1.34
58	9	1.18
42	10	1.06

• Now plot the Discharges on a linear scale and Return periods on Logarithmic scale, and plot a trendline for the points with an R² value as close to '1.0' as possible and find out the equation for the trendline as shown below.

isaageRern Peri 0.361 2e0.02 18х R2 0.9885 10.00 1.00 20 40 60 80 100120 140160180 200 0.10 Discharge .Dischargevs Return Period -Expon. (Discharge vs Return Period)

• For the 80-year Return period Discharge, solve the equation y = 0.3612e^0.0218xby taking y=80yrs and find x.
• We get the discharge for 80-year return period as = 247.7 m³/s, which is the required solution.

(a) (ii)

• Here, we are estimating the 80-year return period discharge from 10-year flood discharge data and assuming that the trend of rainfall discharges in the coming years would be similar. The results may not be accurate as the flood discharges in the following years may follow a different pattern and as annual rainfall is an uncertain parameter subject to high uncertainty. It is recommended to consider a larger set of annual rainfall data to get a much better perspective of variation in annual rainfall parameters.

(b)

ver Page No. Date tine to peak & hs Volume runo 240000 m3 Nlow fntipolati the valu inbutal and plot he shou balsus 2-ho,

2-Hr Unit hydrograph
Time (hours)	Runoff (m3/s)
		0	0
2	14.352
4	28.704
6	43.055
8	34.4448
10	25.8336
12	17.2224
14	8.6112
16	0

2-Hr Unit Hydrograph 50 E 30 O 20 10 10 12 14 16 18 0 4 6 Time (hrs)

• To find out Flood hydrograph of 6-hr duration with varying effective rainfall values, we use the convolution method.
• In this method, the 2-hr Unit hydrograph is delayed by 0hrs, 2hrs, and 4hrs, and the ordinates for these rainfall events are multiplied with their corresponding effective rainfall value for that 2hr interval, R1, R2, R3 respectively. Effective rainfall values are taken in 'cm' as by the definition of the Unit hydrograph, it is the hydrograph for 1cm of runoff or effective rainfall.
• To obtain 6-hr Direct runoff Hydrograph, these three 2hr rainfalls are superimposed and their ordinates at each interval are added to get ordinates of 6-Hr DRH.
• By adding a baseflow value of 5m³/s to the ordinates of 6-hr DRH we get 6-hr Flood hydrograph.
• The results are tabulated as shown below,

  6-hr DRH and Flood Hydrograph
  Time (hours)	Ordinate of 2-Hr UH (m3/s)	2-Hr UH ordinate for Runoff R1 = 0.9cm (m3/s)	2-Hr UH ordinate for Runoff R2 = 1.9cm, delayed by 2hrs (m3/s)	2-Hr UH ordinate for Runoff R3 = 1.4cm, delayed by 4hrs (m3/s)	6-Hr Direct Runoff Hydrograph (m3/s)	Baseflow (m3/s)	6-Hr Flood Hydrograph (m3/s)
  								1	2	3 = R1*Ordinate of 2hr Uh	4 = R2*Ordinate of 2hr Uh	5 = R3*Ordinate of 2hr Uh	6 = 3+4+5	7	8 = 6+7
  								0	0	0	0	0	0	5	5
  2	14.352	12.9168	0	0	12.9168	5	17.9168
  4	28.704	25.8336	27.2688	0	53.1024	5	58.1024
  6	43.055	38.7495	54.5376	20.0928	113.3799	5	118.3799
  8	34.4448	31.00032	81.8045	40.1856	152.99042	5	157.99042
  10	25.8336	23.25024	65.44512	60.277	148.97236	5	153.97236
  12	17.2224	15.50016	49.08384	48.22272	112.80672	5	117.80672
  14	8.6112	7.75008	32.72256	36.16704	76.63968	5	81.63968
  16	0	0	16.36128	24.11136	40.47264	5	45.47264
  18	0	0	0	12.05568	12.05568	5	17.05568
  20	0	0	0	0	0	5	5

• 
  180 160 140 120 100 80 60 40 20 15 10 25 Time (hrs) Storm-1, R1-9mm -storm-2, R2-19mm Storm-3, R3-14mm 6-Hr Direct Runoff Hydrograph _Baseflow 5m3/s 6-Hr Flood Hydrograph
  

• We have arrived at the required solution.