(civl253)[2010](f)midterm~wmma^_10066.pdf

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CIVL253 CHYDROLOGY

Mid-term Examination (21 October 2010)

(Solutions)

Problem 1 (15%)

Consider five raingauges in Hong Kong Territory whose rainfall records and geographical characteristics are given in the table. Compare the accuracy of the following point rainfall estimation methods, namely, arithmetic averaging, normal ratio, and inverse distance with b=1 and 2 for the July 1977 rainfall amount at Station 212 by using other stations as index stations.

Stn. No. Record Length (yrs) Total Rainfall (mm) Distance to Stn-212 (km) Elevation (m) July 77 Rainfall (mm)

52 32 77,120 3.5 330 317

75 32 76,480 6.5 130 473

157 17 43,214 6.8 10 389

212 20 45,520 200 302

Solution:

.

By arithmetic average (AA) method: P212, AA = (317+473+389)/3 = 393.0 mm

.

By normal ratio (NR) method: P 1 . PPP . 1 . 317 473 389 .

212, NR 52 75 157

= ++= ++

... .

N 3 NNN 3 NNN

212 . 52 75 157 .. 52 75 157 .

where Nx = Total rainfall at station-x/ Record length of station-x; that is, N52=77120/32=2410mm; N75=76480/32=2390mm; N157=43214/17=2542mm; N212=45520/20=2276mm.

P212, NR 1 . 317 473 389 .

= ++= 0.161

..

2276 3 . 2410 2390 2542 .

Hence, P212,NR = 0.161(2276)=366.0 mm.

. By inverse distance method (b=1): Based on the distance between the three index stations and stn-212, the corresponding reciprocal of the distance can be computed as 1/d52=1/3.5=0.286; 1/d75 = 0.154; 1/d157=0.147. The weighting factor for each index station can be determined as W52=0.286/(0.286+0.154+0.147)=0.286/0.587=0.487; W75 = 0.154/0.587 =0.262; W157 = 0.147/0.587 = 0.251.

The estimated July rainfall at stn-212 is the weighted average of the three index stations as P212,InvD(b=1) = 0.487(317)+0.262(473)+0.251(389)=376.0 mm.

. By inverse squared distance method (b=2): Based on the distance between the three index stations and stn-212, the corresponding reciprocal of the distance can be computed as 1/(d52)2=1/(3.5)2=0.082; 1/(d75)2 = 0.024; 1/(d157)2 =0.022. The weighting factor for each index station can be determined as W52=0.082/(0.082+0.024+0.022)=0.082/0.127=0.643; W75 = 0.024/0.127 =0.186; W157 = 0.022/0.127 = 0.170.

The estimated July rainfall at stn-212 is the weighted average of the three index stations as P212,InvD(b=2) = 0.643(317)+0.186(473)+0.170(389)=358.4 mm.

. According to the actual observed July 1977 rainfall at stn-212, i.e., 302mm, we can easily compute the error associated with each method. They are:

ErrAA = 91.00 mm; ErrNR = 64.04 mm; ErrINV(b=1) = 73.96 mm; and

ErrINV(b=2) = 56.36 mm.

It can be seen that inverse squared distance method yields the most accurate

estimation in this case.

Problem 2 (25%)

The following table contains the records of rainfall and surface runoff data of a particular storm event for a watershed with the drainage area of 8.4 km2.

(a)

Determine the rolling-time maximum rainfall depth and intensity for durations of 30-, 60-, and 120-min. (8