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Transcript of IDR Curves
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University of Guyana
Faculty of Technology
ENGINEERING HYDROLOGYASSIGNMENT #3
Rainfall Intensity-Duration AnalysisStatistical Series, return values and IDR curves
[30 Minutes, 6 Hours & 24 Hours Rainfall in Georgetown, up to 2004]
LECTURER: Mr.Veecock
13th
October, 20147-10-
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Group Members:
LEWIS, Natasha Reg. # 14/0933/0021
EDWARDS, Eketa Reg. # 13/0933/2194
CLARKE, Chrysann Reg. # 13/0933/1392
CARRYL, Larry Reg. # 13/0933/1426
TAKCHANDRA, Jaikeshan Reg. # 13/0933/1323
LEWIS, Jayson Reg. # 14/0933/2062
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Calculations:
Tabulated Values for Xi,
,
( ), m and
, are shown in the appendix.
For 30 Minute Readings
n= 25
Xi= 783.2
Therefore: x =
= = 31.328
Sx, by square of derivatives =
=
= = 9.043
Sn, for n=25, = 1.0915. [from Table A.4]
Yn , for n=25, = 0.5309 [from Table A.4]
Therefore, finding XTrusing:
When YTr= 0.3665, for 2-year period:
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Then: X2 = 31.328 + ( )* 9.043
= 29.966
When YTr= 1.4999, for 5-year period:
Then: X5 = 31.328 + ( )* 9.043
= 39.356
When YTris given as: -(0.834+2.303log(log(Tr/Tr-1)))
Then, for a 30-year period: Y30= -(0.834+2.303log(log(30/30-1))) = 3.385
Then: X30 = 31.328 + ( )* 9.043
= 54.974
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For 6 Hour Readings
n= 25
Xi= 2158.5
Therefore: x = =
= 86.34
Sx, by square of derivatives =
= = = 21.435
Sn, for n=25, = 1.0915. [from Table A.4]
Yn , for n=25, = 0.5309 [from Table A.4]
Therefore, finding XTrusing:
When YTr= 0.3665, for 2-year period:
Then: X2 = 86.34 + (
)* 21.435
= 86.34 + ( )* 21.435
= 86.34 + ()* 21.435= 86.34 + (-3.228)
= 83.11
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When YTr= 0.1.4999, for 5-year period:
Then: X5 = 86.34 + (
)* 21.435
= 86.34 + ()* 21.435
= 86.34 + ()* 21.435= 86.34 + (19.029)
= 105.369
When YTris given as: -(0.834+2.303log(log(Tr/Tr-1)))
Then, for a 30-year period: Y30= -(0.834+2.303log(log(30/30-1))) = 3.385
Then: X30 = 86.34 + ( )* 21.435
= 86.34 + ( )* 21.435
= 86.34 + ()* 21.435= 86.34 + (56.049)
= 142.389
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For 24Hour Readings
n= 45
Xi= 4451.9
Therefore: x = =
= 98.9
Sx, by square of derivatives =
= = = 25.638
Sn, for n=45, = 1.1519. [from Table A.4]
Yn , for n=45, = 0.5463 [from Table A.4]
Therefore, finding XTrusing:
When YTr= 0.3665, for 2-year period:
Then: X2 = 98.9 + (
)* 25.638
= 98.9 + ( )* 25.638
= 98.9 + ()* 25.638= 98.9 + (-4.002)
= 94.898
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When YTr= 1.4999, for 5-year period:
Then: X5 = 98.9 + (
)* 25.638
= 98.9 + ()* 25.638
= 98.9 + ()* 25.638= 98.9 + (21.224)
= 120.124
When YTris given as: -(0.834+2.303log(log(Tr/Tr-1)))
Then, for a 30-year period: Y30= -(0.834+2.303log(log(30/30-1))) = 3.385
Then: X30 = 98.9 + ( )* 25.638
= 98.9 + ()* 25.638
= 98.9 + ()* 25.638= 98.9 + (63.181)
= 162.081
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Data set
Duration
(hrs)
Rainfall (mm) Intensity (mm/hr)
0.5 29.966 59.9 2 Year Return Period
6 83.11 13.9
24 94.898 4.0
0.5 39.356 78.7 5 Year Return Period
6 105.369 17.624 120.124 5.0
0.5 54.974 109.9 30 Year Return Period
6 142.389 23.7
24 162.081 6.8
0.5, 59.9
6, 13.924, 4.0
0.5, 78.7
6, 17.624, 5.0
0.5, 109.9
6, 23.724, 6.8
y = 42.893e-0.104x
y = 55.67e-0.105x
y = 76.904e-0.107x
0.0
20.0
40.0
60.0
80.0
100.0
120.0
0 5 10 15 20 25
Intensity(mm/hour)
Rainfall Duration (Hours)
Intensity-Duration Curves (with trendline approximation)
2-Year 5-Year 30-Year Expon. (2-Year) Expon. (5-Year) Expon. (30-Year)
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Appendix One (Prerequisite calculations)
24 Hour Rainfall data
Year Xi m n+1/m Xi- (Xi-X)^2 (Xi)^2
1960 61 45 1.0 -37.9 1438.8 3,721.00
1961 69 42 1.1 -29.9 895.9 4,761.00
1962 83 31 1.5 -15.9 253.8 6,889.001963 125 7 6.6 26.1 679.6 15,625.00
1964 141.7 6 7.7 42.8 1829.2 20,078.89
1965 93.7 21 2.2 -5.2 27.4 8,779.69
1966 96.5 23 2.0 -2.4 5.9 9,312.25
1967 119.9 8 5.8 21.0 439.7 14,376.01
1968 85.3 30 1.5 -13.6 185.8 7,276.09
1969 97 22 2.1 -1.9 3.7 9,409.00
1970 100.8 16 2.9 1.9 3.5 10,160.64
1971 86.6 29 1.6 -12.3 152.1 7,499.56
1972 98.9 20 2.3 0.0 0.0 9,781.21
1973 81.5 33 1.4 -17.4 303.8 6,642.25
1974 174 1 46.0 75.1 5635.3 30,276.00
1975 106 12 3.8 7.1 50.0 11,236.00
1976 118.1 9 5.1 19.2 367.4 13,947.61
1977 79.8 35 1.3 -19.1 366.0 6,368.04
1978 92 27 1.7 -6.9 48.0 8,464.00
1979 73.7 39 1.2 -25.2 636.6 5,431.69
1980 104.1 15 3.1 5.2 26.7 10,836.81
1981 110.8 11 4.2 11.9 140.9 12,276.64
1982 100.4 17 2.7 1.5 2.2 10,080.16
1983 68.5 43 1.1 -30.4 926.1 4,692.25
1984 93 26 1.8 -5.9 35.2 8,649.00
1985 70.7 40 1.2 -28.2 797.0 4,998.49
1986 70.2 41 1.1 -28.7 825.5 4,928.04
1987 146.2 4 11.5 47.3 2234.3 21,374.44
1988 146.3 3 15.3 47.4 2243.8 21,403.69
1989 93.2 25 1.8 -5.7 32.8 8,686.24
1990 80.2 34 1.4 -18.7 350.9 6,432.04
1991 99 19 2.4 0.1 0.0 9,801.00
1992 74 38 1.2 -24.9 621.6 5,476.00
1993 90.2 28 1.6 -8.7 76.2 8,136.041994 100 18 2.6 1.1 1.1 10,000.00
1995 153 2 23.0 54.1 2923.4 23,409.00
1996 105.3 14 3.3 6.4 40.6 11,088.09
1997 82.8 32 1.4 -16.1 260.2 6,855.84
1998 97.3 21 2.2 -1.6 2.7 9,467.29
1999 105.4 13 3.5 6.5 41.8 11,109.16
2000 78.2 36 1.3 -20.7 429.8 6,115.24
2001 114.2 10 4.6 15.3 233.1 13,041.64
2002 75.5 37 1.2 -23.4 549.0 5,700.25
2003 68 44 1.0 -30.9 956.7 4,624.00
2004 141.9 5 9.2 43.0 1846.3 20,135.61
4451.9 28,920.48 469,351.89
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6 Hour Rainfall date
Year Xi m n+1/m Xi- (Xi-)^2 (Xi)^21980 59.8 24 1.1 -26.5 704.4 3,576.04
1981 110.7 4 6.5 24.4 593.4 12,254.49
1982 81.3 13 2.0 -5.0 25.4 6,609.69
1983 63.7 22 1.2 -22.6 512.6 4,057.69
1984 62.1 23 1.1 -24.2 587.6 3,856.41
1985 70.7 19 1.4 -15.6 244.6 4,998.49
1986 68.8 20 1.3 -17.5 307.7 4,733.44
1987 146.2 1 26.0 59.9 3583.2 21,374.44
1988 109 5 5.2 22.7 513.5 11,881.00
1989 89.2 11 2.4 2.9 8.2 7,956.64
1990 73.1 18 1.4 -13.2 175.3 5,343.61
1991 100.8 6 4.3 14.5 209.1 10,160.64
1992 97.8 8 3.3 11.5 131.3 9,564.84
1993 113.2 3 8.7 26.9 721.5 12,814.24
1994 87.4 12 2.2 1.1 1.1 7,638.76
1995 95.3 9 2.9 9.0 80.3 9,082.09
1996 89.9 10 2.6 3.6 12.7 8,082.01
1997 114.4 2 13.0 28.1 787.4 13,087.36
1998 76.2 15 1.7 -10.1 102.8 5,806.44
1999 74 17 1.5 -12.3 152.3 5,476.00
2000 77.8 14 1.9 -8.5 72.9 6,052.84
2001 64.1 21 1.2 -22.2 494.6 4,108.812002 75.5 16 1.6 -10.8 117.5 5,700.25
203 59.1 25 1.0 -27.2 742.0 3,492.81
2004 98.4 7 3.7 12.1 145.4 9,682.56
2158.5 11,026.70 197,391.59
30 Minute Rainfall Data
Year Xi m n+1/m Xi- (Xi-)^2 (Xi)^2
1980 31.8 10 2.6 0.5 0.223 1,011.24
1981 36.5 6 4.3 5.2 26.750 1,332.25
1982 20.8 23 1.1 -10.5 110.839 432.64
1983 28.2 17 1.5 -3.1 9.784 795.24
1984 19.4 25 1.0 -11.9 142.277 376.36
1985 36 7 3.7 4.7 21.828 1,296.00
1986 21.5 21 1.2 -9.8 96.590 462.25
1987 56.5 1 26.0 25.2 633.630 3,192.25
1988 37 4 6.5 5.7 32.172 1,369.00
1989 28 18 1.4 -3.3 11.076 784.00
1990 50 2 13.0 18.7 348.644 2,500.00
1991 32 9 2.9 0.7 0.452 1,024.00
1992 33.5 8 3.3 2.2 4.718 1,122.25
1993 26 19 1.4 -5.3 28.388 676.00
1994 28.6 15 1.7 -2.7 7.442 817.96
1995 31.2 12 2.2 -0.1 0.016 973.44
1996 36.9 5 5.2 5.6 31.047 1,361.61
1997 31 13 2.0 -0.3 0.108 961.00
1998 28.6 16 1.6 -2.7 7.442 817.96
1999 21.4 22 1.2 -9.9 98.565 457.96
2000 24.9 20 1.3 -6.4 41.319 620.012001 19.5 24 1.1 -11.8 139.902 380.25
2002 31.6 11 2.4 0.3 0.074 998.56
2003 28.3 15 1.7 -3.0 9.169 800.89
2004 44 3 8.7 12.7 160.580 1,936.00
783.2 1,963.03 26,499.12
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Appendix Two (tables)