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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)