Question

The following data are annual maximum floods Q (in m/s) for 7 years of record from 2005-2011. Using frequent factor method (parametric analysis), determine the 200-year flow assuming that the flows follow (a) log-normal distribution and (b) Log-Pearson Type III distribution YEAR 2005 2006 2007 2008 2009 2010 2011 Q (m/s) 2400 3093 1680 2640 3787 3360 3413

Answer 1

a)Log- Normal distribution is the special case of log-pearson distribution in which = 0

Cs

so from following data we get

$\bar{z}$ = 3.450754

$\sigma_{z}$ = 0.1204

K₂(when = 0 ) = 2.576

Cs

z₂₀₀= $\bar{z}$ + K₂$\sigma_{z}$

z₂₀₀= 3.7609044

X₂₀₀= Antilog (z₂₀₀)

X₂₀₀= 5766.4 m³/sec

b)

YEAR FLOOD, X (m^3/SEC) Z=LOGX Z-MEAN (Z-MEAN)^2 2005 2400 3.380211 -0.070542758 0.004976281 2006 3093 3.49038 0.03962592 0.001570214 2007 1680 3.225309 -0.225444718 0.050825321 2008 2640 3.421604 -0.029150073 0.000849727 2009 3787 3.578295 0.127541305 0.016266785 2010 3360 3.526339 0.075585277 0.005713134 2011 3413 3.533136 0.082382288 0.006786841 (Z-MEAN)^2 = 0.086988302 MEAN = 3.450754

FROM THIS TABLE WE DETERMINE $\sigma_{z}$   

$\sigma_{z}$ = 0.1204

$C_{s} = \frac{N\sum (z-\bar{z} )^{3}}{(N-1)(N-2)\sigma _{z}^{3}}$

= -1.1644

Cs

from Log-pearson Type iii distribution

K₂ = 1.201

z₂₀₀= $\bar{z}$ + K₂$\sigma_{z}$

z₂₀₀= 3.5954

X₂₀₀= Antilog (z₂₀₀)

X₂₀₀= 3939.13 m³/sec