Solve problem $6\mathrm{.}24,$ Hydrosystems Engineering

Uncertainty Analysis

Yeou$-$Koung Tung,

$6\mathrm{.}24$ Refer to the annual maximum flood data in Table $6\mathrm{.}3.$ Since the flood magnitude of a specified return period $(Q_T)$ is determined on the basis of sample statistics, such as sample mean $(\frac{?}{\text{b}\text{a}\text{r}}(Q))$ and sample standard deviation $(s_Q),$ the estimated $Q_T$ also is subject to uncertainty. Assuming that the flood data follow a lognormal distribution, use the nonparametric, unbalanced bootstrap algorithm $($with $1000$ replications$)$ to estimate the magnitude of the $100-$year flood $(=Q_T=100)$ and its associated error. Compare with the results obtained from Prob. $6\mathrm{.}22.$ Furthermore, based on the $1000$ bootstrap samples generated, assess the probability distribution and $90$ percent confidence interval for $Q_T=100.$

$6\mathrm{.}22$ Refer to the annual maximum flood data in Table $6\mathrm{.}3.$ Use the jackknife method to estimate the magnitude of a $100-$year flood and its associated error assuming that the flood data follow a lognormal distribution.

TABLE $6\mathrm{.}3$ Annual Maximum Floods for Mill Creek Near Los Molinos, California

$\backslash$table$[[$Year$,$Discharge $(f\frac{t^3}{s}),$Year,Discharge $(f\frac{t^3}{s})$