Statistical approach to design floods, short record

When only a few years of annual maximum flood data are available, the design flood of a required return period T (often much larger than the record length N) is estimated by flood frequency analysis, which fits a probability distribution to the data and extrapolates.

Procedure

1. Prepare the data. Take the annual maximum flood series (one peak per year), check that it is homogeneous, independent and free of gross errors.
2. Choose a distribution. The common ones are Gumbel (extreme value type I), log-Pearson type III and log-normal.
3. Compute the statistics of the sample: mean $\bar x$, standard deviation $\sigma$ (with $N-1$), and the skewness coefficient (if needed).
4. Apply the general equation (Chow):

$$x_T=\bar x+K_T\,\sigma$$

For Gumbel's method with a small sample, use the reduced mean $\bar y_n$ and reduced standard deviation $S_n$ for the given N:

$$K_T=\frac{y_T-\bar y_n}{S_n},\qquad y_T=-\ln\left[\ln\frac{T}{T-1}\right]$$

5. Compute the confidence limits, important for short records, because the sampling error is large:

$$x_T'=x_T\pm f(c)\,S_e,\qquad S_e=\frac{b\,\sigma}{\sqrt N},\quad b=\sqrt{1+1.3K_T+1.1K_T^2}$$

6. Graphical check. Plot the data with a plotting position $T=(N+1)/m$ on probability paper, fit a straight line, and extrapolate; check that the points fit the assumed distribution.
7. Design flood. For a structure of life n years and acceptable risk R, use $T=\dfrac{1}{1-(1-R)^{1/n}}$, then find $x_T$ as above.

Remarks

• The shorter the record, the wider the confidence interval and the less reliable the extrapolation to T > 2N.
• The short record can be improved by regional flood frequency analysis, by transposing data from nearby gauged catchments, by a partial-duration series, or by generating floods from rainfall (unit hydrograph or rational method) when rainfall records are longer.
• In Nepal, where many catchments are ungauged or have short records, WECS/DHM regional equations are also used.