Appendix A. Extreme event tutorial.
Estimation of extreme event statistics via Pearson Type III function
Extreme statistics are estimated from a series of annual extreme observations as :
(A.1) |
where, Y is an annual extreme observation (H_{a} or L_{a}) and the Pearson type-III function is described by three parameters, a mean (), a standard deviation () and the coefficient of skewness (). From this distribution, we estimated the T-year high flow (Y~H_{a}) or low flow (Y~L_{a})events as:
(A.2) |
where and are estimated by the mean and standard deviation, respectively of the annual extremes (i.e., and s_{d}) and is a frequency factor whose estimator is related to the probability of non-exceedance of a given event (1–1/T) and coefficient of skewness via the gamma distribution. We then estimated the coefficient of skewness as:
(A.3a) |
where is the cube of the standard deviation of annual extremes and,
(A.3b) |
Frequency factors ( ) for 2- and 10-year high and low flows were computed from H_{a} and L_{a} and used with estimates of the mean and variance of high- and low-flow series to estimate 7-day, 2-year, and 10-year high and low flows using tabled values (Haan 1977).
LITERATURE CITED
Haan, C. T. 1977. Statistical Hydrology. Iowa State University Press, Ames, Iowa, USA.