John L. Sabo and David M. Post. 2008. Quantifying periodic, stochastic, and catastrophic environmental variation. Ecological Monographs 78:19–40.

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.