ETL 1110-2-537

CECW-EH

Technical Letter

31 October 1997

No. 1110-2-537

and Vettering, W. T. (1990). *Numerical Recipes*

This letter presents a methodology for computing the

uncertainty about nonanalytic frequency curves. This

702 pp.

situation arises when estimating flow-frequency curves

from hypothetical events, regulated frequency curves,

and stage-frequency curves. The method involves the

application of order statistics to compute the

Approved for public release, distribution is unlimited.

uncertainty distribution.

This letter applies to all HQUSACE elements and

USACE commands where estimates of uncertainty

(1) The uncertainty in a frequency curve that is

about nonanalytic frequency curves are required. The

estimated from a graphical fit of ordered observations

primary expected application is in developing

(e.g., peak annual regulated flows or stages) may be

uncertainty relationships for use in risk-based analysis

calculated from order statistics. No assumption need

of flood damage reduction projects.

be made concerning the analytic form of the frequency

curve. Under these circumstances, the statistic derived

to estimate uncertainty is termed "nonparametric" or,

more to the point, "distribution free." Note that the

procedures outlined in EM 1110-2-1619, Section 4,

Flood Damage Reduction Studies.

should be utilized if an analytic distribution such as

the log-Pearson III can be used to approximate the

frequency curve.

New York, 488 pp.

(2) The order statistic approach is limited to

calculating uncertainty in the estimated frequency

curve for the range of observed data or, alternatively,

the equivalent length of record. Extrapolating the

384 pp.

estimates beyond the range of data is performed by

using asymptotic approximations of uncertainty

distributions. The order statistic and asymptotic

(1963). *Introduction to the Theory of Statistics*.

estimates of uncertainty are matched at the limits of

McGraw-Hill, New York, 564 pp.

the observed data.