Welcome to the Unofficial
PeakfqSA/EMA-Peak Home Page
hosted by Tim Cohn
20 March 2014
Introduction PeakfqSA/EMA-Peak is an implementation of the Expected
Moments Algorithm (EMA) for flood frequency analysis. It is intended to
serve the same purpose as PEAKFQ, the current and
official flood frequency program supported by USGS.
Statistical Aspects of PeakfqSA PeakfqSA uses Cohn et al.'s
(1997) Expected Moments Algorithm to estimate flood frequency based on
at-site ("Station") systematic and historical annual peak flow data
possibly combined with regional ("Generalized") flood frequency
information. PeakfqSA/EMA-Peak is documented in a set of papers published
in Water Resources Research (see below).
History of PeakfqSA The underlying idea for the Expected Moments
Algorithm (EMA) was first suggested by Bill Lane of the U.S. Bureau of Reclamation, and developed
jointly by Tim Cohn and Bill Lane. Subsequent testing and research on
confidence intervals, low outliers, skewness, and other features, have been
performed by a group of researchers including John
England, Veronica Webster Griffis, and Jery Stedinger.
The computer software for EMA is called PeakfqSA/EMA-Peak and
was developed at the U.S.
Geological Survey by Tim Cohn. PeakfqSA/EMA-Peak is expected to be
available eventually as part of a future and official USGS software release
of PEAKFQ. In the meantime, enjoy this unofficial version of the
Version 0.998 and 0.997 contain improvements in numerical precision and function evaluation.
Versions 0.995 and 0.996 incorporates much more accurate confidence interval
calculations employing Inverse-Gaussian-Quadrature procedures. These are accurate over
a very wide range of skews, employ stable numerical methods that do not rely on
numerical derivatives and therefore
provide smooth curves in all cases, and are much -- two orders of magnitude -- faster to compute.
Version 0.993 also reports the MSE of at-site skew estimates, as well as the
corresponding effective record length (ERL).
Version 0.992 incorporates the three-sweep low-outlier detection
procedure devised by Stedinger and Lamontagne .
Version 0.974 introduced
regional information related to M, S, and G.
It also provided the variance of the (log10) of the quantile estimator,
which is useful when computing weighted averages (e.g. with regional equations
to estimate quantiles).
Old Versions of Software
Site last updated 20 March 2014
Griffis, V. W.,
J. R. Stedinger, T. A. Cohn, "LP3 Quantile
Estimators with Regional Skew Information and Low Outlier Adjustments,"
Water Resources Research 40(10), 2004.
Cohn, T., W. L. Lane
and J. R. Stedinger, "Confidence
Intervals for EMA Flood Quantile Estimates," Water Resources
Research, 37(8), 2001.
Cohn, T., W. L. Lane
and W. G. Baier, "An Algorithm for
Computing Moments-Based Flood Estimates when Historical Flood Information
is Available," Water Resources Research, 33(9), pp. 2089-2096,
Comments or suggestions?