Evaluation of the expected moments algorithm and a multiple low-outlier test for flood frequency analysis at streamgaging stations in Arizona

Scientific Investigations Report 2014-5026
Prepared in cooperation with the Flood Control District of Maricopa County
By: , and 



Flooding is among the costliest natural disasters in terms of loss of life and property in Arizona, which is why the accurate estimation of flood frequency and magnitude is crucial for proper structural design and accurate floodplain mapping. Current guidelines for flood frequency analysis in the United States are described in Bulletin 17B (B17B), yet since B17B’s publication in 1982 (Interagency Advisory Committee on Water Data, 1982), several improvements have been proposed as updates for future guidelines. Two proposed updates are the Expected Moments Algorithm (EMA) to accommodate historical and censored data, and a generalized multiple Grubbs-Beck (MGB) low-outlier test. The current guidelines use a standard Grubbs-Beck (GB) method to identify low outliers, changing the determination of the moment estimators because B17B uses a conditional probability adjustment to handle low outliers while EMA censors the low outliers. B17B and EMA estimates are identical if no historical information or censored or low outliers are present in the peak-flow data. EMA with MGB (EMA-MGB) test was compared to the standard B17B (B17B-GB) method for flood frequency analysis at 328 streamgaging stations in Arizona. The methods were compared using the relative percent difference (RPD) between annual exceedance probabilities (AEPs), goodness-of-fit assessments, random resampling procedures, and Monte Carlo simulations. The AEPs were calculated and compared using both station skew and weighted skew. Streamgaging stations were classified by U.S. Geological Survey (USGS) National Water Information System (NWIS) qualification codes, used to denote historical and censored peak-flow data, to better understand the effect that nonstandard flood information has on the flood frequency analysis for each method. Streamgaging stations were also grouped according to geographic flood regions and analyzed separately to better understand regional differences caused by physiography and climate.

The B17B-GB and EMA-MGB RPD-boxplot results showed that the median RPDs across all streamgaging stations for the 10-, 1-, and 0.2-percent AEPs, computed using station skew, were approximately zero. As the AEP flow estimates decreased (that is, from 10 to 0.2 percent AEP) the variability in the RPDs increased, indicating that the AEP flow estimate was greater for EMA-MGB when compared to B17B-GB. There was only one RPD greater than 100 percent for the 10- and 1-percent AEP estimates, whereas 19 RPDs exceeded 100 percent for the 0.2-percent AEP. At streamgaging stations with low-outlier data, historical peak-flow data, or both, RPDs ranged from −84 to 262 percent for the 0.2-percent AEP flow estimate. When streamgaging stations were separated by the presence of historical peak-flow data (that is, no low outliers or censored peaks) or by low outlier peak-flow data (no historical data), the results showed that RPD variability was greatest for the 0.2-AEP flow estimates, indicating that the treatment of historical and (or) low-outlier data was different between methods and that method differences were most influential when estimating the less probable AEP flows (1, 0.5, and 0.2 percent). When regional skew information was weighted with the station skew, B17B-GB estimates were generally higher than the EMA-MGB estimates for any given AEP. This was related to the different regional skews and mean square error used in the weighting procedure for each flood frequency analysis. The B17B-GB weighted skew analysis used a more positive regional skew determined in USGS Water Supply Paper 2433 (Thomas and others, 1997), while the EMA-MGB analysis used a more negative regional skew with a lower mean square error determined from a Bayesian generalized least squares analysis.

Regional groupings of streamgaging stations reflected differences in physiographic and climatic characteristics. Potentially influential low flows (PILFs) were more prevalent in arid regions of the State, and generally AEP flows were larger with EMA-MGB than with B17B-GB for gaging stations with PILFs. In most cases EMA-MGB curves would fit the largest floods more accurately than B17B-GB. In areas of the State with more baseflow, such as along the Mogollon Rim and the White Mountains, streamgaging stations generally had fewer PILFs and more positive skews, causing estimated AEP flows to be larger with B17B-GB than with EMA-MGB. The effect of including regional skew was similar for all regions, and the observed pattern was increasingly greater B17B-GB flows (more negative RPDs) with each decreasing AEP quantile.

A variation on a goodness-of-fit test statistic was used to describe each method’s ability to fit the largest floods. The mean absolute percent difference between the measured peak flows and the log-Pearson Type 3 (LP3)-estimated flows, for each method, was averaged over the 90th, 75th, and 50th percentiles of peak-flow data at each site. In most percentile subsets, EMA-MGB on average had smaller differences (1 to 3 percent) between the observed and fitted value, suggesting that the EMA-MGB-LP3 distribution is fitting the observed peak-flow data more precisely than B17B-GB. The smallest EMA-MGB percent differences occurred for the greatest 10 percent (90th percentile) of the peak-flow data. When stations were analyzed by USGS NWIS peak flow qualification code groups, the stations with historical peak flows and no low outliers had average percent differences as high as 11 percent greater for B17B-GB, indicating that EMA-MGB utilized the historical information to fit the largest observed floods more accurately.

A resampling procedure was used in which 1,000 random subsamples were drawn, each comprising one-half of the observed data. An LP3 distribution was fit to each subsample using B17B-GB and EMA-MGB methods, and the predicted 1-percent AEP flows were compared to those generated from distributions fit to the entire dataset. With station skew, the two methods were similar in the median percent difference, but with weighted skew EMA-MGB estimates were generally better. At two gages where B17B-GB appeared to perform better, a large number of peak flows were deemed to be PILFs by the MGB test, although they did not appear to depart significantly from the trend of the data (step or dogleg appearance). At two gages where EMA-MGB performed better, the MGB identified several PILFs that were affecting the fitted distribution of the B17B-GB method.

Monte Carlo simulations were run for the LP3 distribution using different skews and with different assumptions about the expected number of historical peaks. The primary benefit of running Monte Carlo simulations is that the underlying distribution statistics are known, meaning that the true 1-percent AEP is known. The results showed that EMA-MGB performed as well or better in situations where the LP3 distribution had a zero or positive skew and historical information. When the skew for the LP3 distribution was negative, EMA-MGB performed significantly better than B17B-GB and EMA-MGB estimates were less biased by more closely estimating the true 1-percent AEP for 1, 2, and 10 historical flood scenarios.

Study Area

Publication type Report
Publication Subtype USGS Numbered Series
Title Evaluation of the expected moments algorithm and a multiple low-outlier test for flood frequency analysis at streamgaging stations in Arizona
Series title Scientific Investigations Report
Series number 2014-5026
DOI 10.3133/sir20145026
Year Published 2014
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Arizona Water Science Center
Description Report: viii, 61 p.; Appendixes
Country United States
State Arizona
Datum North American datum 1983
Projection Universal Transverse Mercator
Online Only (Y/N) Y
Additional Online Files (Y/N) Y
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