Identification of Outliers in Flood Frequency Analysis: Comparison of Original and Multiple Grubbs-Beck Test

At-site flood frequency analysis is used to estimate
flood quantiles when at-site record length is reasonably long. In
Australia, FLIKE software has been introduced for at-site flood
frequency analysis. The advantage of FLIKE is that, for a given
application, the user can compare a number of most commonly
adopted probability distributions and parameter estimation methods
relatively quickly using a windows interface. The new version of
FLIKE has been incorporated with the multiple Grubbs and Beck test
which can identify multiple numbers of potentially influential low
flows. This paper presents a case study considering six catchments in
eastern Australia which compares two outlier identification tests
(original Grubbs and Beck test and multiple Grubbs and Beck test)
and two commonly applied probability distributions (Generalized
Extreme Value (GEV) and Log Pearson type 3 (LP3)) using FLIKE
software. It has been found that the multiple Grubbs and Beck test
when used with LP3 distribution provides more accurate flood
quantile estimates than when LP3 distribution is used with the
original Grubbs and Beck test. Between these two methods, the
differences in flood quantile estimates have been found to be up to
61% for the six study catchments. It has also been found that GEV
distribution (with L moments) and LP3 distribution with the multiple
Grubbs and Beck test provide quite similar results in most of the
cases; however, a difference up to 38% has been noted for flood
quantiles for annual exceedance probability (AEP) of 1 in 100 for one
catchment. This finding needs to be confirmed with a greater number
of stations across other Australian states.

• Ayesha S. Rahman
• Khaled Haddad
• Ataur Rahman

• Floods
• FLIKE
• probability distributions
• flood frequency
• outlier.

[1] V. W. Griffis, andJ. R.Stedinger,“The LP3 distribution and its
application in flood frequency analysis, 2. Parameter estimation
methods,” J. of Hydrol. Engineering, vol. 12(5), pp. 492–500, 2007.
[2] B. Bobée, G. Cavidas, F. Ashkar, J. Bernier, and P. Rasmussen,
“Towards a systematic approach to comparing distributions used in
flood frequency analysis,” J Hydrol,vol. 142, pp. 121–136, 1993.
[3] T. A. McMahon, and R. Srikanthan, “Log Pearson III distribution is it
applicable to flood frequency analysis of Australian streams?,” J Hydrol,
vol. 52(139), pp. 147, 1981.
[4] R. M. Vogel, T. A. McMahon, and F. H. S.Chiew,“Flood flow frequency
model selection in Australia,” J Hydrol,vol. 146(421), pp. 449, 1993.
[5] B. C. Bates, A. Rahman, R. G. Mein, and P. E. Weinmann, “Climatic
and physical factors that influence thehomogeneity of regional floods in
south-eastern Australia,” Water Resour Res, vol. 34(12), pp. 3369–3381,
1998.
[6] R. Merz, G. Bloschil, and G. Humer,“National flood discharge mapping
in Austria,” Nat Hazards, vol. 46, pp. 53–72, 2008.
[7] A. Meshgi, and D. Khalili, “Comprehensive evaluation of regional flood
frequency analysis by L-abdLHmoments. 1. A re-visit to regional homogeneity,”Stoch Environ Res Risk Assess, vol. 23, pp. 119–135,
2009a.
[8] A. Meshgi, and D. Khalili, “Comprehensive evaluation of regional flood
frequency analysis by L-abdLHmoments. II. Devewlopment of LHmoments
parameters for the generalized Pareto and generalizedlogistic
distributions,”Stoch Environ Res Risk Asses,vol. 23, pp. 137–152,
2009b.
[9] E. H. Ishak,A. Rahman, S. Westra, A. Sharma, and G. Kuczera,
“Preliminary analysis of trends in Australian flood data,” in Proc.World
Environmental and Water Resources Congress, American Society of
Civil Engineers (ASCE), Providence, Rhode Island, USA, 2010, pp. 120-
124.
[10] E. H. Ishak, K. Haddad, M. Zaman, and A. Rahman,“Scaling property of
regional floods in New South Wales Australia,”Nat Hazards, vol. 58, pp.
1155–1167, 2011.
[11] K. Haddad, A.Rahman, andG. Kuczera,“Comparison of ordinary and
generalised least squares regression models in regional flood frequency
analysis: a case study for New South Wales,”Aust J Water Resour,vol.
15(2), pp. 59–70, 2011.
[12] K. Haddad, A. Rahman, and J. R. Stedinger,“Regional Flood Frequency
Analysis using Bayesian Generalized Least Squares: a Comparison
between Quantile and Parameter Regression Techniques,”Hydrol
Process,vol. 25(1), pp. 14, 2012.
[13] K. Haddad, and A. Rahman,“Regional flood frequency analysis in
eastern Australia: Bayesian GLS regression-based methods within fixed
region and ROI framework—quantile regression versus parameter
regression technique,”J Hydrol,vol. 430–431, pp. 142–161, 2012.
[14] A. Rahman, K. Haddad, M. Zaman, G. Kuczera, P. E. Weinmann, and
W. Weeks, “Regional flood estimation in Australia: an overview of the
study for the upgrade of Australian Rainfall and Runoff,”in
Proc.Hydrology and Water Resources Symposium, Engineers Australia,
Sydney, Australia, 2012, pp. 1441–1448.
[15] K. Haddad, A. Rahman, M. Zaman, and S. Shrestha,“Applicability of
Monte Carlo cross validation technique for model development and
validation in hydrologic regression analysis using ordinary and
generalised least squares regression,”J Hydrol,vol. 482, pp. 119–128,
2013.
[16] A. S. Rahman, A. Rahman, M. Zaman, K. Haddad, A. Ashan, and M.
A. Imteaz, “A Study on Selection of Probability Distributions for At-site
Flood Frequency Analysis in Australia,”Natural Hazards,vol. 69, pp.
1803-1813, 2013.
[17] C. Cunnane,“Factors affecting choice of distribution for flood
series,”HydrolSci J,vol. 30, pp. 25–36, 1985.
[18] C. Cunnane,“Statistical distributions for flood frequency analysis,”in
Proc.Operational hydrological Report No. 5/33, World Meteorological
Organization (WMO), Geneva, Switzerland, 1989.
[19] K. M. Conway,“Flood frequency analysis of some NSW coastal
rivers,”Thesis (M. Eng. Sc.), University of New South Wales, Australia,
1970
[20] R. A. Kopittke, B. J. Stewart, andK. S. Tickle,“Frequency analysis of
flood data in Queensland,” inProc. Hydrological Symposium, Institution
of Engineers Australia, National Conference, 1976, Publication No.
76/2, 20:24.
[21] Institution of Engineers Australia (I.E. Aust.), Australian Rainfall and
Runoff: A Guide to Flood Estimation, 2001.
[22] Institution of Engineers Australia (I.E. Aust.), Australian Rainfall and
Runoff: A Guide to Flood Estimation, 1987.
[23] Interagency Advisory Committee on Water Data (IAWCD),Guidelines
for Determining Flood Flow Frequency: Bulletin 17-B.Hydrol.
Subcomm., Washington, DC, 1982.
[24] A. Rahman, P. E. Weinmann,and R. G. Mein,“At-site flood frequency
analysis: LP3-product moment, GEV-L moment and GEV-LH moment
procedures compared,” in Proc. Hydrology and Water Resource
Symposium, Brisbane, 1999, pp. 715–720.
[25] G. Kuczera,“Comprehensive at-site flood frequency analysis using
Monte Carlo Bayesian inference,” Water Resour Res,vol. 35(5), pp.
1551–1557, 1999.
[26] R. J. Nathan, and P. E. Weinmann,“Application of at-site and regional
flood frequency analyses,”in Proc. International Hydrology Water
Resources Symposium, Perth, 1991, pp. 769-774.
[27] K. Haddad, and A. Rahman, “Investigation on at-site flood frequency
analysis in south-east Australia,”IEM Journal, The Journal of The
Institution of Engineers, Malaysia, vol. 69(3), pp. 59-64, 2008.
[28] K. Haddad, A. Rahman,“Selection of the best fit flood frequency
distribution and parameter estimation procedure: a case study for
Tasmania in Australia,”StochEnv Res Risk Assess,vol. 25, pp. 415–428,
2010.
[29] T. A. Cohn, J. F. England, C. E. Berenbroc, R. R. Mason,J. R. Stedinger,
and J. R. Lamontagne,“A generalized Grubbs-Beck test statistic for
detecting multiple potentially influential outliers in flood series,”Water
Resources Research, vol. 49, pp. 5047–5058, 2013.
[30] W. O. Thomas,“A uniform technique for flood frequency analysis,”J.
Water Resour. Plann. Manage,vol. 111(3), pp. 321–337, 1985.
[31] B. Saf,“Assessment of the effects of discordant sites on regional flood
frequency analysis,”J Hydrol,vol. 380 (3–4), pp. 362–375, 2010
[32] R. J. Beckman, and R. D. Cook, “Outlier … … ….s.”
Technometrics,vol. 25(2), pp. 119-149, 1983.
[33] J. R. Stedinger, R. M. Vogel, and E. Foufoula-Georgiou, Frequency
Analysis of Extreme Events, chap. 18, pp. 99, McGraw Hill, New York,
1993.
[34] V. Barnett, and T. Lewis,Outliers in Statistical Data, John Wiley, New
York, 1994.
[35] W. Thompson,“On a criterion for the rejection of observations and the
distribution of the ratio of deviation to sample standard deviation,”Ann.
Math. Stat.,vol. 6, pp. 214–219, 1935.
[36] F. E. Grubbs, “Procedures for Detecting Outlying Observations in
Samples,”Technometrics,vol. 11(1), pp. 1-21, 1969.
[37] F. E. Grubbs, G. Beck,“Extension of sample sizes and percentage points
for significance tests of outlying observations,”Technometrics,vol.
4(14), pp. 847–853, 1972.
[38] G. Tietjen, and R. Moore,“Some Grubbs-type statistics for the detection
of several outliers,”Technometrics,vol. 14(3), pp. 583–597, 1972.
[39] B. Rosner,“On the detection of many outliers,”Technometrics,vol. 17(2),
pp. 221–227, 1975.
[40] B. Rosner,“Percentage points for a generalized ESD many outlier
procedure,”Technometrics,vol. 25(2), pp. 165–172, 1983.
[41] P. Prescott, “An approximate test for PILFs in linear
models,’Technometrics,vol. 17(1), pp. 129–132, 1975.
[42] P. Prescott,“Examination of the behaviour of tests for outliers when
more than one outlier is present,”Appl. Stat.,vol. 27, pp. 10–25, 1978.
[43] J. Gentleman, and M.Wilk, “Detecting PILFs. II. Supplementing the
direct analysis of residuals,”Biometrics,vol. 31(2), pp. 387–410, 1975.
[44] M. Marasinghe,“A multistage procedure for detecting several PILFs in
linear regression,”Technometrics,vol. 27(4), pp. 395–399, 1985.
[45] P. Rousseeuw, and B. V. Zomeren,“Unmasking multivariate PILFs and
leverage points,”J. Am. Stat. Assoc., vol. 85(411), pp. 633–639, 1990.
[46] A. Hadi, and J. Simonoff,“Procedures for the identification of multiple
outliers in linear models,”J. Am. Stat. Assoc.,vol. 88(424), pp. 1264–
1272, 1993.
[47] C. Spencer, and R.McCuen,“Detection of PILFs in Pearson type III
data,”J. Hydrol. Eng.,vol. 1, pp. 2–10, 1996.
[48] P. Rousseeuw, and A. Leroy,Robust Regression and Outlier Detection,
John Wiley, Hoboken, N. J, 2003
[49] S. Verma, and A. Quiroz-Ruiz,“Critical values for six Dixon tests for
outliers in normal samples up to sizes 100, and applications in science
and engineering,”Rev. Mex. Cienc. Geol.,vol. 23(2), pp. 133–161, 2006.
[50] W. J. Dixon, “Analysis of extreme values,”Ann. Math. Stat.,vol. 21(1),
pp. 488–506, 1950.
[51] W. J. Dixon, “Ratios involving extreme values.”Ann. Math. Stat.,vol.
22(1), pp. 68–78, 1951.
[52] Interagency Advisory Committee on Water Data (IAWCD), Robust
National Flood Frequency Guidelines: What is an Outlier? Bulletin 17-
C, 2013.
[53] J. R. Lamontagne, J. R. Stedinger, T. A. Cohn and N. A. Barth “Robust
national flood frequency guidelines: What is an outlier?”In Proc.World
Environmental and Water Resources Congress,ASCE, 2013.
[54] A. J. Gotvald, N. A. Barth, A. G.Veilleux, and C. Parrett C,“Methods for
determining magnitude and frequency of floods in California, based on
data through water year 2006,”U.S. Geological Survey, Reston, Virginia,
2012.
[55] R. H. McCuen, B. M.Ayyub,“Probability, statistics, and reliability for
engineers and scientists,”A Chapman & Hall book, USA, 1996.
[56] L. R. Beard, “Statistical methods in hydrology, Civil works investigation
project CW-151,”U.S. Army Corps of Engineers, Sacramento,
California, 1962.
[57] M. A. Benson,“Uniform flood-frequency estimating methods for federal
agencies,”Water Resour. Res.,vol. 4(5), pp. 891–908, 1968.
[58] W. Kirby, “Computer-oriented Wilson–Hilferty transformation that
preserves the first three moments and the lower bound of the Pearson
type 3 distribution,”Water Resour. Res.,vol. 8(5), pp. 125l–l254, 1972.