On the use of a four-parameter kappa distribution in regional frequency analysis

ABSTRACT New developments are presented enabling the using a four-parameter kappa distribution with the widely used regional goodness-of-fit methods as part of an index flood regional frequency analysis based on the method of L-moments. The framework was successfully applied to 564 pooling groups and was found to significantly improve the probabilistic description of British flood flow compared to existing procedures. Based on results from an extensive data analysis it is argued that the successful application of the kappa distribution renders the use of the traditional three-parameter distributions such as the generalized extreme value (GEV) and generalized logistic (GLO) distributions obsolete, except for large and relatively dry catchments. The importance of these findings is discussed in terms of the sensitivity of design floods to distribution choice.

[1]  L. Baise,et al.  A global index earthquake approach to probabilistic assessment of extremes , 2007 .

[2]  T. Kjeldsen,et al.  A bivariate extension of the Hosking and Wallis goodness‐of‐fit measure for regional distributions , 2015 .

[3]  J. Vrijling,et al.  The estimation of extreme quantiles of wind velocity using L-moments in the peaks-over-threshold approach , 2001 .

[4]  D. Burn.  Evaluation of regional flood frequency analysis with a region of influence approach , 1990 .

[5]  J. R. Wallis,et al.  Regional Frequency Analysis: An Approach Based on L-Moments , 1997 .

[6]  Richard M. Vogel,et al.  Flood-Flow Frequency Model Selection in Southwestern United States , 1993 .

[7]  J. R. Wallis,et al.  Regional precipitation-frequency analysis and spatial mapping for 24-hour and 2-hour durations for Washington State , 2007 .

[8]  Jonathan R. M. Hosking,et al.  The four-parameter kappa distribution , 1994, IBM J. Res. Dev..

[9]  Konstantinos Tolikas,et al.  Modelling the distribution of the extreme share returns in Singapore , 2009 .

[10]  Q. J. Wang,et al.  The utility of L-moment ratio diagrams for selecting a regional probability distribution , 2001 .

[11]  T. Kjeldsen,et al.  Regional parent flood frequency distributions in Europe - Part 2: Climate and scale controls , 2014 .

[12]  J.-S. Park,et al.  Modelling Korean extreme rainfall using a Kappa distribution and maximum likelihood estimate , 2002 .

[13]  Y. Shao,et al.  L-Moments and fuzzy cluster analysis of dust storm frequencies in Iran , 2012 .

[14]  Jeong-Soo Park,et al.  LH-moment estimation of a four parameter kappa distribution with hydrologic applications , 2014, Stochastic Environmental Research and Risk Assessment.

[15]  A. Brath,et al.  Climate, orography and scale controls on flood frequency in Triveneto (Italy) , 2016 .

[16]  James H. Lambert,et al.  A Methodology for , 2000 .

[17]  B. Parida.  Modelling of Indian summer monsoon rainfall using a four-parameter Kappa distribution , 1999 .

[18]  J. Hosking,et al.  Comment on “Two‐Component Extreme Value Distribution for Flood Frequency Analysis” by Fabio Rossi, Mauro Florentino, and Pasquale Versace , 1986 .

[19]  Roland Schulze,et al.  A methodology for the estimation of short duration design storms in South Africa using a regional approach based on L-moments , 2001 .

[20]  T. Kjeldsen,et al.  Regional parent flood frequency distributions in Europe – Part 1: Is the GEV model suitable as a pan-European parent? , 2014 .

[21]  J. Hosking.  Nonparametric Confidence Regions for L -Moments , 2015 .

[22]  Towards statistical modeling of tsunami occurrence with regional frequency analysis , 2012 .

[23]  J. R. Wallis,et al.  Some statistics useful in regional frequency analysis , 1993 .

[24]  T. Kjeldsen,et al.  A formal statistical model for pooled analysis of extreme floods , 2009 .

[25]  Hon Keung Tony Ng,et al.  Ordered Data Analysis, Modeling and Health Research Methods , 2015 .