A nested multivariate copula approach to hydrometeorological simulations of spring floods: the case of the Richelieu River (Québec, Canada) record flood

Floods have potentially devastating consequences on populations, industries and environmental systems. They often result from a combination of effects from meteorological, physiographic and anthropogenic natures. The analysis of flood hazards under a multivariate perspective is primordial to evaluate several of the combined factors. This study analyzes spring flood-causing mechanisms in terms of the occurrence, frequency, duration and intensity of precipitation as well as temperature events and their combinations previous to and during floods using frequency analysis as well as a proposed multivariate copula approach along with hydrometeorological indices. This research was initiated over the Richelieu River watershed (Quebec, Canada), with a particular emphasis on the 2011 spring flood, constituting one of the most damaging events over the last century for this region. Although some work has already been conducted to determine certain causes of this record flood, the use of multivariate statistical analysis of hydrologic and meteorological events has not yet been explored. This study proposes a multivariate flood risk model based on fully nested Archimedean Frank and Clayton copulas in a hydrometeorological context. Several combinations of the 2011 Richelieu River flood-causing meteorological factors are determined by estimating joint and conditional return periods with the application of the proposed model in a trivariate case. The effects of the frequency of daily frost/thaw episodes in winter, the cumulative total precipitation fallen between the months of November and March and the 90th percentile of rainfall in spring on peak flow and flood duration are quantified, as these combined factors represent relevant drivers of this 2011 Richelieu River record flood. Multiple plausible and physically founded flood-causing scenarios are also analyzed to quantify various risks of inundation.

[1]  C. Genest,et al.  The Advent of Copulas in Finance , 2009 .

[2]  Amir AghaKouchak,et al.  Changes in concurrent monthly precipitation and temperature extremes , 2013 .

[3]  Bernard Bobée,et al.  On the tails of extreme event distributions in hydrology , 2008 .

[4]  M. Kendall.  A NEW MEASURE OF RANK CORRELATION , 1938 .

[5]  Matthias Fischer,et al.  Multivariate Copula Models at Work: Outperforming the desert island copula? , 2007 .

[6]  Vijay P. Singh,et al.  Identification of suitable copulas for bivariate frequency analysis of flood peak and flood volume data , 2011 .

[7]  M. Sklar.  Fonctions de repartition a n dimensions et leurs marges , 1959 .

[8]  R. Nelsen.  An Introduction to Copulas , 1998 .

[9]  Witold F. Krajewski,et al.  Examining Flood Frequency Distributions in the Midwest U.S. 1 , 2011 .

[10]  Alexandre Roy,et al.  Simulation hydrologique des derniers jours de la crue de printemps: le problème de la neige manquante , 2010 .

[11]  Taha B. M. J. Ouarda,et al.  Étude de la loi conjointe débit-niveau par les copules : Cas de la rivière Châteauguay , 2008 .

[12]  Jean‐François Quessy,et al.  Comparison of the interannual variability of spring heavy floods characteristics of tributaries of the St. Lawrence River in Quebec (Canada) , 2012 .

[13]  S. Simonovic,et al.  Bivariate flood frequency analysis. Part 2: a copula‐based approach with mixed marginal distributions , 2009 .

[14]  M. J. Frank.  On the simultaneous associativity ofF(x,y) andx +y -F(x,y) , 1979 .

[15]  H. Akaike.  A new look at the statistical model identification , 1974 .

[16]  Lan Zhang,et al.  Bivariate Rainfall and Runoff Analysis Using Entropy and Copula Theories , 2012, Entropy.

[17]  I. Olkin,et al.  Families of Multivariate Distributions , 1988 .

[18]  D. Clayton.  A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence , 1978 .

[19]  M. J. Frank.  On the simultaneous associativity ofF(x, y) andx+y−F(x, y) , 1978 .

[20]  V. Singh,et al.  Bivariate Flood Frequency Analysis Using the Copula Method , 2006 .

[21]  C. Genest,et al.  Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask , 2007 .

[22]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[23]  Eckhard Liebscher,et al.  Construction of asymmetric multivariate copulas , 2008 .

[24]  B. Bobée,et al.  Multivariate hydrological frequency analysis using copulas , 2004 .

[25]  Alireza Nazemi,et al.  Application of copula modelling to the performance assessment of reconstructed watersheds , 2011, Stochastic Environmental Research and Risk Assessment.

[26]  Daniel Lavallée,et al.  Un système de prévision appliqué aux crues subites de la rivière Châteauguay , 2000 .

[27]  John Karl Böhlke,et al.  Assessing denitrification in groundwater using natural gradient tracer tests with 15N: In situ measurement of a sequential multistep reaction , 2004 .

[28]  M. Khaliq,et al.  A copula-based multivariate analysis of Canadian RCM projected changes to flood characteristics for northeastern Canada , 2014, Climate Dynamics.

[29]  C. De Michele,et al.  On the Use of Copulas in Hydrology: Theory and Practice , 2007 .

[30]  M. Tedesco,et al.  An updated Antarctic melt record through 2009 and its linkages to high‐latitude and tropical climate variability , 2009 .

[31]  Gene E. Likens,et al.  Trends in stream nitrogen concentrations for forested reference catchments across the USA , 2013 .

[32]  Ann De Schepper,et al.  A copula test space model how to avoid the wrong copula choice , 2008, Kybernetika.

[33]  Marius Hofert,et al.  Sampling Archimedean copulas , 2008, Comput. Stat. Data Anal..

[34]  Martin Beniston,et al.  Trends in joint quantiles of temperature and precipitation in Europe since 1901 and projected for 2100 , 2009 .

[35]  P. Pilon,et al.  Hydrometeorological aspects of flood hazards in Canada , 1995 .

[36]  D. Helsel,et al.  Statistical methods in water resources , 2020, Techniques and Methods.

[37]  C. Cunnane.  Unbiased plotting positions — A review , 1978 .