Copula-based IDF curves and empirical rainfall thresholds for flash floods and rainfall-induced landslides

Summary Floods, landslides and debris flows are natural events that occur all over the world and are often induced by extreme rainfall conditions. Several extreme events occurred in Slovenia (Europe) in the last 25 years that caused 18 casualties and approximately 500 million Euros of economic loss. The intensity–duration–frequency (IDF) relationship was constructed using the Frank copula function for several rainfall stations using high-resolution rainfall data with an average subsample length of 34 years. The empirical rainfall threshold curves were also evaluated for selected extreme events. Post-event analyses showed that rainfall characteristics triggering flash floods and landslides are different. The sensitivity analysis results indicate that the inter-event time definition (IETD) and subsample definition methodology can have a significant influence on the position of rainfall events in the intensity–duration space, the constructed IDF curves and on the relationship between the empirical rainfall threshold curves and the IDF curves constructed using the copula approach. Furthermore, a combination of several empirical rainfall thresholds with an appropriate high-density rainfall measurement network can be used as part of the early warning system of the initiation of landslides and debris flows. However, different rainfall threshold curves should be used for lowland and mountainous areas in Slovenia.

[1]  S. Kazama,et al.  Assessment of snowmelt triggered landslide hazard and risk in Japan , 2009 .

[2]  Matjaž Mikoš,et al.  History and present state of the Slano Blato landslide , 2005 .

[3]  Pietro Aleotti,et al.  A warning system for rainfall-induced shallow failures , 2004 .

[4]  Demetris Koutsoyiannis,et al.  A mathematical framework for studying rainfall intensity-duration-frequency relationships , 1998 .

[5]  M. Mikoš,et al.  The Stogovce landslide in SW Slovenia triggered during the September 2010 extreme rainfall event , 2011 .

[6]  Karmen Fifer Bizjak,et al.  Site and laboratory investigation of the Slano blato landslide , 2009 .

[7]  Davide Tiranti,et al.  Estimation of rainfall thresholds triggering shallow landslides for an operational warning system implementation , 2010 .

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

[9]  Fausto Guzzetti,et al.  Rainfall thresholds for the possible occurrence of landslides in Italy , 2010 .

[10]  Gianfausto Salvadori,et al.  Frequency analysis via copulas: Theoretical aspects and applications to hydrological events , 2004 .

[11]  Carlo De Michele,et al.  Extremes in Nature : an approach using Copulas , 2007 .

[12]  Francesco Serinaldi,et al.  Asymmetric copula in multivariate flood frequency analysis , 2006 .

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

[14]  Peter S. Eagleson,et al.  Identification of independent rainstorms , 1982 .

[15]  Rao S. Govindaraju,et al.  Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas , 2008 .

[16]  Lorenzo Marchi,et al.  Impact of uncertainty in rainfall estimation on the identification of rainfall thresholds for debris flow occurrence , 2014 .

[17]  Shenglian Guo,et al.  Drought Analysis Using Copulas , 2013, Springer Water.

[18]  J. Godt,et al.  Early warning of rainfall-induced shallow landslides and debris flows in the USA , 2010 .

[19]  Barry A. Palynchuk,et al.  Threshold analysis of rainstorm depth and duration statistics at Toronto, Canada , 2008 .

[20]  M. Mikoš,et al.  Delineation of risk area in Log pod Mangartom due to debris flows from the Stoze landslide , 2007 .

[21]  Mitja Brilly,et al.  Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River , 2015 .

[22]  Fausto Guzzetti,et al.  Geomorphological Mapping to Assess Landslide Risk: Concepts, Methods and Applications in the Umbria Region of Central Italy , 2012 .

[23]  Fabrizio Durante,et al.  On the return period and design in a multivariate framework , 2011 .

[24]  Sandrine Anquetin,et al.  Sensitivity of the hydrological response to the variability of rainfall fields and soils for the Gard 2002 flash-flood event , 2010 .

[25]  Vijay P. Singh,et al.  IDF Curves Using the Frank Archimedean Copula , 2007 .

[26]  Robert Y. Liang,et al.  Probabilistic landslide hazard assessment using Copula modeling technique , 2014, Landslides.

[27]  M. Komac,et al.  Landslide susceptibility map of Slovenia at scale 1 : 250,000 , 2006 .

[28]  Matjaž Mikoš,et al.  Reinforced concrete shafts for the structural mitigation of large deep-seated landslides: an experience from the Macesnik and the Slano blato landslides (Slovenia) , 2012, Landslides.

[29]  Renzo Rosso,et al.  Bivariate Statistical Approach to Check Adequacy of Dam Spillway , 2005 .

[30]  Matjaž Mikoš,et al.  Sediment production and delivery from recent large landslides and earthquake-induced rock falls in the Upper Soča River Valley, Slovenia , 2006 .

[31]  Andrea Petroselli,et al.  Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation , 2012 .

[32]  B. Yan,et al.  Coincidence probability of precipitation for the middle route of South-to-North water transfer project in China , 2013 .

[33]  L. Gottschalk,et al.  Derivation of low flow distribution functions using copulas , 2014 .

[34]  F. Catani,et al.  Analysing the relationship between rainfalls and landslides to define a mosaic of triggering thresholds for regional-scale warning systems , 2014 .

[35]  Jun Yan,et al.  Modeling Multivariate Distributions with Continuous Margins Using the copula R Package , 2010 .

[36]  Eric Gaume,et al.  Hydrological analysis of a flash flood across a climatic and geologic gradient: The September 18, 2007 event in Western Slovenia , 2010 .

[37]  M. Brilly,et al.  Flood frequency analyses, statistical trends and seasonality analyses of discharge data: a case study of the Litija station on the Sava River , 2016 .

[38]  Marco Borga,et al.  Hydrometeorological Analysis of the 29 August 2003 Flash Flood in the Eastern Italian Alps , 2007 .

[39]  Matjaž Mikoš,et al.  Characteristics of the extreme rainfall event and consequent flash floods in W Slovenia in September 2007 , 2009 .

[40]  Matjaž Mikoš,et al.  Trivariate Frequency Analyses of Peak Discharge, Hydrograph Volume and Suspended Sediment Concentration Data Using Copulas , 2014, Water Resources Management.

[41]  S. L. Gariano,et al.  Rainfall thresholds for shallow landslide occurrence in Calabria, southern Italy , 2013 .

[42]  Yang Hong,et al.  Evaluation of past, present and future tools for radar-based flash-flood prediction in the USA , 2014 .

[43]  Mitja Brilly,et al.  Hydrologic conditions responsible for triggering the Stože landslide, Slovenia , 2004 .

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

[45]  Niko E. C. Verhoest,et al.  A comparative copula‐based bivariate frequency analysis of observed and simulated storm events: A case study on Bartlett‐Lewis modeled rainfall , 2011 .

[46]  Hubert H. G. Savenije,et al.  HESS Opinions "Topography driven conceptual modelling (FLEX-Topo)" , 2010 .

[47]  M. Borga,et al.  Flash flood warning based on rainfall thresholds and soil moisture conditions: An assessment for gauged and ungauged basins , 2008 .

[48]  M. Rossi,et al.  The rainfall intensity–duration control of shallow landslides and debris flows: an update , 2008 .

[49]  A National Warning System for Rainfall-Induced Landslides in Slovenia , 2014 .

[50]  Vijay P. Singh,et al.  Gumbel–Hougaard Copula for Trivariate Rainfall Frequency Analysis , 2007 .

[51]  B. Rémillard,et al.  Goodness-of-fit tests for copulas: A review and a power study , 2006 .

[52]  H. Joe.  Multivariate models and dependence concepts , 1998 .

[53]  M. Borga,et al.  Estimation of debris flow triggering rainfall: Influence of rain gauge density and interpolation methods , 2015 .

[54]  Matjaž Mikoš,et al.  Case Study: Numerical Simulations of Debris Flow below Stoze, Slovenia , 2006 .

[55]  Abdul Aziz Jemain,et al.  IDF relationships using bivariate copula for storm events in Peninsular Malaysia , 2012 .

[56]  N. Caine,et al.  The Rainfall Intensity - Duration Control of Shallow Landslides and Debris Flows , 1980 .

[57]  Isabel F. Trigo,et al.  Shallow and deep landslides induced by rainfall in the Lisbon region (Portugal): assessment of relationships with the North Atlantic Oscillation , 2005 .

[58]  Veronika Bačová Mitková,et al.  Joint modeling of flood peak discharges, volume and duration: a case study of the Danube River in Bratislava , 2014 .

[59]  M. Rossi,et al.  Rainfall thresholds for the initiation of landslides in central and southern Europe , 2007 .

[60]  Alessio Ferrari,et al.  Monitoring and prediction in early warning systems for rapid mass movements , 2014 .

[61]  K. V. Kumar,et al.  Integrating intensity–duration-based rainfall threshold and antecedent rainfall-based probability estimate towards generating early warning for rainfall-induced landslides in parts of the Garhwal Himalaya, India , 2014, Landslides.

[62]  Floyd A. Huff,et al.  Time distribution of rainfall in heavy storms , 1967 .

[63]  M. Borga,et al.  Comprehensive post‐event survey of a flash flood in Western Slovenia: observation strategy and lessons learned , 2009 .

[64]  Konstantine P. Georgakakos,et al.  Evaluation of real-time flash flood forecasts for Haiti during the passage of Hurricane Tomas, November 4–6, 2010 , 2013, Natural Hazards.

[65]  David R. Maidment,et al.  Handbook of Hydrology , 1993 .

[66]  Shenglian Guo,et al.  Flood Coincidence Risk Analysis Using Multivariate Copula Functions , 2012, Springer Water.

[67]  Ioannis K. Tsanis,et al.  Application of the HBV hydrological model in a flash flood case in Slovenia. , 2010 .