Top

Water Resources Management

Published in:

19-01-2022

Multivariate Flood Frequency Analysis Using Bivariate Copula Functions

Authors: Homa Razmkhah, Alireza Fararouie, Amin Rostami Ravari

Published in: Water Resources Management | Issue 2/2022

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Multivariate analysis of flood frequency was used extensively in water resources research. Often the only flood peak or volume is analyzed with statistical distributions, but for a perfect and exact result, the four main characteristics of a flood event, as well as peak, volume, duration, and time-to-peak, are needed. For this reason, multivariate statistical approaches like copula functions developed. This research aims to define and use the bivariate copula (2-copula) probability distribution functions (PDF) for flood characteristics multivariate analysis. When the joint distribution of characteristics such as volume and peak is known, it is possible to define the probability of simultaneous occurrence of design volume and peak flow values.

previous article Solving Complex Rainfall-Runoff Processes in Semi-Arid Regions Using Hybrid Heuristic Model

next article Potential Performance of Hydraulic State Estimation in Water Distribution Networks

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Akaike H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19(6):716–723CrossRef

Archer D (1998) Flood frequency analysis. In: Encyclopedia of Hydrology and Lakes. Encyclopedia of Earth Science. Springer, Dordrecht

Ash RB (2008) Basic probability theory (Dover ed.), Mineola, N.Y.: Dover Publications. pp 66–69

Ayantobo O, Li Y, Song S (2019) Multivariate drought frequency analysis using four-variate symmetric and asymmetric Archimedean copula functions. Water Resour Manag 33:103–127CrossRef

Box GEP, Cox D (1964) An analysis of transformation (with discussion). J Roy Statist Soc Ser B 26:211–246

Brenchmann EC, Schepsmeier U (2013) Modeling dependence with C- and V-Vine copulas: the R package CDVine. J Statist Soft 52(3):1–27

Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach (2^nd ed.), Springer-Verlag

Chen L, Guo S, Yan B, Liu P, Fang B (2010) A new seasonal design flood method based on bivariate joint distribution of flood magnitude and date of occurrence. Hydrologic Sci 55(8):1264–1280CrossRef

De Michele C, Salvadori G, Canossi M, Petaccia A, Rosso R (2005) Bivariate statistical approach to check adequacy of dam spillway. J Hydrol Eng 10(1):50–57CrossRef

Dupuis DJ (2007) Using copulas in hydrology: benefits, cautions, and issues. J Hydrol Eng 12(4):381–393CrossRef

Evans M, Rosenthal JS (2010) Probability and statistics: the science of uncertainty (2nd ed.), New York: W.H. Freeman and Co

Everitt BE (2006) The Cambridge dictionary of statistics (3rd ed.), Cambridge, UK: Cambridge University Press

Favre A-C, El Adlouni S, Perreault L, Thiémonge N, Bobée B (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40(1):W01101CrossRef

Ganguli P, Reddy MJ (2013) Probabilistic assessment of flood risks using trivariate copulas. Theoretic Appl Climatol 111:341–360CrossRef

Genest C, MacKay RJ (1986) Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données. Canad J Statat 14(2):145–159CrossRef

Genest C, Favre A-C (2007) Everything you always wanted to know about copula modeling but were afraid to ask. J Hydrol Eng 12(4):347–368CrossRef

Ghizzoni T, Roth G, Rudari R (2010) Multivariate skew-t approach to the design of accumulation risk scenarios for the flooding hazard. Adv in Water Resour 33:1243–1255CrossRef

Goda K (2010) Statistical modeling of joint probability distribution using copula: Application to peak and permanent displacement seismic demands. Struc Safet 32:112–123CrossRef

Grimaldi S, Serinaldi F (2006) Asymmetric copula in multivariate flood frequency analysis. Adv in Water Resour 29(8):1155–1167CrossRef

Gumbel EJ (1960) Bivariate exponential distributions. J Americ Statist Assoc 55:698–707CrossRef

Gumbel EJ, Mustafi CK (1967) Some analytical properties of bivariate extreme distributions. J Americ Statist Assoc 62:596–688

Joe H (1997) Multivariate models and dependence concepts. Chapman and Hall, CRC, Boca RatonCrossRef

Lorenz M, Bliefernicht J, Haese B, Kunstmann H (2018) Copula-based downscaling of daily precipitation fields. Hydrolog Proc 32:3479–3494CrossRef

McElreath R (2016) Statistical rethinking: a Bayesian course with examples in R and Stan. CRC Press

Nelsen RB (1999) An introduction to copulas. SpringerCrossRef

Nelsen RB (2006) An introduction to copulas. Springer

Palynchuk BA, Guo Y (2011) A probabilistic description of rainstorms incorporating peak intensities. J Hydrology 409:71–80CrossRef

Park KII (2018) Fundamentals of probability and stochastic processes with applications to communications, Springer

Razmkhah H (2018) Parameter uncertainty propagation in a Rainfall – Runoff model; Case study: Karoon III river basin. Water Resour 45(1):34–49

Razmkhah H, Saghafian B, AkhoundAli AM, Radmanesh F (2016a) Rainfall-Runoff modeling considering soil moisture accounting algorithm, case study: Karoon III river basin. Wat Resource 43(4):699–710CrossRef

Razmkhah H, AkhoundAli AM, Radmanesh F, Saghafian B (2016b) Evaluation of rainfall spatial correlation effect on rainfall-runoff modeling uncertainty, considering 2-copula. Arab J Geoscience 9:323CrossRef

Razmkhah H, AkhoundAli AM, Radmanesh F (2017) Correlated parameters uncertainty propagation in a Rainfall-Runoff model, considering 2-copula, case study: Karoon III river basin. Env Model Assess 22:503–521CrossRef

Reddy MJ, Ganguli P (2012) Bivariate flood frequency analysis of upper Godavari river flow using Archimedean copulas. Water Resour Manag 26(14):3995–4018CrossRef

Renard B, Lang M (2007) Use of a Gaussian copula for multivariate extreme value analysis: Some case studies in hydrology. Adv Water Resour 30:897–912CrossRef

Salvadori G, De Michele C (2007) On the use of copulas in hydrology: Theory and practice. J Hydrol Eng 12(4):369–380CrossRef

Schwarz GE (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464CrossRef

Serinaldi F, Grimaldi S (2007) Fully nested 3-copula: Procedure and application on hydrological data. J Hydrol Eng 12(4):420–430CrossRef

Singh VP (1987) Hydrological frequency modeling. Reidal, BostonCrossRef

Singh K, Singh VP (1991) Derivation of bivariate probability density functions with exponential marginals. Stoch Hydrol Hydraul 5:55–68CrossRef

Sklar A (1959) Fonctions de repartition an dimensions et leurs marges. Publications De L’institut Statistique De L’universite De Paris 8:229–231

Taddy M (2019) Business data science: Combining machine learning and economics to optimize, automate, and accelerate business decisions. McGraw-Hill, New York

Vittal H, Singh J, Kumar P, Karmakar S (2015) A framework for multivariate data-based at-site flood frequency analysis: Essentiality of the conjugal application of parametric and nonparametric approaches. J Hydrol 525:658–675CrossRef

Wang C, Chang N-B, Yeh G-T (2009) Copula-based flood frequency (COFF) analysis at the confluences of river systems. Hydrol Process 23(10):1471–1486CrossRef

Wit E., Heuvel EVD, Romeijin JW (2012) All models are wrong...’: an introduction to model uncertainty. Statistica Neerlandica 66(3):217–236

Yue S (2001) A bivariate gamma distribution for use in multivariate flood frequency analysis. Hydrol Process 15(6):1033–1045CrossRef

Yue S, Quarda T, Bobee B, Legendre P, Bruneau P (2002) Approach for describing statistical properties of flood hydrograph. J Hydrologic Eng 7(2):147–153

Yue K-X, Xiong L, Gottschalk L (2014) Derivation of low flow distribution functions using copulas. J Hydrology 508:273–288CrossRef

Zening W, Chentao H, Wang H, Zhang Q (2020) Reservoir inflow synchronization analysis for four reservoirs on a multivariate copula model. Water Resour Manag 34:2753–2770

Zhong M, Zeng T, Jiang T, Wu H, Chen X, Hong Y (2021) A copula-based multivariate probability analysis for flash flood risk under the compound effect of soil moisture and rainfall. Water Resour Manag 35(4):1–16

Title: Multivariate Flood Frequency Analysis Using Bivariate Copula Functions
Authors: Homa Razmkhah
Alireza Fararouie
Amin Rostami Ravari
Publication date: 19-01-2022
Publisher: Springer Netherlands
Published in: Water Resources Management / Issue 2/2022
Print ISSN: 0920-4741
Electronic ISSN: 1573-1650
DOI: https://doi.org/10.1007/s11269-021-03055-3

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Other articles of this Issue 2/2022

Town-Level Aquatic Environmental Sensitivity Assessment Based on an Improved Ecological Footprint Model

An Efficient Approach for Nodal Water Demand Estimation in Large-scale Water Distribution Systems

Translational Platform for Increasing Water Use Efficiency in Agriculture: Comparative Analysis of Plantation Crops

Comparative Study of Flood Coincidence Risk Estimation Methods in the Mainstream and its Tributaries

European Multi Model Ensemble (EMME): A New Approach for Monthly Forecast of Precipitation

Comparison of Self-Organizing Map, Artificial Neural Network, and Co-Active Neuro-Fuzzy Inference System Methods in Simulating Groundwater Quality: Geospatial Artificial Intelligence