Gumbel–Hougaard Copula for Trivariate Rainfall Frequency Analysis
- 1 July 2007
- journal article
- Published by American Society of Civil Engineers (ASCE) in Journal of Hydrologic Engineering
- Vol. 12 (4), 409-419
- https://doi.org/10.1061/(asce)1084-0699(2007)12:4(409)
Abstract
Joint distributions of rainfall intensity, duration, and depth or those of rainfall intensity and duration, rainfall depth and duration, and rainfall intensity and depth are important in hydrologic design and floodplain management. Considering the dependence among rainfall intensity, depth, and duration, multivariate rainfall frequency distributions have been derived using one of three fundamental assumptions. Either the rainfall intensity, duration, and depth have been assumed independent, or they each have the same type of marginal probability distribution or they have been assumed to have the normal distribution or have been transformed to have the normal distribution. In reality, however, rainfall intensity, duration, and depth are dependent, do not follow, in general, the normal distribution, and do not have the same type of marginal distributions. This study aims at deriving trivariate rainfall frequency distributions using the Gumbel–Hougaard copula which does not assume the rainfall variables to be independent or normal or have the same type of marginal distributions. The trivariate distribution is then employed to determine joint conditional return periods, and is tested using rainfall data from the Amite River Basin in Louisiana.Keywords
This publication has 18 references indexed in Scilit:
- Bivariate Statistical Approach to Check Adequacy of Dam SpillwayJournal of Hydrologic Engineering, 2005
- Multivariate hydrological frequency analysis using copulasWater Resources Research, 2004
- A derived flood frequency distribution for correlated rainfall intensity and durationJournal of Hydrology, 2000
- A Semiparametric Estimation Procedure of Dependence Parameters in Multivariate Families of DistributionsBiometrika, 1995
- Bivariate exponential model applied to intensities and durations of extreme rainfallJournal of Hydrology, 1994
- Statistical Inference Procedures for Bivariate Archimedean CopulasJournal of the American Statistical Association, 1993
- The Joy of Copulas: Bivariate Distributions with Uniform MarginalsThe American Statistician, 1986
- On the probabilistic structure of storm surface runoffWater Resources Research, 1985
- A new look at the statistical model identificationIEEE Transactions on Automatic Control, 1974
- A Bivariate Extension of the Exponential DistributionJournal of the American Statistical Association, 1961