Typhoons are an inevitable and frequently occurring natural hazard in Taiwan which cause severe economic damage and loss of life. The common practice for flood-mitigation planning and design uses univariate frequency analysis. However, separate univariate analysis cannot reveal the significant relationship among correlated variables. This study therefore employs copulas to construct the joint distribution of rainfall depth and duration for typhoon data. Using copulas to construct a multivariate distribution means that the effects of marginal variables can be separated from that of dependent variables. We derive the depth-duration-frequency (DDF) formula based on using copulas to represent the joint distribution of rainfall depth and duration. Typhoon data recorded at the Kaohsiung Weather Station located in southern Taiwan are used as an example to illustrate the proposed methodology. The marginal distributions for rainfall depth and duration are fitted as the three-parameter gamma and Gumbel distributions, respectively. The Plackett copula is selected to construct the DDF curves. The DDF allows rainfall depth for a specific rainfall duration and return period to be estimated. This DDF formula improves the understanding of complex hydrologic processes and enhances the design safety criterion of hydraulic structures.
Keywords: bivariate distribution, copula, depth-duration-frequency, frequency analysis, joint probability, return period