In previous chapters, we have discussed the Archimedean and non-Archimedean copula families. In this chapter, we will introduce entropic copulas. To be more specific, we will concentrate on the entropic copulas (i.e., most entropic canonical copulas) for the bivariate case. With proper constraints (e.g., the pair rank-based correlation coefficients), the bivariate entropic copula may be easily extended to the higher dimension.

In this chapter, we focus on the copula applications to at-site bivariate/trivariate drought analysis. In a case study, drought variables are separated from long-term daily streamflow series, i.e., drought severity, drought duration, drought interarrival time, and maximum drought intensity. Drought severity and duration are applied for bivariate drought frequency analysis. Drought severity, duration, and maximum intensity are applied for trivariate drought frequency analysis. The Archimedean, meta-elliptical, and vine copulas are adopted for the bivariate/trivariate analyses. The case study shows that the copula approach may be properly applied for drought analysis.

Bivariate or multivariate frequency analysis entails univariate distributions that are determined by empirical fitting to data. The fitting, in turn, requires the determination of distribution parameters and the assessment of the goodness of fit. In practical applications, such as hydrologic design, risk analysis is also needed. The objective of this chapter, therefore, is to briefly discuss these basic elements, which are needed for frequency analysis and will be needed in subsequent chapters.

In this chapter, we will illustrate the application of copulas in rainfall frequency analysis. This chapter is divided into two parts: (1) rainfall depth-duration frequency (DDF) analysis; and (2) multivariate rainfall frequency (i.e., four-dimensional) analysis. The rainfall data from the watersheds in the United States are collected and applied for analyses. The Archimedean, meta-elliptical, and vine copulas are applied to model the dependence among rainfall variables. Application shows that the DDF may be modeled by the Gumbel–Hougaard copula. Both vine and meta-elliptical copulas may be applied to model the spatial dependence of rainfall variables. Compared to the vine copula, modeling is easier to do when applying the meta-elliptical copula.

In this chapter, we will introduce the last application of the book, i.e., interbasin transfer. In this process, there are two main components: donor and receiver basins. The purpose of interbasin transfer to redistribute water from a water-rich region to the region with water shortage. The interbasin transfer may help reducing the impact of dry conditions in the region with water shortage.

Similar to the Archimedean copulas, the non-Archimedean copulas can be classified as one-parameter non-Archimedean bivariate copulas, two-parameter non-Archimedean bivariate copulas, and multivariate (d ≥ 3)$d\ge 3)$ non-Archimedean copulas. In recent years, successful applications of non-Archimedean copulas, such as meta-elliptical copulas and Plackett copulas, have been reported in hydrology and water resources management. In this chapter, we will focus on Plackett copulas and more specifically bivariate and trivariate Plackett copula.

In this chapter, we will illustrate the application of copulas in rainfall frequency analysis. This chapter is divided into two parts: (1) rainfall depth-duration frequency (DDF) analysis; and (2) multivariate rainfall frequency (i.e., four-dimensional) analysis. The rainfall data from the watersheds in the United States are collected and applied for analyses. The Archimedean, meta-elliptical, and vine copulas are applied to model the dependence among rainfall variables. Application shows that the DDF may be modeled by the Gumbel–Hougaard copula. Both vine and meta-elliptical copulas may be applied to model the spatial dependence of rainfall variables. Compared to the vine copula, modeling is easier to do when applying the meta-elliptical copula.