Copula-Based Pooled Frequency Analysis of Droughts in the Canadian Prairies

This paper studies the frequency analysis of droughts using a copula with the application of regionalization in the context of a bivariate homogeneity analysis. Drought events indicated by severity and duration were extracted from monthly flow averages. A K-means clustering algorithm was used to form initial regions. A fuzzy C-means algorithm was used to form the final groups of sites that meet the criteria of bivariate discordancy, bivariate homogeneity, and size. The application of the Gumbel, Clayton, and Frank copulas for bivariate drought frequency analysis was studied. Results show the importance of a clear definition of drought in every scenario since, in our example, the longest drought does not necessarily correspond to the most severe one. Another important observation of this study was that, given the average annual rainfall of a catchment, droughts seem to occur in almost all regions, humid or arid. However, areas with higher annual rainfall can experience shorter but more severe drought. The procedures of this study are applicable for flood frequency analysis as well. Furthermore, ungauged sites can be integrated in the procedure of regionalization.