A bivariate analysis of the volume and duration of low-flow events

Abstract

: The knowledge of the volume and duration of low-flow events in river channels is essential for water management and the design of hydraulics structures. In this study, both preceding characteristics, X ₁ and X ₂, are considered simultaneously via two types of bivariate distributions whose marginals are exponential. One of these bivariate distributions has been presented by Nagao and Kadoya (1971) and the other has been used by Singh and Singh (1991) to the study of rainfall intensity and rainfall depth. The results are applied to the low-flow series (“peaks-below-threshold”) of Lepreau River (station 01AQ001) in New Brunswick, Canada. These results show that the model that was successfully employed by Singh and Singh (1991) to study rainfall, presents certain difficulties when a very strong correlation, ρ, between the two random variables X ₁ and X ₂, exists. The model by Nagao and Kadoya (1971) seems to be more satisfactory for such situations, although this model seems also to be quite sensitive to variations in ρ.