Origin and variability of statistical dependencies between peak, volume, and duration of rainfall-driven flood events

Abstract

Floods are among the most common and impactful natural events. The hazard of a flood event depends on its peak (Q), volume (V) and duration (D), which are interconnected to each other. Here, we used a worldwide dataset of daily discharge, two statistics (Kendall's tau and Spearman's rho) and a conceptual hydrological rainfall-runoff model as model-dependent realism, to investigate the factors controlling and the origin of the dependence between each couple of flood characteristics, with the focus to rainfall-driven events. From the statistical analysis of worldwide dataset, we found that the catchment area is ineffective in controlling the dependence between Q and V, while the dependencies between Q and D, and V and D show an increasing behavior with the catchment area. From the modeling activity, on the U.S. subdataset, we obtained that the conceptual hydrological model is able to represent the observed dependencies between each couple of variables for rainfall-driven flood events, and for such events, the pairwise dependence of each couple is not causal, is of spurious kind, coming from the "Principle of Common Cause".

Figure 1

Boxplots of the measures of dependence (Spearman’s rho in upper panels and Kendall’s tau in lower panels) as function of the catchment area, for each couple of flood variables (Q–V in the left column, Q–D in the right column, V–D in the intermediate column), using stations with at least 40 events and the 90th percentile of daily discharge as threshold. The catchment area is divided in four classes: small (500, 5000] km², medium (5000, 50,000] km², large (50,000, 500,000] km², and very large (500,000, 5,000,000] km².

Figure 2

Comparison between observed (using 90th percentile of daily discharge as threshold) and simulated pairwise dependencies in terms of boxplots, for U.S subdataset. Spearman’s rho is in the left panel, and the Kendall’s tau in the right panel.

Figure 3

Path diagram between meteorological (exogenous) variables I and W, and the flood (endogenous) variables: Q, V, D. I and W can be dependent (represented by a curved line with arrowheads at each end) or independent (represented with the symbol × on the curved line) each other. The connection between each meteorological variable and each flood variable is filtered by the catchment descriptors (A, k, in this case) and represented by an arrow that goes from each cause to the effect.