The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs
Article first published online: 17 JUN 2013
©2013 The Authors. Water Resources Research published by Wiley on behalf of the American Geophysical Union.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Water Resources Research
Volume 49, Issue 6, pages 3423–3442, June 2013
How to Cite
2013), The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs, Water Resour. Res., 49, 3423–3442, doi:10.1002/wrcr.20221., and (
- Issue published online: 25 JUL 2013
- Article first published online: 17 JUN 2013
- Accepted manuscript online: 2 APR 2013 03:05AM EST
- Manuscript Accepted: 25 MAR 2013
- Manuscript Revised: 4 FEB 2013
- Manuscript Received: 23 OCT 2012
- Engineering and Physical sciences Research Council “UK Infrastructure Transitions Research Consortium”. Grant Number: EP/I01344X/1
- dependence structures;
- multivariate distributions
 The information contained in hyetographs and hydrographs is often synthesized by using key properties such as the peak or maximum value Xp, volume V, duration D, and average intensity I. These variables play a fundamental role in hydrologic engineering as they are used, for instance, to define design hyetographs and hydrographs as well as to model and simulate the rainfall and streamflow processes. Given their inherent variability and the empirical evidence of the presence of a significant degree of association, such quantities have been studied as correlated random variables suitable to be modeled by multivariate joint distribution functions. The advent of copulas in geosciences simplified the inference procedures allowing for splitting the analysis of the marginal distributions and the study of the so-called dependence structure or copula. However, the attention paid to the modeling task has overlooked a more thorough study of the true nature and origin of the relationships that link , and I. In this study, we apply a set of ad hoc bootstrap algorithms to investigate these aspects by analyzing the hyetographs and hydrographs extracted from 282 daily rainfall series from central eastern Europe, three 5 min rainfall series from central Italy, 80 daily streamflow series from the continental United States, and two sets of 200 simulated universal multifractal time series. Our results show that all the pairwise dependence structures between , and I exhibit some key properties that can be reproduced by simple bootstrap algorithms that rely on a standard univariate resampling without resort to multivariate techniques. Therefore, the strong similarities between the observed dependence structures and the agreement between the observed and bootstrap samples suggest the existence of a numerical generating mechanism based on the superposition of the effects of sampling data at finite time steps and the process of summing realizations of independent random variables over random durations. We also show that the pairwise dependence structures are weakly dependent on the internal patterns of the hyetographs and hydrographs, meaning that the temporal evolution of the rainfall and runoff events marginally influences the mutual relationships of , and I. Finally, our findings point out that subtle and often overlooked deterministic relationships between the properties of the event hyetographs and hydrographs exist. Confusing these relationships with genuine stochastic relationships can lead to an incorrect application of multivariate distributions and copulas and to misleading results.