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The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs

[1] The information contained in hyetographs and hydrographs is often synthesized by using key properties such as the peak or maximum value X(p), 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...

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Autores principales: Serinaldi, Francesco, Kilsby, Chris G
Formato: Online Artículo Texto
Lenguaje:English
Publicado: BlackWell Publishing Ltd 2013
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4303924/
https://www.ncbi.nlm.nih.gov/pubmed/25653461
http://dx.doi.org/10.1002/wrcr.20221
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author Serinaldi, Francesco
Kilsby, Chris G
author_facet Serinaldi, Francesco
Kilsby, Chris G
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description [1] The information contained in hyetographs and hydrographs is often synthesized by using key properties such as the peak or maximum value X(p), 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 [Image: see text], 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 [Image: see text], 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 [Image: see text], 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.
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spelling pubmed-43039242015-02-02 The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs Serinaldi, Francesco Kilsby, Chris G Water Resour Res Regular Articles [1] The information contained in hyetographs and hydrographs is often synthesized by using key properties such as the peak or maximum value X(p), 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 [Image: see text], 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 [Image: see text], 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 [Image: see text], 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. BlackWell Publishing Ltd 2013-06 2013-06-17 /pmc/articles/PMC4303924/ /pubmed/25653461 http://dx.doi.org/10.1002/wrcr.20221 Text en ©2013 The Authors. Water Resources Research published by Wiley on behalf of the American Geophysical Union. http://creativecommons.org/licenses/by/3.0/ 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.
spellingShingle Regular Articles
Serinaldi, Francesco
Kilsby, Chris G
The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs
title The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs
title_full The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs
title_fullStr The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs
title_full_unstemmed The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs
title_short The intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs
title_sort intrinsic dependence structure of peak, volume, duration, and average intensity of hyetographs and hydrographs
topic Regular Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4303924/
https://www.ncbi.nlm.nih.gov/pubmed/25653461
http://dx.doi.org/10.1002/wrcr.20221
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