Uncertainty, entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling

Koutsoyiannis, D

dc.contributor.author	Koutsoyiannis, D	en
dc.date.accessioned	2014-03-01T01:23:18Z
dc.date.available	2014-03-01T01:23:18Z
dc.date.issued	2005	en
dc.identifier.issn	0262-6667	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16886
dc.subject	Entropy	en
dc.subject	Hydrological design	en
dc.subject	Hydrological extremes	en
dc.subject	Hydrological statistics	en
dc.subject	Power laws	en
dc.subject	Risk	en
dc.subject	Scaling	en
dc.subject	Uncertainty	en
dc.subject.classification	Water Resources	en
dc.subject.other	Approximation theory	en
dc.subject.other	Correlation methods	en
dc.subject.other	Entropy	en
dc.subject.other	Maximum principle	en
dc.subject.other	Normal distribution	en
dc.subject.other	Random processes	en
dc.subject.other	Autocorrelation properties	en
dc.subject.other	Coefficient of variation (CV)	en
dc.subject.other	Hydrological processes	en
dc.subject.other	Maximum entropy (ME)	en
dc.subject.other	Hydrology	en
dc.subject.other	entropy	en
dc.subject.other	hydrological modeling	en
dc.subject.other	power law	en
dc.subject.other	stochasticity	en
dc.title	Uncertainty, entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling	en
heal.type	journalArticle	en
heal.identifier.primary	10.1623/hysj.50.3.381.65031	en
heal.identifier.secondary	http://dx.doi.org/10.1623/hysj.50.3.381.65031	en
heal.language	English	en
heal.publicationDate	2005	en
heal.abstract	The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation (CV) and lag one autocorrelation. In this first part of the study, the marginal distributional properties of hydrological variables and the state scaling behaviour are investigated. Application of the ME principle under these very simple conditions results in the truncated normal distribution for small values of CV and in a nonexponential type (Pareto) distribution for high values of CV. In addition, the normal and the exponential distributions appear as limiting cases of these two distributions. Testing of these theoretical results with numerous hydrological data sets on several scales validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes. Both theoretical and empirical results show that the state scaling is only an approximation for the high return periods, which is merely valid when processes have high variation on small time scales. In other cases the normal distributional behaviour, which does not have state scaling properties, in a more appropriate approximation. Interestingly however, as discussed in the second part of the study, the normal distribution combined with positive autocorrelation of a process, results in time scaling behaviour due to the ME principle. Copyright © 2005 IAHS Press.	en
heal.publisher	IAHS PRESS, INST HYDROLOGY	en
heal.journalName	Hydrological Sciences Journal	en
dc.identifier.doi	10.1623/hysj.50.3.381.65031	en
dc.identifier.isi	ISI:000229683900001	en
dc.identifier.volume	50	en
dc.identifier.issue	3	en
dc.identifier.spage	381	en
dc.identifier.epage	404	en