Optimal decomposition of covariance matrices for multivariate stochastic models in hydrology

Koutsoyiannis, D

dc.contributor.author	Koutsoyiannis, D	en
dc.date.accessioned	2014-03-01T01:15:01Z
dc.date.available	2014-03-01T01:15:01Z
dc.date.issued	1999	en
dc.identifier.issn	0043-1397	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13288
dc.subject	Covariance Matrices	en
dc.subject	Stochastic Model	en
dc.subject.classification	Environmental Sciences	en
dc.subject.classification	Limnology	en
dc.subject.classification	Water Resources	en
dc.subject.other	hydrological model	en
dc.subject.other	hydrology	en
dc.subject.other	modeling	en
dc.subject.other	parameterization	en
dc.title	Optimal decomposition of covariance matrices for multivariate stochastic models in hydrology	en
heal.type	journalArticle	en
heal.identifier.primary	10.1029/1998WR900093	en
heal.identifier.secondary	http://dx.doi.org/10.1029/1998WR900093	en
heal.language	English	en
heal.publicationDate	1999	en
heal.abstract	A new method is proposed for decomposing covariance matrices that appear in the parameter estimation phase of all multivariate stochastic models in hydrology. This method applies not only to positive definite covariance matrices (as do the typical methods of the literature) but to indefinite matrices, too, that often appear in stochastic hydrology. It is also appropriate for preserving the skewness coefficients of the model variables as it accounts for the resulting coefficients of skewness of the auxiliary (noise) variables used by the stochastic model, given that the latter coefficients are controlled by the decomposed matrix. The method is formulated in an optimization framework with the objective function being composed of three components aiming at (1) complete preservation of the variances of variables, (2) optimal approximation of the covariances of variables, in the case that complete preservation is not feasible due to inconsistent (i.e., not positive definite) structure of the covariance matrix, and (3) preservation of the skewness coefficients of the model variables by keeping the skewness of the auxiliary variables as low as possible. Analytical expressions of the derivatives of this objective function are derived, which allow the development of an effective nonlinear optimization algorithm using the steepest descent or the conjugate gradient methods. The method is illustrated and explored through a real world application, which indicates a very satisfactory performance of the method.	en
heal.publisher	Druckmaschinen Gmbh Leipzig, Leipzig, Germany	en
heal.journalName	Water Resources Research	en
dc.identifier.doi	10.1029/1998WR900093	en
dc.identifier.isi	ISI:000079430100024	en
dc.identifier.volume	35	en
dc.identifier.issue	4	en
dc.identifier.spage	1219	en
dc.identifier.epage	1229	en