Wavelet-Based Rainfall–Stream Flow Models for the Southeast Murray Darling Basin
Publication: Journal of Hydrologic Engineering
Volume 19, Issue 7
Abstract
This study compares time series models for stream flow that use lagged rainfall as an exogenous variable with models that use a small subset of discrete wavelet coefficients of lagged rainfall with cross product and quadratic terms of the wavelet coefficients. The models require the calculation of a moving discrete wavelet transform (MDWT) that is implemented as a multiscale transform. A comparison is made using data from three catchments in the Murray Darling Basin in Australia. For finite impulse response models, the adjusted coefficient of determination, (), increased with the MDWT from 0.36 to 0.46 for the Tooma River Basin (TRB), from 0.43 to 0.52 for the Jingellic Catchment (JC), and from 0.56 to 0.59 for the Ovens Catchment (OC). The autoregressive models with exogenous input (ARX) with the wavelet transform further improved these results. The MDWT is based on a Haar wavelet so the wavelet coefficients have a physical interpretation. Predictions are further improved by a two-stage prediction procedure, in which an improved prediction is found as a quadratic function of the original prediction.
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Acknowledgments
This study was funded by the Australian Research Council through grant DP0877707 and by the Goyder Institute for Water Research. The researchers are grateful to Prof G. M. Zuppi (dec.) of the School of Advanced Studies in Venice for advice, to the developers of the R project for software code, and to the Murray Darling Basin Authority and the Australian Bureau of Meteorology for providing meteorological data.
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Published In
Journal of Hydrologic Engineering
Volume 19 • Issue 7 • July 2014
Pages: 1283 - 1293
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Nov 16, 2012
Accepted: Aug 7, 2013
Published online: Aug 10, 2013
Discussion open until: Jan 10, 2014
Published in print: Jul 1, 2014
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