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Correlation Measures for Solute Transport Model Identification and Evaluation

  • Fred Sonnenwald
  • Virginia Stovin
  • Ian Guymer
Chapter
Part of the GeoPlanet: Earth and Planetary Sciences book series (GEPS)

Abstract

Correlation measures are used in a range of applications to quantify the similarity between time-series, often between model output and observed data. A software tool implemented by the authors uses optimisation to identify a system’s Residence Time Distribution (RTD) from noisy solute transport laboratory data. As part of the further development of the tool, an investigation has been undertaken to determine the most suitable correlation measures, both for solute transport model identification as an optimisation constraint and as an objective means of solute transport model evaluation. Correlation measures potentially suitable for use with solute transport data were selected for evaluation. The evaluation was carried out by manipulating synthetic dye traces in ways that reflect common solute transport model discrepancies. The conditions tested include change in number of sample points (discretisation/series length), transformation (scaling, etc.), transformation magnitude, and noise. BLC, \({\chi ^{2}}\), FFCBS, \(\mathrm R ^{2}\), RMSD, \(\text{ R}_\mathrm{t}^{2}\), ISE, and APE show favourable characteristics for use in model identification. Of these, \(\text{ R}^{2}\), \(\text{ R}{}_\mathrm{t}^{2}\) and APE are non-dimensional and so are also suitable for model evaluation.

Keywords

Sample Point Model Identification Solute Transport Correlation Measure Dynamic Time Warping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Civil and Structural EngineeringThe University of SheffieldSheffieldUK
  2. 2.School of EngineeringUniversity of WarwickCoventryUK

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