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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anderson M, Woessner W (1992) Applied groundwater modeling: simulation of flow and advective transport. Academic, London
Berndt DJ, Clifford J (1994) Using dynamic time warping to find patterns in time series. In: Technical report WS-94-03, The AAAI Press, Melno Park, California, pp 359–370
Boudraa AO, Cexus JC, Groussat M, Brunagel P (2008) An energy-based similarity measure for time series. Eurasip J Adv Signal Process
Chen L, Ozsu MT, Oria V (2005) Robust and fast similarity search for moving object trajectories. In: Widom J, Ozcan F, Chirkova R (eds) Proceedings of the ACM SIGMOD international conference on management of data, Baltimore, MD, pp 491–502
Cox CS, Boucher AR (1989) Data based models: an automatic method for model structure determination. In: IEE colloquium model validation control system design simulation, London, UK, pp 2, 1–2, 4
Fischer HB (1967) The mechanics of dispersion in natural streams. J Hydraul Div ASCE 93(6):187–215
George SC, Burnham KJ, Mahtani JL, Inst Elect Engineers L (1998) Modelling and simulation of hydraulic components for vehicle applications–a precursor to control system design. In: International conference on simulation ’98, 457. Institute of Electrical Engineers, London, pp 126–132
Ghosh AK (2007) Introduction to linear and digital control systems. Prentice-Hall, India
Greenwood P, Nikulin M (1996) A guide to chi-squared testing, vol 280. Wiley-Interscience
Hattersley JG, Evans ND, Hutchison C, Cockwell P, Mead G, Bradwell AR, Chappell MJ (2008) Nonparametric prediction of free-lightchain generation in multiple myelomapatients. In: 17th International federation of automatic control world congress (IFAC), Seoul, Korea, pp 8091–8096
Kashefipour S, Falconer R (2000) An improved model for predicting sediment fluxes in estuarine waters. Proceedings of the fourth international hydroinformatics Conference, Iowa, USA,
Miskiewicz J (2010) Entropy correlation distance method. The euro introduction effect on the consumer price index. Phys A 389(8):1677–1687
Moriasi DN, Arnold JG, Van Liew MW, Bingner RL, Harmel RD, Veith TL (2007) Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans ASABE 50(3):885–900
Movahed MS, Jafari GR, Ghasemi F, Rahvar S, Tabar MRR (2006) Multifractal detrended fluctuation analysis of sunspot time series. Theory Exp J Stat Mech
Nash JE, Sutcliffe JV (1970) River flow forecasting through conceptual models part i–a discussion of principles. J Hydrol 10(3):282–290
Rodgers JL, Nicewander WA (1988) Thirteen ways to look at the correlation coefficient. Am Stat 42(1):59–66
Rutherford JC (1994) River mixing. Wiley, Chichester, England
Stovin VR, Guymer I, Chappell MJ, Hattersley JG (2010) The use of deconvolution techniques to identify the fundamental mixing characteristics of urban drainage structures. Water Sci Technol 61(8):2075–2081
The MathWorks Inc (2011) MATLAB R2011a. Natick, MA
Vlachos M, Kollios G, Gunopulos D (2002) Discovering similar multidimensional trajectories. In: Agrawal R (ed) 18th International conference on data engineering. Proceedings, IEEE computer society, pp 673–684
Wang Q, Shen Y, Zhang JQ (2005) A nonlinear correlation measure for multivariable data set. Phys D 200(3–4):287–295
Ye JC, Tang Y, Peng H, Zheng QL, ieee (2004) Ffcbs: a simple similarity measurement for time series. In: Proceedings of the 2004 international conference on intelligent mechatronics and automation, pp 392–396
Young P, Jakeman A, McMurtrie R (1980) An instrumental variable method for model order identification. Automatica 16(3):281–294
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sonnenwald, F., Stovin, V., Guymer, I. (2013). Correlation Measures for Solute Transport Model Identification and Evaluation. In: Rowiński, P. (eds) Experimental and Computational Solutions of Hydraulic Problems. GeoPlanet: Earth and Planetary Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30209-1_28
Download citation
DOI: https://doi.org/10.1007/978-3-642-30209-1_28
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30208-4
Online ISBN: 978-3-642-30209-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)