Correlation Dimension as a Proxy for the Number of ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Correlation Dimension as a Proxy for the Number of Parameters Required to Model Risk of Groundwater Arsenic Contamination: An Assessment Using Ordinary Logistic Regression
Paper
Author:Faisal Hossain <fhossain@tntech.edu> (Tennessee Technological University)
Jason Hill <ajhill21@tntech.edu> (Tennessee Technological University)
Presenter:Faisal Hossain <fhossain@tntech.edu> (Tennessee Technological University)
Date: 2006-06-18     Track: Special Sessions     Session: Groundwater Optimal Management Session
DOI:10.4122/1.1000000340
DOI:10.4122/1.1000000341

The Correlation Dimension (CD) of an attractor provides information on the number of variables present in its non-linear deterministic variability. In this study we demonstrate a physical connection between the CD and the mathematical modeling of risk of arsenic contamination in groundwater using Ordinary Logistic Regression (OLR). Our database comprised the nation-wide arsenic survey completed in 1999 by the British Geological Survey (BGS) in collaboration with the Department of Public Health Engineering (DPHE) in Bangladesh, wherein, Hossain and Sivakumar (2005) reported CD values ranging anywhere from 8 to 11 for shallow aquifers (depth < 150 m) depending on the region and geology. Using 12 physically meaningful parameters from the universal set of variables that define the geo-chemical regime of aquifers and hence arsenic concentration, we demonstrate that CD is a reliable proxy for the minimum number of parameters required in the OLR model to accurately predict arsenic contamination at non-sampled wells. To the best of our knowledge, this work represents the very first attempt to inject non-linear deterministic paradigms in the linear stochastic modeling of the risk of arsenic contamination in shallow aquifers of Bangladesh.