Spatial pattern of arsenic contamination in shallow wells of Bangladesh: regional geology and nonlinear dynamics

Since the discovery of large-scale arsenic contamination of groundwater in Bangladesh more than a decade ago, studies related to its spatial characterization have relied on geostatistical approaches and the classical notion of linear stochastic dynamics. This study explores an alternative nonlinear approach, with a motivation to possibly achieve more cost-effective solutions for Bangladesh. It investigates the existence of nonlinear deterministic and chaotic dynamic behavior in the spatial pattern of arsenic contamination in the shallow wells (depth < 150 m). The database comprises the nationwide arsenic survey completed in 1999 by the British Geological Survey (BGS) in collaboration with the Department of Public Health Engineering (DPHE) of Bangladesh. Distinction is made in terms of regional geology (Pleistocene vs. Holocene deposits/Northwest vs. Southwest) to understand the geologic dependency. Identification of possible presence of nonlinear deterministic and chaotic patterns is made via the Grassberger-Procaccia correlation dimension algorithm. The analysis yields correlation dimension values ranging anywhere from 8 to 11 depending on the region, suggesting that the arsenic contamination in space, from a chaotic dynamic perspective, is a medium- to high-dimensional problem. The dimension results also indicate that the spatial dynamics of arsenic may be moderately sensitive to geology, with Pleistocene aquifers appearing to require a minimum of about two less dominant processes/variables for its description when compared to that required by the Holocene aquifers. Based on these results, a qualitative discussion is also cast on the potential opportunities offered by a nonlinear deterministic and chaotic dynamic approach towards improving cost-effectiveness in siting new safe wells.