RESEARCH ARTICLE 10.1002/2014WR016394 Improving the accuracy of risk prediction from particle-based breakthrough curves reconstructed with kernel density estimators Erica R. Siirila-Woodburn 1,2 , Daniel Fern andez-Garcia 1 , and Xavier Sanchez-Vila 1 1 Hydrogeology Group, Department of Geotechnical Engineering and Geosciences, Universitat Polite ` cnica de Catalunya, Barcelona, Spain, 2 Now at Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California, USA Abstract While particle tracking techniques are often used in risk frameworks, the number of particles needed to properly derive risk metrics such as average concentration for a given exposure duration is often unknown. If too few particles are used, error may propagate into the risk estimate. In this work, we provide a less error-prone methodology for the direct reconstruction of exposure duration averaged concentration versus time breakthrough curves from particle arrival times at a compliance surface. The approach is based on obtaining a suboptimal kernel density estimator that is applied to the sampled particle arrival times. The corresponding estimates of risk metrics obtained with this method largely outperform those by means of traditional methods (reconstruction of the breakthrough curve followed by the integration of concentration in time over the exposure duration). This is particularly true when the number of particles used in the numerical simulation is small (<10 5 ), and for small exposure times. Percent error in the peak of averaged breakthrough curves is approximately zero for all scenarios and all methods tested when the number of par- ticles is 10 5 . Our results illustrate that obtaining a representative average exposure concentration is reliant on the information contained in each individual tracked particle, more so when the number of particles is small. They further illustrate the usefulness of defining problem-specific kernel density estimators to prop- erly reconstruct the observables of interest in a particle tracking framework without relying on the use of an extremely large number of particles. 1. Introduction The process of computing both environmental and human health risk begins with an examination of the environmental concentration statistics, all of which are typically derived from breakthrough curves (BTCs). Of specific importance is the temporally averaged concentration over the exposure duration, ED [T], which is considered the true amount of exposure posing some adverse effect. The U.S. EPA Risk Assessment Guid- ance for Superfund [U.S. EPA, 1989, 2001] recommends that the exposure concentration, C, to be used in risk assessment calculations be defined as ‘‘the arithmetic average of the concentration that is contacted over the exposure period.’’ In hydrogeology, work has been made to link risk with environmental processes through a number of physi- cal parameters which would affect the concentration BTC signal in the modeling process. For example, Andric ˇevic ´ and Cvetkovic ´ [1996] showed that geologic heterogeneity and uncertainty in the sorption esti- mate are important factors in determining risk. Maxwell et al. [1998] showed that risk decreased as subsur- face heterogeneity increased. Enzenhoefer et al. [2012] explained how the time between peak and bulk solute breakthrough, important in risk analysis, increase in the presence of fractured media, or as aquifer heterogeneity increases. Siirila and Maxwell [2012b] showed that the statistical anisotropy of the aquifer and the inclusion of small-scale processes such as kinetic sorption and local dispersion in contaminant transport modeling could potentially raise risk over the remediation action level. de Barros and Fiori [2014] found simi- lar results regarding the importance of statistical anisotropy and transverse dispersion in determining the uncertainty of environmental concentration distributions. These works suggest that hydrogeologic parame- ters and processes are important in accurately assessing risk. But, despite this body of literature, it should be pointed out that the emphasis in many papers is in either the peak concentration or the shape of the tail in the BTC. Rather, the U.S. EPA and other agencies propose evaluating risk from some representative Key Points:  We develop a new methodology to reconstruct breakthrough curves from tracked particles  Error is evaluated as a function of the number of particles used  The new method outperforms traditional reconstructions for risk metrics Correspondence to: E. R. Siirila-Woodburn, erwoodburn@lbl.gov Citation: Siirila-Woodburn, E. R., D. Fern andez- Garcia, and X. Sanchez-Vila (2015), Improving the accuracy of risk prediction from particle-based breakthrough curves reconstructed with kernel density estimators, Water Resour. Res., 51, doi:10.1002/ 2014WR016394. Received 11 SEP 2014 Accepted 13 MAY 2015 Accepted article online 20 JUN 2015 V C 2015. American Geophysical Union. All Rights Reserved. SIIRILA-WOODBURN ET AL. IMPROVED ACCURACY RISK FROM KDE RECONSTRUCTED BTCS 1 Water Resources Research PUBLICATIONS