An edited version of this paper was published by AGU. Copyright (2015) American Geophysical Union.
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...

An edited version of this paper was published by AGU. Copyright (2015) American Geophysical Union.
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 (<105), 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 particles 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 properly reconstruct the observables of interest in a particle tracking framework without relying on the use of an extremely large number of particles.
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 (<105), 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 particles 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 properly reconstruct the observables of interest in a particle tracking framework without relying on the use of an extremely large number of particles.

Citation

Siirila, E., Fernandez, D., Sanchez, F. Improving the accuracy of risk prediction from particle-based breakthrough curves reconstructed with kernel density estimators. "Water resources research", Juny 2015, núm. 6, p. 4574-4591.