An automatic locally-adaptive method to estimate heavily-tailed breakthrough curves from particle distributions

Particle tracking methods to simulate solute transport deal with the issue of having to reconstruct smooth concentrations from a limited number of particles. This is an error-prone process that typically leads to large fluctuations in the determined late-time behavior of breakthrough curves (BTCs). Kernel density estimators (KDE) can be used to automatically reconstruct smooth BTCs from a small number of particles. The kernel approach incorporates the uncertainty associated with subsampling a large population by equipping each particle with a probability density function. Two broad classes of KDE methods can be distinguished depending on the parametrization of this function: global and adaptive methods. This paper shows that each method is likely to estimate a specific portion of the BTCs. Although global methods offer a valid approach to estimate early-time behavior and peak of BTCs, they exhibit important fluctuations at the tails where fewer particles exist. In contrast, locally adaptive methods improve tail estimation while oversmoothing both early-time and peak concentrations. Therefore a new method is proposed combining the strength of both KDE approaches. The proposed approach is universal and only needs one parameter (α) which slightly depends on the shape of the BTCs. Results show that, for the tested cases, heavily-tailed BTCs are properly reconstructed with α ≈ 0.5.