Reactive Particle-tracking Solutions to a Benchmark Problem on Heavy Metal Cycling in Lake Sediments

TL;DR

This paper demonstrates that reactive particle-tracking models can effectively simulate complex, variable geochemical behaviors in lake sediments, capturing data noise and variability better than traditional Eulerian models, with minimal computational cost.

Contribution

The study introduces a reactive particle-tracking approach that accurately replicates complex geochemical variability and enhances data noise representation compared to Eulerian models.

Findings

Particle-tracking models closely match Eulerian solutions in unperturbed conditions.

Perturbed particle-tracking models better capture data variability.

The method resolves noisy gradients with minimal additional computational cost.

Abstract

Geochemical systems are known to exhibit highly variable spatiotemporal behavior. This may be observed both in non-smooth concentration curves in space for a single sampling time and also in variability between samples taken from the same location at different times. However, most models that are designed to simulate these systems provide only single-solution smooth curves and fail to capture the noise and variability seen in the data. We apply a recently developed reactive particle-tracking method to a system that displays highly-complex geochemical behavior. When the method is made to most closely resemble a corresponding Eulerian method, in its unperturbed form, we see near-exact match between solutions of the two models. More importantly, we consider two approaches for perturbing the model and find that the spatially-perturbed condition is able to capture a greater degree of the variability present in the data. This method of perturbation is a task to which particle methods are uniquely suited and Eulerian models are not well-suited. Additionally, because of the nature of the algorithm, noisy spatial gradients can be highly resolved by a large number of mobile particles, and this incurs negligible computational cost, as compared to expensive chemistry calculations.