Quantifying particle dispersal in aquatic sediments at short time scales: model selection

Abstract

In a pulse-tracer experiment, a layer of tracer particles is added to the sediment-water interface, and the down-mixing of these particles is followed over a short time scale. Here, we compared different models (biodiffusion, telegraph, CTRW) to analyse the resulting tracer depth profiles. The biodiffusion model is widely applied, but entails 2 problems: (1) infinite propagation speed-the infinitely fast propagation of tracer to depth, and (2) infinitely short waiting times-mixing events follow each other infinitely fast. We show that the problem of waiting times is far more relevant to tracer studies than the problem of propagation speed. The key issue in pulse-tracer experiments is that models should explicitly account for a finite waiting time between mixing events. The telegraph equation has a finite propagation speed, but it still assumes infinitely short waiting times, and, hence, it does not form a suitable alternative to the biodiffusion model. Therefore, we advance the continuous-time random walk (CTRW), which explicitly accounts for finite waiting times between mixing events, as a suitable description of bioturbation. CTRW models are able to cope with lateral spatial heterogeneity in reworking, which is a crucial feature of bioturbation at short time scales. We show how existing bioturbation models (biodiffusion model, telegraph equation, non-local exchange model) can be considered as special cases of the CTRW model. Accordingly, the CTRW model is not a new bioturbation model, but a generalization of existing models.