Three perspectives on modelling groundwater contamination – An industry case study

By James Fannon, Alina Dubovskaya, Robert Garvey, Susan Fennell and Laura Marie Keane

Groundwater contamination occurs when potentially hazardous material, typically arising from anthropogenic sources such as industrial or agricultural activities, makes its way (via percolation) from the ground surface to the water table.

In this blog post, we document a recent industry project carried out by several MACSI researchers with Syngenta, a Swiss-based agrochemical and seed manufacturer who aim to provide products to help farmers achieve global food security in a sustainable manner. The project was broadly concerned with modelling the movement and degradation of a foreign chemical species, which arises due to pesticide application at the soil surface, in a soil profile. Syngenta were particularly interested in investigating the potential utility of an Agent-Based Model (ABM) to describe the spatial and temporal evolution of the contaminant, as opposed to the more standard PDE-based approach.

In this blog post, we document a recent industry project carried out by several MACSI researchers with Syngenta, a Swiss-based agrochemical and seed manufacturer who aim to provide products to help farmers achieve global food security in a sustainable manner. The project was broadly concerned with modelling the movement and degradation of a foreign chemical species, which arises due to pesticide application at the soil surface, in a soil profile. Syngenta were particularly interested in investigating the potential utility of an Agent-Based Model (ABM) to describe the spatial and temporal evolution of the contaminant, as opposed to the more standard PDE-based approach.

Figure 1: A: Schematic of the contaminant transport problem and relevant degradation processes. Here x=H denotes the position of the water table. B Schematic of the ABM approach. Here blue circles represent different chemical agents at the current time step, while light blue circles show the same agents at the next step. If an agent is removed from the system (through degradation or due to an absorbing boundary) it is shown with a crossed circle. The soil surface is modelled as a reflecting boundary while the water table is an absorbing boundary.

In order to do so, MACSI researchers developed an object-oriented ABM to describe pesticide evolution in the soil profile, as illustrated in figure 1. This model took into account the dominant physical processes at work in the subsurface, namely advection (as a result of groundwater flow), diffusion, degradation of the contaminant agents due to the microbial action, and photolysis (a contaminant degradation process caused by sunlight) close to the soil surface (top 3mm approximately).
While it only acts over a short range, photolysis is of particular importance as it can degrade the contaminant at a much faster rate than microbial action alone, and it is poorly-represented in current PDE models of Environmental Fate, which are concerned with processes at the metre scale. Syngenta’s motivation for this project was to evaluate whether an ABM approach could represent surface processes more accurately than current models while retaining the features of conventional models.
The importance of photolysis is evidenced in figure 2, where we compare the chemical evolution in the soil as a result of applying pesticide during very dry and wet seasons. In the latter case, pesticide is quickly washed down through the soil by the infiltrating rainwater, and hence photolysis has little to no influence (figure 2, B). However during dryer weather the pesticide resides closer to the soil surface for a much longer period, thus underdoing more degradation than can be accounted for via microbial action alone (figure 2, A). Indeed, in the case illustrated below, almost 20% of the total chemical concentration is lost due to photolysis.

A                                                                                            B

Figure 2: Amount of chemicals (percent of initial mass) in the soil as a function of time. Different colours denote concentrations in different soil horizons (as indicated by the legend). The total chemical concentration in the case of no photolysis (i.e. constant microbial decay only) is given by the dashed line.

As the chemical agents are assumed to be subject to constant microbial degradation, this ABM approach is limited by the fact that a large number of agents are initially required to obtain sensible results in the long term, which restricts its computational efficiency. Nonetheless, it provides a useful plug-and-play code which can be used to explore the effects of changes in the model and can be easily modified to incorporate more complicated physical effects, such as non-Markovian processes.

However in addition to the ABM, MACSI researchers also considered two additional modelling perspectives for this problem; namely a Markovian and PDE approach. The former approach was used to describe the contaminant evolution as a Markov chain, and can be thought of as an approximation of the ABM approach which enables results for the expected distribution of particles to be calculated more efficiently. As applied mathematicians, we could also not help ourselves from forming a continuum description of the problem, and hence a one-dimensional reaction-diffusion model was developed. While this naturally incorporates simple transport and degradation, we also discussed how more complicated processes, such as photolysis and sorption of chemical to the soil matrix, can be incorporated into the model. These auxiliary approaches provided a means of validating the ABM in a very simple case (i.e. constant advection, diffusion, and degradation), and also allowed us to address some reservations raised by Syngenta regarding a PDE modelling approach.

Overall we found that the ABM approach represents a promising method for exploring the contaminant evolution problem, and may form a particularly useful tool for prototyping and determining whether a given physical phenomenon has a significant practical effect. However, once prototyping and model development has been finalised, we recommend formulating a continuum description of the model as opposed to running large-scale ABM simulations, which are very computationally expensive. As researchers, it was particularly interesting to see how three disparate approaches could be used to tackle the same problem. This industry project underscored for us how effective collaboration can yield greater understanding of a problem, how insights from one model could fuel development of another, and how as applied mathematicians we should be careful not to let our biases (PDEs in this case!) dismiss other modelling approaches.

 

James Fannon, Alina Dubovskaya, Robert Garvey, Susan Fennell and Laura Marie Keane are PhD students and Research Assisants at MACSI