One of the most recent advances is transport modeling is the Continuous Time Markov Chain (CTMC) model. Unlike traditional advection-dispersion equation (ADE) solvers that require temporal and spatial discretization and the evolution of a concentration field, CTMCs are built on evolving a stochastic state that represents being in the i-th cell. This fundamentally discrete in space framework can be evolved exactly in time using a matrix exponential, eliminating any error from time stepping. There is an uncertainty in the time it takes to move to a neighboring node though because all we know is “we were in the i-th cell” but exactly where cannot be known. This uncertainty creates a predictable spread that is similar to the numerical dispersion seen in other methods, but is intrinsic model uncertainty that can be tuned and controlled in novel ways not possible with classical ADE solvers. We’re actively working on improving and expanding the CTMC for transport in permeable systems, so keep an eye open.
Comparison from Engdahl (2026) showing equivalence between random walk particle tracking and CTMC simulations in 2D heterogeneous flow fields. The article describing the model is open access and can be found here: Representing uncertain solute transport in porous media with continuous time Markov chains
Watersheds are complex systems and investigating their behaviors takes special tools. We use the integrated hydrologic modeling platform ParFlow (see codes page) to create physically based geometries and define watershed properties for direct numerical simulation. These simulations allow us to test feedbacks between surface and groundwater, simulate land surface processes, and simulate chemical changes over time.
Chemical reactions are ubiquitous in nature but predicting where, when, and how fast they are going to occur is challenging. We have ongoing projects looking at where reactions occur in river corridors and their affect on Carbon, and nutrient cycling, reactions within water distribution systems, and remediating large-scale environmental contamination.
Animation of mixing limited reactive transport simulated using our complex particle reaction algorithm, which can be downloaded from the “codes” page.
Shallow geophysics provide a glimpse into the unknown. Our team uses ground penetrating radar to detect the depth to water in surgical aquifers, but also to image the sedimentary structures. These data are crucial for understanding flow and transport processes and are also essential for building geologically realistic models of the subsurface architecture. We use the information to generate statistical models of the distribution of material in the subsurface.
Geophysics also let us see inside other materials like permeable concrete. This is a time lapse survey of an infiltration and draining test to estimate lateral flow out of the installation on the WSU main campus.
There is a lot of water on the planet but getting it to the right place at the right time with sufficient quality can be a challenge. Much of the world relies on surface water resources to meet demand but when that falls short the backup plan is groundwater. The problem is that groundwater is extracted when it is needed but it isn’t replenished. Artificial recharge puts that water back and refills the reservoir already in the subsurface. This has many environmental benefits and can often be done without large modifications to the operation of water users.
Synthetic plastic fibers enter the environment every day primarily from our wastewater. Some fibers can pass directly through treatment plants and others end up in soils when waste sludge is used as fertilizer. The scientific community doesn’t yet know how putting large volumes of plastic into the environment will change, but we do already know that they can have significant adverse impacts on fish and other organisms. Based on estimated values from the literature, if we took mass of fibers entering the environment annually and made a lightweight fleece blanket out of them, that blanket could cover the entire Seattle-Tacoma International Airport twice. Compound that over a half-century of accelerating plastic use and you can see the magnitude of the problem. Our goal is to develop predictive numerical models to determine where micro-fiber accumulation is the heaviest so ecologists can focus on studying their impacts in those areas and determining any long-term ecosystem impacts.
The image to the right shows some trajectories of fibrous objects moving through a coarse gravel. Each color is a single fiber at different times and the units are millimeters.
