Next Generation Computers Warrant Next Generation Groundwater Models.

Modern hydrologic models have extraordinary capabilities for representing complex process in surface-subsurface systems. These capabilities have revolutionized the way we conceptualize flow systems, but how to represent uncertainty in simulated flow systems is not as well developed. Currently, characterizing model uncertainty can be computationally expensive, in part, because the techniques are appended to the numerical methods rather than seamlessly integrated.

A review of spatial Markov models for predicting pre-asymptotic and anomalous transport in porous and fractured media.

Heterogeneity across a broad range of scales in geologic porous media often manifests in observations of non-Fickian or anomalous transport. While traditional anomalous transport models can successfully make predictions in certain geological systems, increasing evidence suggests that assumptions relating to independent and identically distributed increments constrain where and when they can be reliably applied. A relatively novel model, the Spatial Markov model (SMM), relaxes the assumption of independence.

Reactive particle-tracking solutions to a benchmark problem on heavy metal cycling in lake sediments.

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.

Predicting the enhancement of mixing-driven reactions in nonuniform flows using measures of flow topology.

The ability for reactive constituents to mix is often the key limiting factor for the completion of reactions across a huge range of scales in a variety of media. In flowing systems, deformation and shear enhance mixing by bringing constituents into closer proximity, thus increasing reaction potential. Accurately quantifying this enhanced mixing is key to predicting reactions and typically is done by observing or simulating scalar transport.

Scalar dissipation rates in non-conservative transport systems.

This work considers how the inferred mixing state of diffusive and advective-diffusive systems will vary over time when the solute masses are not constant over time. We develop a number of tools that allow the scalar dissipation rate to be used as a mixing measure in these systems without calculating local concentration gradients. The behavior of dissipation rates is investigated for single and multi-component kinetic reactions and a commonly studied equilibrium reaction.

Using groundwater age distributions to estimate the effective parameters of Fickian and non-Fickian models of solute transport.

Groundwater age distributions are used to estimate the parameters of Fickian, and non-Fickian, effective models of solute transport. Based on the similarities between the transport and age equations, we develop a deconvolution based approach that describes transport between two monitoring wells. We show that the proposed method gives exact estimates of the travel time distribution between two wells when the domain is stationary and that the method still provides useful information on transport when the domain is non-stationary.

Non-Fickian dispersion of groundwater age.

We expand the governing equation of groundwater age to account for non-Fickian dispersive fluxes using continuous random walks. Groundwater age is included as an additional (fifth) dimension on which the volumetric mass density of water is distributed and we follow the classical random walk derivation now in five dimensions. The general solution of the random walk recovers the previous conventional model of age when the low order moments of the transition density functions remain finite at their limits and describes non-Fickian age distributions when the transition densities diverge.