On the exploration of river transport modeling based on the hyporheic zone exchange by means of residence times
Creators: name: Aghababaei, Mohammad
Publisher: name: Washington State University
Year: 2024
Subjects: subject: Mathematical/Numerical Modeling
subject: Memory function
subject: River Mixing
subject: Solute Transport
subject: Temporal moments analysis
subject: Tracer Tests Data Analysis
subject: Environmental Engineering
subject: FOS: Environmental engineering

description: River corridors are crucial in the fate and transport of various substances, such as nutrients, contaminants, and weathering products. Water quality management depends on practical and useful tools to simulate solute transport in river corridors. However, predicting solute transport in streams is one of the most difficult challenges in surface water quality modeling, especially when supporting tracer test data are no available for these streams. Practical simulation of solute transport in river corridors often relies on one-dimensional transport models with solute flux between the river channel and the hyporheic zone governed by a mass exchange term, most generally expressed using the ‘memory function’ formalism, a focal point of this dissertation. For practical one-dimensional modeling of solute transport in river corridors, this information is the state-of-the-art and includes the vast majority of alternative model descriptions mathematically. Despite the generality of the memory-function form, at least two questions remain that limit our understanding of their utility.
description: First, it is unknown whether or not these models can capture the full range of river corridor transport behavior as reflected in river tracer tests. Tracer tests involve injection of a dye or other tracer at an upstream location and monitoring of tracer concentrations with time (a “breakthrough curves”, BTC) at some downstream location. The BTC gives the distribution of tracer times to the downstream location. A longstanding puzzle is weather or not the memory-function class of models can simulate all important aspects of the travel time distributions.
description: Here I solve this puzzle by finding the mathematical links between the shape of the memory function and the shape of the BTC, in terms of the statistical (temporal) moments of the travel-time distribution. I use these results to investigate the general capability of the memory function form to accommodate specific scaling of river tracer temporal moments reported in the literature, and I apply the method to identification of model parameters in application to two recent tracer tests. The applications involve a simple numerical solution to the memory function river corridor transport model calibrated using measured temporal moments of the tracer test BTCs. The numerical model is validated only for the classical case of the “Transient Storage Model” (to be defined) without lateral inflow, the analytical solution for which I adapt from an existing solution for mobile-immobile exchange in porous media. It should be noted that the temporal moments results obtained here in the context of river corridor transport also apply to one-dimensional transport in two-domain (mobile-immobile) porous media, when governed by a two-domain memory function model.
description: Second, to date, solutes entering the river channel from the hyporheic zone are always so far assumed to be instantaneously mixed across the river channel, and the impact of this assumption remains untested. The memory function-based models and those they encapsulate generally assume that when solute returns to the river from the hyporheic zone, that solute is instantaneously mixed laterally within the river. However, it is well-known that complete lateral mixing in a river takes time, giving rise to the concepts of pre-asymptotic dispersion and the “mixing length” of transport distance necessary for asymptotic dispersion conditions. Here I build on the notion that solute mass entering the river from the hyporheic zone is in fact not instantly mixed laterally in the river channel, and that this delay affects the rate at which such mass can re-enter the hyporheic zone. I assume that this delay is akin to, and occurs on the same time scale as, the transition to Taylor’s asymptotic dispersion, and thus I use established models of this transition to adjust the rate coefficient for mass returning to the hyporheic zone after escaping that zone to join the river. To develop such a model, I considered three domains: river channel, hyporheic zone, and a boundary layer between them. Since generally more biogeochemical reactivity and microbial biomass occurs in the boundary layer between the main river flow and hyporheic zone, it is useful to consider the boundary layer in the mathematical modeling of solute transport in rivers. I first developed the new three-domain model (called River-PhEDEx) and then solved the developed model numerically and test the capability of the model in simulation of the solute transport process for a real case of the Sturt River dataset.