Reply to comment by J.-P. Renaud et al. on “An assessment of the tracer-based approach to quantifying groundwater contributions to streamflow”

This is the published version. Copyright Wiley [Commercial Publisher

An assessment of the tracer-based approach to quantifying groundwater contributions to streamflow

This is the published version. Copyright American Geophysical Union[1] The use of conservative geochemical and isotopic tracers along with mass balance equations to determine the pre-event groundwater contributions to streamflow during a rainfall event is widely used for hydrograph separation; however, aspects related to the influence of surface and subsurface mixing processes on the estimates of the pre-event contribution remain poorly understood. Moreover, the lack of a precise definition of “pre-event” versus “event” contributions on the one hand and “old” versus “new” water components on the other hand has seemingly led to confusion within the hydrologic community about the role of Darcian-based groundwater flow during a storm event. In this work, a fully integrated surface and subsurface flow and solute transport model is used to analyze flow system dynamics during a storm event, concomitantly with advective-dispersive tracer transport, and to investigate the role of hydrodynamic mixing processes on the estimates of the pre-event component. A number of numerical experiments are presented, including an analysis of a controlled rainfall-runoff experiment, that compare the computed Darcian-based groundwater fluxes contributing to streamflow during a rainfall event with estimates of these contributions based on a tracer-based separation. It is shown that hydrodynamic mixing processes can dramatically influence estimates of the pre-event water contribution estimated by a tracer-based separation. Specifically, it is demonstrated that the actual amount of bulk flowing groundwater contributing to streamflow may be much smaller than the quantity indirectly estimated from a separation based on tracer mass balances, even if the mixing processes are weak

Hydrologic response of catchments to precipitation: Quantification of mechanical carriers and origins of water

This is the published version. Copyright American Geophysical Union[1] Precipitation-induced overland and groundwater flow and mixing processes are quantified to analyze the temporal (event and pre-event water) and spatial (groundwater discharge and overland runoff) origins of water entering a stream. Using a distributed-parameter control volume finite-element simulator that can simultaneously solve the fully coupled partial differential equations describing 2-D Manning and 3-D Darcian flow and advective-dispersive transport, mechanical flow (driven by hydraulic potential) and tracer-based hydrograph separation (driven by dispersive mixing as well as mechanical flow) are simulated in response to precipitation events in two cross sections oriented parallel and perpendicular to a stream. The results indicate that as precipitation becomes more intense, the subsurface mechanical flow contributions tend to become less significant relative to the total pre-event stream discharge. Hydrodynamic mixing can play an important role in enhancing pre-event tracer signals in the stream. This implies that temporally tagged chemical signals introduced into surface-subsurface flow systems from precipitation may not be strong enough to detect the changes in the subsurface flow system. It is concluded that diffusive/dispersive mixing, capillary fringe groundwater ridging, and macropore flow can influence the temporal sources of water in the stream, but any sole mechanism may not fully explain the strong pre-event water discharge. Further investigations of the influence of heterogeneity, residence time, geomorphology, and root zone processes are required to confirm the conclusions of this study

Use of groundwater lifetime expectancy for the performance assessment of a deep geologic waste repository: 1. Theory, illustrations, and implications

Long-term solutions for the disposal of toxic wastes usually involve isolation of the wastes in a deep subsurface geologic environment. In the case of spent nuclear fuel, if radionuclide leakage occurs from the engineered barrier, the geological medium represents the ultimate barrier that is relied upon to ensure safety. Consequently, an evaluation of radionuclide travel times from a repository to the biosphere is critically important in a performance assessment analysis. In this study, we develop a travel time framework based on the concept of groundwater lifetime expectancy as a safety indicator. Lifetime expectancy characterizes the time that radionuclides will spend in the subsurface after their release from the repository and prior to discharging into the biosphere. The probability density function of lifetime expectancy is computed throughout the host rock by solving the backward-in-time solute transport adjoint equation subject to a properly posed set of boundary conditions. It can then be used to define optimal repository locations. The risk associated with selected sites can be evaluated by simulating an appropriate contaminant release history. The utility of the method is illustrated by means of analytical and numerical examples, which focus on the effect of fracture networks on the uncertainty of evaluated lifetime expectancy.Comment: 11 pages, 8 figures; Water Resources Research, Vol. 44, 200

Use of groundwater lifetime expectancy for the performance assessment of a deep geologic radioactive waste repository:2. Application to a Canadian Shield environment

Cornaton et al. [2007] introduced the concept of lifetime expectancy as a performance measure of the safety of subsurface repositories, based upon the travel time for contaminants released at a certain point in the subsurface to reach the biosphere or compliance area. The methodologies are applied to a hypothetical but realistic Canadian Shield crystalline rock environment, which is considered to be one of the most geologically stable areas on Earth. In an approximately 10\times10\times1.5 km3 hypothetical study area, up to 1000 major and intermediate fracture zones are generated from surface lineament analyses and subsurface surveys. In the study area, mean and probability density of lifetime expectancy are analyzed with realistic geologic and hydrologic shield settings in order to demonstrate the applicability of the theory and the numerical model for optimally locating a deep subsurface repository for the safe storage of spent nuclear fuel. The results demonstrate that, in general, groundwater lifetime expectancy increases with depth and it is greatest inside major matrix blocks. Various sources and aspects of uncertainty are considered, specifically geometric and hydraulic parameters of permeable fracture zones. Sensitivity analyses indicate that the existence and location of permeable fracture zones and the relationship between fracture zone permeability and depth from ground surface are the most significant factors for lifetime expectancy distribution in such a crystalline rock environment. As a consequence, it is successfully demonstrated that the concept of lifetime expectancy can be applied to siting and performance assessment studies for deep geologic repositories in crystalline fractured rock settings.Comment: 14 pages, 14 figures; Water Resources Research, Vol. 44, 200

Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches

A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used to solve the Laplace-transformed diffusion equation, producing a time-domain solution after a numerical Laplace transform inversion. Motivated by the needs of numerical methods posed in Laplace-transformed space, we compare five inverse Laplace transform algorithms and discuss implementation techniques to minimize the number of Laplace-space function evaluations. We investigate the ability to calculate a sequence of time domain values using the fewest Laplace-space model evaluations. We find Fourier-series based inversion algorithms work for common time behaviors, are the most robust with respect to free parameters, and allow for straightforward image function evaluation re-use across at least a log cycle of time