Age-distribution estimation for karst groundwater: Issues of parameterization and complexity in inverse modeling by convolution

Abstract

This manuscript was handled by P. Baveye, Editor-in-ChiefKeywords: Groundwater Karst Parameter estimation Inverse modeling Groundwater age s u m m a r y Convolution modeling is useful for investigating the temporal distribution of groundwater age based on environmental tracers. The framework of a quasi-transient convolution model that is applicable to twodomain flow in karst aquifers is presented. The model was designed to provide an acceptable level of statistical confidence in parameter estimates when only chlorofluorocarbon (CFC) and tritium ( 3 H) data are available. We show how inverse modeling and uncertainty assessment can be used to constrain model parameterization to a level warranted by available data while allowing major aspects of the flow system to be examined. As an example, the model was applied to water from a pumped well open to the Madison aquifer in central USA with input functions of CFC-11, CFC-12, CFC-113, and 3 H, and was calibrated to several samples collected during a 16-year period. A bimodal age distribution was modeled to represent quick and slow flow less than 50 years old. The effects of pumping and hydraulic head on the relative volumetric fractions of these domains were found to be influential factors for transient flow. Quick flow and slow flow were estimated to be distributed mainly within the age ranges of 0-2 and 26-41 years, respectively. The fraction of long-term flow (>50 years) was estimated but was not dateable. The different tracers had different degrees of influence on parameter estimation and uncertainty assessments, where 3

Residence time distributions for hydrologic systems: Mechanistic foundations and steady-state analytical solutions

“…It is only applicable for a few cases, typically for homogeneous confined aquifers with possibly varying thickness (Etcheverry, 2001), aquitards where mass transfer with the surroundings compartments can be neglected (Bethke and Johnson, 2002;Castro et al, 1998), highly localized samplings close to the system inlet (Leray et al, 2012;Marçais et al, 2015), or fractured and karst systems (Bockgård et al, 2004;Burton et al, 2002;Knowles et al, 2010;Long and Putnam, 2006;Long and Putnam, 2009). …”

“…Systems presented in section 3 -and more generally, any system whose flow paths are analytically described -can be plugged together to generate composite RTDs. Examples of linear combinations include the exponential and dispersion models (Stolp et al, 2010), exponential and shape-free models (Goderniaux et al, 2013), two piston flow models (Eberts et al, 2012), exponential and piston-flow models (Eberts et al, 2012;Solomon et al, 2010), two exponential-piston-flow models (Green et al, 2014), and multiple dispersion models (Engdahl and Maxwell, 2014;Long and Putnam, 2009;McCallum et al, 2014).…”

Residence times of groundwater and nitrate transport in coastal aquifer systems: Daweijia area, northeastern China

“…Lumped parameter models (LPMs) have been effectively used for estimating groundwater MRT in many natural systems, particularly in karst aquifers (Mangin, 1994;Zuber et al, 2004;Olsthoorn, 2008;Long and Putnam, 2009). Although these models are simple and represent ideal systems, they require less data than more complex methods.…”

Physical and Chemical Controls on the Simultaneous Occurrence of Young and Old Groundwater Inferred From Multiple Age Tracers

“…Common tracer interpretation models include lumped parameter models (e.g., Amin & Campana, 1996;Maloszewski & Zuber, 1982, 1996Zuber, 1986) and direct age models (Ginn, 1999;Goode, 1996). In several studies the groundwater age distributions determined from these models have been employed to assist in the characterization of groundwater dynamics (e.g., Corcho Alvarado et al, 2007;Eberts et al, 2012;Gusyev et al, 2013;Long & Putnam, 2009;Solomon et al, 2010;Troldborg et al, 2007;Zuber et al, 2005).…”