On the timescales characterizing groundwater discharge at springs
Introduction
In many hydrogeological environments, management decisions involving groundwater resources must be based on data with limited spatial distribution. For example, in some regions, ground-water emerging at springs provides the only available means for obtaining information about the regional scale subsurface hydrology. Therefore, although the spatial distribution of aquifer data such as hydraulic conductivity and head might be unavailable, temporal variations in properties of the springs such as temperature (Bundschuh, 1993) or discharge (Mangin, 1984, Leonardi et al., 1996, Angelini, 1997) can be used to characterize the groundwater system as a whole.
Here I use a number of simplified models and time series analysis to obtain characteristic timescales representing hydraulic and transport processes. The models employed are often termed “gray-box”, integral balance, or lumped parameter models because physical properties are spatial averages, and the detailed spatial variability of hydrogeologic variables is ignored. Gelhar (1993), however, noted that “lumped-parameter models are often consistent with the kind of limited data that is available for analyzing such problems”. Fortunately, in many cases, details necessary to predict phenomena at local scales are not necessary to understand the regional flow (Duffy and Lee, 1992).
As examples, I consider large springs in the Oregon and California Cascades. Despite the large size of the recharge areas (hundreds of square kilometers), few (and in some cases no) wells exist in the recharge areas (Caldwell and Truini, 1997). Thus, inferences about the groundwater hydrogeology must be based primarily on measurements at the springs. Although these springs are remote, they provide water for hydroelectric plants and irrigation, spawning grounds for salmon and trout, and habitat for threatened and endangered aquatic species. As usual, one of the goals for the hydrogeologist is to describe quantitatively the properties that characterize the springs and associated aquifers in a manner that might be useful in resource management decisions. For the examples I studied, three timescales characterize the water discharged at the springs, and are related to (1) the time of peak discharge at the spring; (2) the long term response of the spring to temporal changes in recharge; and (3) the mean residence time of water in the aquifer. Because these timescales are related to physical properties, the timescales can also be used to infer properties of the aquifers such as their transmissivities.
Section snippets
Geological and hydrological setting
I consider a set of eight large springs in the Oregon and California Cascades (see Fig. 1) that discharge groundwater from basalt and basaltic andesite aquifers (Sherrod, 1991, Rose et al., 1996): the Deschutes River, Quinn River, Cultus River, Browns Creek and Fall River in central Oregon, and the Rising River, Big Springs and Crystal Lake Springs along Hat Creek in northern California. Precipitation in the Cascades occurs primarily during the winter months as snow, and groundwater recharge is
Hydraulic timescale, Th
In this section, I consider models that can be used to infer a hydraulic timescale, Th, over which changes in input to the system (recharge) are reflected in changes in output (discharge). Th characterizes, for example, long term changes in discharge related to droughts. Here I first follow the approach used by Manga (1997), because it was found to be the most straightforward technique for determining Th for the springs in the Cascades.
The evolution of a water table in an unconfined aquifer,
Frequency–domain analysis
Gelhar and Wilson (1974) show that the water balance for an unconfined aquifer can be simplified to a linear relationship between the average water level and the rate of discharge if the change in water level is small compared to the total thickness of the aquifer. For this so-called linear reservoir model, the relationship between the spectral density of discharge, Sout, and that of recharge, Sin, iswhere ω is the frequency. Definitions of spectra are given by Duffy and Gelhar
A second hydraulic timescale: the time lag, Tlag
Previous studies of the springs in the Oregon Cascades have noted that peak discharge occurs in summer and sometimes in fall even though peak snowmelt occurs during the springtime (Whiting and Stamm, 1995, Manga, 1996). In Fig. 7, the hydrographs for the Quinn River and runoff-dominated Deer Creek for water year 1990 (October 1–September 30) are shown. The gauging stations are located only a few hundred meters apart and differ in elevation by 24 m. Peak discharge at the spring (Quinn River), at
Groundwater age, Tage
The mean age Tage (also called mean transit time or turnover time) is related to the volume of mobile water in the aquifer and the volume added per unit time,where is the mean recharge rate, the mean aquifer thickness, and φ the effective porosity. While both Tage and Th depend on geometrical properties of the aquifer, such as its mean thickness, Tage does not depend on hydraulic properties such as hydraulic conductivity, K.
An estimate of the reasonable range of possible ages
Discussion and concluding remarks
The timescales that describe discharge variations at the springs represent aquifer behaviour over large scales and long times. For the aquifers and springs studied here, the only data available are interpolated climate data (Daly et al., 1994), temperature measurements (Manga, 1998), gauging measurements of spring discharge, and, in a few cases, concentrations of nonpoint source environmental tracers. The application of lumped-parameter models and the use of time series analysis, indicate that
Acknowledgements
The author thanks E.R. James, M.O. Saar, T.P. Rose and an anonymous reviewer for thoughtful comments and helpful suggestions. B. Hudson, T.P. Rose and M.L. Davisson are thanked for providing the 3H and 3He data. This work was supported by the National Science Foundation, grant EAR9701768.
References (51)
Modeling annual variations of spring and groundwater temperatures associated with shallow aquifer systems
J. Hydrol.
(1993)Analyse statistique des hydrogrammes de décrue des sources karstiques
J. Hydrol.
(1972)- et al.
The hydrogeology of Kilauea volcano
Geothermics
(1993) - et al.
Modelling of a fractured basaltic aquifer with respect to geological setting, and climatic and hydraulic conditions: the case of perched basalts at Garni (Armenia)
J. Hydrol.
(1996) - et al.
Determining the turnover time of groundwater systems with the aid of environmental tracers 1: models and their applicability
J. Hydrol.
(1982) Pour une meilleure connaissance des systèmes hydrologiques à partir des analyses corrélatoire et spectrale
J. Hydrol.
(1984)- et al.
Study of hydrographs of karstic aquifers by mean of correlation and cross-spectral analysis
J. Hydrol.
(1995) - et al.
Isotope hydrology of voluminous cold springs in fractured rock from an active volcanic region, northeastern California
J. Hydrol.
(1996) - et al.
The hydrology and form of spring-dominated channels
Geomorphology
(1995) Correlation and spectral analysis of two hydrogeological systems in central Italy
Hydrol. Sci. J.
(1997)
The problem of modeling limestone springs: the case of Bagnara (North Apennines, Italy)
Groundwater
Flow in Porous Media
One-dimensional springflow model for time variant recharge
Hydrol. Sci. J.
Heat flow, arc volcanism, and subduction in northern Oregon
J. Geophys. Res.
Karst springs hydrographs as indicators of karst aquifers
Hydrol. Sci. J.
Thermal and tectonic implications of heat flow in the Eastern Snake River Plain, Idaho
J. Geophys. Res.
Basin-scale geohydrologic drought flow features of riparian aquifers in the southern Great Plains
Water Resour. Res.
Regionalized drought flow hydrographs from a mature glaciated plateau
Water Resour. Res.
A statistical-topographic model for mapping climatological precipitation over mountainous terrain
J. Appl. Meteorol.
Physical and Chemical Hydrogeology
A frequency domain approach to water quality modeling in groundwater: theory
Water Resour. Res.
A frequency domain analysis of groundwater quality fluctuations: Interpretation of field data
Water Resour. Res.
Base flow response from nonpoint source contamination: simulated spatial variability in source, structure, and initial condition
Water Resour. Res.
The possible use of tritium for estimating groundwater storage
Tellus
Cited by (98)
Response of spring yield dynamics to climate change across altitude gradient and varied hydrogeological conditions
2024, Science of the Total EnvironmentFault-controlled springs: A review
2022, Earth-Science ReviewsCitation Excerpt :Quantifying spring discharge, particularly its temporal variations, provides valuable information on both ecological requirements and changes to driving factors that control spring flow. For example, spring discharge rates have been used to estimate groundwater recharge (e.g., Segadelli et al., 2021), the baseflow contribution of springs to streams (e.g., Fournier et al., 1976; Fournier, 1989; Friedman and Norton, 2007), geothermal heat flux (e.g., Fournier et al., 1976; Mariner et al., 1990), and lag times between recharge and changes in spring discharge (e.g., Manga, 1999; Celico et al., 2006). Additionally, knowledge of spring discharge rates provide insight into aquifer characteristics (e.g., permeabilities, vertical fluxes), which are useful for constraining hydrogeological models (e.g., Manga, 1997; Saar and Manga, 2004; Martínez-Santos et al., 2014).
Geological permeability controls streamflow generation in a remote, ungauged, semi-arid drainage system
2021, Journal of Hydrology: Regional StudiesCitation Excerpt :Diffuse groundwater discharge to streams is seasonally variable in response to water table fluctuations, and the zone of groundwater discharge can expand and contract spatially during wetting and drying cycles (Gutiérrez-Jurado et al., 2019; Zimmer and McGlynn, 2017). Groundwater discharge from springs is characteristically driven by regional-scale hydraulic gradients (over tens or hundreds of kilometers) with water fluxes relatively consistent on seasonal and annual timescales (Manga, 1999). These multi-scale groundwater discharge processes combine with rainfall runoff and bank storage to drive streamflow generation within semi-arid watersheds (Shanafield et al., 2021).
Decadal scale recharge-discharge time lags from aquifer freshwater-saltwater interactions
2020, Journal of HydrologyManagement and research strategies of karst aquifers in Greece: Literature overview and exemplification based on hydrodynamic modelling and vulnerability assessment of a strategic karst aquifer
2018, Science of the Total EnvironmentCitation Excerpt :However, discharge of karst springs is strongly dependent on rainfall events and/or diffuse river recharge (ex. Manga, 1999). According to future climate projections, a large decrease in precipitation is predicted in the Mediterranean region and this may cause a reduction in the quality and quantity of karst water resources (Christensen et al., 2007).
Water temperature fluctuation patterns in surface waters of the Tatra Mts., Poland
2018, Journal of Hydrology