Patterns and dynamics of river–aquifer exchange with variably-saturated flow using a fully-coupled model
Introduction
River–aquifer exchange is an important process in riparian systems (Sophocleous, 2002). The rate of exchange controls biogeochemical conditions in the hyporheic zone, groundwater recharge, moisture availability in the riparian zone and river flows during dry periods (O’Connor and Harvey, 2008, Fleckenstein et al., 2006, Niswonger, 2005). Exchange can be highly variable in time and space due to the temporal dynamics of river flows and geologic heterogeneity at the river–aquifer interface (Fleckenstein et al., 2006, Krause et al., 2007). Whereas in humid climates, with commonly high water tables, exchange between the river and aquifer (gains or losses) is predominantly by saturated flow, in arid and semi-arid regions the saturated connection can be lost due to large water table depths (Perterson and Wilson, 1988, Fleckenstein et al., 2006). In these systems, flow between the river and underlying aquifer becomes variably saturated. This condition is often referred to as hydraulically disconnected (e.g. Stephens, 1996), although the term is somewhat misleading as it implies a lack of feedback between the two systems (Fleckenstein et al., 2006).
In arid and semi-arid regions where deep groundwater levels are common, an understanding of river–aquifer exchange is crucial to answer questions of ecologic conservation and water management (Fleckenstein et al., 2006, Niswonger, 2005, Sophocleous, 2002). In highly heterogeneous aquifers, where percolation is inhibited by layers or lenses of low-permeability sediments, perched saturated zones can form between the river and the deep water table. These perched zones can significantly reduce seepage rates from the river into the subsurface and even generate baseflow where the river is gaining water from an underlying perched layer (Niswonger and Fogg, 2008). Patterns of alluvial heterogeneity can determine water availability for phreatophytes in the riparian zone (Niswonger, 2005). Preferential flow paths in areas of high permeability, on the other hand, can be responsible for immense seepage losses over relatively short river reaches (Fleckenstein et al., 2006).
The importance of heterogeneities at the groundwater–surface water interface on river–aquifer exchange has been highlighted by several recent studies (Nyquist et al., 2008, Krause et al., 2007, Fleckenstein et al., 2006, Conant, 2004). Nyquist et al. (2008) used electric resistivity measurements to resolve heterogeneity induced patterns of groundwater re- and discharge at the meter-scale. They could correlate consistent groundwater seeps (during high and low flows) with geologic subsurface structure. Krause et al. (2007) observed losing and gaining conditions occurring simultaneously at a river reach. Intensive spatial variability of exchange fluxes at the groundwater–surface water interface was attributed to geomorphic and geologic heterogeneities (Krause et al., 2007). Fleckenstein et al. (2006) demonstrated the importance of aquifer heterogeneity on river–aquifer exchange in an alluvial aquifer system with a deep water table that was characterized by variably saturated flow. Conant (2004) used an empirical method based on streambed temperature to determine small-scale groundwater–surface water interactions. All those studies indicate that patterns of river–aquifer exchange at smaller scales (reach and riverbed) are more complex than previously assumed.
Traditionally the focus of studies including river–aquifer interactions was on a regional or watershed-scale (Nobi and DasGupta, 1997, Perkins and Sophocleous, 1999, Pucci and Pope, 1995). The representation of the river–aquifer interface in numerical models was crude and hydraulic parameters were often assumed to be homogenous over larger river reaches. For questions concerning regional water balances, e.g. for large-scale water management (e.g. Rodríguez et al., 2006), this approach is still commonly used. Models of river–aquifer interactions to support environmental management, however, need to account for the smaller scale patterns and dynamics of river–aquifer exchange (Dahl et al., 2007) and require a different modeling approach.
With advances in computational capabilities, new integrated models have emerged that are able to simulate the hydrologic cycle as a quasi-continuum (Jones et al., 2008, Kollet and Maxwell, 2006, Panday and Huyakorn, 2004). Complex physically-based models have been applied to problems of river–aquifer interactions at scales ranging from the watershed-scale (Werner et al., 2006, Qu and Duffy, 2007, Heppner and Loague, 2008, Li et al., 2008, Jones et al., 2008, Kollet and Maxwell, 2008) and river-scale (Scibek et al., 2007, Fleckenstein et al., 2006) over the reach-scale (Niswonger, 2005, Lautz and Siegel, 2006, Brookfield et al., 2009) to the scale of individual riffles in the channel (Storey et al., 2003, Cardenas and Wilson, 2006). Several studies have specifically addressed effects of geologic heterogeneities at the river–aquifer interface. Kalbus et al. (2008) related aquifer heterogeneity to variations in groundwater discharge to a stream based on measurements of streambed temperature and simulated streambed temperatures for different geostatistical models of aquifer heterogeneity. Maxwell and Kollet (2008) demonstrated the effects of three-dimensional subsurface heterogeneity on runoff generation. Niswonger (2005) used a numerical model in combination with a geostatistical representation of alluvial aquifer heterogeneity on a 100 m reach of the Cosumnes River in California to investigate the impact of river–aquifer interactions on riparian vegetation. He could show good spatial correlations between simulated perched saturated zones and the distribution of riparian phreatophytes. A similar approach was used by Fleckenstein et al. (2006), who simulated river–aquifer exchange for a set of different heterogeneity models for the lower Cosumnes River basin aquifer over more than 50 river-kilometers to asses how textural heterogeneity influences seepage patterns and river low flows. Because of the relatively large scale of their model domain they had to upscale aquifer parameters from the geostatistical heterogeneity model (see also Fleckenstein and Fogg, 2008) and chose a simplified representation of unsaturated flow between the river and the deep water table to keep computational costs at a reasonable level (Fleckenstein et al., 2006). Bruen and Osman (2004) explicitly modeled unsaturated flow using Richard’s equation, but their study was limited to two-dimensions. This demonstrates that modeling groundwater–surface water interactions under highly heterogeneous conditions, considering variably saturated flow and exchange processes from the reach to the river or basin-scale, remains a computational challenge. However, studies that integrate local river–aquifer exchange processes over longer river reaches are needed e.g. to assess effects of hyporheic nutrient attenuation on river water quality, groundwater recharge from rivers with deep water table or environmental flows in intermittent or ephemeral rivers.
In this study, an approach is presented that investigates the effects of structural heterogeneity in aquifer properties on river–aquifer interactions in a 5 km long hypothetical river reach. It is based on the alluvial aquifer model for the Cosumnes River by Fleckenstein et al. (2006). The Cosumnes River is one of the last free-flowing rivers in California with significant stretches of riparian ecosystems in its lower reaches, which are threatened by abstraction of groundwater (Fleckenstein et al., 2004). It represents a typical alluvial-fan river–aquifer system with a deep water table as it is commonly found in semiarid and arid regions. Due to groundwater overuse and climate change such systems may also become more common in other regions. The study uses geostatistical techniques to resolve geologic heterogeneity at different scales; at the hydrofacies scale (∼100–2000 m) and at a finer sub-hydrofacies scale (∼10–50 m). Hydrofacies are defined as lithologic units that were formed under a specific depositional environment (e.g. in a channel of an alluvial system) and are characterized by a distinctive hydraulic conductivity range (see also Fleckenstein et al., 2006 or Ouellon et al., 2008). The fully integrated, parallel surface–subsurface flow code PARFLOW is used to numerically simulate river–aquifer exchange under variably-saturated flow conditions. Exchange is simulated for more than 100 realizations of aquifer heterogeneity to assess the impacts of sub-hydrofacies scale heterogeneity using a Monte Carlo approach. The aim of this study is to obtain new insights into the patterns and dynamics of exchange in such systems. Results can provide a basis for new management strategies for such river systems that are affected by growing groundwater withdrawals and by loss of riparian ecosystems. In particular the following two questions are addressed: (1) does geologic heterogeneity at the scale of alluvial hydrofacies affect the spatial patterns and volumes of exchange between the river and the aquifer? (2) how important are geologic heterogeneities on the sub-hydrofacies scale for patterns and volumes of exchange (assuming a typical variability of hydraulic conductivity within a hydrofacies)?
Section snippets
Methods
To address the objectives of this study a combination of geostatistical simulation techniques and integrated surface–subsurface numerical flow modeling are used. Representation of geologic heterogeneity is realized by a geostatistical model that generates heterogeneity on two different scales, the hydrofacies scale (∼100–2000 m) and the sub-hydrofacies scale (∼10–50 m). The uncertainty resulting from the inherently incomplete knowledge of texture variations within hydrofacies is addressed by a
Definitions
Before presenting the results, a number of terms need to be defined, which will be used to describe and quantify the spatial and temporal exchange behavior of the river–aquifer system:
The local seepage Sx (m3) quantifies the local seepage exchange between the river and the subsurface. It is defined as:where st,x (m3) indicates the seepage exchange for a single stress period t (d) at river cell x, and is equivalent to the amount of water a single river cell exchanges with the
Discussion and conclusions
This study combines geostatistical simulations to represent complex aquifer structure at a hydrofacies and sub-hydrofacies-scale with parallel computing for transient, coupled surface and variably-saturated subsurface flow to simulate patterns and dynamics of river–aquifer exchange in a typical alluvial system with a deep water table. This approach goes beyond previous modeling studies of such systems, which either used a two-dimensional representation of the system (Bruen and Osman, 2004) or
Acknowledgements
Part of this work was conducted during the first author’s visit to Lawrence Livermore National Laboratory (LLNL) in 2006. The help and assistance from staff at LLNL and the financial support from the Department of Hydrology at the University of Bayreuth is greatly appreciated.
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