Water exchanges through the streambed are mainly induced by variations in stream morphology, hydraulic permeability, and hydrological conditions and span a broad range of spatial scales (Figure 1.3) [127, 192, 184, 20]. The spatial variability of the hyporheic zone reflects on hyporheic residence times (i.e., the amount of time that a particle of river water spends within the hyporheic sediments, in contact with the groundwater environment, before re-emerging into the river), which range from seconds to tens of years and impact the hyporheic biogeochemical patterns [20, 116]. Bed topography basically defines the spatial scale of the hyporheic pathways (Figure 1.7). Small streambed geomorphologic features, such as ripples and dunes, give rise to short flow paths that reach shallow depths (centimeters or decimeters) with short residence times (e.g., from minutes to hours) [63, 149, 21], whereas longer flow paths infiltrating up to several tens, hundreds, or even thousands of meters [157]
are driven by larger geomorphological features, like pool-riffle pairs, step-pool sequences, or meander bends, with longer residence times (from some days up to years) [116, 20]. Laterally, hyporheic mixing can be limited in small rivers confined by hillslopes or may extend deeply into the riparian zone (i.e., the horizontal extension can vary from hundreds of meters to more than a kilometer, [179]), including the wider floodplain and enhancing the formation of a vast habitat suitable for many microbial communities [180, 210, 178].
Flow interactions between streams and riverbed are responsible for solute transport within the sediments and play an important role in the ecology of the river environment. Reactive processes (e.g. chemical reactions or microbial growth) in the fluvial sediments depend on water flow and solute transport within the porous medium and are, thus, controlled by hydraulic properties of the granular material and presence of dissolved reactants or nutrients [41, 191].
These properties are in turn affected by solute transport and reactive processes and may change over time but, for the sake of simplicity, they are usually assumed as constant in describing and analyzing the interactions among rivers and aquifers. Different causes can induce a temporal variability, including
Fig. 1.7 Hyporheic flow patterns induced by different morphological features, i.e., ripples, dunes, bars, and meanders, and associated with different scales of stream topography. Complex interactions between these features and larger groundwater discharge/recharge pathways exist. From Stonedahl [184].
physical (e.g., particle deposition), chemical (e.g., dissolution or precipitation), microbial (e.g., production of gas by microorganisms or production of biomass), and thermal factors, influencing, for example, reaction rates.
Hyporheic exchanges have been studied and quantified adopting three main methods: physically-based models, stream transport models based on stream tracer tests, and field measurements. The first hydrodynamic model of hyporheic flow (APM, Advective Pumping Model) was proposed and experimentally validated by Elliott and Brooks [63, 62] although the river-sediment exchange induced by pressure variations was previously observed and discussed by Savant et al. [167]. The APM analyzes the exchange due to advective porewater flow (pumping) separately from the exchange resulting from trapping and release of porewater during bedform migration (turnover). The model assumes a sinusoidal head distribution at the bed surface that results from the interaction of the flow field with two-dimensional idealized bedforms (dune or ripple) and drives water through the sediments (see Figure 1.8). The shape of the head distribution used in the model was observed in experimental studies [65].
Starting from a Darcy groundwater flow model and an empirical formulation of the bedform-induced hydraulic head at the streambed interface, Elliott and Brooks derived an implicit analytical description of flow field and residence time distribution into a homogeneous porous bed induced by idealized bedforms.
The approach proposed by Elliott and Brooks [63, 62] considers only one scale of topography, ignoring the fractal natural of topography that leads to complex interactions between a wide range of scales. Many other available process-based models also focus on only one scale of topography, e.g., they either incorporate large-scale features such as meanders and bars while ignoring the finer details [19, 132], or they consider only small features like dunes and ripples [187, 37]. This limitation was overcome with the introduction of a physically based multiscale model proposed by Stonedahl et al. [184]. The two-dimensional bedform-induced pumping model for dunes and ripples was extended to three dimensions, integrating pore water flow field due to single-bedform with exchange induced by larger-scale topography such as bars and meanders through a spectral scaling approach [213]. This analysis showed that all scales of topographic features contribute to interfacial flux and residence time distributions, but that ripple and dune scales tend to both contribute more than and interact nonlinearly with meanders [184].
Fig. 1.8 Schematic representation of (top) sinusoidal head distribution adopted in the Advective Pumping Model for hyporheic flow below a stream bedform and (bottom) streamlines deriving from the flow field solution. From Elliott and Brooks [63].
The most widely used experimental approach for quantifying hyporheic exchange and characterizing transport properties is a stream tracer injection experiment combined with modeling of breakthrough curves [212, 205]. In a typical stream tracer study, a nonreactive solute tracer (e.g., chloride or bromide) is injected into the stream at a constant rate, and solute concentrations are monitored and sampled over time at downstream sampling stations [114].
The tracer-experiment data are then analyzed to estimate parameters not directly measurable and required in stream transport models for predictive purposes. These models, referred as phenomenological model, distinguish from the physically-based models because they do not focus on the physical principles governing the exchange flow and the water storage. Differently, these models aim to integrate at the reach scale the complex physical transport processes occurring at fine scales by calibrating the model to the results of a conservative solute tracer experiment conducted in the reach of interest [20]. Therefore, existing hyporheic models can be distinguished in physically based models and phenomenological models depending on the adopted approach and the provided information [20].
Since tracer experiment results are very sensitive to the experimental setup, as argued by Harvey and Wagner [96], the model parameters and the results achieved from the tracer tests for a particular system cannot be extended to another one with different characteristics. The history of in-stream tracer concentrations combined with solute transport simulations allows to quantify the physical parameters that characterize solute advection (which describes the rate at which the tracer moves downstream), longitudinal dispersion (which accounts for in-stream longitudinal mixing that cause the spreading of the peak solute concentration), lateral inflow of groundwater (which increases the rate of flow and dilutes the tracer), and storage zone exchange (which considers the transfer of solute between the active channel and dead or slowly moving zones in the stream or in the subsurface). The Transient Storage Model (TSM) proposed by Bencala and Walters [18] is the most commonly used model to analyze tracer data and to study hyporheic exchange, allowing to extract hyporheic residence times from breakthrough curves. Tracer concentrations are estimated using a differential equation that takes into account the variations associated with advection, dispersion, groundwater influx, and one or more storage zones, while hyporheic residence times are calculated from subsurface tracer data by
monitoring the arrival time of the tracer at wells [200] or with surface water sampling [100, 205].
Conventional field methods for identifying zones of upwelling and down-welling and quantifying hyporheic exchange include direct measurements of hydraulic head gradients or hydraulic flux near the streambed interface from seepage meters and piezometers [59, 2, 164]. In situ measurements are very useful to characterize the site of interest and/or to calibrate two or three-dimensional numerical groundwater flow models. However, they are represen-tative of very local conditions and realizing a number of point measurements suitable to represent the spatial variability of the topographical, hydraulic and physical characteristics of the sediments is extremely difficult or impossible and an upscaling is therefore necessary. Recently, a growing number of thermal applications dealt with innovative methodologies consisting in the measurement of temperature time series within the river or riverbed [101, 118, 102]. These techniques are advantageous since temperature sensors are easier to install in comparison to piezometers, as well as being cheaper.