Sinuosity-driven hyporheic exchange in meandering rivers



[1] A model for the evaluation of the intra-meander hyporheic exchange fluxes is presented. The method relies on a physically-based morphodynamic model to predict the characteristics of the flow field in a meandering river and the temporal evolution of its planimetry. The hyporheic fluxes induced at the meander scale by the river sinuosity can therefore be computed. The application of the model to a simulated case has shown the fundamental role of the river planimetry on the hyporheic exchange pattern at the meander scale, and its influence on the long-term evolution of the hyporheic exchange.

1. Introduction

[2] Rivers and aquifers do not exist as separate entities, and their interaction gives rise to an exchange of water and solutes. These fluxes lead to the creation of an interface region, namely the hyporheic zone, whose hydrodynamical, physiochemical and biotic characteristics are different from both the river and the subsurface environments [Brunke and Gonser, 1997]. The effects of these exchange processes on both the river and the subterranean environments are manifold. First, the hyporheic zone acts as a storage zone, which temporarily traps stream-transported solutes and then releases them after some time. This behavior has been shown to influence the stream transport of nutrients and pollutants [e.g., Nordin and Troutman, 1980; Bencala and Walters, 1983; Wörman et al., 2002]. Secondly, the metabolic activity of the hyporheic microorganisms significantly alters the in-stream concentration of chemicals, both at the reach scale [Findlay et al., 1993] and at the basin scale [Harvey and Fuller, 1998]. The survival and growth of the hyporheic microfauna in turn relies on a constant supply of dissolved oxygen and nutrients from the stream and the aquifer [Jones and Mulholland, 2000]. The hyporheic exchange is also important for riparian vegetation, as the oxygen flux from the stream regulates the redox conditions in the aquifer and therefore the dynamics of nutrients and trace metals [Brunke and Gonser, 1997].

[3] Due to this increasing awareness of the environmental importance of hyporheic exchange, many researchers have analyzed the hydrological processes that control the exchange of water and solutes between the surface and subsurface water. It is now understood that these fluxes are caused by the interaction between the stream and a number of geomorphological features, including bedforms [Elliott and Brooks, 1997; Packman and Brooks, 2001; Marion et al., 2002; Boano et al., 2006], channel bends [Cardenas et al., 2004], and land surface topography [Worman et al., 2006]. Among these features, channel bends represent an important factor that regulates the overall shape of hyporheic flow paths [see, e.g., Wroblicky et al., 1998].

[4] To date, most field studies on hyporheic exchange have focused on gravel-bed, mountain streams in low-order catchments [Harvey and Bencala, 1993; Wondzell and Swanson, 1996; Haggerty et al., 2002; Kasahara and Wondzell, 2003; Storey et al., 2003]. In such streams the hyporheic exchange is governed by pool-riffle sequences and/or secondary channels, while the influence of channel bends is usually minor. On the other hand, the role of stream curvature is expected to be of paramount importance in higher order catchments, where meanders represent the prevailing river pattern [Lautz et al., 2006; Peterson and Sickbert, 2006; Lautz and Siegel, 2006]. In the present paper, a theoretical analysis of the hyporheic exchange induced by the sinuous shape of a meandering river has been presented. A physically-based model was adopted to simulate the flow conditions in a meandering river, and the consequent intra-meander hyporheic flux was evaluated. The model was applied to a simulated case, and the fundamental role of the river planimetry was clearly demonstrated. The described approach thus provides a useful tool for the prediction of the hyporheic exchange at the meander scale.

[5] The effects of temporal evolution of the meandering planimetry on the magnitude and pattern of the hyporheic flow were also studied. While previous studies focused on the variations of hyporheic exchange in response to seasonal discharge and precipitations fluctuations [Wroblicky et al., 1998; Storey et al., 2003] and to storm events [Wondzell and Swanson, 1996; Boano et al., 2006], the longer time scales that characterize changes in river morphology have prevented a detailed observation of the long-term behavior of the hyporheic zone. In order to overcome this difficulty, we simulated the temporal evolution of a river, and the resulting hyporheic exchange flow has been evaluated for different stages of the meander age. The results of the simulations demonstrate the crucial importance of the morphodynamic processes on the evolution of the hyporheic zone.

2. Methods

[6] The meandering evolution of a river is governed by the hydrodynamic action of the river, whose flow field in turn depends on the geometry of the streambed [Dietrich and Smith, 1983]. The estimation of the flow field is thus a critical step, and different models have been proposed for this purpose [e.g., Ikeda et al., 1981; Johannesson and Parker, 1989; Zolezzi and Seminara, 2001]. The Zolezzi and Seminara [2001] approach is the most complete in the linear context, and has been adopted in this paper.

[7] In the Zolezzi and Seminara [2001] model, a curvilinear reference system was adopted with the streamwise and the spanwise coordinates, s and n, respectively. The flow field was modeled through the 2D shallow water equations, coupled with the Exner equation for the mass conservation of the bed sediments. This system was solved using a perturbative method, and the depth-averaged velocity was obtained as a Fourier series, u(s, n) = equation imageum(s) sin Mn, where

display math

represents the mth Fourier mode, M = equation image (2m + 1)π, C(s) is the stream curvature, and gjpm and λmj are two coefficients that depend on the Shield stress, the relative roughness (i.e., the ratio between the mean diameter of the sediments and the water depth), and the aspect ratio (i.e., the ratio between the river half width and the water depth). The model also provided the solution for the local stream depth, which was used to evaluate the boundary conditions for the hyporheic flow model (see below).

[8] In order to predict the evolution of the river planimetry, the river was described as a planar curve, coinciding with its axis, that migrates as a consequence of the erosion and deposition processes. The displacement rate of each point of the curve was modeled as ζ = E · ub, where ζ is the normal-to-curve migration rate, E is the erodibility coefficient of the banks, and ub is the velocity excess at the external bank with respect to the section-averaged velocity. The erodibility coefficient, E, is a property of the soil material. The excess-bank velocity, ub, was obtained from equation (1), and the temporal evolution of the river planimetry was simulated (see Camporeale et al. [2005] for more details).

[9] The vertical components of the exchange flux at the meander scale can be neglected with respect to the horizontal ones, and a 2D Cartesian system {x, y} was thus adopted. The hyporheic exchange was modeled according to the Laplace equation [see Harvey and Bencala, 1993]. The part of the aquifer that is bound by the inner bank of the meander was considered (see Figure 1), and this domain was discretized with a finite element method. The boundary conditions for the hydraulic head along the river boundary correspond to the values of the free surface elevation at the river bank, which were evaluated using the aforementioned morphodynamic model. The other boundary was obtained by simply linking the two extreme points of the river reach, and it was assigned a linear variation of the head h as a boundary condition. The influence of this simplified boundary condition was verified to be limited to a small region near the corresponding boundary.

Figure 1.

River planimetries with equipotential lines (solid lines) and hyporheic flow paths (dashed lines) for different meander ages. The interval between two consecutive panels is approximately equal to a century. The intra-meander hyporheic flow is driven by the differences in the hydraulic head between the upstream and the downstream part of the stream. The hyporheic flux at the meander neck progressively increases due to the steepening of the hydraulic gradient.

[10] After the Laplace equation had been solved and the hydraulic head, h(x, y), had been obtained, the velocity field was evaluated through the Darcy equation, equation image = −K · ∇h, where K is the hydraulic conductivity. The exchange flux was then computed as

display math

where q(s) is the exchange flux between the stream and the hyporheic zone per unit river length, dB(s) is the river depth at the bank, equation image(s) is the Darcy velocity at the river-aquifer interface, and equation image denotes the normal vector entering the river boundary. A constant value for the hydraulic conductivity coefficient, K, was adopted in this analysis.

3. Results

[11] A numerical example was considered in order to analyze the hyporheic exchange fluxes that are induced by the river sinuosity. The morphodynamic model was applied to compute the flow field and the planimetric evolution of a river with a mean discharge Q = 23 m3/s, a mean bed slope S = 7 · 10−3, a mean depth d = 0.5 m, and a constant erodibility coefficient E = 3 · 10−8.

[12] The evolution of the meandering river was simulated, and four different planimetries were selected for the analysis of the hyporheic exchange fluxes, as shown in Figures 1a–1d. The time interval between two successive planimetries approximately corresponds to a century. The different stages of the planimetric evolution, from slightly meandering (Figure 1a) to close to cutoff (Figure 1d), were analyzed. The changes in the flow pattern in the hyporheic zone induced by the progressive increase in river sinuosity should be noticed. The most evident feature is the steep hydraulic gradient in correspondence of the ‘neck’ of the meander. This zone is formed by the erosion and deposition mechanisms, which gradually reduce the distance between river sections with very different water surface elevations. This situation determines the presence of a steep hydraulic gradient, which in turn results in a strong intra-meander flow. A comparison of the four panels shows that the intensity of this flow pattern increases as the meander shape evolves.

[13] The key influence of the river planimetry on the overall flow pattern can also be appreciated. When the sinuosity is relatively low, as in Figures 1a and 1b, water enters the hyporheic zone from the upstream part of the reach and basically flows in the x direction, which also corresponds to the average river direction. This picture of the flow paths is due to the almost symmetrical shape of the river, which leads to a slope of the groundwater head h(x, y) that is nearly constant in the x direction. As the sinuosity increases and the river shape becomes increasingly more skewed (Figures 1c–1d), the symmetry of the river reach is lost and considerable components of the hyporheic flux appear in the y direction. Therefore, the simulations show the fundamental role played by the river sinuosity in controlling the hyporheic exchange at the meander scale.

[14] The exchange flux between the river and the hyporheic zone was quantified by equation (2) for the four river planimetries. Since the river curvature determines a transversal superelevation of the water surface and thus a variation in the river depth, d(s, n), with respect to its section-averaged value, the corresponding contributions to the total exchange flux were considered. The total flux was therefore divided into its two components, q = qa + qs, where qa is the exchange flux due to the section-averaged river depth, and qs is the contribution to the flux due to the superelevation of the water surface induced by the stream curvature. The total exchange flux q and the contribution qs have been plotted in Figures 2a–2d against the normalized river coordinate, s* = s/smax. The values of the total hyporheic flux, q, were found to be comparable with those observed in many field studies [e.g., Harvey and Bencala, 1993; Wroblicky et al., 1998; Storey et al., 2003]. The significance of the sinuosity-induced fluxes for the hyporheic exchange at the meander scale has thus been confirmed.

Figure 2.

Total hyporheic exchange flux per unit length q (solid line), and superelevation-induced contribution qs (dashed line) for different meander ages. The values of the total flux are comparable with those found by Harvey and Bencala [1993] (up to 800 L/d/m), Wroblicky et al. [1998] (10–300 L/d/m), and Storey et al. [2003] (200–500 L/d/m). The evolution of the river planimetry results in an increase of the exchange flux of about an order of magnitude.

[15] The temporal evolution of the hyporheic exchange can be deduced from a comparison of the four panels in Figures 2a–2d. A progressive increment up to an order of magnitude in the total flux, q, can be observed in correspondence to the meander neck, at s* ≈ 0.1 and s* ≈ 0.9. This increasing trend of the hyporheic exchange can have significant ecological implications, e.g. on the stream transport of solutes and on the vegetation patterns. A meander cutoff eventually straightens the river course, and allows the migration process to restart. The exchange with the hyporheic zone thus evolves with a periodic cycle, with phases of constant growth that are occasionally interrupted by sudden decreases.

[16] Finally, the component of the exchange flux due to the transversal slope of the water surface, qs, have also been shown in Figures 2a–2d. The values of qs are one or two orders of magnitude lower than the total flux, q. The effects of the surface slope on the hyporheic exchange can therefore be neglected at the meander scale, and the simple adoption of the section-averaged value for the river depth is fully justified. However, the existence of hyporheic flow paths at smaller scales than the meander wavelength is suggested by the behavior of qs, which is much less regular than q, particularly for Figures 2c–2d. At this local scale, the lateral superelevation of the water surface induced by the stream curvature can contribute to the hyporheic exchange together with other factors that are important at the same scales, such as riffles and secondary channels [Kasahara and Wondzell, 2003].

4. Conclusions

[17] A theoretical analysis of the intra-meander flux induced by river sinuosity has been discussed in this work. The exchange between a river and the hyporheic zone at the meander scale has been evaluated with the use of a physically-based morphodynamic model. This model has provided a realistic estimate of the flow field and the river depth, and has also described the evolution of the river planimetry under the hydrodynamical forcing of the stream flow. The results have then been adopted to evaluate the hyporheic exchange fluxes at the meander scale.

[18] The study of a simulated example has shown that the fluxes induced by the river sinuosity are of the same order of magnitude as those observed in the field. The river planimetry has been shown to govern the pattern of intra-meander hyporheic flow paths. The transversal slope of the water surface has been shown to have marginal influence on the exchange with the hyporheic zone at the meander scale, while it could concur with other morphologic features to determine the hyporheic flow at smaller scales. The model has also demonstrated that the progressive elongation of the meander leads to the formation of a region of increased flux in correspondence to the meander neck. The exchange with the hyporheic zone thus increases with the growth of the meander length, and is eventually reduced by the decrease in river sinuosity induced by the occurrence of meander cutoffs.


[19] The authors would like to thank Regione Piemonte and the CRC Foundation (Fondazione Cassa di Risparmio di Cuneo) for their financial support to the present research.