Initial measurements and conceptualization
Streambed geomorphology exerts a strong control on the hyporheic exchange processes (Findlay
1995; Azizian et al.
2017) and spatial heterogeneities and local anomalies in sediment composition are thought to constrain the distributions in flow paths and residence times within the hyporheic zone (Mermillod-Blondin et al.
2015; Malenda et al.
2019). Here, a combination of geophysical and hydrological investigative methods was applied in a small boreal stream and the results emphasized the close connection between the spatial variability of local streambed structures, their hydraulic properties and the vertical extent of the hyporheic zone. The in-situ observations of the stream reach displayed several sections where hydraulic conductivity in the sediments would likely vary and thus strongly affect the hyporheic exchange properties. The modelled resistivity values can be related to observed physical characteristics of the streambed, which allows for the identification of heterogeneities in the subsurface by way of inverse-modelled resistivity sections. Rocks and stones are likely the cause of near-surface resistive anomalies at
x = 0.6, 1.6, 2.4, 3 and 4–6 m (Fig.
6), which will strongly affect the hyporheic flow paths and makes the common assumption of well-behaved Tothonian flow cells used in hyporheic studies questionable. Irregular flow patterns around small-scale (i.e. stones and cobbles) heterogeneities have previously been shown in laboratory flumes (Fox et al.
2016; Stonedahl et al.
2018) or in numerical studies (Sawyer et al.
2011; Hester et al.
2013), but have not, to the authors’ best knowledge, been identified for in-situ conditions in an active natural stream. As a direct consequence, the spatial variability in the occurrence of such structures will introduce uncertainty in estimates or models aiming to quantify surface-water/groundwater interaction, depending on the geometry and flow of the river or stream. Results indicate that observed rockier sections (Fig.
6, where
x is 4.4–4.8 m, and Fig.
9) directly led to the largest modelled tracer penetration, while these sections also likely were the most uncertain in the inverse modelled. While regional models might not be strongly impacted by this scale of heterogeneity, smaller models investigating chemical or ecological processes may be influenced. Structures which may have meaningful influence on these processes may be missed entirely with even a small (10 cm) increase in electrode spacing (Fig. S2 of the
ESM). Thus, in order to capture the spatial variability in the hyporheic flow field, particularly in postglacial regions with ubiquitous till coverage, a sufficiently high spatial resolution of the observations is needed, i.e. an electrode spacing and model resolution that reflects the scale of the governing processes and constraining factors that control the exchange fluxes.
The length of electrodes used in this study (10 cm) was equal to the electrode spacing which violates the assumption of electrodes as point sources. This violation was thought to be necessary in order to provide sufficient contact between the electrode and soil. Smaller, plate-formed electrodes could have been used but installing the electrodes may have disturbed the sediments more than the chosen method. Investigations of similar-scale tests (Clement and Moreau
2016) have shown that while the embedment, position and size of electrodes strongly influence measurements of apparent resistivity, these influences would be less than the order-of-magnitude differences in materials measured during the study. Additionally, no temperature correction was carried out during the inversion process. Thus, the changes in modelled resistivity during and after the tracer test are most likely more relevant to examine as opposed to the absolute accuracy of the resistivity models, the uncertainty of which is hard to ascertain given that no subsurface ground truth is available.
Different layers of streambed sediment were identifiable from the modelled section, which appeared to have had important influence over the results measured during the subsequent tracer injection. The differences in electrical resistivity and dielectric permittivity in the case of GPR, likely are indicative of different geological layers or anomalies. While they cannot be independently related to grain-sizes or soil types with certainty, the changes in modelled resistivity or reflections from a radargram can be linked with observations and conceptual models of the streambed. In particular, a geological layer with lower resistivity was likely present at around 0.2 m depth from
x range 0–2.5 m along the section (Figs.
5,
6 and
7), whereas this layer extended to depths corresponding to around 0.3–0.4 m below the streambed interface for the stream section between 2.4 and 4 m. Further downstream this layer was less apparent due to the presence of more resistive anomalies (likely rocks) in the streambed interface but appears to continue up to around 0.3 m towards the end of the section. This conceptual understanding of the layering and heterogeneity was further strengthened by the apparent penetration of the tracer into the streambed sediment, which was evident during the tracer injection (Fig.
5b). This relationship between apparent different layers observed in pretracer ERT measurements and apparent tracer penetration (Fig.
9) supports the hypothesis that geophysical characterisation can give important insight into the heterogeneity of the hyporheic zone, and that this heterogeneity plays an important role in exchange processes. As the local soils are comprised primarily of glacial till, heterogeneity in the hyporheic zone would likely be heightened as a result of the variability in the grain-size distribution compared to regions with more geologically well-sorted soils. While different geological settings would almost certainly give rise to different measurement results, the differences in in-situ electrical resistivity may quite often coincide with differences in hydraulic conductivity between media (Reynolds
2011). Longitudinal characterisation using ERT methods could prove invaluable in identifying areas of low and high variability in permeability in the subsurface, highlighting the fragmentation of flow paths in the hyporheic zone and also be greatly beneficial in numerical model refinements.
The GPR results generally correspond with the ERT measurements, as more signal scattering was detected from 4 to 6 m along the stream section, which is indicative of blockier sections due to differences in permittivity between the rocks and surrounding sediments. However, layers were interpreted from the GPR measurements which were not as evident in the ERT sections; nevertheless, the main zone of increased conductivity identified in the ERT section also corresponded with the silty layer (Fig.
9) observed in the GPR profile at depths between 0.1 and 0.3 m. This layer was found to have roughly the same depths along the profile, although the estimated depth in this case was based on the assigned velocity used during analysis. The combined geophysical methods gave a good indication of the structure and composition of the streambed sediment and were useful in delineating the hyporheic zone, something that has been shown previously, even when conductivity of the infiltrating water may not be vastly different, as in the case of coastal hyporheic zones, for example as seen in Bianchin et al. (
2011).
Time-lapse resistivity measurements
In addition to providing the spatial distribution of apparent penetration depths of the highly conductive tracer, the time-lapse modelling demonstrated that the tracer likely was influenced by preferential flow paths due to, for example, the presence of stones or sandy sediments, and that the arrival and exit of the tracer from the sediments occurred rapidly. The first ERT measurements taken after the tracer injection started (ERT 1, Fig.
4) were initiated immediately and took roughly 45 min to be completed; however, this measurement failed to capture the rising limb of the breakthrough curve which is indicative of quick solute transport paths within the stream sediments and the measurement was very similar to the other ERT measurements during the tracer test. Thus, the tracer appeared to infiltrate the hyporheic zone rather quickly, to depths up to 0.3–0.4 m, through highly conductive pathways in distinct sections of the stream reach, while other sections likely with lower hydraulic conductivity restricted the hyporheic flow and almost no influence was seen from the tracer within the streambed. It should be restated, however, that smoothing during the inverse modelling process will likely exaggerate the apparent penetration depths. Additionally, the assumed conductivity of the water layer was initially set to be representative of the pretracer test’s stream-water conductivity, which may further influence apparent tracer penetration. This apparent penetration of the tracer was largely similar to model results when a thin conductive layer was fixed in the upper portion of the model (Fig.
5d). The most notable difference in the models (Fig.
5c,d) was that the introduction of an assumed conductive layer appeared to elongate and flatten any conductivity anomalies, for example between x = 2.4 and 3.2 m (Fig.
5c,d). The areas with the greatest penetration interpreted from increases in conductivity showed little to no change in depth. However, in the model with the more conductive layer (Fig.
5d), some near-surface anomalies, which were assumed to be associated with rocks and stones, were no longer identifiable (x = 5–6 m) and which likely indicates a loss of near-surface resolution with this assumed conductive layer. A very rough estimate using the total measurement time and the apparent penetration depth yields a water velocity in the hyporheic zone on the scale of 10
–4 m/s. Assuming Darcian flow, with a hydraulic conductivity in the sediments of 10
–4 m/s and a porosity of 0.2, this would result in a specific discharge of 2 × 10
–5 m/s and a hydraulic gradient of 0.2, which would correspond with a 2-cm change in hydraulic head over a distance of 10 cm. Assuming a depth of 0.2 m and stream width of 0.3 m, this also compares with an average stream velocity of roughly 0.12 m/s. These estimates are to be used as a basis for discussion, as more precise estimates would require much higher temporally resolved ERT measurements where a time step of 45 min fails to adequately capture the introduction of tracer into the sediments, detailed modelling and/or more precise estimates or porosity. Similarity between time-lapse measurements however indicates that while this type of investigation may not be suitable for shedding light on the transient nature of tracer introduction into the hyporheic zone, they may be appropriate for characterising small-scale heterogeneities in the flow paths in the sediments.
The apparent resistivity of the subsurface during the tracer injection plateau period (ERT 1 to ERT 4, Fig.
4) was roughly stable with less than 10% variation seen between measurements (Fig.
6), but the results demonstrated that the tracer following termination of the injection was removed rapidly (ERT 5, Figs.
4,
5 and
6). Thus, the general interpretation is that the residence times in the measured stream section may generally be consistently short, although large variability was found in the streambed composition and distribution of flow paths. General calculations of bulk resistivity using Archie’s law and comparing modelled resistivity support the conclusion that tracer penetration occurs quite rapidly. Increases in resistivity seen in the time-lapse modelling (Fig.
6) are likely an artefact of the modelling process although such increases occasionally coincide with high-resistivity anomalies (Fig.
5); this is because, given the short time scale, the consistency of the stream water’s background conductivity, and the absence of any artificially introduced resistive material, it is unlikely that any decreases in conductivity occurred during the experiment. As the tracer would almost certainly decrease the resistivity drastically in the top layers, this sharp boundary might be difficult for the modelling software to accurately capture, and some erroneously modelled positive resistivity changes occur in the deeper sections. Moreover, increases in resistivity seen in the final measurement (Fig.
6f) correspond roughly to the locations of many of the anomalies from the initial measurement (Fig.
5a), which likely represents rocks. This could be a result of some residual tracer present in the hydraulic pathways, which could result in some variability arising in the modelling iterations.
The interpretation of the hyporheic flow paths based on the ERT measurements during the tracer test correspond generally in shape with generic modelled hyporheic flow paths (Ward et al.
2013b; Tonina et al.
2016). However, local heterogeneities were shown to heavily impact the distribution of flow paths, indicating that the streambed structure plays a vital role for hyporheic exchange processes such as the physical extent and also, although not assessed here, the residence time within the hyporheic zone. Thus, the penetration depth of the tracer varied greatly along the stream reach. Sections which showed less variability in modelled resistivity values such as 0–2 m along the measured reach, were also found to have more shallow tracer penetration depths, predominantly around 0.2 m into the streambed (Figs.
4b and
5a). However, sections that showed higher levels of spatial variability in the modelled resistivity values also corresponded with the greatest penetration depths of the tracer. This was seen at 2.4, 3.6 and 4.4 m along the measured section (Fig.
6). This is likely due to heterogeneities in the streambed composition and topology such as stones and cobbles, creating steps in the surface-water profile that generate larger hydraulic gradients that induce the hyporheic exchange (Morén et al.
2017) and result in greater penetration depths, which is seen in time-lapse ERT measurements. Similar increases in hyporheic exchange have been shown for logs or other obstacles in the stream (Sawyer et al.
2011). While it was possible to observe many of these rocks and stones visually, there were several heterogeneities in the subsurface which were not visually apparent (i.e. buried rocks), notably the resistivity anomalies from 4.4 to 4.8 m along the stream reach. Additionally, at least some of the current transmitted during the ERT measurements was carried through the surface water rather than through the sediments, which could lead to erroneous modelling of very low-resistivity layers. However, the coincidence between the lowered-resistivity sections and the heterogeneities seen in the initial measurements indicate that surface features solely do not account for the behaviour of the tracer seen in the ERT measurements—for example, an abrupt deep penetration occurs at roughly 4.8 m, as seen in the ERT profile (Fig.
6). This penetration corresponds with subsurface layering interpreted from GPR data, but not surface features such as stream water depth (Fig.
9), although when isolines corresponding to percent differences between ERT measurements are superimposed on the GPR layer model, the greatest apparent penetration appears to coincide with the deepest apparent stream depth at
x = 3.2 to
x = 3.6 m (Fig.
9). The influence of subsurface structures on the apparent tracer penetration can be inferred from the variance in penetration corresponding with highly resistive anomalies, for example at
x = 3.8 to
x = 4.8 m (Fig.
9). The selection of a 25% resistivity change may be slightly arbitrary, considering that any decrease in resistivity should be the result of the tracer. However, given the uncertainty inherent in inverse modelling and geophysics, this level was considered to be appropriate for illustrative purposes and further discussion. Additionally, the roughly constant flow of water in the stream would likely result in a more uniform layer with decreased resistivity than was seen in the time-lapse measurements. Moreover, the presence of areas showing slight decreased resistivity values after the termination of the tracer injection in areas corresponding to the sections with deepest assumed tracer penetration (Fig.
6) indicated that there was likely some tracer still evident in these sections during the final measurement. This also indicated that the measured anomalies were likely primarily a result of a spatial heterogeneity in streambed conductivity within the hyporheic zone rather than an effect of currents going through the surface water, since the tracer-laden stream water would have been flushed much more quickly.
Spatial behaviour of uncertainty
Variability between the two modelled reciprocal resistivity measurements also appears to be influenced by the heterogeneity of the streambed. As the granite cobbles observed in the stream would have resistivity values greatly and abruptly differing from the surrounding sediments by several orders of magnitude (Reynolds
2011), it is reasonable that the inversion modelling process have the highest errors and/or uncertainty (due to for example equifinality of models) over these sections. Lower resistivity changes in the time-lapse model results correspond with the conceptual model of the measured section created from the original ERT and GPR measurements. Greater uncertainty in these regions, seen in time-lapse measurements taken during the tracer test, is then still acceptable, as the decreases in modelled resistivity adhere to the conceptual understanding of the tracer transport through the streambed. An increase in model variance in the x- and z-directions between reciprocal resistivity measurements at a given location could therefore be strongly indicative of abrupt changes in composition and hydraulic characteristics of the sediments. The greatest differences seen in the reciprocal measurements appear to correspond exactly where the tracer was modelled to have the greatest penetration, likely due to presence of heterogeneities such as rocks, where drastic differences in electrical resistivity would be difficult to model. Absolute differences between the reciprocal models were quite low regardless of depth; however, the largest differences between the models were found in the shallowest regions, which is likely due to using volume-averaged modelling to represent nonlinear heterogeneous geological features. Theoretically, at larger depths, which correspond to a larger electrode spacing, small-scale heterogeneities cause less variation in the measurements. Conversely, at more shallow depths, which correspond to a smaller electrode spacing, these heterogeneities would occupy a larger relative volume and play a more important role in the model; thus, differences in measurements would likely be magnified in these smaller volumes. The switch in sign of the average difference in the model layers between 0.1 and 0.3 m (Fig.
7b) corresponds roughly to the layer found in the GPR profiles. This could be another indication of a layer with differing electrical, and likely hydraulic, characteristics as more of the current would be directed towards this more conductive layer when measuring in a particular direction depending on proximity of the active electrodes, and corresponds with GPR layer analyses.
The protocol used to collect the ERT measurement also had the electrode sets with the largest spacing first, which was related to the deepest measurements in the inversion modelling process where little relative change was seen. Given apparent rapid penetration of the tracer into the sediments and the time required per resistivity measurement, it would have been desirable to have the shallowest measurements occur first. However, the time between each individual measured electrode-set would still be quite large, so it is not certain that this would capture the rising stage of the tracer breakthrough curve via ERT measurements. The implication for this experiment was that some of the information relating to the rising stage of the tracer breakthrough curve was missed. In future studies, a better representation of the dynamic nature of the rising and falling stage of the tracer breakthrough curve might reduce uncertainties connected to the distribution of flow paths within the hyporheic zone.