In order to quantify stream-aquifer interactions, we look at the groundwater discharge-recharge along the stream in terms of exchange flow per unit area.
Figure 3.6 shows the values of the vertical component of the groundwater velocity beneath the stream bed along the stream network for the different simulated systems. The maps highlight whether the river is gaining (positive values, blue colors) or losing (negative values, red colors). Different gradations of these two colors indicate the intensity of the exchange flux. Table 3.3 indicates the fraction of gaining and losing cells over the total number of river cells for each simulation and shows quantitatively the difference in gaining and losing conditions along the river network when different modeling assumptions are made. It can be observed that the main river is alternating between gaining and losing, as suggested by the geomorphological configuration of the catchment in previous studies [60]. Moreover, the patterns of exchange fluxes are very similar among the different scenarios; the only system that shows a substantially different behavior is the “Homogeneous Aquifer Case”, where the losing conditions increase considerably along the tributaries, while the main stem becomes more gaining. This can be explained considering a higher value of the average hydraulic conductivity of the domain in comparison with the heterogeneous case, that entails a drop in the water table. According to equations (3.2), the total exchange flux between the river and the aquifer is directly proportional to river width and river stage. Therefore, water exchange fluxes along the tributaries will be higher when increased values of width and stages are considered (“Constant River Parameters Case”). Finally, another observation that emerges from the results is related to the strong influence of the structure of the river network. The spatial patterns of groundwater recharge and drainage can be strongly affected by the position of the stream network within the catchment. The position of a stream in its river network, in fact, determines if a reach receives groundwater, loses water into the aquifer, or it is neutral. In this study, we considered a single level of detail in the representation of streams in the model and this could be explain the stability of GW-SW exchange flux patterns, at least partially. Future investigations could
Fig. 3.6 Intensity of vertical exchange velocity qz(m/s) for different simulations.
Gaining and losing conditions are represented in blue and in red, respectively. Deeper colors indicate higher intensity of exchange flows.
be conducted to analyze the effect of capturing different levels of representation of the stream network.
Figure 3.7a represents the vertical exchange velocity qz (m/s) as a function of the position along the main channel for the different cases. Positive values represent water gaining river conditions and negative values represent losing river conditions. The exchange velocity behavior is very similar for most of the cases, with the exception of (i) the “Homogeneous Case”, as already noted in the previous figure, and (ii) the “Smoothed Ground Surface Case”. In this latter case, the vertical exchange velocity shows a more regular pattern, with less oscillations, due to the fact that a narrower range of spatial scales is driving GW-SW interactions. Table 3.4 shows some statistical parameters (i.e., mean
Table 3.3 Percentage of gaining and losing river cells for different simulations. The amount in parentheses indicates the variation of the percentage fraction of gaining and losing river cells respect to the reference case (“Complete Case”).
Losing conditions Gaining conditions
(%) (%)
Complete case 32.6 67.4
Constant Recharge 33.0 (+0.4) 67.0 (-0.4) Constant River Parameters 31.6 (-1.0) 68.4 (+1.0) Smoothed Ground Surface 34.7 (+2.1) 65.3 (-2.1) Simplified Geology 33.7 (+1.1) 66.3 (-1.1) Homogeneous Aquifer 72.4 (+39.8) 27.6 (-39.8)
value and standard deviation) of vertical exchange velocity along the main river for the different simulations. The only case with meaningfully different values is the “Homogeneous Case”, for which the prevalence of gaining conditions can be observed: the mean value of qz is about three times the value obtained for the other cases since the increase of losing conditions along the tributaries is compensated by a more gaining main reach. Moreover, the standard deviation of qz for the “Smoothed Ground Surface Case” is lower than the other cases, indicating a reducing dispersion of exchange flux values.
The degree of change among the different sets of vertical exchange velocity data is examined graphically through the box plots represented in Figure 3.7b, that highlight the associated variability. The vertical exchange velocities show almost equal distributions for most cases, with very similar values of median and mean. The only exception is the “Homogeneous Case”, which exhibits more variability in the statistical parameters. In order to quantitatively compare these differences, we ran a statistical test (two-tailed t-test) and the results highlight that the “Homogeneous Case” is the only case statistically different from the other cases (p < 0.05).
A more detailed quantification of the variability of the modeled exchange velocity under different hydrogeological conditions is represented in Figure 3.8. The scatter plots show the comparison between the vertical exchange flow per unit area obtained at each river cell for the complete model, qzcompl, and for each simplified system, qzsimpl. The different series of exchange velocity
Fig. 3.7 (a) Exchange vertical velocity along the main river and (b) boxplots of the vertical exchange fluxes for different simulations. Quantiles are determined in correspondence to 5, 25, 50, 75 and 95% of the numerical data. The cross markers indicate the mean value of each series.
values compare well for the simulations with constant recharge, constant river parameters and simplified geology: in fact all points are most closely aligned along the 1:1 line of best fit with limited scatter, as confirmed by the values of the coefficient of determination, R2. The smoothed-ground surface case shows a lower correlation (with R2 equal to 0.5695), while the R2 value of the homogeneous system (very close to zero) indicates the total lack of correlation, highlighting that there does not exist a meaningful relationship between the two variables, i.e., the exchange velocity estimated for the homogeneous system is substantially different from the values estimated with the full model. Moreover, it can be observed that the “Homogeneous Case” tends to overestimate the values of groundwater inflow/outflow, while in the “Smoothed Ground Surface Case” there is the presence of both over/underestimation clusters.
The discrepancy that emerges from the scatter plot for the “Smoothed Ground Surface Case” was not distinctly visible through the boxplots. This means that the total fluxes occurring in the system are nearly equal in both the “Smoothed Ground Surface Case” and the “Complete Case”, so the average behavior of the system is unchanged. However, the dispersion highlighted by the scatter plot indicates the presence of local variations of gaining and losing conditions induced by local variations of ground and riverbed elevations. These variations of elevation entail a shift from gaining to losing (and vice versa) conditions at specific points, with a resulting redistribution of exchange fluxes within the aquifer. This result confirms the relevance of topographic description of the study area in determining local river-aquifer interaction patterns since the landscape topography is among the main factors that influence groundwater flow [40].
Overall, we can state that the similarity between the structure of ground-water discharge patterns under different hydrogeological conditions – with the exception of the homogeneity condition – represents a significant result since it shows how a detailed description of some hydrological factors has a marginal effect on the structure of subsurface flow patterns.
Fig. 3.8 Comparison of the vertical exchange flux per unit of length obtained for the complete system, qzcompl, and for each simplified system, qzsimpl. The R2 indicates the coefficient of determination between the two estimates.
Table 3.4 Statistical parameters of vertical exchange velocity along the main river for different simulations. The values in parentheses indicate the percent variation with sign respect to the reference case (“Complete Case”).
Mean Value (m/s) Std Deviation (m/s)
Complete case 2.10 · 10−6 6.07 · 10−6
Constant Recharge 2.08 · 10−6 (-0.9%) 6.06 · 10−6 (-0.2%) Constant River Parameters 2.36 · 10−6 (+12.5%) 6.15 · 10−6 (+1.3%) Smoothed Ground Surface 2.17 · 10−6 (+3.3%) 5.20 · 10−6 (-14.3%) Simplified Geology 2.20 · 10−6 (+4.8%) 6.17 · 10−6 (+1.6%) Homogeneous Aquifer 7.02 · 10−6 (+243.3%) 8.59 · 10−6 (+41.5%)