Introduction

Interactions between surface water and groundwater play a pivotal role in the hydrological cycle. Baseflows in streams and wetlands often rely on groundwater levels, which may need to remain close to the surface to provide adequate support for local fauna and flora (Winter 1999; Sophocleous 2002). Conversely, infiltration from rivers, lakes and wetlands can be a major source of recharge for aquifer systems, particularly in arid and semiarid settings. A variety of climatic, geological and biotic factors affect stream–aquifer exchange flows. However, flow direction is ultimately controlled by the relative hydraulic head. As a result, actions such as groundwater pumping may affect surface-water bodies by reversing hydraulic gradients (Llamas 1988; Zume and Tarhule 2008; Martínez-Santos et al. 2008; Ivkovic 2009). This often leads to adverse environmental effects as well as conflicts among competing users (Bernaldez et al. 1993). Being able to characterize and quantify exchange flows at the interface is thus crucial for the protection of water resources.

A variety of methods exist to identify and quantify interactions between groundwater and surface-water systems, including direct measurements, mass balance approaches, heat tracing, Darcian techniques, frequency analyses and numerical methods (Kalbus et al. 2006; Castaño et al. 2008). Direct measurements, for instance, can be carried out by means of seepage meters (Landon et al. 2001; Kelly and Murdoch 2003). These are simple and relatively inexpensive, but a significant number of measurements may be required to adequately characterize a given stream. Mass balance approaches, on the other hand, encompass a variety of procedures that range from differential stream gauging and hydrograph separation methods to solute and environmental tracers (Horton 1933; Kalbus et al. 2006).

Heat tracing techniques bank on the assumption that the temperature of groundwater is usually a lot more stable than that of surface water. Gaining reaches are thus characterized by relatively constant sediment temperatures, whereas losing reaches tend to present significant variability over short periods of time (Constantz et al. 2001). Many analytical solutions have been developed to calculate seepage rates based on temperature profiles measured beneath the streambed (Theis 1935), a description of which is beyond the scope of this report.

Frequency analyses provide a different perspective on baseflow processes by drawing statistical correlations between different datasets. Perhaps the most common application is the flow-duration curve, where the relationship between streamflow magnitude and frequency is derived. Approaches such as this allow for the combination of streamflow and rainfall monitoring to examine aquifer–river connectivity, and have been successfully applied within urban environments (Brodie et al. 2007).

Darcian approaches may provide an accurate quantification of exchange flows over a given area provided that both the permeability of the terrain and the hydraulic gradient are sufficiently well known. Since aquifer–river interactions are inherently complex, Darcian techniques are usually applied in the context of numerical models (Rodríguez et al. 2006). Indeed, numerical methods have long since been advocated as valuable means to model the surface-water/groundwater interface. This is largely because models are efficient in dealing with large amounts of information, and can simultaneously tackle dynamic interrelations between complex systems. However, models are simplified approximations to reality and thus subject to limitations and uncertainties. Pitfalls to look out for include the use of models outside their validated scope, models developed with insufficient data and/or overemphasis on inverse approaches (Refsgaard et al. 2005). Be as it may, comparative studies often point at numerical models as one of the most adequate techniques to deal dynamically with complex hydrogeological systems (Sophocleous et al. 1995; Conrad and Beljin 1996).

Whatever the methodological choice, aquifer–river interactions may prove significantly more challenging to assess in urban than in rural areas. This is largely because the main recharge and discharge elements of the water balance in city entourages differ from those in natural systems. Besides, the urban underground presents a variety of structures and drainage networks that may modify natural groundwater flow patterns. Finally, leaks from supply and wastewater systems can also induce significant fluctuations in groundwater levels (Foster and Chilton 2004; Vázquez-Suñé et al. 2005).

A comprehensive study of such complex settings often requires complementary research approaches, which almost inevitably implies the need for enormous amounts of data. This largely explains why there is still comparatively little published material on urban hydrogeology (Lerner 2002). A significant part of the existing literature deals with groundwater quality and the fate of contaminants in urban aquifers (Grischek et al. 1996; Howard et al. 1996; Meriano and Eyles 2003; Bauer et al. 2004), whereas other authors address specific engineering-related problems (Samper et al. 2006, 2007; Epting et al. 2008), or focus on quantifying different elements of the water balance (Yang et al. 1999; Kim et al. 2001; Morris et al. 2006). Take for instance the work of Lerner (2002), who highlights a variety of methods to identify and quantify urban groundwater recharge mechanisms, including numerical models and solute balance approaches; or Meyer (2005), who adopts a statistical approach to evaluate the effects of urbanization on baseflows. Overall, however, the field of urban hydrogeology remains open to contributions from all angles.

Numerical groundwater models in urban environments are also relatively scarce. Fewer still deal with aquifer–river exchange. Nevertheless, it is also true that numerical approaches have gained recognition over time as valuable means to study the aquifer–river interface in heavily populated contexts. Jusseret et al. (2009), for instance, used a classic three-dimensional groundwater flow model to assess the relative importance of the various recharge sources of a shallow aquifer system and its interaction with an urban river. Ellis et al. (2007), on the other hand, adopted a numerical approach to investigate the processes and features controlling the temporal and spatial variations in the groundwater flow contribution to an urban river. These authors also went on to explore fluid mixing at spatial scales from a single point in the river bed to the sub-catchment scale in order to evaluate the associated contaminant fluxes. Further to these, Reinstorf et al. (2009) coupled surface water and groundwater numerical codes with a mass balance model to quantify fluxes of xenobiotics within a heavily industrialized area.

However, models are subject to the difficulties that often hamper urban hydrogeological studies. In particular, quantifying (and distinguishing between) natural recharge in parks and gardens, the infiltration due to network losses, or the upward discharge from underlying aquifer units into urban alluvial systems can prove challenging (Marcos et al. 2006). Hence, recharge is often obtained via inverse calibration to match observed groundwater heads. This may present practical inconveniences derived from the correlation between recharge and permeability (Sanford 2002). These can however be addressed to a large extent by relying on comprehensive field data.

The present study aims at quantifying aquifer–river flows within an urban setting. This is achieved by means of a modeling-based methodology. Care is taken to obtain a plausible estimate of groundwater recharge, as well as to evaluate the spatial and time variations associated with human activities and the associated seasonal fluctuations in the system. Modeling results are discussed in the light of comprehensive field information, showing the extent to which anthropogenic actions are responsible for variations at the surface-water/groundwater interface.

Study area

This study focuses on two of the main suburbs of Langreo, a 46,000-people town located in northern Spain. These suburbs rest on the narrow alluvial plain that constitutes the bottom of the Nalon River valley (Figs. 1 and 2). From a regional perspective, this area belongs in the Cantabrian belt, an abrupt mountain range that extends across 480 km in parallel to Spain’s northern coastline. This mountain chain mostly comprises Mesozoic and Paleozoic rocks, and is bounded by the Galician massif to the west and the Pyrenees to the east.

Fig. 1
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Geographical setting of the study area

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Fig. 2
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Geological setting of the study area

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From the surface hydrology viewpoint, the Cantabrian belt is best described as a succession of short, fast-flowing rivers that run from south to north. Abrupt Paleozoic and Mesozoic outcrops, impervious for practical purposes, surround the Quaternary deposits towards the east and the west of catchments such as the Nalon valley (Fig. 2). This, together with a strong streambed gradient, constrains the formation of meanders to a large extent. As a result, alluvial materials adopt a corridor-like appearance along the river. Deposits are more important from the hydrogeological viewpoint in those areas where valleys become wider. These locations are also relatively flat and favour urban agglomeration.

Langreo is a suitable location to examine urban aquifer–river connectivity for a variety of reasons. For one, the alluvial system has been thoroughly characterized following several geological, geophysical and hydrogeological studies (TI-IAC 2006; INGE 2008; OHL 2009). In addition, the alluvial plain becomes extremely narrow towards the upstream and downstream ends of the city, both horizontally and vertically. For practical purposes, this means that the system can be assumed to be ‘self-contained’, that is, hydrogeologically isolated from the remainder of the catchment. No significant channelling or impermeabilization works have been carried out in the urban segment of the river, which implies that the surface-water system remains connected to the aquifer throughout. Finally, the 3.5 km2 site is manageable enough in size to characterize and to gain a sufficiently good intuitive knowledge of its hydrogeological behaviour.

The city presents a typical urban layout characterized by a major presence of paved areas, roads and buildings (Fig. 2). Impervious asphalt covers the vast majority of the alluvial plain, whose broadest section spans a little over 1 km. The ground surface is tilted towards the river with varying degrees of inclination. Sectors closer to the hills may present topographic gradients up to 5/100, but gradually relax to 1 to 2/100 near the river channel.

The study site is located approximately 205 m above sea level, and presents a temperate, humid climate. Average yearly temperature is 13.2°C, January being the coolest month (7.6°C) and August the warmest (19.1°C). Rainfall amounts to 1073 mm/year, and takes place over approximately 134 d/year. The area is particularly wet during the winter season (November to February), and the summer is sufficiently mild to present precipitation values in excess of 40 mm/month. Table 1 compares the historical averages for rainfall and rainy days with measured values during this study (INGE 2008). As shown, 2008/2009 was unusually humid except for the summer season (June to September).

Table 1 Comparative overview of the monthly rainfall and number of rainy days (values for the 2008/2009 period correspond to weather station 1218D, located in the neighbouring town of Muñera)
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Over 40 boreholes have been used to characterize the urban underground, which presents a roughly uniform composition. From top to bottom it typically comprises 1–3 m of debris, 2–4 m of fine alluvial materials and 3–5 m of coarse river sediments. These are all underlain by lutite and shale, impervious for practical purposes. Most buildings rest on alluvium, with only a few basements and garages reaching the Paleozoic materials. Except the shallower ones, which are kept dry by means of pumps, basements flood most of the time. At the time of this study, the town did not feature major underground structures such as tunnels or multi-storey parking, although major tunnelling works are currently underway.

From the hydrogeological perspective the system is best described as a shallow alluvial aquifer whose piezometric oscillations are largely controlled by the river. Pumping-test data suggest that the three permeable layers described above can be assumed to operate as a single hydrogeological unit (OHL 2009). System recharge takes place through two main mechanisms, namely direct rainfall through permeable soil and leakage from the city supply and wastewater networks. Discharge takes place through evapotranspiration in green areas as well as through a series of pumps. The latter are located in basements and garages, and operate between autumn and spring at a constant 2–3 m drawdown.

Although the river is highly regulated by upstream dams, stages present important seasonal variations (up to 3 m). Average yearly streamflow is 56 m3/s, but may range widely (between 3 and 1,250 m3/s). This all implies that the river may either behave as a source of aquifer recharge or as a discharge outlet. Table 2 presents a statistical overview of the river stage values for the period under consideration. As shown, seasonal fluctuation was significant, although river stage remained roughly stable within both the winter and summer seasons. From a streamflow viewpoint, water withdrawal from the river for urban supply purposes and discharges from the wastewater network do not affect the river segment under consideration. This is because these take place up and downstream the system, respectively.

Table 2 Stream stage in the study site (all values are in meters above sea level; stream gauge numbering begins from the south; see Fig. 1). SD standard deviation
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Methods

Field campaigns and model development

Given their inherent complexity, evaluations of aquifer–river connectivity almost necessarily call for numerical modeling approaches. In this case, modeling work is based on the results from three field campaigns. The first one of these focused on aquifer characterization, comprising geophysical studies, numerous pumping and permeability tests, and the installation of 25 piezometers and six stream gauges (TI-IAC 2006). This was followed by two monitoring campaigns, lasting for 14 weeks each (June 2008–September 2008 and November 2008–February 2009), which served the purpose of gathering daily-scale piezometric and stream stage data under summer and winter conditions.

Processing MODFLOW Pro (PMWIN) was the software chosen for modelling work (Chiang and Kinzelbach 2001, Chiang 2005). PMWIN Pro is a three-dimensional groundwater flow and mass transport modelling package that provides a graphical user interface for the classic finite-difference MODFLOW code (McDonald and Harbaugh 1988), whose reliability and robustness has been tested extensively.

The model grid spans a surface of 2,560 × 2,380m. Approximately half of this area corresponds to alluvial deposits, and has been modeled in 10 × 10m active cells. Cells are uniform in size throughout the system. The alluvial aquifer is defined as a single layer, which is in turn allowed to switch between confined and unconfined behavior as needed. Confined storage coefficient (specific storage multiplied by the layer thickness) is used to calculate the rate of change in storage if the layer is fully saturated. Conversely, the program uses specific yield if the layer is only partially saturated. The transmissivity of each cell thus varies with the saturated thickness of the aquifer. Paleozoic outcrops are considered impervious for practical purposes and make up the lateral boundaries of the system.

The elevation of the layer top corresponds to the topographic elevation of the terrain. The grid bottom in turn corresponds to the depth of the Paleozoic layer as inferred from the information from 27 fully penetrating boreholes and 12 geophysical cross-sections (Fig. 1). The remainder of the grid bottom has been obtained through geostatistical interpolation (Cressie 1990).

Time is discretized in daily intervals as per the available river-stage data. Two transient-state simulations were carried out to evaluate aquifer–river interactions over the winter and summer seasons (high waters and low waters). Each of the two simulations spans a 98-d period, equivalent to 14 weeks.

About 30 field tests, including Lugeon, Lefranc and pumping-recovery tests, have been carried out to characterize the system’s hydrogeological parameters. Tests were roughly equally distributed throughout the system, although the available information is more comprehensive to the eastern margin of the river. Hydraulic conductivity has been observed to range between 0.1 and 15 m/d, whereas specific yields are in the order of 5–15%. For modeling purposes, both hydrodynamic parameters have been extrapolated via kriging based on data from the field campaign.

Recharge is assigned on a cell-by-cell basis. The main input parameter is net infiltration, which is assumed constant during each stress period. Two recharge areas were defined for this purpose, corresponding to paved and green sectors of the city (‘urban’ and ‘natural’ recharge areas hereon). The former accounts for leaks from water and wastewater distribution networks, and applies to about 75% of the model’s active cells. These correspond to areas taken up by roads and buildings, as pipes run parallel to the urban grid. According to the staff at the local water-supply company, leaks from the water and wastewater networks within the study area amount to approximately 2,300 m3/d (J.E. Granda, Aguas de Langreo, personal communication, January 2010). This value corresponds to approximately 30% of the water running daily through both pipelines, which serve an urban population in the order of 32,000 people.

Natural recharge, on the other hand, corresponds to direct rainfall recharge and makes up the remaining 25% of the model surface. This essentially corresponds to parks, as well as to green areas located towards the outskirts of the town (Fig. 1). Natural recharge is estimated by means of parameter fitting. The implications of this course of action are discussed later on. Modelling-wise, both network losses and natural infiltration are assumed uniform in space, but not in time. In other words, each stress period uses a different value for network losses and natural recharge, but these values may change from one stress period to the next.

Evapotranspiration is also defined on an areal basis. PMWIN’s evapotranspiration package requires three parameters to be given for each cell, namely the maximum evapotranspiration rate (m/d), the elevation of the evapotranspiration surface (m), and the extinction depth (m). For each stress period, water is removed from the model depending on the elevation of the water table. If the water table is at or above the elevation of the evapotranspiration surface, the model will use the maximum allowed rate. Conversely, no water will be removed if the water-table elevation remains below the extinction depth. Evapotranspiration is assumed to vary linearly in between. In the case at hand, the evapotranspiration surface was assumed to coincide with the topographic surface, whereas maximum daily-scale rates were defined according to the National Weather Agency’s potential evapotranspiration records. Except, that is, for paved areas, where evapotranspiration was assumed zero. Several extinction depths were tried during the calibration process (1–3 m), with negligible effect on the results.

Pumps were modeled as constant head boundaries. In other words, pumps are allowed to extract as much water as needed in order to keep the water table at a suitable depth. City council data indicate that most buildings use one or two pumps, the majority of which operate at a constant drawdown to maintain the level below the bottom of basements and garages (4–5 m below ground surface). For modeling purposes, a density of one pump per building has been assumed. In the absence of more specific data, each pump is placed arbitrarily near the corresponding structure.

Daily river-stage was measured at six gauging stations. For modeling purposes, river stages are assumed to account for overland flow. This is justified by the narrowness of the alluvial catchment, the daily-scale information available, the comparative abundance of paved surfaces and the natural inclination of the land towards the stream.

To account for exchange flows between the aquifer and the stream at each cell, MODFLOW uses a variety of parameters, including the hydraulic conductivity of the riverbed (m/d), river stage (m), elevation of the riverbed bottom (m), width of the river (m), length of the river within the cell (m), and the thickness of the riverbed (m). All except for the stream stage are grouped under a single parameter named river conductance. This accounts for the material and characteristics of the riverbed and the immediate environment. Since it is difficult to quantify in the field, this parameter is adjusted during model calibration.

Model calibration

Model calibration is often used to estimate recharge rates from hydraulic heads, hydraulic conductivity and other parameters (Chiang 2005). This is achieved through simultaneously adjusting the values of whichever of these parameters are not sufficiently known until a good match is achieved between the calculated levels and a long dataset of observed hydraulic heads. Once this is done, those values that yield the best correlation are generally assumed true. Long observation series and wide spatial distributions of the monitoring wells usually provide some degree of quality assurance.

Scanlon et al. (2002), however, argue that this approach may sometimes prove misleading. This is because some parameters are highly correlated. Take for instance hydraulic conductivity and recharge. Simultaneous estimation of these will thus yield the optimal ratio, rather than the best estimate for their absolute values. Results could therefore be untrue even if they reproduce observed piezometric series sufficiently well. In the case at hand, this pitfall is prevented by relying on a large set of field tests to characterize the spatial distribution of hydraulic conductivity and specific yield. Field measurements are assumed true and are not allowed to change at all during the calibration process.

Inverse calibration implies that those parameters to be adjusted must be defined manually on a one-by-one basis for each of the model’s stress periods (98 in this case). Since this is extremely tedious, the model was run first with 14 weekly stress periods in order to perform several quick sensitivity analyses. The weekly-scale model was calibrated using the PEST parameter estimation module. PEST is an automated parameter fitting application that carries out several model runs to find the likely value of an unknown parameter, in this case natural recharge. This is achieved through identifying those recharge values that minimize the sum of squared deviations between calculated and observed hydraulic heads.

In this case, model calibration was carried out under transient conditions for both the summer and winter seasons. Initial hydraulic heads are obtained from water-table data at the beginning of each field campaign. Natural recharge was adjusted to match observation datasets from 24 monitoring wells. The automated calibration approach allows for the discrimination of urban and natural recharge. Figure 3 shows their proportional distribution. Due to the pre-eminence of paved zones (and, hence, the comparatively larger area designated as network leaks), natural infiltration makes for a small fraction of the system’s recharge flows.

Fig. 3
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Calculated natural aquifer recharge and measured rainfall versus time

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Parameter fitting renders different seasonal trends in natural recharge. It is a lot more variable during the winter, when there seems to be some correlation between model-calculated natural recharge and actual rainfall (i.e. natural recharge is generally observed to increase during rainy periods, whilst it diminishes in drier spells). Conversely, the model yields a lower and more stable recharge estimate during the summer. In the absence of long rainy periods, this could be attributed to irrigation of municipal parks and gardens, which can be rather uniform across time. As explained later, another important factor from the numerical perspective is the fact that the river behaves as a net loser during most of the summer. This in practice implies that the river yields part of the recharge needed. Hence, natural recharge cells barely need to contribute any water.

Figure 4 presents the scatter correlation between observed and calculated groundwater levels for the optimal natural recharge adjustment. A statistical analysis is also shown in Table 3. Calibration results indicate that the model is able to replicate aquifer behaviour to an acceptable extent for both summer and winter conditions. Thus, the Pearson coefficient (R 2) for calculated-observed values exceeds 0.9 in both cases, whereas the absolute average error in calculated levels is slightly less than 1 m for both winter and summer conditions.

Fig. 4
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Weekly-scale model calibration for a summer conditions and b winter conditions. Observed vs. calculated values

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Table 3 Statistical parameters of model calibration runs. Values refer to groundwater levels (m.a.s.l.)
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Figure 5 plots the observed and calculated piezometric trends. As expected, the water-table depth is slightly lower during the summer. Observed values do not show steep variations, which could be perceived as relatively unusual for a shallow alluvial aquifer subject to pumping. Causes should be found in the fact that there are many pumps operating at a small constant drawdown and openly interfering with one another. As a result, drawdowns are relatively uniform over time throughout most of the system. In other words, one large, shallow pumping cone predominates over many small, deep ones.

Fig. 5
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Model calibration: observed vs. calculated evolutions in representative zones of the system. Discontinuous lines represent observed values, whereas continuous lines correspond to model outputs. Refer to Fig. 1 for the location of each piezometer (OBSNAM observation point)

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Piezometric observations are generally stable in both cases. There are, however, subtle trends in field data which the model roughly replicates. Thus, levels in summer present a smooth upturn, whereas they tend to remain stable or fall slightly over the winter. This is best perceived in some of those piezometers closer to the river (PZ3, PI1, PI5, PI3), whereas those located further inland generally appear more stable (PZI2). As explained later on, these fluctuations are attributed to the effects of pumping, and hence, to the evolution of the system across the full hydrological cycle.

Varying natural recharge modifies the results of the calibration process. A good adjustment is still obtained for values of twice and half the automated estimate, although the statistical correlation diminishes in comparison with Table 3. Modifying natural recharge by a factor of ten yields significantly worse results (note that this implies a relatively small change to the overall recharge, as infiltration in green areas averages less that 5% of the total recharge). The reason is different for increased and decreased recharge values. If recharge is increased, permeability becomes the controlling parameter for groundwater heads. This means that the aquifer will be able to evacuate all surplus recharge into the fixed head cells and the river as long as permeability is sufficiently high. Hence the calibration may still look reasonable at the expense of increasing outflows via these two “open-ended” elements of the water budget (i.e. these cells will take or release as much water as needed in order to match calculated values to field observations). However, there is a point when recharge simply exceeds the conveyance capacity of the aquifer. Water is unable to escape quickly enough, so the level rises and the adjustment is lost. Conversely, when recharge is decreased, fixed-head cells can make up for the losses. The combined effect of low recharge and the river acting as a drain cause the water table to drop. Levels fall below the constant head of fixed cells, which in turn begin to release water. The adjustment may still look acceptable, but the water balance indicates that the pumps are yielding large amounts of water to the aquifer—which in practice is absurd.

Finally, a sensitivity analysis was carried out next in order to assess the importance of river conductance on the calibration. In practice, conductance is likely to change along the river depending on those parameters described earlier on. However, in the absence of specific data an average conductance value was assumed for the whole stream segment. A broad interval (10–104 m2/d) was tested in order to evaluate the potential effect of wide fluctuations on modelling results. The best fit was obtained towards the lower side of this range, although the differences in the calibration are relatively small, even for very large values (104 m2/d). This is because groundwater levels are mostly controlled by aquifer hydraulic conductivity if streambed conductance is assumed to be sufficiently high (>5 m2/d). For very low conductance values (<0.1 m2/d) the adjustment is soon lost.

Results and discussion

Figure 6 presents cumulative aquifer–river flows. As shown, the river presents a slightly gaining behaviour throughout the winter. This regime is, however, inverted in the summer. Indeed, at the beginning of the summer season the water table was observed to be lower than during the winter season. In other words, despite a rainy spring the river was already recharging the aquifer by the time the field campaign begun. This is attributable to the small size of the alluvial system, which can experience a significant lowering of the water table due to pumping throughout the other 9 months of the year.

Fig. 6
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Cumulative river–aquifer exchange flows for each of the three transient-state model runs

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Two daily-scale simulations were carried out to assess aquifer–river connectivity over the winter season. The first one takes pumping into account, whereas the second simulation does not. The purpose of this exercise was to evaluate the effect of pumping on exchange flows. Figure 6 allows one to observe how the stream should present a net gaining behaviour in the absence of pumping, and also how pumping-induced drawdowns eventually invert the trend. Joint interpretation of Figs. 6 and 7 leads to the conclusion that the aquifer–river system was close to a hydrodynamic equilibrium throughout the winter campaign. Indeed, during these 14 weeks, the river only gained an average 200 m3/d, that is, 0.002 m3/s over a 2 km segment. Causes should be found in sustained groundwater pumping over the autumn and winter seasons. Pumping lowers the water table to prevent flooding in the shallower basements. This eventually offset stream baseflows, but was not enough to detract water from the river itself during the 14-week period under consideration.

Fig. 7
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Daily river–aquifer flows under the summer and winter conditions

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A similar thing occurred in the summer, although exchange flows fluctuated more widely. At the beginning of the summer campaign, the water table was sufficiently low to reverse aquifer–river flows. The system, however, remained relatively close to equilibrium, i.e. the river lost 3,500 m3/d, equivalent to 0.04 m3/s, along the segment under consideration. With most pumps at a stop, aquifer recharge due to river and network losses gradually caused the water table to recover. Some pumps became operational again at the end of the summer, thus bringing exchange flows closer to zero. This interpretation seems in agreement with the obtained pumping estimates for the winter and summer simulations (Fig. 8).

Fig. 8
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Daily-scale estimation of urban groundwater pumping for the winter and summer seasons. Discharge into fixed-head cells

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Overall, aquifer–river exchange is close to negligible in relation to total streamflow. Take for instance the case of a steady-state run with maximum winter recharge and no pumps operational. In the absence of other boundary conditions, this scenario would imply that all system inflows (recharge) should eventually turn into streamflow. In other words, the river would be gaining about 2,500 m3/d for the whole segment under consideration, i.e. 0.03 m3/s. Streamflows, however, nearly always exceed 3 m3/s, and may exceptionally reach over 1,200 m3/s.

While the calculated baseflows are comparatively small, the value rendered by the model seems plausible in the light of other estimates present in the literature (Ellis et al. 2007; CHT 2009). Also, geological and geomorphological factors play a key role in the case at hand. The stream in this part of the basin runs mostly along an abrupt riverbed carved into impervious materials. Alluvial systems have only developed in areas such as Langreo, where the valley becomes a little wider. This implies that streamflows rely almost solely on surface runoff, as well as on two upstream reservoirs which prevent floods and maintain suitable environmental flows all year long. According to modelling results, the alluvial system could convey a total baseflow in the order of 1 Mm3/year. However, these also suggest that river stage largely controls the elevation of the water table in the urban area.

One further aspect about the summer run needs to be considered. As shown in Figs. 6, 7 and 8, the model reflects stronger trends regarding piezometric heads, river–aquifer flows and pumping. These trends are observed to relax over time. In the view of the authors, this can be attributed to using an initial distribution of water-table heads, which, on average, is slightly below their actual elevation. This in turn stems from the fact that part of the observation network was still being put into place during the first few weeks of the summer. A lesser density of piezometric observations implies that the geostatistical interpolation for the model’s initial groundwater heads could have yielded a slightly inaccurate distribution in some areas. Winter results present no such shortcoming, as all piezometers had been drilled by then and could be monitored from the outset.

Figure 9 compares measured evapotranspiration values against modelling results. A reasonably good fit is obtained for the winter season, whereas no real correlation exists for the summer. This is largely because of the way the model deals with this factor. As explained earlier, MODFLOW only considers direct evapotranspiration from the water table, assuming it to decrease linearly until the extinction depth is reached. In other words, the model will not take any water out of the system once the water table falls below the extinction depth. During the winter season the water table is sufficiently high, so the model does not fall as short of the observed trend. In summer, however, the water table is lower. For modelling purposes this implies that there is little room for evapotranspiration during this season. It also explains why the model renders a higher evapotranspiration rate in winter.

Fig. 9
figure 9

Measured evapotranspiration (ETP) vs. modeled evapotranspiration (ET) in a summer conditions and b winter conditions. Measured evapotranspiration values correspond to weather station 1218D, located in the neighbouring town of Muñera

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Overall, the above allows one to conclude that the model behaves reasonably well. Modelling results are, however, of limited value. From an overall perspective, any model is a simplification of reality. Results should therefore be handled with care and taken as an approximation subject to confirmation from complementary studies. More specifically, the predictive ability of this model is constrained by the absence of some potentially relevant data. In particular, despite the absence of major underground structures, a more accurate distribution of basements and pumps would have helped obtain more reliable outputs. The same applies to riverbed data, whose influence on the results could only be evaluated by means of a sensitivity analysis.

The available information does not allow for an evaluation of model performance across a full hydrological cycle. Hence, the calibration was restricted to moments when the water table was largely stable. While this does not necessarily detract from the calibration, it is also true that the transition between the summer and winter seasons could not be assessed.

Conclusions

Despite their practical importance, urban aquifers remain relatively poorly known in most regions worldwide. This is largely due to the difficulties involved in performing comprehensive hydrogeological studies in urban settings, as well as to the complexity of most city undergrounds. Numerical models are advocated as adequate tools to simultaneously integrate such complex datasets in a dynamic manner in order to obtain approximate estimations for all elements of the water budget.

In this study, a numerical model was developed and calibrated to evaluate aquifer–river connectivity in a small urban alluvial aquifer of northern Spain. Model calibration suggests that the model is able to replicate the behavior of the physical system sufficiently well. Results show aquifer–river connectivity to be modified by human activities, more specifically pumping drawdowns derived from the need to keep the water table below shallow basements and garages. Thus, the river presents a gaining behavior for most of the rainy season, gradually becoming a losing stream as the effects of sustained pumping become more evident. During the summer, the river is a net loser due to the drawdowns induced throughout spring and winter. Recharge takes place mostly during autumn, when the water table is still sufficiently low for pumps to remain at a stop.

An attempt was made to discriminate direct rainfall recharge from leaks from the water and wastewater networks. This is achieved by defining an average loss for the distribution networks and estimating natural recharge by means of automated parameter fitting. While the results are coherent with field observations, such an estimate should be taken as a first approach, contingent on the results of complementary studies.