Estimation of recharge in mountain hard-rock aquifers based on discrete spring discharge monitoring during base-flow recession

The two study areas of Mt. Prinzera and Mt. Zirone are located near the confluence between the Taro and Ceno streams, about 36 km SW of the town of Parma, in the western sector of the Northern Apennines (Emilia-Romagna Region, Italy; Fig. 1). The Northern Apennines are a typical thrust-fold chain originated from the convergence and collision between the Eurasian and African plates after the consumption of the paleo-Tethys oceanic crust of the Ligurian-Piedmont basin. Some ophiolitic bodies outcrop along the chain as isolated remnants of obducted oceanic crust. These are mostly peridotites, serpentinites, gabbros and basalts formed in the Middle to Upper Jurassic (Marroni et al. 2010) that today are embodied within allochthonous Ligurian silty-clayey complexes (Abbate 1986; Bortolotti et al. 2001).

Mt. Prinzera and Mt. Zirone are ophiolitic mountainous reliefs (olistolithes) mainly consisting of strongly serpentinized peridotites (Di Dio et al. 2005; Venturelli et al. 1997) outcropping along an orographic culmination of the external portion of the liguride units. The Mt. Prinzera ophiolitic structure covers an area of about 0.9 km² reaching a peak elevation of 725 m above sea level (asl); it is about 250 m thick and gently dips to the north. The Mt. Zirone ophiolite covers an area of about 2.6 km² with a maximum elevation of 707 m asl; it is 50 m thick and dips to the northwest. The ophiolitic rock masses have a very low matrix permeability but appear extensively fractured thus behaving as aquifers. Hydraulic tests provided a hydraulic conductivity ranging between 1.1 × 10⁻⁷ and 5.7 × 10⁻⁷ m/s for these units (Segadelli et al. 2017a). The olistolithes of Mt. Prinzera and Mt. Zirone are bordered and underlain by low-permeability deposits (Figs. 2 and 3) that are predominantly characterized by polygenic breccias made out of blocks of limestones or marly limestones inside a silty-clayey matrix with mineral cement (Segadelli et al. 2017a, b). It is reasonable to assume that these lower permeability units behave as aquitards, since the fine-grained matrix clearly dominates over the limestone blocks (Fig. 3c). Several perennial springs are located at the contact between the ophiolitic aquifers and the aquitard unit. These springs represent the whole outflow of the aquifers following the conceptual model proposed by Segadelli et al. (2017b) for Mt. Prinzera (Fig. 4).

The climate in the Mt. Prinzera and Mt. Zirone areas is midway between Mediterranean and oceanic, with humidity levels typical of boreal mountain zones close to the sea (Costantini et al. 2013; Nistor 2016). The average annual rainfall is about 1,000 mm/year and the seasonal rainfall distribution is that typical of the Northern Apennines with a main peak in autumn and a secondary peak in spring (Antolini et al. 2017). The driest season is summer-early autumn followed by a dry period of secondary importance in early winter.

A detailed field survey was carried out to identify all the perennial springs pertaining to the two investigated aquifers. The limited extent of the aquifers favoured this activity. The surveys were carried out in April 2012 and in May 2016 at Mt. Prinzera and Mt. Zirone, respectively. Seven springs were identified in the area of Mt. Prinzera and five at Mt. Zirone. All the perennial springs are located at the contact between the ophiolitic massif and the underlying aquitard units (Fig. 2). Nine out of the total 12 springs are exploited for public supply of drinking water. The remaining three are not exploited and respond to the description of rheocrene springs following Springer and Stevens (2009).

Discharge was monitored on a weekly basis in all the springs of Mt. Prinzera between September 2012 and September 2013, whereas the springs of the Mt. Zirone area were monitored between October 2016 and October 2017. In both cases, the monitoring lasted for at least a hydrogeologic year, i.e. from the beginning of the recharge season (corresponding to a systematic increase of water levels and/or spring flow rates) to the end of base-flow recession in the next calendar year. The field measurements of discharge (Q) were performed following an irregular timeframe due to logistic constraints (see Tables S1 and S2 in the electronic supplementary material (ESM). Discharge measurements were performed using the volumetric method due to the relatively low flow rates. In the case of springs exploited for public water supply, the time to fill a 20-L graduated bucket was measured to obtain discharge. In the case of non-exploited springs, flumes and weirs were used to convey all the water inside a smaller graduated container. Measurements were repeated at least three times at each monitoring point for the sake of accuracy. Groundwater parameters (temperature: T, electrical conductivity at 25 °C: EC, and pH) were measured on-site by means of a portable device (Eutech Instrument, Thermo Fisher Scientific Inc.) concurrently with each discharge measurement.

A power-law correlation was found by Gargini et al. (2008) between the average annual discharge of a spring from field monitoring (Q_A) and its average discharge during hydrological recession in the low flow season, i.e. summer in the investigated climate (Q_S). Such correlation was derived experimentally starting from a large dataset of 11 hydrogeologic years of discharge monitoring on more than 80 springs in hard rock aquifers in turbiditic formations of the Northern Apennines and is expressed as in Eq. (1):

The coefficient A and the exponent B were obtained from the linear fitting on a log-log plot of field data pertaining to springs with similar recession coefficients (α). The coefficient α is derived from the exponential model proposed by Maillet (1905). In particular, Gargini et al. (2008) proposed six different couples of values for A and B corresponding to different ranges of α (“classes of α”, from here on; Table 1). The data within each of the six classes of α were aligned on a log-log plot of Q_A VS Q_S with a high coefficient of correlation (R²) between 0.99 and 0.97. The rationale for choosing the Maillet model for the analysis of recession hydrographs is provided in the following section.

Equation (1) was applied to the springs of the Mt. Prinzera and Mt. Zirone to predict an average annual discharge (Q_AE, where the subscript E indicates an indirect estimate of Q_A through the equation) starting from base-flow recession monitoring (Q_S).

The actual averaged annual discharge Q_A was determined for each spring from field data. To account for the uneven distribution of Q measurements over the hydrogeologic year, Q_A was determined for each spring by disaggregating the flow rates measurements in four seasons (fall: from start of the hydrogeologic year to December 31st; winter: from January 1st to March 31st; spring: from April 1st to June 30th; summer: from July 1st to end of the hydrogeologic year) and by averaging the four mean seasonal values. Q_S was determined for each spring by averaging only the flow measurements selected for the recession analysis (criteria for the selection are in the next section).

The estimated annual flow rates Q_AE were compared to the average annual discharge from field monitoring Q_A. The goodness of the prediction was quantified separately for Mt. Prinzera and Mt. Zirone using the normalized root mean square deviation (NRMSD), expressed as in Eq. (2):where Q_{A max} and Q_{A min} are the maximum and minimum averaged annual flow rates from field measurements, respectively, and n is the number of monitored springs.

The depletion hydrograph of springs and streams is the stage of the hydrograph along which the discharge decreases over time. The literature has been mostly focused on the base-flow recession, i.e. the late stage of the depletion hydrograph when streams are fed exclusively by groundwater discharge with no disturbances from recharge processes. In this stage, the recession behavior is expected to provide information on some intrinsic aquifer features (e.g. Azeez et al. 2015; Tague and Grant 2004).

One of the first studies about base-flow recession hydrographs is that of Boussinesq (1904), who proposed a nonlinear quadratic behavior of aquifer discharge during recession. That model is an exact solution of the diffusion equation (Boussinesq 1877) that describes groundwater flow through a porous medium. The solution is based on the Dupuit-Forcheimer assumptions which represent the first mathematical formulation of the ideal “Dupuit aquifer” (Dupuit 1863; Troch et al. 2013).

An approximation of the exact solution provided by Boussinesq is the linearized model proposed by Maillet (1905). Following Maillet, the relationship between the groundwater discharge of a spring or into a stream and time follow the exponential decay of Eq. (3) in the absence of outer influences such as precipitation, surface storage, groundwater abstraction or evapotranspiration:

where Q and Q₀ are the flow rates (L³/T) at time t and at the beginning of the base-flow recession stage, respectively, and α is a time constant (T⁻¹) representing storage lag-time. α is related to the time required to halve the base-flow discharge (t_0.5) and can be expressed as in Eq. (4):

From a mathematical viewpoint, Eq. (3) is probably the most convenient description of base-flow recession among existing models (Dewandel et al. 2003). However, rigorous hydrological analyses applied mostly to streams have demonstrated that the linearized Maillet model is inadequate to describe the whole range of groundwater discharge behaviors during base-flow recession. Semi-logarithmic recession hydrographs of actual rivers are generally concave, suggesting that α is not constant but instead decreases with decreasing groundwater discharge into the stream (Brutsaert and Nieber 1977; Moore 1997; Shaw and Riha 2012; Wittenberg 1994). When analyzing the literature about recession analysis, one has to take into account that the recession hydrograph of a stream can be more complex than that of a spring because stream flow is more subject to interactions with other components of the hydrological cycle such as interflow, precipitation, evapotranspiration acting within the root zone, and river bank filtration, or it may be influenced by the initial moisture conditions of the watersheds (Kirchner 2009; Shaw and Riha 2012). Differently, the base-flow recession hydrograph of a spring is expected to be a mere expression of the averaged hydrogeological features of the discharging aquifer. Because of that, the recession trends of nonkarstic springs are more likely to fit simpler models such as the linearized Maillet solution, compared to streams. For instance, Dewandel et al. (2003) showed that the recession hydrographs of springs fed by ophiolite hard rock aquifers were well reproduced either by the Maillet or the Boussinesq models, depending on aquifer features.

Notwithstanding the limitations associated with the Maillet model, it was decided to use this equation to analyze base-flow recession, for two reasons: (1) the correlation between annual and base-flow discharge proposed by Gargini et al. (2008), which is the object of validation in this study, was built on that model; (2) the model allows a simple and straightforward analysis of recession hydrographs, which is consistent with the deliberately simple approach that is proposed here for recharge estimation. It is worth noting that the recession analysis is performed with the sole scope of arranging the spring hydrographs into different classes (i.e., ranges of α values) representing different “types” of recession behaviors (see previous section). To this scope, a certain degree of approximation caused by linearization may be tolerable. Moreover, the subdivision in recession classes was validated using a second type of analysis: the so-called “recession plot” (Brutsaert and Nieber 1977) which represents another derivation of the quadratic Boussinesq model. In such analysis, the first time derivative of the discharge (dQ/dt) is plotted as a function of mean discharge (Q_m) within the dt interval, on a log-log plot. The relationship is expected to be linear with a variable range of slopes. The analysis has been successfully applied in hydrological studies of stream recession (e.g. Kirchner 2009; Shaw and Riha 2012). The slopes of the recession plots were compared with the α of Maillet to verify if the same arrangement in recession classes proposed by Gargini et al. (2008) was still discernible. More details on the development of recession plots are in the ESM.

For the application of the Maillet model, a time period corresponding to base-flow recession was selected within the two hydrogeologic years covered by the monitoring. In both cases, the recession season was initiated on July 1st and lasted up until the end of the hydrogeologic year, in analogy with the recession period previously considered by Gargini et al. (2008). The choice to fix a “standard” beginning of the recession season to July 1st (regardless to the specific shape of each hydrograph) was made to test the feasibility of proposing a standard monitoring period for the estimation of recharge in climate zones similar to that of the Northern Apennines. As a first step, the recession hydrographs were handled to minimize disturbances from significant recharge events. In particular, only the progressively decreasing values of discharge were considered, making sure to keep at least three measurements for each spring. Attention was also paid to obtain a good fit of the Q data along an exponential trend line with R² > 0.90. The Maillet coefficient α was extracted from the equation of the same exponential trend line.

A hydrogeologic year was identified between 25 October 2012 and 28 August 2013 at Mt. Prinzera and between 17 October 2016 and 7 September 2017 at Mt. Zirone. Q_A values in the range of 0.04 to 2.69 L/s and of 0.11 to 1.42 L/s were determined from field measurements at Mt. Prinzera and Mt. Zirone, respectively, whereas Q_S values ranged between 0.01 and 0.85 L/s at Mt. Prinzera and between 0.04 and 1.30 L/s at Mt. Zirone (Table 2). The complete data-set of Q measurements is in the ESM together with the complete spring hydrographs and rainfall data from preexisting meteorological stations. Recession analysis with the Maillet model was performed on each spring hydrograph (Fig. 5) to determine α and the corresponding A and B parameters that drive the correlation between Q_A and Q_S.

All the seven springs fed by the Mt. Prinzera aquifer, except for P01, had at least one out of seven measurements of Q excluded from the recession analysis. In particular, the Q measurement of 14 July showed a deviation from the recession trend (increasing Q compared to the previous measurement) in the hydrographs of P02–P07, most likely induced by the rainfall events between 11 and 14 July (35 mm in total; see ESM). For springs P02 and P07, one and two other Q values were excluded from the analysis, respectively, for the same reason as already mentioned. In spring P05, a decreasing trend of four consecutive Q measurements was identified starting from 21 July; the former three values were excluded because they did not follow a decreasing trend. In general, the recession hydrographs of Mt. Prinzera suggest that all the springs, with the exception of P01, are responsive to rainfall events occurring during the low-flow season, likely because these are connected to shallower groundwater flow systems with a lower bulk discharge compared to spring P01.

Six measurements of Q were performed at the five springs of Mt. Zirone during the low-flow season. In springs Z01, Z02 and Z04, the Q measurements of 15 and 25 July were excluded from the recession analysis since these are higher than the preceding Q value on the hydrograph. These anomalies are likely related to the rainfall events between 11 and 14 July (38 mm in total), and that of 24 June (10 mm). In the case of spring Z05, the Q values deviating from the decreasing trend and excluded from the analysis are that of 25 July and 8 August. The deviation of 8 August may be related to a local rainfall not detected by the available pluviometers. Spring Z03 shows a decreasing trend of three consecutive Q measurements starting from 25 July; the former three values on the hydrograph were not considered since they do not follow a decreasing trend. In general, the recession hydrographs of the springs of Mt. Zirone appear less smooth compared to Mt. Prinzera. This is also reflected by the lower degree of correlation of the Q measurements on the semi-log plots, with Z04 and Z05 showing a R² of 0.89 and 0.81, respectively, marginally below the fixed threshold of 0.90. This may be due to a higher reactivity to rainfall events in the Mt. Zirone aquifer compared to Mt. Prinzera, possibly driven by some intrinsic features of the aquifer, e.g. smaller aquifer basin and/or higher permeability, shallower and/or faster recharge pathways. Alternatively, the less frequent and more abundant rainfall events of the summer 2017 (Mt. Zirone monitoring) may have caused more significant deviations of Q from the decreasing recession trend, compared to summer 2013 (Mt. Prinzera monitoring). In particular, 13 days of rainfall were registered out of 69 with an average of 14 mm/day during the summer of the hydrogeologic year 2016–2017, whereas during the summer of year 2012–2013, rainfall events occurred on 17 out of 58 days with an average of 6 mm/day. Nevertheless, such interannual variability was considered as an opportunity to verify the effectiveness of the proposed method in different meteorological conditions.

The Maillet coefficient α ranges between 2.7 × 10⁻² and 3.0 × 10⁻³ days⁻¹ in the springs of Mt. Prinzera and between 4.3 × 10⁻² and 3.0 × 10⁻³ days⁻¹ in the springs of Mt. Zirone. In Table 2, each spring is ranked according to the classes of α identified by Gargini et al. (2008). The coefficient α of each spring was compared with the slope of the recession plot (S) of the same spring, showing a good linear correlation between the two on a log-log plot with R² of 0.87 (Fig. 6). The comparison suggests that the classes of α proposed by Gargini et al. (2008) are still discernible when considering the slope of a recession plot. Because of this observation, the Maillet model is considered to be a proper tool for identifying classes of recession behavior in the type of springs that are investigated within this research.

The values of Q_AE range between 0.02 and 2.28 L/s at Mt. Prinzera and between 0.15 and 1.48 L/s at Mt. Zirone. A comparison between Q_A and Q_AE is shown in Fig. 7. In the case of Mt. Prinzera, the NRMSD between Q_A and Q_AE is 6.3%, suggesting an overall good prediction. P06 and P07 are the springs where Q_A and Q_AE show the greatest differences compared to absolute values of averaged annual discharge. It is worth noting that these are the springs with the lowest averaged annual flow rates in the Mt. Prinzera area, in the order of 1 × 10⁻² L/s, and the Q measurements in the field were likely affected by a higher relative error compared to the other springs. At Mt. Zirone, Q_A and Q_AE show larger differences between each other compared to the springs of Mt. Prinzera, with an NRMSD of 14.5%. The noisier summer hydrographs typically observed in the Mt. Zirone springs along with the smaller number of available Q measurements compared to Mt. Prinzera may have lead to higher uncertainties in the Q_AE prediction. In the case of Mt. Zirone, a continuous monitoring of flow rates (or a higher frequency of discontinuous measurements) may have helped increase the accuracy of Q_S estimates and the consequent prediction of Q_AE.

The sum of Q_A in the springs of Mt. Prinzera is equal to 3.79 L/s, whereas the sum of Q_AE is 3.41 L/s, with a small difference between the two of 0.38 L/s. In the case of Mt. Zirone, the sum of Q_A and Q_AE is respectively 2.31 and 2.41 L/s, with a difference of 0.11 L/s.

Since the monitored springs of Mt. Prinzera and Mt. Zirone are the discharge outlets of a well-delimited aquifer system, the sum of averaged annual discharges of the two groups of springs over their catchment area corresponds to the recharge (“R” from now on) of the aquifer, assuming a steady-state condition over the hydrogeologic year. Such a condition is plausible in the presence of short and relatively quick groundwater flow paths from the recharge area to the discharge points. Short and quick flow paths were inferred in the two aquifers based on the temperature and electrical conductivity of spring water (see data of T and EC in the ESM). In detail, the average annual water temperature ranges between 10.3 and 12.5 °C at the springs of Mt. Prinzera and between 10.4 and 12.5 °C at the springs of Mt. Zirone, showing values very similar or slightly lower than the average annual air temperature measured at the selected meteorological stations (12.0 °C in hydrogeologic year 2012–2013 and 12.5 °C in 2016–2017, respectively for Mt. Prinzera and Mt. Zirone). Shallow groundwater temperature is expected to be 1 to 2 °C higher than the average annual air temperature (Anderson 2005; Benz et al. 2017). If the temperature of groundwater discharging from springs is similar to air, it likely means that the temperature signal of the recharging water is preserved down to the discharge points, which can be explained assuming short and shallow flow paths through the aquifer. The average annual EC of spring water ranges between 281 and 474 μS/cm at Mt. Prinzera and between 218 and 522 μS/cm at Mt. Zirone. Such values are in the low range of EC previously observed in literature for groundwater in ophiolitic aquifers (typically up to 2,000 μS/cm; e.g. Abdalla et al. 2016; Dewandel et al. 2005; Güler et al. 2017), suggesting a short groundwater–rock interaction time. In particular, EC values <850 μS/cm are representative of quick shallow groundwater circulation following Dewandel et al. (2005).

For the estimation of R, a total catchment area of 771,478 m² was considered for Mt. Prinzera and of 534,000 m² for Mt. Zirone (i.e. the extent of the ophiolitic outcrops), whereas the monitored hydrogeologic years lasted for 307 and 325 days, respectively. R values of 130 and 117 mm throughout the hydrogeologic year was estimated for the Mt. Prinzera from Q_A and Q_AE, respectively, whereas at Mt. Zirone R values of 121 and 127 mm were derived from Q_A and Q_AE, respectively. In both settings, estimation of R from Q_A or Q_AE shows small differences (13 mm at Mt. Prinzera, corresponding to the 10.6% of averaged R, and 6 mm for Mt. Zirone, equal to 4.5% of averaged R).

The values of R are consistent with that estimated from an annual water budget in the two aquifers (R_wb; see ESM), when assuming a much higher infiltration potential at Mt. Zirone compared to Mt. Prinzera. Such higher infiltration is justified by a more pronounced stress-release condition (testified by rock slope deformations and fractures with larger aperture and higher persistence) and a higher percent of bedrock outcrop at Mt. Zirone compared to Mt. Prinzera, as discussed in section S6 of the ESM.

A coefficient of infiltration (C) was estimated for the two aquifers of Mt. Prinzera and Mt. Zirone corresponding to the ratio between R throughout the monitored hydrogeologic years (derived by Q_A or Q_AE) and the precipitation over the aquifer catchment during the same time span (P, equal to 1,011 and 632 mm, from Mt. Prinzera and Mt. Zirone, respectively; see ESM). The estimated C values are 0.13 or 0.12 at Mt. Prinzera, and 0.19 or 0.20 at Mt. Zirone, starting from Q_A or Q_AE, respectively. The higher C values detected for Mt. Zirone compared to Mt. Prinzera are consistent with the observed higher reactivity to rainfall events for Mt. Zirone, suggesting a higher hydraulic conductivity or the occurrence of faster or preferential recharge pathways compared to Mt. Prinzera. The hypothesis is also consistent with the formerly inferred higher infiltration potential compared to Mt. Prinzera. The values of C estimated for Mt. Prinzera and Mt. Zirone are similar to that experimentally derived for Northern Apennine turbiditic aquifers by various authors, ranging between 0.13 and 0.17 (Gargini et al. 2014; Piccinini et al. 2013; Vincenzi et al. 2014). Such similarity in terms of hydrodynamic properties also enhances the idea that the turbiditic units in the Northern Apennines behave as hard rock aquifers as much as peridotitic ophiolites.