Groundwater flow dynamics of weathered hard-rock aquifers under climate-change conditions: an illustrative example of numerical modeling through the equivalent porous media approach in the north-western Pyrenees (France)

Abstract

A numerical groundwater model of the weathered crystalline aquifer of Ursuya (a major water source for the north-western Pyrenees region, south-western France) has been computed based on monitoring of hydrological, hydrodynamic and meteorological parameters over 3 years. The equivalent porous media model was used to simulate groundwater flow in the different layers of the weathered profile: from surface to depth, the weathered layer (5 · 10⁻⁸ ≤ K ≤ 5 ·  10⁻⁷ m s⁻¹), the transition layer (7 · 10⁻⁸ ≤ K ≤ 1 ·  10⁻⁵ m s⁻¹, the highest values being along major discontinuities), two fissured layers (3.5 · 10⁻⁸ ≤ K ≤ 5 ·   10⁻⁴ m s⁻¹, depending on weathering profile conditions and on the existence of active fractures), and the hard-rock basement simulated with a negligible hydraulic conductivity (K = 1 10 ⁻⁹). Hydrodynamic properties of these five calculation layers demonstrate both the impact of the weathering degree and of the discontinuities on the groundwater flow. The great agreement between simulated and observed hydraulic conditions allowed for validation of the methodology and its proposed use for application on analogous aquifers. With the aim of long-term management of this strategic aquifer, the model was then used to evaluate the impact of climate change on the groundwater resource. The simulations performed according to the most pessimistic climatic scenario until 2050 show a low sensitivity of the aquifer. The decreasing trend of the natural discharge is estimated at about −360 m³ y⁻¹ for recharge decreasing at about −5.6 mm y⁻¹ (0.8 % of annual recharge).

Un modèle numérique d’écoulement d’eaux souterraines de l’aquifère cristallin altéré d’Ursuya (une ressource en eau majeure dans le nord-ouest des Pyrénées, sud-ouest de la France) a été exécuté sur la base du suivi des paramètres hydrologiques, hydrodynamiques et météorologiques sur trois ans. Le modèle équivalent milieu poreux a été utilisé pour simuler les écoulements d’eaux souterraines dans les différentes couches du profil d’altération : de la surface vers la profondeur, la couche altérée (5 · 10⁻⁸ ≤ K ≤ 5 ·   10⁻⁷ m s⁻¹), le niveau de transition (7 · 10⁻⁸ ≤ K ≤ 1 ·  10⁻⁵ m s⁻¹, les valeurs les plus élevées étant le long des principales discontinuités), deux horizons fissurés (3.5 · 10⁻⁸ ≤ K ≤ 5 ·   10⁻⁴ m s⁻¹, dépendant des conditions du profil d’altération et de l’existence de fractures actives), et le socle simulé avec une conductivité hydraulique négligeable (K = 1 10 ⁻⁹). Les propriétés hydrauliques de ces cinq couches de calcul démontrent à la fois l’impact du degré d’altération et des discontinuités sur l’écoulement des eaux souterraines. Le bon accord entre les conditions hydrauliques simulés et observés ont permis de valider la méthodologie et son utilisation proposée pour l’application à des aquifères analogues. Dans le but d’une gestion à long terme de cet aquifère stratégique, le modèle a été ensuite utilisé pour évaluer l’impact du changement climatique sur les ressources en eaux souterraines. Les simulations réalisées selon le scénario climatique le plus pessimiste jusqu’en 2050 montrent une faible sensibilité de l’aquifère. La tendance à la baisse du débit naturel est estimée à environ −360 m³ a⁻¹ pour une recharge diminuant d’environ −5.6 mm a⁻¹ (0.8 % de la recharge annuelle).

Se calculó un modelo numérico de las aguas subterráneas del acuífero cristalino meteorizado de Ursula (una importante fuente de agua para la región noroeste de los Pirineos, suroeste de Francia) basándose en el control de los parámetros hidrológicos, hidrodinámicos y meteorológicas lo largo de tres años. El modelo de medios porosos equivalentes se utilizó para simular el flujo del agua subterránea en las diferentes capas del perfil meteorizado: desde la superficie hasta la profundidad, la capa meteorizada (5 · 10⁻⁸ ≤ K ≤ 5 ·   10⁻⁷ m s⁻¹), la capa de transición (7 · 10⁻⁸ ≤ K ≤ 1 ·   10⁻⁵ m s⁻¹, siendo los valores más altos a lo largo de las principales discontinuidades), dos capas fisuradas (3.5 · 10⁻⁸ ≤ K ≤ 5 ·   10⁻⁴ m s⁻¹, dependiendo de las condiciones del perfil meteorizado y de la existencia de fracturas activas), y el basamento de roca dura simulado con una conductividad hidráulica insignificante (K = 1 10 ⁻⁹). Las propiedades hidrodinámicas de estas cinco capas de cálculo demuestran el impacto tanto del grado de meteorización como de las discontinuidades en el flujo del agua subterránea. Un muy buen acuerdo entre las condiciones hidráulicas simuladas y las observadas permiten la validación de la metodología y su uso propuesto para su aplicación en acuíferos análogos. Con el objetivo de una gestión estratégica a largo plazo de este acuífero, a continuación, se utilizó un modelo para evaluar el impacto del cambio climático sobre los recursos de agua subterránea. Las simulaciones realizadas de acuerdo con el escenario climático más pesimista hasta 2050 muestran una baja sensibilidad del acuífero. La tendencia a la disminución de la descarga natural se estima en aproximadamente −360 m³ año⁻¹ para una disminución de la recarga en alrededor de −5.6 mm año⁻¹ (0.8 % de la recarga anual).

根据过去三年的水文、水动力和气象参数监测结果,计算了Ursuya风化结晶岩含水层(法国西南部比利牛斯山脉西北部的主要水源)地下水数值模型。采用等量孔隙介质模型模拟了风化剖面不同地层的地下水水流:从地表到深部,风化层(5 · 10⁻⁸ ≤ K ≤ 5 ·   10⁻⁷ m s⁻¹),过渡层((7 · 10⁻⁸ ≤ K ≤ 1 ·   10⁻⁵ m s⁻¹,沿主要间断点的最高值),两个断裂层(3.5 · 10⁻⁸ ≤ K ≤ 5 ·   10⁻⁴ m s⁻¹,取决于风化剖面条件和是否存在活跃断裂),及用可以忽略的水力传导率(K)模拟的硬岩基底。这五个计算层的水动力特性显示出了风化程度和间断点对地下水流的影响。模拟的水力情况和观测到的水力情况高度一致可以确认方法的有效性,并可在类似含水层中应用。为了长期管理这个具有战略性的含水层,因此模型用来评估气候变化对地下水资源的影响。根据到2050年最悲观的气候情景,进行的模拟显示出含水层的敏感性很低。天然排泄量下降的趋势估算为大约-360 m³ y⁻¹,因为补给量下降大约为-5.6 mm y⁻¹(每年补给量的0.8 %)。

Um modelo numérico de águas subterrâneas do aquífero cristalino intemperizado de Ursuya (uma das principais fontes de água do noroeste da região dos Pirineus, sudeste da França) tem sido calculado baseado no monitoramento de parâmetros hidrológicos, hidrodinâmicos e meteorológicos ao longo de três anos. O modelo de meios porosos equivalente foi usado para simular o escoamento das águas subterrâneas em diferentes camadas do perfil intemperizado: a partir da superfície até a profundidade, a camada intemperizada (5 · 10⁻⁸ ≤ K ≤ 5 ·   10⁻⁷ m s⁻¹), a camada de transição (7 · 10⁻⁸ ≤ K ≤ 1 ·   10⁻⁵ m s⁻¹, sendo os maiores valores ao longo das principais descontinuidades), duas camadas fissuradas (3.5 · 10⁻⁸ ≤ K ≤ 5 ·   10⁻⁴ m s⁻¹, dependendo das condições dos perfis intemperizados e da existência de fraturas ativas), e o embasamento de rocha dura simulado com uma condutividade hidráulica (K = 1 10 ⁻⁹) negligenciada. As propriedades hidrodinâmicas dessas cinco camadas de cálculo demonstraram tanto o impacto do grau do intemperismo quanto o das descontinuidades no escoamento de águas subterrâneas. A ótima concordância entre as condições hidráulicas simuladas e as observadas permitiu a validação da metodologia e sua proposta de utilização para aplicação em aquíferos análogos. Com o objetivo de gerenciamento a longo prazo desse aquífero estratégico, o modelo foi, então, usado para avaliar o impacto das mudanças climáticas nos recursos hídricos subterrâneos. O desempenho das simulações de acordo com o cenário climático mais pessimista até 2050 mostra uma baixa sensibilidade do aquífero. A tendência da diminuição da descarga natural é estimada em aproximadamente −360 m³ y⁻¹ para uma diminuição da recarga em aproximadamente −5.6 mm y⁻¹ (0.8 % da recarga anual).

Introduction

Water resources (surface water and groundwater) are directly affected by global warming. The temporal and spatial evolutions of the hydrological cycle induced by climate change are largely documented (e.g. Brouyère et al. 2004; Kumar 2012; Neukum and Azzam 2012; Zhou et al. 2010). Many scientific studies have been carried out focusing on surface-water systems (Treidel et al. 2012), but before 2010 only a few studies discussed the evolution of groundwater resources in the next decades (e.g. Aguilera and Murillo 2009; Bloomfield et al. 2003; Bouraoui et al. 1999; Eckhardt and Ulbrich 2003). However, the impact of climate variations on groundwater resources is an important aspect for future water management (Taylor et al. 2012). Nowadays, this topic is handled more frequently in the literature (e.g. Allen et al. 2010; Virdi et al. 2013; Bertrand et al. 2014; Klove et al. 2014; Landes et al. 2014), especially on the theme of models for forecasting groundwater flow for efficient groundwater management (e.g. Mahmoodzadeh et al. 2014; Molina et al. 2013; Shamir et al. 2015).

The study described here deals with this topic in the specific hydrogeological context of fractured-rock aquifers. The materials of the study area are characterized by a high degree of weathering, and can be considered as an interesting hard rock aquifer comparable to those developed in tropical and sub-tropical areas where groundwater modeling is poorly documented (e.g. Australia, Banks et al. 2009; Malawi, Chilton and Smith-Carington 1984; Burkina Faso, Courtois et al. 2010; India, Dewandel et al. 2006; Central African Republic, Djebebe-Ndjiguim et al. 2013). Fractured-rock environments are an important field of study due to their abundance and increasing uses for water supply worldwide (Ayraud et al. 2008; Bertrand et al. 2010; Glynn and Plummer 2005; Berkowitz 2002).

Different approaches exist to model groundwater flow in discontinuous aquifers. The ‘equivalent porous media’ approach has been used in this study (e.g. Abusaada and Sauter 2013; Boronina et al. 2003; Carrera et al. 1990; Davison 1985; Hsieh and Neuman 1985). Here, the primary and secondary porosity and the hydraulic conductivity distribution are replaced by a continuous porous medium having equivalent hydraulic properties (Cook 2003).

The modeling strategy described in this report is applied to the gneissic aquifer of the Ursuya massif, in a specific geological context of hard rock aquifers exhibiting a high degree of weathering. The weathering profile developed in hard rock aquifers is of primary importance for flow conditions in such media (Ayraud et al. 2008; Dewandel et al. 2006; Hrkal et al. 2009; Jaunat et al. 2012; Wyns et al. 2004). Indeed, numerous studies highlight that the degree of weathering is one of the major parameters constraining the groundwater flows in hard rock media (Koïta et al. 2013; Lachassagne et al. 2011). The first aim of the study is to assess the impact of this weathering profile and of the geological discontinuities on groundwater flows by the use of numerical modelling tools. The study also aims to assess the impact of the regional projected climate conditions on the local groundwater resources since the study site is one of the main drinking-water-supply resources of the north-western Pyrenees region.

The differential groundwater flowpaths of this system have been previously defined according to geochemical and isotopic investigations on groundwater and recharge waters (Jaunat et al. 2012, 2013). These results, with a significant database of 3 years, and with the monitoring of runoff, hydraulic head and climate parameters, allowed the establishment of a groundwater flow model in finite elements. Long-term predictive simulations were then performed (up to 2050) to estimate the potential evolution of the groundwater resources in relation to climate change.

General setting

Geological situation

Located in the north-western Pyrenees (south-western France), 25 km from Bayonne city and from the Atlantic coast, the Ursuya Massif is the first relief of the north-western part of the Pyrenees coming from the north. The Ursuya Mount is constituted of Precambrian crystalline metamorphic formations (basic gneisses and pargneisses; Boissonnas et al. 1974) distributed between the Nive River bed—at 40 m above sea level (ASL) and 678 mASL (Ursuya Mount, Fig. 1a). Thin sections of metamorphosed limestone have also been observed in some boreholes (Armand et al. 1995; Boissonnas et al. 1974) but their distribution is poorly defined. It is the same for some pegmatite lenses (Ondarroa et al. 1998).

Fig. 1

a Ursuya Massif topography, lithology and location of monitoring points; b discontinuities runoff network and location of gauging stations. These maps are the result of the combination of Boissonnas et al. (1974) data, aerial photo imagery interpretation, field observations and drill cutting information

These Precambrian crystalline formations are strongly fractured and show a high density of lineaments (Fig. 1b, Boissonnas et al. 1974; Jaunat 2012) mainly attributed to the Hercynian tectonic but also to a post-Hercynian evolution (Engeser and Schwentke 1986; Feuillée and Rat 1971; Larrasoaña et al. 2003; Turner 1996). The map of lineaments shows a NW–SE major orientation, which is in agreement with the geological context of the Pyrenees (e.g. Mattauer and Henry 1974).

The study site (Fig. 1a) is composed of an important layer of weathered material (frequently more than 10 m thick) covering a fissured layer. The transition between these two layers is gradual with an increasing weathering from the fissured to the weathered layer. This lithology is typical of crystalline aquifer profiles with three superimposed layers (from surface to depth: weathered, transition and fissured) when the profile is completely preserved (Chilton and Smith-Carington 1984; Chilton and Foster 1995; Courtois et al. 2010; Dewandel et al. 2006; Hrkal et al. 2009; Lachassagne et al. 2011; Wyns et al. 2004).

Hydroclimatology

Recorded data

The climate of the study area is temperate oceanic. The mean annual precipitation amount in the weather station of Biarritz-Anglet, 25 km from the study area (−1°31′54″; 43°28′18″; 69 mASL), is about 1,510 mm y⁻¹ (calculated from 1964–2012 data from Meteo France). The estimated effective rainfall, using a Penman–Monteith computation, is 653 mm y⁻¹ (Jaunat et al. 2013). The effective rainfall is the amount of rainfall remaining after evapotranspiration and which will be available for both runoff and groundwater recharge (Hiscock 2005).

Rainfall height (mm), air temperature, relative humidity, wind speed, sunshine and atmospheric pressure have also been measured directly at a dedicated weather station on the Ursuya Massif (550 mASL, Fig. 1a) during the study period. The knowledge of these parameters provides an accurate characterisation of annual precipitation but also evapotranspiration and effective rainfall of the study area. The mean annual precipitation and estimated effective rainfall on the Ursuya Mount, calculated from this monitoring during the 3 years of measurements, are 1,440 and 624 mm y⁻¹ respectively. The effective rainfall corresponds to 43 % of the total precipitation, which is similar to the Meteo France record at the weather station of Biarritz-Anglet (43 % for 1964–2012).

Climate projections

Besides high uncertainties, Pagé and Terray (2010) and Chauveau et al. (2013) agree with a decreasing trend of precipitation in the southwest of France (from 0 to −15 % until 2070) especially in western Pyrenees. For temperature, an increase between 1.5 and 2.8 °C is expected until 2050 for the southwest of France, but the Atlantic Ocean has a high capacity to absorb energy and to reduce the warming rates in the areas near the coast (Merot et al. 2013). The rising temperatures will result in an increase in the evapotranspiration rate and consequently, combined with a decrease in rainfall amount, aquifer recharge is expected to decrease in the Western Pyrenees region for the next few decades.

Hydrogeological properties

Significant groundwater flows take place in these formations. Between 1994 and 2003, 43 boreholes were drilled over the Ursuya Massif area in order to respond to the increasing water demand in the north-western Pyrenees. Of these boreholes, 34 were dry or too unproductive to allow viable sustainable exploitation. Presently, only 8 boreholes still exist on the study area (Fig. 1a and Table 1), of which merely 5 are operating (Osp5, Ar3, Ar5, Pit11 and Pit16). These boreholes have allowed lots of geological observations despite the few hydrodynamic investigations that were carried out. The hydraulic conductivities vary from 2 · 10⁻⁷ to 1 · 10⁻⁴ m s⁻¹, storage coefficients from 9 · 10⁻⁵ to 1 · 10⁻² and transmissivity from 1 · 10⁻⁵ to 4 · 10⁻³ m s⁻². These values and the observed heterogeneity are characteristic of fissured media (Blouin et al. 2013; Dewandel et al. 2005; Maréchal et al. 2004; Taylor and Howard 2000). In addition to these boreholes, 190 springs have been recognized among which 101 are exploited (Fig. 1a). These springs feed an important surface flow network often developed along discontinuities (Fig. 1b). This surface drainage system is in constant relation with groundwater, draining or feeding it, depending on the geological and geomorphological contexts and also on the hydrodynamic level of the water table.

Table 1 Characteristics of the boreholes existing in the study area

Based on groundwater geochemistry, isotopic analyses, modelled ages and the lithological conditions described earlier, different flowpath configurations have been described for the aquifer of the Ursuya Massif in Jaunat et al. (2012). Thus, in the fissured zone, when it is outcropping, the shallow water flows rapidly along the fissures of the gneissic rock. Where the fissured layer is underlying a weathered one, the groundwater can circulate in both. According to the degree of weathering, mixing between water from these two layers is allowed.

Methods

Groundwater modeling

The numerical translation of the conceptual model described previously has been realized in finite elements with the FEFLOW code 6.0 (Finite Element Subsurface Flow and Transport Simulation System; Trefry and Muffels 2007). The development of a numerical hydrodynamic model requires several steps: implementation of geometry, hydrodynamic parameters, values of recharge rates and volumes of groundwater withdrawals.

Horizontal and vertical discretization

The extent of the numerical model covers an area of 45 km² discretized via a triangular mesh of 74,777 elements per layers (Fig. 2a). This irregular triangulation is based on the set of points with available information; thus, the mesh is refined around springs, wells, streams and along the mapped lineaments.

Fig. 2

Geometry of the finite element groundwater model (a magnification factor of 2 is applied to the vertical axis; a full area; b zoomed cross section)

The vertical discretization of the different layers has been reproduced through five calculation layers: the weathered layer, the transition one, two fissured layers and the bedrock. Paragneisses and gneisses, with similar hydraulic characteristics, have not been distinguished in the numerical model.

The representation of the horizontal extension of these layers is based on the local map (Fig. 1a). The vertical extent of each layer was approached through the lithological descriptions obtained from the 26 drillings conducted on this area over the past decades and for which information is available, literature review—Table S1 of the electronic supplementary material (ESM) and field investigations.

The weathered layer, when existing, is represented by a layer, 20 m thick maximum with an increasing thickness gradient (Fig. 2b). The transition layer between weathered and fissured materials is simulated through a layer 10 m thick maximum also with a thickness gradient. The two fissured layers are simulated by an upper layer 15 m thick and a maximum thickness of the underlying layer of 20 m (Fig. 2b). The hard rock basement is simulated through an idealized layer hydrodynamically homogenous with negligible hydraulic conductivity and specific storage (K = 1 · 10⁻⁹ m s⁻¹ and S _s = 1 · 10⁻⁶ m⁻¹; e.g. Maréchal et al. 2004; Walker et al. 2001) and highly thick (from the bottom of the fissured layer to −600 mASL) avoiding edge effects in the numerical calculations.

Input and calibration data

Boundary conditions

Potential groundwater flows and exchanges through the limits of the aquifer have been computed with fixed hydraulic heads (Dirichlet-type boundary conditions). Only the western limit formed by the Nive River (Fig. 1) is simulated through Cauchy-type boundary conditions. The relationships between the surface flow network and the sub-surface were also simulated by Cauchy-type boundary conditions all over the modelled area. These boundary conditions allow simulation of interactions between streams and groundwater, through a layer that is more or less clogged (Diersch 2010; Trefry and Muffels 2007). The transfer rate is then defined through this conductance parameter which has been adjusted during the calibration procedure.

Hydrodynamic parameters

In order to simulate accurate groundwater flow, the values of specific storage and hydraulic conductivity used in the model are based on data from pumping tests conducted in the non-exploited boreholes still existing on the study area (Table 1). Given the low density of this dataset and its poor spatial distribution, a bibliographical review has been conducted in order to ascertain and validate hydrodynamic parameters of the different layers of the weathered profile of the aquifer of the Ursuya Massif (Table S2 of the ESM). These values were then adjusted during the calibration phase in steady state and transient regimes. These adjustments are based on lithological and structural properties and concern especially major fractures that can act as preferential flow pathway. Data on aperture, filling, continuity or wall roughness for individual discontinuities are inaccessible at the study site scale. Nevertheless, the localization of the discontinuities network (Fig. 1b) has been essential in the calibration process in order to implement preferential flow conditions along it and to ascertain its role in the groundwater flows. Lithological field observations were also relevant to adjust hydrodynamic properties. Thus, clay and sand contents in weathered and transition layers, presence of pegmatite and metamorphosed limestone lenses, and rate of fissuring of the fissured layers are some properties that were used to localize adjustments of hydrodynamic parameters in a realistic way.

Recharge, withdrawals and hydraulic head

The weekly volumes of withdrawals in the exploited boreholes (Ar5, Osp5, Pit11 and Pit 16; Fig. 1a) were provided by operators. The measured hydraulic heads (hourly to weekly time steps based on different operators) have been used for the model calibration at transient state.

Hydraulic heads of non-exploited boreholes (Ip2, Osp9, Pe4 and Pe5; Fig. 1a) and runoff volumes recorded at the height gauging stations (Fig. 1b) have also been used for the model calibration. Hydraulic heads in non-exploited boreholes and water levels in streams were measured by automatic water level sensors “Schlumberger Mini-Diver” and were recorded at an hourly time step. For the streams, five to seven gaugings per station were conducted, distributed throughout the water cycle, in order to convert the measured water level to flow rate. These measurements were conducted continually between August 2009 and June 2012.

The monitoring of weather parameters directly at the study site allows one to define accurate precipitation conditions and effective rainfall amount on a weekly basis. The recharge of the aquifer (part of the effective rainfall that reaches the saturated zone) has been computed based on these results, and considering the influences of the vegetation cover and the soil characteristics on the amount of infiltrated water. Then, different sectors where defined from this analyse and adjusted during the steady-state calibration phase, with extreme amounts of infiltration water between 20 % of the effective rainfall (mean about 80.4 mm y⁻¹) where the soil is thick and strongly clayey and 90 % of the effective rainfall (mean about 400 mm y⁻¹) where the soil is absent as is the vegetal cover (Armand et al. 1995). The mean annual volume of recharge water computed using these values corresponds to 8.3 · 10⁶ m³ y⁻¹ for the whole study area, which represents 0.2 m³ m⁻² y⁻¹.

Predictive simulation and groundwater response to climate change

Data used

In this study, spatial data from SCRATCH2010 models (produced by the CERFACS; European Centre for Research and Advanced Training in Scientific Computation; Pagé and Terray 2010), updated in 2012, has been used. The spatial resolution is about 8 km, with a monthly time step. The method of downscaling used for the production of these data is widely developed in Boé et al. (2006) and Boé and Terray (2008). This treatment was performed on data from the ARPEGE models V4.6 (research action on small and large scale) produced by the CNRM (National Centre for Meteorological Research).

Precipitation data and effective precipitation resulting from the A2 and B1 scenarios have been used in this study. The A2 and B1 scenarios, which were developed by the Intergovernmental Panel on Climate Change (IPCC), reflect two contrasting future greenhouse gas emission situations based on different hypotheses of economy and population trends in the future (IPCC 2013, 2014; Nakicénovic et al. 2000). A2 is characterized by high emissions of greenhouse gases and is considered as a pessimistic scenario, while B1 is considered as an optimistic one.

Simulation of climate change scenarios

Forecast simulations were performed for a period of 49 years, between 2001 and 2050. A monthly time step was adopted for these simulations and the amount of recharge water was estimated using the data presented earlier from the predictive scenarios. The forecasted amounts of effective precipitation have then been corrected with the soil and the vegetation factors previously discussed, in order to consider only the infiltration water in the numerical model.

The groundwater withdrawals were also introduced to achieve these forward simulations. Average monthly volumes were calculated using the 3 years of available data (July 2009 to July 2012). These monthly withdrawals were repeated identically during the 49 years of simulation. Without precise predictive demographic data, this treatment seems appropriate for the evaluation of the impact of climatic trends on groundwater resources in a realistic way (this fact will be discussed later on).

Results and discussion

Calibration and validation of the numerical model

Steady-state calibration

The numerical model has been initially calibrated in steady state, using the 2011 data, a period for which the available dataset is the most complete. This step allowed a first assessment of the model characteristics before switching to the transient state regime.

The steady-state calibration was based on the altitude of the 198 perennial springs identified in the study area. The steady-state calibration consisted of the restitution by the model of a hydraulic head pattern in agreement with the seeping altitude of these springs (Fig. 3). At the end of the calibration phase, 170 observation points showed a difference of less than 10 m between simulated and observed hydraulic heads, of which 120 are less than 5 m. Differences of about 10–15 m were observed for 22 calibration points and the simulated levels presented a difference of 15–20 m with the measured altitude for six springs. Besides this good correlation between computed and observed hydraulic heads, the mean absolute error (MAE, corresponding to the mean of the absolute value of the residual, Anderson et al. 2015) about 0.89 m revealed an overall good result.

Fig. 3

Correlation between simulated and observed hydraulic heads in steady state

The 3-year runoff-volume dataset has also been used for the calibration procedures. The exploited volumes from the springs emerging in the eight controlled watershed (Urr, Urc, Bas, Hey, Lat, Lou, Etc., Cos, Fig. 1b) were added to that measured at the gauging stations, in order to precisely identify groundwater outflows in these areas. These volumes were compared with the simulated outflows from the numerical model for the same areas. The results showed a positive correlation between simulated and measured outflows.

The simulated outflow for the whole watershed was slightly higher than the measured one (respectively 11,682,693 and 11,149,625 m³ y⁻¹), with a ratio [simulated volumes/measured volumes] of about 0.95.

Transient calibration

In a transient regime calibration, the simulation period should be long enough and the data available have to be adequate, accurate and complete. On the Ursuya Massif, recharge data, withdrawals and hydraulic head variations have been precisely recorded since July 2009. These data are recorded in different time steps (from hourly for recharge and hydraulic heads to weekly for exploited volumes); therefore, the model is calibrated in transient state over a period of 3 years (July 2009 to July 2012), at a weekly time step. Hourly values of recharge have been summed on a weekly basis and weekly means of hydraulic heads have been used for the calibration. Results are presented at an annual scale so as to facilitate the reporting of results.

The comparison of measured and simulated hydraulic heads shows a good restitution of the water table by the model (Fig. 4). The total mean absolute error (MAE) of about 1.9 m confirms the realism of the numerical model. The individual MAE is less than 1 m for the boreholes Ar5, Osp9 and Ip2 (respectively 0.74, 0.29 and 0.32 m, Fig. 4). It is slightly higher for Pit11, Pe5, Pe4 and Osp5 (respectively 1.56, 1.38, 2.62, 6.44 m, Fig. 4) but in an acceptable range beside the range of hydraulic heads variability of these boreholes.

Fig. 4

Simulated and observed hydraulic heads in transient state for boreholes between July 2009 and July 2012. MAE mean absolute error

Accuracy of flow conditions through hydrodynamic numerical modeling

The hydrodynamic properties of the calculation layers used in the numerical model of the Ursuya aquifer are presented in Fig. 5. Values of hydraulic conductivity are computed based on the local dataset and bibliographical review and are adjusted through the calibration process in steady and transient regimes. These implemented hydrodynamic properties allow for representing flow conditions quite close to field observations, and describe the strong influence of the weathered profile and of the hard rock discontinuities on the groundwater flow in crystalline aquifers.

Fig. 5

Maps of computed hydraulic conductivity for the four first layers. (Not shown: hydraulic conductivity of bedrock horizon is homogeneous with a value about 1 · 10⁻⁹ m s⁻¹)

These results allow the establishment of a conceptual model available for weathered hard rock aquifers with heterogeneous geographical weathering and erosion mechanisms (Fig. 5; Table 2):

Table 2 Ranges of hydraulic conductivities K (m s⁻¹) imputed in the Ursuya aquifer numerical model and summary of K along the weathered profile

• 1. The weathered layer, besides having a high porosity, always has low permeability (5 · 10⁻⁸ ≤ K ≤ 5 · 10⁻⁷ m s⁻¹ in the Ursuya Massif). This layer, when saturated, is considered as a capacitive one and ensures a storage function. The lowest values are here linked to differential weathering processes due to the presence of pegmatite (Boissonnas et al. 1974; Ondarroa et al. 1998) in one area of the study site (Olhasso on Fig. 5).

• 2. In the transition layer, the original structure of the bedrock is preserved. It is thus possible to observe the influence of regional fractures in this layer with higher values along major discontinuities (1 · 10⁻⁶ ≤ K ≤ 1 · 10⁻⁵ m s⁻¹). However, beside these preferential pathways, this layer displays a quite low permeability (7 · 10⁻⁸ ≤ K ≤ 3 · 10⁻⁷ m s⁻¹).

• 3. The fissured layer is generally characterized by a dense fissuring network and ensures a transmissive function along active discontinuities (1 · 10⁻⁶ ≤ K ≤ 5 · 10⁻⁴ m s⁻¹). In addition, this study’s results highlight the fact that the erosion process has to be considered. Indeed, where the weathered profile is complete, the hydraulic conductivity of the lower fissured layer is higher than that of the upper one (1 · 10⁻⁶ and 8 · 10⁻⁷ m s⁻¹ respectively).

• 4. Where the transitional and/or weathered materials are eroded, and in case of regional extent erosion processes, the porosity of the fissured layer could be clogged (4 · 10⁻⁸–7 · 10⁻⁸ m s⁻¹ for the upper fissured layer and 4 · 10⁻⁸–3.5 · 10⁻⁸ m s⁻¹ for the lower fissured one in Petchoenea zone and Ursuya Mount area in Fig. 5), except along some of the major discontinuities. A multiple phasing of the weathering processes can then be suspected. Fissures are progressively filled up by clay-rich materials and are then obliterated by the weathering process (Dewandel et al. 2006). These sealed fissures explain the low permeability observed in these parts of the aquifer.

• 5. On the other hand, if the weathered material’s disappearance is the result of recent fluvial erosion, it could be expected that the local porosity of fissures is still conductive and that the global hydraulic conductivity of the fissured layer is favourable to groundwater flow. This can be observed along the Nive River (Fig. 5), where the lack of weathered and transitional materials is related to mechanical processes, induced by fluvial erosion. In this case, the recent erosion of the unconsolidated surrounding materials allows a favourable porosity (Cho et al. 2003; Dewandel et al. 2006; Lachassagne et al. 2001; Taylor and Howard 2000) for both the upper and the lower fissured layers, with the value of K respectively between 7 · 10⁻⁶ and 1 · 10⁻⁶ m s⁻¹.

This model, displayed in Table 2, is in agreement with the results obtained during the past few decades on weathered profiles of crystalline aquifers (Acworth 1987; Courtois et al. 2010; Dewandel et al. 2006, 2011; Houston and Lewis 1988; Howard et al. 1992; Lachassagne et al. 2011; Maréchal et al. 2004; White et al. 2001; Wyns et al. 2004).

In the Sohano and Mendurria zones, the permeability is also lower, with values respectively between 4 · 10⁻⁸ and 8 · 10⁻⁷ m s⁻¹ for the upper fissured layer and 3.5 · 10⁻⁸ and 1 · 10⁻⁷ m s⁻¹ for the lower one. Unfortunately, these geographical sectors have never been subject to drilling and no data exist. The lack of knowledge around these areas does not allow for conclusions on the origin of the low permeability values; however, even if uncertainties remain about the geometry and the hydrodynamic properties implemented in these zones, they allow a realistic transcription of the global morphology of the hydraulic heads.

In the same way as for hydraulic conductivities, data on specific storage are based on local datasets and bibliographical review. They were then adjusted through the calibration process in a transient state regime. For the weathered layer, values from 1.3 · 10⁻⁴ to 5.5 · 10⁻³ m⁻¹ are reported in the literature (Dewandel et al. 2006; Domenico and Mifflin 1965), whereas concerning the fissured layer, values between 3.3 · 10⁻⁶ and 7.0 · 10⁻³ m⁻¹ are proposed (Dewandel et al. 2011; Domenico and Mifflin 1965; Lee and Lee 2000). The values obtained for the aquifer of Ursuya after the calibration phase are about 5 · 10⁻⁴ m⁻¹ for the weathered layer, 1 · 10⁻⁴ m⁻¹ for the transition layer, and 5 · 10⁻⁵ m⁻¹ for the two fissured layers. For these two layers, S _s is locally higher along some discontinuities (1 · 10⁻⁴–5 · 10⁻⁴ m⁻¹).

Impact of climate change on water resources

Recharge evolution

Future rainfall amount and effective precipitation estimated until 2050 are presented, at an annual time step, in Fig. 6. According to the A2 scenario, in the study area, annual rainfall amount is decreasing between 2001 and 2050 (−5.0 mm y⁻¹; R = 0.4) as is effective precipitation (−5.6 mm y⁻¹; R = 0.4). Indeed, despite low correlation coefficients induced by significant inter annual variations, a decreasing trend is highlighted (Fig. 6). The average rainfall calculated from data according to the B1 scenario between 2001 and 2050 does not show any declining trend, and neither does the effective precipitation (Fig. 6). According to the B1 scenario, the hydroclimatology of the region should be exposed to only little changes, thus this climatological hypothesis has not been simulated.

Fig. 6

Forecast of annual rainfall and effective precipitation (with corresponding regression lines: a _A2 = −5.6 mm y⁻¹ and R _A2 = 0.42; a _B1 = 0.3 mm y⁻¹ and R _B1 = 0.02) in the north-western Pyrenees until 2050, according to scenarios A2 and B1

Impact of climate change on hydraulic heads and groundwater storage

Estimated changes in rainfall amount are relatively low until 2050 in the north-western Pyrenees (Fig. 6), similarly the changes in groundwater heads and aquifer storage. The computation of the annual hydraulic head median is presented in Fig. 7, according to the forecasted scenario A2, for the eight monitored boreholes.

Fig. 7

Annual median of hydraulic heads in monitored boreholes simulated between 2005 and 2050 and corresponding regression line with 95 % confidence and prediction intervals

These simulated hydraulic heads show heterogeneous decreasing trends with a maximum depletion of −0.13 m y⁻¹ for Pit16 (decrease in head about 5.85 m over 45 years) and a minimum of −2.6 10⁻³ m y⁻¹ for Ar5 (decrease in head about 0.12 m over 45 years). The significance of this decreasing trend is not robust regarding the linear correlation coefficient for Ar5 and Osp9 (correlation coefficient of 0.30 and 0.40 respectively; Fig. 7). For the other observation points, the correlation is higher: R values from 0.49 (Pit16) to 0.73 for Pe4. The global mean of decrease in heads is about −2.12 m between 2005 and 2050 and is in the range of inter-annual variations of hydraulic heads.

Hydraulic heads observed from the few boreholes existing on the Ursuya Massif offer only a local vision of the hydrodynamic evolution of the aquifer. Groundwater storage is more representative at the aquifer scale. Figure 8 represents the annual volumes outgoing and ingoing the system and the annual balance. The outgoing volumes include natural and artificial ones, with an average groundwater storage withdrawal from boreholes of about 5,000 m³ y⁻¹. A logical correlation appears clearly between the storage fluxes computed and recharge amount estimations (Fig. 6). Thus, groundwater storage is in deficit during the driest years (e.g. 2006 in the historical period, 2018 and 2026 in the projected period), while the balance is positive during the rainy years (e.g. 2004 in the historical period, 2025 and 2030 in the projected period); however, the simulations do not highlight a reliable long-term trend, and consequently do not highlight a long-term trend for the recharge evolution in the coming decades.

Fig. 8

Annual volumes outgoing and ingoing the system and annual balance

The low impact of changes in recharge is thus clearly highlighted by the evolution of groundwater storage. These results also show that groundwater depletion by actual borehole exploitation is negligible beside the groundwater storage variations generated by inter-annual variations in recharge amount.

Impact of climate change on natural discharges

In order to precisely determine the potential changes on a global scale, the natural aquifer discharges have been computed to assess the groundwater volume variations in response to climate change. Therefore, this computed discharge represents the outflows of springs, which are used for drinking water and/or generate runoff on the Ursuya Massif (Fig. 1b); furthermore, the methodology used for the calibration procedure shows that the natural groundwater outflow is well transcribed by the numerical model.

The simulated annual median of natural discharge (Fig. 9) shows a significant decreasing trend of −360 m³ y⁻¹ (R = 0.6) between 2001 and 2050. Assuming a linear decrease, without considering the inter-annual variations, this tendency would lead to a total decrease of about 17,640 m³ of the natural outflow of the Ursuya aquifer in 2050, relative to the current discharge. Nevertheless, these results should be considered in the context of the actual exploited volumes from this aquifer (1.5 10⁶ m³ y⁻¹ from the springs and 1.8 10⁶ m³ y⁻¹ with boreholes). The calculated 50-year decrease corresponds to only 1.3 % of the exploited volumes of spring water and to 1.1 % of the total collected volume.

Fig. 9

Natural annual outflows simulated between 2005 and 2050 and corresponding regression line with 95 % confidence and prediction intervals

In conclusion, this long-term simulation, and the low decrease discharge calculated, has to be carefully considered. If climate change does not seem to be a crucial parameter in the five future decades for the Ursuya aquifer, longer simulations could show more worrying results.

Uncertainties and perspectives

The results of the simulation of climate change impacts on groundwater resources are naturally affected by a number of uncertainties (Demissie et al. 2015). Among them, some inaccuracies in the input geometry and hydrological data are difficult to avoid in numerical groundwater models at the aquifer scale (Ghanbari and Bravo 2011; Refsgaard et al. 2010), mainly because of the poor distribution of field data. Another source of inaccuracies in forecast models lies in the input of hydroclimatic data, the predictions of the future climatic variables (Nakicénovic et al. 2000) and the limitations of the current downscaling techniques (Jackson et al. 2011; Prudhomme and Davies 2008; Serrat-Capdevila et al. 2007). Therefore, it is obvious that the predictive modeling of groundwater evolution, under changing climate conditions, leads to an accumulation of uncertainties; thereby, the results of such simulations should be regarded only as a probable trend of evolution.

This tendency could largely be influenced by socio-economic development. On the one hand, the climate change models are based on worldwide socio-economic forecasts (Nakicénovic et al. 2000), while on the other hand, the local choices of policymakers have a strong influence on the groundwater evolution. Peculiarly, land cover changes will impact both the soil permeability and therefore the infiltration rate, as well as the groundwater use for irrigation purposes or alternatively for the drinking-water supply. Indeed, the evolution of groundwater use is another socio-economic parameter that should be considered regarding the demographic evolution. For example, in the Pyrénées-Atlantiques, which is the French administrative division where this study has been conducted, the forecasted demographic annual trend is between +7 and +12 % between 2010 and 2030 (INSEE 2010). It is then likely that the increase in water abstraction from the aquifer of Ursuya will be at least as impactful as the influence of climate change. Unfortunately, accurate prospective data on demographic and future water needs at a longer time scale, and at a local scale, are scarce, especially for such rural areas. In accordance with Döll (2009), Holman (2006), Holman et al. (2012), Kurylyk and MacQuarrie (2013), and Vouillamoz et al. (2015), it seems unreasonable to project climate change for a century and assume that water supply needs and land cover conditions will be intransient. Half a century in scale seems to be the upper limit that groundwater modeling simulation can provide relevant information for, even regardless of future demographic and land use changes. Beyond that time, pertinent groundwater modeling simulation needs increased effort to assess future changes of the socioeconomic environment, land cover, water uses and climate conditions.

Summary and conclusions

In this study, a groundwater model of a singular fissured aquifer with a high degree of weathering has been developed. The proposed methodology combined the finite element numerical solution with the equivalent porous media model, to adequately model the hydrogeological characteristics measured on the crystalline aquifer of Ursuya. The geometry of the conceptual model of hard rock aquifers developed over the last decade (Wyns et al. 2004) has been numerically transcribed thanks to five calculated layers representing the weathering profile of such media—one weathered layer separated from the two fissured ones by a transition zone, overlying the hard rock basement. The monitoring network, deployed in 2009 on the study site, not only allowed the research team to obtain accurate data (meteorological data, hydrodynamic parameters, geometry of the system) that can be used in the numerical model, but it also confirms the very good agreement between simulated and measured parameters (notably for hydraulic heads and runoff volumes). Hydrodynamic properties of Ursuya aquifer were precisely described and the predominant influence of the weathered profile was clarified as well as the role of the geological discontinuities in such a hard-rock aquifer with a high degree of weathering.

Regarding the aim of long-term management of this resource, forecast simulations have been conducted based on the computed model. The most pessimistic climate projection (scenario A2 from the IPCC), at a half-century scale, in the north-western Pyrenees, shows a slight decreasing of the effective precipitation, around 5 mm y⁻¹. Groundwater modeling simulation from these data showed that climate change will not significantly modify the groundwater flows in the coming decades; nevertheless, a decrease in the flow of springs and streams is probable, but will not endanger the water resource. Longer simulations could show more worrying results, but it seems unreasonable to project climate-change-effect consequences beyond a 50-year forecast without precise socio-economic predictions on demographic trends, land use modifications and water-use evolution.