The numerical model tested and evaluated in this manuscript is an improved version of the model introduced in the study by Chen and Goldscheider (2014), which in turn has been derived from the distributed hydrologic–hydraulic water quality simulation model – the Storm Water Management Model (SWMM, version 5.0), described in Rossman (2010). The hydrological conceptual model was developed mainly based on the geologic study by Wagner (1950), the speleological investigation by the regional caving club (Höhlenverein Sonthofen, 2006) and numerous tracer tests and hydrogeological field observations by Goldscheider (2005). Additional tracer experiments by Göppert and Goldscheider (2008) and Sinreich et al. (2002) improved this conceptual model. The current catchment model is constructed by using a combined lumped and distributed modeling approach. Basically, the lumped model represents water storage and drainage in the soil and epikarst. The distributed model represents the underground karst drainage network in the karst area, and the network of surface streams in the non-karst area; these linear structures drain the flow generated from the lumped model. Compared to the earlier catchment model by Chen and Goldscheider (2014), new developments are (1) the updated model adopts the HBV-snow routine and is able to simulate snow storage and snowmelt and their influence on groundwater recharge processes (described in Sect. 3.3). (2) The earlier model considers baseflow (slow flow) as a constant value, which is insufficient for long-term climate-change impact predictions; in the updated model, we applied the linear reservoir approach by Hartmann et al. (2011) to simulate transient slow-flow components, depending on groundwater recharge and recession coefficient. (3) The laterally adjacent and hydrogeologically connected non-karst area is included in the current model domain; the updated model is able to simulate variable infiltration of surface runoff from the non-karst area into the underground karst drainage network. (4) In the updated model, the spatial discretization of the catchment area is much finer by using the elevation bands approach, which allows for a better representation of the spatial variability in meteorological variables.

Due to the new developments, the current model is able to simultaneously simulate all system outlets for a complete hydrological year, including periods of snow accumulation, snowmelt and rainfall; additionally, the current model is able to reproduce system discharge behavior during drought periods, as the system baseflow was implemented as a function of groundwater recharge and recession coefficient. In this study, the simulation started in late autumn (November 2013), during very low-flow condition. The discharge of QS during this time consists of slow-flow components from the karst aquifer. This hydrologic state was used to define the initial model condition. In total, 76 model parameters (Supplement) are considered for the model setup: (1) model parameters x1–x20 define the main hydrological processes of the unsaturated zone in the individual karst subcatchments and the top layer of the low-permeability Flysch rocks, (2) model parameters x21–x76 describe the geometry and hydraulic properties of the karst drainage conduit network as well as surface stream channels in the non-karst area.

Four observation locations in the studied catchment were considered here: (1) QS at 1035 m a.s.l. in the valley, (2) QA at 1080 m a.s.l., (3) QE at 1120 m a.s.l. and (4) a gauging station (SR) at 1122 m a.s.l. quantifying the surface runoff from the upper part of Schwarzwasser valley. Hourly-measured discharges at the above-mentioned monitoring stations are used, whereas the measurements for QS and QA are available from November 2013 to October 2014 and for QE and SR only from July to October 2014. For the same period, we interpolated the meteorological data (hourly precipitation, air temperature and relative humidity) from nine weather stations (Fig. 1b) across the study catchment at a 100 m × 100 m grid resolution using combined inverse distance weighting and linear regression gridding. Mean areal precipitation and potential evapotranspiration for individual subunits are determined based on the interpolated meteorological data, in which hourly potential evapotranspiration is estimated using a modified Turc–Ivanov approach after Wendling and Müller (1984), described in Conradt et al. (2013).

We applied the HBV-snow routine for simulating snow accumulation and melt. The HBV model is described in various articles, e.g., Bergström (1975, 1995), Kollat et al. (2012) and Seibert (2000). We further modified the calculation of snowmelt using the approach proposed by Hock (1999), to simulate more realistic hourly-varying snowmelt in mountainous catchments: M=MF+α×I×(t-Ts),t>Ts0,t≤Ts where M is snowmelt (mm h-1), MF is melt factor (mm h-1 ∘C-1), α is radiation coefficient, I is potential clear-sky direct solar radiation at surface (W m-2), t is measured hourly air temperature (∘C) and Ts is threshold temperature (∘C) for snow melting. The melt factor and the radiation coefficient are empirical coefficients and can be estimated by model calibration. The distributed potential clear-sky direct solar radiation is dependent on surface topography and calculated with 100 m × 100 m grid resolution for the investigated area using the approach developed by Kumar et al. (1997) and a digital elevation model for the study area.

To understand water storage processes within the catchment, we estimated the temporary water storage volumes for the entire catchment (Eq. 5), karst area (Eq. 6) and non-karst area (Eq. 7): St,catchment=St0,karstaquifer+∑t0t(Pt,catchment-ETt,catchment-Qt,catchment),St,karst=St0,karstaquifer+∑t0t(Pt,karst+Rt,allogenic-ETt,karst-Qt,karst),St,nonkarst=∑t0t(Pt,nonkarst-Rt,allogenic-ETt,nonkarst-Qt,nonkarst). Surface runoff from the non-karst area can infiltrate into the underground karst drainage network through the conduits C34–C38 constructed in the upper part of the valley (Fig. 1c). This flow is considered as allogenic recharge into the karst aquifer and was taken into account for the storage calculation for the karst and non-karst areas. Additionally we simulated the temporary subsurface water storage volume for the karst aquifer (Eq. 8): St,karstaquifer=St0,karstaquifer+∑t0t(Rt,autogenic+Rt,allogenic-Qt,karst), where St, Pt, ETt, Rt and Qt are the storage, precipitation, evapotranspiration, recharge and discharge in volume at time step t (t0 is first simulation time step). The simulated temporary storage volumes for the whole catchment (St,catchment), karst area (St,karst), non-karst area (St,nonkarst) and karst aquifer (St,karstaquifer) are the absolute volumes, whereas the storage for the karst aquifer (St,karstaquifer) only describes the ground water storage in the karst aquifer. The calculation of the initial water storage volume in the karst aquifer is based on the approach introduced by Bonacci (1993): St0,karstaquifer=k×Qt0,karstaquifer, where Qt0,karstaquifer is the discharge from the karst aquifer at the first simulation time step and k is the recession coefficient, which can be derived by analyzing the karst spring discharge hydrograph during low-flow conditions.

The focus of this analysis is to quantify the impact of varying climate conditions on the water fluxes and storages throughout the model domain and to identify the hydrological processes most sensitive to potential climate change within the study catchment. We chose the probabilistic scenarios of precipitation and temperature by Frei (2004) for the northern Alps as the basis for our study. The median values (q0.5) and the confidence intervals (q0.025 to q0.975) of the probabilistic scenarios for years 2030, 2050 and 2070 were derived in Frei (2004) and given in Table 1. We used a delta approach to project the potential climate-change scenarios in the investigated catchment by changing precipitation and temperature time series for the pre-defined months (December–February, March–May, June–August and September–November) by a given delta (percentage or value). For the analysis, we first focused on the median climate scenarios of years 2030, 2050 and 2070 (described in Sect. 4.3.1) to better understand the general trend of the climate-change projections. In the second part of the analysis, we considered the uncertainty in the climate scenario for 2070 and estimated its impact on the simulated water fluxes and storages across the model domain (described in Sect. 4.3.2). To consider the climate-change scenario uncertainty, 1000 uniformly distributed random samples within the defined confidence intervals for the deltas of precipitation and temperature are used.

Figure 4 shows the simulated karst spring discharges as well as the surface runoff generated from the non-karst area of the final calibrated model. The transient and highly variable discharge behavior at the four spatially distributed model outlets is simultaneously simulated at an hourly time step. The quality of the model simulation is demonstrated by two different statistical criteria, the RMSE and the Nash–Sutcliffe coefficient (NSC): RMSE values are 0.118 m3 s-1 for QS, 0.448 m3 s-1 for QA, 0.419 m3 s-1 for QE and 0.248 m3 s-1 for SR. NSC values are 0.71 for QS, 0.80 for QA, 0.74 for QE and 0.66 for SR. However, only one complete hydrological year of data can be obtained in the test site and used for this study. To better evaluate the model, we performed a split-sample test with the existing data (Supplement) that showed that we can obtain stable model parameterization and prediction with this relatively short observation period.

For a simulation period of about 330 days, we estimated that about 5 % of the total precipitation (52.79 MCM

MCM for million cubic meters

We compared the estimated water storages for the whole catchment, karst area, non-karst area and karst aquifer to better understand different storage processes (snow storage, soil water storage and subsurface water storage) in the model domain (Fig. 6). It is considered that in the simulated winter and early spring (November 2013–March 2014), the catchment water storage dynamics are mainly characterized by snow storage change in both the karst and non-karst areas. Afterwards, snowmelt (April–May 2014) led to rapidly decreasing catchment snow storage, but increasing storage in the karst aquifer as subsurface water in both fast and slow paths. During the rainfall season in the simulated summer and autumn (June–October 2014), the catchment storage is mainly characterized by subsurface water storage in the karst aquifer, while during medium and high flows the water is also stored intermittently in the top layer of the non-karst area.

An overview of the change in water fluxes and storages under changing climate conditions (median climate scenarios and uncertainty in the climate scenario 2070) is given in Table 2.

In this study, the karst catchment model simultaneously simulates the transient and highly variable discharge behavior at the four model outlets. The model evaluation using different approaches indicates that the results are satisfying (described in Sect. 4.1). The previous studies have demonstrated that the model adequately represents the hydraulic processes observed in the karst aquifer and is able to transform them into realistic catchment responses during rainfall periods (Chen and Goldscheider, 2014; Chen et al., 2017). The current model represents the dominant flow process for the investigated karst catchment during low-flow conditions. During the snow accumulation period (November 2013–February 2014), the karst system was undersaturated, and QS discharged the whole catchment, while other karst springs (QA and QE) were dry and no significant surface runoff generated from the non-karst area. The simulation is consistent with our measurements and field observations. Furthermore, the current study shows that the snow dynamic reflected in the major karst springs (QS and QA) is reproduced in the model. It indicates that the model represents the recharge process driven by the snow accumulation and melting in the studied karst catchment. However, no snow observations to validate the accuracy of simulated snow accumulation and melting are available. For this reason, we developed the multi-step calibration procedure to achieve an efficient calibration of the snow model (described in Sect. 3.4.2). To more realistically simulate snowmelt and its spatial pattern in complex mountainous topography, we applied the extended snowmelt equation from Hock (1999) that considers the distributed potential clear-sky direct solar radiation, which is calculated based on a digital elevation model for the study area with 100 m resolution. Warscher et al. (2013) pointed out that the HBV approach is too simple for modeling distributed complex snow dynamics in mountainous environments, but it is the best estimation that we can obtain due to the lack of data. Therefore, the results concerning the simulated snow storage are associated with uncertainty and should be interpreted carefully.

We find that the surface runoff generated from the non-karst area is much less than the effective precipitation for the non-karst area. The reason is that the allogenic recharge leads to significant loss. This model behavior represents the conceptualization of our understanding about the hydraulic connection between the karst and non-karst areas. However, the model evaluation shows that the model underestimated the surface runoff generated from the non-karst area in response to heavy rainfall events (Fig. 4). This could be explained by an oversimplification of the complex hydrological situation in the non-karst area under-representing its runoff dynamics. Furthermore, the estimated low evapotranspiration (and very high recharge rates) for the investigated catchment appears unusual. Very high recharge rates in mountainous karst areas, ranging between 60 and 90 %, are also reported in the literature (e.g., Malard et al., 2016). In Alpine regions, low temperatures and high precipitation favor low evapotranspiration. In the elevated parts of our test site, soil and vegetation are almost entirely missing, and the limestone is extremely karstified, so that water infiltrates directly into open fractures. Hence, the high recharge rates are in accordance with our previous hydrogeological conceptual model, which is based on detailed field investigations, including 18 tracer tests (Goldscheider, 2005; Göppert and Goldscheider, 2008; Sinreich et al., 2002). The overall size of the karst system, the catchment areas of the individual springs and the general configuration of the underground drainage network are well-known. Yet, our quantification of recharge is still associated with uncertainties. Possible reasons include the following: (1) the interpolation of precipitation is uncertain. Most weather stations used for interpolation are located outside the study area, at lower elevations. Uncertainty depends on the density of observation points and the interpolation method (e.g., Ohmer et al., 2017). Increase in precipitation with elevation should also be taken into account. (2) Discharge quantities during very high-flow conditions are also uncertain. Water stages were continuously measured at all gauging stations, and numerous flow measurements (salt-dilution method) were performed to establish rating curves, which were used to obtain continuous hydrographs for all system outlets. However, most flow measurements were done during low- to moderately high-flow conditions, and the rating curves had to be extrapolated for very high flows. Therefore, substantial uncertainties have to be expected for very high-flow conditions (e.g., Baldassarre and Montanari, 2009; Coxon et al., 2015). (3) Another source of uncertainty is that sublimation from snow was not taken into account in the current model. However, some studies suggest that snow evaporation can be significant in some high-elevation catchments (e.g., Leydecker and Melack, 2000).

It is well known that long-term trends of karst aquifer dynamics (e.g., spring discharge, groundwater level) are affected mainly by regional precipitation patterns (e.g., Ma et al., 2004; Hao et al., 2006; Jia et al., 2017; Hartmann et al., 2012). In comparison to these earlier studies, our current study shows significant short-term aquifer responses to changes in hydro-meteorological conditions. The simulations demonstrate that the seasonal discharge pattern is controlled by the temporal distribution of precipitation on the one hand, and by the temperature pattern on the other hand. The snow storage in the catchment is highly sensitive to temperature variations, which can shift the seasonal patterns of snowmelt and aquifer recharge. A similar recharge pattern that strongly depends on seasonal snow accumulation and melting has been observed in other Alpine karst systems (Finger et al., 2013; Gremaud, 2011). Previous studies suggest decreasing spring discharge with increasing temperatures, as a result of increased evapotranspiration (e.g., Loáiciga et al., 1999). Our findings suggest that the extremely high recharge rates in our studied karst system will reduce the impact of rising temperatures on aquifer dynamics.

For the studied karst aquifer, due to its characteristic duality of flow and storage and additional spatially heterogeneous distributed drainage structure, the impacts of the varied climate conditions on QS, QA and QE are distinct. The simulations demonstrate well that QE is highly sensitive to changing climate conditions. The explanation is that QE acts as the highest overflow outlet of the studied karst aquifer, and its activation is strongly controlled by the hydrodynamic conditions in the karst drainage network, which are in turn highly sensitive to recharge and fast-flow processes. In contrast, QS is the lowest outlet for the karst aquifer and its discharge is “guaranteed” by the long-term water storage in matrix. Accordingly, QS is the most “robust” in the face of changing climate conditions. Under the simulated climate scenarios, QA shows a mixed character. On the one hand, the QA discharge is significantly less influenced than QE; and on the other hand, QA's discharge pattern can be more easily shifted than QS. It demonstrates well that the high permeability flow in the conduit network with less water-storage capacity is sensitive to changing hydrological conditions, while the low-permeability flow in the matrix with greater water-storage capacity is more resistant. In the non-karst area, the varied climate conditions affect the snow accumulation and melting patterns. As the non-karst and karst areas are hydraulically connected in the upper part of the valley, the predicted earlier-starting snowmelt can generate more runoff in the non-karst area which partly infiltrates into the underground drainage network leading to greater loss for the surface runoff and increased allogenic recharge to the karst aquifer.

For the current analysis, we used a pragmatic approach to analyze potential climate-change scenarios. The uncertainties in the climate scenarios were considered based on a random sampling approach. The final results indicate the impacts of the seasonal changes in the pattern of precipitation and temperature on the spatially varied hydrological processes within the catchment. Additionally, we investigated the flow exceedance probability of karst springs and surface runoff from the non-karst area (Supplement) and find that the simulated climate conditions affect the frequency and amplitude of catchment flows. This suggests that the impacts of the temporally stochastic distributions of meteorological parameters and their variability on the catchment flow dynamics should be systematically investigated.