A 10-year record of input and output observations was available. Starting from the hydrological year 2002/03, it envelops well the stormy period that began in January 2007. It included daily rainfall measurements and stream discharge measurements from stream sections 1 and 2 (Fig. 1). We obtained the discharge of the entire system with a simple topography-based up-scaling procedure that is described in more detail in Hartmann et al. (2012a). Irregular (weekly to monthly) observations of DOC, DIN and SO42- concentrations are available for precipitation and at weir 1. DOC, NO3-, SO42- and NH4+ (since January 2010) samples were filtered (0.4 µm) before the analysis. NH4+ concentrations were measured by spectrophotometry (Milton Roy Spectronic). Weekly DOC, SO42- and NO3- samples were pooled to provide volume weighted biweekly (until March 2009) and monthly (thereafter) samples. DOC samples were acidified with 0.5 mL HCl 25 % and were measured with a Maihak TOCOR 100 and a CPN TOC/DOC analyser (Shimadzu Corp., Japan). NO3- and SO42- concentrations were determined by ion chromatography with conductivity detection. DIN input was then calculated as the sum of NO3--N and NH4+-N. Since NH4+ is either transformed into NO3- or absorbed in the soil, NH4+ concentrations in runoff are very small or not detectable. Therefore we calculated DIN outputs as NO3--N. Additionally, irregular observations of snow water equivalent at the plateau allowed for independent setup of the snow routines.

Kyrill in the year 2007 and some similarly strong storms subsequent to 2008 caused some major windthrows as well as single tree damages. A windthrow disturbance of ∼ 5 ha occurred upstream of weir 1. Though no direct measurements exist as to the total extent of the windthrow area we estimate that 5–10 % of the study site has been subject to windthrow (Kobler et al., 2015). We did not observe a significant change in intra- and interannual variability in DOC concentrations and discharge before and during the wind disturbance period (Fig. 2a, e). Runoff concentrations of DIN showed clear responses to the disturbances. With the first windthrow event it started to increase until 2008/09 and slowly decreased again in 2010/11 (Fig. 2c). Comparison of DOC concentrations with discharge before and during the wind disturbance period revealed a similar pattern. As shown by other studies on DOC mobilization (e.g., Raymond and Saiers, 2010), a positive correlation between concentrations and discharge (on log10 scale) occurred for DOC with concentrations up to 6 mg L-1 during high discharge (similar to Hagedorn et al., 2000). However, there was no obvious difference between the pre-disturbance period (Fig. 2b).

With 14 model parameter that controlled the hydrodynamics and 7 parameters that allow for the non-conservative solute transport, the calibration of the model was a high-dimensional problem. For that reason we have chosen the Shuffled Complex Evolution Metropolis (SCEM) algorithm (Vrugt et al., 2003), which proved to be capable of exploring high-dimensional optimization problems (Fenicia et al., 2014; Feyen et al., 2007; Vrugt et al., 2006). As performance measure we used the Kling–Gupta efficiency (KGE; Gupta et al., 2009). For calibration, KGE was weighted equally among all solutes, one-third for the discharge of the entire system and two-thirds for the discharge of weir 1, whose observation precision was regarded to be more reliable than the up-scaled discharge. KGE is defined as KGE=1-(r-1)2+(α-1)2+(β-1)2,withα=σSσOandβ=μSμO, where r is the linear correlation coefficient between simulations and observations, and μS/μO and σS/σO are the means and standard deviations of simulations and observations, respectively. α expresses the variability and β the bias.

To check for the stability of the calibrated parameters, we perform a split-sample test (Klemeš, 1986). Since the pre-disturbance time series was too short to be split into two equally long periods, we perform a both-sided split-sample test by bootstrapping two independent 4-year time series of observations (first sample: discrete sampling of 50 % of the values of each observed time series; second sample: remaining 50 % of the observations). We calibrate our model with the first sample and evaluate it with the second sample, and vice versa. A parameter set is regarded stable when the calibration with both samples yields similar parameter sets and their KGE concerning discharge and the solutes does not reduce significantly when applying them to the other sample.

After the model evaluation, we use the different components of the KGE in Eqs. (5) and (6) to explore the impacts of the storm disturbance period on the hydrochemical components. By assuming that the model is able to predict to hydrochemical behaviour that prevailed without the impact of the storms adapting the hydrochemical parameters of the model in Eqs. (3)–(4) and analysing the difference between the adapted hydrochemical simulations and the non-adapted simulations, we are able to quantify the change in solute mass balance due to the storm impact. We define the time span for our adaption as the time when the different components of KGE exceed the range of their pre-disturbance variability. During this time period we compensate for the apparent deviations by adapting the hydrochemical parameters. This is done twice – once by manual adaption and another time using an automatic calibration scheme. Their new values will indicate changes in the seasonality, production or interannual variations.

The signal of the storm impact will travel at various velocities and via pathways through the karst system. While fast flow paths and small storages will transport the signal rapidly to the system outlet, slow pathways and large storages will delay and dilute the signal. Transit time distributions indicate how fast surface impacts travel through the hydrological system. We derive transit time distributions from the model by performing a virtual tracer experiment with continuous injection over the entire catchment at the beginning of the impact of the stormy period. When a model compartment reaches 50 % of the tracer concentration is considered median transit time. The thus-derived transit times will elaborate how the hydrological system propagates the signal through the system including all slow and fast pathways as defined by Eqs. (12) and (18). As for DIN and DOC we assume complete and instantaneous mixing with each model storage (soil, epikarst, and groundwater) at each compartment; the time that we refer to as “mean transit time” of a model compartment is the time the virtual tracer needs to pass through the particular model storage. In combination with the fluxes that are provided from each of the model compartments, it is possible to quantify the fractional contribution of fast and slow flow paths, respectively. We will apply the virtual tracer from the previously assessed beginning of the impact until the end of the time series to assess the transit time distribution. In addition, we apply a second virtual tracer that also lasts only for the disturbance period (as estimated in Sect. 3.3) to evaluate the filter and retardation potential of the karst system.

Table 1 shows the calibrated parameters for the two samples. They indicate a thick soil and a relatively thin epikarst. The dynamics expressed by the storage constants indicate days and weeks for the conduits (model compartment i=Z) and the epikarst, respectively. The distribution coefficient of the groundwater is larger than the soil/epikarst storage constant. For DOC and DIN there are a natural production rates of 1.6–1.8 and -1.35-0.1 mg L-1, respectively. The DOC distribution coefficient is between 0.9 and 1.1. The phase shift and amplitude for DIN showed that there is a seasonal variation in DIN net production, with its maximum release at April each year for both of the samples. SO42- is dominated by the concentration in the precipitation input with some leaching in the soil and sulfides in the dolomite. Its variability constant is quite low (< 0.1). Weighted KGEs, as well as their values for the individual simulation variables, are relatively stable. Overall, calibration on both samples provided similar parameter values. Due to its higher stability concerning the evaluation period, we chose the second sample for further analysis.

The discharge simulations follow adequately the variations in the observations (Fig. 4), although some small events are not reproduced by the model and although the simulations of the weir's discharge tend to underestimate peak flows. No obvious differences can be seen between the pre-disturbance and wind disturbance period. The hydrochemical simulations tend to follow the observations as well (Fig. 5). However, there is sometimes some underestimation of the DOC peaks for the pre-disturbance period. The DIN simulations appear to be more precise during the pre-disturbance period, but there is a systematic underestimation when the disturbance takes place.

There is a deviation between pre-disturbance and disturbance period simulated and observed variability and bias for DIN (Fig. 6). A similar tendency can be found for DOC. However, only for DIN are the deviations different to the variations already found during the pre-disturbance period (which is also the calibration/validation period). The variations in DOC appear to be systematic, too, but they fall within its ranges of variability during the pre-disturbance period.

The very first signs of the impact were found on 1 May 2007, and they lasted to the end of the hydrological year 2010/11. In a first trial (Table 2), the model parameters for the DIN production were adapted manually to compensate for the changes in observed DIN concentrations with a focus on reducing the difference indicated by the bias, β, and variability, α, components of KGEDIN. In a second trial, we use an automatic calibration scheme to achieve the optimum KGEDIN. As indicated by the highest KGE (Table 2), the automatic calibration provided the highest KGEDIN, but this is achieved by improving variability α and correlation r. Almost no improvement is reached for the bias β. Even though resulting in a slightly lower improvement of KGEDIN the manual calibration results in a much more acceptable reduction in the bias (Fig. 6). Its parameter values showed a production rate, PDIN, of DIN almost 2 mg L-1 larger than the pre-disturbance value; an amplitude, ADIN, around 1 mg L-1 smaller; and a phase shift, SPH,DIN, towards a week earlier in the year, resulting in a more acceptable simulation of DIN dynamics during the disturbance period (Fig. 7).

The transit time distributions show that the soil and epikarst system reacts quite rapidly to the virtual injection. Fifty percent of the injection concentration is reached within ∼ 60 days (Fig. 8a), while most of groundwater system requires ∼ 100 days to reach 50 % of the injection concentration, with a few flow paths requiring up to 300 days (Fig. 8c). A similar behaviour is found when the impact ends (Fig. 8b, d). This behaviour also shows that some of the slowest flow paths just reach the input concentration before they start to decline again.

Most of the calibrated model parameters are in ranges that are in accordance with other modelling studies or field evidence. General differences between the calibrated parameter values of the both-sided split-sample test may mostly be due to the comparatively low resolution of the hydrochemical variables (SO4, DOC and DIN), which actually increased as a result of the bootstrapping procedure. However, the good multi-objective simulation performance of the model, as well as its evaluation by the split-sample test, indicate an overall acceptable performance of the model. At almost 3–8 days the epikarst storage constant is in accordance with field studies on the epikarst storage behaviour that found retention times of some days to a few weeks (Aquilina et al., 2006; Perrin et al., 2003). The soil and the epikarst storage capacity are quite large. These high values may be explained by structural errors of the model that result in unrealistic calibrated parameter values, in particular possible parameter interactions between their storage capacities and storage coefficients. Since the soil and the vegetation controls the fraction of rain that is lost to evapotranspiration, this high calibrated value might be due to tree roots ranging through the soil into the epikarst (Heilman et al., 2012) or rock debris (Hartmann et al., 2012a).

Similar to the epikarst storage constant, the conduit storage constant, KC, is, with its value of 1.1 days, in the range of previous modelling studies (Fleury et al., 2007; Hartmann et al., 2013a). The high values of the epikarst variability constant and the groundwater constant indicate a low development of preferential flow paths in the rock, which is typical for dolomite aquifers (Ford and Williams, 2007). A low degree of karstification was already known for our study site (Jost et al., 2010) and the calibrated recharge areas fall well within the ranges found in previous modelling studies (Hartmann et al., 2012a, 2013c).

The hydrochemical parameters mostly show realistic values. A DOC production parameter, PDOC, of ∼ 1.6–1.8 mg L-1 resulted in realistic simulated concentrations at the weir. For DIN production the two calibration samples result in values of -1.4 and 0.1 mg L-1, going along with amplitudes of 3.4 and 1.8, respectively. Hence, there appears to be some correlation between the production and amplitude parameters, PDIN and ADIN. Negative values indicate that, during some periods of the year, all DIN is consumed by plants or soil organisms and that the production period is shorter but more pronounced due to its larger value of amplitude. However, we expect these differences to be minor since the phase shift SPH,DIN of both calibration samples is almost the same, as well as their annual maximum (PDIN+ADIN) of 2.01 and 1.95 mg L-1. This behaviour indicates a maximum of DIN production and leaching at the time of the year when snowmelt reaches its maximum (March to April) and when DIN uptake by plants is still low (Jost et al., 2010). The dissolution equilibrium concentrations of 2.7–3.1 mg L-1 for SO42- indicate the abundance of the precipitation input, oxidation of sulfides (e.g. pyrite) in the dolomite and traces of evaporates in the small Plattenkalk occurrences (Kralik et al., 2006).

The deviation between simulated and observed time series (Fig. 5) already indicates that DIN is the only solute that shows a clear impact of the storms. This is further corroborated by considering the individual components of KGE in Fig. 6. It is well known that nitrate leaching to the groundwater increases sharply after tree damage (dieback) in forests where N is not strongly limited (Bernal et al., 2012; Griffin et al., 2011; Huber, 2005). Such disturbances disrupt the N cycle. The loss of tree N uptake favours nitrification of surplus NH4+ by microorganisms. Moreover, above- (i.e. foliage) and belowground (i.e. fine roots) litter from dead trees enhances the mineralization of organic matter, ammonification and nitrification. Both processes are accelerated by increased soil moisture and soil temperature due to the loss of the forest canopy. Subsequently, leaching of N increases with increased seepage fluxes due to decreased interception and water uptake by trees. Since the simple DIN routine of the model cannot take into account such changes, the underestimated DIN concentrations and their amplitude show the effect of forest disturbance on the leaching of DIN from the studied catchment. There is also an apparently systematic deviation of the DOC variability α. But its variations during the pre-storm period are similarly large, thus pointing to a negligible effect of forest disturbance on DOC leaching. Numerous studies have identified the forest floor as a DOC source (Borken et al., 2011; Michalzik et al., 2001). Windthrow generally causes a (short-term) pulse of above- and belowground litter (Harmon et al., 2011). Thereby, mineralization of the surplus litter input concurrent with improved soil climatic conditions likely increased the leaching of DOC from the forest floor (Fröberg et al., 2007; Kalbitz et al., 2007). Concurrent, increased soil water, surface and shallow subsurface flow may favour increased soil DOC leaching to downslope surface waters (Monteith et al., 2006; Neff and Asner, 2001; Sanderman et al., 2009). In mountainous catchments the latter flow paths are likely due to the steepness of the catchment slopes (Boyer et al., 1997; Sakamoto et al., 1999; Terajima and Moriizumi, 2013). The missing signal of forest disturbance on DOC concentrations at weir 1 even shortly after the disturbance may be due to the minor extension of the disturbed area, the minor increase of surface and shallow subsurface flow due to the relative low slope of the disturbed area, the buffering of increased topsoil DOC leaching due to absorption of DOC within the subsoil (Borken et al., 2011; Huber et al., 2004), missing DOC-rich riparian source areas (i.e. wetlands, floodplains) and the reduction in pre-disturbance organic matter input to soil (i.e. litter, root exudates; Högberg and Högberg, 2002). Theoretically, hydrological processes such as a decrease in transpiration or an increase of groundwater recharge may also occur. But these superficial changes are probably minor considering the typically high karstic infiltration capacities that remove surface water quite rapidly (Hartmann et al., 2014b, 2015). Therefore, hydrological impacts of windthrow on karst systems (for instance on transpiration) may not be as pronounced as in non-karstic domains because a large fraction of the infiltration during high flow periods will not be available for transpiration anyway. Consequently, a disturbance-caused impact on DOC availability could also be hidden because increased infiltration and DOC leaching during strong rainfall events may just not be detectable considering the weekly to monthly sampling of DOC. For a better understanding of disturbance-induced changes in DOC, more sampling in high temporal resolution of DOC concentrations at the weir (Fig. 1) should be undertaken to elucidate the effect of forest disturbance on DOC dynamics and to improve the simulation of DOC production and transport within the studied ecosystem

Our results corroborate findings from many other studies that extreme events such as during the wind disturbance period in our study can result in a significant increase in DIN in the runoff, despite the area impacted being relatively small (5–10 % of the watershed). Particularly in karst catchments, such changes can happen quickly and prevail for a significant duration, in our case more than 2 years after the last storm. Due to subsurface heterogeneity, the impact did not travel uniformly through the system. Instead, it split into different pathways and mixed with old water that percolated prior to the impact. In our system, large parts of the water travelled rapidly through the system. However, a smaller number of pathways had large storages of old water and slow flow velocities, resulting in significant retardation. Taking into account that forest disturbances will most probably increase with climate change (Seidl et al., 2014), DIN mobilization as observed in our study may occur more often and become more intense. The hydrological system may dilute and delay rapid shifts of N concentration, and it will “memorize” the impacts for some time. However, our present analysis showed that the timescale of the wind disturbance on DIN production and leaching from the soil exceeds the timescale of transit of the disturbance through the system. This is most probably due to the small size and the subsurface karstic behaviour of our study site favouring faster flow paths and lower system storage than hydrological systems with larger extent or with other types of geology.