Daily hydro-meteorological data were available for the period 1 October 2009–30 September 2016 (Fig. 2). Precipitation P (mmd-1) and mean daily temperature T (∘C) were available from the Monschau–Kalterherberg meteorological station operated by the German Weather Service (Deutscher Wetterdienst DWD station 3339), located 9 km north-west of the Wüstebach catchment. The precipitation data were corrected for evaporation and wind drift losses according to Richter (1995) and as described in detail by Graf et al. (2014). Stream discharge Q (mmd-1) at the outlet of the Wüstebach was observed with a V-notch weir for low-flow measurements and a Parshall flume for medium to high flows (Bogena et al., 2015). Daily potential evaporation EP (mmd-1) was estimated using the Penman–Monteith equation. Daily depth-weighted average soil water content for the study period was estimated from a network of soil moisture sensors placed at 5, 20 and 50 cm depths at >100 locations across the study catchment as described by Graf et al. (2014) and Bogena et al. (2015). In addition, throughfall rates PE (mmd-1) were measured at one continuously forested location in the study catchment (Fig. 1) with an array of samplers as described in detail by Stockinger et al. (2015) over irregular intervals over the period 1 October 2012–30 September 2016.

Regular weekly δ18O data from bulk precipitation samples collected in a cooled wet deposition gauge at the meteorological station Schleiden–Schöneseiffen (Meteomedia station) 3 km north-east of the catchment were available for the period 1 October 2010–24 September 2012. After that, precipitation was sampled at half-daily intervals until 30 September 2016 using an automatic, cooled sampler (Eigenbrodt GmbH, Germany). The half-daily samples were precipitation volume weighed to daily sampling intervals (Stockinger et al., 2016, 2017). Weekly stream water grab samples for stable water isotope analysis were taken at the outlet of the Wüstebach catchment in the 1 October 2010–30 September 2016 period (Fig. 3a; Bogena et al., 2020).

Isotope analysis was carried out using laser-based cavity ring-down spectrometers (L2120-i/L2130-i, Picarro Inc.). Internal standards calibrated against VSMOW, Greenland Ice Sheet Precipitation (GISP) and Standard Light Antarctic Precipitation (SLAP2) were used for calibration and to ensure long-term stability of analyses (Brand et al., 2014). The long-term precision of the analytical system was ≤0.1 % for δ18O.

To survive, plants need continuous access to water to satisfy canopy water demand. The root systems of vegetation are therefore adapted to provide access to water volumes that correspond to annual water deficits that result from the combination of (1) the phase lag between and (2) the difference in the respective magnitudes of seasonal precipitation and solar radiation signals (Donohue et al., 2012; Gentine et al., 2012; Gao et al., 2014). On a daily basis, these water deficits SD,j(t) can be estimated as the cumulative sum of daily throughfall PE (mmd-1) minus transpiration ET (mmd-1). The maximum deficit SD,j for a specific year j is then equivalent to the soil water volume that was accessible to and actually accessed by vegetation through its root system for transpiration during the dry season over that period when ET exceeded PE (deBoer-Euser et al., 2016; Nijzink et al., 2016a; van Oorschot et al., 2021): 1SD,jt=∫t0tPEt-ETtdt,if SD,jt≤0,0,if SD,jt>0,2SD,j=max⁡SD,jt, where t is the time step (d) and t0 is the last preceding time step for which the storage deficit SD,j(t)=0. As an approximation, Eq. (1) implies that if SD,j(t)=0, the water content in the root-accessible pore space at day t is at field capacity and cannot hold additional water. If water supply then exceeds canopy water demand on that day, i.e. PE(t)–ET(t)>0, this water surplus is drained from the root zone, e.g. to recharge groundwater or directly to the stream, and cannot be used for transpiration.

Daily throughfall PE, i.e. precipitation that actually reaches the soil, was estimated on the basis of the water balance of a canopy interception storage (Nijzink et al., 2016a): 3dSItdt=Pt-EIt-PEt, where EI (mmd-1) is daily interception evaporation and SI (mm) the canopy interception storage. For each time step, EI can then be computed as 4EIt=EPt,if Eptdt<SIt.SItdt,if EPtdt≥SIt.

This then further allows us to estimate PE according to 5PEt=0,if SIt<Imax,SIt-Imaxdt,if SIt≥Imax, where Imax (mm) is the canopy interception capacity. In the absence of more detailed information PE was estimated with a range of different interception capacities, i.e. Imax=0, 1, 2, 3, and 4 mm, in a sensitivity analysis approach.

Note that the catchment average PE after deforestation was estimated as the area-weighted mean of PE in the deforested area (21 % of the catchment area) computed with an assumed Imax=0mm and PE from the remaining area computed based on the above range of Imax between 0 and 4 mm. In a next step, assuming negligible groundwater imports or exports (cf. Bouaziz et al., 2018), data errors and storage changes, long-term mean transpiration ET¯ was estimated according to the water balance: 6E‾T=P‾E-Q‾, where P‾E (mmd-1) is the long-term mean throughfall and Q‾ (mmd-1) is the long-term mean observed stream discharge. Daily transpiration ET (mmd-1) for use in Eq. (1) is then estimated by scaling the long-term mean transpiration to the signal of daily potential evaporation to approximate the seasonal fluctuation of energy input (Bouaziz et al., 2020): 7ETt=EPt-EItE‾TE‾P-E‾I.

A range of previous studies provided evidence that mature forests develop root systems that allow access to sufficiently large porewater storage volumes SU, max to bridge droughts with return periods TR∼40 years (Gao et al., 2014; deBoer-Euser et al., 2016; Nijzink et al., 2016a; Wang-Erlandsson et al., 2016). The maximum annual water deficits SD,j (Eq. 2) for all j years in the pre-deforestation study period were therefore used to fit a Gumbel extreme value distribution (Gumbel, 1941). This subsequently allowed the estimation of a water deficit with a 40-year return period, which is for this study defined as vegetation-accessible water storage SU, max so that SU, max=SD,40yr.

Note that due to the limited length of the data series, the SU, max estimates are rather uncertain and need to be understood as merely indicative approximations. This is in particular true for the post-deforestation period, where attempts to explicitly link SU, max to a specific return period are subject to additional uncertainty: as the catchment was not reforested and natural recovery of vegetation is negligible (see aerial images in Fig. 1), it is not implausible to assume that the development of the root system after the disturbance is far from equilibrium and likely to be actively evolving over time. Also note that although ET is, for brevity, referred to as transpiration throughout this paper, it also contains soil evaporation. However, no explicit and quantitative distinction could be made between these two fluxes with the available data. A further critical assumption of the above method required that roots do not tap the groundwater and that water for transpiration is exclusively extracted from the unsaturated soil. In contrast to other landscapes (Fan et al., 2017; Roebroek et al., 2020), it is likely that this assumption largely holds in the Wüstebach as throughout the catchment the groundwater levels, also in the riparian zone, remain largely below a depth of 50 cm during the relatively dry growing season (Bogena et al., 2015), when storage deficits SD typically accumulate (∼May to October) and no roots have so far been observed for the dominant picea species below that depth in the Wüstebach catchment. This is also broadly consistent with the results of Evaristo and McDonnell (2017), who show rather limited groundwater use by picea species.

A semi-distributed, process-based catchment model, iteratively customized and tested within the previously developed DYNAMITE modular modelling framework (Hrachowitz et al., 2014; Fovet et al., 2015), was adapted with additional, hydrologically passive storage volumes to allow for simultaneous representation of water fluxes and tracer transport (Hrachowitz et al., 2013) based on the general concept of storage-age selection functions (SAS; Rinaldo et al., 2015). This model type was chosen over simpler, more data-based methods (e.g. McGuire and McDonnell, 2006; Kirchner, 2016) as it did not only allow a simultaneous representation of water and tracer fluxes, but also allowed attribution of an observed pattern to specific process hypotheses and the associated model parameters that represent (sub-surface) system properties, thereby providing potential quantitative mechanistic explanations of why deforestation affects the hydrology in the Wüstebach. As an intermediate model type between purely data-driven (e.g. Kirchner, 2016) and spatially explicit physically based models (e.g. Maxwell et al., 2016), it requires assumptions about underlying processes and effective parameters and does not allow a detailed spatial analysis. Yet this model type provides the possibility of testing these process hypotheses at the scale of the semi-distributed model units, thereby integrating and accounting for the natural heterogeneity of system properties across the model domain (Hrachowitz and Clark, 2017).

The model was run with a daily time step and has a total of 14 free calibration parameters, which were calibrated for the model to simultaneously reproduce flow and δ18O dynamics in the stream. The uniform prior parameter distributions (Table 2) were sampled using a Monte Carlo approach with 3×106 realizations. To limit equifinality (Beven, 2006) and to ensure robust posterior parameter distributions for a meaningful process representation (e.g. Kuppel et al., 2018b), an extensive multi-objective calibration strategy was applied. Briefly, this was done using a total of 14 performance metrics that describe the model's skill in reproducing different signatures associated with streamflow (EQ) and δ18O dynamics (Eδ18O) as shown in Table 3.

To be accepted as feasible, solutions had to exceed a threshold value of 0.5 for all performance metrics, with the exception of ENS,δ18O, for which a threshold of 0.2 was used. To further constrain the model, we only accepted solutions that could reproduce the dynamics in observed soil moisture as well as the average observed magnitudes of canopy throughfall. To do so we used a simplified limits-of-acceptability approach (e.g. Coxon et al., 2014) with a rectangular step function so that all solutions that fall within the limits of the step function receive a weight of 1 while all others are assigned a weight of 0 and are thus rejected (Bouaziz et al., 2021). More specifically, we rejected solutions whose modelled normalized relative soil moisture fell outside the acceptable limits, here defined as ±0.15 of the observed relative soil moisture, in more than 75 % of the time steps in the calibration periods. Similarly, we rejected solutions for which the modelled mean ratio PE/P in the continuously forested part of the catchment was outside ±0.15 of the observed mean ratio PE/P=0.71. This strategy was chosen instead of directly calibrating the time series of associated model variables SU (Eq. 20) and PE (Eq. 18) to explicitly account for commensurability errors between the point scale and the scale of the model application (Bouaziz et al., 2021). Subsequently, the 14 metrics of the solutions retained as feasible were combined into two equally weighted classes, describing streamflow (Q) and tracer (δ18O) dynamics, respectively. This then allowed us to obtain solutions with balanced overall model performances using the mean Euclidean distance DE (–) from the “perfect” model (i.e. DE=1; Hrachowitz et al., 2014; Hulsman et al., 2020): DE=141-12∑n=1N1-EQ,n2N+∑m=1M1-Eδ18O,m2M, where N=12 is the number of different performance metrics describing streamflow and M=2 the number of different performance metrics for δ18O. To construct the posterior parameter distributions and the corresponding model uncertainty intervals, the retained parameter sets where then weighted according to a likelihood measure L=DEp (cf. Freer et al., 1996), where the exponent p was set to a value of 10 to emphasize models with good overall calibration performance.

In a first step, the model was calibrated for the pre-deforestation period 1 October 2009–31 August 2013. Note that due to a lack of regular and weekly δ18O precipitation data before 1 October 2010, the performance metric Eδ18O describing the δ18O dynamics was computed from that date onwards only. The feasible parameter sets were then used to test the model without further calibration in the post-deforestation period. In a second step, the model was re-calibrated for the 1 September 2013–30 September 2016 post-deforestation period and the changes in the resulting model performance and posterior distributions compared to those from the pre-deforestation calibration. The estimation of the effects of deforestation on TTDs is based on model parameter sets obtained from calibration in the pre-deforestation and post-deforestation periods, respectively.

Initial analysis of water balance data suggests that the hydro-meteorological conditions as expressed by the aridity index IA=E‾P/P‾ do not show significant differences between the pre-deforestation (IA=0.50±0.02) and post-deforestation periods (IA=0.51±0.03), respectively (Fig. 5a). However, and in spite of these comparable climatic conditions, the results show a shift in the partitioning of water fluxes between runoff Q and actual evaporation EA (note that EA=EI+ET). While the fraction of precipitation that was released into the atmosphere as vapour was reduced (E‾A/P‾; Fig. 5a), the mean runoff ratio (CR=1-E‾A/P‾) increased correspondingly from CR=0.55±0.04 to CR=0.68±0.03 after deforestation of 21 % of the catchment with p=0.049 based on a Wilcoxon rank sum test. In absolute terms this entails that, notwithstanding rather stable mean annual precipitation P=1269±24 mmyr-1 and potential evaporation EP=632±9 mmyr-1 over the entire study period, the annual actual evaporation EA decreased from 576±11 to 401±6 mmyr-1, whereas annual runoff Q increased by ∼25 % from 694±47 to 870±63 mmyr-1.

In spite of similar climatic conditions, the above is reflected in a significantly higher (p=0.047) mean annual maximum storage deficit in the pre-deforestation period than in the post-deforestation period. In the pre-deforestation period values between 105±23 mm for Imax=0mm and 95±21mm for Imax=4mm, respectively, were found (Fig. 5b), whereas in the post-deforestation period the mean storage deficit only reached between 49±10 and 33±7 mm for the same values of Imax (Fig. 5b). Note that in both periods, SD,j is relatively insensitive to the magnitude of Imax (cf. Gerrits et al., 2009). From the above maximum annual storage deficits SD,j, the corresponding catchment-scale vegetation-accessible water storage capacity, assuming vegetation adaptation to dry conditions with 40-year return periods (see Sect. 4.1), was estimated at values of SU, max=258±125 mm for the pre-deforestation (R2=0.91, p=0.04; Fig. 5c) and SU, max=101±149 mm for the post-deforestation period (R2=0.83, p=0.27; not shown).

While the volume-weighted mean δ18O compositions of observed precipitation with -7.9 ‰ and stream water with -8.2 ‰ are comparable, a substantial difference in their fluctuations, with standard deviations of 3.6 ‰ and 0.2 ‰, respectively, is evident (Fig. 3a, b). This difference suggests a remarkably elevated degree of damping rarely found elsewhere (e.g. Speed et al., 2010), indicative of the importance of old water contributions to the stream in the study catchment. No significant difference in damping ratios was observed between the pre- and post-deforestation periods, which further corroborates the prevalence of old water.

Tracking the δ18O signals through the model then allowed us to estimate TTDs. Note that any results reported hereafter are necessarily conditional on the assumptions made in and the uncertainties arising from the modelling process.

In general and consistent with the observed high degree of damping, it was found that pre-deforestation of the system was characterized by rather old water. The range of truncated TTDs of stream water exhibits considerable variability in response to changing wetness conditions, with on average about 27 % of the discharge younger than 3 years (Fig. 9b, c). In spite of the low mean Fyw∼0.12 (Fig. 10a), stream water can contain up to 34 % water younger than 3 months (i.e. Fyw∼0.34) for individual storm events in the wet period while frequently dropping to <1 % during elongated summer dry periods (Figs. 8c, 9a), similar to what has been reported elsewhere (e.g. Gallart et al., 2020b). It can also be observed that the age composition of stream water (Fig. 9c) and the associated Fyw (Fig. 10a) do considerably vary throughout wet periods. Dry periods are characterized by considerably less variability and more stable stream water TTDs. This is further corroborated by the significantly higher sensitivity of Fyw to changes in streamflow in wet-up and wet periods (dFyw/dQn∼0.35 and 0.25, respectively) as compared to dry periods (dFyw/dQn∼0.05; Fig. 10c). In spite of the low mean Fyw∼0.12 (Fig. 10a), the above also entails that very fast switches towards higher young water fractions can be observed when the system is wetting up after dry periods as well as for storm events throughout the wet season. In general, the above observations are also encapsulated in the catchment-overall storage-age selection functions ω that represent the ratio of stream water TTD over the combined RTD of all model storage elements (Benettin et al., 2015a). While for dry periods undersampling of young water ages with relatively little variability is evident, it can also be seen that in particular during wet-up and wet periods a considerable yet highly variable preference for very young water can be seen (Fig. 11a), similar to what has been reported previously in other environments (e.g. Benettin et al. 2015a; Remondi et al., 2018).

The overall picture did not change in the post-deforestation period. Similarly to the pre-deforestation period, the TTDs can exhibit considerable variability. However, in contrast to the pre-deforestation period, and depending on the wetness conditions, considerable shifts towards younger water can be observed for the TTDs (Fig. 9d–g). There are little discernible changes in Fyw during the dry summer months (Fig. 9d). However, storms in wet-up periods, mostly during autumn, led to considerable increases in the fractions of water younger than 10–20 d (Fig. 9e). During wet periods clear shifts towards younger water can be observed throughout the entire spectrum of tracked ages (Fig. 9f). During the wet period ∼36 % of the stream water is on average younger than the tracked 3 years (Fig. 9i). The mean Fyw only slightly increased to 0.13 (Fig. 10b) compared to 0.12 in the pre-deforestation period (Fig. 10a), which corroborates earlier results by Stockinger et al. (2019) that suggested only minor fluctuations in mean Fyw over multiple moving time windows. For individual winter storm events, Fyw slightly increased to up to ∼0.37 (Figs. 9j, 10b) compared to Fyw of up to ∼0.34 in the pre-deforestation period (Figs. 9c, 10a). Besides the generally higher Fyw during wet periods, the Fyw became more sensitive to flow during wet conditions, with dFyw/dQn∼0.36 (Fig. 10d), similar to what has been previously reported by von Freyberg et al. (2018) and Gallart et al. (2020a). The above-described post-deforestation changes are also manifest in the corresponding storage-age selection function ω (Fig. 11b) for that period. While the degree of undersampling of young water during dry periods significantly decreased, a substantially higher preference for young water during wet-up and wet periods can be observed than during the pre-deforestation period, with a clear overall shift towards younger water for all wetness conditions.

The observed post-deforestation changes to the hydrological response, in particular the increase in CR from ∼0.55 to ∼0.68, correspond well to the findings of an earlier study in the Wüstebach, based on a shorter study period (2011–2015; Wiekenkamp et al., 2016), which estimated an increase in CR from ∼0.58 to ∼0.66 during that period using eddy-covariance measurements. The overall pattern found here also broadly reflects the effects of land cover/use change in many different environments (Creed et al., 2014; Jaramillo and Destouni, 2014; Renner et al., 2014; van der Velde et al., 2014; Moran-Tejada et al., 2015; Nijzink et al., 2016a; Zhang et al., 2017; Jaramillo et al., 2018). The vast majority of these studies suggest that forest removal leads to an increase in the runoff ratio CR at the cost of reduced evaporation EA, although the magnitudes of these changes do substantially vary between individual catchments and studies, which is consistent with our physical understanding of the importance of forest for transpiration in hydrological systems.

Under the assumption that reduction of EA is largely a direct consequence of forest removal in the Wüstebach, a plausible hypothesis to directly attribute this shift in water partitioning from EA to Q to a physical process can be formulated as follows: the roots of harvested trees stopped extracting water for transpiration from the sub-surface. In addition, the limited turbulent exchange of vapour at depth effectively limits soil evaporation to the first few centimetres of the soil (e.g. Brutsaert, 2014). Thus, the felling of trees led to a situation where under comparable atmospheric water demand EP, water volumes held at depths below that and previously within the reach of active roots became largely unavailable for transpiration and evaporation after deforestation. This implies that the water volumes accessible to satisfy atmospheric water demand, i.e. SU, max and Imax, are drastically reduced. Most notably, the available water balance data suggest that catchment-scale SU, max decreased from pre-deforestation SU, max=258±125 mm to post-deforestation SU, max=101±149 mm.

Note, however, that in particular the estimates for the post-deforestation period are characterized by considerable uncertainty and therefore need to be understood as merely indicative, as they are inferred from only 3 years of data and a system that is likely to be far from equilibrium, because the deforested part cannot have adapted yet (e.g. Nijzink et al., 2016a; Teuling and Hoek van Dijke, 2020). These considerable uncertainties are also reflected in the surprisingly low post-deforestation SU, max.

Notwithstanding these limitations, the above results illustrate that here the reduction of transpiration due to deforestation is likely a direct consequence of the considerable reduction of SU, max and thus the catchment-scale sub-surface pore volume between field capacity and permanent wilting point that can be actively accessed by vegetation to satisfy the evaporative demand. These post-deforestation decreases in transpiration due to reductions in accessible water volumes SU, max further lead to reduced soil water storage deficits SD,j (Eq. 2) in dry seasons, which is consistent with observed post-deforestation increases in soil moisture (Wiekenkamp et al., 2016).

The model application provided further evidence for the central role of SU, max as a dominant control on the hydrological response as well as for the direct effects of deforestation on SU, max. The model calibration in the pre-deforestation period resulted in a set of solutions that could simultaneously reproduce multiple signatures, as expressed by 14 individual performance metrics, while also satisfying two additional limits-of-acceptability constraints. Overall this suggests a rather robust representation of the system.

In a next step, the parameter sets obtained from the calibration in the pre-deforestation period were used to run the model without further re-calibration in the post-deforestation period. This entails the implicit and clearly wrong assumption that the physical characteristics of the system remained unaffected by deforestation. As a consequence, that model exhibited a considerably reduced ability to reproduce the hydrological response in the post-deforestation period, in particular high flows as well as the runoff ratio CR. The latter implies that the model also overestimates post-deforestation evaporative fluxes EA. Therefore, it can, without re-calibration, not deal with the observed changes in the partitioning between drainage and evaporative fluxes (Fig. 5a). A likely explanation for the pattern produced by the model is that, in contrast to the real world, no reduction in EA due to the reduced forest cover is achieved because the model still relies on the catchment-scale vegetation-accessible storage volume SU, max that characterizes the extent of the catchment-scale active root system before deforestation. This SU, max falsely provides sufficient water supply to sustain EA at high levels comparatively close to EP throughout the year (see red line in Fig. 2b), although, in the parts of the catchment where trees were removed, water stored at depths below a few centimetres is not available for significant evaporation anymore in reality. Such an overestimation of SU, max implies also that in the model a more pronounced water storage deficit can and does develop throughout dry periods. The model therefore assumes that soils dry out to deeper depths. Consequently, to establish connectivity and to eventually generate flow during and after rainstorms, more water needs to be stored in the model than in the real-world system to overcome this deficit. This water is then in the model held against gravity and thus only available for evaporation but not for drainage, thereby underestimating in particular the magnitude of high flows. Although it is reasonable to assume that groundwater recharge is affected in a similar way, the model can better reproduce low flows. The reason for this is that the draining groundwater body, which sustains summer low flows, is, due to limited recharge during these drier periods, largely disconnected from and thus largely unaffected by sub-surface–vegetation interaction in shallower parts of the sub-surface. In the parts of the catchment where trees were removed, a similar reasoning also holds for the interception capacity Imax and the associated likely overestimation of interception evaporation EI, yet, due to the smaller magnitude of Imax, to a lesser extent than for SU, max.

Re-calibration of the model in the post-deforestation period led to a considerably improved representation of the hydrological response and in particular of the high flows as well as the runoff ratio CR. The latter implies that the modelled partitioning of water fluxes and in particular EA (see orange line in Fig. 2b) is more consistent with the observed post-deforestation reductions in EA. In addition, analysis of the modelled fluxes indicates that a higher proportion of flows, mostly during wet-up periods, is rapidly released from the root zones as fluxes RF,H and RF,R (Fig. 4; Table 1), representing preferential flows. Such a post-deforestation increase in preferential flow occurrence is supported by observations recently reported by Wiekenkamp et al. (2020).

It is of course unsurprising that re-calibration leads to an improved model performance in the post-deforestation period. Without further analysis, such a mere model fitting exercise allows in the presence of model equifinality only little insight into the underlying processes (Beven, 2006; Kirchner, 2006). To gain more confidence that the improvements in the recalibrated model are at least partly due to the right reasons (Kirchner, 2006), the changes in the posterior parameter distributions resulting from the two calibration runs were thus analysed. In the pre-deforestation period, the range of the posterior distributions of SU,max,H and SU,max,R (Fig. 8a, b) as well as the modelled catchment average SU, max=240mm, estimated as an area-weighted average of SU,max,H and SU,max,R, come close to the catchment-scale estimate of SU, max=258±125 mm that was directly derived from water balance data without any calibration (Fig. 5c). The modelled post-deforestation reductions of SU,max,H and SU,max,R are evident in the shifts of their respective posterior distributions (Fig. 8a, b) and the lower catchment average SU, max=199mm of the best-performing parameter set, falling into the plausible range of SU, max=101±149 mm as estimated from water balance data. In addition and quite remarkably, the re-calibrated model is able to broadly represent the differences in forest removal on the hillslopes and in the riparian zone. While in the fully deforested riparian area SU,max,R decreased by ∼100 mm (Fig. 8b), SU,max,H on the only partly deforested hillslopes decreased by merely ∼50 mm (Fig. 8a). Similarly, there is little evidence for reductions of Imax,H on the less deforested hillslopes (Fig. 8d). However, a clear decrease in interception capacities by on average ∼2 mm to Imax,R=1.1mm (0.1–1.3 mm; Fig. 8e) can be observed in the riparian zone. Comparing to the posterior distributions of other parameters, the results illustrate that the storage parameters SU, max and Imax of the completely deforested riparian zone, and to a lesser extent of the hillslope, were subject to the most pronounced changes. For most other parameters, the pre- and post-deforestation posterior distributions exhibit much less pronounced differences (Fig. 8). Together, these results suggest that deforestation mostly affects SU, max and Imax, while there is less evidence for systematic changes in other parameters. However, it can also be observed that the individual parameter values associated with the best model solutions in the pre- and post-deforestation periods, respectively, do vary to a stronger degree for most parameters. Notwithstanding the distinct overall effects of forest removal on the individual posterior distributions, this clearly highlights the influence of parameter compensation effects and related uncertainties. This is also illustrated by a few parameters, such as RS,max (Fig. 8c, Eq. 22), that remain poorly constrained.

It was hypothesized above that reductions in evaporative fluxes are directly and exclusively linked to reduced water volumes SU, max and Imax, respectively, which are accessible and available for evaporation and transpiration at the catchment scale. In the theoretical ideal case, the representations of the associated storage capacities in the model, i.e. the parameters SU, max and Imax, should thus be the only ones to significantly change after deforestation. However, note that this is unlikely for two reasons. First, while it is plausible to assume that these storage capacities are significantly affected by forest removal, it is not unlikely that other system characteristics and their mutual interactions, so far unknown and not considered, are similarly influenced, potentially causing considerable ontological uncertainty. Second, model parameter interactions that arise as artefacts to compensate overly simplistic process representations and/or data uncertainty are also likely to affect parameters seemingly unrelated to deforestation. Note that in spite of these uncertainties and the associated compensation effects, in particular SU, max remains rather well constrained. However, after preliminary unsuccessful testing, no further attempts were made to re-calibrate only the above discussed four storage parameters, i.e. SU,max,H, SU,max,R, Imax,H and Imax,R, acknowledging the limitations introduced by parameter compensation effects.

Overall these results suggest that the model formulation together with the multi-objective calibration strategy ensured the identification of solutions that provide a robust description of the system and allow a simultaneous representation of flow and isotope dynamics in the stream. There are indications that at least some processes and parameters can be directly linked to real world quantities. In particular, the results provide strong evidence that the parameters SU,max,H and SU,max,R are not merely abstract quantities, but that it is plausible to assume that they, taken together, provide a catchment-scale representation of vegetation-accessible and vegetation-accessed water volumes, which can be estimated based on water balance data without calibration as defined by Eq. (2), thereby providing an alternative to small-scale in situ observations. As such, the parameter SU, max is also a means to directly and independently estimate the catchment-scale effects of deforestation, and plausibly other types of land cover disturbances, on sub-surface system properties, which underlie and control the changes in the post-disturbance partitioning of water fluxes into drainage and evaporative fluxes.

Tracking water fluxes through the system, it was observed that wet periods are characterized by substantially more variability and more stable stream water TTDs than dry periods. This is largely a consequence of increased bypass flow that has little interaction with resident water as the system gets wetter and that may reach the stream over preferential flow paths and increased contributions from the riparian zone with its shorter flow paths. In other words, in a wet system where little additional water can be stored, the precipitation volumes of individual storm events control the shape of TTDs, resulting in considerable variability (Heidbüchel et al. 2020). In the summer dry season, however, precipitation is to a higher degree buffered in the root zone and used for transpiration (Stockinger et al., 2014). Conversely, streamflow is then mostly sustained by groundwater which is characterized by large volumes of older water. This effectively attenuates fluctuations by the proportionally much lower volumes of younger precipitation water that cannot be stored and is thus quickly released to the stream.

In particular, at the beginning of the wet period, elsewhere also referred to as “autumn flush” (e.g. Dawson et al., 2011), the switches towards younger water at given flow levels occur considerably faster in the post-deforestation period than in the pre-deforestation period. Therefore, where, at the same discharge, previously relatively little young water reached the stream, a much higher fraction of young water can now be observed in the stream. Underlining the role of transpiration (e.g. Douinot et al., 2019; Kuppel et al., 2020), this is a direct effect of the reduced evaporative removal of relatively young near-surface water (Maxwell et al., 2019) in the post-deforestation period, which in turn is intimately linked to the reduced water supply for evaporative fluxes, i.e. smaller storage volumes SU, max and Imax. This modelled relatively young, surface-near water, not taken up by vegetation anymore is thus to a higher degree flushed from the system mostly via preferential flow paths to the stream (i.e. RF,H, RF,R) and thus bypassing older resident water with little exchange, which is consistent with recent observations of more frequent activation of preferential flow paths (Wiekenkamp et al., 2020). Once connectivity and the associated higher degree of bypass flow are established in the wet period, the post-deforestation peak sensitivity of dFyw/dQ to flow increased to ∼0.36, as under these conditions when little additional water can be stored in the shallow sub-surface, Fyw is largely controlled by magnitude of the individual precipitation signals and to a lesser extent by the footprint of the pre-storm history of evaporative fluxes in the shallow sub-surface storage. In contrast, no significant post-deforestation changes could be observed for the sensitivity of Fyw to discharge during dry periods, as during that period, the composition of water ages is controlled by large volumes of old water.

Altogether these results suggest that even in systems dominated by old water, such as the Wüstebach, the removal of forest has the potential to increase the importance of bypass flow through fast flow paths and thus increase the risk of fast, often underestimated propagation of contaminant pulses into groundwater and stream water (e.g. Hartmann et al., 2021).

As emphasized above, all results are conditional on the assumptions made throughout the modelling process. These assumptions, present in model structure, parameterization and parameters, can lead to uncertainties. However, notwithstanding these potential uncertainties, extensive preliminary model testing together with the use of multiple model calibration and evaluation criteria suggests that there is relatively strong evidence to support the main results in this study: the post-deforestation reduction of evaporative fluxes can, at least partially, be linked to a relatively clear reduction in the catchment-scale storage capacities SU, max and Imax, which in turn triggered a shift towards younger water ages in the stream, particularly during wet-up and wet conditions.

This is further corroborated when comparing the estimates of SU, max to estimates of physically plausible upper limits of SU, max. By definition, SU, max is physically bound by the depth of the groundwater table. Although fluctuating, the groundwater table in the Wüstebach remains at depths below 1 m for much of the year even in the riparian zone (Bogena et al., 2015) and can be expected to be considerably deeper on the hillslopes. Thus assuming a conservative upper bound of catchment-average depth of the groundwater table at ∼5 m, assuming that the lowest groundwater table at each point in the catchment is at the elevation of the nearest stream, a porosity of the silty clay loam soil of 0.4 (Bogena et al., 2018) and field capacity at a relative porewater content of 0.5 suggests an upper limit of SU,max,GW∼1000 mm. However, actual roots are very often shallower than these 5 m of the groundwater table. Although sufficient detailed data on root depths are not available in the study catchment, there is no evidence for systematic and widespread roots extending to below 2 m. This is broadly consistent with direct experimental evidence that roots of temperate forests in general (Schenk and Jackson, 2002) and Picea species in particular mostly remain rather shallow (<1 m; e.g. Schmid and Kazda, 2001) and with indirect evidence that Picea species rarely tap groundwater and are thus comparatively shallow (e.g. Evaristo and McDonnell, 2017). As a conservative back-of-the-envelope calculation, assuming thus a maximum plausible catchment-average root depth of 2 m, which comes close to the average observed soil depth reported in Graf et al. (2014), rather suggests a physically plausible upper limit of SU,max,RD∼400 mm, which is not exceeded by the water balance inferred catchment-scale estimates of SU, max=258±125 mm.

Note that the above also suggests the presence of an unsaturated transition zone between the root zone and the groundwater table, i.e. SU,max,TZ=SU,max,GW-SU,max,RD∼600 mm. In the absence of root water uptake and likely negligible soil evaporation in that zone the water content will remain close to field capacity for much of the year, except for days when a wetting front infiltrates towards the groundwater. This transition zone can therefore be considered as hydrologically largely passive so that at timescales of more than a few days dS/dt∼0. However, this zone also provides a mixing volume that affects tracer circulation and thus water ages (Hrachowitz et al., 2015). Given its hydrologically passive nature and following the idea of a parsimonious model to limit uncertainty, we here, in a simplification, implicitly added the mixing volume SU,max,TZ to the passive groundwater mixing volume SS,p.

For a meaningful interpretation, two specific observations resulting from our analysis warrant special scrutiny. First, model calibration-based estimations of hillslope SU,max,H (Fig. 7a) suggest post-deforestation median SU,max,H reductions of ∼25 % as a consequence of clear cutting only ∼10 % of the hillslope part of the catchment (Fig. 1). While this may be surprising at first, it can be plausibly explained by considerable further thinning of the remaining forest on the hillslopes in 2015, 2 years after deforestation, and thus by reduced catchment-scale transpiration demand. However, no detailed and systematic data on the degree of forest thinning are available to meaningfully test this hypothesis.

Second, our results suggest that a passive mixing volume SS,p of at least ∼8000 mm is necessary for the model to attenuate the amplitudes of the precipitation δ18O signals to those in the stream water. Although SS,p is rather well constrained (Fig. 8h), there has in the past been no hydrogeological evidence for the presence of such a surprisingly large groundwater volume nor for its hydrological relevance in the study catchment. Indeed, the authors are not aware of any catchment-scale study that reported similarly high values for SS,p or functionally equivalent parameters (e.g. Birkel et al., 2011a, b; Hrachowitz et al., 2013, 2015; Benettin et al., 2013, 2015a; Harman, 2015; van der Velde et al., 2015). However, to achieve the degree of damping observed in the stream water, such a volume is necessary if the current understanding of conservative tracer dynamics holds (e.g. Maloszewski and Zuber, 1982; McGuire and McDonnell, 2006). Reflecting our insufficient knowledge of the depth to which exchange with surface water occurs (e.g. Condon et al., 2020), a potential explanation for this observation is that the frequently layered and fractured structure of the Devonian shale bedrock may provide relatively high-permeability pathways for the circulation of and exchange with water at depth. Another, yet, given the current understanding of the Wüstebach (e.g. Graf et al., 2014), less likely hypothesis is the presence of significant lateral groundwater exchange (e.g. Bouaziz et al., 2018; Hulsman et al., 2021b). In other words, the possibility exists that the sub-surface catchment does not match with the surface catchment (Fig. 1) and that older groundwater is imported from “outside” the surface catchment, while an equivalent volume of younger groundwater is exported, maintaining the mass balance. These are hypotheses to be tested in future studies, as the currently available data do not allow a conclusive answer to this question.