The study catchment of Chenqi, with an area of 1.25 km2, is located in the Puding Karst Ecohydrological Observation Station in Guizhou Province of south-western China (Fig. 1). It is a typical cockpit karst landscape, with surrounding conical hills separated by star-shaped valleys (Zhang et al., 2011; Chen et al., 2018). The catchment, which is drained by a single underground channel/conduit, can be divided into two units: depression areas with low-elevation (<1340 m) and steeper hillslopes with high elevation ranging from 1340 to 1500 m. The spatial extent of the depression and hillslopes is 0.37 and 0.88 km2, respectively.

Geological strata in the basin include dolostone, thick and thin limestone, marlite and Quaternary soil profiles (see the cross sections of A-A' and B-B' in Fig. 1). Limestone formations dominate the higher elevation areas with 150–200 m thickness, which lie above an impervious marlite formation. Therefore, precipitation recharging can be perched on the impervious marlite layers that discharge in the lower areas (mostly as hillslope springs). In the hillslopes, Quaternary soils are thin (less than 30 cm) and irregularly developed on carbonate rocks. Outcrops of carbonate rocks cover 10 %–30 % of the hillslope area. In the depression, soils are thick (>2 m deep). Dominant vegetation ranges from deciduous broad-leaved forest on the upper and middle parts of the steep hillslopes to corn and rice paddy in the lower gentle foot slopes and depressions, where soils are also thicker. The paddy fields are often flooded for the summer during the heavy rainfall period. Additionally, there are three sinkholes outcropping in the depression where the surface and subsurface runoff can be directly drained into the underground channel during heavy rainfall events.

The catchment is located in a region with a subtropical wet monsoon climate with a mean annual temperature of 20.1 ∘C, highest in July and lowest in January. Annual mean precipitation is 1140 mm, almost all falling in a distinct wet season from May to September and a dry season from October to April. Average monthly humidity is high, ranging from 74 % to 78 %.

In Chenqi catchment, the discharges of a hillslope spring (HS) located at the foot of the eastern steep hillslope and the underground channel at the catchment outlet were measured with v-notch weirs (Fig. 1). Their water levels were automatically recorded by a HOBO U20 water level logger (Onset Corporation, USA) with a time interval of 15 min. Additionally, an automatic weather station was established on the upper hillslope to record precipitation, air temperature, wind, radiation, air humidity and pressure. The data collection ran from 28 July 2016 to 30 October 2017. During the drought period, there were a few times that flow discharges ceased (328 and 713 h of zero flow for outlet and HS, respectively). Although the hillslope flow discharge was much smaller than the outlet discharge, their patterns in temporal variability were similar in terms of flow duration curves (Fig. 2).

For isotope analysis, precipitation, the hillslope spring and catchment outlet flows were intensively sampled during eight rainfall events in the wet season (May–October) using an autosampler set to hourly intervals (from 12 June to 14 August 2017). Groundwater in the low-elevation depressions was also sampled from four wells (Fig. 1), with depth below the ground surface ranging from 13 to 35 m, during four rainfall events. The well screening was installed over the whole depth for each of the wells to reflect local flow exchanges at various depths in the karst. In each event, groundwater samples were collected before, during and after rainfall at each well from multiple depths.

All water samples were collected in 5 mL glass vials. The stable isotope compositions of δ2H (δD) and δ18O ratios were determined using a MAT 253 laser isotope analyser (instrument precision ±0.5 ‰ for δ2H and ±0.1 ‰ for δ18O). Isotope ratios are reported in the d-notation using the Vienna Standard Mean Ocean Water standards. Statistical characteristics of isotope signature are summarized in Table 1.

The model used in this work was based on a simpler framework developed in a previous study to simulate the catchment-scale water and solute transport (Mg and Ca) in the dual flow system of the karst critical zone at daily time steps (Zhang et al., 2017). The original model had no basis for spatially disaggregating differences in flow and tracer dynamics from different landscape units. Here we significantly improved the model structure by separately conceptualizing the dominant hillslope and depression landscape units (Fig. 3), and then used the high-resolution discharge and isotope data to drive the modelling at hourly time steps. In addition, the new model has the parameters to represent passive storage inferred by isotope damping and the capacity to track the ages of water fluxes from various landscape units. As shown in Fig. 3, Chenqi catchment was therefore sub-divided into two spatially distinct units to represent the hillslope and depression. The depression unit was further conceptualized into two flow systems, represented by “fast” and “slow” flow reservoirs which could exchange water. In contrast, the hillslope unit was conceptualized as a single reservoir because of the dominant influence of the thin soil/epikarst on water movement.

The modelling period started on 23 July 2016, but calibration was initiated using available discharge data from 1 November 2016. The preceding 3 months were therefore used as a spin-up period (the mean of precipitation isotope signatures over the sampling period was used for the spin-up period) to fill storages, initialize storage tracer concentrations, and minimize the effects of initial conditions on water age calculations.

The modified Kling–Gupta efficiency (KGE) criterion (Kling et al., 2012) was used as the objective function for calibration. The KGE breaks the goodness of fit into three components, and so is more representative of the overall simulation than the traditionally used Nash–Sutcliffe metric which focuses on flow peaks. This overcomes some limitations of the latter (Schaefli and Gupta, 2007) and balances how well the model captures the dynamics (correlation coefficient), bias (bias ratio) and variability (variability ratio) of the actual response. Using flow and isotopic composition as calibration targets, objective functions were combined to formulate a single measure of goodness of fit: KGE = (KGEd+ KGEi)/2 (where KGEd is discharge and KGEi is isotopic composition).

The time series of discharge and isotope data were different in length. The high-resolution samples for stable isotope composition were collected over eight events from 12 June to 13 August 2017, giving a total of 589 samples. Hence, KGEd and KGEi were each calculated using all the available data for the outlet discharge and isotope ratios, respectively. Additionally, available data such as the discharge and stable isotope signatures of hillslope spring and isotopes in the depression wells were used as qualitative “soft” data to aid model evaluation. A Monte Carlo analysis was used to explore the parameter space during calibration (Table A2) and the modelling uncertainty. In order to derive a constrained parameter set, two iterations were carried out in the calibration. First, a total of 105 different parameter combinations within the initial ranges (initial range 1 in Table 2) were randomly generated as the possible parameter combinations (Soulsby et al., 2015; Xie et al., 2017). After the first calibration using KGE > 0.3 as a threshold, the range of each parameter was narrowed. Then, the narrowed ranges (initial range 2 in Table 2) were used as for the second calibration. From the total of 105 tested different parameter combinations, only the best (in terms of the efficiency statistics) parameter populations (500 parameter sets) were retained and used for further analysis, which included calculation of simulation bounds representing posterior parameter uncertainty (Birkel et al., 2015).

A regional sensitivity analysis (Freer et al., 1996) was further used to identify the most important model parameters. The parameter sets were split into 10 groups and ranked according to the selected objective function. For each group the likelihoods were normalized by dividing by their total, and the cumulative frequency distribution was calculated and plotted. If the model performance is sensitive to a particular parameter there will be a large difference between the cumulative frequency distributions compared to a 1:1 line.

The lc excess describes the deviation of a water sample from the local meteoric water line (LMWL) in dual-isotope space, which indicates evaporation-driven kinetic fractionation of precipitation inputs (Sprenger et al., 2016; McCutcheon et al., 2017). With a known LMWL of δ2H =α⋅ δ18O +β, it was thus proposed by Landwehr and Coplen (2004) that lc excess = δ2H -α⋅ δ18O -β. As oxygen has a higher atomic weight, non-equilibrium fractionation during the liquid-to-vapour phase change will preferentially evaporate (in terms of statistical expectation) 1H2H16O molecules. The isotopic signature of a water sample affected by evaporation thus shows negative lc-excess values, and plots under the LMWL in dual-isotope space (Landwehr et al., 2014). The LMWL of δ2H =7.77⋅ δ18O +4.88 was defined based on a daily value set of an isotope signature at precipitation from August 2016 to September 2017 in Chenqi catchment. The calculated lc-excess values were shown in Table 1.

The storage dynamics of the catchment derived from the model in order to simulate the concurrent flow and tracer response can be disaggregated according to the conceptual stores (Fig. 8). The model structure dictates that the main variability in the runoff response to precipitation is driven by the storage dynamics, depending on hydrological connectivity between the hillslope (Vh) and slow (Vs) and fast (Vf) flow reservoirs (Fig. 3). The modelled storage results show that slow flow reservoir was the largest store in the catchment (> 100 mm with a mean of 245 mm), consistent with the wide distribution of small fractures and matrix pores in the karst critical zone (Zhang et al., 2011, 2017). The fast flow reservoir had the smallest storage (the mean value was only 0.2 mm) because the underground river/conduit volume represents only a very small proportion of the porosity of the entire aquifer. Although the hillslopes cover a larger area than the depression, the thin soil, shallow epikarst and rapid drainage resulted in a relatively small dynamic storage reservoir, with a calibrated mean value of 23 mm. The discharge over the study period showed clear seasonality, which reflects the uneven distribution of precipitation throughout the year (Fig. 4a). This seasonality is mirrored somewhat differently in the storage dynamics of each reservoir (Fig. 8). The storage change in fast flow reservoir was very rapid, especially in the wet season, reflecting rapid recharge and water release. The rapid response of storage to rainfall was also evident in hillslope reservoir because of the low capacity and short response time.

Using flow and isotopes at the catchment outlet as calibration targets, the uncertainty bands for the three storages increase in the order fast flow in the depression < hillslope flow < slow flow in the depression (Fig. 8). Additionally, the uncertainty bands become narrower in the wetter period (Figs. 6 and 8). This indicates that the model structure along with the calibration targets emphasizes the rapid flow component, and the modelling uncertainty increases when flux components from storage units are less closely correlated with the outlet discharge used as the calibration target.

The relative contributions of the different sources to streamflow changed with hydroclimatic conditions, and this could be estimated using the calibrated model. Figure 9 shows that during the dry period (November 2016 to April 2017), underground streamflow was mainly sustained from the small fractures (conceptualized as release from the slow flow reservoir). Overall, this provided the largest proportion (78.4 %) of dry season flows, followed by the hillslope unit contribution (16.8 %). During this period, direct rainfall infiltration contributed only limited water to the underground stream (4.8 %) due to the low rainfall and limited storage, resulting in weak hydrological connectivity between the hillslope and depression. During the wet period, with the resulting rapid increase in storage, the hillslope unit contributes much more water to the underground stream, accounting for the largest proportion (57.5 %) of overall flow, due to the strong hydrological connectivity between the hillslope and depression. Meanwhile, the contribution of direct rainfall infiltration to the underground streamflow also increased (with an overall wet season contribution of 35.6 %). This likely reflects the increased influence of sinkholes and larger fractures as the catchment becomes wetter. In such conditions, during storm events, overland flow and epikarst water were collected by sinkholes and large fractures and recharged to underground stream directly. The relative contribution of small fractures in the slow reservoir decreased substantially (7 %), although the overall magnitude of the water flux to the underground stream increased during the wet period.

The bi-directional exchange between the underground conduit and the surrounding porous matrix is a characteristic feature of the karst critical zone (Zhang et al., 2017). During the dry period, as water table levels in the conduits drop more rapidly than in the matrix, water stored in the matrix drains into conduits and underground channels as baseflow. In the wet season, especially during the periods of highest flow, infiltrated water quickly fills conduits where the water table is higher than the adjacent matrix. Water is temporarily stored in the conduits, and hence induces recharge in the matrix. These bi-directional exchange flows between the underground channels and the matrix were captured by the model (represented by fast and slow reservoirs, respectively) and are shown in Fig. 9, where the negative values represent the flux from conduits to the adjacent matrix. This bi-directional flow was affected by the wetness conditions, being evident in the wet season and indicating both the seasonal and short-term temporal change in hydrological connectivity between the fast and slow flow reservoirs. Despite this, as the parameter Ke that determines the exchange between the fast and slow flow reservoirs is insensitive (Fig. 5), the simulated exchange flux is more uncertain (red lines in Fig. 9) compared with the water fluxes from the direct rainfall and hillslope flow.

The ages of water fluxes from the different landscape units were tracked using the model. The simulated ages were linked to the size of storage in each unit and the ages decreasing in the order of hillslope reservoir < fast flow reservoir < slow flow reservoir, with mean ages of 137, 326 and 493 days over the study period, respectively (Fig. 10). The mean ages of water flux decreased between the dry and wet seasons, ranging from 159, 466 and 528 days for the dry season to 115, 187 and 458 days for the wet season, hillslope, and fast flow and slow flow reservoirs, respectively. The ages of fluxes from hillslope flow and fast flow reservoirs change greatly for each of the rainfall events. For short-term (event based) responses to the rainfall, the ages of water from hillslope flow and fast reservoirs can be as short as 4 and 2 days, respectively. There were 8 and 23 events for the fast flow when the ages of water were less than 5 and 10 days, respectively (see the lowest values in Fig. 10).

The ages of fluxes from the fast flow reservoir in the underground stream generally reflected the integration of younger water fluxes from the hillslope and older fluxes from the slow flow reservoir, as shown in the time-variant flux ages shown in Fig. 10. Consequently, the water age dynamics of the fast flow reservoir were relatively close to the slow flow reservoir in the dry season and close to the hillslope reservoir in the wet season as connectivity changed. This is consistent with the changing storage dynamics shown above. However, a distinct feature in Fig. 10 is that the water ages in the fast flow reservoir were younger than that from the hillslope reservoir during some events in the wet period. This again most likely reflects the role of sinkholes in collecting water with a high proportion of new rainfall (young water) in intense wet season rain events and then recharging underground stream rapidly due to the direct, transient connectivity.

Figure 10 also shows that uncertainty bands increase with age in the three water fluxes, i.e. narrowest for the youngest hillslope flow and widest for the oldest slow flow. However, the seasonal changes of uncertainty bands are different for the three water fluxes. For the hillslope flow and the fast flow in depression, the uncertainty bands reduce in the wet period as ages decrease. In contrast, for the slow flow reservoir, uncertainty bands increase during the wet period (Fig. 10). This underlines the resulting uncertainty for the slow reservoir, reflecting the structural limitations with the model for conceptualizing the flow dynamics of this heterogenous zone during the rainfall season.

The probability density functions (PDFs) of the simulated flux ages from the three reservoirs are shown in Fig. 11 (using the best 500 parameter sets). The ages of fluxes from the fast flow reservoir varied from a few days to over 600 days, and it is clearly evident that the PDF was bimodal, with peaks corresponding to water ages of ∼100 and ∼550 days. From the water age dynamics in Fig. 10, it is equally clear that the bimodal distribution of ages of underground streamflow reflected the seasonality of different water source contributions in the wet and dry seasons. The underground streamflow was dominated by older water from the matrix and small fractures during the dry period and by younger hillslope fluxes during the wet period, respectively. The water age distributions for the hillslope also showed seasonal bimodality in flux ages, albeit less pronounced, though the model has also produced a less smooth distribution of more transient younger ages.

Since the hillslope depression is a typical landform with variable hydrological connectivity in the karst catchments in the south-west of China and elsewhere, the separation of the hillslope and depression in the new model structure improved model performance and yielded more informative results showing clearly the flow and tracer dynamics within different landscape units, as well as tracking spatially distributed storages and ages of water flux. The model was successfully calibrated to the flow and tracer dynamics at the catchment outlet; the results also showed more qualitatively consistent performance in terms of the dynamics of the modelled hillslope fluxes compared with spring discharge and the simulated isotopic composition of fluxes with measurements in the spring and wells. Moreover, the modelling approach is potentially transferable to other cockpit karst catchments with similar landscape organization.

The tracer-aided model supports general appropriateness of the model structure which related connectivity dynamics to storage change within different landscape units. During the dry period, there is weak hydrological connectivity between the hillslope and depression due to the low hydraulic gradients and/or hydraulic conductivity. In contrast, during the wet period, hydrological connectivity between the hillslope and depression strengthens as water storage increases. In the early recession, after heavy rain, large fractures in the hillslope fill, leading to large water fluxes into the depression. Then, as storage declines, fluxes decrease and the hydrological connectivity weakens. Moreover, in each of the units, there is hydrological connectivity and exchange between dual porosity systems that were conceptualized as the slow and fast flow reservoirs in this study. The hydrological connectivity and exchange between the slow and fast flow reservoirs is mainly controlled by the hydraulic gradients between two mediums, rather than the storage. The flow directionality will change with the hydraulic gradient between the two reservoirs. The bi-directional water flux makes it fundamental to consider the directionality of connectivity within the karst critical zone. Direct hydrological connectivity between the surface and subsurface is also important in streamflow generation in karst catchments. Besides infiltration through fractures and the matrix, concentrated infiltration from surface to underground flow systems via sinkholes is a distinct aspect of transient connectivity in karst catchments. This influence is captured by the model conceptualization and shown in the contribution of rainfall to the underground stream in Fig. 9. Although this hydrological connection only occurs during heavy rain in the wet season, it is one of the most distinct hydrological functions of the karst critical zone. In this regard, it is similar to the cracks in soil leading to high percolation via preferential flow paths under flooding conditions (Zhang et al., 2015). In addition, flow paths in urban areas, with transient connectivity of storm drains, have been compared to karst (Bonneau et al., 2017), and whilst this gives similar short response times and a dominance of young water (Soulsby et al., 2014), urban systems are simpler and bi-directional connectivity is less significant.

By characterizing the variable water ages of different landscape units, we can deepen our understanding of the non-linear water storage dynamics and runoff generation processes (Soulsby et al., 2015). Water ages reflect the time variance and non-linearities of how different runoff sources are connected and the dynamics of their relative contribution to runoff generation (Birkel et al., 2012). Recent work has demonstrated the controlling effect of hydrogeological conditions on water ages in karst areas (Mueller et al., 2013). The underground stream water ages at the catchment outlet can be viewed as the time-varying integration of spatially distributed water fluxes from the hillslope unit and small fractures in the depression aquifer, which each have their own age dynamics (Fig. 10). There is a distinct pattern of bimodality in the age distribution of underground streamflow (represented by the fast reservoir in Fig. 11), which reflects the seasonality of the different water sources. Younger waters mainly come from surface water recharge through sinkholes after heavy rain and drainage from the hillslopes, whilst the slow flow reservoir dominates low flows. According to the water age dynamics of different conceptual stores, it can be deduced that storage-driven changes in hydrological connectivity and associated mixing processes largely determine the non-stationary water age distribution of the underground stream. In this sense, karst catchments seem to be subject to the “inverse storage effect”, where periods of high storage facilitate transit of younger water to drainage (Harman, 2015).

It should be noted that the ages derived from the modelling are based on stable isotope tracers, which whilst well suited to characterizing the influence of younger waters, are less well suited to constraining the age of older waters (>5 years) that may be present in deeper aquifers and fine pores that contribute to the slow flow reservoir (e.g. Jasechko et al., 2017). Thus further work is needed to assess the role of these older waters and quantify their influence on the ages of water in the underground channel (e.g. McDonnell and Beven, 2014). That said, the dominance of younger water in the outflow of responsive karst catchments is consistent with recent theoretical (Berghuijs and Kirchner, 2017), larger-scale (Jasechko et al., 2016) and more local studies (Ala-aho et al., 2017b) which show that deeper, oldest groundwater often makes insignificant or limited contributions to streamflow.

There is a marked shift in the isotopic composition of storm event rainfall which effects the short-term response of the catchment outlet; thus, weekly or even daily isotope data would not adequately capture the variability of rainfall isotope signatures at a resolution appropriate to the response times of sub-tropical karst systems (Coplen et al., 2008). The assessment of water ages in the critical zone is highly dependent on the temporal resolution of tracer data in rainfall and streamflow for model conceptualization (Birkel et al., 2012; McDonnell and Beven, 2014). The high-frequency measurements of tracer behaviour enhanced our understanding of catchments' hydrological function and the associated timescales of the celerity of the hydrological response to rainfall inputs and the velocity of water particles. Also, the high-resolution tracer data yielded novel insights into how the model integrates and aggregates the intrinsic complexity and heterogeneity of catchments, in order to reproduce behaviour adequately across a range of timescales (Kirchner et al., 2004). However, it should be noted that in much previous tracer-based modelling, the temporal resolution of hydrometric data (typically hourly) is at a much finer temporal resolution than tracer data, sampled more often at daily or even weekly resolution (Stets et al., 2010; Birkel et al., 2010, 2011; McMillan et al., 2012; Soulsby et al., 2015; Ala-aho et al., 2017a). Here, due to the marked heterogeneity of flow paths in the karst critical zone, and the very rapid (i.e. sub-daily) streamflow responses to high-intensity precipitation, the modelling of flow and tracer dynamics, as well as flux age estimates, need to account for the rapid flow velocities within the karst aquifer. The response time of streamflows/conduit flows or groundwaters level to rainfall is very short in karst catchments, e.g. typically a few hours in small catchments like Chenqi (Zhang et al., 2013; Delbart et al., 2014; Labat and Mangin, 2015; Rathay et al., 2017). Coarser-resolution data would result in increased uncertainty in the short-term components of travel times (Seeger and Weiler, 2014) and a likely bias towards longer transit times (Heidbüchel et al., 2012). Thus a significant advance of the new model used in this study was that observation and model results captured the flashy (sub-daily) responses of flow and isotope signatures at hourly timescales.

The tracer-aided conceptual model used here provided an opportunity to improve the basis for model evaluation and constrain parameter sets, potentially reducing such uncertainty (Beven, 1993). However, high uncertainty always accompanies modelling in such complex landscapes since the tracer-aided model increases model parameterization for the tracer modules. When we further compared the parameter sensitivities when the model was separately calibrated against the outlet discharge and/or water isotopes, using KGEd and KGEi, respectively, the trade-offs associated with different calibration strategies became evident. The sensitivity analysis (using plots similar to those in Fig. 5 and shown in the Supplement) showed that increasing the two sensitive parameters in the isotope module (the coefficient for evaporation fractionation Is and the weighted isotope composition of rainfall input by the parameter τ) results in three parameters in the flow module becoming insensitive when a combined objective function is used. These are the slow reservoir constant (Kf), the exchange constant between the two reservoirs Ke and the ratio of porosity of the quick to slow flow reservoir (f). Consequently, equifinality remains for parameters in the trace-aided model, as the former two sensitive parameters in the isotopic module take functions in the outlet flow (being “old/new”), similar to the latter three parameters in the flow module. The former two sensitive parameters in the isotopic module emphasize atmospheric effects on the outlet flow (being “old/new”). A higher Is indicates more evaporative effect on the stored water, leading to the stored and released water being older, particularly during the dry period. Increasing τ indicates newer rainfall recharge (with more negative isotopic values) into an aquifer, resulting in the stored and released water being newer during the rainfall period. Alternatively, the latter three parameters in the flow module emphasize effects of fast (newer) and slow (older) flows in aquifer on the outlet flow (being “old/new”). More water release from the slow reservoir (larger Kf) and greater release of the slow reservoir into the fast reservoir (larger Ke) could lead to the released water being older in the dry season; a high proportion of the fast flow storage (larger f) and a greater exchange between the fast reservoir and the slow reservoir (larger Ke) could lead to the released water being newer in the wet season. The equifinality for these parameters might only be overcome when we have additional field data to better constrain them (e.g. knowing the evaporative effect on water Is and the weighted isotope composition of rainfall input by the parameter τ). Despite this, using tracers in the model provides evidence of the mixing, flux and age relationships, which would not be possible from flow-related calibration alone.

The modelling uncertainty of hydrological variables in different units relies on connectivity of the units with the outlet if only the flow and isotopes at the catchment outlet are used as calibration targets. For example, since hydrological connectivity between the outlet and the catchment units decreases in the order fast flow in the depression < hillslope flow < slow flow in the depression, the uncertainty bands for the three storages increase in the same order. Also, the modelling uncertainty increases with ages of water sources, contributing into the catchment outlet due to the decrease in variability of the tracer signal in the larger stores. Some of the markedly enriched isotope signals at the outlet during the event peaks are most likely explained by fractionated water being displaced from the paddy fields during event peaks. Hence, the model skill in capturing the effects of evaporative fractionation needs to be further investigated in the model, in terms of both process-based parameterization of fractionation (e.g. Kuppel et al., 2018) and possibly differentiating paddy fields as a separate landscape unit, though of course this would be a trade-off with increased parameterization and further equifinality.