Tracer-aided model and water dynamics tracking
In an earlier paper (Zhang et al., 2019), we describe in detail the development of a tracer-aided hydrological model for the catchment that disaggregates cockpit karst terrain into the two dominant landscape units of hillslopes and depressions. Briefly, the water and tracer movement were simulated using a two-reservoir model that conceptualizes the dual-flow system. The low permeability “slow flow” reservoir represents the fractured matrix blocks of the aquifer, and the highly permeable “fast flow” reservoir represents the large conduits (Fig.2). And the outlet of the fast flow reservoir is the catchment outlet (Fig.2). The water balance for each of the three reservoirs (hillslope unit, fast flow and slow flow reservoirs in depression) in the catchment is expressed as:
\(\frac{dV_{n}}{\text{dt}}=\sum_{i=1}^{k}Q_{n,\text{in},i}-\sum_{j=1}^{m}Q_{n,\text{out},j}\)(8)
where V is storage with the subscript of n=h, f, s , representing hillslope unit, fast flow and slow flow reservoirs, respectively.Qn,in andQn,out are the flow discharges that enter and exit the n th reservoir. The model tracks and simulates the isotope ratios for each reservoir separately, and the complete mixing of the isotope ratios is assumed for the slow and fast flow reservoirs:
\(\frac{di_{s}(V_{s})}{\text{dt}}=\sum_{i=1}^{k}{i_{s,\text{in}}Q_{s,\text{in},i}}-\sum_{j=1}^{m}{i_{s,\text{out}}Q_{s,\text{out},j}}\)(9)
\(\frac{di_{f}(V_{f})}{\text{dt}}=\sum_{i=1}^{k}{i_{f,\text{in}}Q_{f,\text{in},i}}-\sum_{j=1}^{m}{i_{f,\text{out}}Q_{f,\text{out},j}}\)(10)
where i is the δD signature of the storage components (‰). And partial mixing (e.g. the upper active storage mixing with the lower passive storage in Fig.2 since the upper rock fractures/conduits reduce exponentially along the hillslope profile) is assumed for the hillslope according to:
\(\frac{di_{h}(V_{h})}{\text{dt}}=\sum_{i=1}^{k}{i_{h,\text{in}}Q_{h,\text{in},i}}-\sum_{j=1}^{m}{i_{h,\text{out}}Q_{h,\text{out},j}}-i_{h}Q_{e}+i_{\text{pas}}Q_{e}\)(11)
\(\frac{di_{\text{pas}}(V_{\text{pas}})}{\text{dt}}=i_{\text{pas}}Q_{e}-i_{h}Q_{e}\)(12)
where the additional volumes Vpas is the storage of passive reservoir in hillslope which is available to determine isotope storage, mixing, and transport in a way that does not affect the dynamics of water flux volumes \(V_{h}\). Qe is the exchange flux between active storage and passive storage.ih and ipas are the δD signature of the active storage and passive storage. For full details how water and isotope fluxes, storage and water age dynamics are simulated, the reader is referred to Zhang et al. (2019).
The modelling framework was built upon a coupled hydrological and tracer model and calibrated to high temporal resolution hydrometric and isotopic data at the outflow of the Chenqi catchment. Using flow and isotopic composition as calibration targets, objective functions (the modified Kling–Gupta efficiency, KGE) were combined to formulate a single measure of goodness of fit. Additionally, other data such as discharge and stable isotope signatures of the 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 and the modelling uncertainty. A total of 105 different parameter combinations within the initial ranges were randomly generated as the possible parameter combinations. 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. The results showed that this model could capture the flow and tracer dynamics within each landscape unit quite well. In the earlier paper, we showed the strong capacity of this tracer-aided model to track hourly water and isotope fluxes through each landscape unit and estimate the associated storage and water age dynamics. The model could also estimate the ages of water draining the hillslope unit, as well as the fast and slow flow reservoirs (Zhang et al., 2019).
In this study, water flux and storage dynamics were tracked by a tracer-aided model. The tracer-aided model with the calibrated parameters was run multiple times in parallel, tracking the fate of each rainfall event separately. The water from each rainfall hour was uniquely labelled with a specific tracer concentration. In this way, the variation in tracer concentration through time in each water store can be tracked, which reveals the transit time distribution (TTD) and water age distribution of water flux. This method, also used by Remondi et al. (2018), reflects solely the quantity we introduced and for which we know the origin. A total of 892 rainfall events (i.e. rainfall hours) during the study period of 11 November 2016 to 31 October 2017 were separately tracked. Tracking all the hourly inputs of precipitation over the study period and their individual paths to the outlets of hillslope, slow and fast reservoirs enabled the computation of the TTD of rainfall water entering the catchment, the age distribution and young water fraction (Fyw) of water flux.