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.