Time variance of the water age and travel time distributions
The water age pdfs (probability density function) of runoff at outlet of hillslope unit and the catchment (reflecting the integration of the residence times of the contributing water storages) are drawn from a series of tracer-aided model simulations where the water dynamics in each conceptual store are driven by rainfall input over specific periods (Fig. 8). In this study, three times were chosen (t1 : 30 November 2016; t2 : 11 March 2017 and t3 : 12 June 2017) for water age pdf of runoff estimation. These specific times reflect dry conditions (11 March 2017), wet conditions (12 June 2017) and the midpoint (30 November 2016) of the study period (the rainfall and discharge characteristics at each time at the hillslope and outlet are shown in Table 1). The results in Fig.8 show noticeable differences among the water age pdfs corresponding to the three different times. The water age pdfs show a series of pronounced spikes reflecting the impact of the rainfall input within the catchment (shown in Fig. 8). In the dry period, water age of outflow from the hillslope store and catchment outlet are dominated by the old water release. For example, the youngest water with the age of 0 day (the rainfall water converting to outflow at the same rain day) only accounts for 21% and 0.5% of the total discharge at hillslope and catchment outlet on 30 November 2016. In contrast, the probability of a water age of 0 days was 60% and 80% for the hillslope and catchment outlet, respectively, on 12 June 2017. The time variability in pdf of runoff water age indicates a strong and direct effect of precipitation and storage conditions on the shape of individual water age pdfs, both of which affect the time of water exiting the catchment. It is particularly noticeable that the differences in water age pdfs between dry and wet season for runoff at the catchment outlet are much larger than that for the hillslope. For example, the probabilities of a water age of 0 days are 21% to 60% for the hillslope but 0.5% to 80% for the catchment outlet, in dry and wet season. The high storage capacity of the slow flow reservoir in the depression in dry periods can accommodate most rainwater, leading to older water flowing out of the catchment quickly. However, during the wet period, substantial proportions of high intensity rainfall recharge the large fractures and conduits. Therefore, most young water flows out of the catchment through the hydrologically connected flow paths between the hillslope and underground channel, or via sinkholes/large fractures increasing the young water fraction of runoff significantly (Fig.8).
Fig.9 shows the forward-projected transit time distribution (TTD) of rain water entering the catchment on the three dates considered in Fig. 8: this shows the distribution of how long rainfall water entering the system at the reference time ofti (i = 1, 2, 3 in Fig. 9) will spend transiting through the system before it reaches the outlet (Benettin et al., 2015b). The difference among the three transit time pdfs again highlights the effect of time-variance on the transport dynamics emerging at the catchment scale as a result of successive rainfall inputs. Each transit time pdf corresponding to the three start times is multimodal, with more or less pronounced peaks whose magnitudes are strongly synchronous with the hydrologic dynamics. In addition, the temporal evolution of the hillslope and catchment outlet flows (Qs and Q , respectively), are evidence of the correlation between the position of the transit time pdf spikes and the occurrence of the flood events (Fig. 9). The results show that the TTD of entering rain water is affected by the discharge (reflecting the displacement of storage in corresponding conceptual stores). When there was a flood, this part of “old” water stored in the aquifer is displaced in large quantities at high discharge rates (the peaks of pdf in July and August in 2017 shown in Fig.9a and b).
Although the mean transit time (MTT) cannot be calculated from the simulation results due to the short simulation period (only one year), the catchment and hillslope unit controls on the inflow water can be evaluated from the transit time pdfs. For the dry conditions (11 March 2017) with the rainfall of 0.4mm, only 6% of inputs rain water exited the catchment through the conduit over the period from this rain day to the end of the simulation time, a total of 233 days. For the midpoint of this study period (30 November 2016) with the rainfall of 3.9mm, the same percentile of 6% of inputs rain water exiting the catchment took 225 days. For the wet conditions (12 June 2017) with the rainfall of 45.6mm, 16% of inputs rain water exited the catchment on that day, and 6% of inputs rainfall water exiting the catchment only took about 3 hours. The results indicate that most of water entering in dry periods (mainly after the light rains) is stored in the catchment for a long time with high mean transit time. In contrast, in wet periods considerable proportion of new water will exit the catchment in a short time. The patterns of the transit time of outflow from the hillslope unit are similar as the catchment, and 6% of inputs rainfall water exiting the hillslope unit took 203, 106 and about 0.1 days, respectively.