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.