If I understand correctly, colleagues arre measuring the concentration of an isotope in stream or some other catchment outlet. This is quite not a measure of the age of water but the latter has to be inferred from a hypothesis the system behavior, and possibly the knowledge of the distribution of water ages within the control volume, obtained iteratively from an initial data (derived from the isotopic data of precipitation).
Therefore, assume you have measured in the outflow a concentration of 5 of solute X in appropriate units. You mai have the knowledge of the concentration of the same solute in the water of a given age resident in the control volume. It would be a tuple like (7,3,6,2) where the number of concentration is the number of precipitation happened before the present instant. The 5 units out of the tuple can be taken all from the oldest (7) concentration, from the youngest (3,2) where the 3 are out of the 6 of the penultimate concentration.
Therefore a concentration of 5 can be fitted with a water age of 4 in the first case or (3*2+2*1)/5=1.8 in the second case.
In fact, the concentration doesn't identify the exact age of the water but rather a range of ages spanning from the "first in first out" age to the "last in first out" age illustrated in the simple example.
Potentially the old water is infinitely old and, therefore, the lower bound could be very large, while the upper bound for the ages is, clearly, related to the last rainfall age.
So, the division between young water and old water is reasonable. Instead of trying to guess the distribution, you're trying to guess parts of its integral.
Then SAS (StorAge Selection functions,
see this previous post for understanding what they are) are summarizing the mechanics of mixing inside the control volume. If the waters mix a lot the travel time and the residence time should coincides because of the uniform selection of isotopes (or tracers) among the various populations. SAS have a non trivial form if the mixing of waters is incomplete.
Due to the localized nature of water physics, the actual travel times are intricately linked to the specific location from which water emerges or is extracted from the soil. Within the unsaturated zone, it's logical to posit that newly introduced water is the first to flow out for two primary reasons: it occupies the empty pores, and these pores are typically where water is loosely retained. However, when young water mixes with old water in the saturated zone, the aquifer's pressure rises, causing a pressure wave that pushes out the oldest water near the streams.
Consequently, in a typical zeroth-order catchment, runoff tends to adhere to a "last in, first out" (LIFO) logic, while subsurface stormwater tends to expel old water first, following a "first in, first out" (FIFO) logic. Consequently, the recession of the flood wave is expected to contain a higher proportion of old water than young water. In this hypothetical simplified model delineating two distinct dynamics, and drawing from the aforementioned insights, it becomes feasible to estimate the global effect of the system, as proposed by
Rigon and Bancheri in 2022 and applying the recent methods of
TT probability determination.
Vegetation withdrawal we can think to extract water from the places where active roots are, according to root density. Plants with shallow roots should mostly sample young water, while plants with deeper roots wold sample older water but maybe also being effective in mixing water of different ages because of exudation and because of preferential water infiltration close to the roots.
The presentation (under construction) is exemplifying these concepts.
