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Stewart, Michael K.; Morgenstern, Uwe; Gusyev, Maksym A.; Maloszewski, Piotr (2016)
Languages: English
Types: Article
Subjects:
Applications of simple lumped parameter models to describe aspects of hydrological systems rest on assumptions of homogeneity that are rarely valid. The lumped parameters are supposed to represent the quantities within the system as well as those of the overall system, but such quantities will obviously vary greatly from place to place within heterogeneous systems. Less appreciated is the fact that aggregation errors will affect overall system parameters as well. Kirchner (2016a) recently demonstrated that aggregation errors due to heterogeneity in catchments could cause severe underestimation of the mean transit times (MTTs) of water travelling through catchments when simple lumped parameter models were applied to interpret seasonal tracer cycles. Here we examine the effects of such errors on the MTTs and young water fractions estimated using tritium concentrations. We find that MTTs derived from tritium concentrations in streamflow are just as susceptible to aggregation bias as those from seasonal tracer cycles. Likewise, groundwater wells or springs fed by two or more water sources with different MTTs will also show aggregation bias. However, the transit times over which the biases are manifested are very different; for seasonal tracer cycles it is 2–3 months up to about 5 years, while for tritium concentrations it is 6–12 years up to about 200 years. We also find that young water fractions derived from tritium are almost immune to aggregation errors as were those derived from seasonal tracer cycles.

To investigate the implications of these findings for past and future use of tritium for estimating MTTs in catchments and groundwater systems, we examined case studies from the literature in which simple and more complicated lumped parameter models had been used. We find that MTT aggregation errors are small when either component waters are young (less than 6–12 years, as found in many catchments), or component waters have similar MTTs to each other. On the other hand, aggregation errors are large when very young water components are mixed with old components. In general, well-chosen compound lumped parameter models should be used as they will eliminate potential aggregation errors due to the application of simple lumped parameter models. The choice of a suitable lumped parameter model can be assisted by matching simulations to time series of tritium measurements (underlining the value of long series of tritium measurements), but such results should also be finally validated to ensure that the parameters found by modelling correspond to reality.
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