Lumped convolution integral models revisited: on the meaningfulness of inter catchment comparisons

Abstract

The transit time distribution of a catchment is linked to the water storage potential and affects the susceptibility of a catchment to pollution. However, this characteristic of a catchment is still problematic to determine within a catchment and to predict among catchments based on physiographic or geological properties. In this study, lumped response and transit time convolution models coupled with a distributed physically based snow model were applied to simulate the stable water isotope compositions in stream discharge measured fortnightly in 24 meso-scale catchments in Switzerland. Three different types of transfer function (exponential, gamma distribution and two parallel linear reservoirs) in two different implementation variants (strictly mathematical and normalised) were optimised and compared. The derived mean transit times varied widely for one and the same catchment depending on the chosen transfer function, even when the model simulations led to very similar predictions of the tracer signal. Upon closer inspection of the transit time distributions, it appeared that two transfer functions mainly have to agree on an intermediate time scale around three months to reach similarly good prediction results in respect to fortnightly discharge samples, while their short-term and long-term behaviour seem to be of minor importance for the evaluation of the models. A couple of topographic indices showed significant correlations with the derived mean transit times. However, the collinearity of those indices, which were also correlated to mean annual precipitation sums, and the differing results among the different transfer functions, did not allow for the clear identification of one predictive topographical index. As a by-product of this study, a spatial interpolation method for monthly isotope concentrations in precipitation with modest input data requirement was developed and tested.