Journal cover Journal topic
Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Technical note
03 Apr 2017
Review status
This discussion paper is a preprint. It has been under review for the journal Hydrology and Earth System Sciences (HESS). The manuscript was not accepted for further review after discussion.
Nonparametric lower bounds to mean transit times
Earl Bardsley School of Science, University of Waikato, Hamilton 3240, New Zealand
Abstract. Mean transit time μT, also called mean residence time, has been used widely in hydrological studies as an indicator of catchment water storage characteristics. Typically μT is estimated by the nature of catchment transformation of a natural input tracer time series. For example, increased damping and delaying of 18O seasonal isotopic variation may be taken to indicate longer mean transit times. Part of a μT estimation process involves specification of a lumped parameter flow model which provides the basis for a parametric transit time distribution. However, μT estimation has been called into question because catchment flow systems have a degree of complexity which may not justify use of simple parametric distributions. Moving toward a related index, the question is raised here as to the extent to which an arbitrary transit time distribution might enable a model mean transit time to be minimized before the fit to catchment output tracer data becomes unacceptably poor. This minimized mean value μ* represents a lower bound to μT, whatever the true transit time distribution might be. The lower bound is not necessarily an approximation to μT but might serve as an index for catchment comparisons or detect when μT is large. For a linear catchment system a simple nonparametric linear programming (LP) approach can be utilised to obtain μ*, which is conditional on a user-specified acceptable level of data fit. The LP method presented is applicable to both steady state and time-varying catchment systems and has the advantage of not requiring specification of lumped parameter models or use of explicit transit time distributions.

Citation: Bardsley, E.: Nonparametric lower bounds to mean transit times, Hydrol. Earth Syst. Sci. Discuss.,, 2017.
Earl Bardsley
Earl Bardsley


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