Why Does the Convolution Integral Method Provide Systematically Biased Estimates of Watershed Residence Times?

Abstract:

Every observational method for estimating hydrologic residence time comes with built-in biases. For example, each tracer-based method has a range of times that it can grasp. Because of mixing along flow paths, especially at convergence zones like streams, springs and wells, water samples contain a distribution of residence times. An observation method interrogates that portion of the distribution for which it is suited, with different methods interrogating different portions of the distribution and providing different mean residence-time estimates. For this reason, it would be best to employ a suite of observational methods that span the entire distribution. In practice, only one or at best a few methods are applied and the distribution is not thoroughly characterized resulting is biased estimates of the mean. The Convolution Integral Method (CIM) is commonly employed by itself to estimate watershed residence times from records of stable isotopes collected in precipitation and streamflow. Published studies using CIM suggest that watershed residence times are short, on the order of days to years. However, CIM appears to be biased because it uses relatively short-duration records of recent measurements, such that published CIM residence time estimates are similar to the time period of the records used in the analysis. If CIM truncates the older portion of the residence time distribution it underestimates the role of slower processes like deeper-groundwater contributions. The explanation of bias may be broader. We find that a longer time series of input and output does not necessarily improve the method from a mathematical perspective. In any event, when using CIM with stable isotopes there are processes that intrinsically obscure observation of the older portions of the distribution. It is not clear that additional research on this application of stable isotopes can necessarily improve residence time estimates.