Non-stationary nonparametric inference of river-to-groundwater travel-time distributions

- River-to-groundwater travel time distributions change with time.
- We determine these distributions from continuous signals of electric conductivity.
- Our approach does not prescribe a functional shape of the distributions.
- We detrend the data prior to deconvolution.
- We enforce non-negativity and smoothness in time and travel-time.

SummaryThe travel-time distribution between rivers and groundwater observation points and the mixing of freshly infiltrated river water with groundwater of other origin is of high relevance in riverbank filtration. These characteristics usually are inferred from the analysis of natural-tracer time series, typically relying on a stationary input-output relationship. However, non-stationarity is a significant feature of the riparian zone causing time-varying river-to-groundwater transfer functions. We present a non-stationary extension of nonparametric deconvolution by performing stationary deconvolution with windowed time series, enforcing smoothness of the determined transfer function in time and travel time. The nonparametric approach facilitates the identification of unconventional features in travel-time distributions, such as broad peaks, and the sliding-window approach is an easy way to accommodate the method to dynamic changes of the system under consideration. By this, we obtain time-varying signal-recovery rates and travel-time distributions, from which we derive the mean travel time and the spread of the distribution as function of time. We apply our method to electric-conductivity data collected at River Thur, Switzerland, and adjacent piezometers. The non-stationary approach reproduces the groundwater observations significantly better than the stationary one, both in terms of overall metrics and in matching individual peaks. We compare characteristics of the transient transfer function to base flow which indicates shorter travel times at higher river stages.