How does rainfall become runoff? A combined tracer and runoff transfer function approach

Hydrographs are an enticing focus for hydrologic research: they are readily available hydrological data that integrate the variety of terrestrial runoff generation processes and upstream routing. Notwithstanding, new techniques to glean information from the hydrograph are lacking. After early approaches of graphically separating streamflow components, hydrograph separations in the past two decades have focused on tracers as a more objective means to separate the storm hydrograph. These tracer‐based methods provide process‐based information; however, their implicit assumptions limit their applicability and explanatory power. We present a new method for isotope hydrograph separation that integrates the instantaneous unit hydrograph and embraces the temporal variability of rainfall isotopic composition (one of the largest impediments to the standard use of isotopes as tracers). Our model computes transfer functions for event water and preevent water calculated from a time‐variable event water fraction. The transfer function hydrograph separation model (TRANSEP) provides coupled but constrained representations of transport and hydraulic transfer functions, overcoming limitations of other models. We illustrate the utility of TRANSEP by applying it to two rainfall events from a 17 ha catchment at Maimai in New Zealand, where 18 O, rainfall, and runoff data were sampled with a high temporal resolution. We explore which runoff and tracer transfer function (exponential piston flow, gamma distribution, or two parallel linear reservoirs) gave the best results for the proposed model structure and for the example data set. Uncertainty analysis was used to determine if the parameters were identifiable and if the information available for applying TRANSEP was sufficient. The results of the best performing transfer function are considered in detail to identify model performance, illustrate individual event characteristics, and interpret runoff processes in the catchment.