Technical note: Two-component electrical-conductivity-based hydrograph separation employing an exponential mixing model (EXPECT) provides reliable high-temporal-resolution young water fraction estimates in three small Swiss catchments
Authors: Gentile Alessio , von Freyberg Jana , Gisolo Davide , Canone Davide , Ferraris Stefano 
Published: May 2024

Abstract. The young water fraction represents the portion of water molecules in a stream that have entered the catchment relatively recently, typically within 2–3 months. It can be reliably estimated in spatially heterogeneous and nonstationary catchments from the amplitude ratio of seasonal isotope (δ18O or δ2H) cycles of stream water and precipitation, respectively. Past studies have found that young water fractions increase with discharge (Q), thus reflecting the higher direct runoff under wetter catchment conditions. The rate of increase in the young water fraction with increasing Q, defined as the discharge sensitivity of the young water fraction (Sd*), can be useful for describing and comparing catchments' hydrological behaviour. However, the existing method for estimating Sd*, which only uses biweekly isotope data, can return highly uncertain and unreliable Sd* when stream water isotope data are sparse and do not capture the entire flow regime. Indeed, the information provided by isotope data depends on when the respective sample was taken. Accordingly, the low sampling frequency results in information gaps that could potentially be filled by using additional tracers sampled at a higher temporal resolution. By utilizing high-temporal-resolution and cost-effective electrical conductivity (EC) measurements, along with information obtainable from seasonal isotope cycles in stream water and precipitation, we develop a new method that can estimate the young water fraction at the same resolution as EC and Q measurements. These high-resolution estimates allow for improvements in the estimates of the Sd*. Our so-called EXPECT (Electrical-Conductivity-based hydrograph separaTion employing an EXPonential mixing model) method is built upon the following three key assumptions: We construct a mixing relationship consisting of an exponential decay of stream water EC with increasing young water fraction. This has been obtained based on the relationship between flow-specific young water fractions and EC. We assume that the two-component EC-based hydrograph separation technique, using the above-mentioned exponential mixing model, can be used for a time-source partitioning of stream water into young (transit times < 2–3 months) and old (transit times > 2–3 months) water. We assume that the EC value of the young water endmember (ECyw) is lower than that of the old water endmember (ECow). Selecting reliable values from measurements of ECyw and ECow to perform this unconventional EC-based hydrograph separation is challenging, but the combination of information derived from the two tracers allows for the estimation of endmembers' values. The two endmembers have been calibrated by constraining the unweighted and flow-weighted average young water fractions obtained with the EC-based hydrograph separation to be equal to the corresponding quantities derived from the seasonal isotope cycles. We test the EXPECT method in three small experimental catchments in the Swiss Alptal Valley using two different temporal resolutions of Q and EC data: sampling resolution (i.e. we only consider Q and EC measurements during dates of isotope sampling) and daily resolution. The EXPECT method has provided reliable young water fraction estimates at both temporal resolutions, from which a more accurate discharge sensitivity of the young water fraction (SdEXP) could be determined compared with the existing approach. Also, the method provided new information on ECyw and ECow, yielding calibrated values that fall outside the range of measured EC values. This suggests that stream water is always a mixture of young and old water, even under very high or very low wetness conditions. The calibrated endmembers revealed a good agreement with both endmembers obtained from an independent method and EC measurements from groundwater wells. For proper use of the EXPECT method, we have highlighted the limitations of EC as a tracer, identified certain catchment characteristics that may constrain the reliability of the current method and provided recommendations about its adaptation for future applications in catchments other than those investigated in this study.