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On the Balance Equations and Error Estimators for Separating n Time Components of Runoff With One Stable Isotope Tracer

Starting from their first applications in the late 1960s, the mass balance equations for separating storm hydrographs have been analyzed with respect to their solvability and sensitivity to errors. By changing them into a time perspective, it is shown how an iterative extension of the standard two‐component separation can lead to a system of balance equations that allows for separating n time components using one single stable isotope tracer. This new approach is tested for the case n=6 by using the experimental data of the Zastler catchment (18.4 km2, southern Black Forest, Germany). The behavior of several time components is demonstrated. By separating the event water of the last and next‐to‐last event, it is shown how the event water of a certain rainfall‐runoff event contributes to stream discharge over the next two subsequent events. The new separation model offers the possibility of tracing event water over a much longer period after the initial event.