End member mixing analysis (EMMA) is a commonly applied method to identify and quantify the dominant runoff producing sources of water. It employs tracers to determine the dimensionality of the ...hydrologic system. Many EMMA studies have been conducted using two to six tracers, with some of the main tracers being Ca, Na, Cl−, water isotopes, and alkalinity. Few studies use larger tracer sets including minor trace elements such as Li, Rb, Sr, and Ba. None of the studies has addressed the question of the tracer set size and composition, despite the fact that these determine which and how many end members (EM) will be identified. We examine how tracer set size and composition affects the conceptual model that results from an EMMA. We developed an automatic procedure that conducts EMMA while iteratively changing tracer set size and composition. We used a set of 14 tracers and 9 EMs. The validity of the resulting conceptual models was investigated under the aspects of dimensionality, EM combinations, and contributions to stream water. From the 16,369 possibilities, 23 delivered plausible results. The resulting conceptual models are highly sensitive to the tracer set size and composition. The moderate reproducibility of EM contributions indicates a still missing EM. It also emphasizes that the major elements are not always the most useful tracers and that larger tracer sets have an enhanced capacity to avoid false conclusions about catchment functioning. The presented approach produces results that may not be apparent from the traditional approach and it is a first step to add the idea of statistical significance to the EMMA approach.
Key Points
Resulting model of EMMA is highly sensitive to tracer set size and composition
Large tracer sets help to avoid false conclusions about runoff processes
Methodology to add statistical significance to the EMMA approach
In recent years, the analysis of the impact of structural model inadequacies on simulation uncertainty has gained increased attention in hydrological research. One aspect of structural model ...inadequacy is the imperfect numerical integration of differential equation systems. This aspect is still neglected in many rainfall runoff and water balance models. Often process equations are solved by model-specific"ad hoc"-integration schemes. These are time-efficient but can lead to significant inaccuracies. In this study we examine the "ad hoc" numerical integration schemes of the water balance models HBV96 and LARSIM-ME. Comparisons with a more elaborate integration method suggest that both HBV96 and LARSIM-ME are affected by noticeable integration uncertainty in the calculation of interception. In the other model components this is only the case for LARSIM-ME. The overall integration uncertainty of HBV96 appears to be rather low when it is compared directly to the total simulation uncertainty. One reasonOriginal Abstract: In den letzten Jahren ist die Analyse des Einflusses der Modellstruktur auf die Simulationsunsicherheit in den Fokus der hydrologischen Forschung geruckt. Ein weiterhin in vielen Niederschlags-Abfluss- und Wasserhaushaltsmodellen vernachlassigter Aspekt der Modell-Unsicherheit ist die numerische Integration von Prozessgleichungen. Gangige modellspezifische "ad hoc"-Integrationsschemata sind zeiteffizient, konnen aber zu grosseren Ungenauigkeiten fuhren. Hier wird das Ausmass dieser Integrations-Unsicherheit anhand der Wasserhaushaltsmodelle HBV96 und LARSIM-ME untersucht. Vergleiche zwischen deroriginalen"ad hoc"-Losung der Modelle und eines hinsichtlich seiner numerischen Genauigkeit steuerbaren Integrationsalgorithmus legen nahe, dass sowohl HBV96 als auch LARSIM-ME in der Berechnung der Interzeptionsprozesse nennenswerte Unsicherheit aufweisen. Bei den ubrigen Modellkomponenten ist dieses nur fur LARSIM-ME der Fall. Im direkten Vergleich zur gesamten Simulationsunsicherheit fallt die Integrations-Unsicherheit insbesondere bei HBV96 eher gering aus, was unter anderem auf eine im Vergleich zur gewahlten LARSIM-ME-Konfiguration kleine Zeitschrittweite zuruckzufuhren ist. Ob sich die Integrations-Unsicherheit in Folge unregelmassiger Fehleroberflachen nachteilig auf die Parameteroptimierung und damit die Simulationsunsicherheit auswirkt, wird in folgenden Studien untersucht.
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