How many tracers do we need for end member mixing analysis (EMMA)? A sensitivity analysis

Abstract

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. Copyright 2011 by the American Geophysical Union.