Technical Note: A data-driven method for estimating the composition of end-members from streamwater chemistry observations

Abstract. End-Member Mixing Analysis (EMMA) is a method of interpreting streamwater chemistry variations, and is widely used for chemical hydrograph separation. It is based on the assumption that the streamwater is a mixture of varying contributions from relatively time-invariant source solutions (end-members). These end-members are typically identified by collecting additional measurements of candidate end-members from within the watershed, and comparing these to the observations. This technical note introduces a complementary, data-driven method: Convex-Hull End-Member Mixing Analysis (CHEMMA), to infer the end-member compositions and their associated uncertainties from the streamwater observations alone. The method involves two steps. The first step uses Convex-Hull Non-negative Matrix Factorization (CH-NMF) to infer possible end-member compositions by searching for a simplex that optimally encloses the streamwater observations. The second step uses Constrained K-means Clustering (COP-KMEANS) to classify the results from repeated applications of CH-NMF to analyze the uncertainty associated with the algorithm. In an example application using the 1986 to 1988 Panola Mountain Research Watershed dataset, CHEMMA is able to robustly reproduce the three field-measured end-members found in previous research using only the streawater chemical observations. It also suggests the existence of a fourth end-member. Further work is needed to explore the constraints and capabilities of this approach.