The impact of missing sources and the emergence of multiple solutions in sediment fingerprinting: When not all sources are included

Accurate identification of sediment sources is crucial for reliable source apportionment in sediment fingerprinting studies. However, the sensitivity of unmixing models to incomplete source information remains underexplored. This study investigates the impact of missing sources on unmixing model results, assessing the effects of deliberately omitting one source, simulating the effect of oversight or incorrect fieldwork. In this contribution, experimental sediment mixtures with four known sources (S1: 23.3%, S2: 23.3%, S3: 23.3%, and S4: 30%) and 18 geochemical tracers were analysed and the FingerPro unmixing model was implemented to estimate the relative contribution of sediment sources in different scenarios. Initially, the model was tested with all four sources, and the estimated source contributions closely aligned with the theoretical values. Before unmixing, an analysis of the conservativeness index (CI), consensus ranking (CR), and mathematical consistency (CTS) of the tracers was conducted, showing good consistency for most tracers (CTS errors below 0.06) when all four sources were included. However, when one source (S4) was excluded, the predicted source contributions became inaccurate. Additionally, a significant decline in mathematical consistency for most tracers was observed. These results highlight the challenges in achieving accurate source apportionment when critical information is missing. The study emphasises the importance of considering all relevant sources, as the omission of a key source leads to significant errors in interpreting the contributions of the remaining sources, ultimately resulting in incorrect conclusions. Furthermore, the potential use of CI, CR, and CTS tools for evaluating model reliability is discussed, particularly in the presence of missing sources. There is limited understanding of how unmixing models behave when faced with contributions that cannot be explained by the initial sources provided for the unmixing process. Instead of attributing these unexplained contributions to a potential unknown source, the models appear to redistribute them across the initial sources. This research highlights the need for further developments in unmixing models to better handle these limitations, which complicate the accurate estimation and interpretation of results. Missing sources in sediment fingerprinting datasets can lead to multiple solutions, resulting in erroneous model outputs. Our results suggest that these situations can be detected through mathematical consistency analysis (CTS).