Polynomial modelling of high-quality yet incomplete rare earth element data sets and a holistic assessment of REE anomalies

Rare earth elements (REEs) are powerful proxies used in many (bio-)geochemical studies. Interpretation of REE data relies on normalised REE patterns and anomaly quantification, and requires complete data. Therefore, older, high-quality REE data determined by neutron activation or isotope dilution methods are often ignored, as they did not provide complete data. Similarly, modern analytical data can lack certain REEs due to quantification limits, interferences or usage of REE spikes. However, such data may be the only information available since sample material was consumed, sample locations became inaccessible, or samples represent past states of a dynamic natural system. Therefore, the ability to impute such high-quality data is of value for many geoscientific sub-disciplines. We use a polynomial modelling approach to impute missing REE data, verify the method's applicability with a large data set (>13,000 samples; PetDB), and complement three originally incomplete REE data sets. Good fitting results (SD <6%) are supported by Monte Carlo simulations for assessing the model uncertainties (± 12%). Additionally, we provide a procedure to quantify REE anomalies, including uncertainties, which were usually not determined in the past but are essential for scientific comparison of REE anomaly data between different data sets. All Python scripts are provided.