Gaussian process regression as a powerful tool for analysing time series in environmental geochemistry

Monitoring programs require more advanced data management for the registered time series. Classical temporal series decomposition cannot fulfil current needs regarding adequate data representation, optimization of the spatial-temporal sampling resolution and predictive power. In the manuscript at hand, we will demonstrate that Gaussian process regression (GPR) models are a vital machine-learning tool to interpret temporal series, improving understanding of geochemical cycles, providing input data for geochemical models and acting as a guide for future decisions in environmental monitoring. Firstly, we explore the impacts of sampling frequency in the GPR performance for temporal series with variable lengths and sampled frequencies of water discharges. On a second approach, we present the strengths and weaknesses between classical decomposition of temporal series and GPR results for a case study: a 14-year record of water discharge, suspended particulate matter and antimony concentrations in the Garonne River. Our results suggest that (i) even short temporal series with low sampling resolution can be accurately characterized by GPR when presenting well defined seasonal patterns, and (ii) GPR provides more detailed and robust support than classical statistics to identify processes responsible for multi-scale geochemical signals. This work provides a reference for researchers, engineers, and stakeholders for more reliable monitoring, understanding, and managing aquatic ecosystems.