A Bayesian hierarchical spatio-temporal ratio-estimator approach to model phosphorus loading in six Ohio watersheds: the importance of accounting for inter-annual and inter-basin variabilities

Surface water bodies serve a critical role in preserving ecological systems and maintaining biodiversity. Anthropogenic eutrophication of fresh water ecosystems is one of the main causes of surface water quality degradation. Excessive nutrient loading to freshwater bodies is a driving cause of water quality impairments worldwide. Accurately estimating riverine nutrient loads remains an imperative step towards mitigating and managing impairments. Yet, load estimation is often hindered by the sporadic and infrequent monitoring of nutrient concentrations. Several modelling approaches have been proposed and implemented over the years to estimate pollutant loads; yet most suffer from biases and/or from their capabilities to transparently quantify uncertainties. In this work, we propose a spatio-temporal Bayesian hierarchical ratio-estimator model to predict the annual total phosphorus loads between 2005 and 2020 for six intensively monitored watersheds discharging in Lake Erie and the Ohio River-USA. The integration of higher-level Land-Use-Land-Cover predictors proved successful in capturing inter-station variabilities in phosphorus loading. Meanwhile, accounting for annual climatic variability partially helped explain temporal changes in the flow-weighted nutrient concentrations across the six watersheds. The performance of the model was tested against different levels of data censorship. Results showed that under a weekly sampling program, the load estimates from the proposed Bayesian Hierarchical spatio-temporal model were within -19 and 31 % (mean difference of 0.3% across stations and years) from the true loads calculated for years with uninterrupted concentration measurements. Predictions from traditional load estimation methods were found to vary between -56% and 73% from the true loads. Meanwhile, failing to account for the spatio-temporal hierarchical structure of the proposed model, either by adopting a completely pooled or an unpooled model, resulted in a significant drop in the accuracy of the predicted loads and inflated the associated uncertainties.