Hydroclimatic drivers and temporal dynamics of monthly total phosphorus loading in three Lake Erie tributaries: A Bayesian hierarchical modeling approach

Over the past two decades, Lake Erie has experienced recurring harmful algal blooms (HABs), attributed primarily to agriculture practices in the Western Basin and other confounding factors including climate variables, individual management practices, and internal nutrient loading. Modeling this transport is an active area of research with major focus on empirical statistical regression (LOADEST, WRTDS), which lack explanatory power, and highly parameterized physical frameworks (SWAT, SPARROW), which lack flexibility to propagate observational uncertainty and handle dynamic temporal data without massive recalibration. We present a hierarchical Bayesian architecture using a robust Student-t likelihood to jointly estimate hydroclimatic drivers of monthly Total Phosphorus (TP) concentrations and apply it to the Maumee, Sandusky, and Cuyahoga watersheds. Multiple Imputation by Chained Equations (MICE) formally propagates uncertainty from missing data through the posterior, with additional sensitivity analysis determining the effects of prior specification and climate data sources on estimation. Data were retrieved from 1985–2020 from numerous sources covering nutrient, hydroclimate, and land use information. Results indicate discharge and lagged TP are consistent predictors across watersheds. Higher precipitation is associated with increased TP, while higher air temperature generally shows no association, particularly in the Maumee and Sandusky rivers. Results suggest watershed-specific climate metrics may offer improvements over basin-wide averages in capturing the climatic effects on monthly concentrations. Our Bayesian approach provides robust inference into nutrient concentration drivers across diverse systems and our results have practical applications, including potential development of data-driven, targeted water quality management policies, improved forecasting of HABs, and support for adaptive land-use planning.