Model-based assessment and mapping of total phosphorus enrichment in rivers with sparse reference data

Water nutrient management efforts are frequently coordinated across thousands of water bodies, leading to a need for spatially extensive information to facilitate decision making. Here we explore potential applications of a machine learning model of river low-flow total phosphorus (TP) concentrations to support landscape nutrient management. The model was trained, validated, and then applied for all rivers of Michigan, USA to identify potential drivers of nutrient variation, predict alteration in nutrient concentrations from minimally disturbed conditions, and explore reach specific sensitivity to riparian agricultural change. A boosted regression tree model of low-flow TP concentrations trained on natural and anthropogenic landscape predictors accounted for 53 % of variation in cross-validation data, had good accuracy, little bias, and plausible relationships between predictors and response. Percent riparian agricultural cover accounted for the greatest root mean square error reduction in the modeled response (33.2 %), followed by riparian soil permeability (12.9 %), watershed slope (9.6 %), and percent urban cover (9.6 %). An apparent non-linear relationship between TP concentrations and percent riparian agricultural cover suggested steep positive increases in stream TP concentrations between 10 and 30 % upstream riparian agricultural cover. Predicted minimally disturbed TP concentrations were spatially variable and ranged from 7.0 to 48.5 μg l⁻¹, with the highest concentrations in watersheds draining low-permeability lake plain soils. Comparison of minimally disturbed predictions to those from the early 2000s suggested that much of northern Michigan existed close to the reference condition, while lower Michigan streams were often substantially enriched. Our predicted values of minimally disturbed condition generally agree with previous studies but offer greater geographic specificity. Expanded application of machine learning modeling with landscape predictor data have great potential to inform large scale strategy development in landscapes with sparse reference data.