Is ecoregional scale precise enough for lake nutrient criteria? Insights from a novel relationship-based clustering approach

Abstract

While the ecoregional lake nutrient criteria have been widely used in the past two decades, the overconfidence on their applicability may mislead the pollution management decisions, considering the spatial heterogeneity within the ecoregion. The exploration of applicability is thereby important, but is hindered by the difficulty in recognizing reliable relationship patterns between the nutrient and management endpoint. We propose a novel relationship-based clustering approach (RCA) to explore whether the ecoregional scale is precise enough for nutrient criteria. The approach (a) simulates relationships using Bayesian Linear Models, (b) clusters lakes according to relationship similarities via relationship mapping and hierarchical clustering, and (c) identifies reliable relationship patterns based on the leave-one-out cross-validation. The RCA is then employed to explore Chlorophyll a-total phosphorus relationships of 34 lakes in four Ecological Drainage Units (EDUs) in the U.S. Long-term water quality data is from a newly established database (LAGOS-NE). The results show that multiple relationship patterns exist in all the EDUs. The ecoregional relationships misestimate the nutrient effect in over a half of lakes. Therefore, we determine that the ecoregional scale is not precise enough for nutrient criteria and the sub-ecoregional scale is then recommended. Besides, the RCA provides a backward thinking for determining the spatial scale and can be used in some other fields where relationship-based clustering is needed.