Spatial variation in nutrient and water color effects on lake chlorophyll at macroscales

The nutrient-water color paradigm is a framework to characterize lake trophic status by relating lake primary productivity to both nutrients and water color, the colored component of dissolved organic carbon. Total phosphorus (TP), a limiting nutrient, and water color, a strong light attenuator, influence lake chlorophyll a concentrations (CHL). But, these relationships have been shown in previous studies to be highly variable, which may be related to differences in lake and catchment geomorphology, the forms of nutrients and carbon entering the system, and lake community composition. Because many of these factors vary across space it is likely that lake nutrient and water color relationships with CHL exhibit spatial autocorrelation, such that lakes near one another have similar relationships compared to lakes further away. Including this spatial dependency in models may improve CHL predictions and clarify how well the nutrient-water color paradigm applies to lakes distributed across diverse landscape settings. However, few studies have explicitly examined spatial heterogeneity in the effects of TP and water color together on lake CHL. In this study, we examined spatial variation in TP and water color relationships with CHL in over 800 north temperate lakes using spatially-varying coefficient models (SVC), a robust statistical method that applies a Bayesian framework to explore space-varying and scale-dependent relationships. We found that TP and water color relationships were spatially autocorrelated and that allowing for these relationships to vary by individual lakes over space improved the model fit and predictive performance as compared to models that did not vary over space. The magnitudes of TP effects on CHL differed across lakes such that a 1 μg/L increase in TP resulted in increased CHL ranging from 2-24 μg/L across lake locations. Water color was not related to CHL for the majority of lakes, but there were some locations where water color had a positive effect such that a unit increase in water color resulted in a 2 μg/L increase in CHL and other locations where it had a negative effect such that a unit increase in water color resulted in a 2 μg/L decrease in CHL. In addition, the spatial scales that captured variation in TP and water color effects were different for our study lakes. Variation in TP-CHL relationships was observed at intermediate distances (∼20 km) compared to variation in water color-CHL relationships that was observed at regional distances (∼200 km). These results demonstrate that there are lake-to-lake differences in the effects of TP and water color on lake CHL and that this variation is spatially structured. Quantifying spatial structure in these relationships furthers our understanding of the variability in these relationships at macroscales and would improve model prediction of chlorophyll a to better meet lake management goals.