Using a Bayesian hierarchical model to improve Lake Erie cyanobacteria bloom forecasts

The last decade has seen a dramatic increase in the size of western Lake Erie cyanobacteria blooms, renewing concerns over phosphorus loading, a common driver of freshwater productivity. However, there is considerable uncertainty in the phosphorus load-bloom relationship, because of other biophysical factors that influence bloom size, and because the observed bloom size is not necessarily the true bloom size, owing to measurement error. In this study, we address these uncertainties by relating latesummer bloom observations to spring phosphorus load within a Bayesian modeling framework. This flexible framework allows us to evaluate three different forms of the load-bloom relationship, each with a particular combination of statistical error distribution and response transformation. We find that a novel implementation of a gamma error distribution, along with an untransformed response, results in a model with relatively high predictive skill and realistic uncertainty characterization, when compared to models based on more common statistical formulations. Our results also underscore the benefits of a hierarchical approach that enables assimilation of multiple sets of bloom observations within the calibration processes, allowing for more thorough uncertainty quantification and explicit differentiation between measurement and model error. Finally, in addition to phosphorus loading, the model includes a temporal trend component indicating that Lake Erie has become increasingly susceptible to large cyanobacteria blooms over the study period (2002–2013). Results suggest that current phosphorus loading targets will be insufficient for reducing the intensity of cyanobacteria blooms to desired levels, so long as the lake remains in a heightened state of bloom susceptibility.