Castles built on sand or predictive limnology in action? The importance of Bayesian ensembles to support our ecological forecasts

To address the wide range of conceptual and operational uncertainties typically characterizing any modelling exercise, the modelling community in Lake Erie opted for a novel multi-model strategy that aimed to capitalize upon the wide variety of both empirical and process-based models of variant complexity that have been developed in the area over the past decade. Being primarily a reflection of our current level of understanding and existing measurement technologies, the multi-model strategy adopted for Lake Erie accommodates the fact that many different model structures and many different parameter sets within a chosen model structure can acceptably reproduce the observed behavior of a complex environmental system. While this very important notion is still neglected in the modelling literature, there are viewpoints suggesting that environmental management decisions relying upon a single, partially adequate, model can introduce bias and uncertainty that is much larger than the error stemming from a single, partially defensible, selection of model parameter values. Importantly, the practise of basing ecological predictions on one single mathematical model implies that a valid alternative model may be omitted from the decision making process (Type I model error), but also that our forecasts could be derived from an erroneous model that was not rejected in an earlier stage (Type II model error). Recognizing that there is no true model of an ecological system, but rather several adequate descriptions of different conceptual basis and structure, the development of model ensembles is a technique specifically designed to address the uncertainty inherent in the model selection process. Instead of picking the single “best-fit” model to draw ecological forecasts, we can use a multi-model ensemble to derive a weighted average of the predictions from different models.

Notwithstanding the voices in the literature asserting that we are still missing rigorous methodological frameworks to develop multi-model ensembles, the basic framework comprises several steps related to the development of "truly" distinct, site-specific conceptual models, selection of the optimal subset of both data-driven and process-based models, effective combination of these models to synthesize predictions, and subsequent assessment of the underlying uncertainty. This methodological procedure involves three critical decisions aiming: (i) to identify the conceptual or structural differences of the existing models (ensemble members), and thus determine the actual diversity collectively characterizing the model ensemble; (ii) to determine the most suitable calibration/validation domain for evaluating model performance in time and space; and (iii) to establish an optimal weighting scheme in order to assign weights to each ensemble member, when integrating over the individual predictions, and determine the most likely outcome along with the associated uncertainty bounds. In this study, I dissect the two model ensembles developed for the Maumee River watershed and the Lake Erie itself and evaluate their compliance with the aforementioned framework. I provide an overview of all the models used in the area by shedding light on their fundamental assumptions, structural features, and general consistency against empirical knowledge from the system.