A lurking uncertainty in lake ecosystem modeling: can equifinality arise from conceptually similar models?

Vertical one-dimensional aquatic ecosystem models (AEMs) are commonly used to project water quality changes in lakes, ponds and reservoirs. AEMs integrate a physical model, for water temperature dynamics and mixing, and a water quality model, which simulates biogeochemical cycles and ecological processes. Although powerful, assessing the performance of these models is challenging as observational data are often scarce and most models are overparameterized, making them mathematically ill-posed. A promising approach is the use of ensemble modeling to quantify the uncertainties of the underlying mathematical model parameters and the boundary data. In this study, we apply three AEMs (GLM-AED, GOTM-WET, GOTM-Selmaprotbas) to replicate observed long-term water quality dynamics of Lake Mendota, USA. Each model was configured conceptually similar, and parameters were calibrated to the same data, but optimization procedures differed. We assessed model performance through a hierarchical framework to evaluate fits on the state, process and system level. Although all AEMs sufficiently replicated most of the observed data - the states - they differed in their projected reaction pathways - the processes. As an example, modeled nitrate concentrations were close to observed data, but modeled nitrification and denitrification rates differed across models. This highlights the importance of considering the equifinality thesis, meaning that alternative modeling pathways exist simulating the same output data, for aquatic ecosystem modeling as an additional, and crucial, contributor to uncertainty. We recommend that future modeling studies should employ ensemble setups to further explore the role of equifinality.