A review of the current state of process-based and data-driven modelling: guidelines for Lake Erie managers and watershed modellers

Elevated phosphorus (P) loading from the watersheds draining into Lake Erie, particularly from agricultural (53%) and urban (43%) sources, is identified as one of the main drivers of the severe eutrophication. In this study, we present a comprehensive evaluation of 11 process-based models to characterize the water cycle as well as nutrient fate and transport within a watershed context, and to find a robust and replicable way to optimize the modelling strategy for the Lake Erie watershed. Our primary objective is to review the conceptual/technical strengths and weaknesses of the individual models for reproducing surface runoff, groundwater, sediment transport, nutrient cycling, and channel routing, and to collectively guide the management of the Lake Erie Basin. Our analysis suggested that the available models either opted for simpler approximations of the multifaceted, nonlinear dynamics of nutrient fate and transport, and instead placed more emphasis on the advanced representation of the water cycle or, introduced a greater degree of biogeochemical complexity but simplified their strategies to recreate the roles of critical hydrological processes. Notwithstanding its overparameterization problem, the MIKE SHE model provides the most comprehensive 3D representation of the interplay between surface and subsurface hydrological processes with a fully dynamic description, whereby we can recreate the solute transport that infiltrates from the surface to the unsaturated soil layer and subsequently percolates into the saturated layer. Likewise, the physically based submodels designed to represent the sediment detachment and erosion/removal processes (DWSM, HBV-INCA, HSPF, HYPE, and MIKE SHE), offer a distinct alternative to USLE-type empirical strategies. The ability to explicitly simulate the daily plant growth (SWAT and APEX) coupled with a dynamic representation of soil P processes can be critical when evaluating the long-term watershed responses to various agricultural management strategies. Drawing parallels with the (sub) surface and sediment erosion processes, a more complicated physically based approach, e.g., the dynamic wave model provided by MIKE SHE ( coupled with MIKE URBAN or MIKE HYDRO) and SWMM may be more appropriate for realistically simulating the pressurized flow and backwater effects of water routing in both open channels and closed pipes. While our propositions seem to favor the consideration of complex models that may lack the commensurate knowledge to properly characterize the underlying processes, we contend this issue can be counterbalanced by the joint consideration of simpler empirical models under an ensemble framework, which can both constrain the plausible values of individual processes and validate macroscale patterns. Finally, our study discusses critical facets of the watershed modelling work in Lake Erie, such as the role of legacy P, the challenges in reproducing spring-freshet or event-flow conditions, and the dynamic characterization of water/nutrient cycles under the nonstationarity of a changing climate.