A systematic literature review of forecasting and predictive models of harmful algal blooms in flowing waters

Occurrences of harmful algal blooms (HABs) in rivers challenge the belief that rivers are not susceptible to HABs because of their short residence times and fluctuating hydrology. Here we present a systematic literature review of predictive and forecasting models for HABs in flowing waters, including rivers, flowing in-stream reservoirs (e.g., run-of-river reservoirs and lock-and-dam systems) and tidal or estuarine systems with riverine processes. The review aimed to understand current and historical modeling approaches for predicting and forecasting river HABs, without restricting to specific taxa, such as cyanobacteria, or modeling endpoints. The review included 162 articles published over nearly 50 years, covering more than 80 rivers worldwide. Eutrophic, non-wadable rivers with in-stream obstruction were commonly modeled, though diverse environmental characteristics were reported. Most articles used algal biomass or chlorophyll as modeling endpoints, with a quarter using novel or unique endpoints. Algal toxins motivated model development in 23% of the articles, however just 5% used algal toxins as an endpoint. Only 6% of the articles modeled benthic HABs; the rest focused on pelagic HABs. There was no standard model used for modeling river HABs. Process-based models were more common (59%) than data-driven approaches (37%), with model formulations ranging from simple to complex, which contrasts with a lake-focused literature review of HAB models that found data-driven models were more common. Models in river settings shared similar input variables as those previously identified for lakes, such as water temperature, nutrients, and light availability. However, streamflow and other transport metrics took prominence in river models compared to lake models. Algal cell physiology (such as growth, predation, and motility) was routinely included as input data or as mathematical formulations in process-based models and these processes were frequently identified as an important predictor by the articles' authors. Conversely, data-driven models rarely included these processes, instead using predictors related to environmental conditions, such as nutrients, water quality, water temperature, and streamflow. These important proxy predictors have apparent success with modeling overall algal biomass (irrespective of taxa) whereas other factors, such as those related to algal physiology and other biological processes, are likely responsible for more subtle shifts in community composition. These differences highlight the influence of data availability, especially for processes that are difficult, time-consuming, or expensive to measure, on model development and model outcomes, raising questions about the selection of modeling inputs and endpoints. Challenges to advancing river HAB modeling include the lack of site-specific model inputs representing key processes (e.g., photosynthetic parameters and predation rates), overlooked riverine environments like the benthos and side/back-channel areas, lack of information on environmental settings, and poorly reported model performance metrics. This review emphasizes opportunities for advancing river HAB modeling by learning from well-honed estuarine models, supporting current forecasting and operationalization efforts, and developing common datasets for river HAB model development and evaluation.