{"paper_id":"29945a5e-1da3-4e48-b808-1f1501f81494","body_text":"1 \n \nA systematic literature review of forecasting and predictive models \nof harmful algal blooms in flowing waters \nJennifer C. Murphya*, Rebecca M. Gorneyb, Lisa A. Lucasc, Jacob A. Zwartd, Jennfier L. \nGrahamb \na U.S. Geological Survey, Central Midwest Water Science Center \nb U.S. Geological Survey, New York Water Science Center \nc U.S. Geological Survey, Water Mission Area \nd U.S. Geological Survey, Water Mission Area \n*corresponding author, jmurphy@usgs.gov  \n \nThis information product has been peer reviewed and approved for publication as a preprint by \nthe U.S. Geological Survey. \nAbstract \nOccurrences of harmful algal blooms (HABs) in rivers challenge the belief that rivers are not \nsusceptible to HABs because of their short residence times and fluctuating hydrology. Here we \npresent a systematic literature review of predictive and forecasting models for HABs in flowing \nwaters, including rivers, flowing in-stream reservoirs (e.g., run-of-river reservoirs and lock-and-\ndam systems) and tidal or estuarine systems with riverine processes. The review aimed to \nunderstand current and historical modeling approaches for predicting and forecasting river \nHABs, without restricting to specific taxa, such as cyanobacteria, or modeling endpoints. The \nreview included 162 articles published over nearly 50 years, covering more than 80 rivers \nworldwide. Eutrophic, non-wadable rivers with in-stream obstruction were commonly modeled, \nthough diverse environmental characteristics were reported. Most articles used algal biomass or \nchlorophyll as modeling endpoints, with a quarter using novel or unique endpoints. Algal toxins \nmotivated model development in 23% of the articles, however just 5% used algal toxins as an \nendpoint. Only 6% of the articles modeled benthic HABs; the rest focused on pelagic HABs. \nThere was no standard model used for modeling river HABs. Process-based models were more \ncommon (59%) than data-driven approaches (37%), with model formulations ranging from \nsimple to complex, which contrasts with a lake-focused literature review of HAB models that \nfound data-driven models were more common. Models in river settings shared similar input \nvariables as those previously identified for lakes, such as water temperature, nutrients, and light \navailability. However, streamflow and other transport metrics took prominence in river models \ncompared to lake models. Algal cell physiology (such as growth, predation, and motility) was \nroutinely included as input data or as mathematical formulations in process-based models and \nthese processes were frequently identified as an important predictor by the articles’ authors. \nConversely, data-driven models rarely included these processes, instead using predictors \nrelated to environmental conditions, such as nutrients, water quality, water temperature, and \nstreamflow. These important proxy predictors have apparent success with modeling overall algal \nbiomass (irrespective of taxa) whereas other factors, such as those related to algal physiology \nand other biological processes, are likely responsible for more subtle shifts in community \ncomposition. These differences highlight the influence of data availability, especially for \nprocesses that are difficult, time-consuming, or expensive to measure, on model development \nand model outcomes, raising questions about the selection of modeling inputs and endpoints. \nChallenges to advancing river HAB modeling include the lack of site-specific model inputs \nrepresenting key processes (e.g., photosynthetic parameters and predation rates), overlooked \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n2 \n \nriverine environments like the benthos and side/back-channel areas, lack of information on \nenvironmental settings, and poorly reported model performance metrics. This review \nemphasizes opportunities for advancing river HAB modeling by learning from well-honed \nestuarine models, supporting current forecasting and operationalization efforts, and developing \ncommon datasets for river HAB model development and evaluation. \nKeywords \nCyanobacteria, rivers, harmful algal blooms, modeling, data-driven, process-based \n1. Introduction \nHarmful algal blooms (HABs) are a global phenomenon that occur in diverse aquatic \necosystems spanning the freshwater to marine continuum (Glibert, 2017; Howard et al., 2023; \nPeacock et al., 2018; Stauffer et al., 2019). The potential harms associated with blooms include \nexcess algal biomass, degraded water quality, excessive oxygen demand, disrupted aquatic \nfood webs, and production of secondary metabolites, such as taste and odor causing \ncompounds and toxins, all of which may have far-reaching ecologic, economic, and public \nhealth consequences (Brooks et al., 2016; Chorus and Welker, 2021; Huisman and Weissing, \n1994). The organisms responsible for HABs and the environmental conditions that foster their \ndevelopment arise from a complex interplay of physical, chemical, and biological processes that \noccur across various spatial and temporal scales (Burford et al., 2020; Glibert, 2017; Griffith and \nGobler, 2020; Zhou et al., 2020). \nIn freshwaters, prokaryotic cyanobacteria are the primary organisms that cause HABs \nand are the only freshwater taxa known to produce toxins that can adversely affect human \nhealth. However, other freshwater eukaryotic algae (e.g. diatoms and green algae) can cause \nHABs and produce toxins (e.g., chrysophytes and euglenophytes) that affect aquatic organisms, \nparticularly fish (Gorney et al., 2023; Patiño et al., 2023). Key environmental factors that \ninfluence algal community composition and bloom development include water temperature, \nwhich affects algal physiology and growth; light, essential for photosynthesis; and nutrients, \ncrucial for cellular function (Chorus and Welker, 2021; Patiño et al., 2023). Physical processes \nare also important, and in lotic environments hydrodynamic processes moderate the effects of \nwater temperature, light, and nutrients on algal growth (Cha et al., 2017; Chételat et al., 2006; \nGraham et al., 2020; Reynolds and Descy, 1996; Van Nieuwenhuyse and Jones, 1996). Any \nspecific location along a river is inherently connected with upstream physical, chemical, and \nbiological processes (Glibert, 2017; Junk et al., 1989; Thorp et al., 2006; Vannote and Sweeney, \n1980; Walker et al., 2006). Ephemeral connectivity to backchannel areas (Giblin and Gerrish, \n2020; Giblin et al., 2022), reservoir releases and flow control (Graham et al., 2012; Otten et al., \n2015; Williamson et al., 2018), and downstream transport from upstream zones of benthic or \npelagic productivity (Schmadel et al., 2024; Wood et al., 2020) may all contribute to HABs in \nlotic environments. Consequently, the negative effects of freshwater HABs can extend hundreds \nof miles downstream from upstream source areas and eventually impair estuarine and coastal \nenvironments (Miller et al., 2010; Peacock et al., 2018; Preece et al., 2017). \nModels serve as important tools to enhance our understanding of HABs and aid in \nforecasting and management decisions. HAB modeling is performed across various \nspatiotemporal scales, from examining the physiological responses of specific taxa in laboratory \nconditions to analyzing global drivers and simulating long-term changes in occurrence (Burford \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n3 \n \net al., 2020; Lucas and Deleersnijder, 2020; Reynolds, 1998; Stauffer et al., 2019). Modeling \nefforts inform public health protection, mitigation strategies, and resource management. Early \nindicators and near-term event forecasts allow proactive responses to potentially hazardous \nconditions, thereby safeguarding animal and human health and reducing economic losses \n(Petchey et al., 2015). Predictive modeling can help assess outcomes of future scenarios, \nincluding management strategies under changing environmental conditions, ideally supporting \ninformed decision making. Therefore, investment in the development of robust forecasting and \npredictive models has been recognized as a critical need in addressing the challenges posed by \nHABs in freshwaters (Burford et al., 2020; Rousso et al., 2020; U.S. National Office for Harmful \nAlgal Blooms, 2024). \nRousso et al. (2020) systematically reviewed literature on forecasting and predictive \nmodels for harmful cyanobacterial blooms (CyanoHABs) in freshwater lakes and reservoirs. \nTheir review revealed that most lake models were site- and species-specific, primarily focused \non nutrient-enriched systems, and had inconsistent predictor variables across models; \nnonetheless, water temperature, phosphorus, and nitrogen were consistently identified as \nimportant predictor variables across various model types. These findings highlight the \ncomplexity of cyanobacterial community dynamics and bloom formation. The development of \nCyanoHAB models has paralleled advancements in computational capabilities and in monitoring \ntechnologies, such as machine learning, high-frequency sensors and remote sensing. Rousso \net al. (2020) noted that challenges in comparing the performance of different models arise due \nto variability and inconsistent reporting of location and frequency of sampling, analytical \nmeasurement procedures, and monitoring duration, alongside a lack of consistent model \nperformance metrics. A key conclusion of the review was the necessity for establishing a \nCyanoHAB modeling database; the compilation of lake studies reviewed by Rousso et al. (2020) \nserves as a foundational dataset for such an initiative. In contrast, Xia et al. (2019) offer a \nqualitative, albeit non-systematic, literature review of algal blooms in large rivers aiming to \ndefine river blooms, describe their negative effects, and identify likely key drivers. Although, they \npresent a useful conceptual framework for understanding blooms in these systems, the study \ndoes not provide a quantitative comparison of the literature nor an evaluation of different \nmodeling approaches and processes. Given the groundwork laid by Rousso et al. (2020) and \nXia et al. (2019), a systematic literature review of HAB models in lotic settings would provide a \npoint of comparison to similar modeling in lake settings and potentially improve forecasting \ncapabilities and provide insights into future HAB conditions across freshwater systems. \nWe adapted the methods outlined by Rousso et al. (2020) to systematically review the \ncurrent literature for HAB forecasting and predictive models for riverine environments for a more \ncomprehensive view of HAB modeling in freshwaters. In alignment with their definitions, we \ndistinguish between forecasting and predictive models versus models used for \nvalidation/qualitative explorations of observed data. Forecasting and predictive models provide \nfuture estimates focused on informing short-term operational strategies, long-term projections \nused for scenario analysis or estimates between observations temporally or spatially. We \nincluded models used for sensitivity analyses, hindcasting or nowcasting, which were not \nincluded in Rousso et al. (2020). Our review compiled articles with models that estimated HAB-\nrelated variables at locations and (or) times not represented in calibration or training datasets. \nAs such, like Rousso et al. (2020), we excluded models that solely analyzed and interpreted \nempirical data, despite the valuable insights they may provide. Although Rousso et al. (2020) \nfocused exclusively on cyanobacteria, our review encompassed all freshwater taxa associated \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n4 \n \nwith potentially harmful blooms. We organized our findings into four thematic areas: \nenvironmental setting, modeling data, model types, and model application. Within each theme, \nwe present both quantitative and qualitative summaries of the literature and highlight \nadvancements and insights that were beneficial to researchers. Finally, we identify challenges \nfacing the river HAB modeling community and suggest key opportunities for advancing river \nHAB modeling, particularly in the context of HAB management and mitigation.   \n \n2. Methods \nThe systematic literature review was completed in three phases: (1) a literature search \nof major scientific databases, (2) a three-step screening process to identify a final set of articles, \nand (3) extraction of information from each article during a critical review (Figure 1). We largely \nfollowed the steps laid out by Rousso et al. (2020) and described by Pickering and Byrne \n(2014). The benefit of a systematic literature review is that well-defined search queries and \ninclusion/exclusion criteria make the review reproducible and less dependent on the area of \nexpertise of the researchers completing the literature review. \n \n \nFigure 1. Workflow for the systematic literature review, including the number (n) and percentage \n(%) of articles retained after each step. We searched Scopus, Web of Science, ProQuest, and \nU.S. Geological Survey (USGS) publications (USGS Pubs) in the Phase 1 literature search. The \nblue dashed line reflects iterative refinement of Phase 1 search criteria to ensure validation \npapers were captured. This workflow was adapted from that of Rousso et al. (2020). \n \n2.1 Phase 1 – Search queries and literature sources \nDuring Phase 1 of the literature review, we developed a set of queries to use as search \ncriteria in databases of scientific, peer reviewed publications. The search criteria included four \nWeb of \nScience \n Phase 3: Information \nExtraction \nPhase 1: Literature Search \n  Phase 2: Screening - Using \nInclusion/Exclusion Criteria \nDefine search \ncriteria \nPro \nQuest \nScopus \nEvaluate search \ncriteria \nMerge & exclude \nduplicates \n \nStep1: Title & keyword \nassessment \n \nStep 2: Abstract \nassessment \nStep 3: Full-text \nassessment \nRead and \nreview articles \n(n = 162) \nFinal set of \narticles \nUSGS \nPubs \nUsed project-specific \nquestionnaire to \ncollect: \n \n* Author information \n* Site information \n* Geolocation \n* Data characteristics \n* Model type \n* Model performance \n* Model application \n* Lessons learned \n \nn = 1,772 (39%) \nn = 851 (19%) \nn = 162 (4%) \nn = 4,493 (100%) \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n5 \n \ncategories of information (Table 1) used to target publications focused on freshwater algae \nunder bloom conditions, in river settings, that developed or applied predictive or forecasting \nmodels. The four queries were used together, connected with the “and” (i.e., “&”) Boolean \noperator. Queries were refined over several iterations. We used a set of 24 validation papers \n(i.e., papers we knew contained river HAB models; Table SM-1) which we were able to retrieve \nusing the final search criteria (Table 1).  \nIn the spring of 2023, we applied the search criteria to titles, keywords, and abstracts \n(when available) in four scientific databases: Scopus, Web of Science, ProQuest, and the U.S. \nGeological Survey (USGS) Publications Warehouse. We merged results from all four database \nsearches and removed duplicate entries. Phase 1 yielded the titles, keywords, and abstracts for \n4,493 articles meeting our search criteria (Table 1; Figure 1). \n \nTable 1. Search criteria applied in Phase 1 of systematic literature review. All queries were used \ntogether with an “and” (&) operator. * is a wildcard that represents one or more additional \ncharacters. \nType of information Query \nFreshwater algae (\"cyanobacteria*\" OR “cyanophyt*” OR \"blue-green alga*\" OR \n\"harmful alga*\" OR “blue green alga*\" OR “bluegreen alga*” OR \n“phytoplankt*” OR “microalga*” OR “micro-alga*”) \nBloom (“bloom*” OR “HAB*” OR “Harmful Algal Bloom*” OR “cyanoHAB*” \nOR “HCB*” OR “toxi*” OR “cHAB*” OR “nuisance” OR “cyanotox*” \nOR “taste*” OR “odor*” OR “grow*”) \nRiver setting (“freshwater*” OR “river*” OR “stream*” OR “lotic” OR “creek*” OR \n“flowing*” OR “channel*” OR “canal*” OR “ditch*”) \nPredictive or \nforecasting model \n(\"model*\" OR \"forecast*\" OR \"predict*\" OR \"algorithm*\" OR \n\"simulat*\" OR “warn*” OR “program*” OR “early indicat*”) \n \n2.2 Phase 2 – Inclusion/exclusion criteria and screening steps \nPhase 2 involved application of inclusion/exclusion criteria (below) in a three-step \nscreening process to identify the final set of papers to be critically reviewed in Phase 3 (Figure \n1). First, we assessed the title and keywords of each article, then the abstract, and finally the \nentire article to determine whether an article satisfied the inclusion/exclusion criteria. If it \nbecame clear, after screening the title and keywords or abstract, that a paper did not satisfy the \ncriteria, the succeeding screening step(s) were not necessary. A paper needed to meet all three \nrequirements of the inclusion/exclusion criteria and clear all exclusions to be included in the final \nset. The full inclusion/exclusion criteria used during Phase 2 are provided in Table SM-2 in \nSupporting Materials-1. In brief, the inclusion and exclusion criteria stipulated: \n1) The research must have been conducted in freshwater, flowing environments such as rivers, \nstreams, creeks, canals, channels, and ditches, whether natural, constructed, modified, or \nmanaged. Run-of-river reservoirs, lock and dam pools, and rivers in estuarine settings were \nalso included if the corresponding model contained clearly riverine processes (e.g., \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n6 \n \nadvective flow). Models of both real and idealized settings (i.e., observational data were not \nused and instead concepts of the environment were simplified or “idealized” for model \ndevelopment) were included. \n2) Models must have been developed or implemented for prediction (i.e., between \nobservations over time or across space), hindcasting, nowcasting, forecasting, or scenario \nor sensitivity analyses (e.g., related to environmental change or management decisions). \n3) Modeling endpoints must have been measures of algal composition, abundance, biomass, \npresence, or toxicity (e.g., community composition, cell counts, biovolume, toxin \nconcentrations) or related proxies (e.g., chlorophyll, phycocyanin). This included models that \npredicted primary production and algal cellular nutrient content. Novel proxies were also \nconsidered (e.g., metabolism metrics or oxygen dynamics) as long as the stated purpose \nwas for algal bloom prediction or forecasting. Models providing categorical output or \nestimates of bloom risk or probability were also included. \nUsing the inclusion/exclusion criteria (Table SM-2), we retained 1,772 articles (39% of \nthe initial 4,493 articles) after the title and keyword screen, 851 (19%) after the abstract screen, \nand finally 162 articles after the full text screen, which represented just 3.6% of all the articles \nreturned from Phase 1 (Figure 1). We ensured that the final set included only peer reviewed, \nfull-text, peer-reviewed articles written in English. We did not include conference proceedings, \nbook chapters, or proposals. \n2.3 Phase 3 – Information extraction \nAfter completion of Phase 2, each of the 162 articles was critically reviewed. To assist in \nthe extraction of information from each article, we developed a fillable online form using ArcGIS \nSurvey123 (Esri, 2025) with a standard set of questions. A dataset containing the questions \nused in the form and the information extracted from each article is available in Gorney et al. \n(2025). We exported results from our critical review to a comma separated values (CSV) file and \nprepared and analyzed the data using the R statistical software (R Core Team, 2025).  \nInformation on the following topics was retrieved for each article:  \n1) Publication information: Year of publication, affiliation of author, publication outlet \n2) Location information: Name of system, geographic location, field setting, qualitative \nsize of river, pelagic or benthic focus, and noteworthy environmental conditions \ndescribed by the authors (e.g., eutrophic conditions, managed flows, point sources, etc.)  \n3) Model information: Model type(s) (data-driven, process-based, or other), how many \nmodels were developed or used, skill metric(s), and qualitative evaluation of skill \n• If data-driven model: Model sub-type (e.g., linear regression, generalized additive \nmodels, neural networks, etc.) \n• If process-based model: Model sub-type (numerical or analytical), model name (if \navailable), and which processes were represented within the model \n4) Modeling data: Modeling endpoint, input data, monitoring data characteristics (e.g., \nduration and frequency), and monitoring methods used for the endpoint \n5) Model application: How the model was used (e.g., hindcasting, forecasting, prediction \nbetween observations in time or space, scenario analysis, sensitivity analysis); how \nmany and which variables and processes were identified as the most important \npredictors by the authors; the perceived, potential, or actual harms from a HAB that \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n7 \n \nmotivated the modeling; and a concise description of what the authors described as key \npoints and lessons learned from the articles. \n2.4 Model type descriptions \nBecause the focus of this literature review was on models, we classified each article \naccording to the modeling approach used: process-based or data-driven. Process-based \n(mechanistic) models use mathematical equations to represent the physical, chemical, or \nbiological processes that link causes to effects, often through mass balance frameworks. These \nmodels range from complex numerical simulations that approximate solutions under realistic, \nvariable conditions to simplified analytical models that provide exact solutions under idealized \nassumptions. Alternatively, data-driven models, including statistical and machine learning \napproaches, predict outcomes based on observed data without explicitly defining system \nprocesses. They range from simple regressions requiring minimal data to complex neural \nnetworks capable of capturing nonlinear, spatiotemporal patterns, though the latter demand \nlarge datasets and are more challenging to apply in data-sparse environments. Longer \ndescriptions of these model types are available in the Supporting Materials-1. \nArticles containing modeling approaches that did not fit neatly into the process-based or \ndata-driven paradigms were classified as “other”. These include articles that combine process-\nbased and data-driven approaches into one modeling framework (sometimes termed “hybrid” \nmodels or frameworks). Such modeling approaches may combine predictions from process-\nbased and data-driven models, replace parts of a data-driven model with process-based \ncomponents, or use outputs of a process-based model as inputs to a data-driven model \n(Parshotam and Robertson, 2018; Willard et al., 2022).  \nIf an article described more than one model, we extracted the information holistically for \nthe entire paper and noted how many individual models were developed. As such, summaries \nare in relation to the number of articles, not the number of models.  \n \n3. Results and Discussion \nIn total, we critically reviewed 162 articles with publication dates spanning almost 50 \nyears (1975 – 2023). A bibliography containing citations of the 162 articles is available in \nSupporting Materials-2. Additionally, Gorney et al. (2025) contains the information compiled from \neach article during the critical reviews and can be used to locate articles of interest. Reference \nlists for specific topical themes not easily identifiable in Gorney et al. (2025) are provided in \nTable SM-1 in Supporting Materials-1. \nMost lead authors were affiliated with academic institutions (77% of all articles); 22% of \nlead authors were affiliated with government entities, and the remaining 4% were affiliated with \nnongovernmental organizations or consulting firms. Some authors had dual affiliations. Notably, \none article was written by a high school student (Claudson, 1975). Articles were published in a \nwide variety of journals, indicating no preferred publication outlets for the river HAB modeling \ncommunity. There were approximately 73 unique journals names, with many (n=46) represented \nby just one article. The most common journals were Ecological Modeling (18 articles), Water \nResearch (12), and Water (9). Five articles were peer reviewed government publications (Table \nSM-1).  \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n8 \n \nIn comparison to Rousso et al.’s (2020) review of lakes and reservoirs (122 articles, \n1988 – 2019), our review captured 40 more articles and spanned 18 more years. The timespan \nof our review is heavily influenced by the earliest publication in the dataset (1975); if this article \nis excluded, our dataset begins in 1986, around the same time as Rousso et al. (2020). The \nhigher number of articles included in our review can be attributed to our inclusion of all \nfreshwater taxa associated with potentially harmful blooms, as well as the timing of our review \nrelative to Rousso et al. (2020). Had we limited our review to cyanobacteria, 52 articles would \nhave been included, spanning the years 1988 to 2023; if we also constrained our set to the \nsame time span as Rousso et al. (2020), the number of articles would have been 37. The limited \nnumber of cyanobacteria-related river HAB modeling articles compared to lakes reflects the \npropensity for cyanobacteria to dominate in quiescent rather than flowing waters (Chételat et al., \n2006; Reynolds and Descy, 1996) and the relative lack of river-focused cyanobacteria studies \noverall in the literature (Graham et al., 2020). However, the number of articles in our review \nindicates that algal dynamics and algal-related harms in river systems have been a sustained, \nand growing, concern for at least half a century.  \n3.1 Environmental setting \nRepresenting over 80 different rivers worldwide, the models developed in the articles \nwere clustered by continent (Figure 2) and country (Table SM-3). The geographic distribution of \nriver HAB modeling articles was generally similar to that observed for lakes and reservoirs \n(Rousso et al., 2020). Seven percent (n=11) of articles applied models to idealized settings. Of \nthe remaining 151 articles, a majority developed HAB models for river systems in Asia, followed \nby North America and Europe (Table 2). By country, 26% of the articles were for river systems in \nSouth Korea, followed by 21% in the United States and 12% in China (Table SM-3).  \nSouth Korea was a geographic hotspot for river HABs modeling (Figure 2B), and the \nNakdong River–included in 19% of all articles–was a focal point. Furthermore, the top four most \ncommon study locations in the literature review are from the four major river basins in South \nKorea: the Nakdong (n = 29), Han (n = 9), Yeongsan (n = 9), and Geum (n = 8) Rivers. These \nrivers serve as major drinking-water sources for urban centers of South Korea and are used for \nindustrial and agricultural purposes (Srivastava et al., 2015); as such, the modeling emphasis in \nthese systems underscores their societal importance.  \nThe remaining system-specific articles were more widely distributed geographically and \nrepresented over 75 different river systems. Two articles did not report the name of the system \nbeing modeled (Crossman et al., 2021; Wang et al., 2019a), and another two articles modeled \nconditions across multiple systems (Lucas et al., 2009b; Savoy and Harvey, 2023). About a third \nof the system-specific articles (35%) developed HAB models for one of 53 individual systems. \nExcluding these articles that modeled unique systems, the top four South Korean river systems \nand the four articles that did not report a system name or modeled multiple systems leaves \nabout 40% of the system-specific articles (n = 64) that modeled the same system as other \nresearchers. These articles are spread across 23 river systems with between about 2 and 5 \narticles published per system. As observed by Rousso et al. (2020), few modeling efforts \noccurred in South America or Africa (n = 2 each), despite widespread and increasing HAB \noccurrence on these continents (Feng et al., 2024). Both studies in South America were located \nin Brazil – one on a reservoir (de Souza Beghelli et al., 2016), and one at the catchment scale \n(Neres-Lima et al., 2017). The Vaal River in South Africa was the focus of the two studies \nconducted in Africa (Cloot and Roux, 1997; Cloot and Piererse, 1999). Feng et al. (2024) noted \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n9 \n \nthat most HAB studies occur in high-income countries, even though low-income areas may face \nhigher HAB occurrence and risk. Therefore, the distribution of river HAB modeling efforts is \nlikely associated with resources available for monitoring, research, and investment in \nmanagement, as opposed to HAB occurrence and risk. \n \nFigure 2. World map (A) of river systems identified in the articles. Map includes only articles that \ndeveloped models for real systems (151 of 162 articles). Inlays highlight B = South Korea, C = \nEurope, and D = North America.  \n \nTable 2. Number and percent of articles that developed models for real systems (n = 151 of 162 \narticles) across continents. \nContinent Number of \narticles \nPercent of \narticles \nAsia 61 40 \nNorth America 38 25 \nEurope 37 25 \nAustralia 10 6.6 \nSouth America 2 1.3 \nAfrica 2 1.3 \nMultiple continents 1 <1 \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n10 \n \n \nNon-wadable rivers were the overwhelming focus of river HAB modeling efforts (91% of \nstudies in real settings), most of which were likely large enough to support barge traffic (64%). \nAbout half of the articles (47%) describe rivers with in-stream obstructions such as weirs, run-of-\nriver reservoirs, or locks and dams. Given that we included run-of-river reservoirs, there was the \npotential for articles to be included in both our review and that of Rousso et al. (2020). However, \nonly one paper (focused on the Douro River, Portugal) was captured by both reviews (Teles et \nal., 2006). About a third of articles focused on free-flowing rivers that did not have nearby in-\nstream obstructions (31%; Figure 3A). Large rivers with in-stream obstructions were the most \nfrequently modeled systems (41% of all articles), including the four major rivers in South Korea, \nthe Thames River in the United Kingdom, the Xiangxi River in China, and the Seine River in \nFrance. Relatively few studies developed models across a river network or watershed (15%) or \nfocused on rivers in connection with lakes (11%; Figure 3A). Similarly, rivers in estuarine \nsettings (n = 21, Table SM-1) draining to the ocean or noted for having tidal influences were the \nfocus of about 13% (Figure 3A) or 9% (Figure 3B) of the articles, respectively. \n \n   \n \nFigure 3. River setting (A) and environmental characteristics of the river setting or watershed \ndescribed by the article’s author(s) (B) reported in system-specific articles. Percentages will not \nsum to 100% because an article may model a system that includes multiple river settings (e.g., \nreaches that are free-flowing and drain from a lake), and often authors mentioned multiple \nenvironmental characteristics when describing the riverine setting of their modeling effort. Point \nand nonpoint sources in (B) refer only to nutrients. \n \nAuthors included a variety of characteristics when describing the environmental setting \nof the modeled system (Figure 3B), many of which indicated degraded or intensively managed \nsystems. Over half the articles mentioned streamflow modification (56%) in terms of diversions, \npumping, or other human activities that control the flow rate or volume of water (Figure 3B) \nwhich may or may not be related to weirs, dams, or other in-stream obstructions (the latter \npresented in Figure 3A). Similarly, 59% of articles described eutrophic conditions. Point source \n(e.g., wastewater discharges) and nonpoint source (e.g., agricultural runoff) influences were \ndescribed in 38% and 36% of the articles, respectively. Like Rousso et al. (2020), most articles \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n11 \n \nincluded in our review focused on modeling nutrient enriched systems. Although nutrients are a \nconsistent driver of algal biomass standing crop and HAB formation (Chorus and Welker, 2021; \nPatiño et al., 2023), nutrient influence in lotic systems is further moderated by streamflow and \ntransport processes that may disconnect HAB occurrence from source conditions (Giblin and \nGerrish, 2020; Giblin et al., 2022; Graham et al., 2012; Otten et al., 2015; Schmadel et al., 2024; \nWilliamson et al., 2018; Wood et al., 2020). As such, there would be benefits to additional \nmodeling in systems with complex hydrologic characteristics and geomorphic conditions where \ncausal factors of HABs may not be apparent within the mainstem of the river.  \n \n3.2 Modeling data \n \n3.2.1 Modeling endpoints \nOutputs from the models were diverse. Although most of the articles used algal biomass or \na proxy like chlorophyll as the modeling endpoint, a quarter of the reviewed articles (n=42, 26%) \nused endpoints classified as “other”.  Additional endpoints included primary production (n = 5), \nnovel proxies based on oxygen data or metabolism estimates (e.g., Harvey et al., 2024; Wang \net al., 2019b), algal cellular nutrient content (n = 2; Bucci et al., 2011; Thebault and Qotbi, \n1999), concentrations of taste and odor compounds (n = 1; Chung et al., 2016), probabilities of \nbloom occurrence (e.g., Kim et al., 2022c; Kim et al., 2021a; Nietch et al., 2022), categorical \nassignments (e.g., Park et al., 2021), growth rates (Descy et al., 1987; Pinckney et al., 1997), or \nlatent variables (Arhonditsis et al., 2007a; Arhonditsis et al., 2007b), among others. In some \narticles, models used endpoints that were directly linked to potential harms, such as cyanotoxins \n(n=8; Gorney et al., 2025). Other articles related model outputs to a threshold or action level. \nProcess-based models often provided estimates of water quality (e.g., dissolved oxygen or \nnutrient concentrations) and streamflow in addition to an algal-related endpoint. Articles that \nused data-driven modeling techniques often included multiple models that used either the same \nmodeling endpoint to identify the optimal model formulation or used multiple modeling endpoints \nto capture various HAB indicators (e.g., cyanobacteria concentration and probability of \nexceeding a threshold). \nWhen we only considered endpoints that quantified the amount of algae, the presence of \ncertain algal taxa, or both, we encountered a mix of units, analytical methods, and taxonomic \nlevels. These inconsistencies complicated synthesis across the articles—an issue described in \ndetail by Ho and Michalak (2015) for western Lake Erie, USA. About half of the articles (46%, \nn=75) used an endpoint that quantified the amount of algae present; however, these endpoints \nincluded biomass, biovolume, or cell abundance, typically in units of micrograms per liter (µg/L), \ncubic micrometers per liter (µm3/L), or cells per liter (cell/L), respectively. Additionally, these 75 \narticles used a mix of microscopy (n=41, 55%) and laboratory-based pigment analysis (n=32, \n43%) to determine algal quantity endpoints. Some articles used both methods as a means of \nsupplementing the other or to determine taxonomic information. Across all the articles, it was \ncommon for the modeling endpoints to indicate the algal community composition, usually at the \nphylum level or for a particular taxon (41%, n=67). Cyanobacteria were the most common taxa-\nspecific endpoint (32%, n = 52), with genera such as Microcystis and Dolichospermum (formerly \nAnabaena; throughout this manuscript we refer to this taxon using the name used in the \noriginating article) occurring in multiple articles. Notably, these taxa were also the most \nfrequently modeled in lake systems (Rousso et al., 2020), highlighting the ubiquity of these \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n12 \n \norganisms regardless of hydrologic regime. Other than cyanobacteria, green algae \n(chlorophytes) and diatoms occurred in 23% of the articles (n=37). For articles that did not \nprovide taxonomic information (n=95, 59%), the modeling endpoint often represented \nchlorophyll or total phytoplankton. \nChlorophyll was a widely used modeling endpoint across the articles (56% of articles, n = \n90), in spite of a long-debated history over analytical methods and use as an indicator of algal \nbiomass in aquatic systems (Schurmann et al., 2024). Some of the ambiguity around the use of \nchlorophyll is highlighted in previous studies that indicate chlorophyll a content per cell (or per \nunit of biomass) is not consistent across taxa and varies in response to cell physiology and \nenvironmental conditions (Cloern et al., 1995; Foster et al., 2022). Additionally, in situ \nmeasurements via fluorescence sensors are often not directly comparable to extracted \nlaboratory values for a variety of reasons, including light history, cell morphology, \nnonphotochemical quenching, and water column turbidity (Foster et al., 2022). We did not \ndistinguish between chlorophyll a and other chlorophylls in our review and found chlorophyll \ndata were used in a variety of ways. Many articles used chlorophyll concentration (expressed as \nµg/L) directly as a modeling endpoint (e.g., He et al., 2020; Li et al., 2012; Scharfe et al., 2009; \nSu et al., 2022), whereas other articles converted measurements like biovolume (e.g., Thebault \nand Qotbi, 1999) or carbonaceous biomass (e.g., Cerco et al., 2004) to chlorophyll using paired \nobservational data or literature values, and still others proceeded in the reverse direction, \nconverting chlorophyll a to other values like phytoplankton biomass. Thebault and Qotbi (1999) \ncompared the influence of using biomass proxies like chlorophyll and total biovolume in a \nprocess-based model for the Lot River, France, and found inconsistencies in model output \nbetween these measures but generally comparable temporal patterns. Chlorophyll data will \nlikely remain a common modeling endpoint because they are easier and less costly to measure \ncompared to microscopy methods necessary for determining biovolume, cell counts, or \ntaxonomic composition. Chlorophyll was similarly a common endpoint in lake-focused HAB \nmodels, as it was used in 69% of the articles in Rousso et al. (2020). A small subset of lake-\nfocused articles used phycocyanin as a modeling endpoint (6%; Rousso et al., 2020); however, \nphycocyanin was not used in any of the river-focused articles in our literature review, even \nthough cyanobacteria abundance is more closely tied to phycocyanin than chlorophyll in many \nfreshwater systems (Chorus and Welker, 2021).  \nOut of the 162 articles, algal toxin concentrations—a key HAB  concern— were only used as \nthe modeling endpoint for eight articles (8 of 162 or 5%). Of these eight articles, five of the \narticles used an idealized setting to develop models. These five articles focused on \nunderstanding the transport and growth of Prymnesium parvum (golden algae) and associated \ntoxins in riverine systems that have stagnant side- and back-channel areas. Grover et al. (2011) \nderived the first mathematical model that described algal toxin dispersion through this complex \nriverine setting. This research was extended by the four other articles and in Grover et al. \n(2017). Hsu et al. (2013) incorporated the influence of zooplankton and their ability to suppress \nalgal abundance and limit toxin concentrations; Abbas (2015) incorporated longitudinal transport \nand biochemical reaction kinetics into the flowing main-channel portion of the model; Wang \n(2015) incorporated seasonality; and Wang et al. (2015) considered the role of a limiting \nnutrient, namely nitrogen. Ultimately, this set of articles identified a reproduction ratio for P. \nparvum that differentiated between a washout state and a persistence state in complex riverine \nsystems. The other three articles focusing on algal toxins as a modeling endpoint used field \ndata in data-driven or “other” models to predict concentrations of the cyanotoxin microcystin \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n13 \n \neither spatially or temporally in real river settings (He et al., 2021a; He et al., 2021b; Shan et al., \n2022). \n Some articles used endpoints in relation to a quantitative threshold or directly predicted \na potentially harmful state. For example, two South Korean articles developed models that \nlinked estimates of cell density to algal alert thresholds provided by the government (Kim et al., \n2021b; Park et al., 2021). The national South Korean algal alert system was developed in 1997 \nand focuses on cyanobacterial-related harms (Srivastava et al., 2015). Kim et al. (2021a) \nstudied the four major rivers of South Korea (Han, Nakdong, Geum, and Yeongsan) and \nmodeled the probability of exceeding a single total cyanobacterial abundance threshold of 1,000 \ncell/mL. Park et al. (2021) studied a single location on the Nakdong River and developed two \nseparate data-driven models to predict the occurrence of conditions related to four “algal alert” \ncategories (normal, caution, warning, and bloom) based on three cell density thresholds (1,000, \n10,000, and 1 million cells/mL). He et al. (2021b) provided another example of using a threshold \nto indicate harm for a collection of sites in eutrophic urban rivers; focusing on the Binhu River \nNetwork near Taihu Lake, China, those authors used a classification model that predicts the \nprobability of exceeding a microcystin threshold value of 1.0 µg/L. A model developed by Nietch \net al. (2022) for the Ohio River, USA, did not use a quantitative threshold, due to the lack of \navailable data, and instead used a binary endpoint (1 = bloom, 0 = no bloom) based on \nobservational reports of discolored water which were verified to be toxic. Other articles provided \nsemi-quantitative approaches for endpoints that indicate a potentially harmful state. For \nexample, with water suppliers in mind, Rose et al. (2019) developed a risk matrix method to \npredict phytoplankton-based hazards related to treatment (clogging), aesthetics (taste and \nodor), and health (cyanotoxins), based on the proximity of the hazard to the water treatment \nfacility and the severity of the consequence. Alternatively, prior to modeling, Hou et al. (2022) \nused water temperature and bioavailable nutrient concentration data to define five categories \nranging from “Potential HAB” to “No potential HAB” and used output from a process-based \nmodel to predict the probability of these categories to occur under different simulated scenarios. \nThe diversity of the above examples demonstrates the lack of universal thresholds for \nrecreational and drinking water globally (Brooks et al., 2016; Chorus and Welker, 2021) and the \nvarying ways authors define a HAB. Most articles in the literature review did not use a \nquantitative threshold or articulate a clear definition of a HAB (sensu Gorney et al., 2023). We \nestimate that less than a quarter of the articles attempted to model a potentially harmful state. It \nwas much more common for models to predict a continuous endpoint, such as chlorophyll a \nconcentration, without specifying when that endpoint might be indicative of potential harms. \n \n3.2.2 Input variables  \n The most common model input variables were nutrients, specifically nitrogen (N) and \nphosphorus (P), and streamflow (or velocity), used in 72% and 70% of the articles, respectively \n(Figure 4A). About half the articles used input variables such as \n• W at er temperature;  \n• O ther hydrologic variables, such as stage, stratification or vertical mixing information, \nand derived metrics like residence time, flushing rate, or water age;  \n• W ater quality measures other than N and P, such as silica, pH, dissolved oxygen, \nspecific conductance, among others; or  \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n14 \n \n• L ight availability, which includes measures of water clarity like turbidity, suspended \nsediment concentrations, and Secchi depth, in addition to measures like \nphotosynthetically active radiation and irradiance.  \n \nFinally, around 30% of the articles used input variables that represented  \n• weather conditions, such as precipitation, air temperature, wind speed, or wind \ndirection;  \n• algal processes such algal physiology (e.g., cell sedimentation, buoyancy, motility, \nresting stages), grazing pressure, and other biologically/ecologically relevant \ninformation; or  \n• watershed characteristics, such as land use characteristics, connections to source \nareas, among others.  \n \nAlthough subtle, algal processes are likely responsible for important shifts in community \ncomposition such as taxonomic succession within broad phytoplankton groups or the \ndominance of toxigenic strains. However, these types of data are often expensive and difficult to \ncollect, which may partly explain their infrequent use. A small percentage of the articles (less \nthan 10%) did not specify what input variables were used or referred the reader to a different \narticle (Figure 4A).  \n \n \n  \nFigure 4. Model input variables indicated across articles, as a percent of (A) all articles and (B) \ndata-driven articles only. Input variables are ordered from least to most common, and colors \ndenote specific input variables. Note: percentages in each panel will not add up to 100 because \nmost models used multiple input variables. [N, nitrogen; P, phosphorus] \n \n \nRousso et al. (2020) restricted their compilation of input variables to just data-driven \nmodels and found water temperature to be the most common input variable followed by pH, \nlight, total phosphorus (TP), and total nitrogen (TN; Table 3). A direct comparison of input \nvariables for data-driven models between lake and river settings is not possible given the \ndifferent data compilation approaches used by Rousso et al. (2020) and our study; however, \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n15 \n \nbroad patterns are discernable (Table 3). Unlike lakes, hydrologic variables were important input \nvariables for river models – 60% of data-driven models included streamflow, velocity, or other \nhydrologic metrics (Figure 4B); this is not unexpected given that most processes are moderated \nby streamflow in lotic systems (Cha et al., 2017). Hydrology notwithstanding, nutrients (and \nother water quality parameters), water temperature, measures of the light environment, and \nmeteorology were the most commonly included input variables in lake and river models, \nreiterating the importance of these factors in driving algal biomass and community composition \n(Figure 4B; Table 3). Nutrients were used as input variables more often in river models than lake \nmodels, likely because we aggregated all forms of N and P in our literature review, rather than \njust total nutrients (TN and TP) like Rousso et al. (2020) (Table 3).  \n \n \nTable 3. Comparison of the five most common input variables used in lake-focused, data-driven \nmodels reported by Rousso et al. (2020) and the river-focused data-driven models of this study. \nPercentage of river-focused modeling articles using pH is not reported because pH was \nincluded in the “other water quality” variables category in our review. Additionally, Rousso et al. \n(2020) exclusively compiled the percentage of articles that used measures of Secchi depth as \nan input variable, whereas we included more general measures of light availability such as \nturbidity, solar radiation, among others. \nInput variables  \nmost commonly reported \nfor data-driven models  \nPercentage of lake-\nfocused data-driven \nmodeling articles \n(Rousso et al., 2020) \nPercentage of river-focused \ndata-driven modeling articles \n(this review) \nWater temperature 83% 70% \npH 58% --- \nPhosphorus 55% (total P) 67% (all forms of P) \nNitrogen 45% (total N) 70% (all forms of N) \nTransparency 41% (as Secchi depth) 47% (as “Light availability”) \nMeteorology 30% 30% \n \n \n3.2.3 Monitoring data \n With the exception of models developed for idealized settings (n = 11), the quality of the \ncalibration data (input variables and modeling endpoint) is important for ensuring appropriate \nmodel fit, evaluating model quality, and producing reliable, defensible predictions. As such, for \nthe 151 of 162 articles that developed models for real systems, we summarized the monitoring \ndata in terms of frequency, duration, seasonality, and site counts (Figure 5). We found models \nwere typically developed and calibrated using monitoring data composed of discrete water \nquality samples collected year-round at 1 to 10 sites, with sampling frequencies ranging from \nweekly to monthly, over an average duration of five years. However, the distributions of these \ndata characteristics are indicative of a diverse range of data collection regimes (Figure 5). \nAcross the articles, the duration of monitoring ranged from a single year (n = 37) to 35 years (n \n= 1) and was highly skewed with half the articles using 3-years of data or less (Figure 5A). \nSimilar skew occurred for the number of sites monitored (Figure 5B). The number of monitored \nsites per article ranged from 1 to 180 sites, and around 75% of the articles used 10 sites or less. \nIn terms of seasonal representativeness, the majority of articles (60%) used monitoring data that \nwere collected year-round. The remaining articles (if seasonality of monitoring was reported), \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n16 \n \nsampled 1 to 8 months of the year (Figure 5C), presumably focused during the HABs season or \nduring HAB events. Most of the articles (68%) used moderately dense datasets with weekly to \nmonthly collection frequencies, likely reflecting the time and effort required to acquire discrete \nwater samples. Lower sampling frequencies were not common. Datasets with daily or sub-daily \nfrequencies were used in the modeling efforts of 26 articles (17% of 151 articles modeling real \nsystems). Many articles used a combination of monitoring frequencies and durations; 12 articles \npaired daily or sub-daily data collected via in situ sensors with data provided via laboratory \nanalysis from discrete water samples (Table SM-1). Finally, 31 articles did not report at least one \nof the data characteristics presented in Figure 5 and five of these articles did not report \ninformation for any of the four data characteristics or referred the reader to another article. \n \n \nFigure 5. Summary of monitoring data used in articles developing models for real systems (n = \n151) in terms of (A) sampling duration in years, (B) number of sites sampled, (C) number of \nmonths per year sampled, and (D) sampling frequency. Colors represent model type (data \ndriven, process based, and other). Site counts for the 8 articles that used 50 or more sites (50, \n82, 88, 90, 103, 113, 117 and 180) are plotted at x=50. \n \nThe use of daily or sub-daily datasets for modeling river HABs has increased over time, \nstarting with 2 articles in 1994-2003 and rising to 9 articles in 2004-2014 and 15 articles during \nthe last decade of our literature review (2014-2023). The two earliest articles were published in \n1997. One of the two earliest articles used one year of daily chlorophyll concentrations within a \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n17 \n \nmulti-species process-based model and found water temperature, light, and N:P ratio were the \ndrivers of algal growth in the Vaal River, South Africa (Cloot and Roux, 1997). The other article \nused a variable monitoring frequency to model stratification dynamics of Anabaena and \nMelosira (a diatom) behind a river weir in the Murrumbidgee River, Australia. The study included \nsamples collected less than weekly throughout the year, twice weekly during summer months, \nand sub-daily and at multiple depths during several 24-hours periods (Bormans and Condie, \n1998). Similarly, Pathak et al. (2021) used a combination of hourly to weekly water quality \ninformation to model diurnal scale phytoplankton dynamics in the Thames River, UK. Many of \nthe high frequency datasets are composed of chlorophyll concentrations based on fluorescence \nmeasured by in situ sensors. As sensor technology has advanced over the last two decades, \ndeploying and maintaining algal fluorometers has become increasingly common, though still not \nwithout challenges (Foster et al., 2022).  \nWe came across several notable datasets during our literature review. Savoy and \nHarvey (2023) compiled a dataset of daily chlorophyll and explanatory variables for a diverse \nset of 82 river sites across the U.S. Shan et al. (2022) collected high frequency data using buoy-\nmounted systems that measured algal cell counts and microcystin concentrations daily, along \nwith a host of additional water quality and physical parameters, in 4 tributaries to the Yangtze \nRiver, China. Perhaps one of the most impressive datasets is South Korea’s Water Environment \nInformation System (http://water.nier.go.kr/web) operated by the National Institute of \nEnvironmental Research. This dataset contains weekly cell counts for multiple potential \ncyanotoxin-producing taxa as well as other water quality measurements for multiple river \nlocations across South Korea. This database was used by multiple articles in our literature \nreview, including (Kim et al., 2023; Kim et al., 2022a; Kim et al., 2022b; Kim et al., 2022c; Kim et \nal., 2022d; Pyo et al., 2019). \n \n3.3 Model types \nAcross the 162 articles, process-based models were more common than data-driven \nmodels, appearing in 59% and 37% of the articles, respectively. We classified the remaining 4% \n(n = 7) of articles as “other” (Guven and Howard, 2007; He et al., 2021a; Pathak et al., 2021; \nRankinen et al., 2019; Rose et al., 2019; Yan et al., 2021; Table SM-1), which includes hybrid \nmodeling approaches. In contrast, in lake settings Rousso et al. (2020) found that 40% of \narticles used process-based models and 60% used data-driven models. Yet, similar to lake \nmodels (Rousso et al., 2020), the proportion of data-driven river HAB models has increased \nover time (Figure 6A). Since the mid-1990s, articles using data-driven models have increased, \nwith a sharp uptick starting in 2004-2013. Process-based models were dominant in the early \ndecades of river HAB modeling but by the most recent decade (2014-2023), data-driven models \ncomprised almost half of articles (Figure 6). Model types also varied geographically (Figure 2). \nProcess-based models were a popular choice in the U.S., especially in coastal areas, and in \nEurope and South Korea. Data-driven models were most frequently used in South Korea (43% \nof all data-driven articles) followed by the U.S. and China (Table 2). \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n18 \n \n \nFigure 6. Number of modeling articles published by decade (A) and for major sub-types of \nprocess-based (B) and data-driven (C) models. Models are grouped into either numerical or \nanalytical sub-types for process-based models (9 process-based modeling articles that did not \nreport a sub-type are not included) and into machine learning (e.g., neural networks, regression \ntrees), simple statistical (e.g., linear regression, generalized additive models), or Bayesian sub-\ntypes for data-driven models. Note difference in y-axis scale between panel (A) and panels (B) \nand (C). \n \n3.3.1 Process-based models \nOf the 95 articles that used only process-based models, 67% were numerical (n=64), \n23% were analytical (n=22), and the remaining 9 articles were undiscernible based on our \ncritical review. Numerical models can require considerable computing resources, especially for \ndomains described with significant spatial detail and in multiple dimensions. In contrast, \nanalytical models are typically straightforward and efficient to solve. Within river HABs modeling, \nthere has been a steady increase in the number of numerical models over time (Figure 6). The \nincrease in numerical modeling efforts is likely due to computing advances over the last several \ndecades, as well as burgeoning amounts of observational data with which to drive, calibrate, \nand validate such models. The intersection between ecohydrology and modeling is notably \nexemplified by the earliest article in our literature review. Claudson (1975) developed a \nnumerical process-based model for phytoplankton growth in response to chemical and thermal \npollution. The publication outlet, Communications of the Association for Computing Machinery, \nreflects novel application of enhanced computing power that was just becoming available for \npublic use at that time. \nA wide spectrum of processes was included within the process-based models. For \nexample, a simple first-order loss rate may be specified by the user and included in model (e.g., \nEngel et al., 2025; Lucas et al., 1999). Alternatively, more complex approaches can be used to \ndynamically model the zooplankton population and compute grazing or ingestion rates based on \nthe population dynamics (e.g., Wang et al., 2020; Ward et al., 2012). A similar range of \ncomputational complexity was apparent across process-based models to represent turbidity, \nnutrients, hydrodynamics, water temperature, and other influences on algal dynamics. \nRegardless of how it was represented in a model, we combined all such representations of an \nindividual process to convey which processes were included in some manner in the process-\nbased articles we reviewed (Figure 7). Many processes, including streamflow (or velocity), \nnutrient availability (N and P), other water quality properties, water temperature, light, and other \nphysical processes (e.g., antecedent streamflow conditions, channel morphology, wind speed \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n19 \n \nand direction), occurred in over 60% and up to 87% of the process-based modeling articles \n(Figure 7) and were also common input data for many of the data-driven models (Figure 4B).  \n \n   \nFigure 7. Percent of process-based modeling articles that included a representation of the \nprocess listed on the y-axis. Colors correspond to the input variable colors used in Figure 4. The \ncategory “other physical variables” includes additional information that describes the physical \nenvironment including non-precipitation meteorological data (such as wind direction or speed), \nantecedent streamflow conditions, channel morphology, among others. [PAR, photosynthetically \nactive radiation; N, nitrogen; P, phosphorus] \n \nA few processes are noteworthy in their comparison to data-driven models or their \nlimited use in process-based models. Algal cell physiology, which included processes such as \ngrowth, algal cell sedimentation, buoyancy, or motility, was incorporated into the majority (83%) \nof process-based models (Figure 7), but when represented more generally as “algal processes”, \nwas much less common in data-driven models (~22% of data-driven modeling articles). For \ndata-driven models, the “algal processes” input variables in Figure 4B includes algal cell \nphysiology in addition to grazing pressure and other biological/ecological variables. Grazing and \nconnection to source regions or “storage areas” (Grover et al., 2011; Reynolds, 1996; Reynolds \nand Descy, 1996) are potentially important influences on algal processes represented in 40% \nand 26% of process-based modeling articles, respectively. Additionally, given that stratification is \nknown in many cases to permit or promote HAB development (Paerl and Huisman, 2008) and \nwas included in 74% of lake HAB models (Rousso et al., 2020), it is somewhat surprising that \nonly 15% of process-based papers (n=14) in our review included that process, as stratified \nconditions can occur in stagnant side and backwater areas, behind obstructions such as weirs \nand dams, or during extreme low streamflow conditions. Several of the common process-based \nmodels used for rivers (Table 4) can capture stratification processes, if desired. We speculate \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n20 \n \nthat the lack of inclusion of stratification in river models is due to a lack of vertical observations \nin rivers and therefore a lack of evidence about the importance of stratification for HAB \ndevelopment.  \nMany articles used previously published software on which to build process-based \nmodels for river HABs (Table 4), and such software may encompass a single model or a \nframework of models or modules that may be used together. The most common process-based \nmodels cited in Rousso et al.'s (2020) study (their Table 1) did not overlap with any in Table 4 \nherein; this is likely due to differences in dominant governing processes between system types \n(e.g., horizontal transport in rivers, vertical turbulent mixing in lakes). \n \nTable 4. Named process-based models or modeling frameworks implemented in at least three \nreviewed papers. Model domain: H – hydrology and/or hydrodynamics; WQ – water quality (may \ninclude phytoplankton biomass); and E – ecology.  \nModel or \nModeling \nFramework \nModel \ndomain \nNumber of \npapers \nimplementing \nmodel \nReference(s) for model \nEFDC H, WQ 16  (Hamrick, 1992; U.S. Environmental \nProtection Agency, 2025) \nCE-QUAL-W2 \n \nH, WQ, E 7  (U.S. Army Corps of Engineers, 2014; \nWater Quality Research Group, 2025) \nRIVE/AQUAPHY WQ, E 7  (Gamier et al., 1995) \nWASP H, WQ 7  (Ambrose, 2017; Wool et al., 2020) \nRIVERSTRAHLER H, WQ, E 4  (Billen et al., 1994; Gamier et al., 1995) \nINCA/PERSiST H, WQ 3  (Futter et al., 2014; Whitehead et al., \n1998) \n    \nMIKE H, WQ, E 3  (DHI Group, 2025) \nPEGASE/ \nPOTAMON \nH, WQ, E 3  (Descy and Gosselain, 1994; Descy et al., \n2011; Smitz et al., 1997) \nQUESTOR H, WQ 3  (Boorman, 2003a; b) \n \n \n3.3.2 Data-driven models \nA wide range of techniques was used across the 60 data-driven modeling articles. \nSimilar to findings from Rousso et al. (2020) for lake HAB modeling, most river data-driven \nmodeling articles used a single modeling approach (70%). However, one study compared seven \ndifferent machine learning models in a river setting (Su et al., 2022). In total, 43 distinct data-\ndriven techniques were identified across all articles (Table SM-4). Artificial neural networks \n(ANNs) emerged as the most frequently used method, appearing in 18% of the data-driven \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n21 \n \nmodeling articles (n = 11). The next most common approach was multiple linear regression, \nused in 12% of the articles (n = 7), whereas all other techniques were reported in five (8.3%) or \nfewer articles (Table SM-4). When considering all types of neural networks—such as artificial, \nrecurrent, convolutional, autoencoders, transformers, multilayer perceptron, long short-term \nmemory networks, and others—these methods accounted for 40% of all data- driven modeling \narticles. Similarly, when aggregating linear regression-based techniques— including simple and \nmultiple linear regression, generalized linear models, structural equation models, mixed effects \nmodels, hierarchical models, support vector machines, and others—25% of th e data-driven \narticles employed these methods (Table SM-4).  These two categories of techniques were also \nthe two most popular data-driven approaches in the lake HAB modeling review (Rousso et al., \n2020). Of the 73 data-driven lake modeling articles in Rousso et al. (2020), 53% used \nregression techniques (20% used multiple linear regression) and 31% used neural networks \n(20% used artificial neural networks). Rousso et al. (2020) compiled 28 distinct data-driven \ntechniques across the lake models, many of which we also found in the river modeling articles \nincluding logistic regression, support vector machines, recurrent neural network, self-organizing \nmap, evolutionary algorithm (13 lake models used this technique compared to just 1 river \nmodel), multiple types of decision trees, multiple types of Bayesian models, and fuzzy logic \n(Table SM-4). Even amongst the many techniques we identified across the river models, notable \nlake model techniques missing from our compilation include multiple adaptive regression \nsplines, agent model, elastic network, and Cusp catastrophe theory.  \nAt a broader level, machine learning models (including neural networks and other \napproaches) were more prevalent than traditional statistical techniques. Although the use of \nthese methods has historically been similar, machine learning techniques have gained \nprominence over the last decade (Figure 6). Typically, machine learning methods require more \ndata compared to simpler statistical techniques and process-based models. This is due to \nseveral factors: machine learning models have a larger number of parameters to estimate, are \nmore susceptible to overfitting, and excel at identifying patterns in complex, interacting variables \nand non-linear relationships—all of which necessitate larger datasets.  Machine learning articles \nused longer duration monitoring datasets (mean = 7.4 years, median = 6 years) compared to \nsimple statistical (mean = 6.0 years, median = 4 years) or process-based articles (mean = 3.8 \nyears, median = 2 years). Recent increases in environmental data, particularly water quality \ndata (Read et al., 2017), combined with the availability of open-source programming software \nsuch as R and Python that supports machine learning modules, have empowered researchers \nto apply advanced data-driven models to water quality prediction challenges, including riverine \nHABs modeling. As environmental data volume continues to grow and access to open-source \nsoftware expands, we anticipate that the upward trend of applying machine learning models will \npersist.  \nDespite machine learning models using datasets with slightly longer monitoring \ndurations, they typically drew data from fewer sites compared to simple statistical and process-\nbased models. The median number of sites used by machine learning models was 2.5, \ncompared to 11 sites for simple statistical models and 4.5 sites for process-based models. \nNeural networks, the most complex data-driven models, perform best when trained on data from \na diverse range of sites, allowing them to learn general patterns in hydrological and ecological \nphenomena (Kratzert et al., 2024). Therefore, it is surprising that machine learning models \nrelied on the fewest number of sites, although our literature review did identify instances of \nmachine learning models trained on a larger number of sites (e.g., 82 sites in Savoy and \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n22 \n \nHarvey, 2023). Only recently, since 2023, have large, curated datasets of lotic algal biomass, \nsuch as chlorophyll levels, become available, enabling model training across various site types \n(Fernandez et al., 2025; Savoy and Harvey, 2023; Spaulding et al., 2024). In contrast, most \ndata-driven applications we reviewed focused on curating datasets for specific, local HABs \nconcerns. However, we propose that by leveraging these recently published large datasets \nalongside advanced data-driven techniques, prediction accuracy of river HABs can likely \nimprove across a greater number of sites.  \nAs previously mentioned, South Korea, particularly the Nakdong River, is a hotspot for \nriver HAB modeling as 42% (n=25) of all the data-driven modeling articles originated from this \nlocation. The collective research efforts in South Korea offer valuable insights into effective \ndata-driven modeling techniques. Among the reviewed articles, 20 of the 25 South Korean data-\ndriven studies used machine learning techniques, often demonstrating superior performance of \nadvanced machine learning methods compared to traditional approaches. For instance, neural \nnetworks with temporal awareness, such as recurrent neural networks (RNNs), outperformed \nsimpler statistical methods (Jeong et al., 2008; Lee and Lee, 2018). Furthermore, customized \nenhancements to RNNs designed to address missing data and low-frequency events showed \nimproved performance over standard RNNs (Kim et al., 2022d). This collection of articles \nhighlighted the strengths of convolutional neural networks (CNNs) in integrating various data \ntypes. For example, CNNs effectively incorporated hyperspectral chlorophyll a maps, leading to \nimproved predictions compared to the EFDC process-based model (Pyo et al., 2021). \nAdditionally, CNNs were able to use synthetic outputs from an EFDC model to enhance \ncyanobacterial forecasts (Pyo et al., 2020) which could possibly be considered a hybrid \napproach, though we classified this article as data-driven. Their ability to leverage spatial \ninformation gives CNNs a distinct advantage over other data-driven models. Lee et al. (2022) \ndemonstrated that CNNs could use data from multiple sites to enhance predictions at individual \nsites within a river network (Lee et al., 2022). Researchers have also recognized the value of \nsimpler statistical methods for predicting river cyanobacterial blooms. For example, (Kim et al., \n2020) found that a logistic regression model using just water temperature, river velocity, and \nphosphorus concentrations achieved over 75% forecast accuracy in South Korean rivers. The \napplication of data-driven methods in select study systems in South Korea illustrates how in-\ndepth research in specific locations can facilitate the comparison and evaluation of various \nmodeling techniques. \n3.3.3 Other models \n The seven articles containing models we classified as “other” did not fit cleanly into the \nprocess-based or data-driven model categories. Some implemented data-driven models to \nanalyze process-based model outputs in order to draw inferences regarding importance of \nmodel parameters (Guven and Howard, 2007), relations between various environmental \nparameters and chlorophyll concentration (Pathak et al., 2021), or lateral bloom position (Yan et \nal., 2021). Some papers in this category implemented hybrid approaches that combined \nprocess-based and data-driven approaches to predict a HAB-related endpoint. For example, He \net al. (2021a) used outputs of a process-based hydro-biogeochemical model as inputs to an \nANN model to predict microcystin concentrations. Similarly, Rankinen et al. (2019) and Mitrovic \net al. (2006) used process-based models to compute environmental conditions (e.g., runoff, \nstreamflows, nutrient concentrations) as inputs to empirical models that predicted, respectively, \nchlorophyll a concentration and bloom frequency. The “risk matrix” approach of Rose et al. \n(2019) was included in this model category because it represented (relative to the other models \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n23 \n \nin the articles we reviewed) an unusual and “semi-quantitative” approach to assessing \ncyanobacteria-related risk to a water supply.  \n3.3.4 Process-based and data-driven model comparisons \nAmong the 162 articles, 62% reported at least one quantitative measure of model skill. \nThe most used metrics were the coefficient of determination (R²) and root mean square error \n(RMSE), which appeared in 31% and 25% of the articles, respectively, paralleling findings from \nRousso et al. (2020) for lake models. Furthermore, similar to Rousso et al. (2020), we also \nfound a lack of standardization of skill metrics. Across river models, skills metrics categorized as \n\"other\" were used in 28% of the articles, making it the second most frequently reported \ncategory. Unexpectedly, 38% of the articles did not provide a quantitative measure of model \nskill, and a substantial proportion of these articles used process-based models. Across the \nprocess-based modeling articles, 55% did not report any quantitative metrics, compared to only \n12% of data-driven modeling articles (Figure 8). Among the process-based articles that did not \nreport a quantitative skill metric (n = 52), 58% (30 articles) included visual comparisons of \nobserved values and model outputs, either through plots or qualitative descriptions. Model \nperformance metrics enable comparisons across different modeling approaches, driving \nadvancements in both theory and model development (Lewis et al., 2022). Additionally, these \nmetrics effectively capture the insights gained from visual inspections and expert evaluations of \nmodel performance (Gauch et al., 2023). Findings from literature reviews of models in river (this \nstudy) and lake (Rousso et al., 2020) settings emphasize these points in the context of HABs. \nThe standardization of skill metrics and the use of at least one quantitative metric in future HAB \nmodeling studies could result in better comparisons across different approaches and aid in \nmodel selection for river and lake settings.  \nThe quantitative metrics demonstrate a range of skill for river HAB modeling. Within \nindividual articles, R² values were reported in various contexts, including testing datasets, \ntraining datasets, multiple models, and different endpoints. For each article, we recorded the \nhighest and lowest R² values among all HAB-relevant endpoints, excluding any quantitative \nmodel performance metrics related to other physical or chemical outputs. The full range of \nreported R² values spanned from <0.001 to 0.999, with little variation based on the type of \nmodel used (Figure 8). Notably, the lowest R² values reported in process-based modeling \narticles were generally lower than those in data-driven modeling studies. However, the median \nof the highest reported R² values was quite similar between the two modeling types, at 0.77 for \nprocess-based models and 0.78 for data-driven models (Figure 8B).  \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n24 \n \n \nFigure 8. (A) Percentage of articles reporting specific quantitative metrics for assessing model \nskill, categorized by model type. The quantitative metrics are arranged in order of prevalence \namong process-based articles. [RMSE, root mean square error; NSE, Nash-Sutcliffe Efficiency] \n(B) Range of highest and lowest reported R² values from data-driven (n = 21) and process-\nbased (n = 13) modeling articles. \n  \nTo compare the primary predictors of river HABs between process-based and data-\ndriven models, we compiled what the authors identified as the most important predictors \nindicated by their modeling efforts (Figure 9), a topic discussed by most authors (n = 150). \nAllowing the articles’ authors to determine important predictors reconciles the disconnect \nbetween input data and simulated process with data-driven and process-based models. Both \nmodel types use input data in model training or calibration. However, process-based models \nalso use data in additional ways (e.g., setting boundary or initial conditions) and include \nsimulated processes within the model. Input data and simulated processes both have the \npotential to indicate important predictors of river HABs and thus compiling author-reported \npredictors synthesizes these two types of information (Figure 9A). Across these 150 articles, \nauthors identified, on average, three important predictors. Nutrients were identified as the most \nimportant predictor (39%, n = 63). Light availability, streamflow (or velocity), and algal processes \nall ranked 2nd (each at 33%), followed closely by water temperature (30%, Figure 9A). We \nsurmise that broad drivers like nutrients, streamflow, and light are likely decent predictors of \noverall biomass but may struggle to predict finer scale dynamics like seasonal succession in \nalgal community composition. Rousso et al. (2020) compiled the single most important predictor \nfrom each lake-focused article in their review. As a percent of all reviewed lake articles (n = 122) \nthey are: \n• W ater temperature (31.5%) \n• N utrients (23.5%, includes N and P) \n• M etrological variables (12%, includes air temperature, wind speed, air pressure, \nand rainfall)  \n• B iological variables (6%) \n• W ater level (5%) \n• L and use (3%) \n• Streamflow (2%) \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n25 \n \n• O ther water quality (no percentage given, but provided examples for dissolved \noxygen, conductivity, and silica).  \nThree of the five top predictors are shared between lake and river models—nutrients, algal  \nprocesses/biological variables, and water temperature—despite differences in what was \ncompiled during the two literature reviews (i.e., the single key predictor versus all key predictors \nfrom the lake-focused and river-focused literature reviews, respectively; Figure 9A). Not \nsurprisingly, streamflow was ranked as the 3rd most important predictor for river models but \nranked 7th for the lake articles (Rousso et al., 2020). However, light availability ranked as the 2nd \nmost important predictor for river models but was never the primary predictor for lake models \n(Rousso et al., 2020). This discrepancy may be due to differences in how this information was \ncompiled; we used a broad definition of light availability that included measures like \nphotosynthetically active radiation, irradiance, and measures of water clarity (e.g., turbidity, \nSecchi depth) whereas Rousso et al. (2020) compiled exclusively solar radiation.  \nWhen constrained by model type, the primary predictors in river models change \nsubstantially (Figure 9). Within the data-driven articles, nutrients, water temperature, streamflow \n(or velocity), water quality other than nutrients, and light availability remain important predictors \nin 30-55% of the articles (Figure 9B). For process-based articles, the most important predictor \nwas algal processes (includes predation, cell physiology, and other biological/ecological \nvariables), which was identified as a main predictor in less than a quarter of the data-driven \narticles. Algal processes were closely followed by light availability and hydrologic metrics (other \nthan streamflow or velocity, e.g., residence time) for process-based models (Figure 9C). \nNutrients and streamflow (or velocity) have lower importance in process-based articles \ncompared to data-driven articles, and other hydrologic metrics rise in importance (Figure 9). \nSome differences in ranking are related to the input data used to drive data-driven models \n(Figure 4) and the additional processes simulated within process-based models (Figure 7). For \nexample, algal processes are an important feature included in many process-based models, \nthough are rarely included in the input data used to train data-driven models (Figure 4B). Algal \nprocesses encompass information like growth rates, nutrient uptake, cell sedimentation, cell \nmotility, and rates of predation. These processes are not readily observed quantities and are \nrarely, if ever, part of routine or event-based monitoring programs, which data-driven models \nheavily rely upon. Nevertheless, performance of the best models is roughly comparable \nbetween model types (as demonstrated with the median highest-reported R2 values in Figure 8). \nAs such, data-driven models may be capturing algal proliferation as a stochastic process, \nwhereas these are deterministic processes within process-based models.  \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n26 \n \n \nFigure 9. Most important predictors identified by authors during their modeling effort, as a \npercent of all articles that reported this information (A, n = 150), data-driven modeling articles \n(B, n = 56), and process-based modeling articles (C, n = 87), ordered from least to most \ncommon. Colors denote specific variables and are the same between the panels. Note, the “all \narticles” plot includes 7 articles with “other” model types. Percentages in each panel will not sum \nto 100 because most articles reported more than one important predictor. [vel, velocity; N, \nnitrogen; P , phosphorus] \n \n3.4 Model application \nIn over half of the articles (60%), authors articulated multiple purposes for developing or \napplying a HAB model in a given river setting (Figure 10). The most commonly stated purpose \nwas to make predictions between observations in time (40% of articles), followed by testing \ndifferent management or climate scenarios (35% of articles), hindcasting (32%), or conducting \nsensitivity analyses (30%). Both data-driven and process-based models were frequently used to \nmake predictions between observations in time (ranked first or second for model purpose), \nhowever the frequency of other purposes varied according to model type (Figure 10). \n \n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n27 \n \nFigure 10. Purpose of river HAB modeling effort as a percent of all articles (n = 162), data-driven \nmodeling articles (n = 60), and process-based modeling articles (n = 95). Note, the “All articles” \npanel includes seven articles with models classified as “other”. \n \nScenario analysis was the most common purpose of process-based modeling articles \n(41% of all process-based modeling articles; tied with predicting between observations in time) \nyet the 4th most common goal for data-driven models (23% of all data-driven modeling articles; \nFigure 10). The higher use of process-based models for scenario testing is likely because they \nincorporate physical laws and accepted process understanding making them more reliable for \nunobserved conditions. In contrast, data-driven models rely entirely on training data to identify \nrelations between input and output variables and thus may provide less reliable predictions \noutside of the conditions captured in training datasets (Appling et al., 2022). Considering both \nprocess-based and data-driven models (n=57 articles), we identified 17 types of scenarios \n(Figure SM-1). Authors also explored a variety of scenarios related to changes in climate, key \ndrivers (e.g., moisture conditions, light limitation), the physical environment (e.g., riparian zone \ncharacteristics, stratification, land use change), and seasonality. The most common scenarios \nexplored were those related to potential long-term streamflow and nutrient management \nsolutions. The effects of streamflow modification or nutrient reduction strategies on point and \nnonpoint sources were evaluated in 35% and 28% of these articles, respectively (Figure SM-1), \nreiterating the influences of these drivers on accumulation of algal biomass in lotic systems and \nthe ability for managers to manipulate these inputs (as opposed to climate effects) to minimizing \nHAB occurrence.  \nSimilar to our review, Rousso et al. (2020) also found many articles explored longer term \nmitigations strategies particularly for nutrient management. Articles that explored scenarios for \nshort-term mitigations once a HAB was already present were largely absent from the lake \nmodeling literature. For river models, short-term mitigation scenarios mostly focused on the use \nof increased streamflows, often released from an upstream reservoir and dam, to suppress the \nformation of a downstream river HAB (e.g., Mitrovic et al., 2006; Yoshioka and Yaegashi, 2017). \nOnly one article in our review modeled direct HAB management via algicide dosing, specifically \ncopper sulfate (Lewis et al., 2002). Despite the wide range of available short-term mitigation \noptions including physical, chemical, and biological approaches for an established HAB (Burford \net al., 2019), scenario testing for these strategies is largely absent from the HAB modeling \nliterature. We do not know if these studies are not being done or if they are being explored \noutside the realm of predictive and forecasting models and thus would have been excluded from \nour review. \nForecasting, along with hindcasting and predicting between observations in time, was \namong the three most common goals of data-driven modeling articles (32%, 37% and 38% of all \ndata-driven articles, respectively; Figure 10). However, only two process-based modeling \narticles produced forecasts (Ahn et al., 2021; Loos et al., 2020). Within data-driven articles, \nartificial neural networks were the most common modeling approach used for making forecasts \n(n = 5, Table SM-4). Additional forecasting methods were diverse and included multiple linear \nregression, Markov chain, kernel density estimation, long short-term memory, support vector \nmachines, among others. The most common forecasted output from these articles included cell \nabundance or density with an indication of the taxa present. Of all the articles that provided \nforecasts (n = 21), most are short-term with lead times ranging from 1-day to 30-days ahead (n \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n28 \n \n= 20). The forecast horizon for potentially harmful events is not more than a few days to weeks, \ngiven the influence of weather on the physical and chemical environment in aquatic \necosystems  (Benincà et al., 2008; Burford et al., 2020; Petchey et al., 2015). The most \ncommon forecast horizon across the articles was 7 days (n = 10). One article provided a 55-day \nahead forecast (e.g., Kim et al., 2022c; Kim et al., 2021a; Nietch et al., 2022). Some articles \nprovided multiple forecasting windows. Finally, forecasting models were applied primarily in \nSouth Korea (n = 14) with a few in Australia (n = 3), and one each in Portugal, United States, \nGermany and China. \nAn important consideration when defining a HAB is a recognition of perceived, potential, \nor actual harm to humans, animals, the environment, or the economy. We selected this set of \n162 articles for our literature review because HABs were motivating the modeling effort, as \ndescribed by the authors in the title, keywords, or abstract (refer to query keywords, Table 1). \nDuring review of these articles, we cataloged the perceived, potential or actual harms described \nby the authors. Although all articles described at least one harm of concern, about half of the \narticles specified more than one. A broad category of “general ecosystem health”, which \nincludes eutrophication concerns, was indicated as the motivation for HAB modeling in 85% of \nthe articles. The second most frequent concern was negative effects on drinking water (31%), \nfollowed by toxicity and toxin production (23%), and events that affect wild and domestic \nanimals (19%). These potential harms reflect the size and environmental characteristics of the \nriver settings described above, meaning many articles developed models for large rivers and \nrun-of-river reservoirs, which are often used as drinking water sources and for recreation. \nAlthough concerns about algal toxins motivated model development in 23% of the articles \n(n=38), only eight articles explicitly modeled algal toxins in river systems (refer to Modeling \nendpoints section 3.2.1). \n Finally, we summarized key lessons from each article, as indicated by the authors \n(Figure SM-2). Most of the key lessons pertained to the identification of the main processes \ndriving algal proliferation in the environmental setting being modeled. About a third of the \narticles found that streamflow conditions in terms of hydrodynamics, discharge rate, transport \nprocess, water withdrawals, presence of weirs, operation of dams, and variables like water age \nwere key parts of explaining variability in algal abundance and HAB occurrence. Nutrient \nconcentrations and loads were also found to be an important driving factor in 22% of articles. \nHowever, only 9 articles described both streamflow and nutrients as co-drivers. Finally, 19% of \nthe articles (n = 31) had key findings about the specific model presented in the article. For \nexample, these articles described how the model was developed, how the model performed, or \ntested and described the uncertainty associated with the model, as opposed to providing \ninsights into the processes controlling HAB development, duration, or decline.  \n \n3.5 Limitations of our study \nThis systematic literature review has several caveats, especially concerning the statistics \nderived from our final set of 162 articles. As noted in Section 2.3, to collect consistent \ninformation from each critically reviewed article, we populated a fillable form designed for this \nstudy. However, in many cases, the desired information was either not addressed at all, briefly \nalluded to, or described with scant detail in the article. In some cases, the articles referred \nreaders to other papers for such details. At times we made inferences and in other cases we \nwere unable to record information for a particular question. Consequently, there is some \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n29 \n \nuncertainty in the compiled information. Areas in which information was at times incomplete, \nminimal, or completely absent included: \n1. Environmental setting: river size and environmental characteristics \n2. Monitoring data: number of sites, frequency, duration, and/or methods related to the \ncollection and laboratory analysis of the observational data used in the modeling process \n3. Model details (process-based models): processes included and how they were handled in \nthe model (e.g., specification of rate constants versus dynamic computation); solution \nmethods (numerical versus analytical); treatment of time (steady-state versus time-varying) \n4. Model input data or parameters (process-based models): description of all model inputs and \nparameters derived from literature \n5. Model calibration and validation: use of calibration versus validation dataset; specifics about \nthe model formulation; descriptions of how models were validated including calculation of \nquantitative skill metrics \nAdditionally, we acknowledge the diversity of the scientific questions and modeling goals of \nthese 162 articles and that the findings from different scientific questions may not be directly \ncomparable. For example, we compiled the main predictors identified by the authors; however, \nwhat the authors considered a main predictor is highly dependent on the scientific question \nbeing addressed and the parameters for which model sensitivity was tested. This caveat applies \nto many of the questions related to model application, which we attempted to capture using \nquestions about model purpose and key lessons.  \nFurthermore, even though we followed a systematic approach to this literature review \n(similar to Rousso et al., 2020, and described by Pickering and Byrne, 2014) there are two \nplaces where we may have inadvertently excluded a relevant article. First, was during the \ndevelopment of the query used in Phase 1. To address this concern, we used a set of 23 \nvalidation articles containing river HAB models to develop and refine the search query (Table \nSM-1). Second, was during the three-step screening in Phase 2. Here we used explicit \ninclusion/exclusion criteria (Table SM-2), but there may have been slight differences in the \ninterpretation of this criteria depending on the reviewer. Finally, our restriction to only English-\nlanguage articles may be excluding river HAB modeling literature in areas of the world that are \nnot dominated by English speakers. \n \n3.6 Challenges to advancing river HAB modeling \n Using this collection of river HAB modeling articles, we identified three challenges to \nadvancing river HAB modeling. First, is a lack of available data, especially for key processes, \nand the difficulty of incorporating newer data streams such as high frequency in situ data or \nremote sensing to models. Second, is the geographic clustering of modeling efforts and their \nfocus on a particular river archetype which neglects important habitats and areas of the world. \nThird, is the challenge of synthesizing results across various model inputs, model endpoints, \nand model evaluations metrics presented across the articles which are at times poorly reported \nor not comparable. \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n30 \n \n3.6.1 Data gaps \nOne of the most prominent challenges limiting the ability to model water quality in \naquatic systems is the lack of data (Lucas et al., 2025). For process-based water quality \nmodeling generally, “Data related gaps are extensive and include the nearly universal need for \nimproved datasets for model calibration, validation, and specification of boundary conditions; \nbiogeochemical thermodynamic and kinetic rate parameters; constituent sources; and data \ndescribing the physical setting…” (Lucas et al., 2025). These general data needs apply at least \nas aptly to modeling HABs. Rousso et al. (2020) noted a similar challenge for lake HAB models, \npointing to constraints imposed by not only the amount but also the quality of available data \n(including monitoring technologies and data frequencies) and how this influences process-\nbased and data-driven modeling approaches differently.  \nSimilar to the lake-focused review (Rousso et al., 2020), we also found process-based \nmodels for river HABs often used data and parameters that are not readily available or easily \nderived from routine or event monitoring. Process-based models often needed data that \ndescribed biological processes that can act as sources (photosynthesis and growth) and sinks \n(benthic and pelagic grazing, respiration, senescence, sedimentation, motility) on algal biomass. \nA range of mathematical formulations exist for representing these processes in process-based \nmodels, but those formulations rely on kinetic rate parameters that can be species-, location-, \nand time-specific. Unfortunately, parameter values are usually not available for the specific \nsystem, algal assemblage, and time period being modelled, so modelers are often relegated to \nusing values from the literature or “tuning” these parameters during model calibration, a \nsituation that can lead to “equifinality” (i.e., multiple ways for a model to obtain the “right” answer \n(Beven and Freer, 2001)). Some rate parameters for which a fair amount of data and/or \nestimation approaches are often available in the literature include maximum growth rates \n(Eppley, 1972), respiration rates and Chl:carbon ratios (Cloern et al., 1995; Geider, 1987), but \ngrazing rates are frequently unavailable, particularly for benthic grazers, as observations and \ndata for those organisms are sparse or non-existent in many systems. Moreover, invasions by \ngroups such as dreissenid mussels in novel locations can lead to rapid changes in grazing \npressure (Lucas et al., 2016), rendering site-specific grazing data from a few years ago \nobsolete. Two articles in our review that explored the effects of grazing rates on water quality in \nthe Seneca River, NY , USA (Canale and Chapra, 2002; Glaser et al., 2009) and another from \nthe River Rhine, Germany, compared nutrients and grazing pressure as relative controls of algal \ngrowth rates (Schöl et al., 2002).  \nConversely, and also noted by Rousso et al. (2020) for lake systems, we found that \ndata-driven river models tend to leverage relatively easily and routinely measured data that are \nproxies for complex physical and biological processes incorporated more explicitly within \nprocess-based models. For example, using turbidity measurements as a proxy for light \navailability or using wind direction and speed as a proxy for vertical mixing. The simplification of \nthese processes into proxy data or rate parameters is due to the challenge of directly measuring \nthese processes, an issue not likely to be resolved in the near term. Rousso et al. (2020) found \ndata-driven models in lakes tended to use high-frequency in situ fluorescence data more than \nprocess-based models and found that increased data quantity benefits model performance for \ndata-driven models, a pattern we also suspect is present in our review of river models. \nEmerging observational technologies, such as readily available satellite data and in situ \nsensors, are filling some of the gaps in data collection and availability, providing observations of \nrivers at high, and previously unachievable, spatial and temporal resolution. Remote sensing of \nalgal blooms and detection of chlorophyll is expanding, especially in recent years for CyanoHAB \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n31 \n \nmodels in lakes (Rousso et al., 2020) and is already used to provide forecasts in several lake \nsystems (Stauffer et al., 2019). Few of the 162 articles in this review used remote sensing \nimagery in their efforts, with exceptions being Son et al. (2020) who used unmanned aerial \nvehicles and (Pyo et al., 2021) who used hyper spectral imagery. They found that the \ncombination of in situ data, multidimensional imagery, and synthetic output provided \ncomplementary effects in terms of time and spatial discrepancy in data, thereby increasing the \nreliability of a deep learning model. Additionally, in situ sensors continue to advance and provide \nhigh frequency observations for a growing number of HAB indicators, a pattern also observed \nfor lake models (Rousso et al., 2020). Remote sensing can also expand observations to habitat \ntypes, such as side channels and backwaters, that are beyond the spatial domains typically \nmeasured using in situ instruments. However, discrete weekly to monthly sampling remained a \ncommon connecting thread across the 162 articles reviewed herein (Figure 5D). A final hurdle is \nthe integration of spatial and temporal data at different frequencies and resolutions and from \ndifferent sources and methods. Integrated data usage is anticipated to expand the feasibility and \naccuracy of models for the prediction of various water quality variables and has shown promise \nin marine environments (Anderson et al., 2019). Yet, expanded datasets will likely require \nimprovements to older but still popular process-based models and data-driven techniques, in \naddition to a coincident demand for computing power. \n \n3.6.2 Gaps in riverine setting \nThis literature review has identified the most common setting of river HAB modeling over \nthe period of our literature review: eutrophic, non-wadable rivers, likely large enough to support \nbarge traffic, that have some sort of in-stream river obstruction, streamflow modification, or both. \nA similar archetype was used in a review of HAB modeling in large river systems by Xia et al. \n(2019), but extended here for more comprehensive understanding. Xia et al. (2019) found \ncommonalities in river systems such as the nonlimiting role of nutrients, the highly influential role \nof the streamflow regime, and the potential for flow regulation to mitigate bloom formation, \ntopics we also uncovered in our systematic literature review. However, their archetype selection \nof large, nutrient-rich river systems, although prevalent and represents waters that are used as \ndrinking water sources and for recreation, only accounted for approximately a quarter of the \narticles in this literature review. HAB modeling is occurring across rivers with a wide variety of \ncharacteristics (e.g., Figure 3) and sizes, albeit in a limited number of countries (mainly South \nKorea, United States, China, and Australia) and continents (i.e., Europe and Australia). In \naddition to the geographic clustering of river HAB modeling around the world (Figure 2), there \nare two additional gaps in the current literature of river HABs modeling related to environmental \nsetting: (1) benthic HABs and (2) stagnant side and back-channel areas. \nMost articles (real and idealized settings) focused exclusively on pelagic HAB conditions \n(93%), reflecting the focus on non-wadable rivers. Only a small subset of 10 articles (6%) \nincluded efforts to model benthic algae. Benthic accumulations of cyanobacteria are \nunderstudied compared to pelagic blooms (Wood et al., 2020) and were not included in Rousso \net al. (2020). Three studies in our review focused exclusively on benthic taxa and of those, only \none (Lévesque et al., 2012) focused on cyanobacteria. Lévesque et al. (2012) modeled \nabundance of Lyngbya in flowing and impounded portions of the St. Lawrence River, Canada. \nThe other two studies (1) modeled net primary productivity of periphytic microalgae in forested \nstreams near Rio de Janeiro, Brazil (Neres-Lima et al., 2017) and (2) predicted Cladophora \nbelow a dam in Japan to improve operations (Yoshioka and Yaegashi, 2017). The remaining \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n32 \n \nseven articles modeled both pelagic and benthic algal groups. One dealt specifically with \ncyanobacterial taxa in the benthos of urban influenced streams in Saskatchewan, Canada \n(Bergbusch et al., 2021). The rest were broadly focused on periphyton or benthic chlorophyll. \nFor example, Carleton et al. (2009) modeled benthic chlorophyll a along with the percentage \ncyanobacterial biomass of sestonic algae in the shallow, eutrophic Blue Earth River in \nMinnesota, USA, to support the development of numeric nutrient criteria for the management of \nimpaired river systems using the AQUATOX model. \n \nRivers are inherently diverse and many river HAB models overlook possible \ncontributions from productive side or back-channel areas and the connectivity between these \nareas and the main channel (Giblin and Gerrish, 2020; Giblin et al., 2022). These subhabitats, \nand at times, upstream tributaries and structural features (e.g., dams), play an important role in \ncreating areas with low flushing, high nutrients, and/or high residence time that influence algal \naccumulation (Junk et al., 1989; Reynolds and Descy, 1996), yet are poorly captured in river \nHAB models. We identified only 16 articles where connections to productive source areas (e.g., \nside pool, channel, tributary, upstream reservoir, etc.) were found to be important. Five of these \narticles were for idealized settings and (Grover et al., 2011; Grover et al., 2009; Hsu et al., 2013; \nJäger and Borchardt, 2018; Wang, 2015; Wang et al., 2015) three of these developed \ntheoretical models that simulated algal toxin movement from stagnant side and back-channel \nareas to the main channel of a large river (Grover et al., 2011; Hsu et al., 2013; Wang, 2015). \nThis collection of articles ultimately found that a ratio of the strength of longitudinal advection to \nlongitudinal dispersion (known as the Peclet number) was a good predictor of spatial variations \nin algal abundance. Lateral variation in algal abundance and toxin concentration occurred when \nthe stagnant area was hydraulically isolated from the main channel and thus lateral exchange \nwas weak. The rest of the articles modeled real systems, mostly using process-based \napproaches. For example, Yan et al. (2021) modeled transverse distribution of chlorophyll a and \nfound it was most affected by a ratio of chlorophyll a flux between tributaries and the main \nchannel. Higher chlorophyll concentrations were found on different sides of the channel due to \ninfluences from tributaries, changes in river width, and bends in the river. Ultimately, the authors \npoint out few studies have explored this type of transient storage variability in rivers, which we \nalso observed from our review, and more work needs to be done. \n \n3.6.3 Synthesis challenges \nOur literature review highlights noteworthy challenges to the synthesis of historical river \nHAB modeling efforts, which we assert stems from (1) the diversity of models, modeling \nendpoints, and skill metrics used over time, and (2) poorly defined ranges of environmental \ncharacteristics due to limited descriptions of the riverine setting and the input data. Rousso et al. \n(2020) noted similar challenges for modeling CyanoHABs in lakes. Multiple strategic plans for \nHAB research articulate the need for consistent and thorough descriptions of data and models \nas a means for learning from previous efforts and making progress towards operational, end-\nuser-supported forecasting and nowcasting tools (Anderson et al., 2019; Ganju et al., 2016; \nStauffer et al., 2019; U.S. National Office for Harmful Algal Blooms, 2024). Furthermore, more \nthorough descriptions of data and models would allow model developers to identify and select \noptimal solutions given particular environmental settings and modeling objectives.  \nAcross the river HAB literature, quantitative measures of the riverine environment, such \nas drainage area, mean annual streamflow, channel dimensions, stream order, and distance to \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n33 \n \nor from an obstruction, were often absent. This is a lost opportunity because we found, despite \ngeographic clustering within specific countries (Figure 2), the articles represent over 80 different \nrivers and span a range of sizes and environmental conditions. Even when quantitative \ninformation about the riverine environment is available, a variety of measures are provided that \nare not necessarily comparable. Inconsistent and limited reporting of location information \nseverely impedes the development of gradients (e.g., small to large rivers, oligotrophic to \nhypereutrophic) and limits the ability to conduct meta-analyses and derive quantitative \nconclusions. For example, in our literature review we made assumptions about river size by \nreviewing the description of the river setting in the article and at times viewing photos of the \nlocation (or near the location) on the internet. Based on visual assessment, we coarsely \nassigned the river sizes as “small, wadable”, “moderate, non-wadable, likely no barge traffic”, \nand “large, non-wadable, possible barge traffic”. This was ultimately unsatisfying but allowed us \nto make some general conclusions about the size of rivers present across these articles. \nRousso et al. (2020) also highlighted that lack of relevant lake-specific characteristics such as \ntrophic status and circulation patterns in their review of lake HAB models and proposed the \ncreation of a database containing this type of information to make it easier to compare between \nlakes. For rivers, at a minimum, reporting drainage area and mean annual streamflow for the \nriver being modeled is warranted and would improve the ability to quantitatively synthesize \nresults across a range of river sizes. Additional information like trophic status, turbidity, and \nhydrologic characteristics (e.g., 7-day minimum) could further improve the ability to compare \nmodels and results across river systems. \nNo single “standard” modeling approach was identified during our review. We found a \ndiversity of model structures (Table 4 and Table SM-4), input variables (Figure 4 and Figure 5), \nmodel complexity (e.g., process-based models, Figure 7), model endpoints, and model \nvalidation approaches (Figure 8). For example, model skill was challenging to compare across \narticles because, in many cases, a quantitative skill assessment was either not performed or \nonly minimally explained, a finding that is apparent across lake models as well (Rousso et al., \n2020). It was also sometimes unclear which output variables (e.g., the HAB-related modeling \nendpoint or an additional output like nutrient concentrations) were used to calculate the skill \nmetric if one was reported. Moreover, although a few skill metrics were somewhat common \n(e.g., R\n2, RMSE), a vast array of metrics was employed across the reviewed articles, including \ndeviance, Willmott’s Score, mean error, mean absolute error, accuracy, specificity, posterior \npredictive p-value, misclassification rate, Nash-Sutcliffe efficiency, among others. Finally, two \npapers could present a particular metric (e.g., R\n2) for a specific output variable (e.g., chlorophyll \na concentration), but those two metrics may not be entirely comparable because they may have \nbeen computed relative to different kinds and numbers of observational data (e.g., timeseries at \na single location, a single time across multiple locations) or for different kinds of model runs \n(e.g., a calibration run for which model coefficients were adjusted to optimize model-observation \nmatch versus a “validation” run for which coefficients were already independently determined). \nUltimately, the lack of consistent model skill metrics hinders model comparison and the ability to \nidentify promising approaches. \nModeling decisions, including the choice of endpoints (and input variables), were often \nshaped by data availability and practical considerations, which in turn influence the \ninterpretation and application of model results. Gorney et al. (2023) and Ho and Michalak (2015) \ndescribe the nuance of defining a HAB and how a selected HAB definition (whether explicit or \nimplicit) determines the hypothesis that can be tested and how model results may be used. \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n34 \n \nMany of the 162 articles in our review used chlorophyll over more specific, taxa-related \nendpoints, likely because of the comparative ease of the collection and laboratory analysis of \nthis measure. Furthermore, few articles used thresholds or modeling endpoints that were \nexplicitly related to a perceived, potential, or actual harm, such as algal toxin concentration or \nexceedance of algal biomass above a recreational threshold. This topic was not discussed for \nlake models in Rousso et al. (2020), where the discussion of modeling endpoints focused \nexclusively on chlorophyll a, cell concentration, biovolume, and biomass. The wide range of \nendpoints used across the 162 river-focused articles underscores the difficulty of synthesizing \nmodel output and gauging a model’s utility; a more uniform approach to reporting this \ninformation is warranted. \nRelatedly, some of the decisions that led to the use of certain input variables were also \nlikely based on data availability and accessibility which ultimately influences which predictors \nwere deemed important upon the completion of modeling. Potentially important processes were \nonly rarely included (as an equation or a proxy variable) in models. For instance, processes \nsuch as migration of cells, grazing, toxin production, benthic-pelagic interactions, or exchange \nbetween side or back-channel areas with a mainstem were often neglected. Measuring these \nprocesses in real systems is a challenge that results in a lack of observational data. There is \nuncertainty about how to represent some of these processes mathematically. Yet, identifying the \nimportance of a process or variable depends on its inclusion in the model. Some of the \ndifferences between the input variables (Figure 4), simulated processes in process-based \nmodels (Figure 7), and important predictors identified by the authors (Figure 9) demonstrate this \nissue. For example, “algal processes” was used as an input variable in just 23% of the data-\ndriven modeling articles (Figure 4) and was found to be important in the same percentage of \ndata-driven modeling articles (23%, Figure 9). In contrast, process-based models include algal \nprocesses as input data or an internal mathematical process in over 80% of the process-based \nmodeling articles (Figure 7) and algal processes was found to be the most important variable \nacross process-based modeling articles (38% of all process-based modeling articles; Figure 9). \nThe discrepancy in the importance of algal processes for modeling river HABs between data-\ndriven versus process-based model approaches likely stems from whether the data (or \nprocesses) are included in the models in the first place. Data used during model development \nand as input variables often reflects the difficulty associated with measuring, analyzing, and \nincorporating that observational information into a model, and these decisions ultimately dictate \nthe insights that can be gained from the model results. This begs the question: Are we using the \nbest modeling inputs and endpoints or just the easiest ones?  \n  \n3.7 Opportunities for advancing river HAB modeling \n Although challenges abound, our review also highlights opportunities for advancing river \nHAB modeling. In particular, there is much to learn from estuarine HAB models as these model \nformulations include riverine processes and have been advanced by many researchers over \nrecent decades. Additionally, forecasting river HABs is a promising way forward that can \nleverage theoretical or system-specific models and apply these towards user-relevant \nmanagement goals. Finally, community-developed common datasets may serve to encourage \nrapid development of river HAB models that can be readily evaluated and compared. \n3.7.1 Learning from estuarine HAB models \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n35 \n \nIt is crucial to improve our understanding of HAB drivers in freshwater and coastal \nsystems and to view HABs in these domains as connected, both mechanistically and with \nrespect to symbiotic approaches for studying them. Estuaries—aquatic systems where fresh \nriver water meets salty ocean water—a re a physical representation of that connection, and \ncyanotoxins produced in upstream source waters can propagate to estuaries and be taken up \nby mollusks, fish, and mammals and thus lead to human health risks (Miller et al., 2010; Preece \net al., 2017). In our review, 21 articles indicated an estuarine context (Table SM-1). Most used \nprocess-based modeling (76% of the estuarine modeling articles) and around half of these \narticles modeled a system in the United States (52%). Although estuarine HAB modeling \nrepresented a small portion of articles, they provide an interesting view into what advanced and \nspecific models can offer to the river HAB modeling community. \nEstuaries can, in some cases, function like rivers and, for that reason, many of the \nfindings and modeling tools from studies of estuarine phytoplankton dynamics could be \nextended and applied to rivers. For example, if river inflows to an estuary are high enough to \ndominate over tidal influences in governing net horizontal transport, the estuary’s \nhydrodynamics may, in the tidally averaged sense, approximate that of a river, particularly if the \nestuary is relatively narrow, such as a tidal river. Many of the simple (analytical) estuarine \nphytoplankton models (e.g., Qin and Shen, 2021; Wang et al., 2019c) could be applied in rivers; \nin fact, because of their simplifying assumptions regarding geometry and hydrodynamics, some \nof those models may indeed be more appropriate for rivers than for estuaries (e.g., Lucas and \nThompson, 2012; Lucas et al., 2009b). Analogous to the thermal stratification found in some \nrivers or run-of-the-river reservoirs, estuaries typically experience some degree of salinity \nstratification (Fischer et al., 1979) that may be enhanced by thermal stratification (Vroom et al., \n2017). The models and approaches developed to explore the influence of stratification and \nvertical turbulent mixing on estuarine algal blooms (e.g., Burchard et al., 1999; Koseff et al., \n1993; Lucas et al., 1998) could be applied to investigate physical-biological bloom controls \noperating in the vertical dimension of rivers (e.g., interactions between stratification, turbulent \nmixing, cell sedimentation, migration, and buoyancy).  \nAnother relevant theme is the lateral transport of algal biomass from productive side \nsource areas (shoals, in the case of drowned river estuaries) to the deeper main channel (Engel \net al., 2025; Lucas et al., 2016; Lucas et al., 2009a; May et al., 2003); such modeling tools \ndeveloped for studying the estuarine realm could be adapted for the study of algal biomass \nexchange between potentially productive riverine backwaters or side storage areas and the \nmainstem. Finally, much of the multi-dimensional hydrodynamic-ecological software that has \nbeen applied to characterize phytoplankton growth, loss, and two- or three-dimensional \ntransport in estuaries is general enough to capture relevant processes in rivers (as noted in \nTable 4) and other water body types. Examples within this review include EFDC (Environmental \nFluid Dynamics Code; Qin and Shen, 2019) and MIKE (Lubello et al., 2025). Other models such \nas Delft3D (Castro-Olivares et al., 2024), Delft3D-FM (Flexible Mesh; White et al., 2021), and \nSCHISM/CoSiNE (Wang et al., 2020) also have this capability.  \n \n3.7.2 Forecasting and Operationalization \nThere are fewer examples of forecasting HABs for inland waters compared to marine \nsystems, and even less in river than lake systems (U.S. National Office for Harmful Algal \nBlooms, 2024). There are exceedingly few sustained operational forecasting models for HABs in \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n36 \n \nlotic systems, though notable exceptions include the work of Park et al. (2021) in the \nChangnyung-Haman Reservoir, South Korea and Nietch et al. (2022) for the entire 1579 km of \nthe Ohio River (United States). Our literature review identified 21 articles that developed \nforecasting models. Not all of these were operational; many were used for research purposes in \nthe past (i.e., how well did forecasts perform historically). Notably, forecasting efforts were \nheavily concentrated in South Korea, which accounted for 14 of the 21 articles, whereas the \nsecond ranked country in forecasting applications, Australia, contributed only three articles. \nAmong all forecasting applications, predicting HABs seven days into the future was the most \ncommon lead time. The shortest lead time observed was one day, whereas the longest \nextended to 55 days Nietch et al. (2022). There is a growing consensus that regional modeling \nefforts, that can be adapted to specific systems, is likely a productive path forward for inland \nwater (U.S. National Office for Harmful Algal Blooms, 2024), and perhaps especially for rivers.  \nDespite these efforts, there is currently a lack of operationalization in forecasting models. \nFew studies have moved toward implementing early warning systems or actionable measures, \nsuch as information to support beach closures or drinking water treatment decisions. We \nsuspect that the limited application of forecasting is due to the challenges associated with \noperationalizing models for routine predictions. Unlike weather forecasting, there is currently no \nstandardized cyberinfrastructure for river HABs (or other environmental forecasting for that \nmatter) that researchers can use. Furthermore, transitioning models to operation relies on \ncontinued investments in research, monitoring, and cyberinfrastructure (U.S. National Office for \nHarmful Algal Blooms, 2024). As a result, researchers and organizations develop their own \nseparate forecasting systems. This is also reflected in the diversity of models and modeling \napproaches found in our review, which is also apparent for lake models (Rousso et al., 2020). \nThis fragmentation or disconnection often means that river HABs forecasts are produced \nmanually or using highly site-specific, independently developed methods, which hampers a \ncollective ability to efficiently generate important ecological predictions and deepen \nunderstanding of the environment.  \nNonetheless, there are promising avenues for addressing these issues, including \nexamples of national-scale monitoring networks and reporting systems, in addition to \ncommunity-developed tools. South Korea uses an extensive national-scale database of algal \ninformation and provides real-time HAB risk categories based on observed cyanobacteria cell \ndensity for multiple locations on all major South Korean rivers \n(http://water.nier.go.kr/web/algaeStat?pMENU_NO=195). This system is a notable example of \noperational river HAB nowcasting and provides quantitative data along with approachable \nindicators of risk for water supply and recreation. In terms of forecasting, operational \ncommunity-developed tools could facilitate increased forecasting of river HABs in the future. \nSynergistic partnerships between research groups and with funding agencies provide a means \nfor sharing resources (U.S. National Office for Harmful Algal Blooms, 2024). For instance, the \nEcological Forecasting Initiative has established shared cyberinfrastructure to support \nforecasting challenges (Thomas et al., 2023), including a river chlorophyll forecasting challenge \nco-hosted by the Ecological Forecasting Initiative and the U.S. Geological Survey \n(https://waterdata.usgs.gov/blog/habs-forecast-challenge-2024/). We believe that community-\ndriven cyberinfrastructure will promote the iterative improvement of river HABs forecasts, \nultimately supporting decision-making and effective water management.  \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n37 \n \n3.7.3 Towards Common Datasets \nMost articles in our literature review used unique datasets curated for a specific study, \neither based on location, application, or both. This variability poses challenges for collectively \nadvancing river HABs modeling as modeling endpoints, goals, and available input variables \ndiffer across datasets (Figures 4, 5, SM-1, and SM-2). Consequently, applying various types of \nmodels to the same dataset becomes difficult. When one model outperforms another in different \nanalyses, it is often unclear whether the observed differences are because of genuine variations \nin model skill, the specific modeling task, or the dataset used in the modeling process. Rousso \net al. (2010) noted that there were few studies that applied multiple modeling approaches to the \nsame lake. We identified a similar pattern in our review, with the exception of the Nakdong River \nin South Korea. As a focal point for many river HAB models, there is potential for additional \nsynthesis of these articles and modeling approaches. Nevertheless, standardizing datasets for \nmodel training, calibration, and evaluation could accelerate progress in environmental modeling, \nincluding for river HABs. Based on the success of South Korea’s Water Environment Information \nSystem (http://water.nier.go.kr/web) and the many river HAB modeling articles leveraging these \ndata, it would be prudent for a standardized dataset to include cyanobacteria cell counts for \nmultiple potential cyanotoxin-producing taxa, ideally at a weekly frequency, along with \nchlorophyll concentrations and potentially important predictor variables. Based on Figure 9, \nadditional data could include N and P concentrations (in various forms), measures of light \navailability, water temperature, and streamflow (or velocity). Supporting information capturing \nalgal processes such as predation, cell motility, resting states, among others, would also be \nbeneficial. \nIn machine learning, standardized datasets are referred to as “benchmark” datasets, and \nthere are increasingly more examples of these used for environmental applications. For \ninstance, streamflow prediction models have successfully used global benchmark datasets \n(Kratzert et al., 2023), allowing researchers to (1) focus on model improvement rather than \ncollecting and/or curating datasets, and (2) compare model performance to other models \napplied to the same data. Additionally, a freshwater forecasting challenge identified that \nprocess-based models outperformed data-driven models for forecasting water temperature, \nwhereas the opposite was true for forecasting dissolved oxygen (Olsson et al., 2025). Perhaps \nthis can be interpreted as process-based models excelling at deterministic, physics-based \nprocesses whereas data-driven models better capture biological process that are more \ninfluenced by stochastic processes. Recent efforts have been made to curate river chlorophyll \nand ancillary datasets at national scales (Fernandez et al., 2025; Spaulding et al., 2024), which \ncould substantially enhance riverine chlorophyll modeling in support of more comprehensive \nHAB studies. Given the global prevalence of river HABs highlighted in our review, we are \nhopeful that a comprehensive global benchmark dataset will soon be developed, similar to those \nalready available for streamflow (Kratzert et al., 2023). \n \n4. Conclusions \nOur review encompassed 162 articles spanning nearly five decades, modeling over 80 \nrivers globally, and identified several challenges and opportunities for river HAB modeling. Three \nsuch challenges are (1) the limited availability and integration of key and emerging data \nsources, (2) geographic and ecological biases in modeling efforts, and (3) difficulties in \ncomparing and synthesizing results due to inconsistent reporting of river characteristics (e.g., \ndrainage area, mean annual streamflow, etc.) and model evaluation metrics. We also note few \n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 1, 2025. ; https://doi.org/10.1101/2025.09.29.679270doi: bioRxiv preprint \n\n38 \n \nmodeling articles addressed algal toxins, connections to side channels and back waters, or \nbenthic algae. Despite these existing challenges and gaps, promising progress of river HAB \nmodeling is emerging through estuarine modeling efforts, South Korea’s nowcasting algal alert \nsystem, and community-developed tools spearheaded by groups like the Ecological Forecasting \nInitiative. \nOngoing changes in nutrient and climatic conditions underscore the benefits of a broader \nmodeling focus and enhanced, or at least sustained, monitoring. Although nutrients, elevated \nwater temperatures, and low-flow conditions are well-established drivers of HABs in rivers \n(Griffith and Gobler, 2020; Schmadel et al., 2024), changing environmental conditions have led \nto increased HAB occurrence in unexpected environments, including benthic habitats (Wood et \nal., 2020), coastal estuaries (Preece et al., 2017), and low nutrient systems (Reinl et al., 2021). \nThere is a need and an opportunity to model a wider range of systems with emerging algal \nissues, especially where causal factors are less well understood. This includes geographic \nareas where river HAB modeling is largely absent, such as the southern hemisphere and \nequatorial regions. Furthermore, despite many models being used to test scenarios, few studies \nemphasized management, provided strong recommendations regarding data collection, or \ndeveloped strong foundations for operationalized forecasts. Moving forward, the development of \nintegrated approaches, enhancement of model applicability across diverse environments, and \nstrengthening of the connection between research findings and practical management \nstrategies could improve outcomes in addressing HABs in riverine systems and beyond. \nAcknowledgements \nWe thank Maria (Masha) Marionkova for completing initial pulls from scientific databases and \ninitial work on the data collection form; we thank Gabriella Zuccolotto and Sarah Stackpoole for \nproviding critical reviews of a few articles. This work was completed as part of the U.S. \nGeological Survey (USGS) Proxies Project, an effort supported by the Water Mission Area \n(WMA) Water Quality Processes program to develop estimation methods for PFAS, harmful \nalgal blooms, and metals, at multiple spatial and temporal scales. Additional support for this \nwork was from the USGS Integrated Water Availability Assessments (IWAAs) Program, which \nexamines the spatial and temporal distribution of water quantity and quality in both surface and \ngroundwater, as related to human and ecosystem needs and as affected by human and natural \ninfluences. Any use of trade, firm, or product names is for descriptive purposes only and does \nnot imply endorsement by the U.S. Government. \n \nData Release  \nData gathered from literature and presented in this manuscript are available at: Gorney, R.M., \nZwart, J.A., Lucas, LV., and Murphy, J.C., 2025, Data from a systematic literature review of \nforecasting and predictive models for harmful algal blooms in flowing waters: U.S. Geological \nSurvey data release, https://doi.org/10.5066/P1JWCCXF. \nReferences \nAbbas, S.  2015.  Dynamical analysis of a model of harmful algae in flowing habitats \nwith variable rates. 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