Biogeochemical modelling at the river scale: plankton and periphyton dynamics

Emergent spatial patterns of competing benthic and pelagic algae in a river network: A parsimonious basin-scale modeling analysis

Algae, as primary producers in riverine ecosystems, are found in two distinct habitats: benthic and pelagic algae typically prevalent in shallow/small and deep/large streams, respectively. Over an entire river continuum, spatiotemporal patterns of the two algal communities reflect specificity in habitat preference determined by geomorphic structure, hydroclimatic controls, and spatiotemporal heterogeneity in nutrient loads from point- and diffuse-sources. By representing these complex interactions between geomorphic, hydrologic, geochemical, and ecological processes, we present here a new river-network-scale dynamic model (CⁿANDY) for pelagic (A) and benthic (B) algae competing for energy and one limiting nutrient (phosphorus, P). We used the urbanized Weser River Basin in Germany (7th-order; ~8.4 million population; ~46 K km²) as a case study and analyzed simulations for equilibrium mass and concentrations under steady median river discharge. We also examined P, A, and B spatial patterns in four sub-basins. We found an emerging pattern characterized by scaling of P and A concentrations over stream-order ω, whereas B concentration was described by three distinct phases. Furthermore, an abrupt algal regime shift occurred in intermediate streams from B dominance in ω≤3 to exclusive A presence in ω≥6. Modeled and long-term basin-scale monitored dissolved P concentrations matched well for ω>4, and with overlapping ranges in ω<3. Power-spectral analyses for the equilibrium P, A, and B mass distributions along hydrological flow paths showed stronger clustering compared to geomorphological attributes, and longer spatial autocorrelation distance for A compared to B. We discuss the implications of our findings for advancing hydro-ecological concepts, guiding monitoring, informing management of water quality, restoring aquatic habitat, and extending CⁿANDY model to other river basins.

Data assimilation in surface water quality modeling: A review

Data assimilation (DA) techniques are powerful means of dynamic natural system modeling that allow for the use of data as soon as it appears to improve model predictions and reduce prediction uncertainty by correcting state variables, model parameters, and boundary and initial conditions. The objectives of this review are to explore existing approaches and advances in DA applications for surface water quality modeling and to identify future research prospects. We first reviewed the DA methods used in water quality modeling as reported in literature. We then addressed observations and suggestions regarding various factors of DA performance, such as the mismatch between both lateral and vertical spatial detail of measurements and modeling, subgrid heterogeneity, presence of temporally stable spatial patterns in water quality parameters and related biases, evaluation of uncertainty in data and modeling results, mismatch between scales and schedules of data from multiple sources, selection of parameters to be updated along with state variables, update frequency and forecast skill. The review concludes with the outlook section that outlines current challenges and opportunities related to growing role of novel data sources, scale mismatch between model discretization and observation, structural uncertainty of models and conversion of measured to simulated vales, experimentation with DA prior to applications, using DA performance or model selection, the role of sensitivity analysis, and the expanding use of DA in water quality management.

Ecological Functioning of the Seine River: From Long-Term Modelling Approaches to High-Frequency Data Analysis

At the start of the PIREN-Seine program, organic pollution by the effluent of the Parisian conurbation was responsible for episodic anoxia in the lower Seine River, while nutrients from both point and diffuse sources are used to cause eutrophication, a nuisance for drinking water production from surface water and biodiversity. The implementation of the EU Water Framework Directive led to a drastic decrease of organic carbon, phosphorus and ammonium concentrations in surface waters starting in the early 2000s and to a reduction of the frequency and the amplitude of phytoplankton blooms. However, nitrate contamination from fertiliser-intensive agriculture continued to increase or at best levelled off, threatening groundwater resources and causing unbalanced nutrient ratios at the coastal zone where eutrophication still results in harmful algal blooms. High-frequency O2 data combined with models, which have been developed for 30 years, can help discriminate the contribution of auto- vs. heterotrophic metabolism in the CO2 supersaturation observed in the Seine River. Despite the impressive improvement in water quality of the Seine River, episodic crises such as summer low-flow conditions still threaten the good ecological status of both river and coastal waters. Modelling scenarios, including further wastewater treatments and structural changes in agriculture and future changes in hydrology under climate changes, provide the basis for a future vision of the ecological functioning of the Seine River network.

Trajectories of the Seine River Basin

The Seine River basin in France (76,238 km2, 17 million (M) people) has been continuously studied since 1989 by the PIREN-Seine, a multidisciplinary programme of about 100 scientists from 20 research units (hydrologists, environmental chemists, ecologists, biogeochemists, geographers, environmental historians). Initially PIREN-Seine was established to fill the knowledge gap on the river functioning, particularly downstream of the Paris conurbation (12 M people), where the pressure and impacts were at their highest in the 1980s (e.g. chronic summer hypoxia). One aim was to provide tools, such as models, to manage water resources and improve the state of the river. PIREN-Seine gradually developed into a general understanding and whole-basin modelling, from headwater streams to the estuary, of the complex interactions between the hydrosystem (surface water and aquifers), the ecosystem (phytoplankton, bacteria, fish communities), the agronomic system (crops and soils), the river users (drinking water, navigation), and the urban and industrial development (e.g. waste water treatment plants). Spatio-temporal scales of these interactions and the related state of the environment vary from the very fine (hour-meter) to the coarser scale (annual – several dozen km). It was possible to determine the trajectories (drivers-pressures – state-responses) for many issues, over the longue durée time windows (50–200 years), in relation to the specific economic and demographic evolution of the Seine basin, the environmental awareness, and the national and then European regulations. Time trajectories of the major environmental issues, from the original organic and microbial pollutants in the past to the present emerging contaminants, are addressed. Future trajectories are simulated by our interconnected modelling approaches, based on scenarios (e.g. of the agro-food system, climate change, demography, etc.) constructed by scientists and engineers of major basin institutions that have been supporting the programme in the long term. We found many cumulated and/or permanent hereditary effects on the physical, chemical, and ecological characteristics of the basin that may constrain its evolution. PIREN-Seine was launched and has been evaluated since its inception, by the National Centre for Scientific Research (CNRS), today within its national Zones Ateliers (ZA) instrument, part of the international Long-Term Socio-Economic and Ecosystem Research (LTSER) network.

Oxygen data assimilation for estimating micro-organism communities' parameters in river systems

The coupling of high frequency data of water quality with physically based models of river systems is of great interest for the management of urban socio-ecosystems. One approach to exploit high frequency data is data assimilation which has received an increasing attention in the field of hydrology, but not for water quality modeling so far. We present here a first implementation of a particle filtering algorithm into a community-centered hydro-biogeochemical model to assimilate high frequency dissolved oxygen data and to estimate metabolism parameters in the Seine River system. The procedure is designed based on the results of a former sensitivity analysis of the model (Wang et al., 2018) that allows for the identification of the twelve most sensible parameters all over the year. Those parameters are both physical and related to micro-organisms (reaeration coefficient, photosynthetic parameters, growth rates, respiration rates and optimal temperature). The performances of the approach are assessed on a synthetic case study that mimics 66 km of the Seine River. Virtual dissolved oxygen data are generated using time varying parameters. This paper aims at retrieving the predefined parameters by assimilating those data. The simulated dissolved oxygen concentrations match the reference concentrations. The identification of the parameters depends on the hydrological and trophic contexts and more surprisingly on the thermal state of the river. The physical, bacterial and phytoplanktonic parameters can be retrieved properly, leading to the differentiation of two successive algal blooms by comparing the estimated posterior distribution of the optimal temperature for phytoplankton growth. Finally, photosynthetic parameters' distributions following circadian cycles during algal blooms are discussed.

Time-dependent global sensitivity analysis of the C-RIVE biogeochemical model in contrasted hydrological and trophic contexts

Dissolved oxygen within water column is a key variable to characterize the water quality. Water quality modeling has been extensively developed for decades. However, complex biogeochemical cycles are described using a high number of parameters. Hence, parameters' uncertainty constitutes a major problem in the application of these models. Sensitivity analysis allows the identification of the most influential parameters in a model and a better understanding of the governing processes. This paper presents a time-dependent sensitivity analysis for dissolved oxygen using Morris and Sobol methods combined with a functional principal components analysis for dimension reduction. The aim of this study is to identify the most important parameters of C-RIVE model in different trophic contexts and to understand the biogeochemical functioning of river systems. The results indicate that the maintenance respiration of phytoplankton and the photosynthetic parameters (i.e. photosynthetic capacity, the maximal photosynthesis rate and light extinction coefficients) are the most influential parameters during algal blooms. When the river system becomes heterotrophic, the bacterial activities (moderate and high temperature) and the reaeration coefficients (low temperature) affect the most the dissolved oxygen concentration in the water column. An anthropogenic effect (ship navigation) on variation of dissolved oxygen concentration has been identified and the role of this anthropogenic effect evolves with hydrological and trophic conditions.

Estimation of the water quality of a large urbanized river as defined by the European WFD: what is the optimal sampling frequency?

Assessment of the quality of freshwater bodies is essential to determine the impact of human activities on water resources. The water quality status is estimated by comparing indicators with standard thresholds. Indicators are usually statistical criteria that are calculated on discrete measurements of water quality variables. If the time step of the measured time series is not sufficient to fully capture the variable's variability, the deduced indicator may not reflect the system's functioning. The goal of the present work is to assess, through a hydro-biogeochemical modeling approach, the optimal sampling frequency for an accurate estimation of 6 water quality indicators defined by the European Water Framework Directive (WFD) in a large human-impacted river, which receives large urban effluents (the Seine River across the Paris urban area). The optimal frequency depends on the sampling location and on the monitored variable. For fast varying compounds that originate from urban effluents, such as PO[Formula: see text], NH[Formula: see text] and NO[Formula: see text], a sampling time step of one week or less is necessary. To be able to reflect the highly transient character of bloom events, chl a concentrations also require a short monitoring time step. On the contrary, for variables that exert high seasonal variability, as NO[Formula: see text] and O ₂, monthly sampling can be sufficient for an accurate estimation of WFD indicators in locations far enough from major effluents. Integrative water quality variables, such as O ₂, can be highly sensitive to hydrological conditions. It would therefore be relevant to assess the quality of water bodies at a seasonal scale rather than at annual or pluri-annual scales. This study points out the possibility to develop smarter monitoring systems by coupling both time adaptative automated monitoring networks and modeling tools used as spatio-temporal interpolators.

Longitudinal patterns and response lengths of algae in riverine ecosystems: A model analysis emphasising benthic-pelagic interactions

In riverine ecosystems primary production is principally possible in two habitats: in the benthic layer by sessile algae and in the surface water by planktonic algae being transported downstream. The relevance of these two habitats generally changes along the rivers' continuum. However, analyses of the interaction of algae in these two habitats and their controlling factors in riverine ecosystems are, so far, very rare. We use a simplified advection-diffusion model system combined with ecological process kinetics to analyse the interaction of benthic and planktonic algae and nutrients along idealised streams and rivers at regional to large scales. Because many of the underlying processes affecting algal dynamics are influenced by depth, we focus particularly on the impact of river depth on this interaction. At constant environmental conditions all state variables approach stable spatial equilibria along the river, independent of the boundary conditions at the upstream end. Because our model is very robust against changes of turbulent diffusion and stream velocity, these spatial equilibria can be analysed by a simplified ordinary differential equation (ode) version of our model. This model variant reveals that at shallower river depths, phytoplankton can exist only when it is subsidised by detaching benthic algae, and in turn, at deeper river depths, benthic algae can exist only in low biomasses which are subsidised by sinking planktonic algae. We generalise the spatial dynamics of the model system using different conditions at the upstream end of the model, which mimic various natural or anthropogenic factors (pristine source, dam, inflow of a waste water treatment plant, and dilution from e.g. a tributary) and analyse how these scenarios influence different aspects of the longitudinal spatial dynamics of the full spatial model: the relation of spatial equilibrium to spatial maximum, the distance to the spatial maximum, and the response length. Generally, our results imply that shallow systems recover within significantly shorter distances from spatially distinct disturbances when compared to deep systems, independent of the type of disturbance.

Predicting Species-Resolved Macronutrient Acquisition during Succession in a Model Phototrophic Biofilm Using an Integrated 'Omics Approach

The principles governing acquisition and interspecies exchange of nutrients in microbial communities and how those exchanges impact community productivity are poorly understood. Here, we examine energy and macronutrient acquisition in unicyanobacterial consortia for which species-resolved genome information exists for all members, allowing us to use multi-omic approaches to predict species' abilities to acquire resources and examine expression of resource-acquisition genes during succession. Metabolic reconstruction indicated that a majority of heterotrophic community members lacked the genes required to directly acquire the inorganic nutrients provided in culture medium, suggesting high metabolic interdependency. The sole primary producer in consortium UCC-O, cyanobacterium Phormidium sp. OSCR, displayed declining expression of energy harvest, carbon fixation, and nitrate and sulfate reduction proteins but sharply increasing phosphate transporter expression over 28 days. Most heterotrophic members likewise exhibited signs of phosphorus starvation during succession. Though similar in their responses to phosphorus limitation, heterotrophs displayed species-specific expression of nitrogen acquisition genes. These results suggest niche partitioning around nitrogen sources may structure the community when organisms directly compete for limited phosphate. Such niche complementarity around nitrogen sources may increase community diversity and productivity in phosphate-limited phototrophic communities.

Modelling the fate of nitrite in an urbanized river using experimentally obtained nitrifier growth parameters

Maintaining low nitrite concentrations in aquatic systems is a major issue for stakeholders due to nitrite's high toxicity for living species. This study reports on a cost-effective and realistic approach to study nitrite dynamics and improve its modelling in human-impacted river systems. The implementation of different nitrifying biomasses to model riverine communities and waste water treatment plant (WWTP)-related communities enabled us to assess the impact of a major WWTP effluent on in-river nitrification dynamics. The optimal kinetic parameters and biomasses of the different nitrifying communities were determined and validated by coupling laboratory experiments and modelling. This approach was carried out in the Seine River, as an example of a large human-impacted river with high nitrite concentrations. The simulation of nitrite fate was performed at a high spatial and temporal resolution (Δt = 10 min, dx¯ = 500 m) including water and sediment layers along a 220 km stretch of the Seine River for a 6-year period (2007-2012). The model outputs were in good agreement with the peak of nitrite downstream the WWTP as well as its slow decrease towards the estuary. Nitrite persistence between the WWTP and the estuary was mostly explained by similar production and consumption rates of nitrite in both water and sediment layers. The sediment layer constituted a significant source of nitrite, especially during high river discharges (0.1-0.4 mgN h(-1) m(-2)). This points out how essential it is to represent the benthic layer in river water quality models, since it can constitute a source of nitrite to the water-column. As a consequence of anthropogenic emissions and in-river processes, nitrite fluxes to the estuary were significant and varied from 4.1 to 5.5 TN d(-1) in low and high water discharge conditions, respectively, over the 2007-2012 period. This study provides a methodology that can be applied to any anthropized river to realistically parametrize autochthonous and WWTP-related nitrifier communities and simulate nitrite dynamics. Based on simulation analysis, it is shown that high spatio-temporal resolution hydro-ecological models are efficient to 1) estimate water quality criteria and 2) forecast the effect of future management strategies. Process-based simulations constitute essential tools to complete our understanding of nutrient cycling, and to decrease monitoring costs in the context of water quality and eutrophication management in river ecosystems.

Pluri-annual sediment budget in a navigated river system: the Seine River (France)

This study aims at quantifying pluri-annual Total Suspended Matter (TSM) budgets, and notably the share of river navigation in total re-suspension at a long-term scale, in the Seine River along a 225 km stretch including the Paris area. Erosion is calculated based on the transport capacity concept with an additional term for the energy dissipated by river navigation. Erosion processes are fitted for the 2007-2011 period based on i) a hydrological typology of sedimentary processes and ii) a simultaneous calibration and retrospective validation procedure. The correlation between observed and simulated TSM concentrations is higher than 0.91 at all monitoring stations. A variographic analysis points out the possible sources of discrepancies between the variabilities of observed and simulated TSM concentrations at three time scales: sub-weekly, monthly and seasonally. Most of the error on the variability of simulated concentrations concerns sub-weekly variations and may be caused by boundary condition estimates rather than modeling of in-river processes. Once fitted, the model permits to quantify that only a small fraction of the TSM flux sediments onto the river bed (<0.3‰). The river navigation contributes significantly to TSM re-suspension in average (about 20%) and during low flow periods (over 50%). Given the significant impact that sedimentary processes can have on the water quality of rivers, these results highlight the importance of taking into account river navigation as a source of re-suspension, especially during low flow periods when biogeochemical processes are the most intense.

Modelling the fate of nonylphenolic compounds in the Seine River--part 2: assessing the impact of global change on daily concentrations

This study aims at modelling the daily concentrations of nonylphenolic compounds such as 4-nonylphenol (4-NP), nonylphenol monoethoxylate (NP1EO) and nonylphenoxy acetic acid (NP1EC) within the Seine River downstream of Paris City for over a year, firstly in the present state (year 2010) and for years 2050 and 2100 in order to assess the consequences of global change on the fate of nonylphenolic compounds in the Seine river. Concentrations were first simulated for the year 2010 and compared to monthly measured values downstream of Paris. To achieve this goal, the hydrodynamic and biogeochemical model, ProSe, was updated to simulate the fate of 4-NP, NP1EO and NP1EC. The Seine upstream and Oise River (tributaries of the Seine River) concentrations are estimated according to concentrations-flow relationships. For Seine Aval wastewater treatment plant (SA-WWTP), the concentrations are considered constant and the median values of 11 campaigns are used. The biodegradation kinetics of 4-NP, NP1EO and NP1EC in the Seine River were deduced from the results of the companion paper. The Nash-Sutcliffe coefficient indicates a good efficiency to simulate the concentrations of 4-NP, NP1EC and NP1EO over an entire year. Eight scenarios were built to forecast the impacts of global warming (flow decrease), population growth (SA-WWTP flow increase) and optimisation of wastewater treatment (improvement of the quality of effluents) on annual concentrations of 4-NP, NP1EO and NP1EC at Meulan by 2050 and 2100. As a result, global warming and population growth may increase the concentrations of 4-NP, NP1EC and NP1EO, especially during low-flow conditions, while the optimisation of wastewater treatment is an efficient solution to balance the global change by reducing WWTP outflows.

Modeling nitrate fluxes at the catchment scale using the integrated tool CAWAQS

Nitrates fluxes in the Grand Morin basin (1200 km(2)), that is subjected to intense agricultural pressure, are considered using in-stream observations (around 250 sampling days over 5 years) and physically based simulations using the CAWAQS model (CAtchment WAter Quality Simulator). In-stream nitrate concentration averaged 6 mg N L(-1), increasing by approximately 0.2 mg N L(-1) yr(-1) around this value (period 1991-1996). Our results show that, over the period of 1991-1996, the differences between in-stream observed nitrate concentrations and simulated nitrate concentrations result from nitrate losses at the basin scale. These losses are due to denitrification by transfer through wetlands, alluvial plains, the hyporheic zone, and by benthic processes in rivers. A mean annual mass balance at the basin scale indicates that 40% of the infiltration flux (3360 kg N km(-2) yr(-1)) is removed from the system via the river network, 40% is stored in aquifers and 20% is lost by denitrification (period 1991-1996).

Primary production in headwater streams of the Seine basin: the Grand Morin river case study

Periphytic biomass has an important influence on the water quality of many shallow streams. The purpose of this paper is to synthesize the knowledge obtained on periphyton during the PIREN Seine research program. Periphyton was sampled using chl a measurements by acetone extraction and oxygen measurements with microelectrodes. The experiments reveal the presence of an important fixed biomass ranging between 123 and 850 mgchl a m(-2) and the mean gross production (photosynthesis) is shown to range between 180 and 315 mgC m(-2) h(-1). An independent approach was performed using the ProSe model, which simulates transport and biogeochemical processes in 22 km of the Grand Morin stream. A strong agreement between in situ measurements and the model results was obtained. The gross production obtained using ProSe is 220 mgC m(-2) h(-1) for the periphyton, which matches the experimental data. Although the net photosynthetic activity of the phytoplankton (0.84 gC gC(-1) d(-1)) is higher than the periphytic one (0.33 gC gC(-1) d(-1)), the absolute periphytic activity is greater since the mean biomass (3.4 gC m(-)(2)) is 10 times higher than the phytoplanktonic one (0.3 gC m(-2)), due to the short residence time of the water body (1.5d).

Modelling the impacts of Combined Sewer Overflows on the river Seine water quality

To achieve the objectives of the European Water Framework Directive (EWFD), the Seine basin Water Authority has constructed a number of prospective scenarios forecasting the impact of planned investments in water quality. Paris and its suburbs were given special attention because of their impact on the river Seine. Paris sewer system and overflow control is of major concern in future management plans. The composition and fate of the urban effluents have been characterized through numerous in situ samplings, laboratory experiments and modelling studies. The PROSE model was especially designed to simulate the impact on the river of both permanent dry-weather effluents and of highly transient Combined Sewer Overflow (CSO). It was also used to represent the impact of Paris at large spatial and temporal scales. In addition to immediate effects on oxygen levels, heavy particulate organic matter loads that settle downstream of the outlets contribute to permanent oxygen consumption. Until the late 90s, the 50 km long reach of the Seine inside Paris was permanently affected by high oxygen consumption accounting for 112% of the flux upstream of the city. 20% of this demand resulted from CSO. However, the oxygenation of the system is strong due to high phytoplankton activity. As expected, the model results predict a reduction of both permanent dry-weather effluents and CSOs in the future that will greatly improve the oxygen levels (concentrations higher than 7.3 mgO(2) L(-1), 90% of the time instead of 4.0 mgO(2) L(-1) in the late 90s). The main conclusion is that, given the spatial and temporal extent of the impact of many CSOs, water quality models should take into account the CSOs in order to be reliable.

Production vs. respiration in river systems: an indicator of an "ecological status"

The Riverstrahler model of ecological functioning of large drainage networks validated on the Seine river system has been used for calculating the seasonal variations of Production and Respiration at various spatial scales (e.g. according to river orders). Based on the measurements of biological processes, the P/R ratio has led to an evaluation of the "ecological functioning", beyond the notion of "good ecological status". Furthermore, the effects, on the P/R ratio, of the geomorphological and climate factors characterizing the Hydro-Eco-Regions (HER) of the Seine watershed have been quantitatively explored with the model. Whereas one finds a typical upstream-downstream pattern of the P/R ratio variations under the traditional rural conditions that prevailed in the Seine basin until the end of the 18th century, this pattern is strongly affected by the changes in urban populations and the implementation of wastewater collection and treatment, more than by the specificity of the physical factors characterizing the different HER. We have also found that autotrophy (a P/R ratio >1) might leads to eutrophication symptoms when P exceeds 1-2 mg C m(-2) d(-1) and that heterotrophy of the system (P/R ratio< 1) would reveal organic pollution when R exceeds 1-2 mg C m(-2) d(-1), stocks and fluxes of organic matter being expressed in carbon unit. Consequently, the P/R ratio appears as a good indicator of the perturbations caused by human activities in the watershed. The Riverstrahler model is able to quantify this effect.

New tools for modelling water quality of hydrosystems: an application in the Seine River basin in the frame of the Water Framework Directive

The implementation of the European Water Framework Directive requires new tools for predicting the effect of expected measures taken in the watershed on water quality at the scale of large regional river systems. In the Seine basin, four models, developed in a research context, have been chained to each other to simulate water quality and biogeochemical functioning of the hydrosystem from headwater streams to the coastal marine area. All four models are based on a similar deterministic approach and share a common description of the biogeochemical processes, allowing them to exchange information. Each model differently represents the hydro-sedimentological processes, and uses different time and space resolution, in order to tackle with the specific problematic of each sub-system. This cascade of models has been used for testing a prospective scenario of water resources management at the horizon of 2015, established by Water Authorities of the Seine-Normandy district. The simulation predicts a general improvement of water quality concerning those variables linked to point sources of pollution (ammonium, oxygen, phosphate), even if, locally, this improvement can be insufficient for meeting the expected quality standards. The predicted improvement of the quality of the Seine River downstream from Paris and its estuary is large. However, the predicted very significant drop of phosphate contamination, although beneficial for limiting the problems of coastal marine eutrophication, does not lead to a significant control of phytoplankton development in the rivers upstream from Paris. The simulation also predicts a general increase in nitrate contamination mainly linked to diffuse sources from agricultural areas.

Spatial patterns and coexistence mechanisms in systems with unidirectional flow

River ecosystems are the prime example of environments where unidirectional flow influences the dispersal of individuals. Spatial patterns of community composition and species replacement emerge from complex interplays of hydrological, geochemical, biological, and ecological factors. Local processes affecting algal dynamics are well understood, but a mechanistic basis for large scale emerging patterns is lacking. To understand how these patterns could emerge in rivers, we analyze a reaction-advection-diffusion model for two competitors in heterogeneous environments. The model supports waves that invade upstream up to a well-defined "upstream invasion limit". We discuss how these waves are produced and present their key properties. We suggest that patterns of species replacement and coexistence along spatial axes reflect stalled waves, produced from diffusion, advection, and species interactions. Emergent spatial scales are plausible given parameter estimates for periphyton. Our results apply to other systems with unidirectional flow such as prevailing winds or climate-change scenarios.