The Effect of Sediment Supply on Pool‐Riffle Morphology

Downstream width variations can generate pool‐riffle morphology under experimental conditions, in numerical simulations and natural river channels. The present understanding of how pool‐riffle morphology varies with sediment supply and caliber, however, is insufficient due to the limited range of sediment supply rates explored in previous experiments and the little attention paid to sand supply and sediment size distribution in the laboratory and in the field. We present a model of river morphodynamics that can account for the spatial variability of channel width, and we validate the model with experimental data. Model validation shows how this one‐dimensional model can capture pool‐riffle formation, growth, and equilibration with errors that are comparable with those of other 1D models of river morphodynamics. We then apply the validated model to study the effects of sediment supply rate and caliber on pool‐riffle morphology. Model results show that pool‐riffle morphology is resilient to the range of tested sediment supply (i.e., five‐fold the sediment amount, 41‐fold the sand amount and coarsening the gravel supply). Bed and water surface slopes are sensitive to all types of change of sediment supply, whereas the sensitivity of bed surface sediment grain size varies with the type of change. These findings support prior research emphasizing the role of downstream width variations for the development/maintenance of pool‐riffle morphology and can help in the restoration and recovery of pool‐riffle gravel‐bed rivers.

and Milan (2004) suggested that the stability of pool-riffle morphology is achieved when the duration of energy reversal is sufficiently long so that pools can transport the same amount of sediment as the associated upstream riffle (excess energy).
One-dimensional, or cross-sectionally averaged, data may not explain the main physical processes for pool-riffle sequences generated by multidimensional flow structures.From this perspective, the flow convergence routing hypothesis was proposed (Clifford, 1993b;Lisle & Hilton, 1992;MacWilliams et al., 2006;Montgomery & Buffington, 1997;Thompson et al., 1998Thompson et al., , 1999)).Due to the existence of an upstream flow constriction, a narrow zone of high velocity can be identified in the pool and this zone can act as primary transport pathway for sediment routing through pools (Sawyer et al., 2010).A caveat of this theory is that it requires the presence of a bar-induced upstream flow constriction, or more generally, a difference of channel width from upstream riffle to downstream pool.According to the sediment routing hypothesis, which was proposed to explain the maintenance of pool-riffle sequences in sinuous rivers, sediment is mainly routed onto bars rather than through the adjacent pool (Milan, 2013;Whiting & Dietrich, 1991).Some researchers also provide explanations for pool-riffle maintenance from the perspective of bed sediment sorting (Clifford, 1993a;de Almeida & Rodríguez, 2011;Sear, 1996).In the descriptive model of Sear (1996), the surface structure of the riffle is compact, while the pool exhibits a looser structure, leading to a higher critical shear stress requirement for mobilizing the sediment in the riffle compared to the critical shear stress needed to mobilize a gravel of equivalent diameter in the pool.This difference in structure enhances the stability of the riffle (Clifford, 1993a).In addition, pools are usually characterized by a higher availability of fine sediment which is more easily transported, and an increased mobility of coarser fractions due to a higher percentage of sand in the sediment mixture (de Almeida & Rodríguez, 2011;Wilcock & Crowe, 2003).All these factors are conducive to the development of sediment transport reversal at discharges smaller than those responsible for velocity or shear stress reversal.According to Sear (1996), however, the situation is more complicated because sediment transport through pool-riffle pairs is controlled by a combination of factors including flow and bed surface sediment-related properties, with process-based interactions playing a significant role in transport dynamics.De Almeida and Rodríguez (2011) show that riffles located downstream of a similar feature serve as an internal boundary to regulate height difference of contiguous riffle crests, preventing the formation of a flattened bed (downstream riffle control).Recently, channel width variation has also been proven to have the capability to generate and sustain pool-riffle sequences (Chartrand et al., 2018).
Although pool-riffle sequences can remain relatively fixed in location, changes in flow and sediment supply can also affect their morphology.For example, for a 117 m pool-riffle segment of East Creek, CA, the larger the flow magnitude, the more significant the development of pools (Figures 4 and 13 in Hassan et al. (2021)).Sediment supply is also an important factor in determining the morphology of gravel-bed rivers (e.g., Parker, 1991aParker, , 1991b)).The supply can undergo changes primarily due to total (sand and gravel) amount, sand supply rate and content, and gravel sizes and content.These changes in sediment supply can result from various factors, including natural processes such as landslides and vegetation degradation, as well as human activities such as dam construction or removal, gravel mining, deforestation, and land use changes (Benda et al., 2003;Grant, 2001;Pizzuto, 2002).Recent laboratory experiments investigating the impact of sediment supply on pool-riffle sequences reveal that these features persist when the sediment supply rate is doubled (Morgan & Nelson, 2021;Nelson et al., 2015).Sand supply is reported to reduce form roughness through degrading riffles and filling pools (Jackson & Beschta, 1984) since it can increase the mobility of gravel (An et al., 2019;Cui et al., 2003;Curran & Wilcock, 2005;Johnson et al., 2015;Wilcock et al., 2001).The caliber of sediment supply has also been regarded as one of the primary factors influencing pool-riffle morphology with finer gravel lowering entrainment threshold and filling pools (Buffington et al., 2002).
A comprehensive understanding of pool-riffle morphology response to changes in sediment supply rate and caliber is needed to maintain a healthy ecosystem and biodiversity in streams (Lisle & Hilton, 1999;Rhoads et al., 2008).For example, heavy deposition of fine sediment and pool filling during a flood in 1964 caused severe habitat deterioration in gravel-bed rivers in Northwestern California.As a result, the population of anadromous salmonids declined by at least one-half within three decades (Lisle, 1982).Studies have also indicated that in some cases riverbeds downstream of dams undergo coarsening, and no longer provide suitable habitat for salmon spawning and incubation (e.g., Buffington & Montgomery, 1999;Kondolf, 1997).To rejuvenate spawning habitat and restore geomorphic activity, river managers have implemented passive gravel augmentation by adding gravel to the channel downstream of a dam (Harvey et al., 2005;Pasternack et al., 2004).
The role of sediment supply (amount and texture) on the morphology and evolution of pool-riffle sequences has not been fully explored and thus there is a need for more research that can be readily applied to river management and habitat restoration.We hypothesize that in response to changes in sediment supply and caliber, rivers tend toward a new state, which is characterized by different pool-riffle geometries.In this study, following Parker (2004) and de Almeida and Rodríguez (2012), we use a numerical model of mixed-sediment river morphodynamics to examine how pool-riffle sequences adjust in response to upstream variations of sediment supply in terms of increased amount (e.g., driven by land use change or vegetation degradation), increased sand supply (e.g., driven by landslide, hillslope erosion or sand yield after mining), and varying sediment caliber (e.g., gravel mining).The use of numerical simulations has the following advantages: (a) it allows us to explore sediment supply which is difficult to do in the lab (because of the large amounts of sediment and time) and difficult to observe in the field; (b) it provides detailed information on the spatial variability on flow and bed characteristics; and (c) it saves time, money, and human effort significantly.

Previous Experiments Relevant for This Study
The prototype for the simulations in this paper is the pool-riffle experiment conducted at the BioGeoMorphic Experimental Laboratory at the University of British Columbia, Vancouver, Canada (Chartrand, 2017;Chartrand et al., 2018Chartrand et al., , 2023;;Hassan et al., 2021).This experiment was inspired by a 75-m-long reach of East Creek, a small gravel-bedded mountain stream in the University of British Columbia Malcolm Knapp Research Forest.The geometric scale ratio for the experimental channel was 5 (the field: model length ratio).This experiment was originally designed to explore pool-riffle morphodynamic response to downstream width variation and flow discharge (Chartrand et al., 2018).In the experiment, water entered the flume from an upstream tank through a series of stacked 0.05 m plastic pipes collectively called a "flow normalizer" and was recirculated using a pump.Sediment was introduced to the flume via a speed-controlled conveyor, which dumped particles into a mixing chamber called a "randomizer."The flow normalizer and sediment supply randomizer together provided spatially and temporally uniform inlet boundary conditions.
Water and sediment exited the flume through a 1 m long channel section with uniform width of 0.47 m.This outlet configuration was chosen to control the water and sediment boundary conditions.Sediment passed through a particle imaging light box, which provided detailed measurements of 1 Hz time-averaged sediment flux and fractions.The spatial width variation was built with rough-faced veneer-grade D plywood which has a surface roughness that varies from 1 to 4 mm.The flume side wall was high enough to contain all experimental flows.The mobile bed reach started 0.5 m downstream of the flow normalizer and ended 16 m downstream of the normalizer.A schematic representation of the 16 m long flume is presented in Figure 1, where the streamwise distance from the flow normalizer identifies the channel stations.The initial bed surface and sediment supply grain size distributions and their cumulative fractions are also included in Figure 1.
The experiment began with a relatively flat bed of uniform slope (0.015) and consisted of an initial phase (0-43.83hr) and a repeat phase (43.83-79.83 hr).Each phase had three Stages.In the initial phase, Stage 1 was performed with a constant flow rate of 42 L/s and sediment feed rate equal to 0.5 kg/min (0-35.83hr); Stage 2 had a constant flow of 60 L/s and sediment feed rate of 0.8 kg/min (35.83-39.83hr); and Stage 3 was run with a constant flow of 80 L/s and sediment feed rate equal to 1.0 kg/min (39.83-43.83hr).
In each Stage, flow and sediment supply were kept constant until topographic steady state was reached, that is, the rate of change of the spatially averaged bed topography fluctuated about a mean condition, the time-averaged total sediment flux exiting the flume approximated the sediment supply rate, and the time-averaged fractional flux also approximated the fractional supply.Data collected during the experiments were (see Table 1 in Chartrand et al. (2018) for details): (a) time-averaged sediment flux and its grain size distributions at the outlet; (b) water surface elevation and bed elevation at the flume centerline; (c) grain size distributions at the sub-sampling locations (Figure 1); (d) and flume-wide bed topography.

Model Description
A one-dimensional hydro-morphodynamic model that accounts for the non-uniformity of a sand-gravel mixture was implemented and used to study how pool-riffle sequences vary with sediment supply rate and grain size distribution.To adequately account for the presence of a rapidly varying flow with Froude number close to or above critical, the St. Venant equations were implemented for hydraulic calculations (Chaudhry, 2008).Since gravel-bed pool-riffle sequences are often characterized by relatively wide grain size distributions, the grain size specific and total (i.e., summed over all the grain sizes) conservation of sediment mass (Exner equation) was imposed.The grain size specific Exner equation was derived with the aid of the active layer approximation (Parker, 1991b).In active layer formulations, the bed is divided into an upper, mixed active layer whose particles can be exchanged freely with the bedload transport, and a lower substrate with its own vertical stratigraphy.Active layer sediment is exchanged with the substrate as the bed aggrades and degrades.The method of Viparelli et al. (2010) to store and access the grain size stratigraphy was implemented to guarantee mass conservation.
Other simplifications were introduced for a first-order analysis of the problem.The cross section of the flume was approximated as rectangular.This was acceptable since the channel bed elevation in a cross section showed little difference in the flume experiment (see Figure 6 in Chartrand et al. (2018)).The Manning-Strickler relation (Parker, 1990) was adopted for bed Manning roughness n b to account for the spatial and temporal variations in roughness height, which depends on the coarse grain size of the bed surface sediment.The model explicitly accounted for the difference in roughness between the wooden sidewalls and the sediment-covered bed to properly estimate the shear stress acting on the bed (Vanoni & Brooks, 1957) since the flume width was not large enough compared to the water depth.An equivalent grain roughness height k s = 2.5 mm (i.e., the average surface roughness of wooden sidewall) was imposed for the wall and wall Manning roughness n w = 0.0145.Like Qian et al. (2015), the channel Manning roughness n was determined as [(bn b 1.5 + 2hn w 1.5 )/(b + 2h)] 2/3 where b is the channel width and h the water depth.The flume bedload transport rate was calculated by the relation of Wilcock and Crowe (2003) as was done by de Almeida and Rodríguez (2011).

Flow Hydraulics
Flow hydraulics was expressed by the St. Venant equations (Cunge et al., 1980): where t is the time; x is the streamwise coordinate; u is the flow velocity; g is the acceleration due to gravity; S f = n 2 u 2 /R 4/3 is the friction slope; R = bh/(b + 2h) is the hydraulic radius; S 0 is the bed slope.Equation 1 describes fluid mass conservation and Equation 2 describes fluid momentum conservation.
The Manning-Strickler relation was implemented for bed resistance: where α r is a dimensionless coefficient that is specified as 8.1 (Parker, 1991a), and k s is calculated as where d 90 is the diameter of the bed surface size such that 90% of the sediment by weight is finer, and the dimensionless coefficient n k is set equal to 2 (Parker, 2004).
The light table regions are taken to be hydraulically smooth, and the channel roughness was determined by the following relation (Guo, 2015) where f = boundary Darcy-Weisbach friction coefficient; R = 4uR/υ is the Reynolds number; υ is the kinematic water viscosity, equal to 10 −6 m 2 /s in the simulations presented below.

Sediment Mass Conservation
The Exner equation was implemented to describe the conservation of the total (i.e., summed over all the grain sizes) sediment mass and to predict the time rate of change of channel bed elevation: where p is the porosity of the bed material; z b is the bed elevation; Q s = ∑Q si is the total (i.e., summed over all grain sizes) volumetric sediment transport rate and Q si = bq bi is the size-specific volumetric sediment transport rate; q bi is the size-specific unit-width volumetric sediment transport rate.
The sediment grain size distribution was discretized into k characteristic grain size ranges.The equation of conservation of sediment mass with generic grain size d i in the active layer is written as where L a is the active layer thickness; F i , f li are the fractions of sediment with characteristic size d i in the active layer and at the active layer-substrate interface, respectively (Parker, 1991b).
In gravel-bed rivers, when dunes are absent or only poorly developed, the active layer thickness is usually scaled with a typical coarse grain size contained in the surface layer, such as d 90 .Here the following relation was used: where n a is a constant value to modify the active layer thickness; n a = 2 is specified in this paper (Parker, 2004).
The fractions f li are computed differently depending on whether erosion or deposition occurs (Hoey & Ferguson, 1994).In the case of erosion, substrate sediment is transferred to the active layer and f li takes the value of the volume fraction content of sediment with grain size d i in the topmost substrate layer.If aggradation takes place, sediment is transferred to the substrate and f li is a combination of the material from the active layer and from the bedload.Thus, the relation to compute f li takes the form (Hoey & Ferguson, 1994): where f si is the fraction of sediment size d i in the topmost substrate layer (Viparelli et al., 2010); P bi is the fraction of sediment size d i in the bedload; φ is a dimensionless constant characterizing the material released to the substrate as the bed aggrades.φ is specified as 0.7 in this paper (Toro-Escobar et al., 1996).
The Viparelli et al. (2010) procedure to store and access the grain size stratigraphy of the bed deposit was used to update the grain size distribution of the substrate which, in active layer-based models, is the deposit below the active layer.If aggradation occurs, the grain size distribution(s) in the substrate will be updated to account for the newly deposited sediment.If the channel bed degrades, the sediment on the top of the substrate layer is mined and transferred to the active layer.In the simulations presented below, the thickness of each storage layer (i.e., L s ) in the substrate was set equal to 0.02 m, which is around the value of d 90 of the feeding sediment.The number of the storage layers M at each numerical grid j and each time step t + Δt is calculated by the following formula (Viparelli et al., 2010): (10)

Sediment Transport Relation: Wilcock and Crowe (2003)
A sediment transport relation is needed to calculate the size-specific, unit-width volumetric sediment transport rate and solve Equations 6 and 7.The Wilcock and Crowe (2003) formula is one of the widely used equations for estimating fractional transport rates in gravel-bed rivers with mixed sand/gravel sediments.This formula has also been used in previous numerical simulations of pool-riffle morphodynamics (de Almeida & Rodríguez, 2011, 2012).It can be expressed in the following form: where M f is an adjustment factor of the load relation; M f = 1 means no modification for the sediment transport rate;   *  is the size-specific dimensionless sediment transport rate;   * = √ ∕ is the shear velocity and ρ is the water density; τ b = ρgR b S f is the bed shear stress and R b is the hydraulics radius for the bed; s is the ratio of sediment to water density; ϕ i = τ b /τ ri is the relationship between the bed shear stress and a reference value of shear stress τ ri for the sediment size d i .The reference shear stress denotes the shear stress at which a very low but measurable value of sediment transport is observed.It can be determined by the following relation: where d g is the surface geometry median size; τ rm is the value of τ ri corresponding to the d g and can be determined by: where F s is the sand fraction in the surface sediment material.Through this equation the increased gravel mobility in the presence of sand (Wilcock, 1998), which is called "magic sand effect" herein, is explicitly modeled.
The exponent b i characterizes the hiding effect and is given by

The Flow of the Calculations
The following initial conditions were imposed to solve the governing equations: water depth, flow velocity, bed elevation, and the grain size distributions of the active layer and substrate layers everywhere in the domain at t = 0. Having specified the constant boundary condition of each experimental Stage introduced in Section 2, we ran the model on fixed bed conditions to get steady flow as initial conditions for water depth and flow velocity (Equations 1 and 2) and the model was then run for the duration of the corresponding experimental stage.Initial conditions to solve the equations of conservation of sediment mass (Equations 6 and 7) were specified in terms of bed elevation and sediment size distribution.
Boundary conditions of the flow equations were specified as constant flow at the upstream end and the free outflow at the outlet.Flow discharge and water depth (see Table S1 in Supporting Information S1 for details) were imposed as inlet boundary conditions.As in the experiment, water and sediment were fed at inlet grid channel station = 0.4 m (Figure 1).
The MacCormack scheme is an explicit, two-step predictor-corrector scheme (MacCormack, 1969) that is second-order accurate in space and time.This scheme is capable of simulating both sub-and supercritical flows (Chaudhry, 2008).It has been applied for analyzing one-dimensional, unsteady, open-channel flows by Fennema andChaudhry (1986, 1987) and Dammuller et al. (1989).This scheme was adopted here to update flow hydraulics.Once the flow variables in each time step were updated, they were employed in calculations of the sediment transport rate which could then be used to update the bed elevation and grain size distributions in the active layer and substrate layer.In other words, an uncoupled approach was adopted here.When strong interrelation between water flow and sediment movement occurs, the use of an uncoupled approach may lead to unacceptable errors in long-term prediction of river changes (Saiedi, 1997).In the present experiment involving progressive morphological changes of the bed occurring over a long period compared to the hydraulic time scale, the use of an uncoupled approach was justified (Soares-Frazão & Zech, 2011).In the MacCormack scheme, forward finite-differences were used to approximate the spatial derivatives in the predictor part and backward finite-differences were utilized in the corrector part.When solving the equation for sediment mass conservation, the spatial derivatives were discretized using a first-order upwind scheme.Temporal derivatives were discretized using a first-order explicit scheme.The time step was constrained by the Courant-Friedrichs-Lewy condition and a minimum time step was used to update all variables.A uniform grid size of 0.1 m was adopted here.

Overview on the Modeling Study
Two sets of numerical simulations were performed.One set was for model evaluation (i.e., to simulate the experimental conditions reported by Chartrand et al. (2018)), and the other was for exploring the research questions.
Here, the initial phase of the experiments (i.e., Stages 1-3) was adopted to evaluate the numerical model.As in the experiments presented in Section 2, Stage 1 began with a flat bed of slope equal to 0.015 and an initial deposit of grain size distribution equal to the grain size distribution of the sediment feed.The initial bed for Stage 2 was the simulated bed at the end of Stage 1 and the initial bed of Stage 3 was the simulated bed at the end of Stage 2.
The set of simulations to explore our research questions was divided into three groups (Table 1): uniform increase to the sediment feed rate (Group A), variation of the sand supply rate (Group B), and variation of the gravel fraction coarser than 8 mm (referred to as coarse gravel herein; Group C).Here, Cases A1, B1, and C3 were all base cases.Specifically, flow discharge equal to 60 L/s, sediment feeding rate equal to 0.8 kg/min, and a poorly sorted gravel sediment grain size distribution (Figure 1).The initial bed of all cases in Table 1 was the simulated bed at the end of Stage 1 and the simulations continued until the model flume reached steady-state conditions.
In the simulations of Group A, we increased the sediment feed rate up to five times the A1 value but kept the same texture.In Group B simulations we kept the gravel supply rate equal to the B1 rate (0.72 kg/min) and gradually increased the sand supply rate up to 3.28 kg/min corresponding to 41 times the B1 value (0.08 kg/min).Finally, to examine the role of coarse gravel on pool-riffle morphology, in Group C simulations, we maintained the fine sediment (less than 8 mm in size) supply equal to the C3 value of 0.384 kg/min and changed the grain size distribution of the coarse sediment (i.e., see Figure 2b, from C1 to C5) while maintaining its volumetric rate of 0.416 kg/min.

Model Calibration and Evaluation
The initial phase of the experiments presented in Section 2 was used for model calibration and evaluation.
There were two parameters that needed to be determined in our model.The first parameter was the bed porosity p (Equation 6) which, in a morphodynamic model, influences the time scale of bed evolution.Based on measured data, the calculated bed porosity was 0.145 (the mean value at the end of three Stages, see Table S2 in Supporting Information S1 for details).This value seems to be small, as numerical simulations of gravel-bed rivers usually use a value of 0.35 or 0.40.The small bed porosity in the experiment results from the fine infiltration into the coarse bed (e.g., Hill et al., 2017), which happened in Stage 1 of the experiments.There are also studies that have shown that the porosity range for a sand-gravel mixture can vary from 0.1 to 0.5 (Frings et al., 2011;Selby & Hodder, 1993).
The other parameter is the coefficient M f (Equation 11) which can modify the magnitude of the sediment transport rate, as commonly done for the application of morphodynamic models when a problem-specific sediment transport formulation is not available (see e.g., An et al., 2018;Naito & Parker, 2019;Nittrouer & Viparelli, 2014;Viparelli et al., 2011).To calibrate M f , we tried multiple M f values and found that the steady-state results with M f = 0.2 provided the best comparison with the measured data (see Figures S1-S3 in Supporting Information S1 for details), which is of interest for the application runs illustrated in Table 1.This value of M f may appear to be small, but this is not unusually so, given the large uncertainty in sediment transport relations.For instance, Li et al. (2020) employed calibration factors of a similar magnitude when modeling the Minnesota River in the US.
Then we run the numerical simulations with the same duration as that of the experiment using p = 0.145 and M f = 0.2.The model performance is summarized in Figures 3-5.As shown in Figure 3a, at the end of Stage 1, the model was unable to reach steady state as the laboratory flume because simulations were performed with a Note.In Group A, we kept the grain size distributions to be the same as those of experiment, whereas we step increased the feed rate.In Group B, we kept the gravel feed rate the same as that of experiment, but we increased the sand feed rate.In Group C, we maintained a constant supply of sediment with a particle size smaller than 8 mm and only modified the grain size distribution of sediment larger than 8 mm without altering the overall feed rate.A1, B1, and C3 are all base cases.See Figure 2a for the corresponding grain size distributions for Group B cases and see Figure 2b for the grain size distributions for Group C cases.In Table 1, C3 has the same grain size distributions as those of the experiment.Comparatively, the grain size distributions of C1 and C2 are finer, while those of C4 and C5 are coarser.

Table 1
The Sediment Supply in Terms of Feed Rate (Sand and Gravel), Sand Feed Rate, Gravel Feed Rate, Sand Content, and Geometry Median Size Used in the Simulations value of porosity that is likely smaller than the bed porosity in the early stages of the experiments, when fine sediment did not infiltrate in the coarse bed.This is shown in Figure 3a   and the formation of pool-riffle sequences when particle segregation processes that cannot be captured by the mathematical formulation illustrated in Section 3 are not prevalent.
The comparison between measured and numerical sediment loads at the downstream end of the model reach is presented in Figure 3b.In Stage 1, the simulated sediment transport rate was generally higher than the measured data because the loss of fine sediment in the coarse bed was not captured and directly led to a slower numerical build-up of sediment storage.However, in the following Stages 2 and 3, the situation was reversed (Figure 3b) due to the underrepresentation of fines in the modeled bed surface sediment, leading to a slower adjustment speed of the simulated flume bed in response to sediment under-feeding.
The model capability to capture bedload fractions and bed surface fractions is shown in Figures 4 and 5, respectively.In terms of bedload fractions, the simulated results followed the trend of measured fractions of Stages 2 and 3, whereas the measured sand fractions in Stage 1 were significantly lower than the simulated results and feeding fractions (Figures 4a-4c).The occurrence of this phenomenon was indeed caused by the significant infiltration of fine sediment into the coarse bed during the buildup of sediment storage, as mentioned above.
Generally, the simulated results agreed with measured bed surface fractions for all stages (Figure 5).However, measured bed surface fractions of sand were always significantly larger than the simulated results, as shown in Figure 5.This is likely the result of the infiltrated sand being exposed during the degradation process.See more comparisons of bedload fractions in Figures S6-S8 in Supporting Information S1 and of bed surface fractions in Figures S9-S16 in Supporting Information S1.
It may be worth considering running the model with a value of porosity that changes in space and time as fine sediment infiltrates in the coarse matrix.This modeling exercise, however, cannot be performed with an active layer-based model, which can capture the steady state but not the bed evolution process.There are (at least) three reasons why active layer models cannot reproduce infiltration of fine sediment in a coarse bed: 1.The exchange of sediment between the active layer and the bedload transport is modeled in terms of spatial change in bedload transport rates, that in alluvial beds are equal to the transport capacity of the flow.To the best of our knowledge, existing surface-based bedload transport models are not able to account for particle segregation from the bedload transport into the bed deposit (Hill et al., 2017).2. The active layer is a mix layer, thus vertical sorting, infiltration of fine sediment in the coarse active matrix and other particle segregation processes that require elevation-and-grain-size specific formulations for particle entrainment and transport cannot be represented with active layer-based formulations (Blom, 2008;Blom & Parker, 2004;Viparelli et al., 2017).3.In active layer-based models transfer of sediment to the substrate can only be mediated by the active layer (a mix of active layer and bedload sediment is transferred to the substrate) during channel bed aggradation.
For these reasons, the exchange of sediment between the bedload transport and the substrate for different particle segregation mechanisms cannot be accounted for (Viparelli et al., 2022).Despite this, the focus of this study is on the impact of sediment supply on the steady-state pool-riffle morphology, and the time scale difference caused by sand infiltration is not expected to affect this analysis.As shown in Figures S1-S3 in Supporting Information S1, the present model is verified with the capability to reproduce steady-state pool-riffle morphology in terms of flow hydraulics, bed profile and bed surface grain size.

Model Application
We used the validated model to investigate how sediment supply affects pool-riffle morphology (see details of the numerical runs in Table 1).As in Chartrand et al. (2018Chartrand et al. ( , 2023) ) and Hassan et al. (2021), we also focused our analysis on the central riffle and pool located between channel station 6 and 10.5 m.Specifically, corresponding to each case, we investigated the flow hydraulics (i.e., water surface, flow velocity, water depth and bed shear stress, see Figure 6), bed (i.e., bed profile and detrended bed profile by subtracting the underlying slope, see Figure 7), and characteristics of bed grain sorting (i.e., d 90 , d g , σ g , and sand content, see Figure 8; σ g is the geometric standard deviation).The d 90 is quite important in the gravel-bed pool-riffle sequence since it is a key value for bed roughness and important for aquatic habitat wellbeing.Sand content can increase gravel mobility (Curran & Wilcock, 2005).The d g provides an idea of how coarse the overall bed surface is compared to the sediment supply, and σ g provides information on the overall grain size variability of the bed surface sediment.These two parameters (d g and σ g ) are also relevant for habitat restoration and ecological purposes.In addition, we also present the local bed slope of central riffle and pool here (see Figure 7).The local bed slope of riffle was calculated as the bed slope between riffle crest at around station = 6 m and the pool center at about station = 8 m.Similarly, the local pool bed slope was calculated as the bed slope between pool center at around station = 8 m and the pool tail at about station = 10.5 m.
As described in Section 4, we explored the effect of the sediment supply rate and caliber on pool-riffle morphology in three group simulations: Group A simulations (amount of total sediment supply), Group B simulations (sand supply), and Group C simulations (coarse gravel supply).In Figures 6-8, the first column pertains to Group A simulations, plots in the second column describe Group B results and plots in the third column summarize results of Group C simulations.As indicated in the legend, results from different cases are represented with lines of different colors.The change of the above variables including flow hydraulics, bed slope, bed surface grain size characteristics, and detrended central pool-riffle amplitude in each group simulations is summarized in Table 2.

Group A: Effect of the Amount of Total Sediment Supply
In response to the increased sediment supply, bed slope and water surface became steeper, water depth became shallower, flow velocity increased and, as a result, the bed shear stress became larger (Figures 6a-6d).Further, in response to an increased sediment supply rate with no change in grain size distribution from Case A1, the channel bed experienced aggradation (Figure 7a).Due to the fixed downstream bed elevation, aggradation occurred as a rotation around the downstream end with the highest aggradation observed at the upstream end of the model reach (see Figure 7b).As a result, the central riffle became steeper, and the pool became shallower with its bed slope becoming positive (see Figure 7c).
It is important to keep in mind that the model channel had variable width, which is known to generate and maintain the pool-riffle sequence (Chartrand et al., 2018).In response to an increased sediment supply, the reach averaged bed slope increased, but the detrended bed elevation changed slightly (Figure 7d) suggesting that width variations play a prime control on pool-riffle morphology and that the sediment supply rate plays The aggradation depth is the elevation difference between other cases and the first case of each Group (i.e., A1 in Group A, B1 in Group B, and C1 in Group C).The first column pertains to Group A simulations, plots in the second column describe Group B results and plots in the third column summarize the results of Group C simulations.As indicated in the legend, the results from different cases are represented with lines of different colors in panels (a, b, d-f, h-j, and l).The gray arrow in panels (a, b) indicates increasing sediment supply, in panels (e, f) presents increasing sand supply, and in panels (i, j) indicates coarsening gravel supply.Cases A1, B1, and C3 are all base cases.Panel (c) presents the response of local slope of central pool and riffle to the sediment feed rate in Group A, panel (g) shows the corresponding response to the sand feed rate in Group B, and panel (k) summarizes the response to the varying coarse gravel fractions indicated by feeding geometry median grain size.
a secondary role.In this case, the detrended central pool-riffle amplitude experienced a 2.3% reduction over a fivefold increase in sediment supply rate (Table 2).
In terms of the bed surface texture, as can be seen in Figures 8a and 8b, in response to an increase in sediment supply rate the d 90 became smaller and the sand content became larger.In addition, d g and σ g of the bed surface approached those of the sediment supply.This result can be explained in terms of "partial transport": with the increasing bed shear stress, the mobility of coarse grains relative to fine grains increases and consequently the bed surface tends to become unarmored (Parker & Klingeman, 1982).Furthermore, the spatial variation of the d 90 was in phase with the width variation, whereas the sand content was out of phase with the width variation, showing that the bed surface was finest where the channel was narrow, and the bed shear stress was largest regardless of the total sediment supply rate.

Group B: Effect of the Sand Supply
We increased the sand supply up to 41 times the sand supply in Case B1 while keeping the gravel supply fixed (see Figure 2a for the grain size distribution of the sediment supply).The maximum sand supply rate corresponded to 4.56 times the gravel supply rate (the value of 3 was used in An et al. (2019)).As shown in Figures 6  and 7, the response of flow hydraulics and bed profile to the increased amount of sand supply can be divided into two stages by the turning point reached with an 11-fold increase in sand supply rate.
For increasing values of the sand supply rate up to 11 times the Case B1 value, the water surface became milder, water depth increased, flow velocity decreased, bed shear stress became smaller, and the bed slope decreased compared to Case B1.After further increasing the sand supply rate, the water surface steepened slightly, water depth grew shallower, flow velocity increased, bed shear stress intensified slightly, and the bed slope increased slightly compared to the results of Case B6.As noted for the Group A simulations, the fixed bed level at the downstream end of the model reach forced a rotation of the channel bed with the largest degradation upstream, resulting in a milder riffle and a deeper pool.After the turning point, both the pool and riffle experienced little change in bed slope.The detrended central pool-riffle amplitude experienced a slight change (<2.3%, see Table 2).
The presence of a turning point clearly shows that two competing effects are associated with an increasing sand load: the sand effect which promotes the gravel movement and the increasing sediment supply amount which favors aggradation.For sand loads larger than 11 times the Case B1 value, the overload effect became stronger than the effect associated with the fining of the sediment supply.A close look at the numerical results suggests the presence of a balance between the two competing effects from an 8-fold to a 21-fold increase in the sand supply.This balance shows negligible differences in flow hydraulics and bed profile while the bed surface texture, as can be seen in Figures 8e-8g, shows a gradual fining.

Group C: Effect of Coarse Gravel Supply
This group of simulations was specifically designed to study how pool-riffle morphology responds to changes in gravel grain size distribution, with C1 indicating the finest gravel and C5 the coarsest gravel (Table 1, Figure 2b).In response to gravel supply coarsening (Figures 6i-6l), water surface steepened, water depth became shallower, flow velocity increased and thus bed shear stress became larger.These changes in steady-state hydrology corresponded to channel bed aggradation (Figure 7i) with a rotation around the downstream fixed bed level (Figure 7j).In particular, the coarser the gravel load, the steeper the steady state profile, with flume-average bed slope increasing from 1.22% to 2.45% (see Figure 7k).In agreement with the results of the Group A simulations, the riffle became steeper and the pool became shallower (Figure 7k) in response to the change in transport capacity of the flow.The detrended central pool-riffle amplitude experienced a slight change (<3.2%, see Table 2).Not surprisingly, the bed surface texture showed a gravel coarsening here.

Discussion
Here, we summarize a comprehensive set of numerical experiments completed to better understand how bed topography and bed surface grain size sorting respond under differing upstream supplies of sediment and under Note.(a) "+" is increase whereas "−" indicates decrease; (b) the water surface slope and bed slope here are calculated as the slope between the inlet (station 0.5 m) and the outlet (station 16 m); the flow velocity, water depth, bed shear stress, d 90 , d g , σ g , and sand content are the mean value; (c) the variable change in Group A is calculated as the difference between Case A7 and Case A1; the variable change in Group B is calculated the difference between Case B9 and Case B1; the variable change in Group C is calculated as the difference between Case C5 and Case C1; (d) the variable change in Group B-I is calculated as the difference between Case B6 and Case B1; the variable change in Group B-II is calculated as the difference between Case B6 and B9; and (e) the detrended central pool-riffle amplitude is calculated as the difference between the central riffle crest (station 6 m) and the central pool center (station 7.9 m).

Table 2
The Change of Variables in Different Groups of Simulations the influence of downstream width variations.The water supply rate and downstream configuration of width remained fixed across all simulations.Results show an important sensitivity of topography and grain size sorting to upstream supply changes (magnitude and composition), however the longitudinal profile across all supplies exhibits a self-similar downstream pattern of local topographic lows and highs, illustrating the importance of downstream width variations to pool-riffle morphodynamics.In the following discussion, we focus on the challenges of using a one-dimensional numerical model to examine width variable morphodynamics, the role of the upstream supply sand content for overall bed responses, as well as the implications and limitations of our research.

Challenges of Simulating Variable-Width Morphology With a Gravel Mixture
It has been argued that river segments which exhibit two-and three-dimensional flow patterns and structures cannot be reliably evaluated with cross-sectional averaged models because such frameworks cannot produce reliable shear stress estimates (MacWilliams et al., 2006;Thompson et al., 1996).This prior research focused on complex cross-sections, whereas the simulations presented here represent a straight planform configuration with downstream varying width (de Almeida & Rodríguez, 2011).As a result, our approach here is one of reduced complexity in terms of the planform geometry, and we focus on how longitudinal bed topography and grain size respond to differing configurations of downstream width variations.
We also attempted to use Wilcock (2001) in our study to calibrate the Wilcock-Crowe function for grain size mixture transport calculations.We used a coefficient M t to modify the reference shear stress in Equation 14, as represented below.
We found that by modifying the reference shear stress using M t = 1.2, the simulated bed profile and water surface profile still closely matched the measured values (see Figure S17 in Supporting Information S1).However, compared to the ones obtained using the above magnitude-based calibration method with M t , the calculated bed surface fractions deviated further from the measured values (see Figure S18 in Supporting Information S1).

The Explicit and Implicit Effects of Sand Content Based on the Wilcock and Crowe (2003) Formula
Based on Wilcock and Crowe (2003), the impact of sand content on sediment transport rate can be mainly divided into two parts.The first part is the explicit effect, the "magic sand effect," which is reflected in Equation 14.The presence of sand can effectively reduce the reference shear stress, thereby increasing gravel mobility.The second part is the implicit effect, the "hiding effect," which is reflected in Equations 13 and 15.The increase in sand content can lead to a decrease in d g , resulting in more physical exposure of gravel particles on the bed surface, and thus increasing its mobility.Both effects are numerically represented in the simulations, and their combined influences are apparent in the calculated results.To gain a clearer understanding of these two effects, we conducted additional simulations by disabling the "magic sand effect."Specifically, we used a constant reference shear stress by setting F s to 0 in Equation 14.
In our experiment, apart from sand content, another important factor influencing sediment transport rate was the bed slope, which represented the magnitude of bed shear stress.It is difficult to distinguish these two factors when observing the effects on transport.However, changes in bed slope can reflect variations in the effects caused by sand content through the feedback inherent in morphodynamics.This is easily understandable because, for a given flow and sediment supply, if the presence of sand significantly increases the sediment transport rate, the riverbed profile tends toward a smaller slope.Conversely, if the presence of sand does not effectively increase the sediment transport rate, then the river channel tends toward a larger slope to compensate for the reduced sediment mobility.As shown in Figures 9a and 9b, if the magic sand effect is removed from the simulation, the riverbed requires a higher slope to transport the supplied load.Furthermore, the bed surface sand content deviates further from the feeding sand content (Figures 9c and 9d), implying that the sediment transport condition is further away from "full mobility."This suggests that in the context of our study, the magic sand effect is important for achieving the representative topographic profile conditions.
In the Group B numerical simulations, as the sand supply increased from Case B1 to B5, the average slope of the flume decreased regardless of whether the magic sand effect was considered or not.However, when evaluating the full influence of sand content as reflected in the Wilcock-Crowe function, the decrease in riverbed slope was more pronounced with an increasing supply of sand.We think this is because, with an increasing supply of sand, the enhancement of the magic sand effect becomes more prominent.Furthermore, it is interesting that after Case B5 (where the bed surface sand content exceeds 20%), the bed slope was no longer sensitive to the additional sand supply, regardless of whether the magic sand effect was considered or not.For the case when the magic sand effect was considered, this is easier to understand because once the sand fraction reached 20%, further increasing the sand supply could not further reduce the reference shear stress (Equation 14).Last, as shown in Figure 9b, when facing coarsening gravel supply, the sand effect may also have played a role in bed aggradation.Specifically, with a decrease in sand content, the sand effect weakened.As a result, this weakening of the sand effect enhanced bed aggradation.

Implications and Limitations of the Simulations
Salmon spawning and incubation can be influenced by various factors including flow conditions (i.e., water depth and flow velocity), nutrient availability, and sediment composition of the riverbed (Beland et al., 1982;Louhi et al., 2008).As shown in the results section, sediment supply can influence pool-riffle sequences in terms of water depth, flow velocity, and riverbed sediment compositions.The numerical simulations here are based on a 75 m-long reach of East Creek idealized into the laboratory setting.Nonetheless, the insights gained can also be applied to similar river reaches of similar characteristics and provide guidance for the conservation and restoration of fish habitat in pool-riffle sequences.
For descriptive purposes, we define "sensitive" as when the change of variables is larger than 20% (shown in Table 2).Results of the simulations reported here indicate that bed slope and water surface slope are sensitive to changes in upstream sediment supply (i.e., magnitude, supply composition, and sand proportion), whereas flow velocity and water depth are less sensitive.Furthermore, bed shear stress is more sensitive to changes in the sediment magnitudes and composition, than to the specific sand proportion.In terms of the overall trend of bed surface grain size in response to sediment supply changes, all characteristics of bed grain sorting (i.e., d 90 , d g , σ g , and sand content) are not sensitive to the change in sediment amount.In response to the change in sand amount, except d 90 , all the other three characteristics are sensitive.When responding to the change in gravel fractions, d 90 , d g , and σ g are sensitive whereas sand content is not.As shown in Table 2 and Figure 7, the detrended topographic profiles and associated pool and riffle amplitudes are not sensitive to changes in upstream sediment supply magnitude and caliber.In other words, pools and riffles persist.This is consistent with the field observations in Elwha River, USA (see Brew et al., 2015).Before the dam removal, the pools along the Elwha River were situated in areas where there were local reductions in bankfull width.When the dams were removed, a surge of sediment temporarily filled these pools, but over time, most of the pools returned to their original locations., d) cases, in the scenarios where the combined effects of sand content (magic sand effect and hiding effect) were fully considered and when only the hiding effect was considered.For convenience, the feeding sand content change is also included in panels (c, d).
We added data from the simulations to a regime diagram developed by Chartrand et al. (2023, Figure 6), as shown in Figure 10.The simulation results fell within the range of the reported results (field and lab) and followed their theoretical formulation.In addition, in Chartrand et al. (2018Chartrand et al. ( , 2023)), differences between the experimental local slope and theoretical predictions grow as the narrowing condition strengthens.Here, our numerical model shows improved capability to capture the real local slope of pools measured in the prototype experiments.This indicates our model's potential to be used to explore the proposed regime space in more detail and to address open questions that are too time-consuming to pursue in the lab or the field.
The research presented here is an extension of previous laboratory experiments (Chartrand et al., 2018(Chartrand et al., , 2023;;Hassan et al., 2021;Nelson et al., 2015), and should be viewed as such, with the limitations of the Chartrand et al. (2018Chartrand et al. ( , 2023) ) experiments serving as key limitations of this study.The two primary limitations relate to how the experimental side walls were constructed and configured from the flume inlet to the outlet.More specifically, the sidewalls were constructed in a vertical fashion, with a height that could not be overtopped by any of the experimental water supply rates.Hence, the experimental channel was confined within rigid and fixed channel walls, lacking any affects related to water flows spilling onto floodplains, or similar out of bank topographic features of river corridors.Furthermore, the fixed down flume width configuration suggests that adjustments of the flume bed due to changes of the upstream water and sediment supplies are likely constrained to local changes of the flume bed slope as the primary response, and changes of bed surface grain size composition to a lesser degree (Chartrand et al., 2018).As a result, the prototype experiments and the numerical simulations reported here are idealized abstractions of nature, designed to address specific research questions under controlled conditions, and not representative of other important factors such as laterally adjusting sediment routing (e.g., Milan, 2013;Whiting & Dietrich, 1991), and shear stress phase shifts (Wilkinson et al., 2004), bank failure and the role of riparian vegetation (e.g., Braudrick et al., 2009).Nonetheless, generalized scaling results comparing laboratory, numerical and field cases suggest that our overall approach adequately captures key physical processes associated with pool-riffle formation and maintenance (Figure 10).However, important questions remain.Does pool-riffle bed topography drive local river width adjustment (Leopold & Wolman, 1957), or do pre-existing local width variations drive development of pool-riffle sequences?Furthermore, do these two physical attributes develop in parallel from some set of defined conditions, according to mutual feedback, positive and negative, which affect the local flow field and structuring of the bed surface texture?Consequently, further research is needed.

Conclusion
In this study, a one-dimensional hydro-morphodynamic model of gravel-bed pool-riffle sequence was developed, calibrated, and validated against experimental data in terms of flow hydraulics, bed profile and bed surface fractions.The model was proven to have the ability to mimic steady-state pool-riffle morphology under given flow and sediment supply conditions.Then the model was applied to investigate how the sediment supply (i.e., sediment amount, sand amount, and gravel fractions) affects the adjustment of the steady-state pool-riffle morphology.We conducted numerical simulations with constant flow and sediment supply to reach the steady-state pool-riffle morphology to study the long-term effect of sediment supply driven by natural processes or human activity.
In all the simulations, we observed: (a) the bed slope and water surface slope were quite sensitive to the change of sediment supply in terms of sediment amount, sand amount or gravel fractions.(b) all characteristics of bed grain sorting (i.e., d 90 , d g , σ g , and sand content) were not sensitive to the change of sediment amount.In response to the change of sand amount, except d 90 , all the other three characteristics were sensitive.Responding to the change of gravel fractions, d 90 , d g , and σ g were sensitive whereas sand content was not.(c) all the detrended bed profiles were not sensitive to the change of sediment supply; in other words, the pool-riffle sequences may persist in all changes of sediment supply.The findings here can provide support for the regulation of pool-riffle gravel-bed rivers.

Figure 1 .
Figure 1.Schematic illustration of the experimental setup, including an overhead view of the experimental channel, showing the downstream width variation, subsampling locations indicated by red boxes and grain size distributions used in the experiment.The streamwise distance from the flow normalizer identifies the channel stations.Figure is modified from Chartrand et al. (2018).

Figure 2 .
Figure 2. Different grain size distributions considered in (a) Group B and (b) Group C. In panel (b), C3 has the same grain size distributions as those of experiment.Comparatively, the grain size distributions of C1 and C2 are finer, while those of C4 and C5 are coarser.

Figure 3 .
Figure 3.The change of mean flume bed slope and sediment flux exiting the flume over time."Sim."indicates simulated results, and "Mea."represents measured data.Here the time precision of the simulation results is 5 min.

Figure 4 .
Figure 4.The bedload fractions exiting the flume for Stage 1 (panels (a-c)), Stage 2 (panels (d-f)), and Stage 3 (panels (g-i))."Sim."indicates simulated results, "Mea." is the measured data, "Feed."represents the feeding fractions.Plots in the first column pertain to Stage 1, plots in the second column describe Stage 2 results and plots in the third column summarize Stage 3.

Figure 5 .
Figure5.The comparison between the simulated bed surface fractions and the measured data at the end of each stage at Stations 6, 7, 8, and 9 m.See their positions in Figure1.For convenience, the sediment feeding fractions are also added to the figure for reference.The Wolman method which was used to process the experimental data is limited to 2 mm and coarser (i.e., material finer than 2 mm was lumped into one size, the fourth grain size in the measured fractions).Plots in the first column pertain to Stage 1, plots in the second column describe Stage 2 results and plots in the third column summarize Stage 3.

Figure 6 .
Figure 6.Simulation results of flow hydraulics from all simulations.Water surface elevation, flow velocity, water depth, and bed shear stress are shown here.The first column pertains to Group A simulations, plots in the second column describe Group B results, and plots in the third column summarize the results of Group C simulations.As indicated in the legend, the results from different cases are represented with lines of different colors.The gray arrow in panels (a-d) indicates increasing sediment supply, in panels (e-h) presents increasing sand supply and in panels (i-l) indicates coarsening gravel supply.Cases A1, B1, and C3 are all base cases.For convenience, the width variations are shown here.

Figure 7 .
Figure 7. Simulation results of bed profile, aggradation/degradation depth, local bed slope of central pool and riffle, and detrended bed profile (i.e., subtract the underlying bed slope) from all simulations.The aggradation depth is the elevation difference between other cases and the first case of each Group (i.e., A1 in Group A, B1 in Group B, and C1 in Group C).The first column pertains to Group A simulations, plots in the second column describe Group B results and plots in the third column summarize the results of Group C simulations.As indicated in the legend, the results from different cases are represented with lines of different colors in panels (a, b, d-f, h-j, and l).The gray arrow in panels (a, b) indicates increasing sediment supply, in panels (e, f) presents increasing sand supply, and in panels (i, j) indicates coarsening gravel supply.Cases A1, B1, and C3 are all base cases.Panel (c) presents the response of local slope of central pool and riffle to the sediment feed rate in Group A, panel (g) shows the corresponding response to the sand feed rate in Group B, and panel (k) summarizes the response to the varying coarse gravel fractions indicated by feeding geometry median grain size.

Figure 8 .
Figure 8. Simulation results of bed surface grain size characteristics from all simulations.The d 90 , d g , σ g , and sand content are shown here.The first column pertains to Group A simulations, plots in the second column describe Group B results, and plots in the third column summarize results of Group C simulations.As indicated in the legend, the results from different cases are represented with lines of different colors.The gray arrow in panels (a-d) indicates increasing sediment supply, in panels (e-h) presents increasing sand supply and in panels (i-l) indicates coarsening gravel supply.Cases A1, B1, and C3 are all base cases.For convenience, the dashed lines in panels (c, k) and panels (d, l) indicate the corresponding d g and σ g of the sediment supply, respectively.

Figure 9 .
Figure9.The simulated mean bed slope change and sand content change of bed surface for the Group B (a, c) and Group C (b, d) cases, in the scenarios where the combined effects of sand content (magic sand effect and hiding effect) were fully considered and when only the hiding effect was considered.For convenience, the feeding sand content change is also included in panels (c, d).

Figure 10 .
Figure 10.The spatial gradient of width versus local slope for all numerical simulations.The local slope in this figure is calculated as the mean slope of all numerical simulations.Figure is modified from Chartrand et al. (2023).