This report describes the development of a 2D hydraulic model for a 9.2-mi-long reach of the Kalamazoo River from the Trowbridge Dam to the Allegan City Dam (fig. 1). The primary objective was to produce a hydraulic model that estimates depth-averaged surface water velocity throughout the free-flowing part of the study reach, from just below the Trowbridge Dam to about 42,500 ft (8 mi) downstream, to better understand velocity barriers to fish passage and the hydraulic stability of sediments. In the modeling effort, 11 streamflow scenarios were investigated, including 4 scenarios forced with historical streamflow hydrographs covering March 23–April 14, 2023; January 26–February 14, 2024; June 11–12, 2024; and April 4–6, 2025. These historical scenarios include 50-percent and 20-percent annual exceedance probability (AEP) streamflows, as well as low-flow and bankfull-flow periods during which detailed streamflow velocity and water surface elevation (WSE) observations were collected. The historical streamflow scenarios provided model predictions to inform model calibration and validation against WSE and velocity observations. To improve understanding of more generic streamflow behavior, seven quasi-steady streamflow scenarios, ranging from 1,000 to 7,000 cubic feet per second (ft³/s) in 1,000 ft³/s increments, were run. This depth-averaged 2D model does not simulate vertical velocity distributions or rapid velocity fluctuations caused by turbulence, and interpretations of model results are limited to horizontal velocity variability. Furthermore, this model does not simulate rainfall-runoff processes, local contributions to streamflow, or surface water-groundwater interactions.

The ongoing efforts to remediate PCB contamination and improve aquatic connectivity along the Kalamazoo River have generated studies that are too numerous to fully summarize here (Simard, 2003). These studies have focused on a variety of topics including contaminant distributions in biota, sediment, surface water, and groundwater; aquatic ecosystem health; sediment transport; surface water hydraulics; and fluvial geomorphology.

More than 3,000 sediment cores and 6,000 sediment samples have been collected from the river and its floodplains to characterize the horizontal and vertical distributions of sediment size and contaminant concentrations (Arcadis, 2009). In 2000, the USGS and Michigan Department of Environmental Quality collected sediment cores and surveyed transects across the Plainwell, Otsego Township, and Trowbridge impoundments to measure the impounded sediment volumes, investigate their depositional history, and determine contaminant distributions (Rheaume and others, 2002). About 1.2 million cubic yards of accumulated sediment were estimated upstream from the Trowbridge Dam, representing more than 75 percent of the total measured accumulated sediment. In the same study, the researchers identified a distinct depositional sequence within the impoundments, characterized by interbedded lacustrine deposits containing organic-rich silt and clay, fine to medium sand, and minor amounts of gravel overlying predam alluvial deposits consisting primarily of cobbles and gravel. These lacustrine deposits were partially eroded after drawdown of the impoundments as the river channel adjusted toward equilibrium with the increased slope and stream velocity. In some locations, the erosional surface truncating the lacustrine deposits was overlain by alluvial sands and gravels transported by the higher energy conditions postdrawdown (Rheaume and others, 2002). A followup study estimated about 450,000 cubic yards of accumulated sediment in the Otsego City Dam impoundment (Rheaume and others, 2004).

Another study investigated the effects of dam removal on sediment transport in a reach stretching from upstream from the Plainwell Dam to just downstream from the Trowbridge Dam using a calibrated quasi-steady-state one-dimensional (1D) hydraulic and sediment transport model (Syed and others, 2005). The calibrated model indicated that sediment is predominantly transported during high-flow conditions and that mobilized sediments are deposited during the ebb phase of flood peaks. Model results did not indicate a substantial difference in total eroded sediment volume between dam-in and dam-out scenarios. A companion investigation contextualized the Kalamazoo River geomorphological setting, examined planform morphological change using repeat aerial photography and historical surveys, and modeled bank stability using limit equilibrium methods coupled to the previously mentioned 1D hydraulic models (Rachol and others, 2005). The study concluded that the planform of the Kalamazoo River had remained mostly stable over the period of investigation (1830s–1999) and that most planform changes were associated with anthropogenic channelization, inundation because of dam construction, and channel shortening through meander bend cutoffs. The study also identified several channel cross sections with higher stream velocities and shear stresses where banks were predicted to be unstable because of toe erosion.

More recently, AECOM (2023) presented a 100-percent design plan for removal of the Allegan City Dam that included 1D hydraulic modeling results for a 4-mi reach centered on the Allegan City Dam. The plan included dam-in and dam-out scenarios across a wide range of streamflows. The engineering firm WSP (unpub. data) created a 2D hydraulic model reaching from the Trowbridge Dam downstream to the Allegan City Dam for a dam-in scenario and multiple quasi-steady streamflow conditions. This current study builds upon these earlier works by expanding the hydraulic modeling to two dimensions, similar to WSP (unpub. data), and modeling unrestored, free-flowing river reaches to better understand the natural spatial variability in velocities and sediment stability in this river system.

The Kalamazoo River drains 2,020 square miles (mi²) of southwestern Michigan and empties into Lake Michigan near Saugatuck (USGS, 2023). The main stem of the river begins in Albion in eastern Calhoun County at the confluence of the north and south branches, and it flows 123 mi to its outlet (USGS, 2024; fig. 1). The drainage basin relief is 686 ft, and the river descends from Albion to Plainwell (the location of the Plainwell Dam) with an average gradient of 3 feet per mile (ft/mi; USGS, 2024). The gradient steepens to 5 ft/mi between Plainwell and Allegan (the location of the Allegan City Dam) as the river passes through the outer Valparaiso Moraine (not shown) and associated glacial outwash deposits. The river gradient then relaxes to about 0.5 ft/mi between Lake Allegan (the impoundment above the Calkins Bridge Dam) and the Lake Michigan outlet (Rachol and others, 2005). Dams and rapids interspersed along the main stem generate deviations from these average gradients.

Southwestern Michigan is covered in ubiquitous glacial drift of variable thickness exceeding 400 ft at places (Leverett and Taylor, 1915). The surficial deposits are typically well-sorted coarse-grained sand and gravel outwash laid down during the late Pleistocene recession of the Michigan and Saginaw lobes of the Laurentide ice sheet. Several moraine systems consisting of poorly sorted rocky debris and glacial drainageways containing well-sorted coarse-grained deposits are also throughout the basin. Underlying the glacial deposits are Mississippian age sedimentary rocks of the Michigan Basin (Deutsch and others, 1960). The central part of the present-day (2026) river occupies a valley formed during the Pleistocene by a much larger river conveying meltwater from the retreating ice sheet and affected by glacial outburst floods (Kozlowski and others, 2005). This ancestral glacial drainage reorganized several times as the lobes retreated, switching outlets and flow directions and developing terraces as it incised through extensive outwash deposits (Gordon, 1898).

The Kalamazoo River Basin land cover was historically dominantly forest and grassland but transitioned to primarily agricultural (47 percent), forested (30 percent), and urban (8 percent) land cover after European settlement (Kalamazoo River Watershed Council, 2011). Wetlands and lakes compose 15 percent of the drainage basin (Kalamazoo River Watershed Council, 2011). More than 80 percent of the soils in the basin are well drained and sandy (Rachol and others, 2005). The basin has a humid continental climate moderated by a strong lake effect from Lake Michigan. For 1991–2020, average winter temperatures were 27 degrees Fahrenheit (°F) and average summer temperatures were 70 °F. The basin received an average of 37 inches (in.) of annual precipitation (Palecki and others, 2021). For 1981–2010, the most recent period with snowfall climate normals available, the basin averaged 70–80 in. of annual snowfall (Arguez and others, 2010). The USGS streamgage Kalamazoo River at Comstock, Michigan (station 04106000), has been operational from 1931 to present (2026). This upstream site drains 1,010 mi². The minimum, 25-percent, median, 75-percent, and maximum recorded average daily streamflows at this location are 190, 580, 810, 1,200, and 6,800 ft³/s, respectively (USGS, 2025).

This study focuses on a 9.2-mi-long reach of the Kalamazoo River stretching from the Trowbridge Dam to the Allegan City Dam. Here, the river drains about 1,530 mi². The river valley constricts as it cuts through the Valparaiso Moraine (not shown) and diverges from the larger ancestral drainage path that flowed south toward the Paw Paw River (not shown; Colgan and others, 2023). The bankfull river width is about 200 ft. During normal streamflow conditions, the average center channel depth is 3–4 ft in the upper reaches and 6–8 ft in the downstream lower gradient reaches that are affected by backwater from the Allegan City Dam. No major tributaries join the river in this section, and the reach includes segments that are straight and tightly confined by valley walls, as well as meandering segments with wider floodplains and meander scars. Within the reach are several islands, and a major channel bifurcation is 1.8 mi downstream from the Trowbridge Dam. The secondary channel rejoins the main channel 2.7 mi downstream from the Trowbridge Dam.

The 2D implementation of HEC–RAS 6.6 permits simulation of fluid flow on an unstructured mesh of variably sized cells, each with as many as eight sides. This approach allows the modeler to efficiently model in-channel streamflow while also incorporating flow through the floodplain by refining a relatively coarser background mesh to a much finer resolution within the channel. This model domain boundary was manually digitized in the companion geographic information system to the HEC–RAS modeling suite, RAS Mapper, to align with the approximate extent of the floodplain throughout the study reach (fig. 1). The extent of surface water inundation computed by the high-flow scenarios was checked to ensure that the model domain encompassed the entire area of potential flow. The background mesh face length was specified as 100 ft. The channel centerline, riverbanks, and island boundaries were manually digitized to support refinement of the mesh within the channel using a 20-ft face length and to enforce the alignment of mesh edges with important topographic features (fig. 2). A 1-ft-resolution seamless topobathymetric digital elevation model derived from airborne light detection and ranging data collected in November 2016 and multibeam sonar data collected in May 2017 was used to define the model surface elevations (Quantum Spatial, unpub. data, 2017). Bridge structures are not explicitly incorporated in the model geometry because all the bridge spans in the study reach are well above the water at the highest flows modeled in this study. The model’s vertical datum is the National Geodetic Vertical Datum of 1929, in units of feet, and the horizontal coordinate system is Michigan State Plane South, in linear units of feet (European Petroleum Survey Group code 6499). HEC–RAS 6.6 takes advantage of the higher resolution terrain data relative to the model mesh resolution by incorporating subgrid elevation information in hydraulic property tables for each model cell and face. A streamflow hydrograph (specified flux) was used as the model’s upstream boundary condition, and a stage hydrograph (specified elevation) was used as the downstream boundary condition (fig. 1). All other boundaries were zero flux boundaries, but the model domain was large enough to prevent water from interacting with these zero flux boundaries.

We used streamflow estimates from the Trowbridge streamgage as the inputs to the streamflow hydrograph boundary condition for four unsteady historical simulations across a range of streamflow magnitudes, spanning March 23–April 14 (spring), 2023; January 26–February 14 (winter), 2024; June 11–12 (summer), 2024; and April 4–6 (spring), 2025 (fig. 3A–D; USGS, 2025). These streamflow estimates have a 15-minute temporal resolution and are based on a stage-discharge rating curve developed following standard USGS methods (Kennedy, 1983). The peak flows during the spring 2023 event reached 6,800 ft³/s, which represents about a 10-percent AEP streamflow based on the analysis presented in AECOM (2023). The winter 2024 event peaked at 3,980 ft³/s, about a 50-percent AEP streamflow magnitude. The streamflows during the spring 2025 observations were similar in magnitude. The summer 2024 scenario streamflows were fairly stable between 1,000 and 1,100 ft³/s, and this scenario overlaps with the low-flow model validation field data collection period. Additionally, we forced models with seven constant streamflow time series to simulate quasi-steady streamflows ranging from 1,000 to 7,000 ft³/s in 1,000-ft³/s increments. The 1,000-, 4,000-, and 7,000-ft³/s streamflow scenarios are referred to as “low-flow,” “bankfull,” and “high-flow” scenarios, respectively, in subsequent sections of this report. Emphasis is placed on the 4,000-ft³/s streamflow scenario because this streamflow is estimated to be about the bankfull or 50-percent AEP streamflow at this site (AECOM, 2023). The downstream elevation boundary was set as 627.8 ft for all simulations except for the spring 2025 streamflow scenario, for which the downstream elevation boundary was set as 628.1 ft based on field survey observations. The downstream Allegan City Dam is operated to maintain stable water elevations in the upstream impoundment and is able to convey the flood flows simulated here (AECOM, 2023).

All simulations used the Eulerian-Lagrangian shallow water equation solver. Each model was initialized in a dry condition and warmed up with a 6-hour period where the input streamflow linearly increases from 0 ft³/s to the first input streamflow prescribed in the accompanying streamflow scenario during the first 30 minutes of the warmup period. This approach allowed the models to achieve quasi-equilibrium before beginning the unsteady simulations in the case of the historical scenarios. For the quasi-steady simulations, the models were run for an additional 6 hours after the warmup period to ensure steady-state conditions were achieved. Steady-state conditions were verified by inspecting the computed water surfaces and velocities for differences between output intervals. All models were run with a 10-second time step, which yielded a median Courant condition value around 0.1 and maximum Courant condition values less than 2; a value of 3 is the maximum allowed by the Eulerian-Lagrangian shallow water equation solver (USACE, 2025). A simulation was also completed using a 2-second time step, and no substantial differences in model results were identified. Model outputs were generated hourly. The water density was assumed to be 62.4 pounds per cubic foot, and the water temperature was assumed to be 55.4 °F.

In many shallow-flow problems, including streamflow in most rivers, the gravitational and frictional terms are the dominant components of the momentum conservation equation. The Manning’s roughness coefficient (n) scales the bed friction, the momentum loss from the flow to the bed, and other sources of drag, and is frequently used as the calibration parameter in hydraulic simulations of open channel flows (USACE, 2020). Manning’s roughness coefficient is the primary adjustable parameter in this model formulation. We created an initial spatially distributed n value parameterization using the 30-meter (m) resolution 2021 National Land Cover Database (NLCD; Dewitz, 2023). Manning’s roughness coefficients were assigned to the land cover types present in the model domain using default values provided in USACE (2025). The NLCD data had a resolution too coarse to accurately represent the channel and island boundaries of the study reach, so channel and island polygons were manually digitized and were assigned n values overriding the underlying NLCD parameterization (table 1; fig. 4). The n value of the channel polygon was varied from 0.025 to 0.035 during calibration to the historical simulation scenarios. The n values that were used here are similar to those used in the AECOM (2023) and WSP models, and the n value at the cell face centroid was assigned to each cell face.

The model was manually calibrated by iteratively simulating historical streamflow scenarios using a range of channel roughness parameterization n values. The model was calibrated for low-flow conditions by running the summer 2024 scenario with channel roughness parameterization n values of 0.025, 0.03, 0.0315, 0.0335, and 0.035. The model was calibrated for higher streamflow conditions by running the spring 2023, winter 2024, and spring 2025 streamflow scenarios with n values of 0.03,0.0315, and 0.0335. The accuracy of the summer 2024 and spring 2025 models was assessed by comparing model elevation and velocity results against the field measurements. The root mean square error (RMSE; eq. 4) and bias (eq. 5) between observed and modeled WSEs, individual velocity samples, and cross-sectional average velocities were used to assess model performance. The spring 2023 and winter 2024 simulations were assessed similarly, but rather than comparing the model results against spatially distributed WSE and velocity observations, we compared the model results against a time series of WSE observations (hydrograph) at the Trowbridge streamgage. For comparison between observed and simulated WSEs and velocities at discrete points, model results were exported from the model output time step nearest the measurement time using the reference points feature in HEC–RAS. Simulated cross-sectional average velocities at the locations of ADCP cross sections were dynamically generated from the HEC–RAS HDF5 results files using Python. The best model parameterizations for the quasi-steady simulations were selected based on best professional judgment and review of the RMSE and bias values for the various calibration datasets. All the models simulated streamflow with less than a 0.001-percent water volumetric error associated with the numerical solution.RMSE=∑i=1NPredi−Obsi2N(4)andbias=∑i=1NPredi−ObsiN,(5)where

Gridded outputs of flow depth, depth-averaged velocity, and basal shear stress were generated from the calibrated model for each of the quasi-steady streamflow simulations ranging from 1,000 to 7,000 ft³/s. The output grid resolution was 3.28 ft across the wetted part of the model domain. These outputs were further analyzed to evaluate hydraulic conditions relevant to ecological thresholds and sediment mobility within the study reach. Longitudinal profiles of channel-average attributes were calculated by casting cross sections across the channel at a 33-ft along-flow spacing. The gridded model outputs were extracted every 3.28 ft along each cross section to compute cross-sectional averages. Cross-sectional average velocities were computed by calculating the total streamflow perpendicular to each cross section and dividing this value by the cross-sectional wetted area. The channel cross-sectional average values were subsequently smoothed using a three-sample rolling average, generating longitudinal profiles representing overlapping reaches about 100 ft long.

Shear stress outputs were used to evaluate channel bed stability and the potential for sediment deposition in the study reach by applying equations for an explicit, empirical Shields diagram presented in Guo (2020). For each output grid cell, the shear stress (taken for this analysis to be the critical shear stress at which sediment motion would be initiated [τ_c]) was related to a corresponding critical grain diameter (D; in other words, the minimum grain size stable at that streamflow) using equation 6. The dimensionless critical shear stress, or Shields parameter (τ_⁎c), was computed according to equation 7, where the dimensionless sediment diameter (D_⁎) was calculated using equation 8. In equation 9, the critical grain Reynolds number (R_⁎c) was determined from equation 29 in Guo (2020) and was computed by finding the maximum real root of equation 9 with the NumPy function “roots” (Harris and others, 2020).τ_c=τ_⁎c(Δ−1)pgD,(6) τ*c=R*c2D*3,(7) D*=DΔ−1gν21/3,(8)andR*c4+1957R*c3+1627−D*318R*c2−1142D*3R*c−8114D*3=0,(9)where

The τ_c values were computed across a range of D values from 0.01 to 128 millimeters (mm), at intervals of 0.01 mm. A D value was then assigned to the nearest corresponding shear stress value of each output raster cell, for each streamflow scenario ranging from 1,000 to 7,000 ft³/s. For each cell, the D values represent the diameter less than which a grain would be predicted to be mobilized at the simulated streamflow. Any larger grain would be stable at that streamflow. This method is only applicable to noncohesive granular material, which field observations indicate constitutes most of the river bed in the study reach.

Comparisons between the observed and modeled WSE profiles for simulations using different channel roughness values are shown in figure 5A and B for the summer 2024 streamflow simulations. From 0 to 19,500 ft downstream from the Trowbridge Dam, the water surface slope was about 0.003. The water surface slope decreased to about 0.001 from 19,500 to 30,000 ft and then relaxed even farther downstream from this point because of the effect of backwater from the Allegan City Dam. All the modeled water surface profiles matched the general shape of the observed water surface profile (fig. 5A) and had an RMSE less than 0.35 ft (table 2). The model slightly underpredicted WSEs from 16,000 to 24,000 ft and then slightly overpredicted WSEs between 24,000 and 40,000 ft, although the exact magnitude and direction of the residuals varied as a function of the model channel roughness parameterization. The largest discrepancies between modeled and observed WSEs were at riffles, where local WSE slopes were relatively steep compared to the reach average. WSEs generated by the model with the smallest channel roughness parameterization (n=0.025) were generally less than the observed WSEs, whereas WSEs generated by the model with the highest channel roughness parameterization (n=0.035) were generally higher than the observed WSEs. The models with channel roughness parameterization n values of 0.0315 and 0.0335 each yielded 0.20-ft RMSEs, the smallest of the tested parameterizations (table 2). The n=0.025 model had a −0.23-ft WSE bias, and the n=0.035 model had a 0.10-ft WSE bias; the n=0.0315 model had a WSE bias of only −0.01 ft.

All the model parameterizations underpredicted summer 2024 velocities relative to the ADCP-measured values (table 2 and fig. 5C and D). The RMSE between the point ADCP measurements and modeled velocities ranged from 0.59 to 0.65 foot per second (ft/s), and the bias ranged from −0.06 ft/s for the n=0.025 channel roughness parameterization model to −0.38 ft/s for the n=0.035 channel roughness parameterization model (table 2). The n=0.025 channel roughness parameterization model had the smallest RMSE and bias between the observed and modeled cross-sectional average velocities at 0.21 and −0.02 ft/s, whereas the n=0.035 channel roughness parameterization model had the largest at 0.36 and −0.35 ft/s (table 2). The n=0.025 channel roughness parameterization model tended to overpredict cross-sectional average velocities upstream from 18,000 ft, whereas other roughness parameterizations slightly underpredicted velocities in this region. Downstream from about 18,000 ft, all the model parameterizations underpredicted cross-sectional average velocities. The n=0.0315 channel roughness parameterization model was chosen as the optimal parameterization for the quasi-steady streamflow simulations from 1,000 to 3,000 ft³/s based on its minimal WSE bias.

The n=0.03, n=0.0315, and n=0.0335 channel roughness parameterization models were tested for the spring 2023, winter 2024, and spring 2025 streamflow scenarios to evaluate the potential for stage-dependent roughness at higher WSEs relative to the summer 2024 streamflow scenario. As WSEs increase, decreasing composite roughness values are commonly observed (Arcement and Schneider, 1989). Comparisons between the observed and modeled water surface profiles are shown in figure 6A and B for the spring 2025 streamflow simulations. The water surface slope from 0 to 19,500 ft downstream from the Trowbridge Dam decreased to about 0.002, and the water surface slope from 19,500 to 30,000 ft remained about 0.001. In contrast to WSE observations during the low-flow summer 2024 period, the spring 2025 observations indicate that the water surface slope remained about 0.001 nearly to the downstream extent of the study reach. The differences in the modeled WSE profiles were minor; the n=0.03 and n=0.0315 channel roughness parameterization models yielded WSE RMSEs of 0.32 and biases of −0.05 ft and 0.06 ft, respectively (table 3). WSEs were generally overpredicted upstream from 15,000 ft downstream from the Trowbridge Dam, underpredicted from 15,000 to 32,000 ft downstream from the Trowbridge Dam, and overpredicted for the remainder of the study reach. Similar to the summer 2024 simulations, all the channel roughness parameterizations yielded modeled velocities less than the measured velocities for the spring 2025 simulations (fig. 6C and D). The n=0.03 channel roughness parameterization model had the smallest point velocity RMSE and bias, at 0.98 ft/s and −0.39 ft/s, respectively (table 3). The model differed in skill at matching the cross section and longitudinal point velocities, with the n=0.03 channel roughness parameterization having an RMSE of 1.09 ft/s and bias of −0.06 ft/s for cross-section points, and an RMSE of 0.88 ft/s and bias of −0.73 ft/s for longitudinal points. The larger negative bias associated with the longitudinal points is potentially caused by the model not resolving the highest channel velocities because of resolution limitations, or the faster boat travel speed during longitudinal measurements affecting the measured velocities. The n=0.03 channel roughness parameterization also yielded the smallest RMSE and bias values for the cross-sectional average velocity comparisons, at 0.27 ft/s and −0.10 ft/s (table 3), respectively. Average absolute differences between the modeled and measured point velocities and cross-sectional average velocities increased slightly from the low-flow to the bankfull-flow models.

The n=0.0335 and n=0.0315 channel roughness parameterization models overpredicted WSEs at the streamgage for the spring 2023 and winter 2024 streamflow scenarios (fig. 7A and B) with RMSE values of 0.16 and 0.32 ft for the spring 2023 streamflow scenario and 0.14 and 0.28 ft for the winter 2024 streamflow scenario for the n=0.0315 and n=0.0335 channel roughness models, respectively. The n=0.03 channel roughness model indicated close visual correspondence with the observed WSEs at the streamgage and yielded an RMSE of 0.04 ft for the spring 2023 and winter 2024 streamflow scenarios. Based on these results, a channel roughness of 0.03 was selected for the quasi-steady streamflow scenarios from 4,000 to 7,000 ft³/s. Distributed WSE and velocity observations were not available during any of the simulated high-flow periods, limiting our ability to validate high-flow simulations beyond the immediate area near the streamgage. The parameterizations for the quasi-steady streamflow scenarios are provided in table 4.

Maps of modeled flow velocities for the range of streamflow scenarios are provided in appendix 1 (figs. 1.1–1.7). A longitudinal profile of modeled cross-sectional average channel velocities smoothed with a three-sample rolling average for the quasi-steady streamflow scenarios is shown in figure 8A. Cross-sectional average channel velocities were the smallest for the 1,000-ft³/s scenario, which is similar to the summer 2024 streamflow scenario conditions, and cross-sectional average channel velocities were generally greatest for the 7,000-ft³/s scenario. The longitudinal patterns of cross-sectional average channel velocity are generally similar among the seven streamflow scenarios, having high velocities from 500 to 3,600 ft below the Trowbridge Dam, alternating high and low velocities associated with riffle and pool morphology from 3,600 to 18,000 ft below the Trowbridge Dam, and generally smaller and less variable velocities downstream from this distance. For the 4,000-ft³/s streamflow scenario, cross-sectional average channel velocities in the 500–3,600-ft reach were about 4 ft/s, and riffle cross-sectional average velocities were between 4 and 5 ft/s. Cross-sectional average channel velocities decreased to about 2.5–3 ft/s from 18,000 to 23,000 ft because of the valley constriction about 1,000 ft upstream from the Bridge Road crossing. Below the 23,000-ft reach, cross-sectional average channel velocities were variable but generally decreased from 3 to about 2 ft/s.

The Michigan Department of Natural Resources uses guideline flow velocity thresholds for fish passage of 3 and 4 ft/s for Percina caprodes (logperch) and Micropterus dolomieu (smallmouth bass), respectively (M. Diana, Michigan Department of Natural Resources, oral commun., 2024). These thresholds are displayed in figure 8A. In the 4,000-ft³/s scenario, the cross-sectional average channel velocities in the upper reaches of the river upstream from 18,000 ft below the Trowbridge Dam generally exceeded the 3-ft/s velocity threshold associated with logperch, but the 4-ft/s velocity threshold used for smallmouth bass was only exceeded at riffles. Downstream from the 18,000-ft reach, the threshold for both species was generally not exceeded.

Maps of modeled flow depths are provided in appendix 2 (figs. 2.1–2.7). At 1,000 ft³/s, flow is contained within the channel, and the large oxbow about 35,000 ft downstream from the Trowbridge Dam is inundated (app. 2, fig. 2.1). As streamflow increases to 3,000 ft³/s, water enters meander scars and other low-lying areas on the floodplain from 9,000 to 24,000 ft downstream from the Trowbridge Dam and begins to fill the narrow valley 30,000 ft downstream from the dam. Inundation in the reach from 9,000 to 24,000 ft expands at 4,000 ft³/s streamflow, especially in the reach from 15,000 to 24,000 ft (app. 2, fig. 2.4). Streamflows greater than 4,000 ft³/s lead to continuous inundation in this region, and the valley downstream from 25,000 ft becomes completely inundated. Additionally, for streamflows of 6,000–7,000 ft³/s, water begins to flow out of the channel on the river right bank about 5,000 ft downstream from the Trowbridge Dam, bypassing the major bend in the river near 6,000 ft. Planform heterogeneity in the modeled velocities at high streamflows is substantial, with smaller velocities toward the channel margins, in the floodplain, and in secondary channels (app. 1, figs. 1.4–1.7). Fish may seek refuge in these low velocity regions during high-flow events to minimize energy expenditures and then return to main channel habitats as floods recede. Increases in the downstream boundary water elevation would cause increases in inundation depths and extents in the lower reaches of the model and alter velocity distributions.

Maps of the modeled basal shear stresses are provided in appendix 3 (figs. 3.1–3.7). Modeled shear stresses within the channel ranged from 0 to 0.81 pound per square foot (lb/ft²; arithmetic mean [µ]: 0.050, standard deviation [σ]: 0.062) in the 1,000-ft³/s scenario and from 0 to 0.92 lb/ft² (µ: 0.13, σ: 0.062) in the 7,000-ft³/s scenario. At the approximate bankfull flow of 4,000 ft³/s, shear stress ranged from 0 to 0.89 lb/ft² (µ: 0.10, σ: 0.086).

Maps of modeled minimum stable grain sizes are provided in appendix 4 (figs. 4.1–4.7). Values within the channel ranged from 0.01 to 43.3 mm (µ: 2.98, σ: 3.31) in the low-flow 1,000-ft³/s scenario (app. 4, fig. 4.1). Grains in the fine gravel size range and coarser (4–64 mm) were stable throughout most of the reach at this streamflow. Sand and silt grains were predicted to be mobile through most of the reach, even under low-flow conditions; however, in certain pools, channel margins, and the lower reach affected by the Allegan City Dam impoundment, sand was predicted to be stable. In small areas along channel margins and in off-channel areas in the impoundment-affected zone, silt-sized particles were immobile at this streamflow. Cross-sectional averages of estimated channel minimum stable grain size are variable but indicate a general decrease along the longitudinal profile from 0 to 23,000 ft downstream from Trowbridge Dam, at which point the trend flattens out (fig. 8B).

At the approximate bankfull streamflow of 4,000 ft³/s, minimum stable grain size ranged from 0.01 to 47 mm (µ: 5.72, σ: 4.56; app. 4, fig. 4.4). Grains finer than gravel (D less than 2 mm) were predicted to be mobile through the entire main channel under this streamflow condition, including through the main channel of the impoundment. Areas of predicted sand and silt stability were within side channels and some channel margins in the upper reaches of the study area, and in broader off-channel areas with predicted overbank flooding in the lower reaches.

In the high-flow scenario of 7,000 ft³/s, minimum stable grain sizes ranged from 0.01 to 49.3 mm (µ: 7.20, σ: 6.08; app. 4, fig. 4.7). Fine and medium gravel (D=4–16 mm) were predicted to be transported through most of the main channel, and coarse gravel was predicted to be mobile in riffles at this streamflow. The floodplain was almost completely inundated in this simulation, and substantial zones of the floodplain had predicted stability of grains in the sand and silt size range.

Minimum stable grain size results were compared with substrate size measurements made in the study reach in 2023 and 2024 (Vaughan and others, 2023; Roland and others, 2025) to evaluate the degree to which existing substrates may be mobile under a range of streamflow conditions. A total of 2 pebble counts consisting of 100 grain size observations were done on riffles within the study area, along with 3 reach-composite counts of 50, 76, and 51 observations evenly spaced along reaches 0.87-, 0.75-, and 0.75-mi long, respectively.

Observations in the reach-composite pebble counts were geolocated and could therefore be compared directly to the raster outputs. For each streamflow scenario, a stability index (relative substrate stability [RSS]) was computed for each grain size observation (171 total observations across three study reaches) as the ratio of the modeled shear stress at that location to the critical shear stress computed for the grain. RSS values greater than 1 indicate shear stress greater than the critical shear stress for a grain of the observed size, whereas values less than 1 indicate insufficient shear stress to mobilize the grain. The reach-composite observations consisted of one randomly selected grain at each preselected sample location. The randomly selected grains are not a representative grain size selected from a distribution (for example, the median, which is commonly used for bed material transport modeling). Therefore, results should be interpreted with caution because any particular observation (and therefore, substrate stability metric) may not be fully representative of the grain size distribution at the sample location.

For the low-flow 1,000-ft³/s scenario, about the top quartile of observed grains across the three reach-composite pebble counts had estimated RSS values greater than 1 (fig. 9A). The median RSS value at that streamflow was 0.41. RSS values increased steadily with increasing streamflow until the bankfull-flow scenario of 4,000 ft³/s, at which point they continued to increase, but more gradually (fig. 9A). At streamflows greater than bankfull, the bed shear stress increases more gradually with increasing streamflow as water spreads out across the floodplain. The median RSS value for the 4,000-ft³/s scenario was 0.81, indicating that slightly less than one-half of the observed grains were predicted to be mobile at the bankfull streamflow. For the high-flow scenario, the median RSS value was 0.95.

RSS values had a strong negative relation with grain size (fig. 9B). For the 4,000-ft³/s scenario, most grains smaller than 8 mm (fine gravel and smaller) were estimated to be mobile (RSS greater than 1), whereas larger grains were predicted to remain stable at the bankfull streamflow.