Reconstructing the early 19th‐century Waal River by means of a 2D physics‐based numerical model

Suspended‐sediment concentration data are a missing link in reconstructions of the River Waal in the early 1800s. These reconstructions serve as a basis for assessing the long‐term effects of major interventions carried out between 1850 AD and the early 20th century. We used a 2D physics‐based morphodynamic model accounting for the influence of floodplain vegetation to fill in this gap. Historical discharge hydrographs were derived from a correlation between flow discharge records at Cologne and water level measurements of the Rhine branches in the Netherlands, taking into account the discharge distribution between the branches. Historical floodplain sedimentation rates were estimated using old cartographic information and recent geomorphologic field work. The computed historical sedimentation rates are found to be within the range of measured data, which suggests that fine suspended sediment concentrations in the early 1800s were comparable to contemporary ones. The computations show also how vegetation enhances the formation of natural levees close to the main channel and at the same time decreases the sedimentation rates in farther areas of the floodplain. A sensitivity analysis shows suspended sediment composition to have a strong influence on the resulting quantities and patterns of floodplain deposition. The reconstruction has also provided validation of the modelling tools to reproduce the effects of vegetation on sediment dynamics, enabling their implementation to study other cases. Copyright © 2010 John Wiley & Sons, Ltd.     

Stability,morphology and surface grain size patterns of channel bifurcation in gravel–cobble bedded anabranching rivers

This study presents the first detailed field‐based analysis of the morphology of bifurcations within anabranching cobble–gravel rivers. Bifurcations divide the flow of water and sediment into downstream anabranches, thereby influencing the characteristics of the anabranches and the longevity of river islands. The history, morphology, bed grain size, and flow vectors at five bifurcations on the Renous River, New Brunswick, Canada, were studied in detail. The angles of bifurcations within five anabranching rivers in the Miramichi basin were investigated. The average bifurcation angle was 47°, within the range of values cited for braided river bifurcations. Bifurcation angle decreased when anabranches were of similar length. Shields stresses in channels upstream of bifurcations were lower than reported values for braided rivers. Stable bifurcations displayed lower Shields stresses than unstable bifurcations, contrary to experimental results from braided river bifurcations. Bifurcations in anabranching rivers are stabilized by vegetation that slows channel migration and helps to maintain a uniform upstream flow field. The morphology of stable bifurcations enhances their stability. A large bar, shaped like a shallow ramp that increases in elevation to floodplain level, forms at stable bifurcations. Floodplains at stable bifurcations accrete upstream at rates between 0·9 and 2·5 m a^?1. Bars may also form within the entrance of an anabranch downstream of the bifurcation node. These bars are associated with bifurcation instability, forming after a period of stability or an avulsion. Channel abandonment occurs when a bar completely blocks the entrance to one anabranch. The stability of channels upstream of bifurcations and the location of bars at bifurcations influence bifurcation stability and the maintenance of river anabranching in the long term. Copyright © 2006 John Wiley & Sons, Ltd.     

Effects of sediment grain size and channel slope on the stability of river bifurcations

Channel bifurcations can be found in river network systems from high gradient gravel-bed rivers to fine-grained low gradient deltas. In these systems, bifurcations often evolve asymmetrically such that one downstream channel silts up and the other deepens and, in most cases, they eventually avulse. Past analytical and numerical studies showed that symmetric bifurcations are unstable in high and low Shields stress conditions resulting in asymmetric bifurcations and avulsion, while they can be stable in the mid-Shields range, but this range is smaller for larger width-to-depth ratio. Here, using a one-dimensional (1D) numerical model, we show that effects of sediment grain size and of channel slope are much larger than expected for low-gradient systems when a sediment transport relation is used that separates between bedload and suspended load transport. We found that the range of Shields stress conditions with unstable symmetric bifurcations expanded for lower channel slopes and for finer sediment. In high sediment mobility, suspended load increasingly dominates the sediment transport, which increases the sediment transport nonlinearity and lowers the relative influence of the stabilizing transverse bedslope-driven flux. Contrary to previous works, we found another stable symmetric solution in high Shields stress, but this only occurs in the systems with small width-to-depth ratio. This indicates that suspended load-dominated bifurcations of lowland rivers are more likely to develop into highly asymmetric channels than previously thought. This explains the tendency of channel avulsion observed in many systems.     

Effects of helical flow in one‐dimensional modelling of sediment distribution at river bifurcations

Complex flow processes at river bifurcations and the influence of the layout of a bifurcation make it difficult to predict sediment distribution over the downstream branches in case bedload transport dominates. In one‐dimensional models we need a nodal point relationship that prescribes the distribution of sediment over the downstream branches. We have identified which factors need to be included in such a relationship for the division of bedload transport at bifurcations. Next, irrotational flow theory for idealized geometries has been used to derive a simple physics‐based nodal point relationship that accounts for the effects of helical flow in the situation that a channel takes off under an angle from a straight main channel. This first step towards a complete nodal point relationship is applicable to bedload transport situations if the flow is clearly curved and if there is no pronounced bed topography. The relationship has been tested against data from a unique set of laboratory measurements, numerical data and data from a scale model of the Rhine bifurcation at Pannerden in the Netherlands. We find that the derived model yields a reasonable prediction of the sediment division over the downstream branches, and yields better predictions than the Wang et al. model for the situation considered. Considering the relative complexity and limited accuracy of the nodal point relationship for the effect of helical flow alone, however, we conclude thatderiving a practical physics‐based 1‐D relationship including all relevant processes is not feasible. We therefore recommend 2‐D or 3‐D modelling for all cases in general where morphological evolution depends on the division of bedload transport at bifurcations. Copyright © 2012 John Wiley & Sons, Ltd.     

Two‐dimensional and three‐dimensional computational models in hydrodynamic and morphodynamic reconstructions of a river bend: sensitivity and functionality

This study assesses hydrodynamic and morphodynamic model sensitivity and functionality in a curved channel. The sensitivity of a depth‐averaged model to user‐defined parameters (grain size, roughness, transverse bed slope effect, transport relations and secondary flow) is tested. According to the sensitivity analysis, grain size, transverse bed slope effect and sediment transport relations are critical to simulated meander bend morphodynamics. The parametrization of grain size has the most remarkable effect: field‐based grain size parametrization is necessary in a successful morphodynamic reconstruction of a meander bend. The roughness parametrization method affects the distribution of flow velocities and therefore also morphodynamics. The combined effect of various parameters needs further research. Two‐dimensional (2D) and three‐dimensional (3D) reconstructions of a natural meander bend during a flood event are assessed against field measurements of acoustic Doppler current profiler and multi‐temporal mobile laser scanning data. The depth‐averaged velocities are simulated satisfactorily (differences from acoustic Doppler current profiler velocities 5–14%) in both 2D and 3D simulations, but the advantage of the 3D hydrodynamic model is unquestionable because of its ability to model vertical and near‐bed flows. The measured and modelled near‐bed flow, however, differed notably from each other's, the reason of which was left open for future research. It was challenging to model flow direction beyond the apex. The 3D flow features, which also affected the distribution of the bed shear stress, seem not to have much effect on the predicted morphodynamics: the 2D and 3D morphodynamic reconstructions over the point bar resembled each other closely. Although common features between the modelled and measured morphological changes were also found, some specific changes that occurred were not evident in the simulation results. Our results show that short‐term, sub‐bend scale morphodynamic processes of a natural meander bend are challenging to model, which implies that they are affected by factors that have been neglected in the simulations. The modelling of short‐term morphodynamics in natural curved channel is a challenge that requires further study. Copyright © 2014 John Wiley & Sons, Ltd.     

A comparison of one‐ and two‐dimensional approaches to modelling flood inundation over complex upland floodplains

A much understudied aspect of flood inundation is examined, i.e. upland environments with topographically complex floodplains. Although the presence of high‐resolution topographic data (e.g. lidar) has improved the quality of river flood inundation predictions, the optimum dimensionality of hydraulic models for this purpose has yet to be fully evaluated for situations of both topographic and topological (i.e. the connectivity of floodplain features) complexity. In this paper, we present the comparison of three treatments of upland flood inundation using: (a) a one‐dimensional (1D) model (HEC‐RAS v. 3·1·2) with the domain defined as series of extended cross‐sections; (b) the same 1D model, but with the floodplain defined by a series of storage cells, hydraulically connected to the main river channel and other storage cells on the floodplain according to floodplain topological characteristics; (c) a two‐dimensional (2D) diffusion wave treatment, again with explicit representation of floodplain structural features. The necessary topographic and topological data were derived using lidar and Ordnance Survey Landline data. The three models were tested on a 6 km upland reach of the River Wharfe, UK. The models were assessed by comparison with measured inundation extent. The results showed that both the extended cross‐section and the storage cell 1D modes were conceptually problematic. They also resulted in poorer model predictions, requiring incorrect parameterization of the main river to floodplain flux in order to approach anything like the level of agreement observed when the 2D diffusion wave treatment was assessed. We conclude that a coupled 1D–2D treatment is likely to provide the best modelling approach, with currently available technology, for complex floodplain configurations. Copyright © 2007 John Wiley & Sons, Ltd.     

A two‐dimensional morphodynamic model of gravel‐bed river with floodplain vegetation

Artificially straight river channels tend to be unstable, and ultimately develop into river meanders through bank erosion and point‐bar deposition. In this paper account is taken of the effects of riparian and floodplain vegetation on bank strength, floodplain flow resistance, shear stress partitioning, and bedload transport. This is incorporated into an existing 2D hydrodynamic‐morphological model. By applying the new model to an initially straight and single‐threaded channel, the way that its planform and cross‐sectional geometry evolve for different hydraulic and floodplain vegetation conditions is demonstrated. The results show the formation and upstream migration of gravel bars, confluence scouring and the development of meandering and braiding channel patterns. In cases where the channel becomes unstable, the instability grows out of bar formation. The resulting braiding patterns are similar to analytical results. The formation of a transition configuration requires a strong influence from vegetation. Copyright © 2010 John Wiley & Sons, Ltd.     

Reach‐scale channel geometry of a mountain river

Mountain rivers can be subject to strong constraints imposed by changes in gradient and grain size supplied by processes such as glaciation and rockfall. Nonetheless, adjustments in the channel geometry and hydraulics of mountain rivers at the reach scale can produce discernible patterns analogous to those in fully alluvial rivers. Mountain rivers can differ in that imposed reach‐scale gradient is an especially important control on reach‐scale channel characteristics, as indicated by examination of North St Vrain Creek in Colorado. North St Vrain Creek drains 250 km² of the Rocky Mountains. We used 25 study reaches within the basin to examine controls on reach‐scale channel geometry. Variables measured included channel geometry, large woody debris, grain size, and mean velocity. Drainage area at the study reaches ranged from 2·2 to 245 km², and gradient from 0·013 to 0·147 m m^?1. We examined correlations among (1) potential reach‐scale response variables describing channel bankfull dimension and shape, hydraulics, bedform wavelength and amplitude, grain size, ?ow resistance, standard deviation of hydraulic radius, and volume of large woody debris, and (2) potential control variables that change progressively downstream (drainage area, discharge) or that are likely to re?ect a reach‐speci?c control (bed gradient). We tested the hypothesis that response variables correlate most strongly with local bed gradient because of the segmented nature of mountain channels. Results from simple linear regression analyses indicate that most response variables correlate best with gradient, although channel width and width/depth ratio correlate best with discharge. Multiple regression analyses using Mallow's C_p selection criterion and log‐transformation of all variables produced similar results in that most response variables correlate strongly with gradient. These results suggest that the hypothesis is partially supported: channel bed gradient is likely to be a good predictor for many reach‐scale response variables along mountain rivers, but discharge is also an important predictor for some response variables. Copyright © 2004 John Wiley & Sons, Ltd.     

Investigation of spatially distributed braided river flows using a two‐dimensional hydraulic model

This paper reports the application of a two‐dimensional hydraulic model to a braided reach of the Avoca River, New Zealand. Field measurements of water surface elevation, depth and velocity obtained at low flow were used to validate the model and to optimize the parameterization of bed friction. The main systematic trends in the measured flow variables are reproduced by the model. However, field data are characterized by greater spatial variability than model output reflecting differences in the scale of processes measured in the field and represented by the model. Additional model runs were conducted to simulate flow patterns within the study reach at five higher discharges. The purpose of these simulations was to evaluate the potential for using two‐dimensional hydraulic models to quantify the reach‐scale hydraulic characteristics of braided rivers and their dependence on discharge. Changes in flow depth and velocity with increasing discharge exhibit trends that are consistent with the results of previous field investigations, although the tendency for the wetted area of the braidplain within particular depth and velocity categories to remain fixed as discharge rises, as has been noted for several braided rivers in New Zealand, was not observed. Modelled shear stress frequency distributions fit gamma functions that incorporate a distribution shape parameter, the value of which follows clear systematic trends with rising discharge. These results illustrate both the problems of, and potential for, using two‐dimensional hydraulic models in braided river applications. This leads to something of a paradox in that while such models provide a means of generating hydraulic information that would be difficult to obtain in the field at an equivalent spatial resolution, they are, due to the problems inherent to data collection, difficult to validate conclusively. Despite this limitation, the application of spatially distributed models to investigate relationships between discharge and reach‐scale form and process variables appears to have considerable potential. Copyright © 2003 John Wiley & Sons, Ltd.     

Impact of dissipation and dispersion terms on simulations of open‐channel confluence flow using two‐dimensional depth‐averaged model

The flow patterns in confluence channel and the simulation of confluence flow are more complex than that in straight channel. Additional terms in the momentum equations, i.e. dissipation terms, denoting the impact of turbulence, and dispersion terms, denoting the vertical non‐uniformity of velocity, show great impacts on the accuracy of numerical simulations. The dissipation terms, i.e. the product of eddy viscosity coefficient and velocity gradient, are much larger than those of the flow in straight channel. In this study, the zero equation model and the depth‐averaged k‐ε model are used to analyse the impact of eddy viscosity. Meanwhile, the dispersion terms in the momentum equation, depending on the vertical non‐uniformity of velocity, are usually neglected in routine simulation. With the use of detailed experimental data for verification, this study presents the distribution of parameters of vertical non‐uniformity and the intimated connection between non‐uniformity parameters and accuracy of numerical simulations of confluence flow with depth‐averaged models. The results present that simulation accuracy of confluence flow is very sensitive to the turbulence modes, which cannot be handled by normal, simple turbulence model. On the contrary, the impact of dispersion terms is both flow‐condition‐dependent and place‐dependent, and such impact is negligible when secondary circulation is weak. The results indicate the key elements in modelling confluence flow and are helpful for selecting suitable numerical model and solving engineering problems encountered in confluence channel. Copyright © 2013 John Wiley & Sons, Ltd.     

Time–space fractional governing equations of one‐dimensional unsteady open channel flow process: Numerical solution and exploration

Although fractional integration and differentiation have found many applications in various fields of science, such as physics, finance, bioengineering, continuum mechanics, and hydrology, their engineering applications, especially in the field of fluid flow processes, are rather limited. In this study, a finite difference numerical approach is proposed to solve the time–space fractional governing equations of 1‐dimensional unsteady/non‐uniform open channel flow process. By numerical simulations, results of the proposed fractional governing equations of the open channel flow process were compared with those of the standard Saint‐Venant equations. Numerical simulations showed that flow discharge and water depth can exhibit heavier tails in downstream locations as space and time fractional derivative powers decrease from 1. The fractional governing equations under consideration are generalizations of the well‐known Saint‐Venant equations, which are written in the integer differentiation framework. The new governing equations in the fractional‐order differentiation framework have the capability of modelling nonlocal flow processes both in time and in space by taking the global correlations into consideration. Furthermore, the generalized flow process may possibly shed light on understanding the theory of the anomalous transport processes and observed heavy‐tailed distributions of particle displacements in transport processes.     

Sensitivity of simulated flow fields and bathymetries in meandering channels to the choice of a morphodynamic model

Morphodynamic models are used by river practitioners and scientists to simulate geomorphic change in natural and artificial river channels. It has long been recognized that these models are sensitive to the choice of parameter values, and proper calibration is now common practice. This paper investigates the less recognized impact of the choice of the model itself. All morphodynamic models purport to simulate the same flow and sediment dynamics, often relying on the same governing equations. Yet in solving these equations, the models have different underlying assumptions, for example regarding spatial discretization, turbulence, sediment inflow, lateral friction, and bed load transport. These differences are not always considered by the average model user, who might expect similar predictions from calibrated models. Here, a series of numerical simulations in meandering channels was undertaken to test whether six morphodynamic codes (BASEMENT, CCHE‐2D, NAYS, SSIIM‐1, TELEMAC‐2D and TELEMAC‐3D) would yield significantly different equilibrium bathymetries if subjected to identical, initial flow conditions. We found that, despite producing moderately similar velocity patterns on a fixed‐flat bed (regression coefficient r of 0.77 ± 0.20), the codes disagree substantially with respect to simulated bathymetries (r = 0.49 ± 0.31). We relate these discrepancies to differences in the codes' assumptions. Results were configuration specific, i.e. codes that perform well for a given channel configuration do not necessarily perform well with higher or lower sinuosity configurations. Finally, limited correlation is found between accuracy and code complexity; the inclusion of algorithms that explicitly account for the effects of local bed slope and channel curvature effects on transport magnitude and direction does not guarantee accuracy. The range of solutions obtained from the evaluated codes emphasizes the need for carefully considering the choice of code. We recommend the creation of a central repository providing universal validation cases and documentation of recognized fluvial codes in commonly studied fluvial settings. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of hydraulic geometry between sand‐ and gravel‐bed rivers in relation to channel pattern discrimination

A comparison has been made between the hydraulic geometry of sand‐ and gravel‐bed rivers, based on data from alluvial rivers around the world. The results indicate a signi?cant difference in hydraulic geometry among sand‐ and gravel‐bed rivers with different channel patterns. On this basis, some diagrams for discrimination of meandering and braided channel patterns have been established. The relationships between channel width and water discharge, between channel depth and water discharge, between width–depth ratio and water discharge and between channel slope and water discharge can all be used for channel pattern discrimination. The relationship between channel width and channel depth can also be used for channel pattern discrimination. However, the accuracy of these relationships for channel pattern discrimination varies, and the depth–discharge relationship is a better discriminator of pattern type than the classic slope–discharge function. The cause for this difference has been explained qualitatively. To predict the development of channel patterns under different natural conditions, the pattern discriminator should be searched on the basis of independent or at least semi‐independent variables. The relationship between stream power and bed material grain size can be used to discriminate channel patterns, which shows a better result than the discriminator using the slope–discharge relationship. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulation of three‐dimensional flow hydraulics in a braided channel

Results are presented from a numerical simulation of three‐dimensional flow hydraulics around a mid‐channel bar carried out using the FLUENT/UNS computational fluid dynamics (CFD) software package. FLUENT/UNS solves the three‐dimensional Reynolds‐averaged form of the Navier–Stokes equations. Turbulence closure is achieved using a RNG k–ϵ model. Simulated flow velocities are compared with measured two‐dimensional velocities (downstream and cross‐stream) obtained using an electromagnetic current meter (ECM). The results of the simulation are qualitatively consistent with the flow structures observed in the field. Quantitative comparison of the simulated and measured velocity magnitudes indicates a strong positive correlation between the two (r=0·88) and a mean difference of 0·09 m s⁻¹. Deviations between simulated and measured velocities may be identified that are both random and systematic. The former may reflect a number of factors including subgrid‐scale natural spatial variability in flow velocities associated with local bed structures and measurement uncertainty resulting from problems of ECM orientation. Model mesh configuration, roughness parameterization and inlet boundary condition uncertainty may each contribute to systematic differences between simulated and measured flow velocities. These results illustrate the potential for using CFD software to simulate flow hydraulics in natural channels with complex configurations. They also highlight the need for detailed spatially distributed datasets of three‐dimensional flow variables to establish the accuracy and applicability of CFD software. Copyright © 1999 John Wiley & Sons, Ltd.     

Modification and testing of a one‐dimensional energy and mass balance model for supraglacial snowpacks

A one‐dimensional energy and mass balance snow model (SNTHERM) has been modified for use with supraglacial snowpacks and applied to a point on Haut Glacier d'Arolla, Switzerland. It has been adapted to incorporate the underlying glacier ice and a site‐specific, empirically derived albedo routine. Model performance was tested against continuous measurements of snow depth and meltwater outflow from the base of the snowpack, and intermittent measurements of surface albedo and snowpack density profiles collected during the 1993 and 2000 melt seasons. Snow and ice ablation was simulated accurately. The timing of the daily pattern of meltwater outflow was well reproduced, although magnitudes were generally underestimated, possibly indicating preferential flow into the snowpack lysimeter. The model was used to assess the quantity of meltwater stored temporally within the unsaturated snowpack and meltwater percolation rates, which were found to be in agreement with dye tracer experiments undertaken on this glacier. As with other energy balance studies on alpine valley glaciers, the energy available for melt was dominated by net radiation (64%), with a sizable contribution from sensible heat flux (36%) and with a negligible latent heat flux overall, although there was more complex temporal variation on diurnal timescales. A basic sensitivity analysis indicated that melt rates were most sensitive to radiation, air temperature and snowpack density, indicating the need to accurately extrapolate/interpolate these variables when developing a spatially distributed framework for this model. Copyright © 2008 John Wiley & Sons, Ltd.     

Geostatistical analysis of ground‐survey elevation data to elucidate spatial and temporal river channel change

A digital elevation model (DEM) of a fluvial environment represented landform surface variability well and provided a medium for monitoring morphological change over time. Elevation was measured above an arbitrary datum using a ground‐based three‐dimensional tacheometric survey in two reaches of the River Nent, UK, in July 1998, October 1998 (after flood conditions) and June 1999. A detailed geostatistical analysis of the elevation data was used to model the spatial variation of elevation and to produce DEMs in each reach and for each survey period. Maps of the difference in elevation were produced and volumetric change was calculated for each reach and each survey period. The parameters of variogram models were used to describe the morphological character of each reach and to elucidate the linkages between process and the form of channel change operating at different spatial and temporal scales. The analysis of channel change on the River Nent shows the potential of geostatistics for investigating the magnitude and frequency of geomorphic work in other rivers. A flood modified the channel features, but low magnitude and high frequency flows rationalized the morphology. In spite of relatively small amounts of net flux the channel features changed as a consequence of the reworking of existing material. The blocking of chute entrances and redirection of the channel had a considerable effect on the behaviour of the channel. Such small changes suggested that the distributary system was sensitive to variation in sediment regime. Plots of the kriging variances against sampling intervals were used to quantify the temporal variation in sampling redundancy (ranging between ?11 per cent and +93 per cent). These curves illustrated the importance of bespoke sampling designs to reduce sampling effort by incorporating anisotropic variation in space and geomorphic information on flow regime. Variation in the nugget parameter of the variogram models was interpreted as sampling inaccuracy caused by variability in particle size and is believed to be important for future work on surface roughness. Copyright © 2003 John Wiley & Sons, Ltd.     

Spatial variability of three‐dimensional Reynolds stresses in a developing channel bend

Experimental results of the mean flow field and turbulence characteristics for flow in a model channel bend with a mobile sand bed are presented. Acoustic Doppler velocimeters (ADVs) were used to measure the three components of instantaneous velocities at multiple cross sections in a 135° channel bend for two separate experiments at different stages of clear water scour conditions. With measurements at multiple cross sections through the bend it was possible to map the changes in both the spatial distribution of the mean velocity field and the three Reynolds shear stresses. Turbulent stresses are known to contribute to sediment transport and the three‐dimensionality inherent to flow in open channel bends presents a useful case for determining specific relations between three‐dimensional turbulence and sediment entrainment and transport. These measurements will also provide the necessary data for validating numerical simulations of turbulent flow and sediment transport. The results show that the magnitude and distribution of three‐dimensional Reynolds stresses increase through the bend, with streamwise‐cross stream and cross stream‐vertical components exceeding the maximum principal Reynolds stress through the bend. The most intriguing observation is that near‐bed maximum positive streamwise‐cross stream Reynolds stress coincides with the leading edge of the outer bank scour hole (or thalweg), while maximum cross stream‐vertical Reynolds stress (in combination with high negative streamwise‐cross stream Reynolds stress near the bend apex) coincides with the leading edge of the inner bank bar. Maximum Reynolds stress and average turbulent kinetic energy appear to be greater and more localized over the scour hole before final equilibrium scour is reached. This suggests that the turbulent energy in the flow is higher while the channel bed is developing, and both lower turbulent energy and a broader distribution of turbulent stresses near the bed are required for cessation of particle mobilization and transport. Copyright © 2010 John Wiley & Sons, Ltd.     

Assessing the effect of vegetation‐related bank strength on channel morphology and stability in gravel‐bed streams using numerical models

Bank strength due to vegetation dominates the geometry of small stream channels, but has virtually no effect on the geometry of larger ones. The dependence of bank strength on channel scale affects the form of downstream hydraulic geometry relations and the meandering‐braiding threshold. It is also associated with a lateral migration threshold discharge, below which channels do not migrate appreciably across their floodplains. A rational regime model is used to explore these scale effects: it parameterizes vegetation‐related bank strength using a dimensionless effective cohesion, C_r*. The scale effects are explored primarily using an alluvial state space defined by the dimensionless formative discharge, Q*, and channel slope, S, which is analogous to the Q–S diagrams originally used to explore meandering‐braiding thresholds. The analyses show that the effect of vegetation on both downstream hydraulic geometry and the meandering‐braiding threshold is strongest for the smallest streams in a watershed, but that the effect disappears for Q* > 10⁶. The analysis of the migration threshold suggests that the critical discharge ranges from about 5 m³/s to 50 m³/s, depending on the characteristic rooting depth for the vegetation. The analysis also suggests that, where fires frequently affect riparian forests, channels may alternate between laterally stable gravel plane‐bed channels and laterally active riffle‐pool channels. These channels likely do not exhibit the classic dynamic equilibrium associated with alluvial streams, but instead exhibit a cyclical morphologic evolution, oscillating between laterally stable and laterally unstable end‐members with a frequency determined by the forest fire recurrence interval. Copyright © 2008 John Wiley & Sons, Ltd.     

Urban fluvial flood modelling using a two‐dimensional diffusion‐wave treatment,part 2: development of a sub‐grid‐scale treatment

This paper develops and tests a sub‐grid‐scale wetting and drying correction for use with two‐dimensional diffusion‐wave models of urban flood inundation. The method recognizes explicitly that representations of sub‐grid‐scale topography using roughness parameters will provide an inadequate representation of the effects of structural elements on the floodplain (e.g. buildings, walls), as such elements not only act as momentum sinks, but also have mass blockage effects. The latter may dominate, especially in structurally complex urban areas. The approach developed uses high‐resolution topographic data to develop explicit parameterization of sub‐grid‐scale topographic variability to represent both the volume of a grid cell that can be occupied by the flow and the effect of that variability upon the timing and direction of the lateral fluxes. This approach is found to give significantly better prediction of fluvial flood inundation in urban areas than traditional calibration of sub‐grid‐scale effects using Manning's n. In particular, it simultaneously reduces the need to use exceptionally high values of n to represent the effects of using a coarser mesh process representation and increases the sensitivity of model predictions to variation in n. Copyright © 2005 John Wiley & Sons, Ltd.