The frictional resistance characteristics of a bedrock‐influenced river channel

Much of the published literature relating to reach‐scale total ?ow resistance concentrates on alluvial rivers and little mention is made of the more extreme resistance found in bedrock‐in?uenced river systems. This paper presents the results of a detailed investigation of total ?ow resistance variation for ?ve channel types on the Sabie River, South Africa (cohesive mixed anastomosed, uncohesive mixed anastomosed, mixed pool–rapid, alluvial braided and alluvial single thread) over a range of discharges. Manning's ‘n’ and Darcy‐Weisbach f resistance coef?cients are calculated using Barnes' methodology (H. H. Barnes, US Geological Survey Water Supply Paper 1849, 1967). These data are analysed at the scales of channel type and morphologic unit and the resultant resistance values are compared with the literature. Generally the low‐?ow friction values estimated for the bedrock‐in?uenced channel types are higher than any reported. Flow resistance quanti?cation of the alluvial channel type study sites on the Sabie River produced values slightly higher than earlier studies of similar morphologies. In situations where signi?cant areas of irregular bedrock are exposed (cohesive mixed anastomosed and mixed pool–rapid channel types) the high ?ow resistance coef?cients at low discharges probably re?ect energy dissipation due to hydraulic jumps and internal distortions; however, these values fall as discharge increases to values comparable to those recorded for step–pool rivers. It is suggested that the slightly elevated resistance coef?cients recorded in the alluvial channel types are the result of the vegetation roughness component, operating when the macro‐channel bar features are inundated. Copyright © 2004 John Wiley & Sons, Ltd.     

Wind effects on sediment transport by raindrop‐impacted shallow flow: a wind‐tunnel study

In wind‐driven rains, wind velocity and direction are expected to affect not only energy input of rains but also shallow ?ow hydraulics by changing roughness induced by raindrop impacts with an angle on ?ow and the unidirectional splashes in the wind direction. A wind‐tunnel study under wind‐driven rains was conducted to determine the effects of horizontal wind velocity and direction on sediment transport by the raindrop‐impacted shallow ?ow. Windless rains and the rains driven by horizontal wind velocities of 6 m s^?1, 10 m s^?1, and 14 m s^?1 were applied to three agricultural soils packed into a 20 by 55 cm soil pan placed on both windward and leeward slopes of 7 per cent, 15 per cent, and 20 per cent. During each rainfall application, sediment and runoff samples were collected at 5‐min intervals at the bottom edge of the soil pan with wide‐mouth bottles and were determined gravimetrically. Based on the interrill erosion mechanics, kinetic energy ?ux (E_rn) as a rainfall parameter and product of unit discharge and slope in the form of q^bS^c_o as a ?ow parameter were used to explain the interactions between impact and ?ow parameters and sediment transport (q_s). The differential sediment transport rates occurred depending on the variation in raindrop trajectory and rain intensity with the wind velocity and direction. Flux of rain energy computed by combining the effects of wind on the velocity, frequency, and angle of raindrop impact reasonably explained the characteristics of wind‐driven rains and acceptably accounted for the differences in sediment delivery rates to the shallow ?ow transport (R₂ ≥ 0·78). Further analysis of the Pearson correlation coef?cients between E_rn and qS_o and q_s also showed that wind velocity and direction signi?cantly affected the hydraulics of the shallow ?ow. E_rn had a smaller correlation coef?cient with the q_s in windward slopes where not only reverse splashes but also reverse lateral raindrop stress with respect to the shallow ?ow direction occurred. However, E_rn was as much effective as qS_o in the sediment transport in the leeward slopes where advance splashes and advance lateral raindrop stress on the ?ow occurred. Copyright © 2004 John Wiley & Sons, Ltd.     

Effects of sediment load on hydraulics of overland flow on steep slopes

Eroded sediment may have significant effects on the hydraulics of overland flow, but few studies have been performed to quantify these effects on steep slopes. This study investigated the potential effects of sediment load on Reynolds number, Froude number, flow depth, mean velocity, Darcy–Weisbach friction coefficient, shear stress, stream power, and unit stream power of overland flow in a sand‐glued hydraulic flume under a wide range of hydraulic conditions and sediment loads. Slope gradients were varied from 8·7 to 34·2%, unit flow rates from 0·66 to 5·26×10^?3 m² s^?1, and sediment loads from 0 to 6·95 kg m^?1 s^?1. Both Reynolds number (Re) and Froude number (Fr) decreased as sediment load increased, implying a decrease in flow turbulence. This inverse relationship should be considered in modeling soil erosion processes. Flow depth increased as sediment load increased with a mean value of 1·227 mm, caused by an increase in volume of sediment‐laden flow (contribution 62·4%) and a decrease in mean flow velocity (contribution 37·6%). The mean flow velocity decreased by up to 0·071 m s^?1 as sediment load increased. The Darcy–Weisbach friction coefficient (f) increased with sediment load, showing that the total energy consumption increased with sediment load. The effects of sediment load on f depended on flow discharge: as flow discharge increased, the influence of sediment load on f decreased due to increased flow depth and reduced relative roughness. Flow shear stress and stream power increased with sediment load, on average, by 80·5% and 60·2%, respectively; however, unit stream power decreased by an average of 11·1% as sediment load increased. Further studies are needed to extend and apply the insights obtained under these controlled conditions to real‐world overland flow conditions. Copyright © 2010 John Wiley & Sons, Ltd.     

Detection and reconstruction of large‐scale coherent flow structures in gravel‐bed rivers

Large‐scale flow structures (LSFS) in the streamwise direction are important features of gravel‐bed river flows, because they may contribute to sediment transport and gas exchange. In the present study, these structures are detected using Huang's empirical mode decomposition and reconstructed with phase‐averaging techniques based on a Hilbert transform of the velocity signal. The analysis is based on the fluctuating component of 15 quasi‐instantaneous velocity profiles measured with a three‐dimensional (3D) acoustic Doppler velocity profiler (ADVP) in an armoured gravel‐bed river with a low relative submergence of 2.9 (ratio between flow depth and bed grain diameter). LSFS were identified in most of the measured profiles and consistently showed similar features. We were able to characterize the geometry of these large‐scale coherent structures: the front has a vertical linear shift in the time domain and a vertical profile corresponding to a first quarter moon with the apex situated at z/h ≈ 0.4. In the vertical, the front scales with flow depth h, and in the streamwise direction, LSFS scale with three to seven times the mean flow depth. On the bed, the effect of LSFS is a periodic non‐linear variation of the friction velocity on average between 0.90 and 1.10 times the mean value. A model for the friction velocity cycle resulting from LSFS oscillation is presented. Copyright © 2014 John Wiley & Sons, Ltd.     

ADV measurements of velocity distributions in a gravel‐bed flume

Velocity measurements carried out by an acoustic doppler velocimeter (ADV) in a rectangular laboratory ?ume having a gravel bed are presented. The velocity pro?les are measured in six verticals of the channel cross‐section having an increasing distance (from 4 to 38·5 cm) from the ?ume wall. The experimental runs are carried out for ?ve different bed arrangements, characterized by different concentrations of coarser elements, and for the two conditions of small‐ and large‐scale roughness. For both hydraulic conditions, the velocity measurements are ?rst used to test the applicability of the Dean pro?le and of the logarithmic pro?le corrected by a divergence function proposed in this paper. Then, for each value of the depth sediment ratio h/d₈₄, the non‐dimensional friction factor parameter is calculated by integration of the measured velocity distributions in the different verticals of the cross‐section. Finally a semi‐logarithmic ?ow resistance equation is empirically deduced. Copyright © 2003 John Wiley & Sons, Ltd.     

Rill flow resistance law under equilibrium bed‐load transport conditions

In this paper, a recently deduced flow resistance equation for open channel flow was tested under equilibrium bed‐load transport conditions in a rill. First, the flow resistance equation was deduced applying dimensional analysis and the incomplete self‐similarity condition for the flow velocity distribution. Then, the following steps were carried out for developing the analysis: (a) a relationship (Equation  13 ) between the Γ function of the velocity profile, the rill slope, and the Froude number was calibrated by the available measurements by Jiang et al.; (b) a relationship (Equation  17 ) between the Γ function, the rill slope, the Shields number, and the Froude number was calibrated by the same measurements; and (c) the Darcy–Weisbach friction factor values measured by Jiang et al. were compared with those calculated by the rill flow resistance equation with Γ estimated by Equations  13 and 17 . This last comparison demonstrated that the rill flow resistance equation, in which slope and Shields number, representative of sediment transport effects, are introduced, is characterized by the lowest values of the estimate errors.     

Flow threads in surface run‐off: implications for the assessment of flow properties and friction coefficients in soil erosion and hydraulics investigations

Soil surface microtopography produces non‐uniform surface run‐off, in which narrow threads of relatively deep and fast ?ow move within broader, shallower, slower‐moving regions. This kind of ?ow is probably widespread, given that microtopography is itself common. Methods used to record the properties of surface run‐off include grid‐ or transect‐based depth observations, with a single mean ?ow speed derived by calculation from V = Q/WD, and the use of dye timing to estimate velocity, with an effective mean depth calculated from D = Q/WV. Because these methods allow only single, ?ow‐?eld mean values to be derived for V or D, neither is well suited to non‐uniform ?ows. The use of depth data to derive a ?ow‐?eld mean V furthermore implicitly applies area weighting to the depth data; likewise, the use of dye speeds for V inherently overestimates mean V because dye dominantly follows the faster ?ow threads. The associated errors in derived parameters such as friction coef?cients are not readily quanti?ed and appear not to have been addressed previously. New ?eld experiments made on untilled soil surfaces in arid western NSW, Australia, explore these circumstances and the implications for deriving meaningful measures of ?ow properties, including friction coef?cients. On surfaces deliberately chosen for their very subtle microtopography, average thread velocities are shown to be commonly 2·5 times greater than the ?ow‐?eld mean, and locally 6–7 times greater. On the other hand, non‐thread ?ow speeds lie below the ?ow‐?eld mean, on average reaching only 84 per cent of this value, and often considerably less. Flow‐?eld means conceal the existence of regions of the ?ow ?eld whose properties are statistically distinct. Results con?rm that a reliance on ?ow‐?eld average depths yields estimates of friction coef?cients that are biased toward the shallower, high‐roughness parts of the ?ow, while if dye speeds are relied upon the results are biased toward the deeper, smoother threads of ?ow. A new approach to the evaluation of friction coef?cients in non‐uniform ?ows is advanced, involving the determination of separate coef?cients for threads and non‐thread zones of the ?ow ?eld. In contrast, ?ow‐?eld friction coef?cients as they are customarily derived in run‐off plot experiments subsume these distinct coef?cients in proportions that are generally unknown. The value of such coef?cients is therefore questionable. Copyright © 2004 John Wiley & Sons, Ltd.     

Resistance to overland flow due to bed‐load transport on plane mobile beds

During bed‐load transport by overland ?ow, momentum is transferred from the ?ow to the bed via grain collisions, resulting in a decrease in ?ow velocity and an increase in ?ow resistance, herein termed bed‐load transport resistance. In overland ?ow on mobile plane beds, total ?ow resistance f consists of grain resistance f_g and bed‐load transport resistance f_bt. In order to identify and evaluate the relative importance of the factors controlling f_bt, 38 ?ume experiments were performed on slopes of 2·7 and 5·5° using sediment with median diameters of 0·74 and 1·16 mm. All ?ows were supercritical and turbulent. This study is an extension of a recent study by Gao and Abrahams (Earth Surface Processes and Landforms 2004, vol. 29, pp. 423–435). These authors found that f_bt is controlled by three factors: sediment concentration C, dimensionless sediment diameter D_*, and relative submergence h/D, where h is ?ow depth, D is median sediment diameter. However, a new dimensional analysis identi?es two additional factors: Froude number F and slope S. Multiple regression analyses reveal (1) that these ?ve factors together explain 97 per cent of the variance of f_bt, and (2) that S controls f_bt entirely through C. The variable C is therefore redundant, and a new functional equation relating f_bt to D_*, h/D, S and F is developed. This equation may be used to predict f_bt. An advantage of this equation is that it may be used to predict f_bt without measuring bed‐load transport rate. Copyright © 2004 John Wiley & Sons, Ltd.     

A bed‐load transport model for rough turbulent open‐channel flows on plane beds

Data from flume studies are used to develop a model for predicting bed‐load transport rates in rough turbulent two‐dimensional open‐channel flows moving well sorted non‐cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed‐load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed‐load transport rates. The model is based on a revised version of Bagnold's basic energy equation i_bs_b = e_bω, where i_b is the immersed bed‐load transport rate, ω is flow power per unit area, e_b is the efficiency coefficient, and s_b is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for s_b and e_b in terms of G, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed‐load transport equation i_b = ω G ^3·4. This equation applies regardless of the mode of bed‐load transport (i.e. saltation or sheet flow) and reduces to i_b = ω where G approaches 1 in the sheet‐flow regime. That i_b = ω does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that i_b is a transport rate that must be multiplied by s_b to become a work rate before it can be compared with ω. It follows that the proportion of ω that is dissipated in the transport of bed load is i_bs_b/ω, which is approximately 0·6 when i_b = ω. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain‐to‐grain to grain‐to‐bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain‐to‐bed collision than in a grain‐to‐grain one. Copyright © 2006 John Wiley & Sons, Ltd.     

Thresholds and relations for soil‐hydraulic and soil‐physical properties as a function of burn severity 4 years after the 2011 Las Conchas Fire,New Mexico,USA

Wildfire effects on soil‐physical and ‐hydraulic properties as a function of burn severity are poorly characterized, especially several years after wildfire. A stratified random sampling approach was used in 2015 to sample seven sites representing a spectrum of remotely sensed burn severity in the area impacted by the 2011 Las Conchas Fire in New Mexico, USA. Replicate samples from each site were analysed in the laboratory. Linear and linear indicator regression were used to assess thresholds in soil‐physical and ‐hydraulic properties and functional relations with remotely sensed burn severity. Significant thresholds were present for initial soil‐water content (θ_i) at 0–6 cm depth between the change in the Normalized Burn Ratio (dNBR) equal to 618–802, for bulk density (ρ_b) at 3–6 cm between dNBR equal to 416–533, for gravel fraction at 0–1 cm between dNBR equal to 416–533, for fines (the silt + clay fraction) at 0–1 cm for dNBR equal to 416–533, and for fines at 3–6 cm for dNBR equal to 293–416. Significant linear relations with dNBR were present between ρ_b at 0–1 cm, loss on ignition (LOI) at 0–1 cm, gravel fraction at 0–1 cm, and the large organic fraction at 1–3 cm. No thresholds or effects on soil‐hydraulic properties of field‐saturated hydraulic conductivity or sorptivity were observed. These results suggest that ρ_b and LOI at 0–1 cm have residual direct impacts from the wildfire heat impulse. The θ_i threshold is most likely from delayed groundcover/vegetation recovery that increases evaporation at the highest burn severity sites. Gravel and silt + clay thresholds at 0–1 cm at the transition to high burn severity suggest surface gravel lag development from hydraulic erosion. Thresholds in ρ_b from 3 to 6 cm and in silt + clay fraction from 3 to 6 cm appear to be the result of soil variability between sites rather than wildfire impacts. This work suggests that gravel‐rich soils may have increased resilience to sustained surface runoff generation and erosion following wildfire, with implications for assessments of postwildfire hydrologic and erosion recovery potential.     

Flow modelling in gravel‐bed rivers: rethinking the bottom boundary condition

A key problem in computational fluid dynamics (CFD) modelling of gravel‐bed rivers is the representation of multi‐scale roughness, which spans the range from grain size, through bedforms, to channel topography. These different elements of roughness do not clearly map onto a model mesh and use of simple grain‐scale roughness parameters may create numerical problems. This paper presents CFD simulations for three cases: a plane bed of fine gravel, a plane bed of fine gravel including large, widely‐spaced pebble clusters, and a plane gravel bed with smaller, more frequent, protruding elements. The plane bed of fine gravel is modelled using the conventional wall function approach. The plane bed of fine gravel including large, widely‐spaced pebble clusters is modelled using the wall function coupled with an explicit high‐resolution topographic representation of the pebble clusters. In these cases, the three‐dimensional Reynolds‐averaged continuity and Navier–Stokes equations are solved using the standard k ? ε turbulence model, and model performance is assessed by comparing predicted results with experimental data. For gravel‐bed rivers in the field, it is generally impractical to map the bed topography in sufficient detail to enable the use of an explicit high‐resolution topography. Accordingly, an alternative model based on double‐averaging is developed. Here, the flow calculations are performed by solving the three‐dimensional double‐averaged continuity and Navier‐Stokes equations with the spatially‐averaged 〈k ? ε〉 turbulence model. For the plane bed of fine gravel including large, widely‐spaced pebble clusters, the model performance is assessed by comparing the spatially‐averaged velocity with the experimental data. The case of a plane gravel bed with smaller, more frequent, protruding elements is represented by a series of idealized hypothetical cases. Here, the spatially‐averaged velocity and eddy viscosity are used to investigate the applicability of the model, compared with using the explicit high‐resolution topography. The results show the ability of the model to capture the spatially‐averaged flow field and, thus, illustrate its potential for representing flow processes in natural gravel‐bed rivers. Finally, practical data requirements for implementing such a model for a field example are given. Copyright © 2011 John Wiley & Sons, Ltd.     

A wind tunnel investigation of the influences of fetch length on the flux profile of a sand cloud blowing over a gravel surface

Wind tunnel tests were conducted to examine the fetch effect of a gravel surface on the ?ux pro?le of the sand cloud blowing over it using typical dune sand. The results suggest that the ?ux pro?le of blown sand over a gravel surface differs from that over a sandy surface and is characterized by a peak ?ux at a height above the surface while that over a sandy surface decreases exponentially with height. The ?ux pro?le of a sand cloud over a gravel surface can be expressed by a Gaussian peak function: q = a + b exp (?0·5((h ? c)/d)²), where q is the sand transport rate at height h, and a, b, c and d are regression coef?cients. The signi?cance of the coef?cients in the function could be de?ned in accordance with the fetch length of the gravel surface and wind velocity. Coef?cient c represents the peak ?ux height and increases with both wind velocity and fetch length, implying that the peak ?ux height is related to the bounce height of the particles in the blowing sand cloud. Coef?cient d shows a tendency to increase with both wind velocity and fetch length. The sum of a and b, representing the peak ?ux, increases with wind velocity but decreases with fetch length. The average saltation height derived from the cumulative percentage curve shows a tendency to increase with both the fetch length and wind velocity. For any fetch length of a gravel surface the sand transport equation is expressed as Q = C(1 ? U_t/U)(ρ/g)U³, where Q is the sand transport rate, U is the wind velocity, U_t is the threshold velocity measured at the same height as U, g is the gravitational acceleration, ρ is the air density, C is a proportionality coef?cient that decreases with the fetch length of the gravel surface. At a given wind velocity, the sand transport rate over a gravel surface is only 52–68 per cent of that over a sandy surface. The ?ux rate in true creep over a gravel surface increases with wind velocity but decreases with the fetch length, whereas the creep proportion (the ratio of creep ?ux to the sand transport rate) decreases with both the wind velocity and fetch length. Two‐variable (including fetch length and wind velocity) equations were developed to predict the peak ?ux height, average saltation height and transport rate. Copyright © 2004 John Wiley & Sons, Ltd.     

Bedload transport resistance in rough open‐channel flows

During bedload movement by saltation, streamwise momentum is transferred from the ?ow to the saltating grains. When the grains collide with other grains on the bed or in the ?ow, streamwise momentum is reduced, and there is a decrease in streamwise ?ow velocity and an increase in ?ow resistance, herein termed bedload transport resistance f_bt. Based on experiments in two ?umes with ?xed and mobile plane beds and previously published data, an equation is developed that may be used to predict f_bt for both capacity and non‐capacity ?ows. The variables in this equation are identi?ed by dimensional analysis and the coef?cients are determined by non‐linear regression. This equation applies to rough turbulent open‐channel ?ows, where the relative submergence is between 1 and 20 and the entire sediment load moves by saltation. An investigation of the relative magnitudes of f_bt and grain resistance f_c suggests that where dimensionless shear stress θ is less than 1 and saltation is the dominant mode of bedload transport, f_bt/f_c increases with θ but never exceeds 1. Copyright © 2004 John Wiley & Sons, Ltd.     

Relation between flow,surface‐layer armoring and sediment transport in gravel‐bed rivers

This study investigates trends in bed surface and substrate grain sizes in relation to reach‐scale hydraulics using data from more than 100 gravel‐bed stream reaches in Colorado and Utah. Collocated measurements of surface and substrate sediment, bankfull channel geometry and channel slope are used to examine relations between reach‐average shear stress and bed sediment grain size. Slopes at the study sites range from 0·0003 to 0·07; bankfull depths range from 0·2 to 5 m and bankfull widths range from 2 to 200 m. The data show that there is much less variation in the median grain size of the substrate, D_50s, than there is in the median grain size of the surface, D₅₀; the ratio of D₅₀ to D_50s thus decreases from about four in headwater reaches with high shear stress to less than two in downstream reaches with low shear stress. Similar trends are observed in an independent data set obtained from measurements in gravel‐bed streams in Idaho. A conceptual quantitative model is developed on the basis of these observations to track differences in bed load transport through an idealized stream system. The results of the transport model suggest that downstream trends in total bed load flux may vary appreciably, depending on the assumed relation between surface and substrate grain sizes. Copyright © 2007 John Wiley & Sons, Ltd.     

Flow resistance equation for rills

In this paper, a new flow resistance equation for rill flow was deduced applying dimensional analysis and self‐similarity theory. At first, the incomplete self‐similarity hypothesis was used for establishing the flow velocity distribution whose integration gives the theoretical expression of the Darcy–Weisbach friction factor. Then the deduced theoretical resistance equation was tested by some measurements of flow velocity, water depth, cross section area, wetted perimeter, and bed slope carried out in 106 reaches of some rills shaped on an experimental plot. A relationship between the velocity profile, the channel slope, and the flow Froude number was also established. The analysis showed that the Darcy–Weisbach friction factor can be accurately estimated by the proposed theoretical approach based on a power–velocity profile.     

Monitoring gravel augmentation in a large regulated river and implications for process‐based restoration

The artificial gravel augmentation of river channels is increasingly being used to mitigate the adverse effects of river regulation and sediment starvation. A systematic framework for designing and assessing such gravel augmentations is still lacking, notably on large rivers. Monitoring is required to quantify the movement of augmented gravel, measure bedform changes, assess potential habitat enhancement, and reduce the uncertainty in sediment management. Here we present the results of an experiment conducted in the Rhine River (French and German border). In 2010, 23 000 m³ of sediments (approximately the mean annual bedload transport capacity) were supplied in a by‐passed reach downstream of the Kembs dam to test the feasibility of enhancing sediment transport and bedform changes. A 620‐m‐long and 12‐m‐wide gravel deposit was created 8 km downstream from the dam. Monitoring included topo‐bathymetric surveys, radio‐frequency particle tracking using passive integrated transponder (PIT) tags, bed grain size measurement, and airborne imagery. Six surveys performed since 2009 have been described (before and after gravel augmentation, and after Q₂ and Q₁₅ floods). The key findings are that (i) the augmented gravel was partially dispersed by the first flood event of December 2010 (Q₁); (ii) PIT tags were found up to 3200 m downstream of the gravel augmentation site after four years, but the effects of gravel augmentation could not be clearly distinguished from the effects of floods and internal remobilization on more than 3500 m downstream; (iii) linear and log‐linear relationships linking bedload transport, particle mobility, and grain size were established; and (iv) combined bathymetry and PIT tag surveys were useful for evaluating potential environmental risks and the first morpho‐ecological responses. This confirmed the complementary nature of such techniques in the monitoring of gravel augmentation in large rivers. Copyright © 2017 John Wiley & Sons, Ltd.     

Regime theories in gravel‐bed rivers: models,controlling variables,and applications in disturbed Italian rivers

Downstream hydraulic geometry relationships describe the shape of alluvial channels in terms of bankfull width, flow depth, flow velocity, and channel slope. Recent investigations have stressed the difference in spatial scales associated with these variables and thus the time span required for their adjustment after a disturbance. The aim of this study is to explore the consequences in regime models considering the hypothesis that while channel width and depth adjust quickly to changes in water and sediment supply, reach slope requires a longer time span. Three theoretical models were applied. One model incorporates an extremal hypothesis (Millar RG. 2005. Theoretical regime equations for mobile gravel‐bed rivers with stable banks. Geomorphology 64 : 207–220), and the other two are fully physically based (Ikeda S, Parker G, Kimura Y. 1988. Stable width and depth of straight gravel rivers with heterogeneous bed materials. Water Resources Research 24 : 713–722; Parker G, Wilcock PR, Paola C, Dietrich W, Pitlick J. 2007. Physical basis for quasi universal relations describing bankfull hydraulic geometry of single‐thread gravel‐bed rivers. Journal of Geophysical Research 112 , DOI: 10.1029/2006JF000549). In order to evaluate the performance of models introducing the slope as an independent variable, we propose two modifications to previous models. The performance of regime models was tested against published data from 142 river reaches and new hydraulic geometry data from gravel‐bed rivers in Patagonia (Argentina) and north‐eastern Italy. Models that assume slope as a control (Ikeda et al., 1988; or Millar, 2005) predict channel depth and width reasonably well. Parker et al.'s (2007) model improved predictions because it filters the scatter in slope data with a relation slope–discharge. The extremal hypothesis model of Millar (2005) predicts comparably to the other physically based models. Millar's model was chosen to describe the recent changes in the Piave and Brenta rivers due to human intervention – mainly in‐channel gravel mining. The change in sediment supply and recovery was estimated for these rivers. This study supports the interpretation that sediment supply is the key factor guiding morphological changes in these rivers. Copyright © 2013 John Wiley & Sons, Ltd.     

Distorted Froude‐scaled flume analysis of large woody debris

This paper presents the results of a movable‐boundary, distorted, Froude‐scaled hydraulic model based on Abiaca Creek, a sand‐bedded channel in northern Mississippi. The model was used to examine the geomorphic and hydraulic impact of simplified large woody debris (LWD) elements. The theory of physical scale models is discussed and the method used to construct the LWD test channel is developed. The channel model had bed and banks moulded from 0·8 mm sand, and flow conditions were just below the threshold of motion so that any sediment transport and channel adjustment were the result of the debris element. Dimensions and positions of LWD elements were determined using a debris jam classification model. Elements were attached to a dynamometer to measure element drag forces, and channel adjustment was determined through detailed topographic surveys. The fluid drag force on the elements decreased asymptotically over time as the channel boundary eroded around the elements due to locally increased boundary shear stress. Total time for geomorphic adjustment computed for the prototype channel at the Q₂ discharge (discharge occurring once every two years on average) was as short as 45 hours. The size, depth and position of scour holes, bank erosion and bars created by flow acceleration past the elements were found to be related to element length and position within the channel cross‐section. Morphologies created by each debris element in the model channel were comparable with similar jams observed in the prototype channel. Published in 2001 John Wiley & Sons, Ltd.     

Supporting USLE‐MM reliability by analyzing soil loss measurement errors

Sampling the collected suspension in a storage tank is a common procedure to obtain soil loss data. A calibration curve of the tank has to be used to obtain actual concentration values from those measured by sampling. However, literature suggests that using a tank calibration curve was not a common procedure in the past. For the clay soil of the Sparacia (Italy) experimental station, this investigation aimed to establish a link between the relative performances of the USLE‐M and USLE‐MM models, usable to predict plot soil loss at the event temporal scale, and soil loss measurement errors. Using all available soil loss data, lower soil loss prediction errors were obtained with the USLE‐MM (exponent of the erosivity term, b₁ > 1) than the USLE‐M (b₁ = 1). A systematic error of the soil loss data is unexpected for the Sparacia soil because the calibration curve does not depend on the water level in the tank. In any case, this type of error does not have any effect on the b₁ exponent. Instead, this exponent decreases as the level of underestimation increases for increasing soil loss values. This type of error can occur at Sparacia if it is assumed that a soil loss measurement can be obtained by a bottle sampler dipped close to the bottom of the tank after mixing the suspension and assuming that the measured concentration coincides with the actual one. In this case, the risk is to obtain a lower b₁ value than the actual one. In conclusion, additional investigations on the factors determining errors in soil loss data collected by a sampling procedure are advisable because these errors can have a noticeable effect on the calibrated empirical models for soil loss prediction.     

Testing a theoretical resistance law for overland flow on a stony hillslope

Overland flow, sediments, and nutrients transported in runoff are important processes involved in soil erosion and water pollution. Modelling transport of sediments and chemicals requires accurate estimates of hydraulic resistance, which is one of the key variables characterizing runoff water depth and velocity. In this paper, a new theoretical power–velocity profile, originally deduced neglecting the impact effect of rainfall, was initially modified for taking into account the effect of rainfall intensity. Then a theoretical flow resistance law was obtained by integration of the new flow velocity distribution. This flow resistance law was tested using field measurements by Nearing for the condition of overland flow under simulated rainfall. Measurements of the Darcy–Weisbach friction factor, corresponding to flow Reynolds number ranging from 48 to 194, were obtained for simulated rainfall with two different rainfall intensity values (59 and 178 mm hr⁻¹). The database, including measurements of flow velocity, water depth, cross-sectional area, wetted perimeter, and bed slope, allowed for calibration of the relationship between the velocity profile parameter Γ, the slope steepness s, and the flow Froude number F, taking also into account the influence of rainfall intensity i. Results yielded the following conclusions: (a) The proposed theoretical flow resistance equation accurately estimated the Darcy–Weisbach friction factor for overland flow under simulated rainfall, (b) the flow resistance increased with rainfall intensity for laminar overland flow, and (c) the mean flow velocity was quasi-independent of the slope gradient.