Temporal and spatial variations in periglacial soil movements on alpine crest slopes

This paper describes up to ten years of continuous monitoring of frost heave, creep and associated parameters on high mountain crest slopes in the Japanese and Swiss Alps, aiming to evaluate spatial and interannual variations in the rates and controls of soil movement. Shallow frost creep re?ecting diurnal frost heave activity dominates the crest slopes that lack a vegetation mat and have a thin debris mantle with good drainage. Seasonal frost heave activity can induce slightly deeper movement where ?ne soil exists below the depth reached by diurnal freeze–thaw penetration, although the shallow bedrock impedes movements below 20 cm depth. As a result, downslope velocity pro?les display strong concavity with surface velocities of 2–50 cm a^?1. The frost creep rates vary spatially, depending on the soil texture, slope gradient, frequency of temperature cycling across 0 °C and moisture availability during freeze–thaw periods. Soil movements recur in every freeze–thaw period, although with some interannual variations affected by the length of seasonal snow cover and the occurrence of precipitation during freeze–thaw periods. The Swiss Alps encounter more signi?cant interannual variations than the Japanese Alps, re?ecting the large variability of the annual snow regime. Copyright © 2005 John Wiley & Sons, Ltd.     

Sediment movement rates and processes on cinder cones in the maritime Subantarctic (Marion Island)

Sediment transport in the scoria areas of Marion Island is primarily the result of needle‐ice‐induced frost creep associated with diurnal soil frost cycles. Clasts move most rapidly in ?ne textured areas (532 mm a^?1; SD 382), more slowly in stony areas (161 mm a^?1; SD 179), and most slowly in blocky areas (26 mm a^?1; SD 23). Movement rates increase with increasing frost susceptibility of sediments, slope angle and altitude. The heave of dowels indicates that frost heave is active in all the scoria areas examined. The depth of effective frost heave increases with increasing altitude, with frost heave being restricted to the upper 100 mm of the soil in low altitude areas (<200 m). The heave of 150 mm dowels at the higher altitude sites provides evidence for segregation ice formation at depths greater than those associated with needle ice and diurnal soil frost cycles. Vertical movement pro?les show a concave downslope pro?le, with sediment movement rates being most rapid at the soil surface and decreasing rapidly with depth. This pro?le shape is typical of areas dominated by diurnal freeze–thaw cycles and needle ice. The capture of sediments moving downslope in troughs and the sampling of material lifted by needle ice, suggest that sediment transport by needle ice under present conditions is extremely effective. Observations suggest that although both ?ne material and clasts are transported downslope, some preferential transport of clasts occurs. Experiment results and observations of soil frost processes suggest that frost creep associated with needle ice activity is the dominant slope process in the scoria areas of Marion Island. Other slope processes such as slopewash and debris ?ows appear to play a relatively minor and localized role in sediment transport. It is suggested that needle ice activity is likely to be the dominant geomorphic agent in other areas of the Subantarctic with similar climatic characteristics to Marion Island. Copyright © 2004 John Wiley & Sons, Ltd.     

Effects of deforestation and weather on diurnal frost heave processes on the steep mountain slopes in south central Japan

Freezing and thawing processes play an important role for the gravitational transport of surface materials on steep mountain slopes in Japan. The effects of deforestation on frost heave activity were observed through the 2012/2013 winter season in Ikawa University Forest, a southern mountainous area in central Japan (1180–1310 m above sea level). During periods without snow cover, needle ice development prevailed at a clear‐cut site, and the downslope sediment movement of upper soil was 10 to 15 cm through the winter season. At a non‐cut site, rise and fall in the ground surface level prevailed on a weekly scale, with no evident downslope movements at the surface; ice lens formation in the soil layer is assumed. Abrupt changes in the radiation budget, such as the strengthening of nighttime radiative cooling and increases in daytime direct insolation, induced frequent development/deformation of needle ice at the clear‐cut site. In snow‐free periods, the day‐to‐day variability in needle ice growth length and in nighttime averaged net radiation showed significant correlations; cloudy weather with warmer and moist air intrusion associated with synoptic disturbances prevented the occurrence of needle ice. Namely, day‐to‐day weather changes directly affected the mass movement of the upper soil after deforestation. Shallow snow cover occurred discontinuously through the winter and is likely an important factor in keeping the soil moisture sufficiently high in the upper soil layer for initiating needle ice during snow‐free periods. We also discuss contributions of coastal extratropical cyclone activities providing both snow cover and cloudy weather in the southern mountain areas of central Japan to the intra‐seasonal variability in frost heave and its indirect effect on soil creep and landslides on the deforested steep slopes. Copyright © 2015 John Wiley & Sons, Ltd.     

Bank‐collapse processes in a valley‐bottom gully,western Iowa

Widening and bank‐slope reduction of a valley‐bottom gully in western Iowa was correlated to increasing subsurface flow over a 36‐year period. To study bank collapse at this gully, we measured rainfall, air temperature, hydraulic head near the banks and bank movement nearly continuously over a 2‐year period. Styles of movement ranged from imperceptible creep to rapid slab collapses preceded by the formation of tension cracks parallel to the gully walls. Bank movement was commonly correlated to rainfall or snowmelt and associated head increases in the banks. If the banks are modelled as a two‐dimensional slab with an adjacent tension crack partly filled with water, measured heads were sufficient to cause bank failures through reduction of frictional support at the base of the slab. During winter months, air temperature variations across 0 °C were correlated with bank movement: during mildly subfreezing periods banks expanded, and most, but usually not all, of this movement was recovered during above‐freezing periods. This motion is attributed to frost heave followed by thawing. Deformation of the banks by heaving and thawing during winter may weaken them and prime them for failure during spring rains and snowmelt, when the frequency of mass‐wasting events is highest. Copyright © 2008 John Wiley and Sons, Ltd.     

Small‐scale experimental simulation of talus evolution

We investigated a small‐scale laboratory model of a talus slope evolution. Five different size classes of basaltic rock were selected and marked with different colours. Homogenized mixtures of grains of different sizes were dropped from a fixed height onto a tilted experimental board covered with a loose granular layer. This was conducted in a series of regular sequences, and the resulting distribution on the board was studied after each sequence. At the beginning of the experiment, the grains developed a longitudinal gradation similar to natural talus slopes, where small grains settle at the top while the large ones roll down to the distal part. However, after a transient period dominated by single‐particle dynamics on the inert granular medium, the evolution proved to be more variable than expected. Due to the continuous shower of falling grains, the shear stress at the bottom of the upper granular layer increased. This resulted initially in a slow creep down slope that finally collapsed in large avalanches homogenizing the material. The slides occurred at the boundary between a weaker layer created by migration of small grains through the interstices, and marked by a vertical transition between small and large grains. We compare the experimental findings with observations from natural talus slopes, and suggest that similar experiments may be helpful in understanding the evolution of taluses. Copyright © 2009 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.     

Geomorphological characteristics of small debris flows on Junior's Kop,Marion Island,maritime sub ‐ Antarctic

The geomorphological characteristics of small debris flows in a maritime sub‐Antarctic environment are described. The morphological and sedimentological characteristics of the debris flows are comparable to debris flows documented for other parts of the world; their initiation appears closely linked to the unusual environment in which they are found. Sediment supply is generated by diurnal frost heave of loamy sediment associated with Azorella selago. The debris flows are triggered by sediment mobilization upon saturation of the frost‐heaved surface gravel and overland flow over the low‐permeability and frost‐susceptible slope materials. Morphological effects of the flows are short‐lived due to obliteration by subsequent frost heave activity. Copyright © 2000 John Wiley & Sons, Ltd.     

Gelifluction: viscous flow or plastic creep?

This paper reports results from two scaled centrifuge modelling experiments, designed to simulate thaw‐related geli?uction. A planar 12° prototype slope was modelled in each experiment, using the same natural ?ne sandy silt soil. However two different scales were used. In Experiment 1, the model scale was 1/10, tested in the centrifuge at 10 gravities (g) and in Experiment 2, the scale was 1/30, tested at 30 g. Centrifuge scaling laws indicate that the time scaling factor for thaw consolidation between model and prototype is N², where N is the number of gravities under which the model was tested. However, the equivalent time scaling for viscous ?ow is 1/1. If geli?uction is a viscosity‐controlled ?ow process, scaling con?icts will therefore arise during centrifuge modelling of thawing slopes, and rates of displacement will not scale accurately to the prototype. If, however, no such scaling con?icts are observed, we may conclude that geli?uction is not controlled by viscosity, but rather by elasto‐plastic soil deformation in which frictional shear strength depends on effective stress, itself a function of the thaw consolidation process. Models were saturated, consolidated and frozen from the surface downwards on the laboratory ?oor. The frozen models were then placed in the geotechnical centrifuge and thawed from the surface down. Each model was subjected to four freeze–thaw cycles. Soil temperatures and pore water pressures were monitored, and frost heave, thaw settlement and downslope displacements measured. Pore water pressures, displacement rates and displacement pro?les re?ecting accumulated shear strain, were all similar at the two model scales and volumetric soil transport per freeze–thaw cycle, when scaled to prototype, were virtually identical. Displacement rates and pro?les were also similar to those observed in earlier full‐scale laboratory ?oor experiments. It is concluded therefore that the modelled geli?uction was not a time‐dependent viscosity‐controlled ?ow phenomenon, but rather elasto‐plastic in nature. A ?rst approximation ‘?ow’ law is proposed, based on the ‘Cam Clay’ constitutive model for soils. Copyright © 2003 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.     

Physical modelling of rainfall‐ and snowmelt‐induced erosion of stony slope underlain by permafrost

Physical modelling experiments have been carried out in a cold room to test on a small scale, the effects of water supply during the thaw of an experimental slope with permafrost. Permafrost was maintained at depth and a thin active layer was frozen and thawed from the surface. Data from the experiments relate to two different conditions, first with moderate rainfall, and second with heavy rainfall during the thaw period. When moderate rainfall is applied during thaw phases, the experimental slope is slightly degraded. At the scale of the experiment, erosion processes involve frost jacking of the coarse blocks, frost creep and gelifluction that induce slow and gradual down slope displacements of the active layer, but also small landslides leading to large but slow mass movements with short displacements. Changes in experimental slope morphology are marked by the initiation of a small‐scale drainage network and the development of a little crest line which shows a progressive upslope migration. With such boundary conditions, there is not enough water supply to evacuate downslope the whole of the eroded material and a topographic smoothing is observed. When heavy rainfall is applied during thaw periods, rapid mass wasting (small mud‐flows and debris flows) become prominent. Slope failures are largely controlled by the water saturation of the active layer and by the occurrence of steeper slopes. At the scale of the experiment, rates of erosion and maximum incision increase by about 100% leading to significant slope degradation with marked and specific scars comparable to gullying. These morphological changes are dependant on both the size and the frequency of catastrophic events. These experiments provide detailed data that could improve the knowledge of the physical parameters that control the initiation, at a small‐scale, of erosion processes on periglacial slopes with a thin active layer and/or with thin cover of mobilizable slope deposits. Copyright © 2010 John Wiley & Sons, Ltd.     

A conceptual model for determining soil erosion by water

Current estimates of rates of soil erosion by water derived from plots are incompatible with estimates of long‐term lowering of large drainage basins. Traditional arguments to reconcile these two disparate rates are ?awed. The ?ux of sediment leaving a speci?ed area cannot be converted to a yield simply by dividing by the area, because there is no simple relationship between ?ux and area. Here, we develop an approach to the determination of erosion rates that is based upon the entrainment rates and travel distances of individual particles. The limited available empirical data is consistent with the predictions of this approach. Parameterization of the equations to take account of such factors as gradient and sediment supply is required to proceed from the conceptual framework to quantitative measurements of erosion. However, our conceptual model solves the apparent paradox of the sediment delivery ratio, resolves recent discussion about the validity of erosion rates made using USLE erosion plots, and potentially can reconcile erosion rates with known lifespans of continents. Our results imply that previous estimates of soil erosion are fallacious. Copyright © 2004 John Wiley & Sons, Ltd.     

非均匀冻胀条件下铁路纵向变形模型及参数分析

我国是冻土分布大国,寒区铁路轨道普遍遭受地基土冻胀影响。以往的研究偏重地基土的冻胀特征,而对纵向非均匀冻胀变形下铁路与地基土的相互作用关注较少。基于双层弹性地基梁理论,建立铁轨-轨下基础在非均匀冻胀变形作用下的力学模型,给出模型的解析解,结合算例分析夹层弹性系数和冻胀量对轨道位移和内力的影响。结果表明：弹性夹层可以有效减弱铁轨的冻胀变形和应力响应,有利于维护铁轨的运营;铁轨和轨下基础的过渡段长度、凹凸弯折段处的剪力、弯矩随着冻胀位移的增大而增长;夹层弹性系数增大会导致冻胀力对轨下基础的影响逐渐向轨道转移;过渡段的长度只与冻胀量有关。文章提出的计算方法和分析结论可为寒区铁路设计和运营维护提供科学指导。     

复合填料一维冻胀量数值模拟分析

复合填料是以废铸砂、粉煤灰、聚苯乙烯颗粒（EPS）、水泥和水为原料,拌合后形成的一种轻质填筑材料。其中,EPS颗粒含量适当时,能减少或消除复合填料的冻胀和融沉,可作为季节性冻土区的路基填料。假设复合填料中除EPS颗粒外的骨料颗粒、孔隙冰为刚性介质,同时考虑EPS颗粒变形和填料孔隙变形对复合填料冻结过程的影响,在已有的冻土水热耦合分离冰模型的基础上,得到考虑EPS颗粒变形影响的饱和填料一维冻结水热耦合控制方程,进而预测填料的冻胀量。与室内模型试验结果对比表明,本文模型可用于该种具有弹性颗粒复合填料的冻胀量模拟,为工程中冻胀量预测提供依据。     

Past and projected future changes in snowpack and soil frost at the Hubbard Brook Experimental Forest,New Hampshire,USA

Long‐term data from the Hubbard Brook Experimental Forest in New Hampshire show that air temperature has increased by about 1 °C over the last half century. The warmer climate has caused significant declines in snow depth, snow water equivalent and snow cover duration. Paradoxically, it has been suggested that warmer air temperatures may result in colder soils and more soil frost, as warming leads to a reduction in snow cover insulating soils during winter. Hubbard Brook has one of the longest records of direct field measurements of soil frost in the United States. Historical records show no long‐term trends in maximum annual frost depth, which is possibly confounded by high interannual variability and infrequency of major soil frost events. As a complement to field measurements, soil frost can be modelled reliably using knowledge of the physics of energy and water transfer. We simulated soil freezing and thawing to the year 2100 using a soil energy and water balance model driven by statistically downscaled climate change projections from three atmosphere‐ocean general circulation models under two emission scenarios. Results indicated no major changes in maximum annual frost depth and only a slight increase in number of freeze–thaw events. The most important change suggested by the model is a decline in the number of days with soil frost, stemming from a concurrent decline in the number of snow‐covered days. This shortening of the frost‐covered period has important implications for forest ecosystem processes such as tree phenology and growth, hydrological flowpaths during winter, and biogeochemical processes in soil. Published in 2010 by 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.     

Two‐dimensional hydraulic flood modelling using a finite‐element mesh decomposed according to vegetation and topographic features derived from airborne scanning laser altimetry

Airborne scanning laser altimetry (LiDAR) is an important new data source that can provide two‐dimensional river flood models with spatially distributed floodplain topography for model bathymetry, together with vegetation heights for parameterization of model friction. Methods are described for improving such models by decomposing the model's finite‐element mesh to reflect floodplain vegetation features such as hedges and trees having different frictional properties to their surroundings, and significant floodplain topographic features having high height curvatures. The decomposition is achieved using an image segmentation system that converts the LiDAR height image into separate images of surface topography and vegetation height at each point. The vegetation height map is used to estimate a friction factor at each mesh node. The spatially distributed friction model has the advantage that it is physically based, and removes the need for a model calibration exercise in which free parameters specifying friction in the channel and floodplain are adjusted to achieve best fit between modelled and observed flood extents. The scheme was tested in a modelling study of a flood that occurred on the River Severn, UK, in 1998. A satellite synthetic aperture radar image of flood extent was used to validate the model predictions. The simulated hydraulics using the decomposed mesh gave a better representation of the observed flood extent than the more simplistic but computationally efficient approach of sampling topography and vegetation friction factors on to larger floodplain elements in an undecomposed mesh, as well as the traditional approach using no LiDAR‐derived data but simply using a constant floodplain friction factor. Use of the decomposed mesh also allowed velocity variations to be predicted in the neighbourhood of vegetation features such as hedges. These variations could be of use in predicting localized erosion and deposition patterns that might result in the event of a flood. Copyright © 2003 John Wiley & Sons, Ltd.     

Soil production and hillslope transport in mid‐latitudes during the last glacial–interglacial cycle: a combined data and modelling approach in northern Ardennes

The relative efficiency of various hillslope processes through Quaternary glacial–interglacial cycles in the mid‐latitudes is not yet well constrained. Based on a unique set of topographic and soil thickness data in the Ardennes (Belgium), we combine the new CLICHE model of climate‐dependent hillslope evolution with an inversion algorithm in order to get deeper insight into the ways and timing of hillslope dynamics under one such climatic cycle. We simulate the evolution of a synthetic hill reproducing the slope, curvature, and contributing area distributions of the hillslopes of a ~ 2500 km² real area under a simple two‐stage 120‐kyr‐long climatic scenario with linear transitions between cold and warm stages. The inversion method samples a misfit function in the model parameter space, based on estimates of the fit of topographic derivative distributions in classes of soil thickness and of the relative frequencies of the predicted soil thickness classes. Though the inversion results show remarkable convergence patterns for most parameters, no unique solution emerges. We obtain five clusters of good fits, whose centroids are taken as acceptable model solutions. Based on the predicted time series of average denudation rate and soil thickness, plus snapshots of the soil distribution at characteristic times, we discuss these solutions and, comparing them with independent data not involved in the misfit function, we identify the most realistic scenario. Beyond providing first‐order estimates of several parameters that compare well with published data, our results show that denudation rates increase dramatically for a short time at both warm–cold and cold–warm transitions, when the mean annual temperature passes through the [0, ?5 °C] range. We also point to the overwhelming importance of solifluction in shaping hillslopes and transporting soil, and the role of depth‐dependent creep (including frost creep) throughout the climatic cycle, whereas the contributions of simple creep and overland flow are minor. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Radio‐tracking gravel particles in a large braided river in New Zealand: a field test of the stochastic theory of bed load transport proposed by Einstein

Hans A. Einstein initiated a probabilistic approach to modelling sediment transport in rivers. His formulae were based on theory and were stimulated by laboratory investigations. The theory assumes that bed load movement occurs in individual steps of rolling, sliding or saltation and rest periods. So far very few attempts have been made to measure stochastic elements in nature. For the first time this paper presents results of radio‐tracing the travel path of individual particles in a large braided gravel bed river: the Waimakariri River of New Zealand. As proposed by Einstein, it was found that rest periods can be modelled by an exponential distribution, but particle step lengths are better represented by a gamma distribution. Einstein assumed an average travel distance of 100 grain‐diameters for any bed load particle between consecutive points of deposition, but larger values of 6·7 m or 150 grain‐diameters and 6·1 m or 120 grain‐diameters were measured for two test particle sizes. Together with other available large scale field data, a dependence of the mean step length on particle diameter relative to the D₅₀ of the bed surface was found. During small floods the time used for movement represents only 2·7% of the total time from erosion to deposition. The increase in percentage of time being used for transport means that it then has to be regarded in stochastic transport models. Tracing the flow path of bed load particles between erosion and deposition sites is a step towards explaining the interactions between sediment transport and river morphology. Copyright © 2001 John Wiley & Sons, Ltd.