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During rest periods, bedload tracers can be buried, while transport can move them to locations with different bed shear stresses or a different riverbed composition. This affects the mobility of the tracers compared to that of the bedload at the location where the tracers were seeded and has so far limited the explanatory power of field tracer studies on the virtual bedload velocity. This paper proposes a method to assess both the unsteady virtual tracer velocity and the unsteady virtual bedload velocity from field tracer studies. First, the virtual bedload velocity was conceptualized as the velocity of a relay run and contrasted with the velocity of the decelerating runs of bedload tracers. Then, a regression method for deriving the unsteady virtual velocity of bedload tracers was extended to account for tracer slowdown by including a corresponding function of the distance traveled. Finally, data from 65 bedload tracers in the Upper Drava River with very‐high‐frequency (VHF) transmitters were used for method testing. By linking the measured tracer mobility to the hydraulics and bed surface grain size near the seeding location, it was possible to determine the unsteady bedload velocity function as the unsteady tracer velocity function at a travel distance of zero. The tracer travels exhibited increasing slowdown effects with increasing tracer grain size, probably due to the dominant role of advection effects at the study site. The derivation of the bedload velocity ensures comparability to laboratory results and between tracer studies. Key Points Gaps between laboratory and field are bridged by basing bedload tracer analyses on theories from laboratory and considering slowdown Understanding the bedload velocity as that of a relay run as opposed to that of individual tracer runs allowed deriving the bedload velocity The derived formulas describe well the transport of bedload tracers with measured travel distances reaching more than 30 km

Human intervention makes river channels adjust their slope and bed surface grain size as they transition to a new equilibrium state in response to engineering measures. Climate change alters the river controls through hydrograph changes and sea level rise. We assess how channel response to climate change compares to channel response to human intervention over this century (2000–2100), focusing on a 300‐km reach of the Rhine River. We set up a schematized numerical model representative of the current (1990–2020), non‐graded state of the river, and subject it to scenarios for the hydrograph, sediment flux, and sea level rise. We conclude that the lower Rhine River will continue to adjust to past channelization measures in 2100 through channel bed incision. This response slows down as the river approaches its new equilibrium state. Channel response to climate change is dominated by hydrograph changes, which increasingly enhance incision, rather than sea level rise. Plain Language Summary Humans have modified rivers to enable boat traffic, to protect people against flooding, and to provide them with freshwater and energy. When the shape of a river changes, the amount of sand and gravel (sediment) that can move along its bed also changes. In response, rivers change their slope and bed characteristics, so that they can transport as much sediment as they receive from higher up in the basin. This results in changes in bed level, which becomes higher or lower, causing problems for navigation and flood protection. Climate change makes this worse, because it changes the amount of water flowing down the river, and sea level. This further affects the amount of sediment that can move down the river, therefore causing additional bed level change. Here we study how climate change affects the lower Rhine River (Germany‐Netherlands), over the 21st century. This river has been heavily modified by humans, and its bed has been lowering over hundreds of kilometers. With a computer model, we simulate how different scenarios of climate change affect this behavior. We foresee that the ongoing bed level lowering will continue in the upcoming decades, and that it will be enhanced by climate change. Key Points Human intervention will continue to govern channel response in the lower Rhine River by 2100, mainly through channel bed incision Climate change leads to sea level rise and hydrograph adjustment, the latter being dominant and causing enhanced incision Channel response to human intervention slows down as the river approaches its equilibrium state, but response to climate change accelerates

The frictional resistance of river beds affects how water discharge is partitioned between depth and velocity, which is important in many aspects of hydrology, geomorphology, and aquatic ecology. Many of the most widely‐used resistance equations predict reach‐average velocity from relative submergence (RS), the ratio of mean flow depth to a bed roughness height such as the 84th percentile of the bed grain‐size distribution ( D 84 ). Nondimensional hydraulic geometry (HG) is an alternative approach that directly partitions unit discharge into depth and velocity. We show that any RS equation has an implicit or explicit HG equivalent, and the other way round. Analysis of a large set of flow measurements in gravel‐ and boulder‐bed channels confirms previous findings that HG equations using D 84 outperform mathematically equivalent RS equations in predicting velocity. This paradox is explained by mathematical analysis and numerical experiments, both of which show that HG equations are less sensitive to the inevitable measurement uncertainty in the variables required for a prediction and the observed velocity used for testing. We also propose a new, simple and effective HG equation using D 84 to predict depth and velocity from unit discharge. It is derived in the same way as the now widely‐used variable‐power equation equation (Ferguson, 2007, https://doi.org/10.1029/2006wr005422 ) and for deep flows it reduces to an inverted Manning‐type equation. It should be possible to use HG equations for flow resistance in sand‐bed and bedrock rivers, but this may require new definitions of roughness height.

This study initially examines the various sources of flow resistance in sand-bed (lowland) and gravel-bed (mountainous) rivers along with the limitations of traditional estimation methods. The nondimensional hydraulic geometry approach, relating dimensionless flow discharge ( ) to the Darcy-Weisbach friction factor ( ), has demonstrated good performance for both river types, covering shallow to moderately deep flows. However, accuracy in estimating is affected by simplifications like assuming uniform and deep flow, neglecting bed load transport and vegetation effects, which require further evaluation. To address these issues, the proposed method is evaluated using data from four sand-bed rivers in Slovakia (with vegetation), and three gravel-bed rivers in Iran (dominated by cobbles and boulders). Bedforms prove to be significant resistance sources in all studied rivers. The approach yields separate predictors for each river type, showing a satisfactory agreement between observed and calculated values within a maximum deviation of ±20% error bands. These predictors are further validated using field data and established equations from rivers with similar physiographic characteristics. Results indicate the method performs well in predicting flow resistance in sand-bed rivers, slightly overestimating overall (+40%). It effectively captures riverbed features and vegetation influence under small-scale roughness conditions. However, the predictor’s validity for gravel-bed rivers is somewhat limited due to high variability in water-surface profiles, making it challenging to accurately capture flow dynamics under large-scale roughness conditions. Addressing complex characteristics of gravel-bed riverbeds, including boulders and local energy extraction, is crucial for improving the estimation of water-surface profile variations and flow resistance using the hydraulic geometry approach.

What are the main findings? Surface roughness metrics derived from UAV-SfM point clouds effectively characterize grain-size distributions in gravel-bed rivers. A reach-scale grain size–roughness relation was established for riverbeds with wide grain-size variability. What is the implication of the main finding? The integrated relation enables rapid estimation of riverbed grain-size distributions using UAV-SfM-derived roughness. Applicability tests indicate more reliable grain-size estimation for coarser grains than for finer grains in heterogeneous gravel beds. Understanding the sediment grain size distribution in riverbeds is essential for analyzing sediment transport, riverbed morphology, and ecological habitats. Previous studies have shown that riverbed grain size can be inferred from surface roughness using linear relations between manually sampled grain sizes and percentile roughness derived from point-cloud data. However, these relations are often established within narrow grain-size ranges, causing regression coefficients to vary across percentiles and limiting their applicability to broader grain-size variability. This study conducted field investigations and UAV (Unmanned Aerial Vehicle) surveys to examine grain size–roughness relations across four coarse-grained mountainous river reaches in Taiwan, characterized by a wide grain-size distribution (D[sub.16]–D[sub.84]: 2.3–525 mm). High-resolution 3D point clouds were generated using UAV-SfM (Structure-from-Motion) techniques for roughness metric computation. Linear relations between grain size D[sub.i] (i = 16, 25, 50, 75, and 84) and their corresponding percentile roughness RH[sub.i] were developed and evaluated. Results indicate that D[sub.i]-RH[sub.i] relations exhibit moderate to strong correlations (R[sup.2] = 0.60–0.94), and the regression slope increases exponentially with grain size. To address cross-percentile variability, an integrated power-law relation was proposed by pooling all paired D[sub.i]-RH[sub.i] data from Reach R1, yielding a single, continuous reach-scale grain size–roughness correlation. Applicability tests using data from the remaining three reaches show that the integrated relation performs better for coarser grains (D[sub.50]–D[sub.84]) than for finer grains. Future work incorporating more sampling sites across diverse river types will help further refine the integrated relation and improve its cross-reach applicability.

Bridges with shallow foundations are highly susceptible to flood scouring due to their limited embedment depth and small contact area between the soil and foundation. This can lead to foundation voids, posing a serious threat to bridge safety. To prevent and mitigate scouring risks, this paper investigates the riverbed scouring characteristics of shallow foundation bridges under different hydrological conditions.The study found that under high water levels and flow velocities, scour depth significantly increased.Under extreme hydrological conditions, a horseshoe vortex forms at the base of the front end of the bridge pier, causing scour pits on both sides of the upstream face of the foundation, which is the main cause of foundation voids that first appear at 2580 s with a maximum scour depth of -2.51 m and a void area of 0.5%, continuing to increase over time.Based on simulated scouring data, this study proposes a method for converting boundary conditions from a scouring model to a mechanical model. This method utilizes point cloud reverse engineering technology to generate a riverbed surface from the three-dimensional coordinate matrix of the boundary and import it into the structural analysis field. Hydraulic effects are calculated using a CFD model and transferred to the structural domain through fluid-structure interaction technology, achieving multi-physical field coupling among water flow, soil, and structure. This method addresses the current limitations in simulating complex scouring forms in bridge flood damage research, providing reliable technical support for subsequent studies on the damage behavior of shallow foundation bridges under flood scouring conditions.

River beds are traditionally assumed to become mobile at a fixed value of nondimensional shear stress, but several flume and field studies have found that the critical value is higher in steep shallow flows. Explanations for this have been proposed in terms of the force balance on individual grains. The trend can also be understood in bulk‐flow terms if total flow resistance has “base” and “additional” components, the latter due to protruding immobile grains as well as any bedforms, and the stress corresponding to “additional” resistance is not available for grain movement in threshold conditions. A quantitative model based on these assumptions predicts that critical Shields stress increases with slope, critical stream power is near‐invariant with slope, and each has a secondary dependence on bed sorting. The proposed slope dependence is similar to what force‐balance models predict and consistent with flume data and most field data. Possible explanations are considered for the inability of this and other models to match the very low critical values of width‐averaged stress and power reported for some low‐gradient gravel bed rivers. Key Points New conceptual explanation for increase in critical Shields stress with slope Model predicts secondary dependence on bed sorting New model for critical stream power as spinoff

The threshold of incipient bedload motion, expressed either as a critical force or as a critical water discharge, is a key parameter in bedload transport prediction. Measuring the threshold of motion is difficult, and reliable data from natural streams are rare. By recording the vibrations triggered by bedload particles when moving over a steel plate mounted in the channel bed, we determined the time at start and end of bedload transport in four streams, where discharge is continuously monitored. The threshold discharge scatters over approximately one order of magnitude for each stream, reinforcing previous observations that critical discharge is characterized by a distribution of values. We interpret a strong correlation between the discharge at the start of transport and the discharge at the end of transport of the previous event to reflect temporal changes in bed structure and consequent effects on the driving and resisting forces acting on the bed.

Spatial distributions of depth‐averaged water velocity, shear velocity, and apparent bed load velocity are mapped for the first time in a long reach of a wandering gravel bed river, lower Fraser River, British Columbia. Spatially intensive acoustic Doppler current profiler (aDcp) measurements were collected on the falling limbs of two freshets. Flow in the first year was near the threshold of motion, whereas in the second year discharge exceeded bankfull. Spatial distributions are interpolated from the point data using kriging. Joint density functions for shear velocity and flow depth throughout the reach are presented; marginal densities for shear velocity were near normally distributed but depth distributions were positively skewed by deep pools. The uncertainty of the spatial distributions is also assessed based on modeled temporal variability of the flow and bed load transport, measured aDcp error velocities, and calculated interpolation errors. The resulting maps are remarkably coherent, with maximum depth‐averaged velocity, shear velocity, and apparent bed load velocity following the thalweg. Largest values occur in channel bends at zones of flow convergence where the thalweg flow accelerates toward the bank. However, in the lower flow year the highest apparent bed load velocity was observed outside the thalweg in a deep pool downstream of a rapidly eroding cut bank. Erosion at this site was related to a flow confluence with relatively low shear but highly turbulent, strongly three‐dimensional separated flow.

This paper deals with impact of geomorphic responses such asthalweg shifting, sandbar instability, pool-riffle alteration, river bank erosion, channel incision river bed lowering and river bank erosion on riverine land cover dynamics arises by instream and floodplain sand mining in an alluvial reach as Kangsabati River from Mukutmonipur dam to Rajnagar confluence (193 km) during 2002–2016. Four segments i.e. Lalgarh, Mohanpur, Kapastikri and Rajnagar share as 554,656 m ton/year sand from 141 mining sites whereas others segment as Khatra, Raipur, Dherua and Panskura share only 33,497 m ton/year sand from 50 mining sites in the entire channel. Several maps were prepared to identify consequences of morphological responses with the help of field study and GIS technique. Friend and Sinha’s method (Geol Soc Lond 75(1):105–111, 1993) was used to detect planform change with geomorphic responses throughout the course. Pearson correlation matrix is used to establish the relation between geomorphic responses and land cover dynamics incorporates with mining intensity. The result shows that higher value of geomorphic responses decrease sandchar, riparian area but increases channel, mining, pits and clay cover in mining prone segments as Lalgarh, Mohanpur, Kapastikri, and Rajnagar. The lower value of geomorphic responses increase sandchar, riparian area but decreases channel, mining, pit sites and clay cover in sandchar segments as Khatra, Raipur, Dherua and Panskura, respectively. Therefore, sand mining greatly impact on riverine land covers dynamic following instable geomorphic responses. Moreover, this study reveals that sustainable sand mining incorporates with stable geomorphic responses maintain fluvial dynamics controlling of erosion and deposition process.