Water Surface Slope Research Articles

Bifurcation Instability Modulated by a Connecting Channel Leads to Periodic Water Partitioning in a Simple Channel Network

AbstractWater and mass transport in distributary channel networks play an important role in nourishing fluvial and coastal wetlands, and are largely determined by the morphological configurations of channel bifurcations. While the morphological equilibrium of a single channel bifurcation has been extensively studied, the equilibrium configurations of channel networks with connecting channels linking the bifurcating branches, that is, the “bifurcation‐connecting channel” units that are commonly found in rivers, deltas and estuaries, remain elusive. In this simple yet representative channel network of the “bifurcation‐connecting channel” unit, we observed through numerical simulations an oscillatory water partitioning under moderate Shields stress and channel aspect ratio, in addition to the steady‐state solutions reported in previous studies. The oscillatory water partitioning indicates a newly discovered periodic solution, which is an emergent behavior under constant boundary conditions. We found that the periodic solution is primarily due to the dynamic interactions between bifurcation instability and water surface slope advantage in the two branches modulated by the reversable discharges through the connecting channel, under moderate Shields stress and channel aspect ratio. In such cases, the developed slope advantage in the subordinate branch can suppress the deepening of the dominant branch and eventually lead to the shifting of the dominant branch. In contrast, the channel network attains a steady‐state solution when the slope advantage or the bifurcation instability is dominant with relatively low and high Shields stress (or channel aspect ratio). Our results improve the understanding on the evolution and restoration of channel networks under increasing human interventions in global deltas.

Hydraulics of Time-Variable Water Surface Slope in Rivers Observed by Satellite Altimetry

The ICESat-2 and SWOT satellite earth observation missions have provided highly accurate water surface slope (WSS) observations in global rivers for the first time. While water surface slope is expected to remain constant in time for approximately uniform flow conditions, we observe time varying water surface slope in many river reaches around the globe in the ICESat-2 record. Here, we investigate the causes of time variability of WSSs using simplified river hydraulic models based on the theory of steady, gradually varied flow. We identify bed slope or cross section shape changes, river confluences, flood waves, and backwater effects from lakes, reservoirs, or the ocean as the main non-uniform hydraulic situations in natural rivers that cause time changes of WSSs. We illustrate these phenomena at selected river sites around the world, using ICESat-2 data and river discharge estimates. The analysis shows that WSS observations from space can provide new insights into river hydraulics and can enable the estimation of river discharge from combined observations of water surface elevation and WSSs at sites with complex hydraulic characteristics.

Impacts of grade control structures on riverbed degradation

Sediment flux of many rivers has been significantly reduced due to human activities caused by economic development, leading to increasingly severe riverbed degradation. To prevent riverbed degradation, grade control structures (GCSs) have been widely applied in degrading channels. Existing studies have not provided a good understanding of the effects of GCSs on flow characteristics and bed morphology in degrading channels, limiting the management of degrading channels. A series of flume tests with no sediment supply are conducted to investigate the effects of GCSs on upstream water levels and riverbed morphology in degrading channels. The experimental results indicate that: (1) in the initial stage of degradation, the water surface slope in the backwater reach is linearly and negatively correlated with the GCS-height Froude number, based on the average flow velocity upstream of the backwater reach due to GCS and the height of GCS; (2) the effective protection bed length upstream of GCS is approximately equal to the length of the reach where the flow velocity is less than the critical velocity for sediment motion in the backwater zone; (3) for sequential GCSs, the effective protection bed length will decrease if GCS is located in the backwater reach of the downstream GCS. A semi-analytical calculation method of the effective protection length and equilibrium bed profile upstream of GCS in degrading channels is proposed based on the critical condition of sediment motion and weir flow formulas. The computed values by the proposed calculation method agree well with the experimental data of the present study.

Satellite-based water surface slope over a small mountain river in northern China

Satellite altimetry has become a crucial alternative for measuring inland water surface elevations apart from ground observations. Water surface slope (WSS), a fundamental parameter in river discharge simulation, also allowing for assimilating satellite and ground-observed water level data with different observation positions. There are various satellite data products offering precise measurements of river water levels and estimates of WSS on a global scale. However, satellites observation of water surface over small rivers, particularly those in mountainous areas with narrow river channels, continues to be difficult. This study focuses on evaluating the precision of the ICESat-2 ATL03 photon height data in estimating WSS throughout the mountainous river section of Yongding River, which flows across the Hebei Province and Beijing City in northern China. The ICESat-2 ATL03 data with minimum along-track sampling interval of 0.7 m makes it possible to accurately estimate the WSS for small river sections that ranged from 50 to 100 m in width. A histogram-based statistical approach was used for identifying the satellite lidar photon height located right over the water surface. The eleven pairs of satellite virtual stations selected for extracting river water surface elevation and estimating river WSS demonstrated an overall validation correlation coefficient of 0.98. The range of relative error in WSS estimation is between 0.13 % and 9.02 %. The results of this work have important implications for using satellite-based measurements to estimate critical hydrological parameters in small and mountainous river basins in the absence of ground observations.

The effect of emergent vegetation on flow, bedload transport, and bed morphology in a diffluence-confluence unit on a meandering channel

A diffluence-confluence unit on a meandering channel, coupled with the broadening of the divergence zone and meander circulation, promotes sediment deposition on the convex bank, forming shoals to stimulate vegetation growth, which results in water level elevation, velocity reduction, and bank stabilization. Despite these significant impacts, current research on the influence of this channel remains limited. This study conducts a series of flume experiments to quantify the influence of vegetation in a such channel on flow hydraulics, bedload transport, and bed morphology, and their inter-links. The results reveal that increased vegetation cover density subtly influences the flow depth in straight inlet reaches, triggers higher flow depth and fluctuations in the left anabranch, and induces uneven velocity distribution, especially below the crest of the curved channel. Centrifugal forces and vegetation-induced water levels shape the transverse water surface slope, resulting in a downward concave trend and unique slopes within each anabranch. The bedload transport capacity rapidly increases until an armoring layer forms, a process expedited by vegetation, particularly in high discharge conditions. This vegetation effect, amplified with higher density, enhances bedload transport rate and size but is lessened by increased discharge, which also reduces fluctuations during armoring layer formation. The statistical parameters of bed morphology at the grain-scale and structure-form-scale indicate that denser vegetation reshapes erosion dynamics across anabranches, intensifying downstream scouring and propelling the sediment deposition zone, especially under high discharge. Furthermore, the flow bifurcation ratio intensifies with escalating vegetation cover density and is assessed by a modified model consider vegetation effects with heightened precision. The apex scour depth downstream of the unit, induced by the confluence of water from both anabranches, can be characterized as a function of the dimensionless discharge and vegetation density. Concurrently, a refined model for bedload transport rate, influenced by the turbulent kinetic energy arising from emergent vegetation in this intricate reach, is proposed with high accuracy.

Hydraulic River Models From ICESat‐2 Elevation and Water Surface Slope

AbstractForecasting flood and drought events requires accurate modeling tools. Hydraulic river models are based on estimates of riverbed geometry which are traditionally collected in situ. The novel Ice, Cloud and Land Elevation Satellite 2 [ICESat‐2] lidar altimetry mission with 6 simultaneous high‐resolution laser beams provides the opportunity to define river cross‐section geometries as well as observe water surface elevation [WSE] and water surface slope spatially resolved along the river chainage. This paper describes a method to utilize terrain altimetry and water surface slope estimates to define complete river geometries from ICESat‐2 data products, using the diffusive wave approximation to calculate depth in the submerged section not penetrated by the lidar. Exemplifying the method, cross‐sections are defined for a stretch of the Mekong River. Hydrodynamic model results of the stretch are compared with ICESat‐2 WSE estimates and in situ gauging station time series. Insights in river characteristics from satellite imagery and the ICESat‐2 slope estimates allow for fine‐tuning of the cross‐sections using spatially varying Manning numbers. The final model achieves a root mean square error against the ICESat‐2 WSE of 0.676 m and average Kling‐Gupta Efficiency against gauging station time series of 0.880. The method is limited by the diffusive wave approximation resulting in inaccurate cross‐section estimates in sections with supercritical flow or significant acceleration. Errors can be identified from ICESat‐2 WSE estimates and reduced with additional cross‐sections. Combined with hydrological models, the method will allow for cross‐section definition without in situ data.

Siting Considerations for Satellite Observation of River Discharge

AbstractWith growing global capability for satellite measurement of river discharge (flow) comes a need to understand and reduce error in satellite‐based discharge measurements. Satellite‐based discharge estimates are based on measurements of water surface width, elevation, slope, and potentially velocity. Site selection is important for reducing error and uncertainty in both conventional and satellite‐based discharge measurements because geomorphic river characteristics have strong control over the relationships between discharge and width, water surface elevation (or depth), slope, and velocity. A large ground‐truth data set of 8,445 conventional hydraulic measurements, collected by acoustic Doppler current profilers at 503 stations in the United States, was developed and quality assured to examine correlation between river discharge and water surface width, depth, velocity, and cross‐sectional area. A separate database of river surface slope and discharge time‐series was developed from paired continuous monitoring stations to examine slope‐discharge correlations. Results show that discharge correlates most strongly with velocity, cross‐sectional area, depth, width, and slope, in that order. Uncertainty of satellite discharge estimates is affected by observed hydraulic variable and reach‐specific variability in observed variable(s) characteristics including range of variability, georegistration accuracy, and stability over time of relationships between discharge and observed hydraulic variable.

Undervalued dry riverbeds: A key factor in equating intermittent river CO2 emissions to perennial rivers

Intermittent rivers in semiarid and arid regions, constituting over half of the world's rivers, alternate the carbon cycle interactions among the biosphere, hydrosphere, and atmosphere. Inadequate quantification of flow duration and river water surface area, along with overlooked CO2 emissions from dry riverbeds, result in notable inaccuracies in global carbon cycle assessments. High-resolution remote sensing images combined with intensive field measurements and hydrological modelling were used to estimate and extract the flow duration, river water surface area and dry riverbed area of Huangfuchuan, an intermittent river watershed that acts as a major tributary of the Yellow River in semiarid Northwest China. CO2 emission rates and partial pressures in water and air across the watershed were in-situ measured. In 2018, the flow duration of Huangfuchuan increased from less than 5 days in the first-order tributary to 150 days in the sixth-order mainstream. River water surface area estimated by remote sensing extraction plus the hydrodynamic model simulation varied from 3.9 to 88.6 km2 under 5 %–95 % discharge frequencies. CO2 emissions from the water-air interface and dry riverbed in 2018 were estimated at 582.3 × 103 and 355.2 × 103 ton, respectively. The estimated total annual emission (937.5 × 103 ton) aligns closely with the range of emissions (67.3 × 103–1377.2 × 103 ton) calculated for the water-air interface alone, derived using DEM river length and hydraulic geometry method. This similarity can be attributed to the overestimation of flow duration and flow velocity, as well as the over- or under-estimation of river water surface area and slope. The new method proposed in this study has large potential to be applied in estimating CO2 emissions from data-scarce intermittent rivers located in mountainous regions and provides a standardized solution in the estimation of CO2 emission. Results of this research reveal the spatiotemporal distribution of CO2 emissions along an intermittent river system and highlight the substantial role of dry riverbed in carbon cycle.

Flood Propagation Characteristics in a Plain Lake: The Role of Multiple River Interactions

Plain lakes play a crucial role in the hydrological cycle of a watershed, but their interactions with adjacent rivers and downstream water bodies can create complex river–lake relationships, often leading to frequent flooding disasters. Taking Poyang Lake as an example, this paper delves into its interaction with the Yangtze River, revealing the spatiotemporal patterns of flood propagation within the lake and its impact on surrounding flood control measures. The aim is to provide insights for flood management in similar environments worldwide. This study employs a comprehensive approach combining hydrological statistical analysis and two-dimensional hydrodynamic modeling, based on extensive hydrological, topographic, and socio-economic data. The results indicate that the annual maximum outflow from Poyang Lake is primarily controlled by floods within the watershed, while the highest annual lake water level is predominantly influenced by floods from the Yangtze River. The peak discharge typically reaches the lake outlet within 48 h, with the peak water level taking slightly longer at 54 h. However, water storage in the lake can shorten the time that it takes for the peak discharge to arrive. When converging with floods from the Yangtze River, the peak water level may be delayed by up to 10 days, due to the top-supporting interaction. Furthermore, floods from the “Five Rivers” propagate differently within the lake, affecting various lake regions to differing degrees. Notably, floods from the Fu River cause the most significant rise in the lake’s water level under the same flow rate. The top-supporting effect from the Yangtze River also significantly impacts the water surface slope of Poyang Lake. When the Yangtze River flood discharge significantly exceeds that of the “Five Rivers” (i.e., when the top-supporting intensity value, f, exceeds four), the lake surface becomes as flat as a reservoir. During major floods in the watershed, the water level difference in the lake can increase dramatically, potentially creating a “dynamic storage capacity” of up to 840 million cubic meters.

Generation of High‐Resolution Water Surface Slopes From Multi‐Mission Satellite Altimetry

AbstractFor nearly three decades, satellite radar altimetry has provided measurements of the water surface elevation (WSE) of rivers. These observations can be used to calculate the water surface slope (WSS), which is an essential parameter for estimating flow velocity and river discharge. In this study, we calculate a non time‐varying high‐resolution WSS of 11 Polish rivers based on multi‐mission altimetry observations from 11 satellites in the period from 1994 to 2023. The proposed approach is based on a weighted least squares adjustment with an additional Laplace condition and an a priori gradient condition. The processing is divided into river sections not interrupted by dams and reservoirs. After proper determination of the WSE for each river kilometer (bin), the WSS between adjacent bins is calculated. To assess the accuracy of the estimated WSS, it is compared with slopes between gauge stations, which are referenced to a common vertical datum. Such gauge stations are available for 8 studied rivers. The root mean squared error (RMSE) ranges from 4 mm/km to 77 mm/km, with an average of 27 mm/km. However, the mean RMSE decreases to 11 mm/km when the 2 mountain rivers are excluded. The WSS accuracies are also compared with slope data sets based on digital elevation models, ICESat‐2 altimetry, and lidar. For 6 rivers the estimated WSS shows the highest accuracy. The improvement was particularly significant for mountain rivers. The proposed approach allows an accurate, non time‐varying high‐resolution WSS even for small and medium‐sized rivers and can be applied to almost any river worldwide.

System‐Wide Effects of Local Bed Disturbance on the Morphological Evolution of a Bifurcating Channel Network

AbstractDeltaic channel networks are important conduits for water and material supplies to the fluvial and coastal communities. However, increasing human interventions in river deltas have altered the topology and geometry of channel networks as well as their long‐term evolution. While the morphological evolution of a single channel has received extensive studies, the system‐wide morphological responses of channel networks to local disturbances remain largely unclear. Here we investigate the morphological responses of a bifurcating channel network subject to local disturbance of channel deepening due to dredging and sand mining through idealized simulations, and further compare the results with the reference scenarios of a single channel and theoretical analysis of the phase plane. The results show that the infilling of the local deepening is associated with the erosion of the entire branch, which also causes system‐wide effects on the siltation of the other branch. The morphological responses of the bifurcating channel network consist of a relatively short stage for the infilling of the local deepening followed by a relatively long stage for recovering the equilibrium configuration of the river bifurcation. The system‐wide effects of the local disturbance arise from the altered water surface slope and water partitioning downstream of the bifurcation due to the local deepening. Also, the prolonged recovery of the equilibrium configuration is consistent with theoretical analysis, which reveals a slow evolution of the bifurcation when approaching the equilibrium. Our results can help understand the long‐term morphological responses of large‐scale complex channel networks and inform water managements under increasing human interventions.

Hydrodynamic modelling to assess habitat suitability of the Ganga River dolphins

AbstractThe Ganga River hosts a metapopulation of endangered aquatic species. This study uses a hydrodynamic model (HEC‐RAS) to assess the habitat suitability of the Ganga River dolphins (GRDs) in a small reach (7.5 km) of the Ganga River at the upstream of Narora barrage in varying flow. We use Lidar points clouds to generate topography, Acoustic Doppler Current Profiler (ADCP), and differential GPS (DGPS) to measure channel bathymetry and streamwise water surface slope. Further, the water level data from satellite altimeter is used to calibrate the model and discharge measured in field to validate the model output. We found that in the high flow period, the required flow depth for dolphin habitat is available throughout in the study reach. However, in the lean flow, the required flow depth and velocity are available only in some patches. The methodology developed here would be very useful in monitoring hydraulic habitat suitability of aquatic species in ungauged rivers.

River Water Level and Water Surface Slope Measurement From Spaceborne Radar and LiDAR Altimetry: Evaluation and Implications for Hydrological Studies in the Ganga River

River Water Level and Water Surface Slope Measurement From Spaceborne Radar and LiDAR Altimetry: Evaluation and Implications for Hydrological Studies in the Ganga River

Stage‐Slope‐Discharge Relationships Upstream of River Confluences Revealed by Satellite Altimetry

AbstractWith increasing coverage, density, and accuracy of the global inland water altimetry record, remote sensing observations of water surface elevation (WSE) and water surface slope (WSS) are becoming available for the world's rivers. In steady, uniform flows, WSS is invariable, while there is a unique one‐to‐one relationship between WSE and discharge, the rating curve. While the assumptions of steady uniform flow are appropriate for many rivers, they are violated upstream of river confluences. We present a simple analytical hydraulic model of river confluences using the theory of steady, gradually varied flow. We apply the model to four river confluences in the Mississippi‐Missouri river system. We determine the spatial extent of the backwater‐affected zones and map WSE‐discharge and WSS‐discharge relationships. We show that coincident measurements of WSE and WSS from new satellite altimetry missions effectively constrain discharge estimates from space in the backwater‐affected zones upstream of river confluences.

The Effect of Sediment Supply on Pool‐Riffle Morphology

AbstractDownstream width variations can generate pool‐riffle morphology under experimental conditions, in numerical simulations and natural river channels. The present understanding of how pool‐riffle morphology varies with sediment supply and caliber, however, is insufficient due to the limited range of sediment supply rates explored in previous experiments and the little attention paid to sand supply and sediment size distribution in the laboratory and in the field. We present a model of river morphodynamics that can account for the spatial variability of channel width, and we validate the model with experimental data. Model validation shows how this one‐dimensional model can capture pool‐riffle formation, growth, and equilibration with errors that are comparable with those of other 1D models of river morphodynamics. We then apply the validated model to study the effects of sediment supply rate and caliber on pool‐riffle morphology. Model results show that pool‐riffle morphology is resilient to the range of tested sediment supply (i.e., five‐fold the sediment amount, 41‐fold the sand amount and coarsening the gravel supply). Bed and water surface slopes are sensitive to all types of change of sediment supply, whereas the sensitivity of bed surface sediment grain size varies with the type of change. These findings support prior research emphasizing the role of downstream width variations for the development/maintenance of pool‐riffle morphology and can help in the restoration and recovery of pool‐riffle gravel‐bed rivers.

ICE2WSS; An R package for estimating river water surface slopes from ICESat-2

ICE2WSS; An R package for estimating river water surface slopes from ICESat-2

Study of Navigable Flow Conditions in the Intermediate Channel of Decentralized Cascade Locks

In this study, the effects of the different conveyance modes of the intermediate channel in decentralized cascade locks on navigation flow conditions were investigated. A new hybrid numerical simulation method was established to evaluate navigable flow conditions in intermediate channels at different water conveyance modes. This hybrid numerical simulation method was reliably compared by physical modeling tests. We used the 33.73 m class high-head intermediate channel filled with water as a study case. The study used the maximum water surface slope and maximum flow velocity as evaluation indexes for navigable flow conditions. The results showed that the navigable flow conditions of the centralized water conveyance mode were worse compared to the decentralized water conveyance mode in the intermediate channel. Especially in the upstream region of the intermediate channel with a centralized outflow, the navigable flow conditions were exceptionally harsh. We recommend the decentralized outflow mode in the high-head intermediate channel. This study provides an effective numerical simulation method for optimizing the water conveyance mode of the high-head intermediate channel of decentralized cascade locks and saving project investment.

Evaluation of nearshore bathymetric inversion algorithms using camera observations and synthetic numerical input of surface waves during storms

Nearshore bathymetry is difficult to measure using survey methods when wave heights approach the breaking limit. Remote sensing using digital cameras offers a way to observe the surf zone and calculate water depths based on phase speed but comes with its challenges of potentially noisy data that can introduce error into estimates of frequency and wavenumber used in phase speed calculation. This study investigates the robustness of a new version of a bathymetric inversion algorithm (cBathy, version 2.0) in moderate to energetic wave conditions by comparing depth estimates from timeseries’ of pixel intensity with depth estimates from synthetic water level data. The synthetic data are generated by the phase-resolving numerical model, SWASH, and optical data were collected during a field experiment in 2015. Model results from SWASH computed with known bathymetry are used as input to cBathy, and depth estimates are compared to nearshore surveys. Argus camera observations are also used as input to cBathy for the same times as the SWASH simulations. The SWASH simulations resolve breaking waves and do not include (optical) changes to the relation between water surface slope and pixel intensity, termed modulation transfer function, that occur during wave breaking, enabling better estimates from bathymetric inversion algorithms near morphologic features like sand bars. The results indicate that improvements result from eliminating of disruptions to the modulation transfer function caused by wave breaking and residual foam. We show that the use of synthetic wave data is a valuable means of isolating errors in bathymetric inversion algorithms.

Numerical Investigation of Bed Shear Stress and Roughness Coefficient Distribution in a Sharp Open Channel Bend

The helical flow leads to the redistribution of the bed shear stress and roughness coefficient in open-channel bends, influencing the transport of sediment and riverbed evolution process. To explore the mechanisms underlying this redistribution, a 3D numerical simulation of a 180° sharp bend was performed by solving the Reynolds-averaged Navier–Stokes (RANS) equations using the Reynolds stress equation model (RSM) as the anisotropic turbulence closure approach. The results indicate that the high bed shear stress zone appeared in the inner bank region from the 50° to 110° sections, and the section maximum bed shear stress gradually shifted outwards, owing to the advective momentum transport by the circulation cells. The quantitative analyses of the terms in depth-averaged Navier-Stokes equations indicate that the contributions of the cross-stream circulation and cross-flow to the downstream bed shear stress were of the same order of magnitude, and the overall contribution rate of the cross-stream circulation was 20%. The contribution rates of the cross-flow, cross-stream circulation, turbulence, and pressure gradient to the transverse bed shear stress were approximately 30%, 7%, 3%, and 60%, respectively, indicating that the pressure gradient term arising from the transverse water surface slope played a dominant role. The Chezy resistance coefficient showed an overall decreasing trend along the bend. Therefore, an effective expression considering the streamwise variation along the centreline and transverse variation was successfully established to predict the uneven distribution of the Chezy resistance coefficient.

Studying the effect of boiler water releasing in rivers on some water properties (Al-Euphrates River at Al-Mussaib thermal power station as case study)'

Abstract Studying the effect of boiler water released in rivers on some water properties such as density, viscosity was done in this research. Equations of momentum, conversation, turbulence and energy were used with the relation between the temperature and water properties to describe those properties along the study reach. Simplifying of partial equation was done to obtain system of linear equation. Verification of numerical model by conducting comparison of observed data from Euphrates River at Mussaib Thermal Power Station with those computed by the model. The comparison results of density and viscosity show an agreement with using statistical tests such as Chi square and RMSE. The results of the study showed that increasing the bed roughness from 0.04 m to 0.12 m causes a longitudinal retardation of the values of density and viscosity values about (26 and 22%) respectively and vertical advance of these values about (14 and 12% ) respectively. Increasing the water surface slope from (6 cm/km to 12 cm/km) causes a longitudinal advance of density and viscosity values about (19 and 12%) respectively and vertical retardation of these values about (16 and 13%) respectively.