Distribution Of Suspended Sediment Concentration Research Articles

Study on the Vertical Distribution Characteristics of Suspended Sediment Driven by Waves and Currents

Port coasts are affected by waves and tidal currents, and sediment continues to silt up, leading to a reduction in the depth of water in the channel, blocking the channel and seriously affecting the safe operation of ports. The main cause of sediment deposition in ports is suspended sediment transport, and the characteristics of the vertical distribution of suspended sediment concentrations are the embodiment of the suspended sediment transport law. This paper is divided into three parts to study the vertical distribution characteristics of suspended sediment concentrations. Firstly, the shortcomings of the traditional diffusion model were analysed by using the finite mixing theory (FMT); secondly, the sediment mixing length coefficient κs model was introduced and combined with the sediment group settling velocity model to establish the vertical distribution model of suspended sediment concentrations under wave–current; finally, the effects of various factors on the vertical distribution of the suspended sediment concentration were investigated. The results show that the model in this paper has the characteristics of “low variance and low bias”, which solves the problem that κs is difficult to determine. When the model κs < κs′ (κs′ = 0.4), the concentration of suspended sediment predicted by κs′ is overestimated, and vice versa. As the sediment concentration increases, the interaction between particles increases and the vertical distribution of the suspended sediment concentration shows the pattern of “small top and large bottom”. The larger the particle size, the greater the sedimentation rate of the suspended sediment, and a large amount of sediment will be suspended near the bottom without mixing. The higher the wave height, the stronger the boundary layer turbulence and the movement of the water particles’ trajectory, and the smaller the difference in sediment concentration between the bottom and the sea surface.

Modeling of non-equilibrium suspended sediment transport process in open channel flows with vegetation

A mathematical model based on advection-diffusion theory is established to study the non-equilibrium sediment transport process in vegetated channels. The effects of vegetation on velocity distribution and sediment diffusion coefficients were considered, respectively. Validation against experimental data from flume studies confirms the model's ability to accurately predict the longitudinal sediment deposition rate and the vertical distribution of suspended sediment concentration (SSC). A comparative analysis of three sediment diffusion coefficient formulations indicates that the linear-exponential formula provides a more precise estimate of εsz, and the linear-exponential formula performs well in predicting the turbulent diffusion coefficients of both rigid and flexible vegetation when gently swaying. Moreover, the distance required for SSC to regain equilibrium is influenced by the submergence level of the vegetation canopy. At lower submergence levels, the canopy shear vortices significantly affect the vertical exchange of sediment, and the sediment diffusion coefficients exhibit pronounced stratification near the vegetation canopy. An increase in vegetation density at these lower submergence levels intensifies the shear vortices, thereby extending the distance needed for SSC to reach equilibrium. At higher submergence levels, the impact of canopy shear vortices is lessened, which reduces sediment diffusion coefficient stratification characteristics, and the flow is similar to rough boundary layer flow. An increase in vegetation density increases flow resistance, which shortens the distance required for SSC to attain equilibrium. However, further efforts are required to explore turbulent characteristics with highly flexible vegetation motion and the grain size distribution of non-uniform sediments in vegetated flows.

Numerical investigation for the influence of suspended sediment on salinity distribution in the Qiantang Estuary, China

Numerous studies have demonstrated that high suspended sediment concentration (SSC) can change density distribution and affect water mixing, but few scholars have investigated this impact on numerical simulations of estuarian salinity distribution. The Qiantang Estuary is a macro-tidal estuary with high SSC, which has a more significant influence on water density than that of salinity. Therefore, this paper established a three-dimensional (3D) numerical model coupling flow, salinity and SSC based on Delft3D and first analyzes the impact of SSC on salinity distribution under different runoff and tidal conditions in the Qiantang Estuary. The results indicated that simulated salinity generally decreases when considering the impact of SSC, suggesting a weakening effect on saltwater intrusion. The distribution of salinity difference (ΔS) and SSC show a strong spatial and temporal correlation, and ΔS peak increases and shifts upstream as the tidal range increases or runoff discharge decreases. The mechanism of SSC influencing saltwater intrusion can be summarized as follows: On the one hand, SSC increases the water density, which weakens the driving force for saltwater to move upstream, causing a decrease in flood current velocity and water level, and thereby diminishing the advective transport of salinity. On the other hand, SSC enhances density stratification, which weakens vertical turbulence and reduces the dispersive transport of salinity. These combined effects reduce both the advective and diffusive salinity fluxes during the flood tide, ultimately leading to a decrease in upstream salinity. Therefore, neglecting this effect in estuaries with high SSC can cause significant deviations in salinity simulation results, especially under low-flow and high-tide conditions.

The distribution of velocity and sediment concentration under currents in coastal seas

A power law velocity profile for engineering application was obtained based on the field data set of flow velocity and sediment concentration in coastal areas of Jinzhou, Nantong, and Zhoushan. Using theoretical analyses, van Rijn's formula for sediment concentration profile was modified. Tests of the new power-law velocity profile and the modified formula of suspended sediment concentration against a large data set were performed. The results show a good fit to the data and that these two formulae could demonstrate the basic principles of vertical distribution of flow velocity and suspended sediment concentration, respectively.

Estimation of the suspended sediment concentration in ice-covered channels based on the gravitational theory

Rivers in cold high latitude northern regions usually freeze during winter, thereby forming an ice cover on the water surface. The additional ice cover significantly changes the flow characteristics of the rivers and hence affects the process of water and sediment transport. Understanding the vertical profile of suspended sediment concentration (SSC) in ice-covered channel flows is helpful for investigating the sediment deposition and the bed morphology of rivers located in cold regions. To predict the SSC distribution in ice-covered channels, this study is based on the gravitational theory and puts forward a new SSC model by dividing the flow underneath the ice cover into the upper ice layer and the lower bed layer with the maximum streamwise velocity and the zero Reynolds shear stress as the interface. The calculated results of the new SSC model agree well with the collected experimental data, and the accuracy of the prediction results is evaluated by error analysis. Besides, the differences in the governing equations and the prediction accuracy between the gravitational theory and the diffusion theory are discussed, and thus the pros and cons of the proposed SSC model are illustrated. Although the gravitational theory has the controversial point, the validation results and discussions demonstrate that adopting the gravitational theory to estimate the SSC distribution in ice-covered channels is effective. The theoretical approach used herein can provide some guidance for studying the sediment-laden flow of freezing rivers in high-latitude northern regions.

Comparison between Hyperspectral and Multispectral Retrievals of Suspended Sediment Concentration in Rivers

Remote sensing (RS) is often employed to estimate suspended sediment concentration (SSC) in rivers, and the availability of hyperspectral imagery enhances the effectiveness of RS-based water quality monitoring due to its high spectral resolution. Yet, the necessity of hyperspectral imagery for SSC estimation in rivers has not been fully validated. This study thus compares the performance of hyperspectral RS with that of multispectral RS by conducting field-scale experiments in shallow rivers. In the field experiments, we measured radiance from a water body mixed with suspended sediments using a drone-mounted hyperspectral sensor, with the sediment and riverbed types considered as controlling factors. We retrieved the SSC from UAV imagery using an optimal band ratio analysis, which successfully estimated SSC distributions in the sand bed conditions with both multispectral and hyperspectral data. In the vegetated bed conditions, meanwhile, the prediction accuracy decreased significantly due to the temporally varying bottom reflectance associated with the random movement of vegetation caused by near-bed turbulence. This is because temporally inhomogeneous bottom reflectance distorts the relationship between the SSC and total reflectance. Nevertheless, the hyperspectral imaging exhibited better prediction accuracy than the multispectral imaging, effectively extracting optimal spectral bands sensitive to back-scattered reflectance from sediments while constraining the bottom reflectance caused by the vegetation-covered bed.

Overbank Flow, Sediment Transport, and Channel Morphology in the Lower Yellow River: A Review

As a prerequisite and foundation for studying the evolution mechanism of river channels, an in-depth understanding of the cross-sectional morphology adjustment is required. As a starting point, it is crucial to systematically summarize and generalize the research findings on channel morphological adjustment obtained to date, particularly in the context of the significant changes in the water and sediment conditions of large rivers that have occurred worldwide. This paper provides a comprehensive review of the research findings on the three following aspects of the Lower Yellow River: the transverse distribution of overbank flow velocity, the transverse distribution of suspended sediment concentration, and the morphological adjustment of the river cross-section. There are various equations available to predict the lateral depth–average flow velocity distribution. These equations are classified into the two following categories: empirical and theoretical formulas. Theoretical formulas are obtained through consideration of the cross-sectional morphology, accounting for inertial force terms caused by secondary flow, and momentum transfer between the main channel and its floodplain. Similarly, empirical equations and theoretical formulas for sediment concentration transverse distribution are also summarized, given the different influencing factors and assumptions. We also discuss the morphological adjustment of river cross-sections based on the analysis of measured data, mathematical model calculation, and the physical model test. In particular, we propose the idea of revealing channel cross-section morphology evolution mechanisms from the theoretical level of water and sediment movement and distribution. This review aims to enhance understanding of overbank flow, sediment transport, and channel morphology in the Lower Yellow River and may also serve to some extent as a reference for the evolution and management of channels in other rivers.

Spatiotemporal variability of suspended sediment concentration in the coastal waters of Yellow River Delta: Driving mechanism and geomorphic implications

Satellite images have revealed a significant decline in the suspended sediment concentration (SSC) near surface in the coastal waters of Yellow River Delta (YRD) in recent years. However, there is limited information on the spatial disparity in SSC distributions and its dynamic mechanism. In this study, we utilize a well-calibrated SSC retrieval algorithm and a depth-averaged numerical modeling approach to investigate the delta and sub-delta scale variation trends and driving mechanisms of SSC in the coastal waters of YRD over the past few decades. The results of this study demonstrate the existence of high turbidity zones in coastal waters of the northern abandoned delta and the active lobe of the YRD. These zones have experienced general decreasing trends of SSC at the interannual timescale. Additionally, the distribution of SSC is significantly higher in dry seasons compared to that in wet seasons. The magnitude and varying trends of SSC are strongly influenced by the total bottom shear stress (BSS) caused by combined effects of waves and currents, although the wave-induced BSS is found to be less significant that the current-induced one, but vary more significantly due to wind forcing in the Bohai Sea. Furthermore, the grain size of seabed sediments plays a dominant role in the sediment mobilization and resuspension processes over interannual and longer timescales. The distribution of high BSS and sediment mobility zones align with the active areas for morphological changes with the YRD exhibiting net accretion in the active river mouth and erosion in the abandoned delta lobes. These findings highlight the multiscale variations and the close relationship between SSC and BSS, providing valuable insights into sediment dynamics with geomorphic evolution in highly human-interfered deltaic systems.

Google Earth Engine‐Based Estimation of the Spatio‐Temporal Distribution of Suspended Sediment Concentrations in a Multi‐Channel River System of the Yangtze River Basin

AbstractLowland multi‐channel alluvial river systems are highly variable in frequency and magnitude of floodplain inundation and are vulnerable to human activities such as damming. In the Yangtze River Basin, the Three Gorges Dam (TGD) has trapped >80% of upstream sediment supply, causing downstream scouring and rapid geomorphic changes in river and its floodplain lakes. Suspended sediment concentration (SSC) is widely used to monitor river morphodynamics, but traditional measurements of SSC are time consuming, costly and difficult to quantify SSC in a large spatial scale. Using Google Earth Engine and in situ observed hydrological data, we created a multiple linear regression model to map SSC in the multi‐channel system Songzi River of the Yangtze. The new SSC predictive model achieved high accuracy (R2: 0.87) and showed opposite downstream trends in SSC during peak flood years and normal flood years. For the first time, we found that in the peak flood year of 1998 the study rivers exhibit a downstream increase trend of SSC with an abrupt increase in their middle reach, while SSC in normal flood years experiences a downstream decline with minimal changes. A prominent difference in SSC is also revealed after the TGD with a reduction of 60%. Furthermore, SSC in the closely hydrologically connected lakes is more dynamic than the less connected lakes. Our study demonstrates that the proposed method enables to rapidly quantify the spatio‐temporal SSC distribution in the multi‐channel systems on the floodplain of large alluvial rivers and highlights the importance of connectivity in regulating SSC dynamics.

Monitoring Suspended Sediment Concentration in the Yellow River Estuary and Its Vicinity Waters on the Basis of SDGSAT-1 Multispectral Imager

Suspended sediments have profound impacts on marine primary productivity and the ecological environment. The Yellow River estuary and its vicinity waters, with a high dynamic range of suspended sediment concentration (SSC), have important eco-environmental functions for the sustainable development in this region. The multispectral imager (MI) on board China’s first Sustainable Development Goals Science Satellite 1 (SDGSAT-1) features seven high-resolution bands (10 m). This study employs multispectral imagery obtained from SDGSAT-1 with single-band and band-ratio models to monitor the SSC in the Yellow River estuary and its vicinity waters. The results show that SDGSAT-1 images can be used to estimate the SSC in the Yellow River estuary and its vicinity waters. The overall pattern of the SSC exhibits a notable pattern of higher concentrations in nearshore areas and lower concentrations in offshore areas, and the retrieved SSC can attain values surpassing 1000 mg/L in nearshore areas. The R2 values of both the single-band and the band-ratio models for SSC inversion exceed 0.7. The single-band model R(854) demonstrates superior performance, achieving the highest R2 value of 0.93 and the lowest mean absolute percentage error (MAPE) of 44.04%. The single-band model based on SDGSAT-1 R(854) tends to outperform the band-ratio models for waters with algal blooms, which may be used for inversions of SSC and/or suspended particulate matter (SPM) in the waters full of algal blooms and suspended sediments. The monitoring results by SDGSAT-1 suggest that the complex SSC distributions in the Yellow River estuary and its vicinity waters were highly impacted by the river sediments discharge, tide, currents and wind-induced waves.

Semi-analytical modeling of sediment-laden open-channel flows with the effects of stratification, hindered settling, and eddy viscosities.

This study proposes semi-analytical models for simultaneous distribution of fluid velocity and suspended sediment concentration in an open-channel turbulent flow using three kinds of eddy viscosities. Apart from the classical parabolic eddy viscosity which is based on a log-law velocity profile, we consider two recently proposed eddy viscosities based on the concept of velocity and length scales. To deal with the flows with high sediment concentration, several turbulent features such as the hindered settling mechanism and the stratification effect are incorporated in the model. The governing system of highly nonlinear differential equations is solved using the homotopy analysis method (HAM), which produces solutions in the form of convergent series. Numerical and theoretical convergence analyses are provided for all three types of eddy viscosities. The effects of parameters on the derived models are discussed physically. Experimental data on both dilute and non-dilute flows are considered to verify the HAM-based solutions. The effects of the stratification correction factor (β) and the turbulent Schmidt number (α) reveal that they should be determined optimally for applicability of the proposed models in terms of accurate prediction with data. This optimal procedure required further investigation of these parameters, and, thus, an analysis of β and α is carried out, which linked them with the particle diameter through particle settling velocity, reference fluid velocity, and reference sediment concentration by proposing regression equations. Furthermore, using the optimal values of the parameters, the proposed models corresponding to the eddy viscosities based on the exponentially decreasing turbulent kinetic energy function and von Karman's similarity hypothesis are seen to be superior to the model corresponding to a parabolic eddy viscosity. Finally, a comment on the HAM is made where it is observed that the method can remove the numerical singularity of the governing equations at the water surface, which arises because of the consideration of vanishing eddy viscosity thereat.

The Effect of Suspended Sediment Concentration on Acoustic Propagation Based on Satellite Data Inversion

Suspended sediment in seawater not only affects the optical properties of seawater, such as transparency and color, but it also greatly affects the process of underwater acoustic propagation. The underwater acoustic detection equipment is affected by the change in suspended sediment concentration (SSC) in use. To address this problem, this paper deeply investigates the correlation between the characteristic parameters of acoustic propagation and SSC in different types of water bodies. It identifies the statistical characteristics of the temporal and spatial distributions of SSC in the Chinese seas through quantitative inversion based on satellite remote sensing data. It further analyzes the relationship between the concentration and distribution of suspended sediment and the characteristics of acoustic propagation of underwater weapons and equipment. Finally, it quantitatively evaluates the effect of SSC on the acoustic attenuation coefficient. This study can provide valuable references for the functional departments and base-level units of naval forces to make decisions and strategies for using underwater acoustic detection equipment.

Suspended sediment transport generated by non-hydrostatic hydrodynamics in Northern Waters of Aceh, Indonesia

Suspended Sediment transport in the Northern Waters of Aceh is investigated in the domains between 5.4° - 5.65° N Latitude and 95.15° - 95.45° E. Therefore, this study aims to calculate the suspended sediment transport using a non-hydrostatic hydrodynamic model with an output distribution of total suspended sediment concentration. The model was run using tidal components of M2, S2, K1, O1, N2, K2, P1, Q1 and the wind every 6 h in February and August 2019 representing the North East and South West monsoons, as well as sea temperature and salinity data. The results of the model correlated with the Tide Model Driver data obtained, and the simulation results indicated the current in February 2019 is different than in August. The numerical simulation results show that the distribution of suspended sediments in Northern Waters of Aceh is driven by currents. Furthermore, the hydrodynamics and the designed model showed that the distribution value of the surface total suspended sediment concentration was lower in August than in February 2019. The verification results of the surface total suspended sediment concentration between the model and the Visible Infrared Imaging Radiometer Suite showed a good match. These results can facilitate the analysis of limited observation and remote sensing data.

Effect of the Three Gorges Reservoir on vertical distribution of suspended sediment concentration and estimation accuracy of depth‐average concentration in downstream reaches

AbstractThe sediment regime in the middle Yangtze River has been significantly changed from quasi‐equilibrium to nonequilibrium since the impoundment of the Three Georges Reservoir (TGR). To understand the effects of the TGR on vertical distribution of suspended sediment concentration (SSC) and estimation accuracy of mean concentration, vertical sediment concentration and flow velocity data at the Shashi and Jianli hydrological stations in the reach before and after the impoundment were collected. Comparisons and analysis of vertical profiles of SSC before and after the TGR impoundment show that after the impoundment of the TGR, due to the coarsening of sediment particle size, the reduction in sediment load, and the significant decrease in sediment saturation, the vertical distribution of SSC in the downstream reaches became more uneven under medium and low water flows, which was reflected in the vertical gradient and the fluctuation degree of SSC significantly increased. In addition, the depth‐average sediment concentrations were calculated by the selected‐point method and the mean values calculated by the “multi‐point method” were regarded as the “true mean” to evaluate the accuracy of the mean value calculated by the “few‐point method.” It was found that the relative errors for the selected‐point method were mainly positive before impoundment but mainly negative after impoundment. Additionally, the correction factors of one‐point, two‐point, and three‐point methods and the position of the near‐bed substituted point for the five‐point method were given to reduce the error when the point measurements were used to calculate the depth‐average sediment concentration in the downstream reaches.

Downdrift Port Siltation Adjacent to a River Mouth: Effects of Mesotidal Conditions and Typhoon

The Zhuoshui River has one of the highest sediment yields in the world. The riverine sediment may have been transported away from the river mouth by strong tidal currents and deposited in a navigational channel and a harbor basin south of the Zhuoshui River. This study describes the dispersal of riverine sediments in mesotidal conditions, including transport processes of sediments via river plumes, initial deposition, resuspension, and long-term net accumulation. Our results revealed that the distribution of suspended sediment concentration (SSC) and the transport process of the river plume was markedly modulated by tidal currents in a north–south direction. Under high-discharge conditions, energetic winds and ocean currents interrupted the offshore propagation of the sediment-laden river plume with a high SSC to the ocean. The plume, induced by typhoon floods, was either propagated northward due to the Coriolis effect or was deposited near the river mouth. The sediments deposited within the inner shelf were resuspended by intensive tidal currents and transported through southward residual circulations to the navigation channel south of the river mouth.

In-Stream Laser Diffraction for Measuring Suspended Sediment Concentration and Particle Size Distribution in Rivers: Insights from Field Campaigns

This study evaluates the laser in situ scattering and transmissometry (LISST) instrument LISST-SL2, a laser diffraction instrument for suspended sediment sampling in rivers, with concurrent physical measurements of suspended sediment concentration (SSC) and particle size distribution (PSD) as well as velocity measurements by an acoustic Doppler current profiler (ADCP). We collected 136 LISST-SL2 samples along with 61 physical samples for SSC measurement, of which 24 physical samples included PSD measurement during 2018–2020 from 11 sites in Washington state and Virginia. An effective density is required to convert the measured volumetric SSC by the LISST-SL2 into a reported mass SSC, and by default the LISST-SL2 assumes a value of 2.65 g/mL. From our data set, we computed effective densities (mass SSC/volumetric SSC) that ranged from 0.5 to 5.4 g/mL, with a best-fit value of 2.05 g/mL. Additionally, the LISST-SL2 was not able to measure the finest sediment sizes in suspension, which affects the resulting PSD. Therefore, we propose some adjustments of the LISST-SL2 data with a supporting physical sample to account for these effective density and PSD issues. When doing so, we were able to reduce the root-mean square relative error (RMSRE) to 18% from 117% for SSC, and to 26% from 78% for PSD. LISST-SL2 velocities were generally higher than ADCP velocities with a 21% RMSRE. Our results and guidance will allow for more accurate sampling by the LISST-SL2, which has potential for studying spatial and temporal variation of suspended sediment characteristics in rivers.

On the occurrence of low concentration hyperpycnal river plumes in a small mountainous river-canyon system

This study aimed to understand the mechanisms controlling the formation of hyperpycnal river plumes in small mountainous rivers. The suspended sediment concentration (SSC) and grain size distribution in the Gaoping River were obtained by field observations and used as the basis for numerical simulations. The SSC of the Gaoping River during Typhoon Soudelor was lower than 20 g/L according to the real-time SSC estimated using the calibration curve between turbidity and SSC. The calculated median grain size of the suspended sediments was 15.15 μm, which indicated that the silt accounted for a large proportion of the flow. The observed grain-size distribution and SSC were incorporated into a numerical model to examine the conditions under which hyperpycnal river plumes occur. The model results revealed a three-dimensional process near the river mouth: cross-canyon currents converge near the head of the canyon, and the topography of the submarine canyon further confines the path and width of the hyperpycnal river plume. The descending plume continues to move through the steep slope of the submarine canyon. In addition, the simulation results showed that the SSC of the hyperpycnal river plumes increases as the grain size of riverine sediment decreases. However, if the sediment grain size is smaller than 8 μm, most of the suspended sediment remains on the sea surface in a surface plume.

Modeling of suspended sediment concentration - case study in Can Gio, Ho Chi Minh city

The dynamics of suspended sediments are complicated due to the influence of hydrodynamic factors and the characterization of cohesive sediment properties. A one-dimensional model is built to calculate the vertical distribution of suspended sediment concentration (SSC). In the model, parameters that influence the vertical distribution of SSC include the settling velocity (ws) and the diffusion coefficient (Kz). The settling velocity depends on the cohesive sediment properties, and the diffusion coefficient depends on the wave-current dynamics. The model applies measured data in June 2014 on the mud flats in Can Gio, Ho Chi Minh city, Vietnam. In this study, the settling velocity ws is a constant of 0.64 × 10-6 m/s. The diffusion coefficient depends on water depth, wave action, and tidal currents. Under strong wave - medium current conditions, the average Kz is 2.88 × 10-3 m2/s. Under medium wave - strong current conditions, the average Kz is 6.11 × 10-3 m2/s, while under strong wave - strong current conditions, the average Kz can reach 6.59 × 10-3 m2/s. The resulting simulations demonstrate that the SSC increases rapidly near the bottom layers. Here, the clay sediments are easily disturbed by dynamic conditions. At the bottom layer, the SSC is strongly influenced by the current factor, while the role of the wave factor has not been clearly shown.

Typhoon triggers estuarine heavy metal risk by regulating the multifractal grainsize of resuspended sediment

The turbulent boundary layer generated by wind in the estuarine surface water serves as a main factor affecting the distribution of suspended particulate matter (SPM) and suspended sediment concentration (SSC). In this study, representative typhoon-induced variation of surface fine SPM (<63 μm) was simulated in the Yangtze River Estuary (YRE) under two time scenarios. Each scenario contained four grainsize SPM fractions named Fraction 1 (<8 μm), Fraction 2 (8–16 μm), Fraction 3 (16–32 μm), Fraction 4 (32–63 μm). The typhoon-induced resuspended multifractal SSC quantification (TRMSQ) based on the relationship between SPM grainsize and heavy metal adsorption capacity was proposed to assess the variation in the resuspended threat of heavy metal to 6 key estuarine protected objects (three reservoirs & three national reserves) between Scenarios 1 and 2. The results presented that Fraction 3 exhibited the maximum increment in SSC resuspension mass and longest regression time from typhoon. Combined with TRMSQ, chromium (Cr) was calculated to be the riskiest typhoon-induced factor. The integrated resuspended risk of heavy metals for each protected object tends to increase from the northwest of Chongming Island (1.2) towards the maximum turbidity zone (>9) downstream, with an estuary-wide mean of 3.3.

A probabilistic model on streamwise velocity profile in open channels using Tsallis relative entropy theory

The present study uses the concept of information entropy to derive a velocity distribution model in open channel flow. The Tsallis relative entropy theory is explored for that purpose, where the prior probability density function (PDF) is chosen from the maximum Tsallis entropy distribution. Both the cases of the fixed and varying entropy index are considered from the literature. The velocity equations are derived analytically using the homotopy analysis method (HAM) together with the Padé approximation technique in a general framework. The approximations and the HAM-based series solution are verified against laboratory and field data sets. Also, the prediction accuracies of the proposed models are assessed through the measures of statistical errors. It is seen that the model corresponding to the varying index is superior to the other model. The entropy index of Tsallis relative entropy is considered a variable, and the non-unity values of this index justify the applicability of the entropy function. Moreover, it is observed that one of the Lagrange multipliers corresponding to the velocity model with a varying index becomes negligible subject to the data sets considered, and hence, it simplifies the model development mathematically. The proposed approach can be further extended to develop models for estimating the suspended sediment concentration and shear stress distribution.