Sediment transport

Sediment transport is the movement of solid particles (sediment), typically due to a combination of gravity acting on the sediment, and/or the movement of the fluid in which the sediment is entrained. Sediment transport occurs in natural systems where the particles are clastic rocks (sand, gravel, boulders, etc.), mud, or clay; the fluid is air, water, or ice; and the force of gravity acts to move the particles along the sloping surface on which they are resting. Sediment transport due to fluid motion occurs in rivers, oceans, lakes, seas, and other bodies of water due to currents and tides. Transport is also caused by glaciers as they flow, and on terrestrial surfaces under the influence of wind. Sediment transport due only to gravity can occur on sloping surfaces in general, including hillslopes, scarps, cliffs, and the continental shelf—continental slope boundary.

Sediment transport is important in the fields of sedimentary geology, geomorphology, civil engineering and environmental engineering (see applications, below). Knowledge of sediment transport is most often used to determine whether erosion or deposition will occur, the magnitude of this erosion or deposition, and the time and distance over which it will occur.

Wafrica amo 2007209 lrg
Dust blows from the Sahara Desert over the Atlantic Ocean towards the Canary Islands.


Sand blowing off a crest in the Kelso Dunes of the Mojave Desert, California.
Toklat River - East Fork 01
Toklat River, East Fork, Polychrome overlook, Denali National Park, Alaska. This river, like other braided streams, rapidly changes the positions of its channels through processes of erosion, sediment transport, and deposition.
Congo river viewed from Kintambo 1
Congo river viewed from Kinshasa, Democratic Republic of Congo. Its brownish color is mainly the result of the transported sediments taken upstream.


Aeolian or eolian (depending on the parsing of æ) is the term for sediment transport by wind. This process results in the formation of ripples and sand dunes. Typically, the size of the transported sediment is fine sand (<1 mm) and smaller, because air is a fluid with low density and viscosity, and can therefore not exert very much shear on its bed.

Bedforms are generated by aeolian sediment transport in the terrestrial near-surface environment. Ripples[1] and dunes[2] form as a natural self-organizing response to sediment transport.

Aeolian sediment transport is common on beaches and in the arid regions of the world, because it is in these environments that vegetation does not prevent the presence and motion of fields of sand.

Wind-blown very fine-grained dust is capable of entering the upper atmosphere and moving across the globe. Dust from the Sahara deposits on the Canary Islands and islands in the Caribbean,[3] and dust from the Gobi desert has deposited on the western United States.[4] This sediment is important to the soil budget and ecology of several islands.

Deposits of fine-grained wind-blown glacial sediment are called loess.


In geology, physical geography, and sediment transport, fluvial processes relate to flowing water in natural systems. This encompasses rivers, streams, periglacial flows, flash floods and glacial lake outburst floods. Sediment moved by water can be larger than sediment moved by air because water has both a higher density and viscosity. In typical rivers the largest carried sediment is of sand and gravel size, but larger floods can carry cobbles and even boulders.

Fluvial sediment transport can result in the formation of ripples and dunes, in fractal-shaped patterns of erosion, in complex patterns of natural river systems, and in the development of floodplains.

Laysan beach
Sand ripples, Laysan Beach, Hawaii. Coastal sediment transport results in these evenly spaced ripples along the shore. Monk seal for scale.


Coastal sediment transport takes place in near-shore environments due to the motions of waves and currents. At the mouths of rivers, coastal sediment and fluvial sediment transport processes mesh to create river deltas.

Coastal sediment transport results in the formation of characteristic coastal landforms such as beaches, barrier islands, and capes.[5]

A glacier joining the Gorner Glacier, Zermatt, Switzerland. These glaciers transport sediment and leave behind lateral moraines.


As glaciers move over their beds, they entrain and move material of all sizes. Glaciers can carry the largest sediment, and areas of glacial deposition often contain a large number of glacial erratics, many of which are several metres in diameter. Glaciers also pulverize rock into "glacial flour", which is so fine that it is often carried away by winds to create loess deposits thousands of kilometres afield. Sediment entrained in glaciers often moves approximately along the glacial flowlines, causing it to appear at the surface in the ablation zone.


In hillslope sediment transport, a variety of processes move regolith downslope. These include:

These processes generally combine to give the hillslope a profile that looks like a solution to the diffusion equation, where the diffusivity is a parameter that relates to the ease of sediment transport on the particular hillslope. For this reason, the tops of hills generally have a parabolic concave-up profile, which grades into a convex-up profile around valleys.

As hillslopes steepen, however, they become more prone to episodic landslides and other mass wasting events. Therefore, hillslope processes are better described by a nonlinear diffusion equation in which classic diffusion dominates for shallow slopes and erosion rates go to infinity as the hillslope reaches a critical angle of repose.[6]

Debris flow

Large masses of material are moved in debris flows, hyperconcentrated mixtures of mud, clasts that range up to boulder-size, and water. Debris flows move as granular flows down steep mountain valleys and washes. Because they transport sediment as a granular mixture, their transport mechanisms and capacities scale differently from those of fluvial systems.


Suspended sediment from a stream emptying into a fjord (Isfjorden, Svalbard, Norway).

Sediment transport is applied to solve many environmental, geotechnical, and geological problems. Measuring or quantifying sediment transport or erosion is therefore important for coastal engineering. Several sediment erosion devices have been designed in order to quantitfy sediment erosion (e.g., Particle Erosion Simulator (PES)). One such device, also referred to as the BEAST (Benthic Environmental Assessment Sediment Tool) has been calibrated in order to quantify rates of sediment erosion.[7]

Movement of sediment is important in providing habitat for fish and other organisms in rivers. Therefore, managers of highly regulated rivers, which are often sediment-starved due to dams, are often advised to stage short floods to refresh the bed material and rebuild bars. This is also important, for example, in the Grand Canyon of the Colorado River, to rebuild shoreline habitats also used as campsites.

Sediment discharge into a reservoir formed by a dam forms a reservoir delta. This delta will fill the basin, and eventually, either the reservoir will need to be dredged or the dam will need to be removed. Knowledge of sediment transport can be used to properly plan to extend the life of a dam.

Geologists can use inverse solutions of transport relationships to understand flow depth, velocity, and direction, from sedimentary rocks and young deposits of alluvial materials.

Flow in culverts, over dams, and around bridge piers can cause erosion of the bed. This erosion can damage the environment and expose or unsettle the foundations of the structure. Therefore, good knowledge of the mechanics of sediment transport in a built environment are important for civil and hydraulic engineers.

When suspended sediment transport is increased due to human activities, causing environmental problems including the filling of channels, it is called siltation after the grain-size fraction dominating the process.

Initiation of motion

Stress balance

For a fluid to begin transporting sediment that is currently at rest on a surface, the boundary (or bed) shear stress exerted by the fluid must exceed the critical shear stress for the initiation of motion of grains at the bed. This basic criterion for the initiation of motion can be written as:


This is typically represented by a comparison between a dimensionless shear stress ()and a dimensionless critical shear stress (). The nondimensionalization is in order to compare the driving forces of particle motion (shear stress) to the resisting forces that would make it stationary (particle density and size). This dimensionless shear stress, , is called the Shields parameter and is defined as:[8]


And the new equation to solve becomes:


The equations included here describe sediment transport for clastic, or granular sediment. They do not work for clays and muds because these types of floccular sediments do not fit the geometric simplifications in these equations, and also interact thorough electrostatic forces. The equations were also designed for fluvial sediment transport of particles carried along in a liquid flow, such as that in a river, canal, or other open channel.

Only one size of particle is considered in this equation. However, river beds are often formed by a mixture of sediment of various sizes. In case of partial motion where only a part of the sediment mixture moves, the river bed becomes enriched in large gravel as the smaller sediments are washed away. The smaller sediments present under this layer of large gravel have a lower possibility of movement and total sediment transport decreases. This is called armouring effect.[9] Other forms of armouring of sediment or decreasing rates of sediment erosion can be caused by carpets of microbial mats, under conditions of high organic loading.[10]

Critical shear stress

Shields diagram
Original Shields diagram, 1936

The Shields diagram empirically shows how the dimensionless critical shear stress (i.e. the dimensionless shear stress required for the initiation of motion) is a function of a particular form of the particle Reynolds number, or Reynolds number related to the particle. This allows us to rewrite the criterion for the initiation of motion in terms of only needing to solve for a specific version of the particle Reynolds number, which we call .

This equation can then be solved by using the empirically derived Shields curve to find as a function of a specific form of the particle Reynolds number called the boundary Reynolds number. The mathematical solution of the equation was given by Dey.[11]

Particle Reynolds Number

In general, a particle Reynolds Number has the form:

Where is a characteristic particle velocity, is the grain diameter (a characteristic particle size), and is the kinematic viscosity, which is given by the dynamic viscosity, , divided by the fluid density, .

The specific particle Reynolds number of interest is called the boundary Reynolds number, and it is formed by replacing the velocity term in the Particle Reynolds number by the shear velocity, , which is a way of rewriting shear stress in terms of velocity.

where is the bed shear stress (described below), and is the von Kármán constant, where


The particle Reynolds number is therefore given by:

Bed shear stress

The boundary Reynolds number can be used with the Shields diagram to empirically solve the equation


which solves the right-hand side of the equation


In order to solve the left-hand side, expanded as


we must find the bed shear stress, . There are several ways to solve for the bed shear stress. First, we develop the simplest approach, in which the flow is assumed to be steady and uniform and reach-averaged depth and slope are used. Due to the difficulty of measuring shear stress in situ, this method is also one of the most-commonly used. This method is known as the depth-slope product.

Depth-slope product

For a river undergoing approximately steady, uniform equilibrium flow, of approximately constant depth h and slope angle θ over the reach of interest, and whose width is much greater than its depth, the bed shear stress is given by some momentum considerations stating that the gravity force component in the flow direction equals exactly the friction force.[12] For a wide channel, it yields:

For shallow slope angles, which are found in almost all natural lowland streams, the small-angle formula shows that is approximately equal to , which is given by , the slope. Rewritten with this:

Shear velocity, velocity, and friction factor

For the steady case, by extrapolating the depth-slope product and the equation for shear velocity:


We can see that the depth-slope product can be rewritten as:


is related to the mean flow velocity, , through the generalized Darcy-Weisbach friction factor, , which is equal to the Darcy-Weisbach friction factor divided by 8 (for mathematical convenience).[13] Inserting this friction factor,


Unsteady flow

For all flows that cannot be simplified as a single-slope infinite channel (as in the depth-slope product, above), the bed shear stress can be locally found by applying the Saint-Venant equations for continuity, which consider accelerations within the flow.



The criterion for the initiation of motion, established earlier, states that


In this equation,

, and therefore
is a function of boundary Reynolds number, a specific type of particle Reynolds number.

For a particular particle Reynolds number, will be an emprical constant given by the Shields Curve or by another set of empirical data (depending on whether or not the grain size is uniform).

Therefore, the final equation that we seek to solve is:



We make several assumptions to provide an example that will allow us to bring the above form of the equation into a solved form.

First, we assume that the a good approximation of reach-averaged shear stress is given by the depth-slope product. We can then rewrite the equation as


Moving and re-combining the terms, we obtain:

where R is the submerged specific gravity of the sediment.

We then make our second assumption, which is that the particle Reynolds number is high. This is typically applicable to particles of gravel-size or larger in a stream, and means that the critical shear stress is a constant. The Shields curve shows that for a bed with a uniform grain size,


Later researchers[14] have shown that this value is closer to

for more uniformly sorted beds. Therefore, we will simply insert

and insert both values at the end.

The equation now reads:

This final expression shows that the product of the channel depth and slope is equal to the Shield's criterion times the submerged specific gravity of the particles times the particle diameter.

For a typical situation, such as quartz-rich sediment in water , the submerged specific gravity is equal to 1.65.

Plugging this into the equation above,


For the Shield's criterion of . 0.06 * 1.65 = 0.099, which is well within standard margins of error of 0.1. Therefore, for a uniform bed,


For these situations, the product of the depth and slope of the flow should be 10% of the diameter of the median grain diameter.

The mixed-grain-size bed value is , which is supported by more recent research as being more broadly applicable because most natural streams have mixed grain sizes[14]. Using this value, and changing D to D_50 ("50" for the 50th percentile, or the median grain size, as we are now looking at a mixed-grain-size bed), the equation becomes:

Which means that the depth times the slope should be about 5% of the median grain diameter in the case of a mixed-grain-size bed.

Modes of entrainment

The sediments entrained in a flow can be transported along the bed as bed load in the form of sliding and rolling grains, or in suspension as suspended load advected by the main flow.[12] Some sediment materials may also come from the upstream reaches and be carried downstream in the form of wash load.

Rouse number

The location in the flow in which a particle is entrained is determined by the Rouse number, which is determined by the density ρs and diameter d of the sediment particle, and the density ρ and kinematic viscosity ν of the fluid, determine in which part of the flow the sediment particle will be carried.[15]

Here, the Rouse number is given by P. The term in the numerator is the (downwards) sediment the sediment settling velocity ws, which is discussed below. The upwards velocity on the grain is given as a product of the von Kármán constant, κ = 0.4, and the shear velocity, u.

The following table gives the approximate required Rouse numbers for transport as bed load, suspended load, and wash load.[15][16]

Mode of Transport Rouse Number
Initiation of motion >7.5
Bed load >2.5, <7.5
Suspended load: 50% Suspended >1.2, <2.5
Suspended load: 100% Suspended >0.8, <1.2
Wash load <0.8

Settling velocity

Stokes sphere
Streamlines around a sphere falling through a fluid. This illustration is accurate for laminar flow, in which the particle Reynolds number is small. This is typical for small particles falling through a viscous fluid; larger particles would result in the creation of a turbulent wake.

The settling velocity (also called the "fall velocity" or "terminal velocity") is a function of the particle Reynolds number. Generally, for small particles (laminar approximation), it can be calculated with Stokes' Law. For larger particles (turbulent particle Reynolds numbers), fall velocity is calculated with the turbulent drag law. Dietrich (1982) compiled a large amount of published data to which he empirically fit settling velocity curves.[17] Ferguson and Church (2006) analytically combined the expressions for Stokes flow and a turbulent drag law into a single equation that works for all sizes of sediment, and successfully tested it against the data of Dietrich.[18] Their equation is


In this equation ws is the sediment settling velocity, g is acceleration due to gravity, and D is mean sediment diameter. is the kinematic viscosity of water, which is approximately 1.0 x 10−6 m2/s for water at 20 °C.

and are constants related to the shape and smoothness of the grains.

Constant Smooth Spheres Natural Grains: Sieve Diameters Natural Grains: Nominal Diameters Limit for Ultra-Angular Grains
18 18 20 24
0.4 1.0 1.1 1.2

The expression for fall velocity can be simplified so that it can be solved only in terms of D. We use the sieve diameters for natural grains, , and values given above for and . From these parameters, the fall velocity is given by the expression:

Hjulström-Sundborg Diagram

Hjulströms diagram en
The logarithmic Hjulström curve

In 1935, Filip Hjulström created the Hjulström curve, a graph which shows the relationship between the size of sediment and the velocity required to erode (lift it), transport it, or deposit it.[19] The graph is logarithmic.

Åke Sundborg later modified the Hjulström curve to show separate curves for the movement threshold corresponding to several water depths, as is necessary if the flow velocity rather than the boundary shear stress (as in the Shields diagram) is used for the flow strength.[20]

This curve has no more than a historical value nowadays, although its simplicity is still attractive. Among the drawbacks of this curve are that it does not take the water depth into account and more importantly, that it does not show that sedimentation is caused by flow velocity deceleration and erosion is caused by flow acceleration. The dimensionless Shields diagram is now unanimously accepted for initiation of sediment motion in rivers.

Transport rate

Stream Load
A schematic diagram of where the different types of sediment load are carried in the flow. Dissolved load is not sediment: it is composed of disassociated ions moving along with the flow. It may, however, constitute a significant proportion (often several percent, but occasionally greater than half) of the total amount of material being transported by the stream.

Formulas to calculate sediment transport rate exist for sediment moving in several different parts of the flow. These formulas are often segregated into bed load, suspended load, and wash load. They may sometimes also be segregated into bed material load and wash load.

Bed Load

Bed load moves by rolling, sliding, and hopping (or saltating) over the bed, and moves at a small fraction of the fluid flow velocity. Bed load is generally thought to constitute 5-10% of the total sediment load in a stream, making it less important in terms of mass balance. However, the bed material load (the bed load plus the portion of the suspended load which comprises material derived from the bed) is often dominated by bed load, especially in gravel-bed rivers. This bed material load is the only part of the sediment load that actively interacts with the bed. As the bed load is an important component of that, it plays a major role in controlling the morphology of the channel.

Bed load transport rates are usually expressed as being related to excess dimensionless shear stress raised to some power. Excess dimensionless shear stress is a nondimensional measure of bed shear stress about the threshold for motion.


Bed load transport rates may also be given by a ratio of bed shear stress to critical shear stress, which is equivalent in both the dimensional and nondimensional cases. This ratio is called the "transport stage" and is an important in that it shows bed shear stress as a multiple of the value of the criterion for the initiation of motion.

When used for sediment transport formulae, this ratio is typically raised to a power.

The majority of the published relations for bedload transport are given in dry sediment weight per unit channel width, ("breadth"):


Due to the difficulty of estimating bed load transport rates, these equations are typically only suitable for the situations for which they were designed.

Notable bed load transport formulae

The transport formula of Meyer-Peter and Müller, originally developed in 1948,[21] was designed for well-sorted fine gravel at a transport stage of about 8.[15] The formula uses the above nondimensionalization for shear stress,[15]


and Hans Einstein's nondimensionalization for sediment volumetric discharge per unit width[15]


Their formula reads:


Their experimentally determined value for is 0.047, and is the third commonly used value for this (in addition to Parker's 0.03 and Shields' 0.06).

Because of its broad use, some revisions to the formula have taken place over the years that show that the coefficient on the left ("8" above) is a function of the transport stage:[15][22][23][24]


The variations in the coefficient were later generalized as a function of dimensionless shear stress:[15][25]


In 2003, Peter Wilcock and Joanna Crowe (now Joanna Curran) published a sediment transport formula that works with multiple grain sizes across the sand and gravel range.[26] Their formula works with surface grain size distributions, as opposed to older models which use subsurface grain size distributions (and thereby implicitly infer a surface grain sorting).

Their expression is more complicated than the basic sediment transport rules (such as that of Meyer-Peter and Müller) because it takes into account multiple grain sizes: this requires consideration of reference shear stresses for each grain size, the fraction of the total sediment supply that falls into each grain size class, and a "hiding function".

The "hiding function" takes into account the fact that, while small grains are inherently more mobile than large grains, on a mixed-grain-size bed, they may be trapped in deep pockets between large grains. Likewise, a large grain on a bed of small particles will be stuck in a much smaller pocket than if it were on a bed of grains of the same size. In gravel-bed rivers, this can cause "equal mobility", in which small grains can move just as easily as large ones.[27] As sand is added to the system, it moves away from the "equal mobility" portion of the hiding function to one in which grain size again matters.[26]

Their model is based on the transport stage, or ratio of bed shear stress to critical shear stress for the initiation of grain motion. Because their formula works with several grain sizes simultaneously, they define the critical shear stress for each grain size class, , to be equal to a "reference shear stress", .[26]

They express their equations in terms of a dimensionless transport parameter, (with the "" indicating nondimensionality and the "" indicating that it is a function of grain size):

is the volumetric bed load transport rate of size class per unit channel width . is the proportion of size class that is present on the bed.

They came up with two equations, depending on the transport stage, . For :

and for :


This equation asymptotically reaches a constant value of as becomes large.

In 2002, Peter Wilcock and Kenworthy T.A. , following Peter Wilcock (1998),[28] published a sediment bed-load transport formula that works with only two sediments fractions, i.e. sand and gravel fractions.[29] Peter Wilcock and Kenworthy T.A. in their article recognized that a mixed-sized sediment bed-load transport model using only two fractions offers practical advantages in terms of both computational and conceptual modeling by taking into account the nonlinear effects of sand presence in gravel beds on bed-load transport rate of both fractions. In fact, in the two-fraction bed load formula appears a new ingredient with respect to that of Meyer-Peter and Müller that is the proportion of fraction on the bed surface where the subscript represents either the sand (s) or gravel (g) fraction. The proportion , as a function of sand content , physically represents the relative influence of the mechanisms controlling sand and gravel transport, associated with the change from a clast-supported to matrix-supported gravel bed. Moreover, since spans between 0 and 1, phenomena that vary with include the relative size effects producing ‘‘hiding’’ of fine grains and ‘‘exposure’’ of coarse grains. The ‘‘hiding’’ effect takes into account the fact that, while small grains are inherently more mobile than large grains, on a mixed-grain-size bed, they may be trapped in deep pockets between large grains. Likewise, a large grain on a bed of small particles will be stuck in a much smaller pocket than if it were on a bed of grains of the same size, which the Meyer-Peter and Müller formula refers to. In gravel-bed rivers, this can cause ‘‘equal mobility", in which small grains can move just as easily as large ones.[27] As sand is added to the system, it moves away from the ‘‘equal mobility’’ portion of the hiding function to one in which grain size again matters.[29]

Their model is based on the transport stage,i.e. , or ratio of bed shear stress to critical shear stress for the initiation of grain motion. Because their formula works with only two fractions simultaneously, they define the critical shear stress for each of the two grain size classes, , where represents either the sand (s) or gravel (g) fraction . The critical shear stress that represents the incipient motion for each of the two fractions is consistent with established values in the limit of pure sand and gravel beds and shows a sharp change with increasing sand content over the transition from a clast- to matrix-supported bed.[29]

They express their equations in terms of a dimensionless transport parameter, (with the "" indicating nondimensionality and the ‘‘’’ indicating that it is a function of grain size):

is the volumetric bed load transport rate of size class per unit channel width . is the proportion of size class that is present on the bed.

They came up with two equations, depending on the transport stage, . For :

and for :


This equation asymptotically reaches a constant value of as becomes large and the symbols have the following values:

In order to apply the above formulation, it is necessary to specify the characteristic grain sizes for the sand portion and for the gravel portion of the surface layer, the fractions and of sand and gravel, respectively in the surface layer, the submerged specific gravity of the sediment R and shear velocity associated with skin friction .

For the case in which sand fraction is transported by the current over and through an immobile gravel bed, Kuhnle et al.(2013),[30] following the theoretical analysis done by Pellachini (2011),[31] provides a new relationship for the bed load transport of the sand fraction when gravel particles remain at rest. It is worth mentioning that Kuhnle et al. (2013)[30] applied the Wilcock and Kenworthy (2002)[29] formula to their experimental data and found out that predicted bed load rates of sand fraction were about 10 times greater than measured and approached 1 as the sand elevation became near the top of the gravel layer.[30] They, also, hypothesized that the mismatch between predicted and measured sand bed load rates is due to the fact that the bed shear stress used for the Wilcock and Kenworthy (2002)[29] formula was larger than that available for transport within the gravel bed because of the sheltering effect of the gravel particles.[30] To overcome this mismatch, following Pellachini (2011),[31] they assumed that the variability of the bed shear stress available for the sand to be transported by the current would be some function of the so-called "Roughness Geometry Function" (RGF),[32] which represents the gravel bed elevations distribution. Therefore, the sand bed load formula follows as:[30]


the subscript refers to the sand fraction, s represents the ratio where is the sand fraction density, is the RGF as a function of the sand level within the gravel bed, is the bed shear stress available for sand transport and is the critical shear stress for incipient motion of the sand fraction, which was calculated graphically using the updated Shields-type relation of Miller et al.(1977).[33]

Suspended load

Suspended load is carried in the lower to middle parts of the flow, and moves at a large fraction of the mean flow velocity in the stream.

A common characterization of suspended sediment concentration in a flow is given by the Rouse Profile. This characterization works for the situation in which sediment concentration at one particular elevation above the bed can be quantified. It is given by the expression:

Here, is the elevation above the bed, is the concentration of suspended sediment at that elevation, is the flow depth, is the Rouse number, and relates the eddy viscosity for momentum to the eddy diffusivity for sediment, which is approximately equal to one.[34]

Experimental work has shown that ranges from 0.93 to 1.10 for sands and silts.[35]

The Rouse profile characterizes sediment concentrations because the Rouse number includes both turbulent mixing and settling under the weight of the particles. Turbulent mixing results in the net motion of particles from regions of high concentrations to low concentrations. Because particles settle downward, for all cases where the particles are not neutrally buoyant or sufficiently light that this settling velocity is negligible, there is a net negative concentration gradient as one goes upward in the flow. The Rouse Profile therefore gives the concentration profile that provides a balance between turbulent mixing (net upwards) of sediment and the downwards settling velocity of each particle.

Bed material load

Bed material load comprises the bed load and the portion of the suspended load that is sourced from the bed.

Three common bed material transport relations are the "Ackers-White",[36] "Engelund-Hansen", "Yang" formulae. The first is for sand to granule-size gravel, and the second and third are for sand[37] though Yang later expanded his formula to include fine gravel. That all of these formulae cover the sand-size range and two of them are exclusively for sand is that the sediment in sand-bed rivers is commonly moved simultaneously as bed and suspended load.


The bed material load formula of Engelund and Hansen is the only one to not include some kind of critical value for the initiation of sediment transport. It reads:

where is the Einstein nondimensionalization for sediment volumetric discharge per unit width, is a friction factor, and is the Shields stress. The Engelund-Hansen formula is one of the few sediment transport formulae in which a threshold "critical shear stress" is absent.

Wash load

Wash load is carried within the water column as part of the flow, and therefore moves with the mean velocity of main stream. Wash load concentrations are approximately uniform in the water column. This is described by the endmember case in which the Rouse number is equal to 0 (i.e. the settling velocity is far less than the turbulent mixing velocity), which leads to a prediction of a perfectly uniform vertical concentration profile of material.

Total load

Some authors have attempted formulations for the total sediment load carried in water.[38][39] These formulas are designed largely for sand, as (depending on flow conditions) sand often can be carried as both bed load and suspended load in the same stream or shoreface.

See also

  • Civil engineering
  • Hydraulic engineering – Sub-discipline of civil engineering concerned with the flow and conveyance of fluids
  • Geology – The study of the composition, structure, physical properties, and history of Earth's components, and the processes by which they are shaped.
  • Geomorphology – The scientific study of landforms and the processes that shape them
  • Sedimentology – The study of natural sediments and of the processes by which they are formed
  • Deposition (geology) – Geological process in which sediments, soil and rocks are added to a landform or land mass
  • Erosion – Processes which remove soil and rock from one place on the Earth's crust, then transport it to another location where it is deposited
  • Sediment – Particulate solid matter that is deposited on the surface of land
  • Exner equation
  • Hydrology – The science of the movement, distribution, and quality of water on Earth and other planets
  • Flood – Overflow of water that submerges land that is not normally submerged
  • Stream capacity
  • Lagoon – A shallow body of water separated from a larger body of water by barrier islands or reefs


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External links


The ADCIRC model is a high-performance, cross-platform numerical ocean circulation model popular in simulating storm surge, tides, and coastal circulation problems.

Originally developed by Drs. Rick Luettich and Joannes Westerink,

the model is developed and maintained by a combination of academic, governmental, and corporate partners, including the University of North Carolina at Chapel Hill, the University of Notre Dame, and the US Army Corps of Engineers.

The ADCIRC system includes an independent multi-algorithmic wind forecast model and also has advanced coupling capabilities, allowing it to integrate effects from sediment transport, ice, waves, surface runoff, and baroclinicity.


A bedform is a feature that develops at the interface of fluid and a moveable bed, the result of bed material being moved by fluid flow. Examples include ripples and dunes on the bed of a river. Bedforms are often preserved in the rock record as a result of being present in a depositional setting. Bedforms are often characteristic to the flow parameters, and may be used to infer flow depth and velocity, and therefore the Froude number.

Canterbury Bight

Canterbury Bight is a 135 kilometres (84 mi) stretch of coastline between Dashing Rocks (north Timaru) and the southern side of Banks Peninsula (Birdlings Flat) on the eastern side of the South Island, New Zealand. The bight faces southeast, which exposes it to high-energy storm waves originating in the Pacific Ocean (Kirk, 1967). The most frequent wave approach direction for the Canterbury Bight is from the southeast and the most dominant the south with wave heights of over 2m common (Kirk, 1967). The bight is a large, gently curving bend of shoreline of primarily mixed sand and gravel (MSG) beaches. The MSG beaches are steep, highly reflective (of wave energy) and composed of alluvial gravel deposits. The alluvial gravels are the outwash products of multiple glaciations that occurred in the Southern Alps during the Pleistocene (Kirk, 1967). Large braided rivers transported this material to the edge of the current continental shelf, which, due to sea level rise is 50 km seaward of the coasts current position (Kirk, 1967). The MSG beaches of the Canterbury Bight therefore occur where the alluvial fans of the Canterbury Plains rivers are exposed to high-energy ocean swells (Hart et al., 2008). The dominant rock ‘greywacke’ in the Southern Alps is consequently the primary constituent of the MSG beaches (and Canterbury Plains), which is partially indurated sandstone of the Torlesse Supergroup (Hart et al., 2008). River-mouth lagoons are a relatively common occurrence on the MSG beaches of the Canterbury Bight.

Clastic rock

Clastic rocks are composed of fragments, or clasts, of pre-existing minerals and rock. A clast is a fragment of geological detritus, chunks and smaller grains of rock broken off other rocks by physical weathering. Geologists use the term clastic with reference to sedimentary rocks as well as to particles in sediment transport whether in suspension or as bed load, and in sediment deposits.

Coastal sediment transport

Coastal sediment transport (a subset of sediment transport) is the interaction of coastal land forms to various complex interactions of physical processes. The primary agent in coastal sediment transport is wave activity (see Wind wave), followed by tides and storm surge (see Tide and Storm surge), and near shore currents (see Sea#Currents) . Wind-generated waves play a key role in the transfer of energy from the open ocean to the coastlines. In addition to the physical processes acting upon the shore, the size distribution of the sediment is a critical determination for how the beach will change (see Grain size determination). These various interactions generate a wide variety of beaches. (see Beach). Other than the interactions between coastal land forms and physical processes there is also the addition of modification of these landforms through anthropogenic sources (see human modifications). Some of the anthropogenic sources of modification have been put in place to halt erosion or prevent harbors from filling up with sediment. In order to assist community planners, local governments, and national governments a variety of models have been developed to predict the changes of beach sediment transport at coastal locations. Typically, during large wave events, the sediment gets transported off the beach face a deposited offshore generating a sandbar. Once the significant wave event has diminished, the sediment then gets slowly transported back onshore.


In the geography of rivers, streams, and glaciers, a debouch, or debouche, is a place where runoff from a small, confined space emerges into a larger, broader space. The term is of French origin and means to cause to emerge. The term also has a military usage.


GSSHA (Gridded Surface/Subsurface Hydrologic Analysis) is a two-dimensional, physically based watershed model developed by the Engineer Research and Development Center of the United States Army Corps of Engineers. It simulates surface water and groundwater hydrology, erosion and sediment transport. The GSSHA model is used for hydraulic engineering and research, and is on the Federal Emergency Management Agency (FEMA) list of hydrologic models accepted for use in the national flood insurance program for flood hydrograph estimation. Input is best prepared by the Watershed Modeling System interface, which effectively links the model with geographic information systems (GIS).

GSSHA uses a square-grid, constant grid-size representation of watershed topography and characteristics, similar to a digital elevation model representation. Relevant model parameters are assigned to the model grids using index maps. Index maps are often derived from soils, landuse/land cover, vegetation, or other physiographic maps.


Geomorphology (from Ancient Greek: γῆ, gê, "earth"; μορφή, morphḗ, "form"; and λόγος, lógos, "study") is the scientific study of the origin and evolution of topographic and bathymetric features created by physical, chemical or biological processes operating at or near the Earth's surface. Geomorphologists seek to understand why landscapes look the way they do, to understand landform history and dynamics and to predict changes through a combination of field observations, physical experiments and numerical modeling. Geomorphologists work within disciplines such as physical geography, geology, geodesy, engineering geology, archaeology, climatology and geotechnical engineering. This broad base of interests contributes to many research styles and interests within the field.

Hans Albert Einstein

Hans Albert Einstein ( eyen-STYNE, -⁠SHTYNE; May 14, 1904 – July 26, 1973) was a Swiss-American engineer and educator, the second child and first son of Albert Einstein and Mileva Marić. Hans A. Einstein was a long-time professor of Hydraulic Engineering at the University of California, Berkeley.Einstein was widely recognized for his research on sediment transport. To honor his outstanding achievement in hydraulic engineering, the American Society of Civil Engineers established the "Hans Albert Einstein Award" in 1988 and the annual award is given to those who have made significant contributions to the field.

Ice rafting

Ice rafting is the transport of various materials by ice. Various objects deposited on ice may eventually become embedded in the ice. When the ice melts after a certain amount of drifting, these objects are deposited onto the bottom of the water body, e.g., onto a river bed or an ocean floor. These deposits are called ice rafted debris (IRD) or ice rafted deposits. Ice rafting was a primary mechanism of sediment transport during glacial episodes of the Pleistocene when sea levels were very low and much of the land was covered by large masses (sheets) of ice. The rafting of various size sediments into deeper ocean waters by icebergs became a rather important process. Ice rafting is still a process occurring today, although its impact is significantly less and much harder to gauge.

The melting of large icebergs deposits sediment of various sizes, usually referred to as glacial marine sediment, onto the shelf and deeper marine areas.

Ice rafting may be used for analysis of ice drift pattern by matching the rafted sediment with its origin.Ice rafting must also be taken into an account in archaeology and as a possible cause of displacement of archaeological artifacts.


An inlet is an indentation of a shoreline, usually long and narrow, such as a small bay or arm, that often leads to an enclosed body of salt water, such as a sound, bay, lagoon, or marsh.

Longshore drift

Longshore drift from longshore current is a geological process that consists of the transportation of sediments (clay, silt, pebbles, sand and shingle) along a coast parallel to the shoreline, which is dependent on oblique incoming wind direction. Oblique incoming wind squeezes water along the coast, and so generates a water current which moves parallel to the coast. Longshore drift is simply the sediment moved by the longshore current. This current and sediment movement occur within the surf zone.

Beach sand is also moved on such oblique wind days, due to the swash and backwash of water on the beach. Breaking surf sends water up the beach (swash) at an oblique angle and gravity then drains the water straight downslope (backwash) perpendicular to the shoreline. Thus beach sand can move downbeach in a zig zag fashion many tens of meters (yards) per day. This process is called "beach drift" but some workers regard it as simply part of "longshore drift" because of the overall movement of sand parallel to the coast.

Longshore drift affects numerous sediment sizes as it works in slightly different ways depending on the sediment (e.g. the difference in long-shore drift of sediments from a sandy beach to that of sediments from a shingle beach). Sand is largely affected by the oscillatory force of breaking waves, the motion of sediment due to the impact of breaking waves and bed shear from long-shore current. Because shingle beaches are much steeper than sandy ones, plunging breakers are more likely to form, causing the majority of long shore transport to occur in the swash zone, due to a lack of an extended surf zone.

Okavango River

The Okavango River (formerly spelled Okovango or Okovanggo) is a river in southwest Africa. It is the fourth-longest river system in southern Africa, running southeastward for 1,600 km (990 mi). It begins in Angola, where it is known by the Portuguese name Rio Cubango. Further south, it forms part of the border between Angola and Namibia, and then flows into Botswana, draining into the Moremi Game Reserve.

Before it enters Botswana, the river drops 4 m in a series of rapids known as Popa Falls, visible when the river is low, as during the dry season.Discharging to an endorheic basin, the Okavango does not have an outlet to the sea. Instead, it empties into a swamp in the Kalahari Desert, known as the Okavango Delta or Okavango Alluvial Fan. In the rainy season, an outflow to the Boteti River in turn seasonally discharges to the Makgadikgadi Pans, which features an expansive area of rainy-season wetland where tens of thousands of flamingos congregate each summer. Part of the river's flow fills Lake Ngami. Noted for its wildlife, the Okavango area contains Botswana's Moremi Game Reserve.

During colder periods in Earth's history, a part of the Kalahari was a massive lake, known as Lake Makgadikgadi. In this time, the Okavango would have been one of its largest tributaries.

River channel migration

River channel migration is the geomorphological process that involves the lateral migration of an alluvial river channel across its floodplain. This process is mainly driven by the combination of bank erosion of and point bar deposition over time. When referring to river channel migration, it is typically in reference to meandering streams. In braided streams, channel change is driven by sediment transport.

River morphology

The terms river morphology and its synonym stream morphology are used to describe the shapes of river channels and how they change in shape and direction over time. The morphology of a river channel is a function of a number of processes and environmental conditions, including the composition and erodibility of the bed and banks (e.g., sand, clay, bedrock); erosion comes from the power and consistency of the current, and can effect the formation of the river's path. Also, vegetation and the rate of plant growth; the availability of sediment; the size and composition of the sediment moving through the channel; the rate of sediment transport through the channel and the rate of deposition on the floodplain, banks, bars, and bed; and regional aggradation or degradation due to subsidence or uplift. River morphology can also be effected by human interaction, which is a way the river responds to a new factor in how the river can change its course. An example of human induced change in river morphology is dam construction, which alters the ebb flow of fluvial water and sediment, therefore creating or shrinking estuarine channels. A river regime is a dynamic equilibrium system, which is a way of classifying rivers into different categories. The four categories of river regimes are Sinuous canali- form rivers, Sinuous point bar rivers, Sinuous braided rivers, and Non-sinuous braided rivers.

The study of river morphology is accomplished in the field of fluvial geomorphology, the scientific term.


Sediment is a naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of wind, water, or ice or by the force of gravity acting on the particles. For example, sand and silt can be carried in suspension in river water and on reaching the sea bed deposited by sedimentation. If buried, they may eventually become sandstone and siltstone (sedimentary rocks) through lithification.

Sediments are most often transported by water (fluvial processes), but also wind (aeolian processes) and glaciers. Beach sands and river channel deposits are examples of fluvial transport and deposition, though sediment also often settles out of slow-moving or standing water in lakes and oceans. Desert sand dunes and loess are examples of aeolian transport and deposition. Glacial moraine deposits and till are ice-transported sediments.


Sedimentation is the tendency for particles in suspension to settle out of the fluid in which they are entrained and come to rest against a barrier. This is due to their motion through the fluid in response to the forces acting on them: these forces can be due to gravity, centrifugal acceleration, or electromagnetism. In geology, sedimentation is often used as the opposite of erosion, i.e., the terminal end of sediment transport. In that sense, it includes the termination of transport by saltation or true bedload transport. Settling is the falling of suspended particles through the liquid, whereas sedimentation is the termination of the settling process. In estuarine environments, settling can be influenced by the presence or absence of vegetation. Trees such as mangroves are crucial to the attenuation of waves or currents, promoting the settlement of suspended particles.Sedimentation may pertain to objects of various sizes, ranging from large rocks in flowing water to suspensions of dust and pollen particles to cellular suspensions to solutions of single molecules such as proteins and peptides. Even small molecules supply a sufficiently strong force to produce significant sedimentation.

The term is typically used in geology to describe the deposition of sediment which results in the formation of sedimentary rock, but it is also used in various chemical and environmental fields to describe the motion of often-smaller particles and molecules. This process is also used in the biotech industry to separate cells from the culture media.

Shear velocity

Shear Velocity, also called friction velocity, is a form by which a shear stress may be re-written in units of velocity. It is useful as a method in fluid mechanics to compare true velocities, such as the velocity of a flow in a stream, to a velocity that relates shear between layers of flow.

Shear velocity is used to describe shear-related motion in moving fluids. It is used to describe:

Shear velocity also helps in thinking about the rate of shear and dispersion in a flow. Shear velocity scales well to rates of dispersion and bedload sediment transport. A general rule is that the shear velocity is between 5% to 10% of the mean flow velocity.

For river base case, the shear velocity can be calculated by Manning's equation.

Instead of finding and for your specific river of interest, you can examine the range of possible values and note that for most rivers, is between 5% and 10% of :

For general case

where τ is the shear stress in an arbitrary layer of fluid and ρ is the density of the fluid.

Typically, for sediment transport applications, the shear velocity is evaluated at the lower boundary of an open channel:

where τb is the shear stress given at the boundary.

Shear velocity can also be defined in terms of the local velocity and shear stress fields (as opposed to whole-channel values, as given above).


Swash, or forewash in geography, is a turbulent layer of water that washes up on the beach after an incoming wave has broken. The swash action can move beach materials up and down the beach, which results in the cross-shore sediment exchange. The time-scale of swash motion varies from seconds to minutes depending on the type of beach (see Figure 1 for beach types). Greater swash generally occurs on flatter beaches. The swash motion plays the primary role in the formation of morphological features and their changes in the swash zone. The swash action also plays an important role as one of the instantaneous processes in wider coastal morphodynamics.

There are two approaches that describe swash motions: (1) swash resulting from the collapse of high-frequency bores (f>0.05 Hz) on the beachface; and (2) swash characterised by standing, low-frequency (f<0.05 Hz) motions. Which type of swash motion prevails is dependent on the wave conditions and the beach morphology and this can be predicted by calculating the surf similarity parameter εb (Guza & Inman 1975):

Where Hb is the breaker height, g is gravity, T is the incident-wave period and tan β is the beach gradient. Values εb>20 indicate dissipative conditions where swash is characterised by standing long-wave motion. Values εb<2.5 indicate reflective conditions where swash is dominated by wave bores.

Sediment transport
Large-scale features
Alluvial rivers
Bedrock river
Regional processes
Geologic principles and processes
Stratigraphic principles
Petrologic principles
Geomorphologic processes
Sediment transport


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