Streams I: Introduction


  1. film Earth Revealed: movie. Courtesy of Anneberg Media, URL <>.  Requires Windows media Player.  Sign in and view #19 Running Water I: Rivers, Erosion and Deposition, and #20 Running Water II: Landscape Evolution.
  2. film How Stuff Works: Rivers and Streams
  3. Fluvial Geomorphology (pdf) and Sediment Transport Appendix (pdf), in Stream Habitat Restoration Guidelines, 2004, Washington Department of Fish and Wildlife, Site URL: (optional)

Aquatic Habitat Guidelines: An Integrated Approach to Marine, Freshwater, and Riparian Habitat Protection and Restoration, Washington Department of Fish and Wildlife, Site URL: explore the appendices to the Integrated Streambank Protection Guidelines (ISPG), Stream Habitat Restoration Guidelines (SHRG) - the appendices to these manuals have excellent summary overview to hydrology, fluvial geomorphology and sediment transport

The Water Cycle, Water Science Basics, U.S. Geological Survey

Stream flow and Fluvial Processes, Dr. Michael Pidwirny, University of British Columbia Okanagan, Fundamentals of Physical Geography (, page URL:

Erosion and Deposition, Dr. Michael Pidwirny, University of British Columbia Okanagan, Fundamentals of Physical Geography (, page URL:

Landforms on topographic Maps (view Landforms due to streams), Dr. Susan Clark Slaymaker
California State University, Sacramento, page URL: maker/Archives/Geol10L/landforms.htm

NASA Geomorphology From Space: Chapter 4 Fluvial Landforms , site URL:

USGS Glossary of Water terms

Web-based interactive landform Simulation Model, Northern Illinois University, URL: Java base drainage network simulator that allows input on variables such as erodibility, climate, and tectonics.

usgsbook Terms: hydrologic cycle, transpiration, groundwater, permeability, groundwater table, phreatic, vadose, throughflow, runoff, sheetflow, discharge, gaging station, rating curve, baseflow, stream,  headward erosion, nickpoint, rill, gully, load, bedload, suspended load, dissolved load, hydrologic divide, tributary, base level, fluvial, alluvial, competence, capacity, caliber, piping, bedload, suspended load, Hjlstrom curve, cavitation, Bernoulli's Law, hydraulicking, corrosion, corrasion, laminar and turbulent flow, Reynold's number, flow regime, bedform, Froude number, tranquil flow, shooting flow, eddy, vortex, potential energy, kinetic energy.  Test your knowlege: Interactive web crossword / PDF


Basic Hydrology


water cycle

Figure 1. Illustration by John M. Evans USGS, Colorado District, site URL:

Hydrologic Cycle: The continuous movement of water between the hydrosphere, atmosphere, and biosphere. The cycle is succinctly represented by the hydrologic equation:

    Precipitation = EvapoTranspiration + Infiltration + Surface Runoff (P=ET+I+R)
Driving forces: solar energy and gravity

The impact of the hydrologic cycle on landscape development cannot be underestimated. Not only does it illustrate the movement of water between the land, oceans, and atmosphere,  it is also an energy cycle, responsible for shaping and creating landforms.  Through evaporation solar energy is converted to potential energy that is eventually released by rainfall. Raindrop impact loosens soil and rock particles, and incrementally water moves these particle downslope, into channels, and eventually to the ocean. When water flows downhill potential energy converts to kinetic energy, the energy of motion responsible for carving landscapes.    Fluvial activity shapes mountains, river valleys, gullies, and slopes, and transports nearly 90% of all sediment entering the oceans.  Solar energy also drives wind and waves that perform their own work.

Terms and concepts:

  • Ground water: water within the zone of aeration (vadose water) and the zone of saturation (phreatic water).  The groundwater table is the upper boundary of the zone of saturation.
  • Overland flow is surface runoff and is categorized using a variety of terms.  If all soil beneath the surface is saturated the term saturated overland flow applies. If surface runoff is occurring because precipitation exceeds infiltration then that is refered to as Hotonian overland flow. The general term for overland flow that moves over the surface as a thin muddy sheet is called sheetflow.
  • Throughflow: The water the flows through the undersaturated zone during storms.  Considered a component of storm runoff.
  • Surface water (runoff): All terrestrial water in lakes, ponds, sheet flow and stream flow.
  • Stream: The general term for any natural channel through which water flows.  A stream can flow all year around (perennial stream) or only when it rains (ephemeral stream).  The term includes the smallest gully to the largest river.
  • Baseflow: the groundwater contribution to streamflow.
  • Alluvium: The sediment deposited by streams.
  • Basel Level: Base level is the elevation below which a stream cannot erode. The valley floor of a river is graded to whatever the local baselevel may be. Aggredation accompanies a rise in base level. Degradation (erosion) accompanies a lowering of baselevel.

What work is accomplished by streams?

  • weathering - solution and abrasion
  • erosion - scouring
  • transportation - movement of sediment from one place to another
  • deposition - laying down sediment

A stream accomplishes all of these, however one or more process may dominate depending on geology of the basin, climate, and base level. For example deposition prevails where a braided stream flows across an arid alluvial fan, and solution where a tropical stream flows through limestone.  Within a basin these processes will vary both spacially and temporially. Weathering and erosion dominate in finger tip tributaries extending headward into steep slopes.  The sediment is then transportion through the river trunk and eventually deposited at its mouth.  Scouring and sediment transport occurs during floods, and during low flows deep scoured pools are made shallow by deposition.

How is streamflow measured?

Stream discharge (Q), the rate at which water flows through a given cross-sectional area of a channel, is calculated using the equation below. In the field discharge is measured using a current meter and a tape measurer. At a gauging station, stage height is continuously recorded by a recorder attached to a float resting on the water's surface in a stilling well. Discharge is then determined from the rating curve (plot of Q vs depth) for that area of the channel. film River Bollin Field Work - Watch geomorphology students measure discharge of a small stream.

Q (discharge) = wdV 

w = width (usually measured at the top)
d = average depth (taken at defined intervals and average)
V = average velocity 

Velocity is taken at defined intervals:

  1. if depth is <2.5 ft  velocity is measured at 6/10 the total depth measured from the top
  2. if depth is >2.5 ft velocity is measured at 2/10 and 8/10 and averaged

View this video about measuring streamflow on the Salt River, AZ from the USGS Water Science Center
Informative sites: How stream flow is measured? (USGS),  stream gages (, Streamflow and stream gaging (Dr. T. Brikowski, U. Texas-Dallas)

How do streams form?

With the exception of groundwater piping, which will be discuss later, overland flow (sheet flow) is necessary for channel formation.  The rate at which a channel forms depends on vegetation, storm intensity, slope, permeability, and erodibility of the surface.


Sheet flow is dynamically unstable and small irregularities in the surface will cause local concentrations of flow. Eddy formation and flow diversion around obstructions or into hollows initiate scouring.  Once developed, a scoured trough or rill is perpetuated by the continued concentration of flow and migrates upstream by headward erosion of the nickpoint, the inflection where scouring is greatest. Eventually the rill grows into a gully, and if the gully deepens to intersect the groundwater table it will become a permanently flowing perennial stream.  A gully may take only a few days or years to form.  However, a large integrated stream network can take thousands to several millions of year to develop.

pinatubo rills

Figure 2. Network of rills established on tephra-mantled slopes of Pinatubo by rain that fell during the June 15 eruption. Photograph taken June 25, 1991. Rills are typically straight and parallel, reflecting their formation on steep slopes.  (Figure 15 from Major, Janda and Daag, 1999, Watershed Disturbance and Lahars on the East Side of Mount Pinatubo During the mid-June 1991 Eruptions, U.S.Geological Survey, URL:


Because sheetflow is easily deflected it can concentrate in linear depressions, joints, mudcracks, hiking trials or even cow paths. Every irregularity on a slope can potentially influence channel development.   Large slope depressions created by landslides are also popular sites for water to concentrate. Over time streams may establish paths in structural troughs, faults, rift valleys, or linear depressions formed on weak lithologies.  Over time discontinuities in structure and lithology will become etched into the landscape.

Formation by spring sapping, subsurface piping, artesian sapping

Spring sapping, subsurface piping, and artesian sapping, are all forms of erosion by ground water discharge.  This is process is common along contact springs where groundwater flowing along an impermeable bed discharges along a slope and slowly removes the material around it. The seepage pressure of water flowing from a slope will loosen and and removed sediment. If the spring is deep in the slope it will undermine and collapse the overlying material. Spring discharge continues to erodes the channel downslope, while sapping drives headward migration and channel lengthening upslope.   Small mountain creeks that terminate at slope springs are typical formed by this process.

Sediment Load

Load includes all material carried by a stream. It is introduce to the channel through solution, abrasion, mass-wasting, and channel scouring.  The average load of a stream is a function of the climate, geology and slope of its drainage basin.

Particle Load

Bedload is that portion of the particulate load that is transported along the bed by sliding, rolling or hopping. It moves at velocities slower than the flow, and spends most of its time on or near the stream bed.

Bedload transport move filmed and edited by John Gaffney (U of Minn) (more)

mechanisms of grain motion:

  • traction (rolling and sliding)--important factors: frictional drag, lift forces exerted by the flow, and slope
  • saltation (hopping)--grains are temporarily suspended by fluid vortices or by ballistic impact and then released

Sediment Transport movie of bedload (courtesy of Paul Heller UofWY)

Grain movement may be continuous or intermittent depending on the flow regime (strength of flow as defined by Froude Number) and grain size.

Suspended load is fine sediment carried in the body of the flow (fig.3). Suspended load moves at the same velocity as the flow and typically includes clay and fine silt particles having large relative surface areas. The electrostatic attraction between the charges on the particles and the water molecules keeps these particles in suspension. For clay and  fine silt this electrostatic force is large compared to the weight of the particle.  However, once deposited cohesion between particles will inhibit entrainment.  (See Hjulstrom curve below.)

Washed load is that component of suspended load composed of particle sizes not found in the channel bed sediment.

The quantity and quality of the particle load is defined in terms of competence and capacity. Competence is the largest size clast that a stream can carry, whereas capacity is the volume of sediment carried. Competence (caliber) is a function of velocity and slope whereas capacity is determined by of velocity and discharge (volume rate of flow).

Dissolved load includes the chemically dissolved ions carried by the water, and is dependent on climate and rock solubility.

suspended load

Figure 3. Suspended load makes the waters of the Cold River (Alstead, NH) murky after rainfalls. Coarse gravel along the banks is bedload deposited at a higher water level.  Movement of cobbles and boulders transported along the bed can generally be heard but not seen.  The greatest amount of channel scouring occurs during floods.  Floods also precipitate mass movement by removing the stabilizing toes of landslides.

The load of a stream varies with discharge and is greatest during times of flood. At times a landslide in an upstream tributary may introduce an unexpected pulse of sediment into stream.

Figure 4. The Hjulstrom curve (below) shows the velocities required to move and transport sediment. Note that a higher velocity is required to entrain cohesive clay and fine silt than coarse sand, which is cohesionless. However, once fine sediment is entrained a much lower velocity is required to keep it in suspension.  (Vist the USDA Stream Systems Technology Center for a good review of the phi particle size classification.)

Factors that govern the % dissolved and suspended load

  1. Climate: temperature, precipitation (volume, timing and intensity)
    Type and amount of vegetation (dependant on climate)
  2. Geology: rock solubility: (e.g. abundance of carbonates or evaporite deposits)
    erodibility and permeability of materials in the drainage basin
  3. Relief and slope: Affects the potential and kinetic energy of runoff and stream flow
  4. Human activities such as mining, constructure, clear cutting, development, etc.

Go to the FAO World River Sediment Database and record the sediment yields, watershed areas, runoff and rainfall of the following rivers: Ganges, Mississippi, Hudson, and Colorado.  What is the sediment yield/area for each.  How do the vary?  What hypotheses can you make to explain your observations?

Flow Hydraulics

Laminar vs. turbulent flow

Fluid flow is either laminar or turbulent (fig 5).  If flow is laminar water particles follow parallel paths that don't cross. Turbulent flow, on the other hand is chaotic, characterized by instantaneous changes in both particle direction and velocity. Flow paths cross and interact. Variations in velocity, local channel dimensions, roughness, and sediment load produce a variety of turbulent flow phenomena. Bank and bottom rollers, and helical flow are examples, as are vortices caused by flow separation around obstacles.  Helical flow is a spiral, cross-channel and downstream motion of flow, which is important to point bar development in meandering streams.  Eddies and vortices are important to sediment scouring processes and pothole (fig. 6) formation. 

The conditions under which these flows occur are described using a dimensionless number known as Renold's number, shown below.  The Re# for laminar channel flow is around 500. Streams have Re#s >2000 and are therefore characterized by turbulent flow. However, groundwater flowing through a granular aquifer is typically laminar. Re# varies for different systems, such as water flowing through channels or pipes, or smoke rising from a stack.


Renold's Number= pvd/u

p = density (m/l3)
v = velocity (l/t)
= average depth of flow (see below) (l)
= viscosity (m/lt)

Figure 5. Vertical velocity profiles depicting the differences in laminar and turbulent flow.  (R#<500 = laminar flow; R#>2000=fully turbulent flow) Question: Assume a laminar flow condition and a constant flow velocity. What adjustment(s) would result in the flow becoming turbulent?

Figure 6. Potholes carved into the Wingate Sandstone by the Freemont River, near Fruita UT. The basins are carved by turbulent eddies armed with sediment that drill through the bedrock.  (Click to enlarge.) 

Many large high-level potholes in New England stream were carved by aggressive, sediment-laden glacial meltwater stream that accompanied deglaciation. (Examples: Shelburn Falls in the Deerfield River, MA: Sculputured Rocks on the Cockermouth River, Groton, NH; Screw Auger Falls, Gulf Hagas on the West Branch Pleasant River, Maine.)

Flow  regime

Flow regime: Three progressive states of turbulent flow, or flow regime, are defined by another dimensionless number call Froude Number (described below).

    Froude # = v2/(gd)
    v = velocity (l)
    d = average depth of flow (l) (see below)
    g = acceleration due to gravity (l/t2 )  (32 ft/sec2 or 9.8 m/sec2)

F# is often viewed as the ratio of the inertial force (the force acting to sustain the flow) and the gravitational force (the force acting to dampen the flow), as such froude number reflects the strength of the flow. F# is also viewed as the ratio of kinetic (~v2) and potential (gd) energy .

Froude number defines the type of turbulent flow, whether it's shooting (upper flow regime) or tranquil (lower flow regime).  For a given grain size, bedforms in a channel or on a beach will reflect flow regime.   Therefore, once a relationship is determine through experimentation, usually in a flume, bedforms can be used to interpret past conditions of flow strengh and depth.  Flow regime can be observed in the field by noting whether the water surface is in phase (upper flow regime) or out of phase (low flow regime) with the bed.

Approximate F#
Flow Regime
Bedforms (sand)
F# < 1
Tranquil or subcritical flow

low flow regime plane beds and ripples
(quicktime movie)

F = 1

planed-off ripples and upper flow regime plane beds
 (quicktime movie)

F# = > 1
Shooting or supercritical flow

(quicktime movie1/movie 2)

Table 2. Definition of flow regime using froude number. Movies from Paul Hellers Sediment Transport Movie page.

Points concerning flow regime:

  • Flow regime affects the type of bedform that develops and certain characteristics of sediment transport.
  • Under low-flow regime conditions the bedload moves intermittently because it is temporarily incorporated in bedforms, such as ripples and dunes.  This means that a large amount of sediment can be stored in the bed even though over time it is slowly moved downstream.
  • In upper flow regime conditions that typically occur during flooding the movement of sand and granule-size particles is continuous.  The greatest amount of channel scouring occurs during floods.  Deep pools scoured by floods are typically filled in or made shallow during low flow conditions.

For more on bedforms visit the USGS Cross Bedding, Bedform and Paleocurrent site by David Rubin.

Problem: Measuring streamflow on the San Pedro River (view movie from the Arizona Water Science Center).  The flume used to measure flow is specially designed so the the froude # of the flow is equal to 1.  How does this design facilitate the determination of discharge?  If the water in the stilling well is 2 inches what is the flow velocity?

How streams erode their channels

Mechanisms of stream erosion 

  1. Abrasion (corrasion) : Wearing away by debris carried in the flow. Potholes are formed by debris swirling against the bedrock in stationary eddies.
  2. Solution (corrosion): Erosion by chemical solution. Prominent in karst terrains where bedrock is soluble.
  3. Cavitation: Micro-chipping of rock by tiny shockwave produced by bubbled collapse.

    Cavitation and hydraulic lift are explain by Bernoulli's Law, which explains the relationship between velocity and pressure in a flow. The law assumes that the total energy of the system is constant and equal to its potential energy + kinetic energy and existing pressure.   Because density and gravity are constant the only two variables are velocity and pressure.  As one increases the other must decrease.

    An increase in velocity caused by water flowing over a falls or through a constricted portion of a channel forces a decrease in pressure and an rapid bubbling. The bubbles implode when the velocity is again decreased sending shock waves that chip the rock.

  4. Hydraulicking: The lifting and removal of loose material by the force or impact of water (reactive force + lift force).  The shear stress exerted by the flow is dependent on the weight of the water, which increases with flow depth, and the slope of the bed.  As depth and slope increase so does shear stress.  Lift force is related to the vertical pressure and velocity gradient in the flow (see Bernoulli's Law below).


    Total Energy =ph + (1/2) pv2 + P = constant
    cp=density; g=9.8m/sec2; ah=height above base level; v=velocity; P=pressure

    A simplified version of the equation is: P + pv2 = constant

    Potential energy is PE=ph
    Kinetic energy is 1/2 pv
    Pressure F/A is F=ma

    When v increases, P must decrease and visa versa.  Therefore high flow velocity over particle reduces the overlying pressure and aids in the lifting of the grain from the bed.

    Question to ponder: How is Bernoulli's Law also be used to explain the hydraulic lift experienced by particle on the stream bed?

5. Ballistic impact is chipping caused by grains hitting the rock (i.e. formation of chatter marks). This process is more effective in an aeolian environment where grains are small (e.g. fine sand).  Water hydrostatically bonded to a grain will cushion its impact in a streams.  Ballistic impact also aids in sediment entrainment.

Quantitative Geomorphology

Hydraulic Geometry

Hydraulic Geometry (Leopold and Maddock, 1953) is an empirical method used to illustrate the relationship between channel geometry (width, depth, and slope), flow velocity, and stream discharge within a particular drainage basin.  As mentioned above, Stream discharge (Q) is the product of width, depth, and flow velocity.  

    Q = AV = wdV


    Q = discharge (ft3 /sec or m3 /sec)
    A = cross-sectional area = width x depth
    V = Velocity

    Empirical regression equations describe the geometric changes experienced by a channel while adjusting to changes in discharge. Discharge can increase during a flood (at a station) or when tributaries meet (downstream). These geometric changes can be mathematically and graphically displayed.  Exponents will differ slightly from one river system to another depending on climate and local geology.

    Leopold and Maddock (1953) obtained the following results:
    1. At a station (b=.25, f=.4 m=.34)
    2. Downstream values (b=.5, f=.4, and m=1)


    Basic equations describing hydraulic geometry:
    Width = aQb



    Slope = gQz

    If Q = wdV then a*d*k=1 and b+f+m = 1

    To view an informative investigation see  Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine, Robert W. Dudley, 2004, U.S. Department of the Interior, U.S. Geological Survey, Scientific Investigations Report 2004-5042, URL:

    Problem: An  unexpected discovery of the study by Leopold and Maddock was that velocity actually increases downstream.  How do you explain this counter-intuitive conclusion?


Empirical equations relating flow velocity, friction, slope, and hydraulic radius:

1. Chezy equation: v = C(RS)1/2 : v=velocity, C=smoothness coefficient, R=hydraulic radius, S=slope

2. Manning equation: v = (1.49/n) *R2/3S1/2 : n = empirically derived roughness coefficient (manning calculator from LMNO Engineering, Research, and Software, Ltd.) *Questions:

Questions: Although the slope of a river decreases down stream, flow velocity increases. This is evident from the above equations. 

  1. What adjustments can you predict a stream will make after flowing from a silt-dominated channel to one dominated by sand and gravel?
  2. List and briefly described at least two conditions that may lead to changes in channel composition.


Summary of changes that occur in the downstream direction

1. Discharge increases
2. slope
3. n (manning roughness)
decreases; C (Chezy smoothness increases)
4. net forward velocity
5. Area
6. load
7. particle size
decreases*Question: If the gradient of a river decreases downstream, why does the downstream velocity often increase.

Wetted Perimeter and hydraulic radius

    Wetted perimeter(Pw) = w + 2d: Approximates the length of the channel boundary.

    Hydraulic radius (R)= A/Pw: ratio of the area of the stream channel to  the wetted perimeter. This value approximates average channel depth. film Measuring wetted perimeter of a small stream

    An increase in R results in a decrease in frictional resistance exerted by the channel walls

Streams and Energy

Energy is the ability to perform work (Force x distance;  or mass x acceleration x distance). The energy in a stream consists of potential energy (PE=pgh), which is stored energy, and kinetic energy (KE=1/2 mv2), which is the energy of motion.  The potential energy of a river decreases downstream while its kinetic energy increases.

Energy transformations: As water moves down slope potential energy changes to kinetic energy. The work preformed on a stream is accomplished by KE. The rate of transfer of PE to KE, which performs the work of stream flow, is a function of gradient.

The amount of work preformed is a function of available kinetic energy. In a graded profile, the stream has adjusted so that the work needed to transport the sediment through the system is equal to the available energy.

KE is lost by internal friction (fluid friction; governed by both fluid and eddy viscosity), external friction (drag induced by channel walls, and by sediment erosion and transportation. KE is gained by an increase in slope and by an increase in discharge.

Streams Part 1: Introduction / Streams Part 2: Classifications /Streams Part 3: Drainage Basins