T. Perron – 12.001 – Rivers
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Rivers
T. Perron – 12.001 – April 16, 2010
After our discussions of large-scale topography, how we represent topography in
maps, and how topography interacts with geologic structures, you should be
frothing at the mouth with curiosity about how topography forms. We now begin
our all-too-brief tour of surface processes, in which we will review the main
mechanisms that shape topography.
 Why are rivers important?
o Rivers are everywhere [PPT: Allegheny Plateau DEM]
 Most continental landscapes are the product of river erosion and
sediment transport
 Even form on other planets & moons
 Networks on Mars & Titan [PPT: Mars, then Titan]
 Long, sinuous lava flows on Moon, Venus, Io
 So this is a universal geologic process
o Rivers are responsible for most of the mass fluxes across the continents
 Water, rock (as solid particles or in solution), nutrients
 Vital for geology, ecology, human society
o How much water and sediment?
 Freshwater is a rare resource
 Distribution:
 Fraction of earth’s water that is fresh (non-saline): 3%.
 Of freshwater, ~1/3 is groundwater, 2/3 is ice. Only 0.3%
is surface water, and most of this is in lakes.
 Yet rivers do most of the work carrying rock mass.
 Flux of suspended sediment in large rivers to the ocean =
15.5 metric GT/yr. For a rock density of 3T/m3, this is 5 x
109 m3/yr.
 If we divide this flux by Earth’s land surface area of 150
million km2 (how could we estimate this number if we
didn’t know offhand?), we get a globally averaged erosion
rate of ~3 x 10-5 m/yr (30 m/Myr).
T. Perron – 12.001 – Rivers
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 Not far off – typical erosion rates range from a few m/Myr
in arid, tectonically inactive continental interiors
(Australia) to a few km/Myr in the most tectonically
active environments (Taiwan, NZ), with typical erosion
rates of tens to hundreds of m/Myr over much of Earth.
 Why do rivers form?
o P > ET leads to runoff, infiltration, groundwater flow.
 These flows are directed downslope by pressure gradients
induced by gravity. Many paths, surface or subsurface,
eventually lead to river channels.
 Flow paths
 Surface overland flow
 Shallow subsurface flow and return flow
 Deep groundwater flow, including flow up to stream
channels
 Hydrographs
 Precip, stream discharge, groundwater discharge
 Effects of urbanization
o Formation of channels, valleys and networks [PPT: Gabilan]
 If erosion rate depends on flux of water, land surface is unstable
with respect to water erosion  channelization [PPT]
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 The positive feedback makes rivers cut valleys, and the rest of
the landscape slopes toward them
 Other processes prevent channels from forming everywhere
 Thresholds: Finite strength of land surface and river banks
due to
o Cohesive sediment, clays
o Ice
o Vegetation roots
o Particles too large to be transported
 Smoothing by mass movement of soil/sediment [PPT]
o Soil creep
o Landslides
o Rain splash
 Tributary network formation: Larger rivers cut valleys more
rapidly, so smaller streams tend to flow toward them (along the
steepest path), forming tributary networks [PPT: Allegheny]
 Open-channel flow
o For steady (non-accelerating) flow, downslope component of weight of
water must be balanced by shear stress exerted on water due to bed
friction.
o Sediment transport
 Initial motion: lift + drag forces vs. submerged grain weight
 Path once in motion depends on mean velocity, and relative
magnitudes of turbulent flow velocities (u) vs. settling velocity
(w)
 u < w  Bed load (rolling)
 u ~ w  Saltation
 u >> w  Suspension (usually majority of load)
T. Perron – 12.001 – Rivers
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 Erosion and deposition: processes that control changes in bed elevation depend
on whether bed is exposed bedrock, or always covered by sediment
o Exposed BR: what controls the rate at which rivers erode rock?
 Abrasion by BL & SL: velocity, sediment load, rock strength
 Plucking: velocity, rock strength
 Cavitation: turbulent velocity fluctuations, rock strength
 Impact wear by saltating grains
 Local max in plot of erosion rate vs. sed supply
 Local max in plot of erosion rate vs. transport stage
(below threshold vs. suspension)
 Combine to create bullseye of erosion rate contours
 Also depends on rock strength
o Sediment cover: What controls the rate of aggradation or degradation of
an alluvial bed?
 I – O = S, or simplified Exner equation:
o Clearly sediment flux is important in governing erosion rates. What
controls the rate at which rivers transport sediment?
 How can we measure this? Flumes, field monitoring
 In general, sediment flux scales with [a power of] bed shear
stress in excess of the minimum shear stress required to initiate
grain motion
 How do rivers change along their path from headwaters to ocean? [PPT]
T. Perron – 12.001 – Rivers
o If you walked down a river starting from a topographic divide, what
changes in channel geometry, sediment and processes would you see?
[Sketch concave-up long profile]
 Slopes become gentler, until eventually reaching sea level
 No channel  channel
 Less exposed bedrock
 Fining sediment (boulders  gravel  sand  silt)
 [0.1-1] Hillslope; no channel
 [0.01-0.1] Exposed bedrock, boulders
 [0.01] Gravel bed
 [0.001] Gravel  sand transition
 [0.0001] Sand  fine-bed alluvial (mud)
 [0] Water body – the “base level” to which the entire profile
ultimately responds
o Why does sediment get (exponentially) finer downstream?
 Abrasion breaks down grains, so the farther they travel, the
smaller they get
 Selective transport: as slope, and therefore stress, decrease
downstream, the maximum transportable grain size shrinks
o Why are river elevation profiles concave-up?
 Main reason is that drainage area, and therefore discharge,
increases downslope
 Larger discharge generates greater depth (Provided width
does not increase too dramatically). If erosion rate
depends on shear stress, then progressively lower slopes
are required to generate the same stress
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 Discharge-slope-grain size tradeoff maintains concave-up
profile through feedbacks:
o Decline in slope will lead to mantling of bed,
which inhibits erosion, leading to steepening.
o Conversely, increase in slope leads to increase in
tranport, exposing the bed to erosion, which
decreases slope.
 Lesson: the concave-up form is not necessarily a transient
feature, e.g. a consequence of mountains being built.
o How do rivers respond to changing forcing?
 Answer the question by example: drop in sea level
 The lesson: there is a finite response time, and some parts of the
profile will not feel the change until it propagates upstream
 Cross-sectional geometry
o Intuitively we expect that rivers will get wider, deeper, [and maybe
faster or slower, but which – quiz them on this]…but how much?
o Leopold and Maddock (1953), USGS gauge data
 w =aQb, d=cQf, u=kQm
 Because Q = w*d*u, we know ack=1 and b+f+m=1
 Leopold & Maddock found b~0.5, f~0.4, m~0.1. Why does u
increase? Higher Q, finer grains  roughness elements << d, and
flow is, on average, further from bed & banks.
 Planform morphology [PPT: meandering vs. braided]
o Why do some rivers meander?
 Flow-steering instability
 Perturbation in flow path or bed topography steers flow to
one side
T. Perron – 12.001 – Rivers
 Superelevation of water surface along outer part of bend
alters pattern of shear stress
 Stress decreases downstream on inside of bend  point
bar deposition; stress increases downstream on outside of
bend  bed and bank erosion. Requires stabilization of
point bar by vegetation, cohesive sediment, ice, etc.
 This leads to meander growth, which creates a stronger
superelevation, creating a positive feedback
 Meander bends grow until cut off during floods [PPT:
Birch Creek, Alaska]
o Why do others braid? [PPT: Waimakariri]
 High sediment load from upstream  aggradation in channels
 Easily eroded bank material (little or no cohesion)
 Channel widens during high flow, and medial bars are deposited
as flow stage falls
 Why don’t braided streams widen indefinitely? Eventually flow
depth gets so small that stress is insufficient to transport
sediment.
o Why are there floodplains? [PPT: San Juan R, Argentina]
 Lateral bank erosion of rivers (e.g., during meandering) without
downcutting creates a wide valley floor
 Fine sediment deposited across valley floor during floods
maintains ~level surface
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 The flooding process also creates levees
 Depositional systems: What happens when a river meets a body of water?
o Deltas [PPT: Lena, Nile, Eberswalde Delta, Mars]
 Slopes decline to zero, so there’s a downstream decrease in shear
stress  deposition
 River can build outward along the same path, but this leads to a
further decrease in slope
 Eventually the difference in slope is large enough that river
changes course during a flood: avulsion.
 Over time, occupation of, and deposition along, many different
flow paths builds a fan-shaped delta
 Example of what happens when the depositional reach of a river system is
modified: New Orleans and the Mississippi [PPT]
o Original settlement was on natural levees. Later, swamps were
drained and city was expanded into areas below sea level
o Artificial levees were built, preventing overbank flooding. As a
result, less sediment delivered to floodplain. Delta is subsiding in
isostatic response to sediment deposition. Without sediment to keep
pace, land surface sinks further below sea level. Instead, river builds
delta seaward.
o Canals were built to make it easier to get ships into the city, and
swamp vegetation was removed. Previously, these swamps acted as
roughness elements to slow down storm surges.
o These 3 factors dramatically increased the risk exposure of New
Orleans to hurricanes, which bring higher flows & risks of levee
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breaches, and storm surge from the Gulf of Mexico. Both contribute
to flooding of populated areas below sea level.
 We will discuss other human impacts on rivers in the lecture on Earth Science
& Society