1. Quantifying erosion in mountainous landscapes
Eroding landscapes: fluvial processes
Quantifying erosion in mountainous landscapes
National Student Satisfaction survey (4th year)
Mikaël ATTAL
Acknowledgements: Jérôme Lavé, Peter van der Beek and other scientists from LGCA (Grenoble) and CRPG (Nancy)
Marsyandi valley, Himalayas, Nepal

2. Lecture overview I. Bedrock erosion processes
II. Quantifying fluvial (and landscape) erosion on the long-term
III. Quantifying fluvial erosion on the short-term

3. I. Bedrock erosion processes
Plucking (Ukak River, Alaska, Whipple et al., 2000)
Abrasion (bedload impact)
Abrasion (suspended load)
Plucking favoured by jointing (spacing + orientation)
Cavitation (

4. I. Bedrock erosion processes
Abrasion (bedload impact)
Amount of abrasion is a function of: kinetic energy = 0.5mv2; angle of impact; difference in rock resistance between projectile and target

5. BEDLOAD EXERTS A KEY ROLE
I. Bedrock erosion processes
Plucking
Amount of erosion is a function of: joint density; stream power; kinetic energy of impacts = 0.5mv2; angle of impact.
Whipple et al., 2000 (Ukak River, Alaska)
BEDLOAD EXERTS A KEY ROLE

6. I. Bedrock erosion processes
Abrasion by suspended load
Requires turbulence (eddies)  affects mostly obstacles protruding in the channel (e.g. boulders)
Whipple et al., 2000

7. I. Bedrock erosion processesV D
Most of the time, sediment is resting on the bed and protects it from erosion  bedrock erosion (abrasion by bedload impacts + plucking) happens during floods
except for protruding objects which are eroded all the time by suspended load.

8. I. Bedrock erosion processesV D
Consider 1 point in the channel, at a given time, during 1 flow event
Stream power per unit length: Ω = ρ g Q S
Fluvial shear stress: τ0 = ρ g R S
Because sediments in river include a wide range of grain sizes, some particles will move while some others (larger) will rest on the river bed
 TOOLS & COVER
Transport capacity: Qc = k(τ – τc)3/2
where k and τc are constants [Meyer-Peter-Mueller, 1948]

9. I. Bedrock erosion processes
Whipple et al., 2000: process-based theoretical analysis within the frame of the SPL
e = KAmSn = kτa where n = 2a/3
(and m is adjusted to obtain m/n = 0.5)
Remark:
 if n = 1, m = 0.5 and a = 3/2  Incision  Specific Stream power (law 2).
 if n = 2/3, m = 1/3 and a = 1  Incision  basal shear stress (law 3).
Abrasion (bedload)
Not analyzed
Abrasion (suspension)
n = 5/3
a = 5/2
Plucking
n = 2/3 1
a = 1  3/2
Cavitation
n up to 7/3
a up to 7/2

10. II. Quantifying fluvial (and landscape) erosion on the long-term (103-106 years)
1) Fluvial erosion rates using terrace dating
2) Catchment-wide erosion rates using the fluvial network as an “age homogenizer”

11. “Long-term” fluvial erosion rates (103-106 years): fluvial terraces
STRATH TERRACES
Note: rivers can erode and form terraces even without uplift
In lowland areas, where valleys are wide enough to allow rivers to migrate and abandon terraces.
Courtesy J. Lavé

12. Strath terraces: thin (or no) alluvium cover, contact alluvium-bedrock relatively flat
Central Range, Taiwan
Siwaliks hills, Himalayas (J. Lavé)

13. Strath terraces: thin (or no) alluvium cover, contact alluvium-bedrock relatively flat
Siwaliks hills, Himalayas (J. Lavé)

14. Fluvial incision rates using strath terrace dating
Age = n yr h
Incision rate = h/n
Age = 0 yr
Dating methods:
- 14C,
- Optically stimulated luminescence (OSL),
- Cosmogenic nuclides.

15. Fluvial incision rates using strath terrace dating
Bagmati River, Himalayas (Lavé & Avouac, 2000, 2001)

16. Fluvial incision rates using strath terrace dating
Bagmati River, Himalayas (Lavé & Avouac, 2000, 2001)
Terraces are correlated in the field + using remote sensing

17. Fluvial incision rates using strath terrace dating
Bagmati River, Himalayas (Lavé & Avouac, 2000, 2001)
Reminder: the Quaternary Period includes the following epochs: Pleistocene (1.8 Ma  ~12 ka) and Holocene (~12ka  present)
 Relatively constant incision rates since the end of the Pleistocene (PL3 is ~ 22ky old)

18. FILL TERRACES: usually the result of landslides damming the valley (or large alluviation events filling narrow valleys) !
Upstream of the dam
More likely to happen in high relief zone (narrow valleys).
Tal, Marsyandi valley, Himalayas

19. FILL TERRACES: usually the result of landslides damming the valley (or large alluviation events filling narrow valleys) !
image28.webshots.com
Chame, Marsyandi valley, Himalayas
Thick alluvium, up to hundreds of meters, contact alluvium- bedrock highly irregular.
Local effect  must not be used to determine long-term erosion rates.
More likely to happen in high relief zone (narrow valleys).

20. FILL TERRACES: usually the result of landslides damming the valley (or large alluviation events filling narrow valleys) !
The events that lead to the formation of fill terraces are relatively frequent in actively eroding landscapes
Amount of erosion at a given point along the river
Models, long-term measurements
Reality
More likely to happen in high relief zone (narrow valleys).
Time (x 105 years)

21. Terrace dating methods
a) 14C on organic debris in alluvium (up to ~40 ka).
3 carbon isotopes: 12C (natural abundance %), 13C (n.a %) and 14C (n.a. 1 part / trillion).
14C formed in the atmosphere (interaction between cosmic rays and N molecules):
14N + n  14C + p
14C (or radiocarbon) is a radioactive isotope which decays with a half-period of 5730 years.
 Age of terraces can be estimated by counting the number of 14C atoms in organic fragments (assuming that the time between the organism’s death and its incorporation into the alluvium is negligible).
[14C] in the atmosphere is ~ constant (equilibrium between rate of production and decay) and is ~ to [14C] in living organisms.
14Corganism / 14Catm (%)
When organism dies  no more exchange with atmosphere  the number of 14C atoms decreases due to radioactive decay.
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed

22. Terrace dating methods
b) Optically stimulated luminescence: burial ages of quartz or feldspar crystals, ages from 100 yrs to yrs.
Radioactive isotopes + cosmic rays  charge carriers (e.g., electrons e-, electron holes h+) travelling in crystals
Charge carriers can become trapped in lattice defects. They progressively accumulate in these “traps” over geological timescales.
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
Charge carriers

23. Terrace dating methods
b) Optically stimulated luminescence: burial ages of quartz or feldspar crystals, ages from 100 yrs to yrs.
Radioactive isotopes + cosmic rays  charge carriers (e.g., electrons e-, electron holes h+) travelling in crystals
Charge carriers can become trapped in lattice defects. They progressively accumulate in these “traps” over geological timescales.
Exposure to light, heat, or high pressures can release charge carriers from trapping sites  reset the system
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
The release process is associated with a photon release. Number of photons released = f (number of trapped charge carriers released).
Charge carriers

24. Terrace dating methods
b) Optically stimulated luminescence: burial ages of quartz or feldspar crystals, ages from 100 yrs to yrs.
Sunlight releases trapped charge carriers.
If a crystal gets buried, charge carriers are going to accumulate in trapping sites.
The longer the burial, the larger the number of trapped charge carriers.
Optical stimulation (light)
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
 release of charge carriers  release of photons  light emission
The older the terrace, the longer the burial, the higher the number of trapped charge carriers  the larger the number of photons released with the charge carriers  the higher the intensity of the light emitted!

25. Terrace dating methods
c) Cosmogenic Nuclides: exposure ages.
Cosmic rays interact with atoms in the atmosphere and in the rocks exposed at the surface of the Earth  nuclear reactions  cosmogenic nuclides.
Examples: 3He, 10Be, 14C, 21Ne, 26Al, 36Cl.
Stable
T1/2 = 5730 a
T1/2 = 0.73 Ma
T1/2 = 1.5 Ma
Stable
T1/2 = 0.3 Ma
Cosmogenic nuclides accumulate in minerals in the 1-2 m thick layer at the top of the Earth.
Cosmogenic nuclide production rate
The longer the rock exposure, the higher the amount of cosmogenic nuclides
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
Concentration in cosmogenic nuclides in minerals = f (EXPOSURE TIME, latitude, altitude, topography, type of mineral, type of cosmogenic nuclide).
1-2 m
Depth

26. Terrace dating methods
c) Cosmogenic Nuclides: exposure ages.
Beryllium: 9Be = stable isotope; 10Be = cosmogenic isotope formed by interactions between cosmic rays and O, N, Si, Mg, Fe. Beryllium in Quartz frequently used in geomorphology to date objects up to millions of years old.
Chlorine: 35Cl and 37Cl = stable isotopes; 36Cl = cosmogenic isotope formed by interactions between cosmic rays and Ar, Fe, K, Ca, Cl. Chlorine in calcite is a method which begins to be reliable to date objects up to millions of years old.
Boulders on terraces
Boulders on Ancient Lake Terrace Quartzite boulders cover the lake terrace of ancient Lake Bonneville on Antelope Island in Great Salt Lake. Antelope Island State Park, USA.
Bedrock strath terrace
© Scott T. Smith/CORBIS

27. II. Quantifying fluvial (and landscape) erosion on the long-term (103-106 years)
1) Fluvial erosion rates using terrace dating
2) Catchment-wide erosion rates using the fluvial network as an “age homogenizer”
“Detrital methods”
Photo Eric Gayer
Assumption: time spent in the fluvial network is negligible

28. Catchment-wide erosion rates
a) Cosmogenic ages on fluvial sands (Q + Grt).
Courtesy Eric Gayer
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed

29. Catchment-wide erosion rates
a) Cosmogenic ages on fluvial sands (Q + Grt).
Main limitation: assumption that landscape is eroding at a constant rate through time
Erosion
1-2 m
1-2 m
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
Uplift

30. Catchment-wide erosion rates
a) Cosmogenic ages on fluvial sands (Q + Grt).
Main limitation: assumption that landscape is eroding at a constant rate through time
Erosion
1-2 m
1-2 m
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
Uplift

31. Catchment-wide erosion rates
a) Cosmogenic ages on fluvial sands (Q + Grt).
Main limitation: assumption that landscape is eroding at a constant rate through time
Erosion
1-2 m
1-2 m
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
Uplift

32. Catchment-wide erosion rates
a) Cosmogenic ages on fluvial sands (Q + Grt).
Main limitation: assumption that landscape is eroding at a constant rate through time
Erosion
1-2 m
1-2 m
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
Uplift

33. Catchment-wide erosion rates
a) Cosmogenic ages on fluvial sands (Q + Grt).
Main limitation: assumption that landscape is eroding at a constant rate through time
Erosion
1-2 m
1-2 m
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
Uplift

34. Catchment-wide erosion rates
a) Cosmogenic ages on fluvial sands (Q + Grt).
Main limitation: assumption that landscape is eroding at a constant rate through time
Erosion
1-2 m
1-2 m
Landslide
People like Eric Gayer work on correcting this kind of effect by looking at the distribution of ages in the grains,
 gives the impression that the catchment includes zones with low, moderate and extremely high erosion rates!
Uplift

35. Catchment-wide erosion rates
b) Detrital termochronology: fission tracks
pangea.stanford.edu
Fission tracks in zircon or apatite
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
Bernet & Garver, 2005

36. Catchment-wide erosion rates
b) Detrital termochronology: fission tracks
If erosion rate is constant, lag time is constant.
Example: lag-time = 20 Ma
Deposition age (age of sediment td) (Ma)
td = 30 Ma 10 20
tc = 50 Ma 30
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed 40
FT age (tc) 50
Bernet & Garver, 2005 10 20 30 40
50 Ma

37. Catchment-wide erosion rates
b) Detrital termochronology: fission tracks
If erosion rate is constant, lag time is constant.
Example: lag-time = 20 Ma
Deposition age (age of sediment td) (Ma)
td = 20 Ma 10 20
tc = 40 Ma 30
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed 40
FT age (tc) 50
Bernet & Garver, 2005 10 20 30 40
50 Ma

38. Catchment-wide erosion rates
b) Detrital termochronology: fission tracks
If erosion rate is constant, lag time is constant.
Example: lag-time = 20 Ma
Deposition age (age of sediment td) (Ma)
td = 10 Ma 10 20
tc = 30 Ma 30
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed 40
FT age (tc) 50
Bernet & Garver, 2005 10 20 30 40
50 Ma

39. Catchment-wide erosion rates
b) Detrital termochronology: fission tracks
If erosion rate is constant, lag time is constant.
Example: lag-time = 20 Ma
Deposition age (age of sediment td) (Ma)
td = 0 Ma
Slope 1:1
Long lag-time 10 20
Short lag-time
tc = 20 Ma 30
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed 40
FT age (tc) 50
Bernet & Garver, 2005 10 20 30 40
50 Ma

40. Catchment-wide erosion rates
b) Detrital termochronology: fission tracks
If erosion rate is constant, lag time is constant.
Example: lag-time = 20 Ma
Let’s imagine that erosion rate increases at 30 Ma
 Lag-time = 15 Ma
Deposition age (age of sediment td) (Ma)
td = 15 Ma 10 20
tc = 30 Ma 30
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed 40
FT age (tc) 50
Bernet & Garver, 2005 10 20 30 40
50 Ma

41. Catchment-wide erosion rates
b) Detrital termochronology: fission tracks
If erosion rate is constant, lag time is constant.
Example: lag-time = 20 Ma
Let’s imagine that erosion rate increases at 30 Ma
 Lag-time = 15 Ma
Deposition age (age of sediment td) (Ma)
td = 5 Ma 10 20
tc = 20 Ma 30
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed 40
FT age (tc) 50
Bernet & Garver, 2005 10 20 30 40
50 Ma

42. Catchment-wide erosion rates
b) Detrital termochronology: Ar/Ar or K/Ar methods (very simplified here)
39K is stable.
40K decays into 40Ar (gas) with a half-life of 1.25 billion years.
Degassed at high temperature, accumulates in minerals at temperatures < closure temperature
40Ar accumulates in mineral. Amount of 40Ar = f (time since crossing the isotherm)
T = closure temperature  clock starts
Isotherm corresponding to closure temperature
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
T > closure temperature: 40Ar degassed
Biotite: 300 ºC
Muscovite: 400 ºC
Hornblende: 550 ºC

43. Catchment-wide erosion rates
b) Detrital termochronology: Ar/Ar or K/Ar methods (very simplified here)
Central Himalayas, Nepal (Wobus et al., 2005)
Ar/Ar ages on detrital muscovite
Note: 14C in the atmosphere is not perfectly constant and is not exactly = to 14C in organism  corrections needed
Isotherm 400 ºC
 Migration of the MCT?