Geomorphology is the study of landforms and seeks to explain landscape shapes through structures, materials, and processes. It relates to other geological disciplines as tectonics and climate determine geomorphology, while landforms provide evidence of geological history. Geomorphology considers how landforms reveal information like the sense of tectonic motions from fault scarps or past climate from glacial moraines. Quantitative geomorphology models landscape evolution processes like hillslope failure thresholds and drainage network development using concepts from diffusion, hydrology, and soil mechanics. Landforms also provide clues about magnitudes and rates of tectonic deformation when their original shapes and ages are known.

1. 1
Lecture 6: Geomorphology
• Questions
– What is geomorphology? What are the relationships
between elevation, slope, relief, uplift, erosion, and
isostasy?
– How do you measure the rates of geomorphic
processes?
– What does geomorphology have to do with tectonics?
• Reading
– Grotzinger et al. chapters 16, 22
Basic principle:
Every feature of the landscape is
there for a reason. We just have
to be smart enough to figure out
what the reason is.

2. 2
What is Geomorphology?
• Geomorphology is the study of landforms, i.e. the
shape of the Earth’s surface. It attempts to explain
why landscapes look as they do in terms of the
structures, materials, processes, and history
affecting regions.
• Geomorphology relates to all the other disciplines
of geology in two directions:
– Tectonics, petrology, geochemistry, stratigraphy, and
climate determine the geomorphology of the earth and
its regions by controlling the principal influences on
landscape.
– Therefore evidence from observations of the landscape
in turn constrain the tectonic, petrologic, geochemical,
stratigraphic, and climatic history of the earth and its
regions.

3. 3
Uses of geomorphology
• Consider how frequently we infer the geologic history
of a region from observation of the landforms.
• We will see many examples on our field trip:
– Tectonic motions create geomorphic features like fault scarps and
grabens; from observation of scarps and grabens we infer the sense of
tectonic motions and something about their ages.
– Volcanic activity creates calderas; from the form of the caldera we learn
about the mechanism of eruption.
– Granite weathers to rounded jointstones; from observation of the shape of
boulders and outcrops we can quickly map granite plutons; from the shape
of these rocks we infer how they joint and how they chemically weather.
– Resistant and weak strata determine the shapes of cliffs; from distant
observations of cliff shapes and local knowledge of stratigraphy, we can
map outcrops as far as the eye can see.
– Glacial processes create geomorphic expressions such as moraines; from
the position, form, and age of the moraines we learn about paleoclimate
and the nature of glaciers.

4. 4
Geomorphology in the rock cycle
• Every part of the
rock cycle that
occurs at the
Earth’s surface has
geomorphic
consequences

5. 5
Relevance of geomorphology
• Geomorphology is important because people live on
landforms and their lives are affected (sometimes
catastrophically) by geomorphic processes:
• Slope determines whether soil accumulates and makes arable land
• Slope stability controls landslides
• Mountains drastically affect the weather: rainshadows, monsoons
• This is also a two-way process: Human action is one of
the major processes of geomorphic evolution:
• People have been building terraced hillsides for thousands of years
• People dam rivers, drain groundwater, engineer coastlines
• People plant or burn vegetation on a huge scale
• People are paving the world
• People are changing the climate

6. 6
Geomorphic Concepts
• Important: a mountain is a feature of relief, not elevation (a high area of
low relief is a plateau)
– Slope controls the local stability of hillsides and sediment
transport
– Relief controls the regional erosion rate and sediment yield
– Elevation directly affects erosion and weathering only through
temperature, however, high elevation and high relief are
generally pretty well-correlated (with glaring exceptions, like
Tibet and the Altiplano)
• Elevation: height above sea level
• Slope: spatial gradients in
elevation
• Relief: the contrast between
minimum and maximum
elevation in a region
How high is this mountain?

7. 7
Geomorphic Concepts
• Uplift/subsidence
– vertical motions of the crust (i.e., of material points)
• Accumulation/denudation
– vertical change in the position of the land surface with respect
to material points in the bedrock.
• Important: the net rate of change in elevation of the
land surface is the sum of uplift/subsidence rate and
accumulation/denudation rate.
Uplift
Denudation ∆ελεϖατιον =
Υπλιφτ + ∆ενυδατιον
Ελεϖατιον

8. 8
Geomorphic Concepts
• Isostasy
– The result of Archimedes’ principle of buoyancy acting on
the height of the land surface in the limit of long timescale
(fluid-like mantle below the depth of compensation) and long
lengthscale (longer than the flexural wavelength of the
lithosphere).
– The total mass per unit area above some depth of
compensation (in the asthenosphere) should be globally
constant.
– Areas that satisfy the principle of isostasy are called
isostatically compensated.

9. 9
Geomorphic Concepts
• Variation in topography can be compensated through two end-
member mechanisms: differences in the thickness of layers or
differences in the density of layers.
– Isostatic compensation through density differences is Pratt
isostasy (in the pure form each layer is of constant thickness).
– Isostatic compensation through differences in the thickness of
layers (where the layer densities are horizontally constant) is
Airy isostasy.
Air ~0 Air ~0

10. 10
Geomorphic Concepts
• In reality, both mechanisms operate together: neither the
thickness nor the density of the crust is constant.
• However, since the density contrast between crust and mantle is
larger than most internal density differences within either crust
or mantle, the dominant mechanism of isostatic compensation is
variations in crustal thickness, i.e. Airy isostasy.

11. 11
Geomorphic Concepts
• Items for speculation:
– Why is the top of the ocean crust lower than the top of the
continental crust?
– Why is Iceland above sea level?
– Are subduction zone trenches isostatically compensated?
– What controls how long it takes to achieve isostatic
compensation?
– What controls the lengthscale over which isostasy operates?
– What do gravity anomalies have to do with isostasy?
– What happens when you put an ice-sheet on a continent?
What happens when you take it off?

12. 12
Drainage networks and Catchment Areas
• By mapping local
maxima (divides) in
topography, natural
terrains can always be
divided, at all scales
(from meters to 1000
km), into catchment
areas, each exited by one
principal drainage, into
which surface runoff is
channeled
• This is not a necessary
property of any
surface…it is the result
of processes that act to
shape the landscape

13. 13
Geomorphic Concepts
• Fractal geometry
– the forces that shape landscapes are often scale-independent
and lead to hierarchical regularity across scale, often with
fractional scaling relations, hence fractals. The classic
examples:
• Length of a coastline: coastlines get longer when measured with
shorter rulers.
• Branching networks: drainage channels come in all sizes, and join
together to produce networks whose branching statistics are fractal.

14. 14
“Process” geomorphology
• Quantitative, physically based analysis of morphology
in terms of endogenic and exogenic energy sources
• Basics of process geomorphology
– 1) Assume balance between forms and process (equilibrium
and quasi-equilibrium)
– 2) Balance created and maintained by the interaction between
energy states (kinetic and potential); force and resistance.
– 3) Changes in force-resistance balance may push the
landscape and processes too far: thresholds of change exist:
fundamental change of process and thus form.
– 4) Processes are linked with multiple levels of feedback.
– 5) Geomorphic analysis occurs at multiple spatial and
temporal scales.

15. 15
Process
geomorphology
• An example of a
quantifiable
process: hillslope
evolution
• What controls
stability of a
slope? Lithology
and water, mostly

16. 16
Hillslope evolution:
qualitative approach
Some rocks are
resistant to erosion
(they form cliffs),
some are weak (they
form slopes).
Resistant and weak
are qualitative terms,
but useful for
describing landscape
evolution.

17. 17
Hillslope evolution: quantitative approach
• In transport limited situations,
where slope failure does not
occur, evolution of scarps
resembles solutions of the
diffusion equation
∂h
∂t
= D
∂ 2
h
∂x2
∂h
∂t
= C
∂h
∂x
• Physically, this claims that flux of material is proportional to slope
gradient, and slope gradient changes due to flux of material…a diffusive
process.
• Where the slope is concave down it is eroding. Where it is concave up it
is aggrading.
• If you know the “diffusivity of topography” for a region, you can date
fault scarps and terrace edges by the relaxation of their shape.
• However, once a slope reaches a steady profile, or where the limitation is
not transport but slope stability, hillslopes propagate without change in
shape, a wave equation:

18. 18
Hillslope evolution:
quantitative approach
• When does a soil-covered slope
fail and become a stream channel?
– A model for the thickness of soil
cover on every part of a landscape
can be developed by combining a
criterion for failure of a soil layer
with topography and hydrology.
– A Mohr-Coulomb failure criterion for
a plane at the soil-rock interface, στ =
C + (σn - σp)tanφ, can be written
– For given soil density and angle of
internal friction, this gives the degree
of saturation (height of water table)
needed to make the slope unstable.
Some slopes are stable even when
saturated, some slopes are unstable
even when dry.
h
z
=
ρs
ρw
1 −
tanθ
tanφ
⎛
⎝
⎜
⎞
⎠
⎟

19. 19
Hillslope evolution: quantitative approach
• Failure model
– The failure criterion is coupled to a
hydrologic model based on Darcy flow
through the soil,
– This predicts the water level in the soil
needed to drain rainfall q; T is the
transmissivity (integrated permeability)
of the soil, a is the area uphill that drains
through an element of width b, and sinθ
gives the hydraulic head.
– Coupling the above two equations
predicts where the slopes will fail in
each rainstorm. Knowing rain statistics,
it predicts the overall evolution of a
landscape, since failure removes soil and
makes an open channel.
– The resulting rule for a/b is scale
independent, and is an example of a
system that will evolve a fractal
branching network of channels.
h
z
=
q
T
a
bsinθ
QuickTime™ and a
Video decompressor
are needed to see this picture.

20. 20
Feedbacks in geomorphology
• Feedback 1: Erosion is coupled to elevation, a negative
feedback
– High elevation promotes rapid erosion through freeze-thaw processes (a
rapid physical weathering mechanism), sparse vegetation (above the
treeline, roots do not stabilize slopes), increased precipitation (orographic
rainfall).
– There is also a general, though not perfect, correlation between high
elevation and high slope and relief, which promotes physical weathering
and sediment transport.
– Clearly erosion is one of the direct sources of changes in elevation, as well.
– Hence in the absence of tectonic uplift/subsidence, higher terrain will be
lowered fastest, tending to eliminate high slopes and large relief
differences.

21. 21
Feedbacks in geomorphology
• The idea that, in the absence of tectonic disturbance, the negative
feedback between elevation and erosion tends to eliminate relief is
the basis of W. M. Davis’ theory of landscape evolution:

22. 22
Feedbacks in geomorphology
• Feedback 2: Elevation and erosion are coupled to climate
– Topography affects weather patterns: e.g., rain shadow. More
profoundly, the uplift of the Himalaya-Tibet system caused the
onset of monsoonal circulation in south Asia.
– Climate affects erosion as well. This is clear in the case of
glacial episodes: when it gets cold enough, ice can become a
very effective agent of erosion and sediment dispersal. On the
other hand, warm temperatures promote faster chemical
weathering. Higher rainfall always increases both chemical and
physical weathering and erosion.

23. 23
Feedbacks in geomorphology
• Feedback 3: Erosion is coupled to uplift, a positive
feedback
– Because of isostasy, removal of mass from the top of the crust causes it to
rise. Loading of mass on top of the crust causes it to sink. Since isostasy
operates over some finite regional size (flexural wavelength ~100 km), it is
the average mass of crust on that scale that determines uplift. Hence
eroding of valleys can cause the intervening mountains to rise.

24. 24
Feedbacks in geomorphology
• Feedback 3
– There is evidence that this type of valley-incision denudation-
uplift is raising the high Himalaya:

25. 25
Global Synthesis of Erosion
• An example of a process geomorphology idea at the largest scale is
an attempt at the parameterization of global erosion rates
• Given area of a river catchment (km2
) and total sediment load of the river
(Mg/yr), mean sediment yield (Mg/km2
/yr) can be determined for the whole
drainage. Given density of sediment this is equivalent to mean vertical erosion
rate (knowing Mg/km3
, we get km/yr) for the whole drainage

26. 26
Global Synthesis of Erosion
• If we have some idea what the relevant variables are, we can
develop an empirical correlation from which the whole map of the
earth can be filled in from measurements of the major rivers and a
few tributaries.
• One such map is based on the correlation
where E is sediment yield (Mg/km2
/yr), p is rainfall of the rainiest
month (mm), P is mean annual rainfall (mm), H is mean elevation
of the catchment, and α is mean slope.
• This equation shows feedbacks 1 and 2
– E = f(H,α); Elevation -> Erosion -> Change in elevation
– E = f(p,P); Climate -> Erosion
• It also shows some additional relations:
– Episodic heavy rains have a larger effect the same total rain when steady
– Slope and elevation reinforce each other (E depends on their product)
logE = 2.65log(p
2
/ P) + 0.46 logH tanα −1.56

27. 27
Global Synthesis of Erosion
• Since we know slope, elevation, and rainfall statistics everywhere, and can work
our way up river drainages computing average sediment yield, the correlation of
the measured rivers is turned into a global map of sediment yield/erosion rate.
– What are the major features of the resulting map?

28. 28
Geomorphology and Tectonics
• For young tectonic activity, elevation and relief are
direct expressions of tectonic activity.
• For old stable terrains, elevation and relief become
expressions of relative rates of erosion.
– Thus, in California, anticlines are hills or mountains, but in
Pennsylvania, anticlines may just as well be valleys if the
older strata exposed in anticlinal cores are easily eroded.
• Ancient tectonic features must be recognized by the
relations of the rocks around them. Current tectonic
activity can be monitored by seismology and geodesy.
Everything in between depends on geomorphology.
– Geomorphic expression is by far the easiest way to locate
faults at the surface, and far more precise (at the surface) than
seismology.

29. 29
Geomorphology and Tectonics
• When the form of an original geomorphic feature is known, then
the magnitude of tectonic deformation can be determined by
measuring its current shape. Examples:
– fault scarps start from nothing, so height of scarp gives magnitude of total
dip-slip displacement.
– undisturbed drainages presumably go straight across faults; lateral offset
gives total strike-slip displacement.
– marine terraces start at sea-level, so height of wave-cut platform gives
total uplift since abandonment of terrace.
– river terraces start with longitudinal profile of riverbed; disturbances in
shape and slope give total deformation and tilt.
• When, furthermore, the age of the geomorphic feature is also
known, then the rate of tectonic deformation is determined as
well.
– How do you date geomorphology? This is a different problem from dating
rocks!

30. 30
Geomorphology and Tectonics
• Topographic profiles of uplifted
marine terraces at Santa Cruz, CA,
give two kinds of information:
• Total vertical uplift from height of wave-
cut platforms initially at sea level
• Relative deformation along shore from
shape of initial horizontal markers
• What additional type of data would be
useful here?

31. 31
Geomorphology and Tectonics
• Deformation of Ventura River terraces across syncline:
– A surprising result, since transverse ranges are in compression and full of thrust
faults, but you can’t have anticlines without synclines in between! So here there
is net uplift of terraces, but synclinal downwarping in the middle.
– No information on rates…this study was done in 1925 and terraces were not
datable by any technique known then.
– A more up-to-date example: terraces on Kali Gandaki river valley through
Himalayan front. These terraces can now be dated (but note the lowest one…).

32. 32
Measuring Geomorphic Rates
• We have several ways of measuring the rates of landscape
evolution.
– Dating of geomorphic surfaces: Much effort has been directed
towards measuring the age of erosional surfaces (peneplains,
terraces, etc.). using the exposure age of materials on that
surface.
• Thermoluminescence or electron spin resonance
• 14
C dating of organic matter in the soil
• Cosmogenic nuclides: 10
Be, 26
Al, 36
Cl
– Example: clocking development of normal fault scarp in limestone:

33. 33
Measuring Geomorphic Rates

34. 34
Geomorphic Rates
• Measuring “uplift” rates:
– Instantaneous uplift can be measured directly by GPS or
geodetic surveying methods in some cases.
– Uplift over longer timescale is measured by
thermochronology: rocks cool as they move towards the
surface down a geothermal gradient. Various methods are
sensitive to the time since the rock cooled through specific
temperatures:
• Fission tracks anneal above ~240 °C. Knowing U and Th content,
counting of fission tracks gives a time since 240 °C. Knowing the
geothermal gradient converts this into a time since depth of ~6 km.
• He diffuses out of minerals quickly down to a closure temperature of
~75 °C. Knowing U and Th contents, Farley and co-workers have
developed the ability to clock the time since apatite crystals passed
through ~2 km depth.
• Does thermochronology actually measure uplift rates (with respect to
sea level) or erosion rates (motion of material points with respect to
the land surface)?