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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.

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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.

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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.

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Geomorphology in the rock cycle

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

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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

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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?

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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 Δelevation =Uplift + Δenudation

Elevation

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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.

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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

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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.

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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?

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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

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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.

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“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.

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Process geomorphology

• An example of a quantifiable process: hillslope evolution

• What controls stability of a slope? Lithology and water, mostly

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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.

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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∂ 2h∂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:

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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, t = C + (n - p)tanf, 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.

hz

= ρsρw

1−tanθtanφ

⎛ ⎝ ⎜

⎞ ⎠ ⎟

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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 sin 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.

hz

= qT

absinθ

QuickTime™ and aVideo decompressor

are needed to see this picture.

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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.

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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:

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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.

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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.

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Feedbacks in geomorphology• Feedback 3

– There is evidence that this type of valley-incision denudation-uplift is raising the high Himalaya:

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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

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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 a is mean slope.

• This equation shows feedbacks 1 and 2– E = f(H,a); 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(p2 / P)+0.46logH tanα −1.56

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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?

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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.

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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!

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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?

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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…).

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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• 14C dating of organic matter in the soil• Cosmogenic nuclides: 10Be, 26Al, 36Cl

– Example: clocking development of normal fault scarp in limestone:

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Measuring Geomorphic Rates

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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)?