GEOG319 Flashcards
What drives system change in process geomorphology?
Precipitation, temperature, and climate. With enough consistency, this creates environmental factors that drive system change (eg, low temps = high snow = glacial erosion).
What are the 3 types of Equilibrium?
Static
Steady-State
Dynamic
Static Equilibrium
Remain unchanged over time due to perfectly balanced forces, typically maintained by consistent environmental conditions. Time independent (days/months)
Steady-state Equilibrium
Inputs and outputs, long-term, = 0
Offers potential to model long-term responses to changes in input parameters.
Dynamic Equilibrium
Undergo continuous change, but the rates of change are relatively constant, resulting in overall stability or balance over time. Cyclic (millions of yrs)
Recovery Time
Time to return to natural state from perturbation
Reoccurrence Interval
Determines if steady-state is maintained
True or False, landform adjustment to perturbance is magnitude dependent.
True. The size of perturbation = the magnitude of the event. Thus, is magnitude dependent.
Driving Forces
Endogenic (inside Earth)
- Internal heat from radiation, drives tectonics.
Exogenic (from atmosphere, sun)
- Climate, solar radiation, gravity
Resisting Forces
- Lithology
- Friction, viscosity
- Trees, rock pins
- Friction, viscosity
Complexities
- Thresholds
Climate, rock weakness, system returns to new condition/equilibrium state if pushed too far.- Complex response
Response in other parts of the system, which are linked (like the butterfly effect).
Process linkage, can get multiple landforms from one perturbation.
- Complex response
What Can Be Conserved?
Heat, Momentum, Mass
Conservation of Heat (Thermal Diffusion) - 3 Types
Plutons, Ground Water, Atmosphere
Conservation of Heat (Thermal Diffusion) - Plutons
Heat increase through radioactive decay, heat loss to country-rock and crystallisation.
Conservation of Heat (Thermal Diffusion) - Groundwater
Heat gain from geothermal sources, heat loss to cooler rock, water, atmosphere.
Conservation of Heat (Thermal Diffusion) - Atmosphere
Heat gain from Earth and Sun, heat loss to space.
Conservation of Momentum (5)
Wind, Rivers, Ice, Mass Wasting, Flow (rate depends on viscosity).
Conservation of Mass (Elevation)
Change in elevation = uplift - denudation: dz/dt = U - E
U = thermal, tectonic, isostatic buoyancy
E = tectonic, chemical, physical
Basic Conservation Equation Structure
dx/dt = in - out
Geomorphic Transport Functions
Describe the physics of each part of the conservation statement.
Eg: How does ice flow, heat diffuse, rock turn to soil? –> into equation
Geomorphic Transport Function Example: Rivers
E ~ KA^(m)S^(n)
Erosion ~ K x A (upstream area)m x gradientn
Steady-state and GTF
inputs and outputs are equal, because our average value doesn’t change through time. This means dz/dt = 0, and we can make uplift assumptions.
Soil Conservation Equation
dH/dt = SPR - D
Moving Mobile Regolith
Change in thickness = gains - losses.
More soil into one part of slope, soil thickens through time and dR/dt is +
Less soil into one part of slope, soil thins through time and dR/dt is -
Conservation of Water
dh/dt = (R - I) - dQx/dx
Assume steady state and integrate: Qx = (R - I)x
There are gains (Rain, R) and losses (infiltration I) and water discharge on slope (Qx)
Hydrolysis
Addition of hydrogen proton (H+, cation), where that then combines with water and the mineral. The result is the mineral begins to be stripped of big cations (like potassium which is good for plant nutrients), breaking down the rock.
Cation Exchange
Substitution between ions in the mineral and ions in solution. Depletions of base cations in exchange for hydrogen protons (H+) leads to oxides. Cation: positively charged ion
Example of Hydrolysis/Cation Exchange
Plag –> kaolinite (clay)
alteration of silicates to clays
Oxidation
Electron exchange with oxygen, where electrons are negatively charged and losing one makes a mineral more + (occurs everywhere, including below surface!)
Example of Oxidation
Olivine –> Hematite. Iron, magnesium, and sulphide minerals!
Dissolution
Dissolvement of minerals (only happens when minerals are soluble, like calcite).
Example of Dissolution
Halite –> Na and Cl ions
Primary Mineral Stability
Same order as Bowen’s reaction series, where the order of crystallisation represents which forms first. Things like Olivine and Pyroxene weather faster at Earth’s surface as the conditions are low pressure, low temp - meaning, as they don’t form in those conditions, they’re less stable.
So, if you had a parent material rich in quartz = quartz to remain and increase in concentration while other minerals weather and precipitate away.
Dissolution Rates
Fastest for high-temp forming minerals, slowest for low-temp forming minerals.
They are measured on a log scale to represent the major difference in lifetime for such a small mineral.
-13.39 is a much smaller rate than -8.00, so you would expect quartz to have high dissolution rate.
Leeching (Dissolution Rate Controls)
If you are pulling minerals out, but the surface is not being eroded, you are leeching the minerals exposed at the surface - but making it extremely hard to oxidise as all the minerals are trapped in the centre.
pH (Dissolution Rate Controls)
Higher in acidic pH, moderate in alkaline, poor in neutral pH.
Acid has H+, and oxide has OH-, both of which stick to mineral surface and accelerate weathering. Neutral pH lacks both
Fixation/Retardation (Dissolution Rate Controls)
Can oxidise iron, which gets trapped and precipitate back out as platy minerals - slowing down further reactions.
Chelation (Dissolution Rate Controls)
Related to parent material and solution. Where large, organic compounds tend to envelop metal cations - being carried out of the system.
End Products of Dissolution
Solid: new, stable mineral (clay) or old, resistant mineral (quartz).
Dissolved: cations and anions. Can be contained in pore spaces, creating rough minerals.
Mobility
Ability of ions to move, usually through water.
With increasing charge, the element becomes more tightly bound and ions will become smaller.
Comparing ionic radius to charge, increased charge with small radius = high attraction, high mobility (can’t fit in crystal structures). Decreased charge and high radius = low attraction, low mobility (can’t fit in crystal structure).
Ionic Radius/Ionic Charge Ratios
z/r = 2: low charge, big. Stay in dissolved solution.
z/r = 4, z/r 6: special zone, too big to fit into structures, too charged to stick around in dissolved water. Highly immobile, staying in crust as solids.
z/r = 16: high charge, small radius. Instantly form compounds which stick around as dissolved species (…nates). High mobility because form compounds.
Mobile vs Immobile Elements
Calcium, magnesium, sodium, potassium, Iron2+= mobile
Silicon, Iron3+, aluminum = immobile.
Cation Types
Hard Cation = remove electron, complete outer shell (sodium, potassium, calcium), stable, tend to be highly soluble (nitrates, sulphides, etc).
Anions = chuck one electron on, full outer shell.
Intermediate Cation = sometimes take or give, end up with incomplete or complete shell depending on element they interact with.
What are weathering rated dependent on?
Kinetics and Thermodynamics
Kinetics vs Thermodynamics
Kinetics: dissolution rates of the phases (minerals - quartz slow, plag fast), temperature
Thermodynamics: chemical saturation state of the solution. Stable water = easily saturated, slow. Flowing water = not saturated, fast.
Chemical Saturation
Systems further from saturation react faster. Reaches equilibrium if the system is closed. Water flow will affect saturation (stable = slow, flow = fast).
Role of Time in Weathering
Rates change as weathering progresses.
Example: glacial retreat can cause high initial weathering rates, but rates decay rapidly (eg, due to leeching, chemical saturation).
Water and Weathering
Longer residence time = more intimal dissolution, but slower rates as steady-state and saturation is reached.
Soil Water Drainage
Slower groundwater seepage velocities result in more overall weathering.
- More time to dissolve rock - May be slower dissolution rate, but total mass is dissolved longer in the end.
How Does Silicate Weathering Affect Climate?
Carbon dioxide and water and feldspar –> Carbonic Acid (soluble) –> moves to oceans –> meets up with calcium and precipitates out as limestone.
So, the carbon dioxide in atmosphere correlates to major climate changes over geological time. Silicate weathering is a CO2 sink over geologic timescales.
Climate
Broadly controls the balance between chemical and physical weathering processes.
Dry, Cold: physical.
Hot, Wet: chemical. Keeps us away from saturation.
No weathering in wet and cold environments, does not exist.
Arrhenius Exponential Curve
Weathering rates are temperature and precipitation dependent.
Curve can predict silica weathering rates for the surface of an environment depending on temperature and precipitation
Weathering and Erosion
Weathering rates generally scale with erosion rates.
More fresh minerals = more weathering (supply limitation).
Tectonics also control weathering rates. Slow uplift = slow movement of material into weathering zone. So, if you uplift, more material in = more chemical weathering.
Why Do Active Tectonic Landscapes Erode Faster?
Minerals moving through this process slowly, from rock, spend a long time in system weathering. Minerals moving fast spend a much shorter time.
Little erosion = old surface rock = low chemical erosion, but more time
Increased erosion (tectonic) = fresh rock = more minerals for weathering, but less time
At a certain point, chemical weathering can only happen so fast. Thus, any increase in the rate of minerals movement decreases chemical weathering - creating a bell-curve.
Supply Limitation Chemical Weathering
Thick soils, few primary minerals
CDF same everywhere
Mafic
Non-tectonic
Kinetic Control Chemical Weathering
Thin soils (or none), residual primary minerals
CDF should be low, spatially variable, changes with depth.
Felsic, rocky.
Tectonic
The Effects of Vegetation on Weathering
Plants enhance weathering by:
- Producing organic acids
- Disrupting weathered material (tree-throw)
- Stabilize soils, increasing residence time (roots have high tensile strength)
Plants need elements in soil, break down rock to use them = faster weathering rates.
True of False, chemical weathering occurs faster in non-tectonic regions.
True, chemical weathering occurs faster in non-tectonic regions.
Active tectonics = less residence time = faster, but less chemical weathering
Limits on Weathering: Fast vs Slow
At fast erosion rates, weathering is limited by chemical processes, residence time of water in contact with minerals surfaces (kinetic limitation).
At slow erosion rates, weathering is supply-limited (not enough fresh material supply).
Supply-Limited vs Kinetic-Limited
Supply-limited areas: if the erosion rate is increased, total weathering will also increase (as the mineral still has enough time to break down). No primary minerals.
Kinetic-limited areas: if the erosion rate increases, total weathering will decrease (as the mineral does not have enough time). Primary minerals, rich felsic.
Regolith
all altered rock.
Weathered Rock
all rock, excluding soil
Saprolite
Highly weathered rock, chemically altered but maintains structures (joints, bedding, foliation).
Mobile regolith
broken down saprolite, soil.
True or False, everything before saprolite is non-isometric
False, everything before saprolite is isovolumetric (no change in volume)
What if you see all components of a soil profile?
that system has been operating for a long time (supply-limited).
What if components of the soil are missing?
System is operating for short time/interrupted, kinetically-limited.
3 Ways of Measuring Weathering
Mineralogy
Elemental Ratios
Volumetric Strain
Measuring Weathering: Mineralogy
Primary minerals disappear with weathering, secondary appear
Hard, uses thin sections.
Measuring Weathering: Elemental Ratios (CIA, CDF, τ)
CIA: Chemical Index of Alteration. Measure of stable species (eg, Al) to more mobile species (calcium, sodium, and potassium). Values above ~0.5 indicate weathered rock
CDF: Chemical Depletion Fraction. Measure of the concentration of immobile
element in weathered material to parent material. Values near 0
are little weathered.
τ: Mass Transfer Function. Measure of mass loss or gain. It is the ratios of concentrations of the mobile element of interest in the weathered material and parent rock to the same ratio for an immobile element.
Positive values indicate mass gain, negative values indicate mass loss (-1 indicates complete removal).
CIA
Chemical Index of Alteration. is a measure of ~stable species (eg, Al) to more mobile species (calcium, sodium, and potassium). Values above ~0.5 indicate weathered rock
(1 would indicate that everything except Al had weathered away).
Al2O3 / Al2O3 + CaO + Na2O + K2O
CDF
Chemical Depletion Fraction. It is measure of the concentration (C) of an immobile element (i) in the weathered material (w) to the parent material (p). Values near 0 are little weathered and larger values indicate more weathering.
1 - Ci,p/Ci,w
τ
The mass transfer function (τ) for an element (j) is a measure of mass loss or gain. It is the ratios of the concentrations (C) of the mobile element of interest (j) in the weathered material (w) and parent rock (p) to the same ratio for an immobile element (i). Positive values indicate mass gain, negative values indicate mass loss (-1 indicates complete removal).
= (Cj,w/Cj,p) / (Ci,w/Ci,p) - 1
Volumetric Strain (ε)
Measure of volume change in the soil. It is the ratios of density (ρ) and concentrations (C) of an immobile element (i, here it will be Zr) in the parent material (p) and the weathered material (w). Positive values indicate volume expansion, negative values indicate collapse
= PpCi,p/PwCi,w - 1
CIA and CIW are good for…
large-scale sedimentary measurements - not for specific weathering measurements for one rock.
True or False, Chemicals cannot volumetrically expand until reaches soil depth
True, because as saprolite is just highly weathered rock with structure.
Volumetric Strain (ε) Values
ε = 0, isovolumetric
ε > 0, expansion
ε < 0, collapse
Mass Transfer τ Values
τ = 0, no mobilization –> element of interest follows relationship of immobile element.
τ = -1, complete removal –> element of interest has been completely removed from weathered material
τ > 0, mass gain –> element of interest has been introduced to weathered material.
CDF Values
CDF = 0, no weathering
CDF = 1, complete weathering (lost all material).
CDF decreases with elevation (as temp decreases, and chemical weathering rates slow).
Physical vs Chemical Weathering
Physical Weathering: physical damage to rock –> reduction in grain size
Chemical Weathering: changes in chemical composition of rock –> reduction in grain size, mass loss, new minerals.
Physical Weathering: Reduction in Grain Size Methods
Geomorphic fracturing.
- Thermal expansion and contraction
- Frost cracking
- Plants
Grain Size Effects
Breaking rocks into smaller particles (phys weathering) accelerates chemical weathering. Gives higher surface area exposure = increased availability to weathering.
What Is Structure From Motion?
Turning photos into 3D models of something.
Objects look different from different angles, with each view is associated with a different angle. Finding the same point in multiple images, you can reconstruct the 3D location of the point from multiple images by back-calculating the position of cameras.
Georeferencing
combination of ground control points and camera GPS, so real world imagery can be utilised.
No georeferencing
surface model has shape. Mimics landscape well, but it won’t have a correct location in the world (no scale, no location).
Weak georeferencing
Ground control is not well spaced, irregular, or GPS is inaccurate. Leads to surface model having loads of different orientations, with high errors.
Strong georeferencing
Ground control (GPS) used to precision points in photographs. Low error.
Structure From Motion: Limits To Precision
- Photographic
- GCPs (Ground Control Points)
You can keep increasing your ground control precision, but at some point there is a limit to the resulting precision - caused by photographic limits.
Micro SfM
Fancy triangle with bolts, measures depth to rock from triangle over long time = erosion through time. Only gives a small area though.
Creating micro surface images, models were created to give small-scale change detection (mm).
Landslide Classification
by debris, velocity, and main movement type (falls, slide, flow).
Landslide Components
Zone of depletion (source) - crown v Zone of accumulation (deposit) - toe
Soil Mechanics - Material Properties
1) Water content
2) Degree of saturation
3) Void ratio
4) Porosity
Modelling: Options
Two pathways: Analytical (gives you one answer, definitive) vs Numerical (gives many answers)
Modelling: How To Decide?
CHILE or DIANE?
Continuous
Homogenous
Isotropic
Linear
Elastic
DIANE
Discontinuous
Nonhomogeneous
Anisotropic
Not linear elastics.
If your landform fits CHILE< you use continuous modelling. If DIANE, discontinum.
True or False, mountains swell in summer and shrink in winter?
True. Snow melt = filling the mountains = expanding and swelling in summer.
Micro seismicity in the Southern Alps Peaks in Winter
Timeseries of earthquakes shows that during winter, when mountains are found to be small and skinny, earthquakes increase.
Imagine you have a bunch of balls in a ball pit - when they expand, they squish together and fill space, no room for movement. When they get smaller, stress between decreases and they can move around = earthquake.
Coastal Landslide Conditions
Relative humidity more during early hours, as temperature cools and atmospheric water condensing (fog). Temperature and dew point becomes close. This condensation generates more failures.
Preconditioning of slope + triggering of slope = failure.
Preconditioning is usually most important (available moisture and cracking rates, then you are preconditioning a slope to fail as moisture increases and infiltrates those cracks).
Axial strain
how much rock deforms in comparison to original state, where you’d expect sample to compress and get smaller.
3 S’s of Brittle Material Science
- Stiffness
- Strength
- Speed of cracking
Why Do Alpine Rock Slides Happen in Warm Temps?
Permaforest degradation = ice in cracks, holding ice together, then melts, avalanches occurs.
True or False, dry rock is weaker?
False. Wet intact rock is approximately 13% softer, and 30% weaker than when dry.
Stream Power
The amount of energy river has to erode, move sediment.
Omega = pgQS
Conservation of Water
Change in water depth = total gains - total losses.
There are gains (rain, R) and losses (infiltration, I) and water discharge on the hillside, Qx
dh/dt = (R - I) - dQx/dx
Specific Stream Power
How stream power, the amount of energy river has to erode, is applied across a stream - includes width.
W = pgQS/w
Amount of Energy Available to Erode Depends On…
- Slope (potential energy, velocity of flow)
- Discharge (inputs (drainage area, precip) outputs (infiltration, use by biota, evaporation).
Channel Incision
Basal shear stress (exerted by water on channel bed)
Tb = pgQS
Knowing this, we can insert Basal Shear Stress into stream power equations: Omega = TbU, W = TbU/w
Specific Stream Power and Basal Shear Stress (Large W, Small W)
If W is big, and the channel is wide, basal shear stress decreases and the stream power decreases.
If W is small, and the channel is thin, basal shear stress increases and the stream power (omega) increases.
When Do Channels Start?
When the basal shear stress (Tb) exceeds the critical shear stress (Tc).
Tb = force exerted on the bed by water
Tc = force needed to move sediment.
Two Main River Types
Alluvial (water flowing over sediment they’ve deposited), Bedrock (water flowing over rock).
Most rivers begin as bedrock, moving towards alluvial at the mouth.
Erosion of Bedrock
Abrasion
Plucking (Quarrying)
- Hydraulic Wedging
Dissolution
Cavitation
Bedrock vs Alluvial River: Increasing Velocity/Discharge
Water over bedrock will begin to incise. Meanwhile, alluvial will pick more sediment up and deposit it later.
Abrasion
Sediment acts as tools to abrade the bed.
Number of collisions is proportional to sediment concentration. Mass removed is proportional to momentum of impacting particle and erodibility of rock. Large sediment will give larger abrasion.
Low sediment, slow river = little abrasion.
High sediment, high river = high abrasion.
Limits of Abrasion
Rivers can be overwhelmed with sediment, where increased sediment load shields the bedrock and limits abrasion.
Quarrying
Erosion occurs if Tb > Tc (basal shear > critical shear). Rate is depend on excess shear stress. This leads to blocks of rock being moved away, so fractured/platy bedrock required.
Where fractures don’t already exist, hydraulic wedging sees a pressure applied on the rock - which flexes at the sides and opens up a crack. Grains then fill the crack, widening it and holding it open.
Quarrying and Hydraulic Wedging
Where fractures don’t already exist, hydraulic wedging sees a pressure applied on the rock - which flexes at the sides and opens up a crack. Grains then fill the crack, widening it and holding it open.
Pot-holes and Plucking
Particles must decouple from the flow, similar to glacial mechanism.
Either large particles or eddy currents.
Dissolution (River)
Rate of dissolution (erosion) is proportional to:
- Discharge
- Wetted perimeter
- Solute concentration (low concentration = more reactive = more dissolution)
Controlled by chemical saturation, where high saturation will see dissolution occur very slowly/not at all (both kinetics and thermodynamics).
Cavitation
Implosion of vapour bubbles against a surface, causing shock damage.
Requires high velocity and low flow depth
- Not as common in rivers, more common under ice
- Likely an additional process for fluting and potholes (around flow obstructions)
Seen in dams, turbines, ships, etc where velocity is mechanically increased.
Bedrock Channel Shape: E =
Erosion is proportional to upstream area and slope, and coefficient k (density, erodibility).
E = k1A^mS^n
Knowing this equation to solve for Slope, and include concavity, can be used to determine long-term evolution (knick-points, steady-state).
Bedrock Channel are Sensitive Recorders of
Lithology, Climate, Tectonics.
Through changes in:
- Base (knick-points, valley fills)
- Channel steepness/concavity (steady-state response)
How Does Sediment Move?
Suspensed Load: Suspension (grain doesn’t make contact with bed, cloudy water), Saltation (grain bounces on and off bed)
Bedload: Rolling/sliding (grain is almost always in contact with bed)
Detachment: Sediment
- Lift (upwards)
- Drag (horizontal)
Dependent on flow competence: maximum size of material that can be transported
True or False, Velocity starts at zero at the river bed, increasing upwards towards surface.
True, Velocity starts at zero at the river bed, increasing upwards towards surface.
Lift
Function of fluid density, grain diameter, and velocity difference. As fluid becomes more dense, the force becomes bigger.
Grain size bigger, more lift (more to act upon)
Fluid density higher, more lift force.
Drag
More effective force because the coefficient is 10x bigger. This means, in any flow, drag forces are the dominant process acting on sediment.
Function of radius lever.
Torque Required to Move vs Torque Generated by Flow
Torque Required to Move (Tg): lever arm*weight of grain
Torque Generated by Flow (Td): lever arm*drag force
- Transport when Td > Tg
Grain Entrainment
Basal shear stress = critical shear stress. Suggest a linear dependence on grain diameter (assuming perfect sphere).
p(f)gHS = 0g(pp - pf)D
Below 0.1mm, the critical shear stress increases due to:
- Electrostatic forces (clay particles tend to stick together)
Grain hiding (small grains tend not to see the turbulent eddies)
What Happens to the ‘Linear’ Relationship Between Grain Size and Critical Shear Stress
Below 0.1mm, the critical shear stress increases due to:
- Electrostatic forces (clay particles tend to stick together)
Grain hiding (small grains tend not to see the turbulent eddies)
Grain Hiding
If river comprised of cobbles, sands, and clays, river is efficient at washing out smaller grains to leave behind cobbles. Under these cobbles is sand, which could be moved, but is armouring the sand.
More critical shear stress needed to move all grains.
Channel Armouring
Cobbles tend to imbricate, pile up, and point upstream of the river as the flow pushes them over. Water then flows over those cobbles and are very hard to move again - trapping any sediment underneath.
More critical shear stress needed to move all grains.
Equal Mobility Hypothesis
None of these grains move until the bigger grains move, and when they do, everything else moves at equal mobility.
Rivers: Turbulent and Laminar Flow
Top Layer = Turbulent Flow
However, as you move closer to the channel bed, velocity decreases and a boundary is crossed between turbulent layer and laminar sublayer.
If you have small grains (0.01mm), grain diameter is smaller than the laminar sublayer and the turbulent flow cannot reach those small grains. However, as those grains build up (D > delta), they are accessible and the critical shear stress begins to work again.
How Does Sediment Move?
Ballistic
Grain has initial velocity when entering flow. This means, as all objects with initial velocity, it will move in a ballistic trajectory (parabola curve).
Depending on the angle of launch, the parabola will rise (high angle) or low (low angle). Will move in the direction of flow, which means they’ll travel even further than the initial velocity angle.
Ballistic Movement and Grain Diameter
Travel time and distance are greatly increased proportional to grain diameter (lighter particles travel further, as they tend to stay aloft longer).
Sediment Concentration
Largest near bed. Change in concentration with height is proportional to the ratio of the settling velocity/initial velocity
Rouse Number (p)
Determines the transport path of a particle.
Wash load: p ~ 0, settling velocity < shear velocity (or launch velocity)
Suspended load: p < 2.5, settling velocity ~ shear velocity
Bedload (rolling/saltation): p > 2.5, settling velocity > shear velocity
Diffusion
Any gradient driven process that moves material (passive process). Includes heat, concentration, topography (creep), etc.
True or False, Most earth materials have thermal diffusivity values (K) of 1.
True, Most earth materials have thermal diffusivity values (K) of 1.
Estimating Diffusive Systems
Length and time are related in diffusive systems
Sigma = square root of kt
Sigma is the length scale (depth to which the temperature change is still significant).
Thermal Shocks
Chipping, pitting, fracturing of rock due to extreme heat like wildfires. Using sigma = sq root of kt, we can estimate sigma - and the length scale to which temperature change is significant.
Spallation depth increases next to vegetation because it captures heat.
Disintegration vs Spallation
Disintegration: Inter-granular differences in thermal expansion
Spalling: Thermal shock/unloading
Diffusion in Natural Systems
Many surface processes are periodic (daily tides, daily temperature, Milankovitch). Diffusive depth scales for periodic disturbances:
Z = sq root (KP/pi)
Frost Cracking: Result of Thermal Diffusion
Summer warm, diffuses down into permafrost, melting at depth.
Sustained movement of cold, leading to:
- Ice growth
- Influx of water
- Sub-freezing temperatures (capillary action leads water to flow, reaches surface, immediately freezes, move water enters = big ice wedges at surface)
Thermal Diffusion: Frost Cracking Window
Occurs from 3 - 8*C. Effect cm to meters depth, due to thermal diffusion. Surface will have great temperature difference, hence why no frost cracking occurs here (too hot in summer, too cold in winter)
Hillslope Diffusion
Uniform lowering rate.
Uniform regolith production rate.
Uniform mobile regolith thickness.
Requires that flux increases downslope.
Gradient driven process that increases downslope, creating diffusive hillslope shape.
Mobile Regolith
Change in thickness = gains - losses.
Gains come from: weathering producing soil, soil from uphill
Losses come from: movement downhill
Diffusive Hillslopes at Steady-State
Will have constant weathering rates; leading to steepening slopes.
Parabolic
Diffusive Processes
Requires that the processes are gradient-driven. Includes:
- Rain splash
Mobilised sediment, raindrop comes down and hits surface and energy dislodges sediment - travels further downslope (ballistic - larger distance, more initial force). More rain, heavier rain, bigger raindrop = more movement as they displace more mass
- Tree-throw tree with roots on slope, tree can fall any direction - falls upslope sees root mass above hole where roots were, fall downslope root mass moves downward - Creep - Freeze-thaw - Bioturbation Soil thrown downhill when burrowing
Advection
Transport in a flow (active process), moves mass (eg, landslides, debris flows).
Change in quantity (A) through time= velocity * change in A through space.
dA/dt = -vdA/dx
Advection/Diffusion of Solutes
Advection: movement of chemical mass with flowing water.
Diffusion: movement from higher concentration to low concentration.
GW that is not moving at all, pumped with salt, will see high concentration –> moves towards low concentration through DIFFUSION. This leads to a longitudinal change in the salt. Advection however, is responsible for the overall transport of chemical mass in flowing water.
Advection Flow in Rivers
Laminar
- Controlled by molecular viscosity
Turbulent
Controlled by eddy viscosity
Reynold’s Number
(Re) = UH/v (velocity x depth/kinematic viscosity).
Distinguishes between laminar and turbulent.
Re < 500 = 500 laminar
Re > 2000 = 2000 turbulent.
Fr Number
U/square root of gH
(velocity/square root of gravity x depth)
Fr < 1 = tranquil
Fr = critical (plane bed)
Fr > 1 = rapid
True or False, response times are NOT proportional to rates of processes
False. Response times are proportional to rates of processes (soils at 1mm every year, more able to adapt to erosion rates than soils produced at 0.5mm per year).
Feedbacks in Large-Scale Geomorphic Systems (What Affects U and E)
- Elevation (higher physical weathering as elevation increses (cracking, freeze-thaw)
- Precipitation (high precip = high chemical weathering)
- Erosion (glacial decreases = isostatic adjustment)
Steady State in Fluvial Systems
Erosion is a function of slope (S) and discharge (Q). At steady state, erosion is = uplift.
This means uplift is a function of slope x rainfall x area.
Increased uplift –> channel profile steepens
Increased rainfall –> decreased channel profile
Steady State in Cosmogenic Nuclide Exposure Dating
Atoms formed on earth, creating new particles that can be dated through radioactive decay.
Change in nuclides through time = how many are produced - how many decay away.
Through time, depending on different decay rates (different nuclides), the time to reach steady-state changes.
- 14C reaches steady state quick
- 3He is stable, never reaching steady state
Faster rate (of production and decay) = faster response time.
Steady State: Cosmogenic Nuclide and Erosion Removal
Where nuclides are removed through erosion, and nuclide concentration is solved for steady-state, we find
Faster erosion = quicker steady state (response).
What Controls Approach to Steady State?
Geomorphic Transport Function (describes the physics of the process).
- Some will be dependent on perturbations themselves, some independent.
Types of Perturbation
Periodicity (step functions)
- Input bounds (minimum and maximum values)
- Eg, climate, glacial cycles
Events (single perturbations)
- Average values with large events, instant changes (systems return to normal straight after)
Eg, weather, earthquakes
Perturbations: Response Time and Reoccurrence Interval
If response time > reoccurrence interval = change in state
If response time < reoccurrence interval = returns to steady-state
Transience in Fluvial Systems
You change precipitation rate and system responds. Evidence for this:
- Knickpoints
- Steep slopes
- High or low curvatures (0.5 average, more concave = precip, less concave = uplift)
Terraces/gorges
Soil, GTF, and Steady State
dh/dt = SPR - D (SPR = soil production rate - denudation).
SPR - D = 0, then SPR = D
Soil thickness dependent on magnitude of perturbation (big landslide = massive change in soil thickness). Soil response time is independent of magnitude.
SPR = SPRmax x erosion of alpha rate
Hillslope Response Depends on Presence of Soil v Bedrock
If slopes are bedrock = erosion related to rock properties
If slopes are soil = erosion related to slope, soil properties
- Diffusion directly related to slope
- Hillslope failure related to slope, soil cohesion
Low rock strength, high rock uplift: erosion independent of slope or lithology (bedrock), erosion rate varies with slope and soil properties (soil).
High rock strength, low rock uplift: erosion rate varies with slope and rock strength (bedrock), erosion rate varies with slope and soil properties (soil).
Landscape Evolution Model
TTLEM: Start with continuity of mass, applying sensible ‘Geomorphic Transport Functions’ and step through time.
For hillslopes, diffusivity, For rivers, stream power.
TTLEM Changeable Variables
- Initial surface
- Uplift pattern (accounts for tectonics and different uplift rates)
- Uplift rate (spatially, temporally)
- Time steps (usually long-term)
- River incision
- Diffusivity
Sc (critical slope - steepest angle slope can get to before it fails)
TTLEM Changeable Variables: What about when we can’t change directly?
With increasing atmospheric temperatures, warmer air holds more water, so we might want to model increased precipitation rates. But, we don’t have precip to add –> make rivers better at eroding (K bigger)
- Larger, flatter rivers with overall lower elevation environment (hills don’t need to be as steep)
With loss of vegetation –> diffusivity constant increase, or change Ac (critical area gets smaller)
Model results in more hillslopes which are short, less river
