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GEOL 315 Surface & Near-Surface Processes Notes

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Flux

q = {Q \over A}

Humidity

Relative humidity

{\text{vapor pressure of water} \over \text{saturated vapor pressure}}

Absolute humidity

{\text{mass of water vapor} \over \text{volume of air}}

Specific humidity

{\text{mass of water vapor} \over \text{mass of air}}

Vapor Pressure

In air, each component exerts a partial pressure. \Sigma partial pressures = atm pressure. Vapor pressure is the partial pressure of water vapor.

Dew point

Temperature to which a parcel of air must be cooled to reach saturation.


Causes of Rain

Frontal

A warm and cold front collide, pushing the warm front up over the cold, cooling it, and thus causing water vapor to condense out.

Convective

The ground surface, heated by the sun, causes convection, pushing warm, moist air up, cooling it, and thus causing water vapor to condense out.

Orographic

As moist air is pushed up by a mountain range, it cools, causing water vapor to condense out. When the air makes it to the other side of the range, it has rained out a lot of its water, causing a dry “rain shadow” region on the other side of the range.


Infiltration

Soil has a finite but variable capacity to absorb water. Infiltration capacity:

Dry: high infiltration capactity (high tension (?)).

Example Infiltration Graph


The Hazen Method

  1. Collect all the data.

  2. Sort it; rank it (1 = highest).

  3. Calculate the probability.

    100 \times {2 n - 1 \over 2 y}

    y = # of samples
    n = rank


N-T events

New (correct) way to refer to floods or rainfall events: probability.

e.g. 1% chance rainfall event; 10% chance rainfall event

Old way:

“100-yr flood” \to 1% chance per year ({1 \over 100})
“500-yr rainfall event” \to 0.2% chance per year ({1 \over 500})

Retention Curves

Example Retention Curve

Densities



Water \to Streams

Baseflow

How much water flows in the stream when it’s not raining.

Interflow

Downslope flow occuring between the ground surface and water table.

Overland flow

Downslope flow occuring along the ground surface.

Direct precipitation

Precipitation directly into the stream.

How does water get to streams?


Hydrographs

Example Hydrograph


Mineral Formulas

Feldspar

 
Orthoclase:
K-spar: KAlSi_3O_8

Plagioclase:
Na: NaAlSi_3O_8
Ca: CaAl_2Si_2O_8

Quartz
SiO_2
Limestone
CaCO_3
Micas
 
Muscovite: KAl3Si_3O(OH)2
Biotite: K(Mg,Fe)_3(AlSi_3O
)(OH)_2
Clays
 
Kaolinite: Al_2Si_2O_5(OH)_4
Hematite (Rust)
Fe_2O_3

Ion Solubility/Mobility

From most soluble/mobile to least:

  1. Ca^{2+}, Na^+, Mg^{2+} (depends on mineral)
  2. K^+
  3. Fe^{2+}
  4. Si^{4+}
  5. Ti^{4+}
  6. Fe^{3+}
  7. Al^{3+}

Chemical Weathering

Dissolution

Calcite
CaCO_3 + H_2O \to Ca^{2+} + HCO_3^- + OH^-
Quartz
SiO_2 + 2H_2O \to H_4SiO_4

Hydrolysis

K-spar to Kaolinite
 
2KAlSi_3O_8 + 9H_2O + 2H^+ \to Al_2Si_2O_5(OH)_4
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + 2K^+ + 4H_4SiO_4

Redox

Hematite (Rust)
 
4Fe^{2+} + 8OH^- + O_2 \to 2Fe_2O_3 + 2H_2O

Mechanical Weathering

1. Ice wedging

Liquid water enters a small crack in rock, freezes and expands, expanding the crack, then thaws, flowing further into the expanded crack, allowing more water in. When this freezes, it expands the crack even more. This cycle repeats, continually expanding the crack.

2. Root wedging

Roots grow into a crack in rock. As the plant grows into the crack and utilizes the minerals in the rock, it expands the crack and erodes its walls.

3. Salt wedging

Salt water enters a crack in rock and evaporates, leaving behind salt crystals. When heated, the crystals expand, expanding the crack. The salt also helps chemically decompose the rock.

4. Abrasion

Weathering caused by friction between rocks during transport.

5. Unloading

The expansion of rock due to pressure release.

6. Thermal expansion

The expansion of rock due to heating.

7. Hydration & swelling

The expansion of rock due to intake of water (chemical hydration).


Soil Horizons

O: humus
loose, decaying organics
A: topsoil
minerals mixed with organics
E: zone of leaching
mostly quartz sand and silt
B: subsoil
zone of accumulation of clays and iron minerals
C: weathered bedrock
mostly partially weathered bedrock material

The O horizon forms as organics fall to the ground and begin to decay. As they begin to mix with the minerals in the soil, the A horizon is formed. The E horizon is formed by clays and iron minerals being carried down by water to the B horizon, leaving behind fine, light quartz deposits. The C horizon is the lowest layer before the bedrock, and is formed by partially weathered bedrock mixing with material from above.


Baseline Recession Curve

Q = Q_0 e^{-a t}

Erosion by Water


Strahler Stream Classification


Stream Recovery Timescales

Ordered from most sensitive to disturbance to least.

  1. Micro-Habitat (<0.10cm): 1-10yr
  2. Habitat (1-10m): 1-10yr
  3. Reach (10-100m): 10-100yr
  4. Floodplain (10^2-10^3m): 10^3-10^4yr
  5. Watershed (10^3-10^4m): 10^5-10^6yr


Pressure and Hydraulic Head

p_A = \rho g d_A
h_A = {p_A \over \rho g} + z_A

For hydrostatic body with free surface, h_A = d_A + z_A.

h_p = {p \over \rho g}, h_z = z

Specific Yield

S_y = {V_\delta \over V_s}

Darcy’s Law

Q = K A {\Delta h \over L}
K = {\rho g k \over \mu}

Defs (Aquifers, Confining, Wells)

Aquifer

A relatively permeable rock/sediment layer that is useful for water supply (e.g. sand, limestone).

Confining unit

A relatively low-permeability rock or sediment layer (e.g. shale, mud).

Unconfined aquifer

Connected to the water table.

Confined aquifer

Separated from the water table by at least one confining unit.

Potentiometric surface

Where the water table would be if unconfined.

Water table well

A well where the potentiometric surface is at the top of the aquifer.

Artesian well

A well where the potentiometric surface is above the top of the aquifer (due to it being confined).

Flowing well

A type of Artesian well where the potentiometric surface is above the ground surface.


Darcy Revisited

q = {Q \over A} = K {\Delta h \over L}
\mathbf{q} = \mathbf{K} \nabla h
q = K {dh \over dl}

Anisotropy

Isotropic media

Groundwater flows perpendicular to hydraulic head contours.

Anisotropic media

Groundwater flow may not be perp. to head contours.

Causes


Representative Elementary Volume

REV

The scale above which porosity begins to make sense/apply. (Porosity is a macroscopic property.) Usually 3-5cm (?).


Specific Storage

S_s = \rho g (\alpha + \phi \beta)

Fracking

Pros

Cons


Solute Transport

Advection

Groundwater carrying solutes along with it. If just advection, called “plug flow.”

Diffusion

Fick’s Law: q_c = -D_\text{molec} {dc \over dx}

  • D_\text{molec} = coefficient of molecular diffusion
  • {dc \over dx} = concentration gradient
Dispersion

Mechanical mixing

q_c = -D_\text{mech} {dc \over dx}

  • D_\text{mech} = coefficient of mechanical dispersion

D_\text{mech} = \alpha_L |v|

  • v = avg. lin. vel. of the fluid
  • \alpha_L = longitudinal dispersivity of the medium
  • \alpha_T = transverse dispersivity

Longitudinal: parallel to the direction of flow.

Transverse: perpendicular to the direction of flow.

Rule of thumb: \alpha_L \approx 10 \times \alpha_T

Causes of dispersion:

  • Differences in width of pores
  • Friction within pores
  • Path length


Appendix A: Symbols

\rho
= density
\mu
= viscosity
Q
= volumetric flux ({V \over t})
A
= area
\phi
= porosity ({V_\text{pores} \over V_\text{bulk}})
S
= saturation ({V_\text{water} \over V_\text{pores}})
\theta
= moisture content ({V_\text{water} \over V_\text{bulk}})
S_y
= specific yield ({V_\text{water that drains by gravity} \over V_\text{bulk}})
q
= flux per unit area (aka specific discharge) (\mathbf{q} = \mathbf{K} \nabla h)
\mathbf{v}
= avg. linear velocity ({q \over \phi})
K
= hydraulic conductivity ({\rho g k \over \mu})
k
= permeability
p
= pressure
h
= hydraulic head ({p \over \rho g} + z)
z
= elevation relative to datum
\nabla h
= hydraulic gradient ([{dh \over dx}, {dh \over dy}, {dh \over dz}])
t_r
= residence time ({V_\text{res} \over Q})

© Emberlynn McKinney