GEOL 315 Surface & Near-Surface Processes Notes

Flux

q = {Q \over A}

$q$ = flux per unit area $[{\text{L} \over \text{T}}]$
$Q$ = volumetric flux $[{\text{L}^3 \over \text{T}}]$
$A$ = area $[\text{L}^2]$

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:

Differs for different soils.
Differs depending on “antecedent conditions” (how wet it was beforehand).

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

$f_p$ = infiltration capacity
$f_o$ = initial inf. cap.
$f_e$ = equilibrium inf. cap.

Example Infiltration Graph

The Hazen Method

Collect all the data.
Sort it; rank it (1 = highest).
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

Residual moisture content / Residual saturation
Air entry pressure / Capillary fringe

Example Retention Curve

Densities

Quartz: $2650~\text{kg}/\text{m}^3$
Water: $1000~\text{kg}/\text{m}^3$

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 $_3$ O $_8$

Plagioclase:
Na: NaAlSi $_3$ O $_8$
Ca: CaAl $_2$ Si $_2$ O $_8$

Quartz

SiO

_2

Limestone

CaCO

_3

Micas

Muscovite: KAl

3

Si $_3$ O(OH)

2

Biotite: K(Mg,Fe) $_3$ (AlSi $_3$ O)(OH)

_2

Clays

Kaolinite: Al

_2

_2

_5

(OH)

_4

Hematite (Rust)

_2

_3

Ion Solubility/Mobility

From most soluble/mobile to least:

Ca $^{2+}$ , Na $^+$ , Mg $^{2+}$ (depends on mineral)
K $^+$
Fe $^{2+}$
Si $^{4+}$
Ti $^{4+}$
Fe $^{3+}$
Al $^{3+}$

Chemical Weathering

Dissolution

Calcite: CaCO $_3$ + H $_2$ O $\to$ Ca $^{2+}$ + HCO $_3^-$ + OH $^-$
Quartz: SiO $_2$ + 2H $_2$ O $\to$ H $_4$ SiO $_4$

Hydrolysis

K-spar to Kaolinite: 2KAlSi $_3$ O $_8$ + 9H $_2$ O + 2 $H^+$ $\to$ Al $_2$ Si $_2$ O $_5$ (OH) $_4$
$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$ + 2K $^+$ + 4H $_4$ SiO $_4$

Redox

Hematite (Rust): 4Fe $^{2+}$ + 8OH $^-$ + O $_2$ $\to$ 2Fe $_2$ O $_3$ + 2H $_2$ O

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

Interrill
- Raindrop splash
- Overland flow
Rill
- Concentrated flow (steeper than interrill)
Gully erosion
- Big channels
- Carry water during & immediately after rainfall.
- Usually moves less sediment than rill or interrill erosion.
Stream channel erosion
- Scour, bank failure

Strahler Stream Classification

If the node is a leaf (has no children), its Strahler number is one.
If the node has one child with Strahler number $i$ , and all other children have Strahler numbers less than $i$ , the the Strahler number of the node is $i$ again.
If the node has two children with Strahler number $i$ , and no children with greater number, then the Strahler number of the node is $i + 1$ .

Stream Recovery Timescales

Ordered from most sensitive to disturbance to least.

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

Pressure and Hydraulic Head

p_A = \rho g d_A

$p_A$ = hydrostatic pressure at point $A$ $[{\text{F} \over \text{L}^2}]$
$\rho$ = density of medium ( $\rho_w = 1000~\text{kg}/\text{m}^3$ ) $[{\text{M} \over \text{L}^3}]$
$g$ = acceleration due to gravity ( $g = 9.81~\text{m}/\text{s}^2$ ) $[{\text{L} \over \text{T}^2}]$
$d_A$ = depth at point $A$ $[\text{L}]$

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

$h_A$ = hydraulic head at point $A$ $[\text{L}]$
$z_A$ = elevation (relative to some datum = 0) at point $A$ $[\text{L}]$

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

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

$h_p$ = pressure head $[\text{L}]$
$h_z$ = elevation head $[\text{L}]$

Specific Yield

S_y = {V_\delta \over V_s}

$S_y$ = specific yield
$V_\delta$ = vol. water drained by gravity
$V_s$ = vol. sediment

Darcy’s Law

Q = K A {\Delta h \over L}

$Q$ = flux through a sediment $[{\text{L}^3 \over \text{T}}]$
$K$ = hydraulic conductivity of the sediment $[{\text{L} \over \text{T}}]$
$\Delta h$ = difference in head $[\text{L}]$
$L$ = length of sediment $[\text{L}]$

K = {\rho g k \over \mu}

$k$ = hydraulic permeability $[\text{L}^2]$
$\mu$ = viscosity $[{\text{M} \over \text{L} \text{T}}]$

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

Bedding
Grain orientation
Fractures
Layered systems

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)

$S_s$ = specific storage
$\alpha$ = compressibility of the aquifer
$\beta$ = compressibility of water

Fracking

Pros

Encouraging switch from coal to natural gas
- Reduced CO $_2$ emissions
Domestic energy supply
Jobs

Cons

Balancing water resources
Methane leaks
- Flammable water
- Greenhouse gas (negates other advantages?)
Induced seismicity

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 ( ${V_\text{res} \over Q}$ )