Initial Publication Date: October 28, 2005

Group Presentations

Quantitative Problems with GPS

Connect Field and Lab

M. Jordan, B. Kerbert, V. Schielack

Mapping:

  • Calculations of length, scale, area resolution—geometry
  • Surveying: trig problems = surveying
  • Average characteristics of area/volume, spatial statistics

Earth Process Dynamics

  • modeling plate movements
  • erosion and other geomorph
  • hydrologic and biogeochemical processes

3 topics:

  • vectors
  • rates
  • dynamic system modeling

Geodesy: size and shape of earth


Total Volume of Water from a Storm

Math Approach

Flood height: H = f(t) - a function of time

Discharge: D = g(H) - a function of flood height
So, D = g(f(t)), is also a function of time.

The volume of water discharged over time
First of two images of integral equations from discussion notes
or
Second of two images of integral equations from discussion notes
Can be approximated using Riemann sum:

V=S g(f(t))

See photocopied graphs

Geoscience Approach

[nothing written in the notes]


Find the Circumference of the Earth Using a Shadow Stick

Ratio to determine the sun's angle at two different locations (Eratosthenes)
Diagram on photocopies


Estimating Hoizontal Wind from Dopplar Radar

[Note: handwritten copy makes it difficult to distinguish between v, u, u or other similar variables, so there are undoubtedly errors in the transcription.]

Cartesian system: x, y, z; v1, v
Spherical system: r, j, q, ur, uj

Derive a relation between ur and v1:

r2 = x2 + y2

Take D/Dt

2r (Dr/Dt) = 2x (Dx/Dt) + 2y (Dy/Dt) => divide by 2r

(Dr/Dt)= ur ; (Dx/Dt) = v ; (Dy/Dt) = u

ur = (x/r) u + (y/r)v

Approximate v and u as constant V and U
What are they?
Try to find V and U, then minimize equation error

Total error in a horizontal cross-section:

[Do we need long process of working out error equation—includes some lovely integrals, greek letters, derivatives and other such excitement]

Result: aU + bV = c where a, b and c are known constants determined by ur, x, y, r

Similarly, dJ / dV = 0 and dV + eV = f
2 linear algebra equations for V and U, solve them as:

U = answer

V = answer


g Periodic Phenomena—Harmonic analyses (too hard?)

e.g. tides, sea-levels change

Summation of sinusoids
[greek letter that looks like a four that isn't on character map] log-normal distribution and sediment grain-size analysis
|A|, w, f
simply: A sin (+)


Radiometric Decay

Geologic context: how we date rocks

Mathematical context: exponential function and logarithmic

Depending on how presented, could address all 5 of the "over-arching" quantitative skills


Crystallization/Melting

Crystallization/melting of solid solutions mineral (olivine) as single model for magma melting/crystasllization See graph on photocopy


Predicting Catastrophic Events

Dobler, Hutchings, Ormand

Geological contexts:

  • Earthquakes
  • Floods
  • Storms

Mathematical Contexts:

  • Modeling
  • Prediction
  • Error Analysis
  • Probability


Erosion and Deposition Rates

Geological Topic: Erosion and deposition rates
Examples: Grand Canyon (Colorado River), Lake Mead (Hoover Dam)

Math Skills:

  • Estimation of Volume
  • Rates and rates of change of rates, rates of change of volume
  • Modeling


Groundwater Containment Modeling

Chris Gellasch, Janet Andersen, Albert Hsui

  • Install monitoring wells
  • Sampling plan
  • Collect samples & well volumes (averaging)
  • Sample analyses (QA/QC)
  • Plot data on survey map
  • Sketch contours for water table and concentration of containment
  • Determine gradients 3C and 4h


Flow Problem (Heat or Water)

Cathy Summa, Linda Eroh, Moe Muldoon, Steve Leonhardi

Examples of geologic context:

  1. Groundwater flux to well, river, under dam
  2. Continental rifting, 3 sediment transport and mixing

Mathematical context: Differential equations


Geologic hyperspectral Remote Sensing

Deriving viv wind from a radar display (dr/dt)

Mean annual temps on a given j to get a mean G

Atmospheric stability correlates with [??]

Measuring pressure gradients across middle latitude and tropical cyclones

Effects of wind on structure (Bernoulli)



Large Group Work

Predicting how high people will bounce on a trampoline on different planets

Geoscience Approach

Find gravity on each planet
Mass of the person who jumps does not change
Weight divided by gravity
The higher the weight, the lower the jump
Math Approach
F= m * a


Tophographic Maps

  • Contour lines
  • Vertical exaggeration—profiles
  • Orientation

The math:

Slope
Rates
Gradient
Max/min
Directional derivatives
Scales (rep. fraction)
Interpretation
2D and 3D Functions

Applications/Projects:

Pipelines/canals/aquaducts
Orienteering
Optimization (lots)
Meterology
Petrology


True Dip vs. Apparent Dip

  • Visualization
  • Difficulties/obstacles
  • Trigonometry
  • Approximation
  • 2D and 3D
  • Error approximation

Diagram on photocopy