Quantitative Skills > Community > Workshop 2002 > July 25th Afternoon Presentation Notes

Group Presentations

Quantitative Problems with GPS

Connect Field and Lab

M. Jordan, B. Kerbert, V. Schielack


Earth Process Dynamics

3 topics:

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

Predicting Catastrophic Events

Dobler, Hutchings, Ormand

Geological contexts:

Mathematical Contexts:

Erosion and Deposition Rates

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

Math Skills:

Groundwater Containment Modeling

Chris Gellasch, Janet Andersen, Albert Hsui

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

The math:

Directional derivatives
Scales (rep. fraction)
2D and 3D Functions


Optimization (lots)

True Dip vs. Apparent Dip

Diagram on photocopy