Modern GeomorphologyModern Geomorphology

Some interesting links

In this lecture we consider hypothesis and test

Some slides drawn by Dr. Tracy Furutani. Rather heavy modifications to some of her slides are the responsibility of Prof. Smart

Scientific MethodScientific Method

• Science has a hypothetico-deductive framework

• Scientific hypotheses have testable consequences

• We test hypotheses to try to falsify them

• Karl Popper

1934 Popper Logic of Scientific Discovery

http://www.eeng.dcu.ie/~tkpw/

Popper: Popper: HypothesesHypothesesIn Science areIn Science areFalsifiableFalsifiable

First a review:

Mein Kopf !

Basic ConceptsBasic Concepts• Catastrophism

– Flood, Earthquake, Eruption, Tsunamis, Meteors

• Uniformitarianism– Present is key to past, slower processes– Mountain building, Erosion, deposition, glaciers–James Hutton (1726-1797)

Modern SynthesisModern Synthesis

•The Plate Tectonics ParadigmThe Plate Tectonics Paradigm

Uniformitarian and slowUniformitarian and slow

• Sudden Catastrophes cause Mass Extinctions

•Both are correct

Braided Stream

GeomorphologyGeomorphology

Geomorphology is the sub-discipline of geology that describes the physical changes of the surface of the earth over time

Modern approaches to geomorphologyModern approaches to geomorphology

• We use mathematical models and computer simulations to study real-world settings

• Our ideas about the real world must have testable consequences.

• Test them with real-world measurements, models, and/or experiments.

•

Now, down to business:

1. The shape of a bay1. The shape of a bay

• Bays along an active margin coast with a strong longshore current have a characteristic shape.

• Given an erosion-resistant headland, this shape emerges every time.

Dr. Tracy Furutani constructed initial slides for the three examples that follow.

The log spiralThe log spiral

• The shape of a bay shore often conforms to the “log spiral” equation.

• In polar coordinates,

r = exp (-/4)

Physical reason - at first a Physical reason - at first a puzzlepuzzle

Initially, there seemed no obvious reason the log-spiral equation should fit the shape of a shoreline so well

Physical reasonPhysical reason

• Later, derivations of coastline shape that required wave energy to dissipate evenly on the shore had the

log - spiral curve as their solution.• Mystery solved, after we started with a simple assumption

We will consider this process later, when we study active coastlines

First PrinciplesFirst Principles

• This is very common in science. Wherever possible, we try to build mathematical models from assumptions we believe: The laws of thermodynamics, conservation of energy and momentum, are usually a good start.

• We must always check that the assumptions of the version we use are true.

2. The speed and depth of a flood2. The speed and depth of a flood• The Purcell Ice Lobe dammed the Clark's Fork

River about 15,000 years ago, forming Lake Missoula in Oregon and Washington.

• When it melted, floods inundated the Columbia Plateau and Basin. The process of lobe advance, damming, and melt back repeated about 40 times, for about 2000 years.

• The Channeled Scablands landform was the result.

• How deep was the last flood?

The Draining of Glacial Lake Missoula The Draining of Glacial Lake Missoula

Repeated many times, last time about 13000 ya

Dramatic evidence remainsDramatic evidence remains

West Bar, along the Columbia River near Quincy, exhibits “mega-ripples” -- ripples generated by the massive flood

From the From the height andheight and wavelength of the ripples, wavelength of the ripples,

the depth and speed of the flood can be estimated.

B is the wavelength between ripple crests

B

B = 360 feet

HH = 24 feet

You can't see it well here , but there are 40 sets of ripples.

Curve FittingCurve FittingFrom fluid dynamics, there areequations that relate the height (H) or wavelength (B) of a ripple tothe depth (D) of the flood that generated it:

H 0.923 D0.455

B 37.8 D0.348

These are curve fits from experiments; solve these for D, the depth

Let’s try itLet’s try it

• If D = 1200 ft, H = 0.923 x 1200 0.455

• Then H = .923 x 25.18 = 23.24 ft

• Also B = 37.8 x (1200) 0.348

• B = 37.8 x 11.79 = 445.7 ft

• We can try this for different values of depth D and make a table, or we can solve for D in both equations

H 0.923 D0.455

B 37.8 D0.348

From these equations:

If D = 1288 ft, H = 24 ft,

If D = 650 ft, B = 360 ft.

So the depth was somewhere in that range

Frgv 2.1

The speed of the flood (v) is related through the depth (D):

where Fr is the Froude number (varies from 0.5 and 0.9 for this situation) and g is the acceleration due to gravity

Froude numberFroude number

For rectangular cross-sections with uniform depth d, the Froude number can be simplified to:

There are multiple possibilities, so let’s examine a few cases

If Fr = 0.5 and D = 650 ft, v = 72 feet/sec

If Fr = 0.9 and D = 1288 ft, v = 87 feet/sec

Note the rectangular valley shape

ModelsModels

• Scale models are used to study Scale models are used to study complex fluid systems where other complex fluid systems where other approaches aren't usableapproaches aren't usable

http://vulcan.wr.usgs.gov/Projects/MassMovement/pictorial_summary_sept01.html

Buckingham π theoremBuckingham π theorem

• If we have process that is a function of n variables (force, work, volume, velocity, viscosity, density, etc. made of k  fundamental units (mass, length, time, temp, etc.) then the original expression is equivalent to an equation involving a set of p = n − k  dimensionless variables constructed from the original variables. We have already seen an example of a dimensionless number, the Froude number:

There are many commonly used dimensionless numbers. More on this later There are many commonly used dimensionless numbers. More on this later

For rectangular cross-sections with uniform depth d, the Froude Number can be simplified to

SimilitudeSimilitude

• Similitude is a concept used in the testing of models. Reality and the model must be:

• the same shape.

• fluid flow must have the same streamlines

• ratios of all forces acting on reality and model ratios of all forces acting on reality and model are the same.are the same.

Simulation of a meteor impact Tsunami with a partially submerged bursting balloon

3. Detrital hill slope failure3. Detrital hill slope failure

• Over time, the slope of a pile of rocks degrades

• The upper photo was taken in 1997.

• The lower photo is of the same slope in 2007

~55o

~30o and varieshttp://activetectonics.la.asu.edu/carrizo/application_full.html

We considered a huge rock on a slope. What if there are many smaller rocks?

SimilitudeSimilitude• Gravel hit by fine

mist from above models talus slope boulders hit by falling raindrops,

IF the appropriate dimensionless numbers are comparable

A full scale experiment A full scale experiment - - during a during a flood, coarse detrital ripples form over a point bar. flood, coarse detrital ripples form over a point bar. After the flood, waters recede and the ripples are After the flood, waters recede and the ripples are exposed to the weatherexposed to the weather • Identical

triangular ridges of wet fine gravel, hit by water drops from a hose nozzle, model the slumping of a gravel ripple exposed to the rain

Courtesy Dr. Traci Furutani

Hypothesis TestingHypothesis Testing

• We need a way of determining if the data from our experiment is predicted by our model, or is not different from sampling error.

• Discussion: a fair coin

• Null Hypothesis same # Heads & Tails

• Later we will learn two simple methods of Statistical Hypothesis Testing.http://www.kean.edu/~csmart/Geomorphology/Lectures/Hypothesis Testing.ppt