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Useless Arithmetic?. Rory O’Kane Philip Jones. Mathematical Models. Mathematical Fishing How Fast the Rising Sea Following a Wayward Rule Giant Cups of Poison . Mathematical Fishing. Random Cod Facts. Cod is used in fish and chips It is the fish in McDonald’s fish sandwiches

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useless arithmetic

Useless Arithmetic?

Rory O’Kane

Philip Jones

mathematical models
Mathematical Models
  • Mathematical Fishing
  • How Fast the Rising Sea
  • Following a Wayward Rule
  • Giant Cups of Poison
random cod facts
Random Cod Facts
  • Cod is used in fish and chips
  • It is the fish in McDonald’s fish sandwiches
  • Cod eats almost anything
  • They spawn between March and June and release between 2 million and 11 million eggs.



In 1968 810,000 tons of cod were caught from the Grand Banks.

In 1992 the fishing industry collapsed.

Over a decade later the fish population has still yet to increase

This is probably due to dispensation which is a lowering of reproduction rates that occurs when a density of a fish population is no longer sustainable

fishing models
Fishing Models
  • Mathematic models that were used over the years in regard to the cod in the Great Banks predicted that the Grand Banks would still be full of fish.
  • Models such as:
    • Total Allowable Catch
    • Maximum Sustainable Yield
total allowable catch
Total Allowable Catch
  • Only 16% of the cod population were allowed to be caught each year.
  • This value came from models and according to these models the size of the cod population would gradually increase
  • The government trusted these models so much that they built up the fishing industry for the upcoming cod bonanza.
  • Subsidies and tax raises were used to build larger vessels and to rescue floundering seafood companies.
total allowable catch1
Total Allowable Catch
  • Almost every country did the same type of thing including the United States.
  • The TAC did not work.
  • Instead of increasing the population of cod decreased tremendously in the Grand Banks.
  • So the Maximum Sustainable Yield was implemented.
maximum sustainable yield
Maximum Sustainable Yield
  • The MSY is a very simple model
  • The MSY is based on the assumptions that any species in a sea will produce a surplus that can be caught and if you take that amount and no more then there will never be threat of extinction.
  • It does not take into account a couple of very important factors.
problems with msy
Problems with MSY
  • MYS may reduce genetic variabilityin cod populations
    • Cod have 12 notable subpopulations
    • These subpopulations migrate to different shallow areas during the summer
    • If the MSY is followed then the subpopulations that reproduce slowest will have a hard time making it.
problems with msy1
Problems with MSY
  • MSY does not take into account the ecosystem
    • For example:
      • Herring eat cod eggs and mackerel eat herring
      • If the population of mackerel decrease then naturally the population of herring is going to increase and the population of cod is going to suffer.
  • If models are used to predict limits that might not prevent the depletion of cod population should limits be placed on fishing cod at all?
  • Do models such as the MYS provide more of a problem, with the false hope that it brings, rather than a solution?
how fast the rising sea1
How Fast The Rising Sea
  • Since the beginning of time, Earth’s sea levels have been in a constant state of change.
  • Some mechanisms are known and understood, but still there are unknowns
2 types of sea level change isostatic and eustatic
2 Types of Sea-Level change: Isostatic and Eustatic

Isostacy – changes in sea level that result from the moving up and down of the earth’s surface

  • Time Scale: The largest long-term sea level changes are on a 100 million year scale as a result of changes in volume of oceans basins
  • Ex: rise and fall of mid-ocean ridges, upheaval or sinking of tectonic plates
isostatic sea level change
Isostatic Sea-Level Change

When volume of sea basins decrease, sea level rises

When volume of sea basin increases, sea level falls

isostatic sea level change1
Isostatic Sea-Level Change
  • Glaciers weigh land down, also causing sea-levels to rise
eustatic sea level changes
Eustatic Sea-Level Changes

Eustacy – sea-level changes that happen as a result of variations in water volume (i.e Glaciers melting)

Time Frame: 100,000 years to lifetime of a person

other causes of sea level rise
Other Causes of Sea-Level Rise
  • Steric Effect – as temperature rises, water molecules expand
  • Not as important as scientist initially thought

Expected rise from steric effect around Greenland and Antartica

other causes of sea level rise1
Other Causes of Sea-Level Rise
  • Earthquakes and Volcanoes
    • Good Friday Earthquake (1964) sea-level along western Alaska rose 2-3 feet in an instant

Less Dramatic Sea-Level Changes

    • Tides cause sea to rise/fall daily
    • Extraction of Oil cause land to sink
    • Storms such as Hurricanes for short time-period
reasons for concern
Reasons for concern
  • Since humans line the coasts, what would have been a non-issue is now potentially life-threatening
    • Ironic in sense that humans are partly responsible for rise in sea-level
    • Humans already have been impacted; 980 inhabitants of Carteret Atoll moved to higher land in 2005 and 11,000 people of 9 Pacific atolls are in the process of moving to New Zealand

Should top greenhouse emitters be forced to either admit or compensate environmental refuges?

modeling sea level rise
Modeling Sea-Level Rise

2 Approaches to Modeling: Bottom-Up and Top-Down Modeling

Bottom-Up Modeling

  • Usually employed by Global Change Modelers
  • Start with smallest elements (melting Glacier, Cloud, etc.) and integrate other processes
  • Involves long and complicated computer code; super-computers required


  • Bread loaf problem – any errors in assumption are magnified over time
  • Natural Science more complex and unpredictable than classical physics
  • Sin of Commission – Too many variable to handle

Top-Down Modeling

  • Starts with largest element (Greenland Ice Cap, Atlantic Ocean, etc.) hoping to bypass minutiae
  • Physics less important than known behavior
  • Relies on field observation and focuses on connections between processes


  • Numerous uncertainties not addressed; “sin of omission”
ipcc report
IPCC Report
  • Refreshing in objectivity and discussion of errors, uncertainties and missing data
  • Admit that accurate modeling “requires a more critical and quantitative assessment of model uncertainties than is possible at present.”
  • However, downplays complexity and uses error bars to come out with “real predictions”
  • “Assumption upon assumption, uncertainty upon certainty, and simplification upon simplification are combined to give an ultimate and inevitably shaky answer…”
uses of sea level modeling
Uses of Sea-Level Modeling
  • Modeling will never be perfect, but it is possible to predict direction and general magnitude of sea level change
  • Authors propose turn to data-rich qualitative models; find more general answers
    • Ex: Models (quantitative) point to trends while field data relied on too convince politicians that sea level is rising
state of fear
State of Fear
  • Authors agree with Crichton’s negative view of quantitative mathematical modeling
  • Disagrees with Crichton’s skepticism about sea-level rise, based partly on his view that politicized science is bad science

“Politicization is inevitable for a theory that gores so many oxen of the high and mighty. Politicization, however doesn’t necessarily invalidate the science… but it does complicate things.”

following a wayward rule1
Following a Wayward Rule
  • Sea shores experience erosion
  • Erosion causes numerous problems for many people who live on the coast.
  • People with buildings anywhere near the shore line have to worry about the possibility of erosion completely overtaking their homes and businesses.
ramada inn
Ramada Inn
  • One example of this is the Ramada Inn on the coast of the Outer Banks of North Carolina
  • Because of erosion it soon exchanged hands and became the Armada Inn
  • Then it became a Comfort Inn just without the restaurant
  • Now it is a small hotel, merely a fraction of what it once was.

+ erosion =

cape hatteras
Cape Hatteras
  • Cape Hatteras, a lighthouse on the Outer Banks of North Carolina, stands 208 feet tall
  • Because of beach erosion the lighthouse has had to be moved over a quarter of the way inland from its original position.
  • Ironically the lighthouse was originally served to warn sailors about the “graveyard of the Atlantic” and today is acting as a warning to us of the problems of sea erosion.
other problems
Other Problems
  • These cases are not rare but happen all over the world.
bruun rule
Bruun Rule
  • Per Bruun was a Danish American engineer
  • Considered the father of coastal engineering
  • Recognized the strong relation between sea level rise and shore erosion.
  • Created the Brunn rule
some factors of shore erosion
Some Factors of Shore Erosion
  • Primary Factors
    • Sea Level Rise
    • Regional Tectonic Movement (Earthquakes)
some factors of shore erosion1
Some Factors of Shore Erosion
  • Secondary Factors
    • Present-day Erosion Rate
    • Slope of the Mainland
    • Relative Importance of Inundation Versus Erosion
    • Coastal Type
    • Shoreface Slope Previous Sea-level Rise History
    • Upland Geology
    • Upland Morphology
    • Lagoon Size
    • Grain Size and Type
    • Wave Climate
    • Tide Character
    • Width of Continental Shelf
    • Storm Types and Frequency
    • Shoreline Vegetation
    • Sediment Supply
    • Etc…
problems with bruun rule
Problems with Bruun Rule
  • The Bruun Rule only takes into account the rising sea level, the cross shore distance, the depth at the base of the shoreface, and the berm height (the upper beach and dune height ).
  • Despite the fact that this is one of the primary causes for sea erosion it is one of many.
  • However many people in many different countries all around the world still use the model today.
  • Some people claim the model is sufficient enough and has been proven to work. People like P.S Rosen and M.L. Schwartz.
other problems with bruun rule
Other Problems with Bruun Rule
  • The Bruun Rule assumes:
    • There is an offshore depth beyond which amounts of sediment from shallower water will not pass.
      • It has been well established that large storms can carry sand way past this point.
    • Sand movement on the shore face is only caused by waves. Bottom currents are unimportant.
      • The stirring up of the sediment by the undercurrent allows the waves to carry large amounts of sand way past this point.
    • Thick layers of sand without rocks, mud, or other complications is assumed to underlie shore faces.
      • Recent studies have shown that there are rock and mud layers that greatly effect the shape of the shore face.
bruun rule continued
Bruun Rule Continued
  • The Bruun Rule is still used today in:
    • Argentina
    • Australia
    • Barbados Brazil
    • Canada
    • East Asia
    • Eastern Caribbean
    • Egypt
    • Estonia
    • Holland
    • Venezuela
    • Indonesia
    • Japan
    • Lebanon
    • Malaysia
    • New Zealand
    • South Africa
    • United Kingdom
    • United States
    • Uruguay
    • And many other countries
  • Is the Bruun Rule too simple? If it is should a more complicated model be constructed?
milltown dam
Milltown Dam

Behind the dam, spread out in the reservoir, are more than 6 million cubic yards of heavily contaminated soil, at some spots nearly 30 feet deep.

berkeley pit the richest hill on earth
Berkeley Pit: “The Richest Hill on Earth”
  • The largest producer of copper in the world at beginning of 20th century
  • Pit opened in 1955, looking for low grade ore
  • Kept dry by continuous extraction of ground water
  • Pumps shut off in 1982; filling at rate of 5 million gallons a day

1984 2005

the problem
The Problem
  • Common minerals left in mine; pyrite (fools Gold) and chalcopyrite, when mixed with oxygen and water, form sulfuric acid
  • Acid flows through rock and extracts: copper, lead, arsenic, etc.
  • P.H level of 2.6 in pit, 30+ Billion Gallons of Contaminated water over 900 feet deep
    • Once water reaches 1,147 feet, reaches groundwater and will effect towns drinking water
    • Clean-up effort focused currently on preventing the passage of this threshold
more problems
More Problems
  • Hazardous for migrating birds
    • 1995 342 Snow Geese Killed from landing on pit

If water escapes to nearby streams, acid could end up in the Pacific Ocean

    • Berkeley Pit not an isolated instance; mines in AZ and NM will have larger and potentially deadlier lakes
why nothing s being done
Why nothing’s being done
  • Problem is that other mines operate on private land; government takes more relaxed approach
  • Geologist Glenn Miller proposes land to be viewed in 100-200 year context, all public land
    • Should not leave problem for Great-Grand Children for immediate gain
    • Proposes banning open pit mines because underground mining is less damaging

Should companies be allowed to practice Open Pit Mining? Private Land? Also, who is responsible for paying for the clean-up?

what s being done and solutions
What’s being done and solutions?
  • Berkeley Pit declared Superfund site in 1980’s; Fed designate area as one of nations major hazardous waste sites
  • 2003: Lime-Hydroxide plant opened; takes out toxic metals and levels acidity at rate of 50,000 gallons per minute
    • Technology still in question, 500-1000 tons of sludge per day
    • Viewed by environmentalist as “band-aid” approach
what s being done and solutions1
What’s being done and solutions?
  • Possibly good science (i.e. models) and strong enforcement could help prevent future man-made disasters
  • Nevada requires companies to participate in a reclamation bond pool; companies deposit large bonds to repair future pollution problems
    • Issue that companies declare bankruptcy or simply don’t pay
  • One solution (already enacted in Montana) is to ban open-pit mines
    • Potential contamination of Ground-water
    • Run-off and rain still issue for surrounding community
    • Even “clean” mines such as marble mines, still breeding ground for mosquitoes and disease (such as malaria in Africa)
pit lake mathematical modeling
Pit Lake Mathematical Modeling

McDonald Gold Prospect (est. 10,000,000 ounces of Gold)

  • In order to obtain permit, modeling used to predict environmental impact
  • Typical of Pit Lake modeling, accuracy of numbers at each stage dependent upon accuracy of previous stage; chaos theory
  • For example, first step assume time for lake to fill depends upon flow model designed for conceptual model; designed for qualitative guidance but used by consultants for specific prediction
pit lake mathematical modeling1
Pit Lake Mathematical Modeling
  • Model misuse went unchallenged by U.S Geological Survey,
  • “Admit to uncertainties and complexities, yet in the end ignore them and recommend the modeling approach. It is as though admission of fatal flaws somehow erases them.”
  • The political side to modeling is another problem
    • Bureau of Land Management (BLM) tends to have rosy, optimistic predictions; after making predictions don’t revisit predictions once mining has commenced (Tends to be wrong)
    • Consultants that run models, in order to stay in business, come up with answers clients expect and want; “Thou shalt not rock the boat”
    • “political vulnerability of model predictions to distortions, as the truth is molded according to a client’s needs”
final thoughts
Final Thoughts
  • Government should no longer use predictive models
  • After permits granted, close inspection and enforcement of mining regulations is necessary