Models of Human-Environment Interaction 2015-04-08 · Extended study by Dennis Meadows (WORLD3):...
Transcript of Models of Human-Environment Interaction 2015-04-08 · Extended study by Dennis Meadows (WORLD3):...
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System dynamics
Jürgen ScheffranInstitute of Geography, KlimaCampus, Universität Hamburg
Models of Human-Environment InteractionLecture 2, April 8, 2015
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Basic types of dynamic mathematical models
x(t): System state at time t
Dx(t) = x(t+1)-x(t): System change at time t
Dx(t) = f(x,t): dynamic system
Dx(t) = f(x,u,t): dynamic system with control variable u
Dx(t) = f(x,u1,u2,t): dynamic game with control variables u1,u2
of two agents 1 and 2
Dx(t) = f(x,u1,…un,t): agent-based model and social network with control variables u1,…un of multiple agents 1,…,n
How to select control variables?
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System dynamics
System dynamics (Ford 2009):
• approach to understanding the behaviour of complex systems over time.
• deals with internal feedback loops and time delays that affect the behaviour of the entire system.
• use of feedback loops and stocks and flows.
• helps describe how seemingly simple systems display complex dynamics.
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Six shapes representing typical dynamic patterns
Source: Ford 2009
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Exponential growth
Exponential growth: one of the most common time paths by systems in the world.
Exponential growth occur rapid and explosive.
Example: Repeatedly folding a piece of paper in half, doubling its thickness with each fold.
How thick would it be after 43 more folds?
Approximately 450,000 km thick -- more than the distance from the Earth to the moon!
The big explosion in thickness occurs at the end of the plot.
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Exponential growth
Hannon/Ruth (1994) Dynamic Modeling
Population grows with fixed reproduction rate r(birth rate b, death rate d, net birth rate r).
DN = r N = (b-d) N
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Logistic growth
Birth rate declines towards upper limit KPopulation grows until it reaches carrying capacity K.
DN = r (K-N) N N(t) = N(0) exp(r t)
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Logistic growth
Strong growth for small population.
Growth dampened for growing population size.
Growth is strongest when population is half of ecological carrying capacity (limits to growth).
Source: Wissel, 1989
0
0
0
0
( )( 1)
r t
r t
K N eN tK N e
0
( ) ( )(1 / )
N t r N Nr N N K
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Population models show the growth and death of biological populations withcommon features as a function of different environmental factors.
Factors affecting the growth of a population:
• Size or density of population N• Age distribution• Resource availability R• Climate factors (temperature, precipitation, wind etc.) U• Geograpical condition (location of habitat)• Immigration rate I• Birth rate b
Decline of population:• Competitors/enemies• Emigration E• Death rate d
Population models
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Population models
DN: Population change
G: Relative growth of population (birth - death)
M: Relative increase of population by migration (immigration - emigration)
I: Growth or loss by interaction with other populations (predator - prey)
H: Relative growth or loss of population by humans (artificial regeneration - harvest)
DN = G + M + I + H
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World Dynamics
In 1970, Jay Forrester was invited by the Club of Rome to a meeting in Bern, Switzerland and asked if system dynamics could be used to address the predicament of mankind.
WORLD1/WORLD2, Book World Dynamics: interrelationships between world population, industrial production, pollution, resources, and food.
Extended study by Dennis Meadows (WORLD3): The Limits to Growth.
Model showed collapse of the world socioeconomic system sometime during the twenty-first century, if steps were not taken to lessen the demands on the earth's carrying capacity.
Model was used to identify policy changes capable of moving the global system to a fairly high-quality state that is sustainable far into the future.
Long term socioeconomic interactions cause, and limit, exponential growth of world population and industrial output.
Earth’s natural resources are finite and that the exponential growth in their use could ultimately lead to their depletion and hence, to the overshoot and collapse of the world socioeconomic system.
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Limits to Growth: World model for the Club of Rome
Commissioned by the Club of Rome
The Limits to Growth was compiled by a team of experts from the U.S. and other countries.
Using system dynamics theory and computer modeling
12 scenarios showed different patterns —and environmental outcomes— of world development from 1900 to 2100.
Scenarios showed how population growth and natural resource use interacted to impose limits to industrial growth.
There was still room to grow
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Basic population and capital feedbacks
Source: Meadows et al. 1972, The Limits to Growth
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Feedback loops of population, capital, agriculture and pollution
Source: Meadows et al. 1972, The Limits to Growth
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Exemplary data
Source: Meadows et al. 1972, The Limits to Growth
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The complex computer model
Source: Meadows et al. 1972, The Limits to Growth
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Standard world model run
Source: Meadows et al. 1972, The Limits to Growth
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World model with “unlimited” resources and pollution controls
Source: Meadows et al. 1972, The Limits to Growth
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World model: “unlimited” resources, pollution controls, increased agricultural productivity, “perfect” birth control
Source: Meadows et al. 1972, The Limits to Growth
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World model with stabilized population
Source: Meadows et al. 1972, The Limits to Growth
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Stabilized world model II
Source: Meadows et al. 1972, The Limits to Growth
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The Life Cycle Theory of M. King Hubbert
Life cycle theory of oil and gas discovery and production by petroleum geologist M. King Hubbert.
Hubbert took the physical structure of the fossil fuel system into account and assumed that the total amount of oil and gas in the United States (i.e., the amount of oil and gas "in place"), and the "ultimately recoverable" amount of oil and gas in the United States, is finite.
The cumulative production of domestic oil and gas must be less than or equal to the ultimately recoverable amount of oil and gas in the US.
System dynamics stock-flow structure represents Hubbert’s theory (without inflow to Ultimately Recoverable stock which is fixed); resource is produced and consumed at an exponential rate.
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Hubbert’s view of oil and gas discovery and production
Time series graph of oil or gas production must be "hump" shaped: area beneath production curve for oil or gas is the cumulative production of the resource, and the cumulative production of the resource must be finite.
Hubbert argued that the life cycle of oil and gas discovery and production yields a bell-shaped production curve:
1. Period of low resource price and exponential growth in production,
2. Peaking of production when effects of resource depletion cause discoveries of exploratory drilling to drop and resource price to rise
3. Long period of rising costs and declining production as the substitution to alternative resources proceeds.
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King Hubbert’s Life Cycle Theory of Oil and Gas Discovery and Production
Source: http://www.systemdynamics.org/DL-IntroSysDyn/start.htm
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Intellectual Lineage of System Dynamics Energy Modeling
Source: http://www.hubbertpeak.com/hubbert/systemdynamicsenergymodeling
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Global growth patterns of the human sphere
Source: Steffen et al. 2007
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Interactions between human and
environmental change
Source: Costanza et al. 2007
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An Integrated History and future of People on Earth (IHOPE)
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Different modeling approaches and disciplinary preferences
Source: Costanza et al. 2007
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IHOPE modeling framework
Source: Costanza et al. 2007