Resource Issues Impacting National Security IMSM Workshop, 2009

Aaron W. Brown Chad Griep Magathi Jayaram Karthik Raghuram Kirk Soodhalter Duy Vu Jelani Wiltshire

July 28, 2009

Problem Presenter: John Peach MIT Lincoln Laboratory Faculty Mentor: Mansoor Haider North Carolina State University Group 4 (IMSM)

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Outline 1

Introduction

2

Hubbert Linearization and Depletion of Resources

3

ARIMA Model for CO2 emissions

4

World3-03 Model Overview Our Modifications

5

Sensitivity Analysis of World3-03 Model Theory Conclusions in World3-03 Model

6

Optimization of HWI in World3-03 Model

7

Conclusions Group 4 (IMSM)

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Outline 1

Introduction

2

Hubbert Linearization and Depletion of Resources

3

ARIMA Model for CO2 emissions

4

World3-03 Model Overview Our Modifications

5

Sensitivity Analysis of World3-03 Model Theory Conclusions in World3-03 Model

6

Optimization of HWI in World3-03 Model

7

Conclusions Group 4 (IMSM)

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Introduction

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Introduction

Several critical natural resources are close to depletion

Group 4 (IMSM)

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Introduction

Several critical natural resources are close to depletion Has impacts on policy decisions of nations

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Introduction

Several critical natural resources are close to depletion Has impacts on policy decisions of nations Reducing oil production rates, with increasing population ⇒ increased pressure on other resources

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Introduction

Several critical natural resources are close to depletion Has impacts on policy decisions of nations Reducing oil production rates, with increasing population ⇒ increased pressure on other resources Major “escape plan” is to reduce dependence of fossil fuels

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Introduction

Several critical natural resources are close to depletion Has impacts on policy decisions of nations Reducing oil production rates, with increasing population ⇒ increased pressure on other resources Major “escape plan” is to reduce dependence of fossil fuels Has plausibility issues due to resource depletion, and environmental impact issues

Group 4 (IMSM)

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Introduction

Several critical natural resources are close to depletion Has impacts on policy decisions of nations Reducing oil production rates, with increasing population ⇒ increased pressure on other resources Major “escape plan” is to reduce dependence of fossil fuels Has plausibility issues due to resource depletion, and environmental impact issues Need to relook at the situation with a global perspective, and answer some important questions about resource issues impacting national securities!

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Outline 1

Introduction

2

Hubbert Linearization and Depletion of Resources

3

ARIMA Model for CO2 emissions

4

World3-03 Model Overview Our Modifications

5

Sensitivity Analysis of World3-03 Model Theory Conclusions in World3-03 Model

6

Optimization of HWI in World3-03 Model

7

Conclusions Group 4 (IMSM)

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Overview of Hubbert Linearization

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Overview of Hubbert Linearization Hubbert Linearization is often used to determine the amount of a resource available, based on historical production data.

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Overview of Hubbert Linearization Hubbert Linearization is often used to determine the amount of a resource available, based on historical production data. Let Q(t) be the cumulative production of a resource. We assume Q grows logistically so that ! Q dQ = KQ 1 − P(t) = . dt F where F is the total amount of the resource available.

Group 4 (IMSM)

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Overview of Hubbert Linearization Hubbert Linearization is often used to determine the amount of a resource available, based on historical production data. Let Q(t) be the cumulative production of a resource. We assume Q grows logistically so that ! Q dQ = KQ 1 − P(t) = . dt F where F is the total amount of the resource available. Dividing both sides by Q yields ! Q P =K 1− Q F We fit a linear regression for the historical data

Group 4 (IMSM)

P vs Q to determine F. Q

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Example Hubbert Linearization

cadmium

phosphate

10

10

R/P = 10 years

8

7

7

6

6

5

5

4

4

3

3

2

2

1

1

0

0

2

4

6 8 cumulative production

10

12

0

0

1

2

5

x 10

Figure: Cadmium predicted to last for 10 years. r2 = .9105.

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R/P = 8 years

9

8

P/Q

P/Q

9

3 4 5 cumulative production

6

7 9

x 10

Figure: Phosphate predicted to last for 8 years. r2 = .9289.

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Inferences from Hubbert Linearization

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Inferences from Hubbert Linearization

Germanium and Silicon, important solar energy resources are running out soon.

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Inferences from Hubbert Linearization

Germanium and Silicon, important solar energy resources are running out soon. Silicon < 10 years, Germanium < 3 years

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Inferences from Hubbert Linearization

Germanium and Silicon, important solar energy resources are running out soon. Silicon < 10 years, Germanium < 3 years Sulphur, important for fertilizers, besides host of other industries, < 7 years.

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Outline 1

Introduction

2

Hubbert Linearization and Depletion of Resources

3

ARIMA Model for CO2 emissions

4

World3-03 Model Overview Our Modifications

5

Sensitivity Analysis of World3-03 Model Theory Conclusions in World3-03 Model

6

Optimization of HWI in World3-03 Model

7

Conclusions Group 4 (IMSM)

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The Auto Regression Integrated Moving Average Model (ARIMA) If {Xt }, a time series, follows an ARIMA(p, d, q), then, φ(B) (1 − B)d Xt = C + θ(B)at

(1)

φ(B) = 1 − φ1 B − · · · − φp Bp

(2)

where

q

θ(B) = 1 − θ1 B − · · · − θq B ,

(3)

d is the trend differencing order, at is a zero mean white noise process, p is the Autoregressive (AR) order, and q is the Moving-average (MA) order. The regression-times series model has the form: Yt = β0 + β1 X1t + · · · + βk Xkt + Nt , t = 1, ..., n

(4)

where β1 , ..., βk are estimated using Least Squares regression, {Nt } follows an ARIMA(p,d,q) with d=0. Group 4 (IMSM)

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ARIMA fit for CO2 emissions Goal: Model the effects of Coal consumption(Short Tons) X1t and Natural Gas consumption(Billion Cubic Feet) X2t on the trend of annual CO2 emissions (Million Metric Tons) Yt .

Group 4 (IMSM)

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ARIMA fit for CO2 emissions Goal: Model the effects of Coal consumption(Short Tons) X1t and Natural Gas consumption(Billion Cubic Feet) X2t on the trend of annual CO2 emissions (Million Metric Tons) Yt . Model 1: univariate ARIMA(1,0,2) for CO2 from Coal   (1 − 0.99842B) Yt = 1 + 0.89937B + 0.3851B2 at

Group 4 (IMSM)

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ARIMA fit for CO2 emissions Goal: Model the effects of Coal consumption(Short Tons) X1t and Natural Gas consumption(Billion Cubic Feet) X2t on the trend of annual CO2 emissions (Million Metric Tons) Yt . Model 1: univariate ARIMA(1,0,2) for CO2 from Coal   (1 − 0.99842B) Yt = 1 + 0.89937B + 0.3851B2 at Model 2: Regression time series of {Yt } on {X1t } Yt = 1.72222X1t N1t = 0.98067N1t−1 + at

Group 4 (IMSM)

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ARIMA fit for CO2 emissions Goal: Model the effects of Coal consumption(Short Tons) X1t and Natural Gas consumption(Billion Cubic Feet) X2t on the trend of annual CO2 emissions (Million Metric Tons) Yt . Model 1: univariate ARIMA(1,0,2) for CO2 from Coal   (1 − 0.99842B) Yt = 1 + 0.89937B + 0.3851B2 at Model 2: Regression time series of {Yt } on {X1t } Yt = 1.72222X1t N1t = 0.98067N1t−1 + at Model 3: univariate ARIMA(1,0,1) for CO2 emissions from Natural Gas (1 − 0.9903B) Yt = 1.26632 + (1 + 0.46783B) at

Group 4 (IMSM)

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ARIMA fit for CO2 emissions Goal: Model the effects of Coal consumption(Short Tons) X1t and Natural Gas consumption(Billion Cubic Feet) X2t on the trend of annual CO2 emissions (Million Metric Tons) Yt . Model 1: univariate ARIMA(1,0,2) for CO2 from Coal   (1 − 0.99842B) Yt = 1 + 0.89937B + 0.3851B2 at Model 2: Regression time series of {Yt } on {X1t } Yt = 1.72222X1t N1t = 0.98067N1t−1 + at Model 3: univariate ARIMA(1,0,1) for CO2 emissions from Natural Gas (1 − 0.9903B) Yt = 1.26632 + (1 + 0.46783B) at Model 4: Regression time series of {Yt } on {X2t } Yt = 64.40581 + 0.000847Xt , (1 − 0.79171B)Nt = at Group 4 (IMSM)

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Forecasts from the ARIMA Models CO2 emissions for Model 1

10

3

x 10

Carbon Dioxide

Carbon Dioxide

x 10

12

2.5 2 1.5 1

11 10 9 8

0.5 0 1980

CO2 emissions for Model 2

9

13

7 1985

1990

1995

2000 2005 years

2010

2015

2020

6 1980

2025

1985

CO2 emissions for Model 3

1990

1995 years

2000

2005

2010

2005

2010

CO2 emissions for Model 4

200

160 150 Carbon Dioxide

Carbon Dioxide

150

100

140 130 120

50 110 0 1980

1985

1990

1995

Group 4 (IMSM)

2000 2005 years

2010

2015

2020

2025

100 1980

1985

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1990

1995 years

2000

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Outline 1

Introduction

2

Hubbert Linearization and Depletion of Resources

3

ARIMA Model for CO2 emissions

4

World3-03 Model Overview Our Modifications

5

Sensitivity Analysis of World3-03 Model Theory Conclusions in World3-03 Model

6

Optimization of HWI in World3-03 Model

7

Conclusions Group 4 (IMSM)

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Overview and Scope of the World3-03 Model

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Overview and Scope of the World3-03 Model World3-03 simulates interactions between the world’s population, resources, industry, and agriculture.

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Overview and Scope of the World3-03 Model World3-03 simulates interactions between the world’s population, resources, industry, and agriculture. We study Garc´ıa’s implementation of World3-03 in the Vensim Software.

Group 4 (IMSM)

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Overview and Scope of the World3-03 Model World3-03 simulates interactions between the world’s population, resources, industry, and agriculture. We study Garc´ıa’s implementation of World3-03 in the Vensim Software. The purpose of World3-03 is not to make specific predictions, but to explore how exponential growth interacts with finite resources.

Group 4 (IMSM)

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Overview and Scope of the World3-03 Model World3-03 simulates interactions between the world’s population, resources, industry, and agriculture. We study Garc´ıa’s implementation of World3-03 in the Vensim Software. The purpose of World3-03 is not to make specific predictions, but to explore how exponential growth interacts with finite resources. Complexity and size hinders the ability to develop a complete understanding of the model.

Group 4 (IMSM)

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Overview and Scope of the World3-03 Model World3-03 simulates interactions between the world’s population, resources, industry, and agriculture. We study Garc´ıa’s implementation of World3-03 in the Vensim Software. The purpose of World3-03 is not to make specific predictions, but to explore how exponential growth interacts with finite resources. Complexity and size hinders the ability to develop a complete understanding of the model. Over 400 components, including 150 equations and 60 data tables.

Group 4 (IMSM)

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Overview and Scope of the World3-03 Model

Figure: The Full World3-03 Model as Implemented in Vensim Group 4 (IMSM)

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Overview and Scope of the World3-03 Model World3-03 simulates interactions between the world’s population, resources, industry, and agriculture. We study Garc´ıa’s implementation of World3-03 in the Vensim Software. The purpose of World3-03 is not to make specific predictions, but to explore how exponential growth interacts with finite resources. Complexity and size hinders the ability to develop a complete understanding of the model. Over 400 components, including 150 equations and 60 data tables.

Group 4 (IMSM)

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Overview and Scope of the World3-03 Model World3-03 simulates interactions between the world’s population, resources, industry, and agriculture. We study Garc´ıa’s implementation of World3-03 in the Vensim Software. The purpose of World3-03 is not to make specific predictions, but to explore how exponential growth interacts with finite resources. Complexity and size hinders the ability to develop a complete understanding of the model. Over 400 components, including 150 equations and 60 data tables. This relegates us to ‘Blackbox Analysis’

Group 4 (IMSM)

Resource Issues Impacting National Security

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Overview and Scope of the World3-03 Model World3-03 simulates interactions between the world’s population, resources, industry, and agriculture. We study Garc´ıa’s implementation of World3-03 in the Vensim Software. The purpose of World3-03 is not to make specific predictions, but to explore how exponential growth interacts with finite resources. Complexity and size hinders the ability to develop a complete understanding of the model. Over 400 components, including 150 equations and 60 data tables. This relegates us to ‘Blackbox Analysis’ Beneficial to consider a reduced model to gain an intuition to the model.

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Reduction of Energy Network

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Two Other Networks in Reduction

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Limitations of the Model

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Limitations of the Model

Total Fuel for Transportation is primarily dependent upon Service Output and Industrial Output and is not a function of Population or the Gross Domestic Product.

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Limitations of the Model

Total Fuel for Transportation is primarily dependent upon Service Output and Industrial Output and is not a function of Population or the Gross Domestic Product. Total Fuel for Transportation only affects Liquid Fuel Demand and not Electricity Demand.

Group 4 (IMSM)

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Limitations of the Model

Total Fuel for Transportation is primarily dependent upon Service Output and Industrial Output and is not a function of Population or the Gross Domestic Product. Total Fuel for Transportation only affects Liquid Fuel Demand and not Electricity Demand. The interaction between CO2 levels, climate, food supply, water supply, and sea-levels is not fully developed.

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Our Modifications We modified the World3-03 model by adding in electric powered transportation, reducing the need on oil.

Figure: Proposed Implementation of Fraction of Transportation Provided by Electricity Group 4 (IMSM)

Figure: Modifications in the Vensim World3-03 Model

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Outline 1

Introduction

2

Hubbert Linearization and Depletion of Resources

3

ARIMA Model for CO2 emissions

4

World3-03 Model Overview Our Modifications

5

Sensitivity Analysis of World3-03 Model Theory Conclusions in World3-03 Model

6

Optimization of HWI in World3-03 Model

7

Conclusions Group 4 (IMSM)

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Sensitivity Analysis: Theory

We then have the relative time-dependent sensitivity of an output Fi with respect to the parameter Pj given by: ∂Fi Pj × ∂Pj Fi Fi+ − Fi− Pj ≈ + × , Pj − P−j Fi

Si,j =

where P±j = Pj ± δPj and Fi± = Fi (P±j ).

Group 4 (IMSM)

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Conclusions of Sensitivity Analysis in World3-03 Model We (manually) compared 4 variables and 3 parameters.

EROEI of Renewable Electricity (15—25) Fraction of transportation from electricity (25%—35%) Carbon reduction technologies (−.5—−1.5)

Industrial Output

Life Expectancy

CO2 Levels

Human Welfare Index

0.8151

0.0655

-0.0063

0.2570

-0.1804

-0.0100

0.0178

-0.0876

-0.1489

0.0000

-0.0876

-0.0649

Table: Maximum magnitude of relative sensitivies of a small set of variables and parameters in the model. Group 4 (IMSM)

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Conclusions of Sensitivity Analysis in World3-03 Model

Figure: Sensitivity of Human Welfare Index on 3 parameters Group 4 (IMSM)

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Conclusions of Sensitivity Analysis in World3-03 Model

Figure: Sensitivity of CO2 Levels on 3 parameters Group 4 (IMSM)

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Outline 1

Introduction

2

Hubbert Linearization and Depletion of Resources

3

ARIMA Model for CO2 emissions

4

World3-03 Model Overview Our Modifications

5

Sensitivity Analysis of World3-03 Model Theory Conclusions in World3-03 Model

6

Optimization of HWI in World3-03 Model

7

Conclusions Group 4 (IMSM)

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Optimal Policies in World3-03 Model A policy can be interpreted as a combination of parameters: This is a multi-objective optimization problem.

Group 4 (IMSM)

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Optimal Policies in World3-03 Model A policy can be interpreted as a combination of parameters: This is a multi-objective optimization problem. The large set of parameters we are able to and would like to control. The above sensitivity analysis can be used first to find a smaller subset of parameters.

Group 4 (IMSM)

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Optimal Policies in World3-03 Model A policy can be interpreted as a combination of parameters: This is a multi-objective optimization problem. The large set of parameters we are able to and would like to control. The above sensitivity analysis can be used first to find a smaller subset of parameters. The steepest ascent gradient method with multiple initialization can be used to search for the optimal combination.

Group 4 (IMSM)

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Optimal Policies in World3-03 Model A policy can be interpreted as a combination of parameters: This is a multi-objective optimization problem. The large set of parameters we are able to and would like to control. The above sensitivity analysis can be used first to find a smaller subset of parameters. The steepest ascent gradient method with multiple initialization can be used to search for the optimal combination. We will consider the following example: Finding an optimal combination of Industrial Equilibrium Time and Industrial Output Desired per capita to maximize Human Welfare Index (HWI).

Group 4 (IMSM)

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Optimal Policies in World3-03 Model A policy can be interpreted as a combination of parameters: This is a multi-objective optimization problem. The large set of parameters we are able to and would like to control. The above sensitivity analysis can be used first to find a smaller subset of parameters. The steepest ascent gradient method with multiple initialization can be used to search for the optimal combination. We will consider the following example: Finding an optimal combination of Industrial Equilibrium Time and Industrial Output Desired per capita to maximize Human Welfare Index (HWI). The free version of Vensim limited us to a manual method to search for such a optimal combination.

Group 4 (IMSM)

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July 2009

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Optimal Policies in World3-03 Model A policy can be interpreted as a combination of parameters: This is a multi-objective optimization problem. The large set of parameters we are able to and would like to control. The above sensitivity analysis can be used first to find a smaller subset of parameters. The steepest ascent gradient method with multiple initialization can be used to search for the optimal combination. We will consider the following example: Finding an optimal combination of Industrial Equilibrium Time and Industrial Output Desired per capita to maximize Human Welfare Index (HWI). The free version of Vensim limited us to a manual method to search for such a optimal combination. HWI: the average of Human Welfare Index from 2010 to 2100 and Human Welfare Index at the year 2100 Group 4 (IMSM)

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Industrial Equilibrium Policies on HWI

0.65 0.60

Industrial Equilibrium Time = 2000 Industrial Equilibrium Time = 2050 Industrial Equilibrium Time = 4000

0.55

Average Human Welfare Index from 2010 to 2100

0.70

Different Policies for Industrial Equilibrium Time

200

400

600

800

1000

Industrial Output Desired

Figure: The effects of there industrial equilibrium times on Human Welfare Index averaged from 2010 to 2100. Group 4 (IMSM)

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Industrial Equilibrium Policies on HWI

0.55 0.50 0.45 0.40

Industrial Equilibrium Time = 2000 Industrial Equilibrium Time = 2050 Industrial Equilibrium Time = 4000

0.30

0.35

Human Welfare Index at 2100

0.60

0.65

Different Policies for Industrial Equilibrium Time

200

400

600

800

1000

Industrial Output Desired

Figure: The effects of three industrial equilibrium times on Human Welfare Index at the end of the 21st century. Group 4 (IMSM)

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Industrial Equilibrium Policies on HWI

0.68 0.67 0.66 0.65 0.64

Average Human Welfare Index from 2010 to 2100

0.69

Industrial Output Desired = 600

2020

2040

2060

2080

2100

Industrial Equilibrium Time

Figure: The optimal industrial equilibrium time given the industrial output desired 600. Group 4 (IMSM)

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Outline 1

Introduction

2

Hubbert Linearization and Depletion of Resources

3

ARIMA Model for CO2 emissions

4

World3-03 Model Overview Our Modifications

5

Sensitivity Analysis of World3-03 Model Theory Conclusions in World3-03 Model

6

Optimization of HWI in World3-03 Model

7

Conclusions Group 4 (IMSM)

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Conclusions and Future Work

Group 4 (IMSM)

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Conclusions and Future Work

Identified some key parameters and variables in the model with strong sensitivities.

Group 4 (IMSM)

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Conclusions and Future Work

Identified some key parameters and variables in the model with strong sensitivities. Developed a heuristic reduction of the model, (not implemented mathematically).

Group 4 (IMSM)

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Conclusions and Future Work

Identified some key parameters and variables in the model with strong sensitivities. Developed a heuristic reduction of the model, (not implemented mathematically). Would need to obtain full version of Vensim to perform a complete sensitivity analysis to obtain a complete reduced model.

Group 4 (IMSM)

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Conclusions and Future Work

Identified some key parameters and variables in the model with strong sensitivities. Developed a heuristic reduction of the model, (not implemented mathematically). Would need to obtain full version of Vensim to perform a complete sensitivity analysis to obtain a complete reduced model. Would like to explore how climate, sea-levels, food supply, and fresh-water supply interact with the World3-03 model.

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References

Dolores Garc´ıa. A New World Model Including Energy and Climate Change Data. http://europe.theoildrum.com/node/5145. Energy Information Administration. Official Energy Statistics from the U. S. Government. 2009. http://www.eia.doe.gov/emeu/international/contents.html. Donella H. Meadows, Jorgen Randers, and Dennis L. Meadows. Limits to Growth: The 30-Year Update. Chelsea Green, Vermont, 2004. Robert Rapier. Predicting the Past: The Hubbert Linearization. http://www.theoildrum.com/node/2357.

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Thanks

Special thanks to IMSM, NCSU, and SAMSI John Peach Mansoor Haider Chicken Biscuit Procurers

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