Optimization for Sustainability of Integrated Ecological-Economic Model System of Planet

1. Optimization for Sustainability of Integrated Ecological-Economic Model System of Planet Megan Schwarz Johns Hopkins University Dr. Diwekar July 1, 2013

2. What is Sustainability? • “The development that meets the needs of the present without compromising the ability of future generations to meet their own needs” (Brundtland 1987) • Goal: To design a simplified model of the planet to explore regulatory strategies to try to increase sustainability Sustainability: A path through time Heriberto Cabezas, Christopher W. Pawlowski, Audrey L. Mayer, N. Theresa Hoagland Clean Techn Environ Policy 5 (2003) 167–180

3. Natural Resources Resource Pool Primary Producers (Plants) P1 P2 P3 grazing fence Herbivores H2 H1 Domestic H3 Integrated Ecological-Economic Model System of Planet Non-Domestic fence Carnivores C1 C2 Human Households Energy Source Energy Source HH Energy Producer Industrial Sector IS EP Biologically inaccessible resources Inaccessible Resource Pool • Model Adapted from Kotecha, P.; Diwekar, U.; Cabezas, H.. “Model-based approach to study the impact of biofuels on the sustainability of an ecological system” (2011).

4. Basic Mathematics of the Model • Three general types of equations • Basic food web model equations • Macroeconomic model equations • All other algebraic equations • 98 constant parameters • 19 time dependent state variables described by differential equations • 61 model outputs • About 2000 lines of code in Matlab

5. Model Simulation • Looked at how economic and ecological parameters changed over a time period of 200 years with and without the use of biofuel as a source of energy • Two different scenarios • Population Explosion • Increase in Per Capita Consumption

6. Population ExplosionDynamics of Human Population and Primary Producer 2 • The population is expected to peak to about twice today’s sizein the next 50 t0 100 years • A steady drop is then expected due to an aging population and a decrease in fertility rates • Primary producer 2 was the only ecological compartment to reach extinction

7. Increase in Per Capita ConsumptionDynamics of Carnivore 1 and Human Population • Consumption of many resources is estimated to increase by approximately 50% in the next 50 years • Most ecological compartments reached extinction • Shows the catastrophe where limited resources cause loss of human life • Decrease in population sooner with the use of biofuels because compartments reach extinction earlier

8. Conclusions about Model Simulation • Sustainability of even a simple ecosystem may not be intuitive • Use of biomass as a source of energy accelerates the extinction of species • Increasing per capita consumption is more critical than population explosion • The ecosystem can’t sustain high levels of human consumption

9. Numerical Optimization • Goal: increase the lifetime of dying compartments • Increase sustainability of the system • Need a mathematical measure of sustainability • Fisher Information (FI) • FI can be used as a measure of order of a system • Information is a fundamental quantity of a system • Able to incorporate the physics and economics of the model

10. Objective Function • Objective: develop policies so the system FI is close to the FI of a stable system • Base case scenario • Objective Function: minimization of the FI variance: • is the current FI profile • is the targeted FI for the stable base case scenario • T is the total time under consideration

11. Optimal Design Initial Values Optimizer MODEL Numerical Optimization: Non-linear Programming (NLP) Objective Function Decision Variables • Initial values of the decision variable are known • The model calculates the objective function and the optimizer tries to satisfy optimality conditions (Karush-Kuhn-Tucker conditions, KKT) • Optimizer calculates a new value for the decision variable • Iterative sequence continues until the optimization criteria (KKT) are met Model Adapted from: Diwekar, Urmila M. Introduction to Applied Optimization. Norwell, MA: Kluwer Academic, 2003. Print.

12. Design of Techno-economic Policies for Sustainability • Policies (control variables) are used as the decision variables at each time step • Governmental Policies: • Discharge fee charged to the industrial sector (pISHH) • Amount of primary producer 2 consumed by herbivore 1 through grazing • Policy related to Efficiency of Technology: • Amount of primary producer 1 required to produce a unit of the industrial sector product

13. Governmental PolicyDischarge fee charged to the industrial sector (pISHH)

14. Governmental PolicyDischarge fee charged to the industrial sector (pISHH) No Bioenergy Bioenergy

15. Policy Related to Efficiency of TechnologyAmount of primary producer 1 to produce a unit of the industrial sector product

16. Policy Related to Efficiency of TechnologyAmount of primary producer 1 to produce a unit of the industrial sector product No Bioenergy Bioenergy

17. Governmental PolicyThe amount of primary producer 2 consumed by herbivore 1 through grazing

18. Governmental PolicyThe amount of primary producer 2 consumed by herbivore 1 through grazing No Bioenergy Bioenergy

19. Conclusions • Fisher Information is an indicator of sustainability of a system • The discharge fee charged to the industrial sector is most effective in delaying the extinction of dying compartments • The amount of primary producer 1 required to produce a unit of the industrial sector product leads to small delays in the extinction of dying compartments • does not lead to any significant improvement in the model dynamics

20. Future Work • Optimization using different control variables • Multi-variable control • Further model enhancement

21. Acknowledgments • The financial support from the National Science Foundation, EEC-NSF Grant # 1062943 is gratefully acknowledged • Dr. Diwekar • KirtiYenkie • PaholaThathiana Benavides • Professor Takoudis, Professor Jursich, REU program

22. References Cabezas, H., C. W. Pawlowski, A. L. Mayer, and H. W. Whitmore. "On the Sustainability of Integrated Model Systems with Industrial, Ecological, and Macroeconomic Components." Resources, Conservation and Recycling 50.2 (2007): 122-29. Elsevier B.V. Web. Cabezas, Heriberto, N. Theresa Hoagland, Audrey L. Mayer, and Christopher W. Pawlowski. "Simulated Experiments with Complex Sustainable Systems: Ecology and Technology." Resources, Conservation and Recycling 44 (2005): 279-91. Elsevier B.V. Web. Diwekar, Urmila M. Introduction to Applied Optimization. Norwell, MA: Kluwer Academic, 2003. Print. "Finite Difference Schemes." Computational Fluid Dynamics. Brown University, n.d. Web. Kotecha, Prakash, UrmilaDiwekar, and HeribertoCabezas. "Model-based Approach to Study the Impact of Biofuels on the Sustainability of an Ecological System." Clean Technology and Environmental Policy 15.1 (2013): 21-33. Springer Verlag. Web. Meadows, Donella H., Dennis L. Meadows, and Jørgen Randers. Beyond the Limits: Confronting Global Collapse, Envisioning a Sustainable Future. Vermont: Chelsea Green, 1992. Print. "Report of the World Commission on Environment and Development Our Common Future."Brundtland Report 1987. United Nations, n.d. Web. Shastri, Y., and U. Diwekar. "Sustainable Ecosystem Management Using Optimal Control Theory: Part 1 (Deterministic Systems)." Journal of Theoretical Biology 241 (2006): 506-21. Elsevier B.V. Web. Shastri, Yogendra, UrmilaDiwekar, and HeribertoCabezas. "Optimal Control Theory for Sustainable Environmental Management." Environmental Science and Technology 42.14 (2008): 5322-328. American Chemical Society. Web. Shastri, Yogendra, UrmilaDiwekar, HeribertoCabezas, and James Williamson. "Is Sustainability Achievable? Exploring the Limits of Sustainability with Model Systems." Environmental Science and Technology 42.17 (2008): 6710-716. American Chemical Society. Web. United States Census Bureau. U.S. Department of Commerce, n.d. Web. 01 July 2013.

23. Questions?

24. Time average FI for a system with n species: • = cycle time • and are the velocity and acceleration terms of the ecosystem