Abstract
As a key tool in information theory, Fisher Information has been used to explore the observable behavior of a variety of systems. In particular, recent work has demonstrated its ability to assess the dynamic order of real and model systems. However, in order to solidify the use of this metric for measuring sustainability, it is pertinent that Fisher Information be understood both conceptually and practically. As such, this document has been developed as a guide for interpreting Fisher Information as sustainability metric. Moreover, this study provides details on an analytical and numerical approach to estimating Fisher information based on the evaluation of changes in the system’s trajectory for determining stable and unstable regimes in real systems, which might represent sustainable or unsustainable systems. Using this novel approach, the sustainability of US air quality characterized by criteria pollutants (i.e., lead, carbon monoxide, ozone, nitrogen dioxide, and sulfur dioxide) was assessed from 1980 to 2009. Further, the precision of Fisher Information computations was examined, thereby establishing an alternative procedure for evaluating real systems characterized by noisy and sparse datasets. Throughout this article, the reader is led through the analysis of Fisher Information results with the goal of both providing guidance on the interpretation of Fisher Information and giving a more tactile understanding of the results applied to sustainability assessment.
Similar content being viewed by others
References
Cabezas H, Eason T (2010) Fisher information and order. In: Heberling MT, Hopton ME (eds) San Luis basin sustainability metrics project: a methodology for evaluating regional sustainability. US Environmental Protection Agency, USEPA. EPA/600/R-10/1822, Cincinnati, Ohio, pp 163–222
Cabezas H, Fath BD (2002) Towards a theory of sustainable systems. Fluid Phase Equilibr 194–197:3–14
Cabezas H, Pawlowski CW, Mayer AL, Hoagland NT (2003) Sustainability: ecological, social, economic, technological, and systems perspectives. Clean Technol Environ Policy 5:167–180
Cabezas H, Pawlowski CW, Mayer AL, Hoagland NT (2005a) Simulated experiments with complex sustainable systems: ecology and technology. Resour Conserv Recy 44:279–291
Cabezas H, Pawlowski CW, Mayer AL, Hoagland NT (2005b) Sustainable systems theory ecological and other aspects. J Clean Prod 13:455–467
Cabezas H, Whitmore HW, Pawlowski CW, Mayer AL (2007) On the sustainability of an integrated model system with industrial, ecological, and macroeconomic components. Resour Conserv Recy 50:122–129
Chapra SC (2008a) Numerical differentiation. In: Applied numerical methods with MATLAB, for engineers and scientists, 2nd edn. McGraw-Hill, New York, pp 448–471
Chapra SC (2008b) Numerical integration formulas. In: Applied numerical methods with MATLAB, for engineers and scientists. McGraw-Hill, New York, pp 392–425
Chapra SC (2008c) Runge–Kutta methods. In: Applied numerical methods with MATLAB, for engineers and scientists. McGraw-Hill, New York, pp 493–498
Eason T, Cabezas H (2012) Evaluating the sustainability of a regional system using Fisher information, San Luis Basin, Colorado. J Environ Manage 94(1):41–49
Fath BD, Cabezas H, Pawlowski CW (2003) Regime changes in ecological systems: an information theory approach. J Theor Biol 222:517–530
Fisher RA (1922) On the mathematical foundations of theoretical statistics. Philos T R Soc Lond 222:309–368
Jorgensen SE (2006) Eco-exergy as sustainability. WIT Press, Boston
Karunanithi AT, Cabezas H, Frieden BR, Pawlowski CW (2008) Detection and assessment of ecosystem regime shifts from Fisher Information. Ecol Soc 13(1):22
Kates RW, Parris TM (2003) Long term trends and a sustainability transition. Proc Natl Acad Sci USA 100(14):8062–8067
Lawn PA (2003) A theoretical foundation to support the Index of Sustainable Economic Welfare (ISEW), Genuine Progress Indicator (GPI), and other related indexes. Ecol Econ 44(1):105–118
Lotka AJ (1925) Elements of physical biology. Williams and Wilkins, Baltimore
Mayer AL, Thurston H, Pawlowski CW (2004) The multidisciplinary influence of common sustainability indices. Front Ecol Environ 2(8):419–426
Mayer AL, Pawlowski CW, Cabezas H (2006) Fisher Information and dynamic regime changes in ecological systems. Ecol Model 195:72–82
Mayer AL, Pawlowski CW, Fath BD, Cabezas H (2007) Applications of Fisher Information to the management of sustainable environmental systems. In: Frieden BR, Gatenby RA (eds) Exploratory data analysis using Fisher Information. Springer, London, pp 217–244
Murray JD (2002) Models for interacting populations. In: Mathematical biology I: an introduction, vol I. Springer, New York, pp 79–118
Odum HT (1996) Environmental accounting: emergy and environmental decision making, 1st edn. Wiley, New York
Regulation of Fuels and Fuel Additives: Modification of Baselines for Gasoline Produced or Imported for Use in Hawaii, Alaska and U.S. Territories (2007). Fed. Regist., vol 72
Revisions to Lead Ambient Air Monitoring Requirements (2010). Code of Federal Regulations, 40 CFR, Part 58, vol [EPA–HQ–OAR–2006–0735]
Rico-Ramirez V, Quintana-Hernandez PA, Ortiz-Cruz JA, Hernandez-Castro S (2008) Fisher Information: a generalized sustainability index? In: Braunschweig B, Joulia X (eds) 18th European symposium on computer aided process engineering, Lyon, France, 2008. Computer-Aided Chemical Engineering. Elsevier, pp 1155–1160
Rico-Ramirez V, Reyes-Mendoza PA, Ortiz-Cruz JA (2010) Fisher information on the performance of dynamic systems. Ind Eng Chem Res 49(4):1812–1821
Rodionov SN (2005) A brief overview of the regime shift detection methods. Paper presented at the large-scale disturbances (regime shifts) and recovery in aquatic ecosystems: challenges for management toward sustainability, UNESCO-ROSTE/BAS workshop on regime shifts, Varna, Bulgaria, 14–16 June 2005
Scheffer M, Bascompte J, Brock WA, Brovkin V, Carpenter SR, Dakos V, Held H, Van Nes EH, Rietkerk M, Sugihara G (2009) Early-warning signals for critical transitions. Nature 461:53–59
Shastri Y, Diwekar U, Cabezas H (2008) Optimal Control Theory for sustainable environment management. Environ Sci Technol 42(14):5322–5328
United Nations (1987) Our common future. Towards sustainable development. World commission on environment and development, Oxford
United Nations (2005) World summit outcome. Report transmitted to the General Assembly, New York
US Environmental Protection Agency (1973) EPA requires phase-out of lead in all grades of gasoline. http://www.epa.gov/history/topics/lead/03.htm. Accessed 2011
US Environmental Protection Agency (1985) EPA sets new limits on lead in gasoline. http://www.epa.gov/history/topics/lead/01.htm. Accessed 2011
US Environmental Protection Agency (1986) US EPA air quality criteria for lead (Final, 1986). US Environmental Protection Agency, Washington DC
US Environmental Protection Agency (2010a) Air quality trends by pollutant. http://www.epa.gov/airtrends/. Accessed 2010
US Environmental Protection Agency (2010b) National trends in lead levels. http://www.epa.gov/airtrends/lead.html
Volterra V (1931) Variations and fluctuations of a number of individuals in animal species living together. In: Animal ecology. McGraw Hill, New York, pp 409–448
Wackernagel M, Rees WE (1996) Our ecological footprint: reducing human impact on the earth. New Society Publishers, Philadelphia
Zellner ML, Theis TL, Karunanithi AT, Garmestani AS, Cabezas H (2008) A new framework for urban sustainability assessments: linking complexity, information and policy. Comput Environ Urban 32(6):474–488
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Gonzalez-Mejia, A.M., Eason, T., Cabezas, H. et al. Computing and interpreting Fisher Information as a metric of sustainability: regime changes in the United States air quality. Clean Techn Environ Policy 14, 775–788 (2012). https://doi.org/10.1007/s10098-011-0445-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10098-011-0445-2