OUR PROJECTS - Integrated Metrics

Integrated Metrics for Sustainable and Resilient Infrastructures

There are two general considerations associated with the assessment of resilience and sustainability, the overarching consumption, distribution, and use of resources, and the detection of systemic regime shifts. Table 2 summarizes some of the metrics currently in use for quantifying these factors. Each of the measures listed has advantages and disadvantages for quantifying the condition, state, or dynamics of complex systems, as noted, thus the approach in this part of the research will be to compute a suite of metrics, with a goal of discerning comparative directionality (i.e., more or less resilient, sustainable) for alternative scenarios.

The evaluation of regime shifts, which can be interpreted as resulting from both unsustainable and poorly resilient systems, requires an integrative measure of system character. We believe the key to this integration lies in the ability to discern how the behavioral regimes of a system change over time and in response to perturbations, both relatively short term, and of longer durationi. The approach envisioned will rely on the application of information theory (IT) to the analysis of the problem. In this context, IT is used to discern the progression of order in a system. Perfectly ordered systems do not display shifts over time while perfectly disordered systems display shifts in which observable variables not only change but are uncorrelated. Virtually all real systems display behaviors in between these extremes. For example well-functioning ecosystems exist in ordered dynamic regimes in which predictable patterns are observable, yet may evolve to different states over time.

Table 2. Characteristic Resiliency and Sustainability Metricsii

Concept Metric Advantages Disadvantages
Resilience System recovery time and path relative to intensity of disturbance Inherently dynamic measure/incorporates infrastructural and ecological uncertainty/variability Prediction of ultimate recovery regime difficult/some regimes more desirable than others
Resilience Mitigation of aggregate risk Common basis for assessing degree of recovery Relation between human and ecological risk often not clear
Sustainability Ecological footprint/carrying capacity/maximum sustainable yield Balances waste emissions/withdrawal of goods/use of services with ecosystem functioning Rates at which ecosystems supply goods and services often not well understood
Sustainability Life cycle inventory and assessment Relates results of human commerce to common sets of impacts Data needs may be onerous/impact analysis often imprecise
Sustainability Thermodynamic accounting (e.g. exergy, emergy) Unity of expression related to fundamental system properties Human adaptability not considered

We propose to use, in particular, the concept of Fisher Information (FI), which provides a quantitative framework by which one can describe system regimes for which only partial or uncertain knowledge is availableiii. FI is concerned with the ability to estimate the amount of information that can be extracted from a set of data using derivative constructs from time-dependent data. Since it can operate on many types of data, it is an important step for integrating across social, technological, and ecological domains. FI is a measure of dynamic order. Steadily decreasing FI indicates a loss of dynamic order (a system that is shifting to more disordered and less functional states), while increasing FI signifies a system that is changing, but is doing so with its essential organization and function intact. The necessary condition for ordered transitions is that the averaged FI over time must be constant (i.e. ∂ ‹FI› /t ≈ 0).

There have been several applications of the FI approach to complex systems as a means of defining their stability, degree of order, sustainability, and resiliency, beginning with ecological, but progressing to industrial, economic, social, and governmental systemsiv. The results show consistency across systems, with clear indications of system-wide regime shifts. Further, FI approaches show considerable promise as a means for defining integrative indices and trends that describe the dynamic regimes of a system and make plausible projections (for a given set of information) on its future state. It should also be noted that although FI operates on time series information, the period over which shifts may occur is not limited by the temporal interval, thus both long term and short term simulations can be analyzed.

It is possible for some systems to exhibit preferred resilience, such as resource-intensive networks for transportation, but not meet the criteria of sustainability. For this reason three resource utilization metrics will also be used:

  • Material and energy flow analysis and life cycle impact assessment, which follows the material and energy usage throughout all stages of the anticipated life of the infrastructure (including usage by society), and the associated sustainability impactsv. Data on materials and energy will be analyzed through categorization as stocks (accumulated), flows, indirect flows (domestic, imported, or exported), emissions, and for energy the cascade of input energy to lower uses (i.e. electrical and fuel to dissipated heat), and constructing balances for each infrastructural system component (e.g. carbon, ferrous metals, etc.), and energy used. Impact analysis will rely upon a number of assessment tools accepted in the communityvi.
  • Ecological footprint, which is defined as the ratio of the amount of arable land and aquatic resources that must be used to continuously sustain a population to the population's actual regional area (based on its consumption levels and waste generated at a given point in time and according to a stated level of technology)vii.
  • Emergy (embodied energy) analysis, which provides a measure of energy resources invested by the environmentviii. Emergy, usually expressed as solar joules, is the sum of all of the different kinds of energy used, directly and indirectly, to construct and operate a system. Sustainable systems act to minimize emergy in their operation.


i Holling, C. S., and L. H. Gunderson (2002). "Resilience and Adaptive Cycles." In Panarchy: Understanding Transformations in Human and Natural Systems, edited by L. H. Gunderson and C. S. Holling. Washington, DC: Island Press.
ii Mayer A.L., H.W. Thurston, and C.W. Pawlowski (2004). "The multidisciplinary influence of common sustainability indices". Frontiers in Ecology and the Environment 2(8):419-426.
iii Fisher, R.A. (1925) Theory of Statistical Estimation. Proceedings of the Cambridge Philosophical Society, Cambridge: Cambridge Univ. Press.
iv Cabezas, H., C. Pawlowski, A. Mayer, N. Hoagland (2003). "Sustainability: Ecological, Social, Economic, Technological, and Systems Perspectives", Clean Technology and Environmental Policy, 5: 167-180.; Fath, B.D., H. Cabezas, and C.W. Pawlowski (2003). "Regime Changes in Ecological Systems: an Information Theory Approach", Journal of Theoretical Biol. 222(4):517-530.; Mayer, A.L., C.W. Pawlowski, and H. Cabezas (2006), "Fisher Information and Dynamic Regime Changes in Ecological Systems", Ecological Modeling, 195:72-82.
v Graedel, T. E., and B. R. Allenby (2002). Industrial Ecology. Englewood Cliffs, NJ: Prentice Hall.
vi Bare, J. C., G. A. Norris, D. W. Pennington and T. McKone (2002). "TRACI: The Tool for the Reduction and Assessment of Other Environmental Impacts." Journal of Industrial Ecology 6(3-4): 49-78.; Dreyer, L. C., A. L. Niemann and M. Z. Hauschild (2003). "Comparison of three different LCIA methods: EDIP97, CML2001 and Eco-indicator 99 does it matter which one you choose?" International Journal of Life Cycle Assessment 8(4): 191-200.; Miller, S.A., A.E. Landis, T.L. Theis, and R.L. Reich (2007). "A Comparative Life Cycle Assessment of Petroleum and Soybean-Based Lubricants", Environmental Science and Technology 41(11): 4143-4149.; Landis, A.E., S. A. Miller, and T. L. Theis, (2007) "Life Cycle of the Corn-Soybean Agroecosystem for Biobased Production" Environ. Sci. Technol. 41(4):1457-1464.
vii Wackernagel M., and W.E. Rees (2007). "Perceptual and structural barriers to investing in natural capital: Economics from an ecological footprint perspective", Ecological Economics 20 (1), 3-24.
viii Brown, M., and V. Buranakarn (2003), "Emergy Indices and Ratios for Sustainable Material Cycles and Recycle Options", Resources Conservation and Recycling, 38:1-22.