Scaling indicator and planning plane: an indicator and a visual tool for exploring the relationship between urban form, energy efficiency and carbon emissions

Ecosystems and other naturally resilient systems exhibit allometric scaling in the distribution of sizes of their elements. In this paper we define an allometry inspired scaling indicator for cities that is a first step towards quantifying the resilience borne of a complex systems’ hierarchical structural composition. The scaling indicator is calculated using large census datasets and is analogous to fractal dimension in spatial analysis. Lack of numerical rigor and the resulting variation in scaling indicators -inherent in the use of box counting mechanism for fractal dimension calculation for citieshas been one of the hindrances in the adoption of fractal dimension as an urban indicator of note. The intra-urban indicator of scaling in population density distribution developed here is calculated for 58 US cities using a methodology that produces replicable results, employing large census-block wise population datasets from the 2010 US Census 2010 and the 2007 US Economic Census. We show that rising disparity – as measured by the proposed indicator of population density distribution in census blocks in metropolitan statistical areas (using US Census 2010 data) adversely affects energy consumption efficiency and carbon emissions in cities and leads to a higher urban carbon footprint. We then define a planning plane as a visual and analytic tool for incorporation of scaling indicator analysis into policy and decision-making.