A mathematical description of urban metabolism

Abstract

A comprehensive, yet simple, model of the urban metabolism is described using approximately 25 closed-form equations. The equations represent essential interrelationships between the major components of metabolism-materials, water, nutrients, energy, and contaminants. The model expresses the role of infrastructure in the urban metabolism through parameters such as per capita floor space and the density of transportation infrastructure which, as part of a city's material stock, influence the flows of energy and/or water flows through the city. The density of transportation infrastructure is found to be a potentially universal parameter, with a value of 0.10 km ha -1, which is relatively invariant between cities. The model also includes other parameters which, although having more variation, are independent of climate, city size, population, and other unique characteristics of cities. These other parameters include: material intensities, per capita floor space, intensity of water use for cooling, leakage rates for water distribution systems, heating and cooling intensities of buildings, and utilization rates for transportation infrastructure.