Sustainable Urban Energy Systems A Science of Cities Approach Lorraine Sugar PhD Candidate, University of Toronto ONSEP 2016

Why Cities? The global fight for sustainability will be won or lost in the world’s cities In Canada, 81% of the population is considered urban (2011 Census) In Ontario, 86% of the population is considered urban (2011 Census) Source: World Bank

The Science of Cities Rooted in complexity theory Use principles from physics, mathematics, economics, ecology, etc. to understand cities’ form and function Main objectives are to develop coherent theories of urban evolution (i.e., growth and decline) that are descriptive and policy relevant Theories must Account for both dynamics and spatial structure Be empirically testable Ideally be universally applicable

Properties of Complex Systems Some properties include: Feedback loops Emergent properties, learning, and memory Order through self-organization, hierarchy, scaling relationships, etc. Properties observed throughout the natural world (as well as human-made systems!) Properties can be empirically observed in most complex systems Decoding the Matrix!

Scaling Laws in Biology

Implies economy of scale in biological energy consumption Larger organisms consume less energy per unit time and per unit mass than smaller ones Mouse Elephant

Scaling Laws in Biology Another way to visualize: log of both sides, slope reveals scaling relationship Slope = 1 Slope = 3/4 < 1 Sublinear scaling

Scaling Laws in Cities Do scaling laws occur in cities? Yes! Zipf’s Law, 1949: predictable scaling between city rank and population size Available:

Scaling Laws in Cities Slope = β

Scaling Laws in Cities Bettencourt, West, and colleagues, 2007: Strong, consistent scaling empirically observed across many indicators, for as many cities as they could find data

Scaling Laws in Cities Linear scaling, β = 1 Human needs: jobs, housing, power consumption, water consumption

Scaling Laws in Cities Sublinear scaling, β < 1 β ≈ 0.8 Infrastructure, material consumption, economies of scale (similar to biology)

Scaling Laws in Cities Sublinear scaling, β < 1 β ≈ 0.8 Infrastructure, material consumption, economies of scale (similar to biology)

Scaling Laws in Cities Superlinear scaling, β > 1 β ≈ Social aspects, information, wealth, increasing returns to scale (not observed in biology)

Scaling Laws in Cities Superlinear scaling, β > 1 β ≈ Social aspects, information, wealth, increasing returns to scale (not observed in biology)

Scaling Laws and Energy Bettencourt, West, and colleagues (2007) remark on the behaviour of energy-related variables as being “ambivalent”: Linear scaling, β = 1 Household electricity consumption (Germany & China) Sublinear scaling, β < 1 Length of electricity cable (Germany) Superlinear scaling, β > 1 Total electricity consumption (Germany) Dissipative electricity losses (Germany) Slope = β

Scaling Laws and Energy Bettencourt (2013): Energy loss scales superlinearly, similar to other socioeconomic characteristics “This shows how cities are fundamentally different from other complex systems, such as biological organisms or river networks, which are thought to have evolved to minimize energy dissipation.” In other words: cities have evolved to maximize energy consumption and loss

Exploring Policy Relevance Understanding urban growth Combining scaling relationships into a helpful parameter, G Revisiting Kleiber’s Law

Understanding Urban Growth Bettencourt, West, and colleagues (2007) translate observed scaling relationships into 3 regimes of urban growth, driven by: Sublinear scaling, β < 1 Converges at a carrying capacity Linear scaling, β = 1 Exponential growth Superlinear scaling, β > 1 Diverges to a critical point, collapses when resources are scarce

Understanding Urban Growth Bettencourt, West, and colleagues (2007) translate observed scaling relationships into 3 regimes of urban growth, driven by: Superlinear scaling, β > 1 Diverges to a critical point, collapses when resources are scarce Successive cycles of innovation “reset” the singularity, need to occur more and more frequently Energy efficiency technologies?

The Parameter G

How does G change over time? What are the largest drivers of change?

Slope = 1 Slope = 3/4 < 1 Sublinear scaling Mice do not grow into elephants But small cities grow into big cities Body mass includes metabolic cells and structural cells Cities include people and infrastructure (a physical form of wealth) What is the mass of a city? Is there a less “ambivalent” relationship between mass and energy consumption? Revisiting Kleiber’s Law