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Publication Date
25 November 2020

Urban Scaling as Validation for Predictions of Imperviousness

Evaluating process based models of urban growth through statistical scaling theories.
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Demonstration of the scaling relationship between logged population and logged imperviousness observed in our historical data set. This figure shows that the expectation from theory (purple) is much more consistent with an empirically fitted relationship (black) than is a null hypothesis (blue).

We demonstrate a statistically robust scaling relationship between population and urban imperviousness across a 15-year history. We show that Integrated Climate and Land-Use Scenarios (ICLUS) urbanization projections are also consistent with theory. These results demonstrate a theory that can be used to validate other models' predictions of urban growth and land cover change.


A key uncertainty in predicting climate and environmental change is the effect of human changes, such as urbanization and the introduction of impervious surfaces. There are models that generate predictions of how impervious surfaces may change in response to different potential futures, but few tools exist for validating those predictions. We seek to fill that gap by demonstrating the use of empirical scaling laws to validate model predictions.


The decisions that human institutions, like cities or countries, make can have a dramatic influence on the earth system, and the earth system influences human decisions. The earth system modeling community has important tools for modeling long-term interactions between cities and the land surface.  Validating these tools is challenging because even if we know how a particular decision - if made - would influence the earth system, we are not good at predicting what decisions will be made. In this paper, we show that there is a sublinear scaling relationship between a city's population and the total impervious area. This scaling relationship shows us that in cities with larger populations, there is less space available per person, and so impervious surfaces are more intensely used. We then show that ICLUS' predictions about interactions between urban population and imperviousness also predict that these places will be more intensely used, as expected from theory. This helps us quantify how reliable predictions of interactions between human institutions and the earth system might be.

Point of Contact
Christa Brelsford
Oak Ridge National Laboratory (ORNL)
Funding Program Area(s)