Strategies for creating quantitative projections for human systems, especially impervious surfaces, are necessary to consider the human drivers of climate and ecosystem change. 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. We demonstrate a statistically robust sublinear 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, analogous to the ways in which allometric scaling laws in biology have been used to validate process-based models of ecosystem composition under different climate scenarios.