Urban ecosystems are defined by unique relationships between biological diversity and distribution, socio-demographics, and climate. These relationships occur in the context of a changing world: increasing temperatures, a shifting composition of urban residents, and rapid urbanization. It is likely that the relationships which structure the urban environment, such as that between temperature and income, or race-based exposure to heat and greenness, are not temporally stable. As urban temperatures and greenness have well known associations with morbidity, mortality, and mental health, non-stationarity of urban ecological relationships may pose significant challenges to the well-being of urban residents. I tested assumptions about non-stationarity by assessing the change through time of urban ecological relationships at three distinct spatial scales: the urban (single city) scale (chapter 1), at a continental scale (chapter 2), and at a global scale (chapter 3). At each spatial scale I used a multidecadal time series of satellite imagery, coupled with landcover and socio-demographic information, to assess how the dynamics of urban greenness, temperature, and vegetative cooling evolved through time and what factors mediated any change. In chapter 1, where I used Los Angeles, CA as a case study, I found large intra-urban variability in how greenness, temperature, and vegetative cooling changed over time. The consequence of these changes was a weakening of the effectiveness of income as a mediator of urban greenness and temperature (the luxury effect). I corroborated the multidecadal decline in the luxury effect in chapter 2, a continental-scale assessment where I looked at 52 cities from the conterminous United States. In this chapter I additionally compared the biophysical dynamics in every city with a nearby non-urban reference site. Urbanization weakened the relationship between the weather and landcover and the biophysical environment, where the most arid cities were entirely decoupled from precipitation. In chapter 3, I looked at a subset of 266 global cities from 82 countries, finding that the evolving relationship between greenness and temperature led to declines in the cooling effectiveness of urban vegetation. Overall, this dissertation highlights the non-stationarity of urban dynamics, as well as the importance of climatic context in understanding these urban relationships.