You are right, but urban settlements themselves change their climate in terms of evaporation rate due to consumption of water, creating barriers for on wind side and giving corridors etc. However, typically urban centres as centres of consumption have depleted surrounding of vegetation cover altering temperature intensity and local water cycle, are heavy burden on waterways further deteriorating downstream ecosystems affecting their temperature moderating role and water cycle. Construction activities can also add to aerosols, all these conditions are related to intensify climate change in the region of a big urban centre.
Regional climate change has important implications for human comfort, health and well-being. Many examples exist of the vulnerability of urban populations most often the elderly and the poor, associated with heat waves.
Warmer conditions in cities will also increase demand for air conditioning. More air conditioners generate more heat and have significant effects on the local climate, with implications for human comfort and the demand for cooling. At a larger scale, greater use of air conditioning results in more greenhouse gases through increased electricity generation. Cold conditions will also increase demand for heating.
Therefore I guess as an appropriate indicators your can track the per-capita water consumption, per capita energy consumption, change in building structures, and spread of diseases that does not exist before .
I think that the relationship between urbanization and regional climate change can be sensed in the micro level more than the macro one. Urban areas represent what is called the heat islands. Human urban activities, energy consumption, industrialization, and new technologies mainly exist in urban areas. So, it can be said that indicators of climate change at the regional level due to urbanization can be detected from the types of human activities and economy.
You are right, but urban settlements themselves change their climate in terms of evaporation rate due to consumption of water, creating barriers for on wind side and giving corridors etc. However, typically urban centres as centres of consumption have depleted surrounding of vegetation cover altering temperature intensity and local water cycle, are heavy burden on waterways further deteriorating downstream ecosystems affecting their temperature moderating role and water cycle. Construction activities can also add to aerosols, all these conditions are related to intensify climate change in the region of a big urban centre.