Time-series sensor data are used to create prediction models, called city profiles, for understanding city dynamics in the smart-city sector. These city profiles are typically created and updated by the Cloud using reported raw sensor data. However, continuously reporting raw sensor data is not energy efficient for boundary computing resources of a network. Thus, this work considers edge servers that are deployed on the boundary computing resources of a network to collaborate with the Cloud for adaptively mitigate city profiling tasks (i.e., creating city profiles) across an edge server and the Cloud. By maintaining the local city profiles on the edge or the global city profiles on the Cloud, either an edge or the Cloud can dynamically respond to user queries. However, there is a trade-off between the energy consumption of an edge and the response accuracy of the city profiles. This work designs an adaptive city profiling and synchronization approach for edges to decide when, where (i.e., an edge or the Cloud), and how to update and synchronize local and global city profiles such that the energy consumption of the edge is reduced while the accuracy of a city profile can be guaranteed. Extensive simulations are conducted using a real-world temperature dataset to evaluate the performance of the proposed approach. The simulation results indicate an average energy saving of 60% of edges compared with a typical Cloud-based approach while the required accuracy is fulfilled.