An algorithmic architecture for kernel-based modelling of data streams from city sensing infrastructures is introduced. It is both applicable for pre-installed, moving and extemporaneous sensors, including the "citizen-as-a-sensor" view on user-generated data. The approach is centred around a kernel dictionary implementing a general hypothesis space which is updated incrementally, accounting for memory and processing capacity limitations. It is general for both kernel-based classification and regression. An extension to area-to-point modelling is introduced to account for the data aggregated over a spatial region. A distributed implementation realised under the Map-Reduce framework is presented to train an ensemble of sequential kernel learners.