Interactions between urban and geophysical systems have a long history for better and worse, but they have become a key issue for humanity facing both an unprecedented urbanisation (more than a billion more people to be accommodated mainly in cities over the next twenty years) and climate change. These systems have not only a large number of components, but also display an extreme variability over a wide range of space-time scales, an associated non-stationarity and a long range memory. These features urgently require to break methodological deadlocks and to go beyond the systematic recourse to case studies. Multifractals have been a breakthrough in the analysis and simulation of this variability. However, the have been too long limited to scalar valued processes, whereas multi-component behaviour is of primary interest in these complex systems. Recent and broad extensions of multifractals have led to the emergence of multifractal operators. With the help of the generic example of the Levy-Clifford algebra of generators of such stochastic operators, we illustrate the resulting paradigm shift on scaling interactions of complex systems. For instance, there is a surprising entanglement of spherical and hyperbolic geometries that broadly generalises rotation and deformation of flows. https://agu-do03.confex.com/data/abstract/agu/fm19/5/1/Paper_535915_abstract_524426_0.jpg