Searching for the distinctive signature of a city in atmospheric modelling: Could the Multi-Resolution Analysis (MRA) provide the DNA of a city?

In the context of MRA, the urban-building information signal is analysed at different levels that each corresponds to a different scale. At each level the urban signal depicting a city is decomposed into an approximation, a representation at the scale that corresponds to the level, and a detail that is the part removed from the previous level that corresponds to lower scale. One of the major capacities and outputs of the MRA application is the multi-scale representation of the urban information while not losing the ability to recover the original density of urban information due to the tracking of the details. In this paper the results of such an MRA analysis of urban building datasets of European cities (London, Marseille and Nicosia) and North-American cities (New York City, Phoenix and Seattle as well as Oklahoma) are presented; the analysis provides consistent gridded and scaled attributes as well as sub-grid information for a hierarchy of grid sizes, for example used in nested urban simulations. Moreover, through the rigorous scale-adaptive spatially-varying representations that are obtained, a sound basis for consistent inter-comparisons is enabled. Finally, the paper illustrates how the MRA can provide an innovative means to perform analyses and provide unique scale-adaptive descriptions of any urban area - in essence a DNA-like description of a city.