Urban morphology characterization is crucial for the parametrization of boundary-layer development over urban areas. One complexity in such a characterization is the three-dimensional variation of the urban canopies and textures, which are customarily reduced to and represented by one-dimensional varying parametrization such as the aerodynamic roughness length z0\documentclass[12pt]{minimal}
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\begin{document}$$d$$\end{document}. The scope of the paper is to provide novel means for a scale-adaptive spatially-varying parametrization of the boundary layer by addressing this 3-D variation. Specifically, the 3-D variation of urban geometries often poses questions in the multi-scale modelling of air pollution dispersion and other climate or weather-related modelling applications that have not been addressed yet, such as: (a) how we represent urban attributes (parameters) appropriately for the multi-scale nature and multi-resolution basis of weather numerical models, (b) how we quantify the uniqueness of an urban database in the context of modelling urban effects in large-scale weather numerical models, and (c) how we derive the impact and influence of a particular building in pre-specified sub-domain areas of the urban database. We illustrate how multi-resolution analysis (MRA) addresses and answers the afore-mentioned questions by taking as an example the Central Business District of Oklahoma City. The selection of MRA is motivated by its capacity for multi-scale sampling; in the MRA the “urban” signal depicting a city is decomposed into an approximation, a representation at a higher scale, and a detail, the part removed at lower scales to yield the approximation. Different levels of approximations were deduced for the building height H¯\documentclass[12pt]{minimal}
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\begin{document}$$\bar{{H}}$$\end{document} and planar packing density λp\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _\mathrm{p}$$\end{document}. A spatially-varying characterization with a scale-adaptive capacity is obtained for the boundary-layer parameters (aerodynamic roughness length z0\documentclass[12pt]{minimal}
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\begin{document}$$d$$\end{document}) using the MRA-deduced results for the building height and the planar packing density with a morphometric model; an attribute that is shown to be of great advantage to multi-scale and multi-resolution numerical weather prediction models.
