# A Scale-Adaptive Approach for Spatially-Varying Urban Morphology Characterization in Boundary Layer Parametrization Using Multi-Resolution Analysis

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## Abstract

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 \(z_{0}\) and zero-plane displacement \(d\). 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 *approximation*s were deduced for the building height \(\bar{{H}}\) and planar packing density \(\lambda _\mathrm{p}\). A spatially-varying characterization with a scale-adaptive capacity is obtained for the boundary-layer parameters (aerodynamic roughness length \(z_{0}\) and zero-plane displacement \(d\)) 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.

## Keywords

Building morphology Multi-resolution analysis Multi-scale sampling Multi-scale/multi-resolution numerical weather prediction models Subgrid parametrizations## Notes

### Acknowledgments

The authors wish to acknowledge Dr Michael J. Brown from Los Alamos National Laboratory for providing access to the urban building data of Oklahoma City. M. Neophytou also acknowledges Dr Jason Ching (formerly at U.S.-EPA now at NCAR) for stimulating discussions as well as the financial support by the Cyprus Research Promotion Foundation through the research project contract ANABA\(\Theta \)MI\(\Sigma \)H/\(\Pi \)A\(\Gamma \)IO/0308/33.

## Supplementary material

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