One-dimensional urban models embedded in mesoscale numerical models may place several grid points within the urban canopy. This requires an accurate parametrization for shear stresses (i.e. vertical momentum fluxes) including the dispersive stress and momentum sinks at these points. We used a case study with a packing density of 33% and checked rigorously the vertical variation of spatially-averaged total shear stress, which can be used in a one-dimensional column urban model. We found that the intrinsic spatial average, in which the volume or area of the solid parts are not included in the average process, yield greater time-spatial average of total stress within the canopy and a more evident abrupt change at the top of the buildings than the comprehensive spatial average, in which the volume or area of the solid parts are included in the average.
Keywords: Comprehensive spatial average; Effective total shear stress; Intrinsic spatial average; One-dimensional column urban model; Vertical momentum flux.