Equations for the Drag Force and Aerodynamic Roughness Length of Urban Areas with Random Building Heights

We use a conceptual model to investigate how randomly varying building heights within a city affect the atmospheric drag forces and the aerodynamic roughness length of the city. The model is based on the assumptions regarding wake spreading and mutual sheltering effects proposed by Raupach (Boundary-Layer Meteorol 60:375-395, 1992). It is applied both to canopies having uniform building heights and to those having the same building density and mean height, but with variability about the mean. For each simulated urban area, a correction is determined, due to height variability, to the shear stress predicted for the uniform building height case. It is found that u (*)/u (*R) , where u (*) is the friction velocity and u (*R) is the friction velocity from the uniform building height case, is expressed well as an algebraic function of lambda and sigma (h) /h (m) , where lambda is the frontal area index, sigma (h) is the standard deviation of the building height, and h (m) is the mean building height. The simulations also resulted in a simple algebraic relation for z (0)/z (0R) as a function of lambda and sigma (h) /h (m) , where z (0) is the aerodynamic roughness length and z (0R) is z (0) found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.

Runoff Water Quality and Pollutant Mass Loads From Extensive Green Roofs

Green roof mitigation of volume and peak flow-rate of stormwater runoff has been studied extensively. However, due to the common practice of green roof fertilization, there is the potential for introduction of nutrients into local bodies of water. Therefore, this study compares green roof runoff quality with the water quality of precipitation and runoff from a bare shingle roof. The runoff from a demonstration-scale extensive green roof was analyzed during the summer of 2011 for its effect on runoff volume and analyzed during eleven storm events in the fall and winter for concentrations of copper, cadmium, zinc, lead, nitrogen species, total nitrogen, total organic carbon, sulfate, orthophosphate, and other monovalent and divalent ions. The green roof reduced the overall volume of runoff and served as a sink for NO3 - and NH4 +. However, the green roof was also a source for the pollutants PO4 3-, SO4 2-, TOC, cations, and total nitrogen. Metals such as zinc and lead showed trends of higher mass loads in the bare roof runoff than in precipitation and green roof runoff, although results were not statistically significant. The green roof also showed trends, although also not statistically significant, of retaining cadmium and copper. With the green roof serving as a source of phosphorous species and a sink for nitrogen species, and appearing to a retain metals and total volume, the life cycle impact analysis shows minimum impacts from the green roof, when compared with precipitation and bare roof runoff, in all but fresh water eutrophication. Therefore, the best environments to install a green roof may be in coastal environments.