A scale-dependent dynamic subgrid model based on Lagrangian time averaging is proposed and tested in large eddy simulations ͑LES͒ of high-Reynolds number boundary layer flows over homogeneous and heterogeneous rough surfaces. The model is based on the Lagrangian dynamic Smagorinsky model in which required averages are accumulated in time, following fluid trajectories of the resolved velocity field. The model allows for scale dependence of the coefficient by including a second test-filtering operation to determine how the coefficient changes as a function of scale. The model also uses the empirical observation that when scale dependence occurs ͑such as when the filter scale approaches the limits of the inertial range͒, the classic dynamic model yields the coefficient value appropriate for the test-filter scale. Validation tests in LES of high Reynolds number, rough wall, boundary layer flow are performed at various resolutions. Results are compared with other eddy-viscosity subgrid-scale models. Unlike the Smagorinsky-Lilly model with wall-damping ͑which is overdissipative͒ or the scale-invariant dynamic model ͑which is underdissipative͒, the scale-dependent Lagrangian dynamic model is shown to have good dissipation characteristics. The model is also tested against detailed atmospheric boundary layer data that include measurements of the response of the flow to abrupt transitions in wall roughness. For such flows over variable surfaces, the plane-averaged version of the dynamic model is not appropriate and the Lagrangian averaging is desirable. The simulated wall stress overshoot and relaxation after a jump in surface roughness and the velocity profiles at several downstream distances from the jump are compared to the experimental data. Results show that the dynamic Smagorinsky coefficient close to the wall is very sensitive to the underlying local surface roughness, thus justifying the use of the Lagrangian formulation. In addition, the Lagrangian formulation reproduces experimental data more accurately than the planar-averaged formulation in simulations over heterogeneous rough walls.

Cities are well known to be hotter than the rural areas that surround them; this phenomenon is called the urban heat island. Heat waves are excessively hot periods during which the air temperatures of both urban and rural areas increase significantly. However, whether urban and rural temperatures respond in the same way to heat waves remains a critical unanswered question. In this study, a combination of observational and modeling analyses indicates synergies between urban heat islands and heat waves. That is, not only do heat waves increase the ambient temperatures, but they also intensify the difference between urban and rural temperatures. As a result, the added heat stress in cities will be even higher than the sum of the background urban heat island effect and the heat wave effect. Results presented here also attribute this added impact of heat waves on urban areas to the lack of surface moisture in urban areas and the low wind speed associated with heat waves. Given that heat waves are projected to become more frequent and that urban populations are substantially increasing, these findings underline the serious heat-related health risks facing urban residents in the twenty-first century. Adaptation and mitigation strategies will require joint efforts to reinvent the city, allowing for more green spaces and lesser disruption of the natural water cycle.

Urban heat islands (UHIs) exacerbate the risk of heat-related mortality associated with global climate change. The intensity of UHIs is known to vary with population size and mean annual precipitation but a unifying argument is missing, and geographically targeted guidelines for heat mitigation remain elusive. Here we analyze urban-rural surface temperature differences (∆T s) worldwide and find a nonlinear increase of ∆T s with precipitation that is controlled by water/energy limitations on evapotranspiration and that modulates the scaling of ∆T s with city size. We introduce a coarse-grained model linking population, background climate, and UHI intensity and we show that urban-rural changes in evapotranspiration and convection efficiency are the main determinants for warming. The direct implication of these nonlinearities is that mitigation strategies aimed at increasing green cover and albedo are more efficient in dry regions, while cooling tropical cities is a challenge that will require innovative solutions.

Mitigation of the urban heat island (UHI) effect at the city-scale is investigated using the Weather Research and Forecasting (WRF) model in conjunction with the Princeton Urban Canopy Model (PUCM). Specifically, the cooling impacts of green roof and cool (white/highalbedo) roof strategies over the Baltimore-Washington metropolitan area during a heat wave period (7 June-10 June 2008) are assessed using the optimal set-up of WRF-PUCM described in the companion paper by Li and . Results indicate that the surface UHI effect (defined based on the urban-rural surface temperature difference) is reduced significantly more than the near-surface UHI effect (defined based on urban-rural 2 m air temperature difference) when these mitigation strategies are adopted. In addition, as the green and cool roof fractions increase, the surface and near-surface UHIs are reduced almost linearly. Green roofs with relatively abundant soil moisture have comparable effect in reducing the surface and near-surface UHIs to cool roofs with an albedo value of 0.7. Significant indirect effects are also observed for both green and cool roof strategies; mainly, the low-level advection of atmospheric moisture from rural areas into urban terrain is enhanced when the fraction of these roofs increases, thus increasing the humidity in urban areas. The additional benefits or penalties associated with modifications of the main physical determinants of green or cool roof performance are also investigated. For green roofs, when the soil moisture is increased by irrigation, additional cooling effect is obtained, especially when the 'unmanaged' soil moisture is low. The effects of changing the albedo of cool roofs are also substantial. These results also underline the capabilities of the WRF-PUCM framework to support detailed analysis and diagnosis of the UHI phenomenon, and of its different mitigation strategies.

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