FIG. 1. Dimensionless factor K(x, t) that determines the shape of the diurnal cycle of surface heating depending on the orientation of the valleys and the accompanying topographic effects on solar radiation in the (left) S-N and (center) E—W valleys, and (right) differences of K(x, t) between both valleys. The domain of the simulations is 25600 m in the x direction (horizontal coordinate across the valley), 6400 m in the y direction (horizontal coordinate along the valley), and 6400 m in the z direction (vertical co- ordinate). The horizontal grid is uniform and has a resolution of 50m, and the vertical grid is set with terrain-following coordinates stretched with a mini- mum gridcell size of 25 m at the surface and a maximum gridcell size of 121m at the top of the simulation do- main. Although idealized, the topography is loosely based in a reference urban valley, the Aburra valley in the Colombian Andes, where urbanization has been progressing rapidly and the urban area (Medellin city and its neighboring cities) has expanded beyond the valley floor toward the sidewalls, and it is represented by the function (Rampanelli et al. 2004) where z(x) is the height of the terrain above the valley floot (m), / is the maximum depth of the valley (4 = 2000 m). Xo is the x coordinate of the center of the valley (x) = 12.800 m), s, is the width of the sidewalls (s, = 8000 m), and v, is the half-width of the valley floor (v, = 2000m) Equation (3) represents a symmetrical cross section It is important to bear in mind that we are not con- sidering any spatial heterogeneity such as that caused by intraurban variations of pollution (Wilson et al. 2005) and surface energy fluxes (Offerle et al. 2006), which are still very complex issues that are strongly dependent on the particularities of each city. There- fore, we regard our assumption of intraurban homo- geneity as the simplest possibility, although other assumptions may be raised as well. Neither chemical reactions nor the radiative effects of pollutants in the atmosphere are considered, and we do not include moisture in our simulations at this stage. The presence of moisture will play a complex role in conditioning the constant along the y direction. In addition, two 2800-m- length plateaus are included in the modeling domain to have the lateral boundaries far from the top of the sidewalls. The average steepness of the sidewalls is 25%, and the transitions between them and the plateaus and the valley floor are smooth to prevent abrupt changes in wind direction. FIG. 2. Consecutive differences between the longitudinal mean fields of the cross-valley (0) potential temperature in the S—N and E-W valleys: (top left) 0700 to (bottom right) 1700 LST. Isolines are shown every 0.04 K; negative and positive contours are black and orange, respectively. The black triangles in the outline of the orography mark the edges of the urban area. FIG. 3. Vertical 6 profiles taken every hour from 0600 to 1800 LST in the (a)-(c) S—N and (d)-(f) E-W valleys, at (left) the left sidewall, (center) the midvalley, and (right) the right sidewall. Profiles in the sidewalls are taken along the slope (i.e., they are pseudovertical). In all panels, profiles evolve in time from the initial inversion profile to the left to the final well-mixed condition to the right. FIG. 4. Consecutive differences between the 6 profiles in the S-N and E—W valleys (a)-(c) during the morning (from 0600 to 1200 LST) and (d)-(f) during the afternoon (from 1200 to 1800 LST). Differences are shown for the profiles in the center of the valley as well as in the left (west-south) and right (east-north) sidewalls. Each panel shows the hourly differences (gray lines) and the 6-h time average (black line). The dashed line indicates the zero difference value. “1G. 5. Time-height variation of the 6 profiles in the (a)-(c) S—N and (d)-(f) E-W valleys, at (left) the left sidewall, (center) the midvalley, and (right) the right sidewall. Isolines are shown every 1K. FIG. 6. Time variation of the differences between the 6 profiles in the S-N and E-W valleys, at (left) the left sidewall, (center) the midvalley, and (right) the right sidewall. Isolines are shown every 0.04K; negative and positive contours are black and orange, re- spectively. FIG. 7. Consecutive differences between the 6 profiles in the center and along the sidewalls of the (a),(b) S-N and (c),(d) E-W valleys. Each panel shows the hourly differences (gray lines) and the 12-h time average (black line). The dotted line indicates the zero difference value. FIG. 8. Consecutive longitudinal mean fields of the cross-valley w in the (left) S-N and (center) E-W valleys, and (right) difference between both valleys: from 0700 to 1700 LST. Isentropes are shown every 1 K. Contours for differences are every 0.1ms7'. The blac triangles in the outline of the orography mark the edges of the urban area. Fic. 10. As in Fig. 8, but for resolved TKE. Contours for differences are every 0.08m’s~”. Fic. 12. Schematic of the evolution in time of the flow field associated with the tracer dis- tribution for (left) S—N and (right) E—W valleys: from 0700 to 1700 LST. Arrows indicate mean flow and turbulent eddies. The shading indicates the tracer mixing ratio as in Fig. 11. Isentropes are shown every 1K.
