Solar potential scaling and the urban road network topology

We explore the scaling of cities' solar potentials with their number of buildings and reveal a latent dependence between the solar potential and the length of the corresponding city's road network. This scaling is shown to be valid at the grid and block levels and is attributed to a common street length distribution. Additionally, we compute the buildings' solar potential correlation function and length in order to determine the set of critical exponents typifying the urban solar potential universality class.

Figure 1

The base 10 logarithm of Eq. (2), shown in blue, is fitted to the city's potential and the total road network length with $R^2=0.9437$ and a $p$ value $=2.814\times {10}^{-6}$.

Figure 2

Grids of varying sizes are intersected with the road network to each of which corresponds a road network length, a number of buildings, and a total enclosed solar potential are shown in (a)–(d), whereas (e) shows the city's blocks.

Figure 3

The base 10 logarithm of $\widehat{P}$ plotted against the base 10 logarithms of the city's road network length, the grids, and the blocks shown in blue, orange, and green, respectively.

Figure 4

The distance is defined as the shortest path joining the source and destination points along the transportation network shown in red.

Figure 5

The buildings' power correlation function is plotted against their corresponding pairwise distances; the shape preserving splines which fit the data are shown in blue.

Figure 6

The buildings' size correlation function is plotted against their corresponding pairwise distances where the city's topography is not accounted for; the shape preserving splines which fit the data are shown in blue.

Figure 7

The buildings' size correlation function is plotted against their corresponding pairwise distances with the building's elevation taken from sea level. The shape preserving splines which fit the data are shown in blue. The inset shows a scatter plot of the buildings' solar power correlation $C_{\mathrm{solar}\mathrm{power}}$ as a function of the buildings' size correlation $C_{\mathrm{building}\mathrm{size}}$ with elevation taken from sea level.

Figure 8

The clusters' centroids overlaid on the Beirut map.