Assessment of green roof incentive policies in European cities by a fractal analysis
Authors: Versini Pierre-Antoine , Gires Auguste , Tchiguirinskaia Ioulia , Schertzer Daniel 
Published: March 2020

&lt;p&gt;Green roofs represent a market of several tens millions of m&lt;sup&gt;2&lt;/sup&gt; implemented every year in Europe. They appear to be particularly efficient to reduce the potential impact of new and existing urban developments by making the city &amp;#8220;greener&amp;#8221; and more resilient to climate change. Indeed, they provide several ecosystem services, particularly in stormwater management, urban heat island attenuation, and biodiversity conservation. For these reasons, municipalities are implementing specific policies to promote a large diffusion of green roofs on their territory. Nevertheless, to optimize their performances through urban scales, green roofs spatial distribution should be analysed.&lt;/p&gt;&lt;p&gt;In order to study the current green roof implementation and to assess the relevancy of the related policies, a multi-scale analysis based on fractal theory as been conducted. Such analysis, widely used in geophysics, is particularly suitable to characterize spatial fields exhibiting strong heterogeneity over wide range of scales. This fractal analysis was performed here to characterize the spatial distribution of green roofs in several European cities (London, Amsterdam, Geneva, Lyon, Paris, Berlin, Frankfort, Copenhagen, Oslo&amp;#8230;). These cities have been chosen because: (i) GIS database containing the location and geometry of implemented green roofs is available, (ii) they have implemented various kind of green roofs policies.&lt;/p&gt;&lt;p&gt;The results show that every studied city depicts similar behaviour with the definition of three distinct scaling regimes. The second regime (between 16/32 and 512/1024 m) characterizes not only single roofs but their distribution in space which is what we are interested in. The fractal dimension charactering this regime is the most variable, ranging from 0.50 to 1.35 and illustrates some different degrees of progress in urban greening. It has to be noticed that the more ambitious incentive measures (where monetary subsidies are proposed) correspond to the cities characterized by the highest fractal dimension. Nevertheless, as these policies are relatively recent, they cannot completely explain the current green roof distribution (architectural history has also to be mentioned).&lt;/p&gt;&lt;p&gt;The obtained results demonstrate some significant inconsistencies between political ambition and their in situ realization. They illustrate the necessity to better take into account the spatial distribution of green roof implementations in order to optimize their performances. To provide ecosystem services at large scales, green roofs have to be widely and relevantly implemented. Fractal analysis can be seen as innovative multi-scale approach to adjust policies for this purpose.&lt;/p&gt;&lt;p&gt;This work has been made thanks to ANR EVNATURB project (https://hmco.enpc.fr/portfolio-archive/evnaturb/) and the Academic Chair &amp;#8220;Hydrology for Resilient Cities&amp;#8221;, a partnership between Ecole des Ponts ParisTech and the Veolia group.&lt;/p&gt;