Background and Objective:
Ecosystem Services (ES) are benefits that natural systems generate and contribute to human well-being. The study intends to map the supply and demand of an important ES for climate regulation, the cooling given by green infrastructures, in the province of Modena (northern Italy), in order to identify situations of spatial injustice.

Methods:
The cooling capacity given by green infrastructures (supply of ES) was calculated using the InVEST (Integrated Valuation of Ecosystem Services and Tradeoff) software, which calculates the heat mitigation index based on shading, evapotranspiration at albedo and distance from the green infrastructure. The characteristics of vulnerability to heat (demand of ES) considered were age over 80 or under 14, condition of fragility in old age, status of foreigner and low per capita income, obtained through demographic registers or surveillance systems. The cooling capacity given by green infrastructures and the heat vulnerability characteristics were achieved for each municipality in the province of Modena, thus building maps of the supply and demand of the ES.

Results:
The study shows the presence of a lower cooling capacity and, at the same time, a greater concentration of subjects more vulnerable to high temperatures, in the city center and in the flat municipalities, especially the most industrialized. The comparison between the supply and demand maps of ES highlights a situation of social injustice, in which the greatest demand is present in places where the climatic mitigation given by greenery is minimal and where summer heat waves occur.

Conclusion:
This study is a guide for policy makers for a correct urban redistribution and the implementation of nature-based solutions in areas where the demand is higher, using small-scale solutions (e.g. vertical greenery, green roofs) where there is no possibility to increase public green spaces.