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Climate change and the urban heat island effect threaten the sustainability of rapidly growing urban settlements and urban population worldwide1. Such threats may be ameliorated by the ecosystem service of local climate regulation provided by green–blue urban areas (natural, restored, or (re)constructed ecosystems, such as forested land, wetlands, parks)2,3,4. The spatiotemporal relationships existing between natural ecosystems and human societies form the basis of the ecosystem service framework, used to represent such benefits from nature to human well-being5,6. Areas of ecosystem service provision (nature contribution of some supply) and ecosystem service use (human beneficiaries with some ecosystem service demand) in a landscape are then often connected by some form of carrier flow, which can be natural (air and water movement) or depend on human-made infrastructure (e.g., pipelines for water, road network and vehicles for human movement)7,8. Additionally, ecosystem service relevance is scale-dependent, e.g., with carbon sequestration being globally relevant, while recreational areas provide mostly local and regional benefits9,10,11. Over each scale of relevance, it is essential to distinguish the supply and demand sides of spatial ecosystem services relationships2, and the degree to which potential supply (left, Fig. 1) can actually reach and fulfill some actual demand (right, Fig. 1). This may be referred to as the degree of realization of ecosystem service supply and demand12. Conceptually, we define a potential as the hypothetical maximum capacity for a service (supply) or need (demand). In contrast, a realized service quantifies the actual ecosystem service, after consideration of proper spatial flow connections between natural ecosystems and humans. For example, for a city, only part of its total potential ecosystem service demand (Pd) may be actually fulfilled (referred to as the realized ecosystem service demand, Rd, right in Fig. 1) by only part (the realized supply part, Rs, left in Fig. 1) of the city’s total potential ecosystem service supply (Ps). Thus, Rd measures the part of the human demand (for the ecosystem service) actually fulfilled, while Rd quantify the part of the supply used to provide the ecosystem service. The Methods section describes and discusses in further detail this and other term definitions used in the analysis, the relationships between terms, and the calculation methods employed to quantify them.Figure 1Spatial flow dependence of ecosystem services and studied city locations. Schematic of potential and realized supply and demand of flow-dependent ecosystem service (for explanation, see “Methods”).Full size imageIn practice, implementing the concept of ecosystem services into urban landscape management and decision making is still problematic5, with one reason being the challenge to link spatially disaggregated areas of service provision with the human beneficiaries13. In addition, considerable ambiguity still remains, conceptually and in practice, regarding the distinction and quantification of potential and realized ecosystem services supply and demand14. For example, without consideration of the spatial relationship between supply and demand (implicitly or explicitly), it becomes difficult to determine or quantify, in practice, if an actual ecosystem service exists. To contribute to its resolution, we here investigate the degree of supply and demand realization for the urban ecosystem service of local climate regulation using comparative quantitative indicators in and across 660 cities of different sizes and in different parts of Europe (Fig. 2).Figure 2Studied city locations. Map of the European study region and locations of the cities studied. See Supplementary Table 1 for further city data.Full size imageThe potential of green–blue urban areas for cooling cities is generally well established, and has been studied using direct observations15,16, remote sensing17 or modelling based approaches18,19. The regulation of local urban air temperatures by such areas can increase thermal comfort and decrease health risks related to urban heat island (UHI) effects20,21 for urban populations. The UHI effects relate to often-observed higher ambient air temperatures in urban environments compared to their close surroundings20,21. The spatial extents of cities in this study are then considered according to their respective administrative unit definitions.The investigation focuses on urban realization of this ecosystem service because the proportion of the global human population living in urban areas is steadily rising22, and cities are critical for both climate change mitigation and societal adaptation to warming23,24. For adaptation, cities need to handle exacerbated urban warming by UHI effects and provide livable environments for their residents while avoiding detrimental consequences from competing development interests25,26. The UHI effects emphasize the importance of local climate regulation as an essential urban ecosystem service, the actual realization of which depends on city function and form, with the latter including the spatial distribution of green–blue urban areas, as well as temporal changes in this by growing urbanization. The degree to which such growth leads to replacement of moist soils and vegetative cover with paved and impervious surfaces also affects urban surface energy and radiation balances27, and associated land surface temperatures at local human scale, although the relationship with air temperature is complex27. For example the proportion of vegetation in a particular area will regulate the resulting ratio of sensitive to latent heat flux (known as Bowen ratio), which will in turn affect properties of the urban climate27.In reality, a city’s climate consists of a variety of smaller-scale microclimates, which can be modified and leveraged through deliberate design20. This emphasizes the importance of good city planning28, including for conservation, restoration, and construction of new urban green–blue areas29,30. Such areas can provide various services to urban populations, e.g., urban flood mitigation12 and more general health31 and well-being32 benefits, including cooling required to mitigate UHI effects. The latter can be achieved, e.g., by enhanced latent heat flux associated with higher evapotranspiration from green areas and evaporation from blue areas. Through the flow of air and its lateral heat advection, green–blue urban areas can also cool surrounding built parts of the city that would commonly have a demand for such ecosystem service of local climate regulation2. How to measure and predictively quantify the zones of influence of such air cooling by green–blue areas is still a challenging research question, but such zones are reported to be in the range of several hundred meters29,33,34.The aim of the indicators developed and used in this study is to quantify actual realized urban ecosystem service supply in terms of its fulfillment of some actual demand for that ecosystem service of the urban human population. Over each city, such realization and associated indicator values depend both on local conditions (such as natural land-cover areas that can supply the considered ecosystem service) and overall urban form and spatial configuration of the natural and built areas in the urban landscape. At larger scales spanned by multiple cities (such as those over Europe studied in this paper, Fig. 2), the quantitative indicators can be used to detect main ecosystem service realization patterns, similarities and differences among cities. This is done by quantifying indicator statistics across the cities, and assessing ecosystem service realization patterns in terms of how these statistics depend on city characteristics, or associated country or sub-region characteristics, such as population density or socio-economic measures like Human Development Index (HDI) and GDP per capita.A few studies have evaluated spatial dependencies of ecosystem services35,36 and mostly focused on multiple services in a specific study area. Our comparative multi-city study aims instead at revealing possible overarching statistical patterns of the spatially dependent ecosystem service of local climate regulation, and its realization in and across European urban systems. While this urban ecosystem service is important per se, the dependence of its realization on spatial proximity to green–blue areas may also provide useful guidance for further study of other urban ecosystem services that depend on the spatial distribution of green–blue areas and their proximity to human needs within cities2,12,32.Previous multi-city explorations of urban socio-economic growth and human-made infrastructure have revealed and quantified various statistical cross-city patterns37,38,39. Our study hypothesizes that such patterns may also emerge in the cross-city statistics of ecosystem service realization indicators related to green–blue city areas and their provision to urban populations. Identification of such quantitative ecosystem service indicator patterns can increase fundamental understanding of urban ecosystem service conditions, as well as projection capabilities for changes in these conditions under city growth, e.g., in terms of population density, HDI, and GDP per capita.To explore and test the main study hypothesis, we compile and synthesize for all 660 European cities (Fig. 2) high-resolution datasets for city morphology (e.g., land cover) and bio-physical characteristics (e.g. degree of imperviousness, vegetation type and vegetation density), based on previous study reports of the relevance of these parameters for the ecosystem service of local climate regulation2,12, along with city-scale measures of human population, city area, and resulting population density ratio (Supplementary Table 1). Using these data, we evaluate and map total potential ecosystem service supply and demand in each city (Figs. 1, 2, Supplementary Figures 1–3, Methods), and further apply a model of radially decaying ecosystem service supply and demand realization at 20 m resolution (Supplementary Figure 2–3, Methods) to also account for the spatial influence reach of local climate regulation from each location in the city. Furthermore, for comparative multi-city analysis, we quantify a set of directly comparable ecosystem service realization indicators for each city (explained further below) and their resulting statistics across all 660 cities over Europe, and comparatively for cities in different European countries and sub-regions.Indicator definitions and calculationsFor each of the 660 cities, we consider and calculate two basic metrics of urban ecosystem service realization: the ratio of realized to potential ecosystem service supply (Rs/Ps), and the ratio of realized to potential ecosystem service demand (Rd/Pd). For each discretized city pixel within a city, we first calculate its local net potential ecosystem service supply (Ps) or demand (Pd) directly from the urban morphology and bio-physical data (Supplementary Figure 1). For each net supply pixel, we further calculate (as illustrated bottom right in Supplementary Figure 2) that pixel’s ecosystem service realized supply contributions to the surrounding net demand pixels within its spatial influence radius (top, Supplementary Figure 2). Analogously, for each net demand pixel, we calculate the contributions to fulfilling (realizing) its ecosystem service demand from the surrounding net supply pixels that have that net demand pixel within their spatial influence radius. For each pixel of any type, we thus calculate its realized ecosystem service supply Rs or demand Rd in relation to its potential net local supply Ps or demand Pd, respectively (Supplementary Figure 2; see also Supplementary Figure 3 and Supplementary Information for further calculation and mapping details). We further calculate comparative indicators of city-average relative realized ecosystem service supply and demand, Rs/Ps and Rd/Pd, respectively, from the sums of local Rs, Rd, Ps and Pd over all pixels in the city. The city-average supply indicator Rs/Ps thus quantifies the average degree of realized (actually used) ecosystem service supply from all green–blue areas over the whole city (left in Fig. 1). Analogously, the city-average demand indicator Rd/Pd quantifies the average degree of realized (actually fulfilled) ecosystem service demand over each city (right in Fig. 1). For further cross-city comparison, we also calculate indicators for how large area fraction of total city area has a relatively high degree of ecosystem service supply and demand realization, respectively. Local Rs/Ps ≥ 0.5 and Rd/Pd ≥ 0.5 are then selected as illustrative thresholds for such relatively high degree of ecosystem service supply and demand realization, respectively, with the area fractions calculated from the number of pixels with Rs/Ps ≥ 0.5 or Rd/Pd ≥ 0.5 relative to the total number of pixels in each city.Based on the power-law relationships with population density results found for both previous city-average and city-fraction indicators of ecosystem service realization, we also have an opportunity to project indicator values for future scenarios of changed population density, as$$r_{i} = frac{Ri}{{Pi}} = Ai cdot left( {PD} right)^{beta i} le 1$$
(1)
where index i = d represents demand and i = s supply. Furthermore, for city-average indicators, Ri and Pi represent realized and potential ecosystem service, respectively, while for area-fraction indicators, they represent city area with high degree of ecosystem service realization (≥ 0.5) and total city area, respectively. The constraint of (r_{i} le 1) is due to the upper limit of Ri ≤ Pi for both indicator types, with Ai the scale factor and βi the exponent of a power law relationship ri with population density (denoted PD). Based on Eq. (1), a relative measure of ecosystem service realization effectiveness can be estimated from the demand fulfillment ((r_{d})) relative to the supply use ((r_{s})), as:$$Effectiveness = frac{{r_{d} }}{{r_{s} }} = frac{{Ad cdot left( {PD} right)^{beta d} }}{{As cdot left( {PD} right)^{beta s} }} = frac{Ad}{{As}}PD^{{left( {beta d – beta s} right)}}$$
(2a)
with$$r_{d} = Ad cdot left( {PD} right)^{beta d} quad ifquad r_{d} le 1,,,,,r_{d} = 1quad otherwise$$
(2b)
$$r_{s} = As cdot left( {PD} right)^{beta s} quad if,r_{s} le 1,,,,r_{s} = 1quad otherwise.$$
(2c) More

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