Distributions of CO\(_2\) and PM2.5 Emissions from Cities Scale with Population Size

To study the scaling of urban CO\(_2\) and PM2.5 emissions with population in Europe, we consider the Edgar emission database [23, 24] and aggregate it over Local Administrative Units (LAU), using the population size for each city reported in the LAU data. We consider data relative to the year 2018 for which data is available for both CO\(_2\) and PM2.5 emissions. Population sizes and CO\(_2\) emissions are broadly distributed and highly heterogeneous across Europe as illustrated by mapping the \(\log \) of population P and CO\(_2\) emission \(E_}\) (Fig. 1a and b) and by inspecting the distributions of population size and CO\(_2\) emissions of European cities (Fig. S1). The relation between CO\(_2\) emission E and population size P is plotted in Fig. 1c using a double logarithmic scale. We also plot the conditional expectation value of the CO\(_2\) emission for a given population size \(\langle E_}|P\rangle \) which grows as a power law \(P^\beta \), with \(\beta =0.81\). This value is slightly different from the value obtained by fitting all the data (\(\beta _0=0.7\)). The difference is due to the large fluctuations in emissions observed among cities with similar population sizes.

Fig. 1

Scaling of CO\(_2\) emission with urban population. (a) Map of the population values of European urban areas. (b) Map of CO\(_2\) emissions (as logarithm of the number of tons) of European urban areas. (c) Relation between the logarithms of CO\(_2\) emissions (E CO\(_2\)) and population (P), including the expectation value \(\langle E|P \rangle \) ithe fit with \(P^\beta \), with \(\beta =0.81\). Notice that the fit is performed only over the linear part of the curve. We also report the power law fit over all the data, yielding \(\beta _0=0.7\). (d) Data collapse of the conditional distributions of CO\(_2\) emissions at fixed population using \(\beta =0.81\). Data from GISCO-EUROSTAT and EDGAR (v8.0) for the year 2018

A better characterization of the relation between CO\(_2\) emissions and population sizes can be obtained by considering multi-parameter scaling functions. In particular, we evaluate the conditional distribution of CO\(_2\) emissions for a given population size \(\rho (E_}|P)\) and assume that it obeys a scaling function

$$\begin \rho (E_}|P) = P^ \mathcal (E_} P^). \end$$

(2)

The simple form of the scaling function is dictated by normalization of the conditional distribution as can be shown as follows. Consider a generic scaling function for the conditional distribution of two variables x and y, \(\rho (x|y)= y^ f(xy^)\). Normalization implies that \(\int _0^\infty \rho (x|y)dx= \int _0^\infty y^ f(xy^) dx = 1\). Changing variables as \(z=xy^\), we obtain \(y^\int _0^\infty f(z) dx = 1\) which can be only be satisfied if \(a=b\).

Rescaling the measured conditional distributions according to Eq. 2 with \(\beta =0.81\) provides a good data collapse, as illustrated in Fig. 1d. The data collapse also shows that the scaling function has a broad support, indicating that for a given population size CO\(_2\) emission can vary over a range of several order of magnitudes. This implies that the impact of population size on CO\(_2\) emissions is expected to vary from city to city across Europe so that urban scaling only applies on average. This is confirmed by plotting the relation between emission and population size for cities belonging to individual European countries. Estimates of the scaling exponents obtained by fitting separately by country fluctuate considerably (Fig. S2).

To check the robustness of our results, we also consider data from the OpenGHGMap model which reports CO\(_2\) emissions for 108,000 European cities for the year 2018. Plotting in a double logarithmic scale the emission and population for each city reveals a power law behavior with an exponent \(\beta =0.87\) when considering the conditional mean and \(\beta _0=1.2\) when considering all the data (Fig. S3).

Next, a similar analysis is repeated in the case of PM2.5 emission data from the Edgar database. Also in this case, we aggregate emission data into administrative boundaries and study the dependence of emissions on population sizes. The results are summarized in Fig. 2. The distribution across Europe of PM2.5 is heterogeneous with clear peaks in correspondence to large cities (Fig. 2a), emission and population size are related by a power law with exponent \(\gamma =0.72\) that in this case has limited dependence on the way the fit is made, either on the whole data set or on the conditional average (Fig. 2b).

Fig. 2

Scaling of PM2.5 emissions with urban population. (a) Map of PM2.5 emissions (as logarithm of the number of tons) of European urban areas. (b) Relation between the logarithms of PM2.5 emissions (E PM2.5) and population (P), including the expectation value \(\langle E|P \rangle \) and the fit with \(P^\gamma \), with \(\gamma =0.72\). (c) Data collapse of the conditional distributions of PM2.5 emissions at fixed population. Data from GISCO-EUROSTAT and EDGAR (v6.1) for the year 2018

Finally, it is possible to collapse the conditional distributions of PM2.5 emissions at given population size according to the scaling law

$$\begin \rho (E_}|P) = P^ \mathcal (E_} P^), \end$$

(3)

where \(\mathcal \) is a broad scaling function spanning several decades (Fig. 2c).

PM2.5 Concentration Is Only Weakly Dependent on Population

Having analyzed PM2.5 emissions in Europe over a year, we also consider PM2.5 concentrations in the air for European cities over the same period. Simple inspection of Fig. 3a shows that while PM2.5 emissions are extremely heterogeneous geographically (Fig. 2a), concentrations are instead varying more smoothly, with extended proximal areas with similar values of the concentration. When we inspect the relation between PM2.5 concentration and population size, we find only a weak interdependence within very large fluctuations among different cities (Fig. 3b). The conditional mean of PM2.5 concentration at fixed population size scales as a power law \(\langle C|P \rangle \sim P^\delta \) with a small exponent \(\delta =0.08\) only for cities with population less than 10,000 and is independent of population size for larger cities (Fig. 3b). For small cities (\(P<10,000\)), it is still possible to collapse the conditional distributions using

$$\begin \rho (C|P) = P^ \mathcal (C P^), \end$$

(4)

with \(\delta =0.08\). The variations in concentration among cities with the same population are dependent on the country and so does the fitted exponent (Fig. S4). A summary of the estimates of the estimated values of the exponents obtained from conditional expectation values and from all the data (i.e., \(\beta \), \(\beta _0\), \(\gamma \), \(\gamma _0\), \(\delta \) and \(\delta _0\)) is reported in Fig. S5.

Fig. 3

Scaling of PM2.5 concentration with urban population. (a) Map of PM2.5 emissions (as concentration in \(\mu \)g/m\(^3\)) of European urban areas. (b) Relation between the logarithms of PM2.5 concentration (C PM2.5) and population (P), including the expectation value \(\langle C|P \rangle \) and the fit with \(P^\alpha \), with \(\alpha =0.08\). Cities are colored according to the country they belong. (c) Data collapse of the conditional distributions of PM2.5 concentrations at fixed population with \(\alpha =0.08\). Data from GISCO-EUROSTAT and EEA for the year 2018

Urban Emissions Are Multifractal While Pollution Is Not

Given the observed geographical variability in the urban emission and pollution scaling laws, we perform a multifractal analysis [30] of population P, CO\(_2\) and PM2.5 emission (\(E_}\) and \(E_}\)), and PM2.5 concentration C by aggregating them over grids of variable sizes b (Fig. 4a) and then computing the partition function as discussed in the method section. In all cases considered, the partition function scales as a power law with the cell size, \(Z_q(b) \sim b^\) (Fig. S7), defining a set of exponents for the moments \(\tau (q)\), reported in Fig. 4b. For non-multifractal measures on a regular fractal support, the moments exponents should scale as \(\tau (q)=D(q-1)\) where D is fractal dimension of the support, while for a multifractal measure \(\tau (q)\) is a non-linear function of q. The moment exponents for the concentration of PM2.5 follows closely the line \(\tau (q)=2(q-1)\) which indicates that this measure is not multifractal and has a compact support (\(D=2\)). On the other hand, all the other measures reveal multifractal scaling since they deviate from a straight line. As a consequence of this, the Renyi dimension, defined as \(D_q = \tau (q)/(q-1)\) and reported in Fig. 4c, varies with q, with the exception of the one associated with the PM2.5 concentration that is approximately constant.

Fig. 4

Population and emission distributions are multifractal. (a) Illustration of the box counting method in which a measure, in this case PM2.5 emission, is aggregated at different scales. (b) Multifractal scaling exponents \(\tau (q)\) for population, CO\(_2\), PM2.5 emission and concentration. The prediction for non-fractal exponents \(\tau (q)=2(q-1)\) is reported for reference and agrees well with the exponents for PM2.5 concentrations. (c) The corresponding Renyi dimensions \(D_q\). (d) The multifractal spectra for population, CO\(_2\), PM2.5 emission and concentration. Data from GISCO-EUROSTAT, EDGAR (V8.0 and v6.1) and EEA for the year 2018

A non-linear q dependence of \(\tau (q)\) indicates that there is a spectrum of scaling exponents over the study area or in other words that \(\mu _i(b) \sim b^\alpha _i\) for \(b\rightarrow 0\), where \(\alpha _i\) depends on the cell location. The multifractal spectrum (\(\alpha \), \(f(\alpha )\)), estimated as described in the method section, is reported in Fig. 4d. The function \(f(\alpha )\) is the fractal dimension of the set described by the scaling exponent \(\alpha \).

Fig. 5

The role of forests in offsetting CO\(_2\) emissions. (a) The fraction of land covered by forest at the regional level (NUTS2). (b) Quantity of CO\(_2\) removed from the atmosphere by forests per country. (c) Fraction of CO\(_2\) emitted removed by forests for each region. (d) Balance of CO\(_2\) for each region, considering the differences between total emissions and removal from forests. Data from EUROSTAT land cover and the annual European Union greenhouse gas inventory [29]

Emission and Pollution in Major European Cities

Given that urban scaling laws are geographically dependent, it is interesting to investigate the relations between emission and pollution in major cities across Europe. To this end, we consider here cities with a population size larger than 700,000 and study how CO\(_2\) and PM2.5 emissions, \(E_}\) and \(E_}\) are related. To correct for the observed population scaling, we normalize the emission variables according to the mean population scaling, using the rescaled variables \(\tilde_c=E_}/P^\beta \) and \(\tilde_p=E_}/P^\gamma \). The two rescaled variable are not significantly correlated (Persson correlation coefficient \(r=0.25\), \(p=0.2\), see Fig. S8a). We next consider the correlation between PM2.5 emission \(E_}\) and PM2.5 air concentration C. In this case, the concentration of PM2.5 is not rescaled since its average value does not depend on the population for large cities (Fig. 3). In this case, we observe a significant correlation between \(\tilde_p\) and C (\(r=0.49\), \(p=0.016\)). As shown in Fig. S8b, several cities depart from this correlation: cities in northern Italy, like Milan and Turin, have relatively low PM2.5 emission but large PM2.5 concentrations, while Stockholm displays relatively large PM2.5 emissions but low PM2.5 concentrations are recorded. One can explain this observation by geographical consideration: when comparing the map of air concentration with the corresponding elevation map, we see that regions enclosed by mountains such as northern Italy or southern Poland, display very high PM2.5 concentrations (Fig. S9).

Fig. 6

Impact of respiratory diseases in Europe. Map of standardized death rate for (a) lung cancer, (b) acute lower respiratory infections, and (c) chronic obstructive pulmonary disease. Map of population attributable fraction (PAF) to PM2.5 exposure for (d) lung cancer, (e) acute lower respiratory infections, and (f) chronic obstructive. Data from EUROSTAT causes of death database

Role of Forests in Offsetting CO\(_2\) Emissions

The values of CO\(_2\) emissions that we have analyzed do not account for the capture of CO\(_2\) from vegetation and forests. About 30% of European land is covered by forest which thus contribute to offset part of the CO\(_2\) that is emitted. The distribution of forest land is heterogeneous as it is illustrated in Fig. 5a showing the fraction of land covered by forests at regional level, according to the NUTS2 classification. According to the Annual European Union greenhouse gas inventory 1990-2019 [29] in 2018, European forests (including the UK) were estimated to capture a total of 285 million tons of CO\(_2\) representing less than 7% of the CO\(_2\) emitted in the same year in Europe.

Since forest coverage is not uniform throughout Europe, we analyze the amount of CO\(_2\) captured by forests at the country level and find that not surprisingly this value is proportional to the forest area in each country (Fig. 5b). We then estimate the fraction of CO\(_2\) emission that is offset by forests at regional level (Fig. 5c). In most regions, the fraction is less than 10% and it is larger only in a few lowly populated areas. We also compute the CO\(_2\) balance in each region, defined as the difference between emitted and captured CO\(_2\) (Fig. 5d). In all regions with the exception of northern Finland, the balance is positive with more CO\(_2\) emitted than captured. Finally, we also investigate if increasing forest land could have a significant impact in offsetting CO\(_2\) emissions. According to our estimates, even if the entire European land area would be covered by forest, only 30% of the emitted CO\(_2\) would be captured.

Health Impact of PM2.5 Pollution in European Cities

Since long-term exposure to PM2.5 is a known risk factor for several respiratory diseases, we analyzed the mortality due to lung cancer, chronic obstructive pulmonary diseases (COPD) acute lower respiratory infections (ALRI) across Europe at the regional (NUTS2) level (Fig. 6a, b, c). We then used data on PM2.5 concentration to estimate the population attributable fraction (PAF) to PM2.5 exposure or each of these diseases at regional level (Fig. 6a, b, c). The estimate was performed assuming that a long-term concentration of PM2.5 over the year which is equal to the concentration measured in 2018. In reality, however, the PM2.5 concentration decreased in most countries over the past 20 years (Fig. S10a) and therefore the estimated PAF should be considered as a lower bound. The reduction of the PM2.5 concentration in the air across Europe, as well as another important risk factor such as smoking which is also decreasing (Fig. S10b), is likely to be responsible for an observed general decrease in lung cancer mortality (Fig. S10c).