The Relationship between On-Road FFCO 2 Emissions and Socio-Economic / Urban Form Factors for Global Cities: Signiﬁcance, Robustness and Implications

: Transportation accounts for 18% of global fossil fuel carbon dioxide (FFCO 2 ) emissions, especially in urban areas. An improved understanding of on-road FFCO 2 emissions is essential to both carbon science and mitigation policy. Previous studies have identiﬁed the driving factors and quantiﬁed their relationship to on-road FFCO 2 emissions. However, they have been primarily based on case studies conducted in individual cities, and the research results remain inconclusive due to the considerable heterogeneity of cities and associated outcomes. In order to achieve more general results and to further understand their uncertainties, this study explored the relationships between socio-economic / urban form data and self-reported on-road FFCO 2 emissions for a sample of global cities based on the adjusted Stochastic Impacts by Regression on Population, A ﬄ uence and Technology (STIRPAT) model. The robustness and sensitivity of these relationships was evaluated by introducing artiﬁcial errors, conducting cross-validation, and examining various model speciﬁcations. Results indicated that fuel economy ( p -value < 3.1 × 10 − 8 ), vehicle ownership ( p -value < 3.0 × 10 − 4 ), road density ( p -value < 4.4 × 10 − 3 ) and population density ( p -value < 3.1 × 10 − 3 ) were statistically signiﬁcant factors that correlate with on-road FFCO 2 emissions. Of these four variables, fuel economy and vehicle ownership had the most robust relationships. These results o ﬀ er potential policy insights into on-road FFCO 2 emissions mitigation in cities, in addition to o ﬀ ering a means to generate emissions estimates without detailed bottom-up information. methodology, Y.S. and K.R.G.; software, Y.S.; validation, Y.S.; formal analysis, Y.S.; investigation, Y.S.; resources, Y.S.; data curation, Y.S.; writing—original draft preparation, Y.S.; writing—review and editing, Y.S. and K.R.G.; visualization, Y.S.; supervision, K.R.G.; project administration, K.R.G.; funding acquisition, K.R.G. All read


Introduction
On-road transportation provides mobility and accessibility for people and enables the movement of freight, which is an essential part of the economic activity [1]. On-road fossil fuel carbon dioxide (FFCO 2 ) emissions often represent the largest single emitting sector in urban areas and account for 18% of the total FFCO 2 emissions worldwide [2]. In the US, on-road FFCO 2 emissions constitute 43% of the total FFCO 2 in major metropolitan areas [3]. This makes on-road FFCO 2 emissions one of the top priorities for greenhouse gas (GHG) mitigation in the urban domain.
Understanding the relationship between on-road FFCO 2 emissions and their driving factors is critical to both social science and urban policy. Many researches have investigated and identified relationships between certain socio-economic factors and transportation energy use. For example, Lakshmanan and Han [4] identified growth for travel demand, population, and gross domestic product (GDP) as the three most important factors related to transportation energy use and FFCO 2 emissions during 1970-1991 in the US. Cervero and Hansen [5] concluded that travel demand and road supply cause a mutually reinforcing feedback in which road investment induces travel and increasing travel  [11] cited these elasticities from previous studies at various places; b No units were provided for income and fuel demand by Eltony and Al-Mutairi [12]; c Espey [13] summarized this range of elasticities from previous studies at various places.
There is also an extensive literature on the relationship between on-road FFCO 2 emissions (or closely related variables) and aspects of urban form or "urban form factors". For example, whether a compact city form is more or less eco-efficient has been actively discussed in sustainability science. Newman and Kenworthy [11] found an inverse relationship between gasoline consumption and population density based on a database of global cities. Cervero & Landis [14] argued that a decentralized urban pattern undermines the public transit service and causes a mismatch in the job-housing balance, which indirectly encourages private driving and results in more VMT. Wang et al. [15] analyzed urbanization and on-road FFCO 2 emissions data in Beijing from 2000 to 2009 and found that the decentralization of Beijing had a strong aggravating impact on on-road FFCO 2 emissions due to the increasing commute distances and shifting travel mode to private cars instead of public transit.
There are other studies that suggest that compact cities may not be necessarily energy efficient. For instance, compact cities can induce traffic congestion, which lowers the fuel economy, resulting in added fuel consumption [16]. Compact cities may not necessarily reduce VMT because the lack of access to nearby open spaces induces leisure travel demand [17]. Many case studies also did not observe a significant relationship between increasing urban compactness and decreased transportation energy consumption. A case study in the Netherlands by Bouwman and Moll [18] found a 5% difference in the average personal transportation energy use across different urban spatial structures. They concluded that, at least in the Netherlands, the expected negative relationship between urban compactness and personal transportation energy consumption was not observed. In Britain, Echenique et al. [19] conducted scenario analyses on three regions based on travel demand models and found that the impact of the urban spatial structure on transportation energy consumption is negligible compared to other socio-economic factors and population growth.
As for the relationships between socio-economic factors and on-road FFCO 2 emissions, previous research also reported a wide range of elasticities between urban form factors and various on-road transportation measures (Table 2). Table 2.
Elasticities between urban form factors and transportation demand reported in previous research.

Previous Studies
Elasticity of Elasticity to Elasticity Value Study Area Cervero and Hansen [5] Lane Miles (Unit: lane-miles) Vehicle Miles Traveled (Unit: vehicle-miles) 0. 59 Counties in California, USA Barla et al. [9] Residential density (Unit: residences per km 2 ) Transportation GHG emissions (Unit: grams of CO 2 equivalent) −0.12 to −0.07 Quebec, Canada Hansen and Huang [20] Lane To sum up, previous studies on the relationship between socio-economic/urban form factors and transportation energy consumption or FFCO 2 -related emissions remain inconclusive due to limitations in the sample size (i.e., single city studies), differences in the precise metric examined and underlying model construction. Moreover, previous results also showed a wide range of elasticities of various determining factors to the environmental impact, possibly due to the heterogeneity of the study areas and data sources. This study, by contrast, aims to examine a large cross-section of cities at the global scale with a multivariate approach, to quantitatively estimate the relationships between FFCO 2 emissions and key socio-economic/urban form factors and assess their robustness.

Methods and Data
The study area considered in this research consists of a series of global cities. These cities were selected according to four criteria. First, they must cover a wide range of socio-economic and urban form characteristics to reduce the sampling bias. Second, they must have an area that is large enough for the calculation of certain urban form indices (such as population centrality). Third, they must be the industrial, financial or political center of the surrounding regions. Finally, they must have reported FFCO 2 emissions available in existing databases. Using data meeting these criteria from the World Bank, the C40 project and the Millennium City Database (MCD), 58 global cities (Appendix A Figure A1 and Table A1) were selected for this study [27][28][29].
The foundation of the analysis used here is the IPAT model relating environmental impact (I) to a multiplicative product of population (P), affluence (A) and technology (T) [30]. Through this form (I = P × A × T), the IPAT model describes the relationship among these variables as interdependent [31].
A weakness of the IPAT model is that it is a conceptual framework that cannot be tested or falsified. Dietz and Rosa [32,33] modified the IPAT model into the Stochastic Impacts by Regression on Population, Affluence and Technology (STIRPAT) model. A scaling factor was added, resulting in where a is the scaling factor, e is the error term and b, c and d are the exponents of P, A and T. This formula can be converted into a linear form with a log transformation.
This form allows quantitative analyses such as linear multiple regression to be performed and the results to be evaluated. Therefore, it can be used to test hypotheses regarding causal relationships.
Another weakness of the IPAT model is that it assumes that the relationship between I and each of the driving factors is proportional and monotonic, which may not be true in reality [31]. On the other hand, a STIRPAT model with exponential parameters allows non-proportional and non-monotonic relationships to be falsified [31]. However, limitations still exist for the STIRPAT model, as it assumes that there is no residual non-linearity after the log transformation.
Based on previous literature, this study uses on-road FFCO 2 emission data as the environmental impact (I); Population density to represent P; Affluence (A) is represented by per capita GDP; and a variety of socioeconomic/urban form factors to represent technology (T) in the STIRPAT model. The socio-economic/urban form factors included road density, road length per capita and population centrality, miles per gallon and vehicles owned per capita. These factors were chosen because of their correlations with the energy consumption in the previous literature. A summary of the regression variables and their sources is provided in Tables 3 and 4. Data quality was examined for all of the input variables. For example, the population density data had an 87.8% accuracy when validated by the United States census data [34]. Road network data, on average, had errors from ground truth amounting to less than 6 m in England [35] and France [36]. The on-road FFCO 2 emission data were collected from the C40 project [23] and the Millennium City Database [37]. There were no quantitative Sustainability 2020, 12, 6028 5 of 25 quality evaluations, but only qualitative descriptions for the remainder of the data. Additional details regarding the data sources and data uncertainties are included in Appendixes A.1-A.3. Table 3. Urban form and socio-economic variables used in this study and their references.
(2) Except for the area, all other variables have a coefficient of variation less than 1, which suggests that, compared to a standard normal distribution, these variables are more concentrated toward their means. This indicates that extreme values or outliers are more likely on the right side of the distribution. Combining the information provided by the skewness and the variation indicates that caution should be exercised when interpreting regression results for cities that are less centralized and more fuel-efficient.
We first performed a series of single linear regressions between each of the variables in Table 3 to briefly examine their correlations as well as exclude explanatory variables with potential multicollinearities. These single linear regressions were log-transformed, so that the slope coefficients could be interpreted as an elasticity, which describes the percentage change of one variable in response to the percentage change of another variable.
A series of regressions were then conducted by running an ordinary least square (OLS) regression on every possible combination of the independent variables. For each combination, the following items were calculated:

•
An adjusted R 2 of the regression equation; • A p-value for each independent variable; • A variance inflation factor (VIF) for the coefficient of each independent variable. VIF is calculated as 1/(1 − R i 2 ), where R i 2 is the coefficient of determination of a constructed regression equation with the corresponding independent variable i as a function of all the other independent variables. It is a factor that measures how much the variance of an estimated regression coefficient is increased because of collinearity with other independent variables; • The Semi-partial R-squared. This is calculated as R 2 − R i 2 , where R 2 is the coefficient of determination of the regression equation with the combination of all independent variables, and R i 2 is the coefficient of determination of the regression equation with the combination of all independent variables except variable i. This semi-partial R-squared value describes the amount of on-road FFCO 2 emission variation explained by the variation in the independent variable i while excluding the impacts from other independent variables (eliminating collinearity).
The final OLS regression model was chosen based on the following criteria: • All independent variables in the OLS regression model are statistically significant with a p-value less than 0.05; • All VIF values are less than 10 (according to [45], a VIF larger than 10 could be considered as having a high collinearity); • While satisfying the previous two criteria, the regression model with the highest adjusted R 2 was chosen.
This study conducted a 10-fold cross validation to assess the model's sensitivity. The 58 C40/MCD cities were split into 10 subsets. Cities were randomly chosen for each subset. For one round of cross-validation, one subset was held out, and the model was trained based on the rest of the subsets. The trained model was then used to predict values for the subset that was removed. The predicted values were then compared with the actual values for the removed subset to calculate errors. This procedure was repeated until all 10 subsets had been used as the validation set, yielding 10 sets of coefficients and errors. The whole cross-validation process was, again, repeated 10 times to obtain a distribution of 100 coefficients (10 re-sampling rounds repeated 10 times).
Besides data-resampling, another attempt to assess the model sensitivity is by examining model specifications. Neumayer and Plümper [46] believed that uncertainty in social science data analysis is caused more by improper model specifications than random sampling errors. They argued that: " . . . inferences become more valid if estimated results are sufficiently independent from the model specification, that is, if all plausible alternative specifications give similar results".
This study included seven socio-economic/urban form factors as independent variables in a multivariate regression. All possible combinations of these seven factors were regressed against per capita on-road FFCO 2 emissions. Thus, the number of different model specifications that contained a specific independent variable was 2 7 − 1 = 127 (the NULL model without any explanatory variables was not considered).
A further sensitivity assessment was conducted by adding the errors and observing the variation of the coefficients and the significance for each independent variable. An artificially introduced error was generated as a random sample from a normal distribution (assuming that, in real world, datasets have uncertainties that follow normal distribution) with mean = 1 and standard deviation = σ. This error was then applied to per capita on-road FFCO 2 emissions and the socio-economic/urban form factors to simulate their uncertainties. The new dataset with the artificial error was then used to train the regression model. The whole process was repeated 100 times and yielded 100 sets of coefficients for all independent variables.  Table 5 summarizes the single linear regression results among all variables in log-log form. The relationship between population density, PD, and on-road FFCO 2 emissions, E, exhibits a negative elasticity (slope = −0.26; p < 0.01; R 2 = 0.13). This is consistent with the previous literature, where increases in population density are correlated with declines in per capita on-road FFCO 2 emissions [9,47]. Previous research also found that PD had a significant relationship to vehicle ownership and vehicle use, while almost no relationship to fuel economy [25,26]. The single regression results here are consistent with those findings with an insignificant relationship (p < 0.21) between PD and fuel economy (miles per gallon -MPG), and a significant relationship (p < 0.01) between PD and vehicles owned per capita, VOPC. PD is positively correlated to road density, RD (slope = 0.42; p < 0.001; R 2 = 0.44). However, the elasticity is smaller than 1, meaning that for every 1% increase in PD there is a less than 1% increase in RD. There is a weak but significant relationship between PD and population centrality, PC (slope = 0.08; p < 0.01; R 2 = 0.11). This suggests that for larger values of PD, the population distribution is more centralized. However, the strength of the elasticity should not be over-interpreted because the correlation is weak. PD has a negative relationship to VOPC (slope = −0.36, p < 0.01, R 2 = 0.12). This supports the hypothesis of Karathodorou et al. [25] that urban density discourages people from purchasing vehicles.

Single Regression
For each pairwise regression, the slope coefficient, the R 2 (in parentheses) and the p-values (in brackets) are provided. Statistically significant values (p ≤ 0.05) are in red; insignificant values are in blue.
It is expected that MPG will be negatively related to E, and the single regression results indicate that it has the highest elasticity (−3.35) among all the variables. As such, MPG alone can explain 40% of the variation in per capita on-road FFCO 2 emissions. The relationship between MPG and PD is weak (R 2 = 0.03). Karathodorou et al. [25] arrived at the same conclusion. Their explanation was that population density has both positive and negative impacts on fuel economy. For example, high urban density limits parking space and encourages people to purchase smaller, potentially more fuel-efficient cars. However, high density can also lead to congestion, inducing less efficient "stop and go" driving.
PC has a positive relationship to E, which suggests that decentralized cities tend to have greater per capita emissions. This would support the theory that a sprawling urban form increases on-road per capita FFCO 2 emissions [14,48]. However, the correlation is not very significant (p-value = 0.09).
Both per capita GDP and VOPC have positive, large and significant relationships to E. However, per capita GDP and VOPC are highly correlated (R 2 = 0.68). This indicates that it is not proper to include both as explanatory variables in the multiple regression model due to multi-collinearity. Table 6 summarizes the statistically significant variables that were included in the multivariate regression model construction (adjusted R 2 = 0.68). A combination of fuel economy (represented by miles per gallon, MPG), vehicles owned per capita, road density and population density remain the best predictors of total per capita on-road FFCO 2 emissions in the sample of cities examined. Figure 1 illustrates the corresponding correlation result from the single regression and multiple regression for these predictors. The circles in Figure 1 represent the variations of the dependent variable (DV) and the independent variables (IV). The top row of Figure 1 illustrates the relationships between the DV and IV in a single regression model (while ignoring the impacts of other IVs); the bottom row illustrates the relationships between the same combination of DV and IV in the multiple regression model (while controlling the rest of the IVs).  The multivariate regression results indicate that the elasticity (−2.67) of MPG to per capita onroad FFCO2 emissions (E) was the largest among all explanatory variables. Moreover, MPG is least influenced when comparing its relationship within the single regression (R 2 = 0.4 when ignoring other factors) versus the multiple regression (semi-partial R 2 = 0.23 when controlling other factors) models. This suggests that MPG is relatively independent of other explanatory variables. Sensitivity analysis results also indicated that MPG has the most robust relationship to on-road FFCO2 emissions.

Multivariate Regression
Both the elasticity and explanatory power of VOPC decreased in the multiple regression model (elasticity = 0.25, semi-partial R 2 = 0.08) when compared to the single regression model (elasticity = 0.91, R 2 = 0.42). Although the GDP per capita (GDPPC) was assumed to represent the affluence factor in the IPAT model, it was excluded in the multivariate regression model in favor of VOPC. This was due to the fact that there is a high correlation between GDPPC and VOPC (R 2 = 0.68; p < 0.001; see Section 3.1). VOPC was selected not only because it yielded a mathematically better regression model with smaller residuals, but also because it is based on the physical relationship between VOPC and The multivariate regression results indicate that the elasticity (−2.67) of MPG to per capita on-road FFCO 2 emissions (E) was the largest among all explanatory variables. Moreover, MPG is least influenced when comparing its relationship within the single regression (R 2 = 0.4 when ignoring other factors) versus the multiple regression (semi-partial R 2 = 0.23 when controlling other factors) models. This suggests that MPG is relatively independent of other explanatory variables. Sensitivity analysis results also indicated that MPG has the most robust relationship to on-road FFCO 2 emissions.
Both the elasticity and explanatory power of VOPC decreased in the multiple regression model (elasticity = 0.25, semi-partial R 2 = 0.08) when compared to the single regression model (elasticity = 0.91, R 2 = 0.42). Although the GDP per capita (GDPPC) was assumed to represent the affluence factor in the Sustainability 2020, 12, 6028 9 of 25 IPAT model, it was excluded in the multivariate regression model in favor of VOPC. This was due to the fact that there is a high correlation between GDPPC and VOPC (R 2 = 0.68; p < 0.001; see Section 3.1). VOPC was selected not only because it yielded a mathematically better regression model with smaller residuals, but also because it is based on the physical relationship between VOPC and on-road FFCO 2 emissions. GDPPC does not directly and immediately impact on-road transportation FFCO 2 emissions but has a gradual rather than immediate influence on the vehicle market.
The elasticity of RD to on-road FFCO 2 emissions in the multiple regression model was estimated as 0.39, which was within the range of previously reported elasticities [20,22,47,49]. However, RD had an insignificant relationship to emissions in the single regression model (elasticity = 0.09, R 2 = 0.01; p < 0.58). Further examination of the correlation matrix revealed that RD was independent of all other socio-economic/urban form factors, except for PD and PC. This suggests that the proportion of variation of E caused by RD was masked by the correlation between E and PD. This has indicated that RD alone does not have a significant relationship to E, but when holding PD constant, RD became significant with a larger elasticity (elasticity = 0.39, R 2 = 0.04; p < 0.001).
The elasticity of PD to on-road FFCO 2 emissions (-0.27) in the multivariate results was within the reported range from previous studies [9,[23][24][25][26]. These previous studies, mostly individual city case studies, reported a negative relationship between PD and on-road FFCO 2 emissions with weak to insignificant explanatory power. By contrast, we report here a significant relationship (p-value < 0.003). However, the relatively low R 2 (0.13 in single regression and 0.05 in multiple regression) suggests that PD would be a poor predictor of future emissions. Figure 2 summarizes the regression residuals. These residuals were examined for patterns that would violate OLS assumptions. The quantile-quantile (QQ) plot between the residual and standard distribution suggests that residuals are normally distributed. The residual histogram has −0.14 skewness and −0.42 kurtosis, which suggests that the distribution of residuals is slightly left-skewed and slightly lighter-tailed than a normal distribution. The skewness and kurtosis of residuals yields a p-value of 0.99 for the Jarque-Bera normality test [50], which indicates that there is not a statistically significant difference between the residual distribution and normal distribution. All of these measures indicate that the log-transformed multivariate regression model is appropriate for this study.
significant difference between the residual distribution and normal distribution. All of these measures indicate that the log-transformed multivariate regression model is appropriate for this study.

Sensitivity Analysis Result
This study used the coefficient of variance (CV), which is defined as the ratio of standard deviation over the mean, to measure distribution dispersion. There is no objective standard for assessing the CV value. However, CV can be used to compare the relative variability between variables with different units (given that all variables are measured on a ratio scale).

Sensitivity Analysis Result
This study used the coefficient of variance (CV), which is defined as the ratio of standard deviation over the mean, to measure distribution dispersion. There is no objective standard for assessing the CV value. However, CV can be used to compare the relative variability between variables with different units (given that all variables are measured on a ratio scale).
Statistics of coefficients based on data-resampling (Table 7) showed that all coefficients retained the same sign after 100 rounds of cross-validation. The coefficients from the original model were also within the 95% confidence interval for the mean of these 100 coefficient sets. This suggests that all coefficients have a robust relationship to per capita on-road FFCO 2 emissions [51]. Among the regression coefficients, MPG had the smallest CV value. This suggested that compared to other independent variables, MPG is the least sensitive to data re-sampling. Results also showed that MPG and VOPC remained 100% significant in all rounds of data resampling compared to 70% for PD and RD. This indicated that MPG and VOPC are relatively more robust to data resampling compared to RD and PD. Statistics of coefficients based on different model specifications (Table 8) showed that the final coefficient values for all four variables in the original model were outside of the 95% confidence interval for the mean of 127 model specifications. Only the MPG coefficient retained the same sign in all 127 models. This suggested that MPG had a more robust relationship with per capita on-road FFCO 2 emissions compared to vehicles owned per capita, population density and road density. The relatively smaller CV value also indicated that the MPG coefficient varied less about its mean than the other variables in the model. All of the MPG coefficients remained statistically significant in all models, while VOPC, PD and RD had 50%, 45% and 25% significant coefficients, respectively. This again indicated that MPG was relatively more robust by having relatively more significant relationships in different model specifications. The statistics of the regression coefficients subjected to artificially introduced errors (Table 9) showed that all variables retained the same sign in all repetitions at all error levels. When the standard deviation (σ) of the artificial error was at 0.05, all four independent variables remained 100% significant. With σ increasing, the coefficient of variation range increased for all independent variables. Regression coefficients for the vehicles owned per capita varied the least by having the smallest CV value at all error levels. In addition, VOPC was also the only variable that remained 100% significant in all repetitions when the standard deviation of artificial errors had increased to σ = 0.3. MPG and population density remained 100% significant until σ was raised above 0.1. Road density remained 100% significant only when σ was at or below 0.05. Table 9. Statistical summary of regression coefficients with artificially introduced errors.

Statistical Summary of Regression Coefficients
Miles

Discussion
Given the explanatory power, independence and robustness of the fuel economy within the regression results presented here, improving the fuel economy offers an effective and reliable tool for policymakers to mitigate FFCO 2 emissions. However, the fuel economy has not shown a significant improvement across the world. In Australia, the Survey of Motor Vehicle Usage (SMVU) conducted by the Australian Bureau of Statistics indicated that the fuel economy (12 L per 100 km) has not changed much between 1976 and 2018 [52]. In Britain, fuel economy improvement has significantly slowed since the mid-1980s [53]. Fuel economy improvements were potentially offset by the increased vehicle weight [53] or the increased vehicle use [54]. In the United States, the fuel economy has been stagnant for the past 30 years [7]. Vehicle technology developments were mostly focused on improving vehicle performance, and especially the engine size and maximum speed, rather than fuel efficiency. Furthermore, vehicles in the US have become 20% heavier and 25% faster, while the fuel economy has remained constant since 1985 [7]. The Global Fuel Economy Initiative (GFEI) report for the International Energy Agency [42] found that the global fuel economy increased 1.7% annually between 2005 and 2011. This indicated that the global fuel economy improvement would very likely lag behind the GFEI target of halving new vehicle fuel economy by 2030. On the other hand, the global production and purchase of hybrid/electric vehicles are still limited due to a lack of charging infrastructure [55] and insufficient mileage [56].
The decline of the elasticity and explanatory power of VOPC in the multivariate results versus the single regression model indicates that the impact of VOPC on FFCO 2 emissions is subject to the influence of other socio-economic/urban form factors. Similar conclusions were drawn by Karathodorou et al. [25], who regressed the vehicle ownership against a series of factors and found significant relationships with population density, GDP, road length per capita, public transit per capita and external costs (such as maintenance, taxes, parking, tolls and depreciation). The VOPC elasticity (0.25) derived from the multiple regression model in this study is close to the elasticity (0.338) calculated by Jones and Kamman [57], who regressed the household carbon footprint against vehicle ownership controlling for income, carbon intensity of electricity, home size, persons per household and population density.
The four variables identified in this analysis as significant and robust have potential policy interventions, assuming an interest in mitigating GHG emissions. However, the availability of policy options is likely a reflection of the interactions between local and provincial or national governments, not to mention the general nature of government purview and structure. For example, the fuel economy has typically been established at the national/federal level, given the inefficiency and challenges associated with attempting to regulate the fuel economy in local markets. The control over the number of vehicles owned per capita or vehicle ownership in general is rare and likely difficult to enact. Road density and population density, however, are attributes often considered part of the urban planning effort, though not necessarily in relation to FFCO 2 emissions. Given the fact that these two urban form attributes are significant variables in explaining on-road FFCO 2 emissions, they may take on added meaning when considering urban form in GHG mitigation planning. As with much consideration of GHG mitigation at the urban scale, these on-road FFCO 2 emission drivers are one factor in a number of competing interests and needs of the planning processing cities.
The quantification of on-road FFCO 2 emissions at a high spatiotemporal resolution adds useful information content to urban GHG inventories. Traditional "bottom-up" approaches require extensive local traffic activity data, such as traffic counts, VMT, fleet composition and fuel types. However, collecting, assimilating and analyzing these data are usually labor-intensive and costly. Although more cities have begun to participate in measuring and reporting their local GHG inventories [58], detailed local transportation data are still not universally available. This has limited most bottom-up on-road FFCO 2 inventories to local efforts and case studies within the developed cities.
This study explored the relationships between on-road FFCO 2 emissions and socio-economic/urban form factors from a global perspective. All input data used in this study are globally available from either existing public databases or remote sensing data products. The findings of this study might assist in generating on-road FFCO 2 emission estimates in developing cities with insufficient local transportation data. Given the importance of on-road FFCO 2 emissions in cities and the potential for local government influence over aspects of on-road travel, this study demonstrates a more amenable approach to establishing baseline on-road emissions and setting mitigation targets for areas where the traditional bottom-up approach is unsuitable.

Conclusions and Future Work
This study aims to enhance the understanding of driving factors for on-road FFCO 2 emissions for global cities. Beyond individual single-city case studies, the most common form of analysis to date, it offers general outcomes across a diverse sample of cities. Using a STIRPAT regression model approach, the results identified the fuel economy, vehicle ownership, population density and road density as having significant relationships with on-road FFCO 2 emissions. Among these factors, the fuel economy has the strongest, most independent and robust relationship with on-road FFCO 2 emissions. The relationship between vehicle ownership and on-road FFCO 2 emissions appears strong in a single regression model, but when controlling for other factors, declines in marginal explanatory power (semi-partial R 2 = 0.08). Population density and road density have significant but relatively weak relationships to on-road FFCO 2 emissions.
The outcome of the study may provide a potential method for scientists in the field of carbon studies to quantify carbon footprints in urban areas where alternative methods prove too costly or not possible due to local data constraints.
The characteristics of the relationships identified in this study can also provide valuable information support for policy making, especially for global city mayors. In order to achieve the goal of sustainability and mitigate on-road FFCO 2 emissions, an emphasis on improving the fuel economy and public transportation (to reduce vehicle ownership per capita) should still be the focus in the near future. On the other hand, although increasing population density and reducing road density still have a positive impact on reducing on-road FFCO 2 emissions, priority should be given to the improvement of fuel economy and public transportation, since their relationships are relatively more significant and robust.
A number of caveats to the work presented here are worth mentioning. First, it takes time to observe the significant changes caused by socio-economic/urban form factors. For example, the impacts of GDP or income on fuel consumption are mainly reflected through the variation of vehicle ownership and distance traveled [12,13]. These effects could take years to become significant. Due to this lagged effect, long-term elasticity is usually larger than short-term elasticity. This study was based on cross-sectional data. Therefore, not all the estimated elasticities reflect long-term effects. This could lead to an underestimation of elasticities when compared with other studies that used panel data. In future studies, both the short-term and long-term elasticities should be considered and reported based on both spatial and temporal data.
Data quality is another major caveat for this study. Although a careful examination and prudent approximation were implemented during the data assimilation process, the wide range of data types, formats, vintages and spatial/temporal resolutions can still result in considerable output uncertainty. This study took the approach of addressing the uncertainty issue by conducting sensitivity analyses based on the artificially introduced errors. Given enough information regarding the data quality assessment, a more detailed uncertainty analysis could be conducted to improve the model precision.
Another limitation of this study is that it primarily focused on the explanatory variables that were included in the final multiple regression model. This was purely based on the mathematical reason that these explanatory variables yielded the least residuals and most significances without multi-collinearity. This does not mean that other socio-economic factors were not important. Future work should focus more on other factors that had strong and significant relationships with per capita on-road FFCO 2 emissions but were excluded in this study due to multi-collinearity, such as GDP per capita and road length per capita.

. Population Density
Population density is defined in this study as population divided by city area in square kilometers. Population density is calculated based on LandScan [38] which is a global population dataset developed by Oak Ridge National Laboratory (ORNL) using spatial data and imagery analysis. It disaggregates sub-national census counts to a 1 km 2 grid based on multi-variable spatial modeling. Many datasets are included in the modeling process, such as administrative boundaries, land cover, elevation, slope, coastlines and high-resolution imagery. Each grid cell is assigned a likelihood factor based on these data to predict the possible occurrence of population. The census result is then further disaggregated based on each cell's likelihood factor. Transportation on-road emissions are more likely associated with people's total movements during a day rather than where people sleep. Therefore, compared to traditional household survey statistics, LandScan is better suited for this proposed study due to the fact that it represents the ambient population (average population within 24 h).
For verification and validation purposes, Dobson et al. [34] utilized the LandScan data based on state population with a 30 s by 30 s grid for the southwestern United States. The gridded results were aggregated to counties and compared to the county census data (which was a local census in comparison with the sub-national census for LandScan). Results showed that 87.8% of simulated population corresponded to the census data (meaning 12.2% of the population was placed in an incorrect county). Dobson et al. [34] concluded that LandScan was the most suitable global database to estimate population compared to previous population databases.

.2. Road Network Characteristics
Road Density was estimated using city area and a road network basemap, OpenStreetMap (OSM). Per capita road length was estimated using the OSM road network and urban population derived from LandScan. OSM is a crowd-source project under the Open Database License where individuals collaborate and contribute road-related geospatial data worldwide [39]. OSM data sources include aerial imagery, GPS, and field maps based on local knowledge. These data sources are integrated into geospatial databases and updated regularly by the public OSM community (consists of worldwide GIS professionals, cartographers, and engineers).
Various quality assessments of OSM have been conducted worldwide [35,36,59]. Haklay [35] compared OSM in England versus products from the Ordinance Survey (British government mapping agency). Results showed that OSM was, on average, within 6 m of the ground truth and covered over 80% of motorways. Girres and Touya [36] extended Haklay's [35] work to France by comparing OSM to an institutionalized reference map from the French National Mapping Agency. Girres and Touya [36] expressed conclusions similar to those of Haklay [35], specifically that OSM has fairly good locational accuracy (0-6 m away from ground truth on average) but the attribute accuracy was rather poor. For example, only 43% of roads were named, and 49% of residential and local roads were misclassified. Highways and primary roads on the other hand, achieved almost 100% correct classification. Forghani and Delavar [59] compared OSM to the official reference map published by the Municipality of Tehran separated in grids. They concluded that about 80% of Tehran was covered with fairly good quality OSM data. However, the spatial distribution of uncertainty varies by region. This may be, again, due to the heterogeneous coverage and lack of standards in the submitted geospatial data format.
Many of these assessments have concluded that OSM is a good representation of roads, yet all share concern about the data quality in specific regions. Due to the fact that OSM is "volunteered geographical information (VGI)" [60], its data quality varies by location and topic. Developed, populated, and urbanized places receive more data with good quality, while rural areas in general are less represented with relatively poorer quality [35].
This study focuses on major global cities and primary roads, which are represented with high accuracy in OSM (0-6 m away from ground truth on average) according to Girres and Touya [36]. Plus, the spatial calculation approach used in this study requires spatial accuracy rather than attribute accuracy. Therefore, OSM is considered well-suited for this research.

.3. Population Centrality
There were many definitions of population centrality. The Wheaton index [61] measures how fast populations accumulate along the route between local activity centers and the city edge. The Wheaton index can be described by the formula: where t is the distance to the local CBD, is the cumulative proportion of population at distance t; b is the distance from the CBD to city edge. The Wheaton index can be interpreted as the area of cumulative distribution of population from 0 to t. When 100% of inhabitants are concentrated at the CBD, the Wheaton index equals 1. When the inhabitants are uniformly distributed, the Wheaton index equals 0.
Massey and Denton [62] proposed an area weighted index to describe population centrality. It measures the cumulative proportion of population compared to the cumulative proportion of land area around the CBD. This index can be described by the following formula in discrete form, where land areas in different zones are ordered from close to faraway based on their distance to CBD: where is the cumulative proportion of population at zone i; is the cumulative proportion of land area through zone i. The area weighted centrality index ranges from −1 to 1. It equals 0 when the population is uniformly distributed. A positive value indicates people are more concentrated around the CBD compared to a uniform distribution. Negative values indicate inhabitants are further away from CBD compared to a uniform distribution. Therefore, the area-weighted centrality index can be interpreted as the proportion of people needed to relocate in order to achieve a uniform distribution around CBD.
Bento et al. [47] used an index of population centrality which examines the percentage of population living within a percentage of distance from local activity centers to the edge of the city. For example, if city A has 80% of people living within the 20% of distance from local activity centers to the edge of the city, and city B has 20% of people living within 80% of that distance, city A will be considered more centralized than city B. This spatial index is independent of city and population size.
Estimation of population centrality requires information about the location and size of local activity centers. Various studies have been conducted to delineate activity centers according to their thermal, spectral, spatial and physical characteristics. Examples include identifying the ground surface temperature difference between an activity center and non-activity center areas [63]; detecting the shadows caused by high buildings [64]; comparing the building density with the aid of remote sensing images [65]; and mapping the socio-economic activities by the constraint of road network [66]. However, these are all case studies that use either high spatial/spectral resolution remote sensing images or local activity data, which are either expensive or challenging to adopt for global scale research. For the purpose of this study, there are no known comprehensive datasets that record the geographical locations of activity centers at the global scale.
This study proposes a fast and economic way to delineate activity centers based on impervious surface area (ISA) and road network data. A previous study by Wu and Murray [67] confirmed that, compared to other land use types, activity centers have the largest share of impervious surface and least share of vegetation coverage. Moreover, since activity centers are the center of socio-economic activities in an urban area, major roads converge to provide accessibility for suburban areas [68]. Combining the information of ISA and road density, a GIS hot-spot analysis was performed to identify the locations and sizes of clustered pixels with large ISA values and high road density ( Figure A2).
As Taubenböck et al. [69] pointed out, the producer's accuracy for CBD classification (which measures the probability that ground features are accurately classified as such) cannot be calculated due to the lack of a comprehensive reference dataset or ground-truth. This study followed the approach of Taubenböck et al. [69] to calculate the user's accuracy (which measures the probability that map classifications are actually present on the ground) through visual inspection with map [70]. Results showed that out of 145 global cities, 106 had their identified activity centers within 3 km of local ground truths, yielding a user's accuracy of 73%. Figure A2 showed the locations of the largest activity center that was identified by the hot-spot spatial analysis for several global cities.
Sustainability 2020, 12, x FOR PEER REVIEW 18 of 25 local ground truths, yielding a user's accuracy of 73%. Figure A2 showed the locations of the largest activity center that was identified by the hot-spot spatial analysis for several global cities. This study defines population centrality following the Bento et al.'s [47] definition, which is the ratio of the cumulate population at distances from activity centers to the average population at distances from activity centers. Suppose a city has activity centers and is divided into grid cells of equal area: where is the proportion of population that was attracted by the activity center for the grid cell, is the distance from the grid cell to the activity center, is the average population for a single cell.
The calculation of uses the Landscan population data at 1 km 2 spatial resolution. Considering that cities may be polycentric with multiple activity centers, this study further divided into portions by the attractive power of each nearby activity center. The definition of attractive power follows the Newton's law of universal gravitation. For any two objects with mass and , the attracting force between them is: In this case, is represented by the intensity value for each activity center (size*ISA*road density). Assuming a city has n activity centers, each activity center will have its own attracting power (k = 1,2,…n) to the local population. Thus, for the 1 km 2 grid cell with population P, After the and have been quantified, the overall population centrality can be calculated. When the value of population centrality is small it indicates people are living in a clustered or compact pattern near the activity center. When this value is large it indicates people live far away from the activity center, or in a sprawl pattern.
Calgary, Canada and Naples, Italy are two examples that illustrate the difference of population centrality ( Figure. A3). Calgary is a relatively more centralized city with population centrality score where Pop xy is the proportion of population that was attracted by the yth activity center for the xth grid cell, Distance xy is the distance from the xth grid cell to the yth activity center, Pop is the average population for a single cell.
The calculation of Pop xy uses the Landscan population data at 1 km 2 spatial resolution. Considering that cities may be polycentric with multiple activity centers, this study further divided Pop xy into portions by the attractive power of each nearby activity center. The definition of attractive power follows the Newton's law of universal gravitation. For any two objects with mass m 1 and m 2 , the attracting force between them is: In this case, m 2 is represented by the intensity value for each activity center (size*ISA*road density). Assuming a city has n activity centers, each activity center will have its own attracting power F y (k = 1,2, . . . n) to the local population. Thus, for the xth 1 km 2 grid cell with population P, After the Pop xy and Distance xy have been quantified, the overall population centrality can be calculated. When the value of population centrality is small it indicates people are living in a clustered or compact pattern near the activity center. When this value is large it indicates people live far away from the activity center, or in a sprawl pattern.
Calgary, Canada and Naples, Italy are two examples that illustrate the difference of population centrality ( Figure A3). Calgary is a relatively more centralized city with population centrality score as 0.403. Naples as a relatively decentralized city has population centrality score as 1.002. These two cities represent the upper and lower boundaries of population centrality for 145 global cities. as 0.403. Naples as a relatively decentralized city has population centrality score as 1.002. These two cities represent the upper and lower boundaries of population centrality for 145 global cities. The urban GDP data were obtained from the Global Metro Monitor [41]. This publication is a product of the Brookings institution's metropolitan policy program (www.brookings.edu).
Global Metro Monitor has various data sources across the world. For U.S. metropolitan areas, the employment data come from the Local Area Unemployment Statistics (LAUS) program supervised by the U.S. Bureau of Labor Statistics [41]. The LAUS program provides monthly and annual-average employment estimates at the county and city scale based on the Current Population Survey, which is a monthly sample survey of approximately 60,000 households conducted by the US Census Bureau [71]. The population data is measured by U.S. Census Bureau's Population Estimates Program, which relies on decennial census data to provide population estimates [71].
For Europe, the economic, population and labor force data are provided by Cambridge Econometrics, which is a consulting agency in the United Kingdom. Their data are primarily based on the Eurostat [41].
Eurostat data are collected from national statistics following the Eurostat quality assessments [41]. This process is enforced by the European Statistical Law to guarantee the validity and consistency of the national reports.
For cities that are outside of United States and Europe, economic data are obtained from Oxford Economics, which is a consulting agency who provides data and analytical results for governments and Non-Government Organizations (NGO) at the global scale. According to Berube et al. [41], data sources for Oxford Economics come from various national statistical agencies or local data providers.
Per capita GDP for global cities were calculated based on these data by the Global Metro Monitor program. Complicated data sources make it very difficult to quantify the overall uncertainty. Although different agencies should use the best available data, uncertainties or errors will inevitably propagate and aggregate. Caution should be exercised when using and interpreting the GDP data for this study. This study used the per capita GDP data for the year 2011, which is the same year as vehicle ownership and fuel economy data (described next). The urban GDP data were obtained from the Global Metro Monitor [41]. This publication is a product of the Brookings institution's metropolitan policy program (www.brookings.edu).
Global Metro Monitor has various data sources across the world. For U.S. metropolitan areas, the employment data come from the Local Area Unemployment Statistics (LAUS) program supervised by the U.S. Bureau of Labor Statistics [41]. The LAUS program provides monthly and annual-average employment estimates at the county and city scale based on the Current Population Survey, which is a monthly sample survey of approximately 60,000 households conducted by the US Census Bureau [71]. The population data is measured by U.S. Census Bureau's Population Estimates Program, which relies on decennial census data to provide population estimates [71].
For Europe, the economic, population and labor force data are provided by Cambridge Econometrics, which is a consulting agency in the United Kingdom. Their data are primarily based on the Eurostat [41].
Eurostat data are collected from national statistics following the Eurostat quality assessments [41]. This process is enforced by the European Statistical Law to guarantee the validity and consistency of the national reports.
For cities that are outside of United States and Europe, economic data are obtained from Oxford Economics, which is a consulting agency who provides data and analytical results for governments and Non-Government Organizations (NGO) at the global scale. According to Berube et al. [41], data sources for Oxford Economics come from various national statistical agencies or local data providers.
Per capita GDP for global cities were calculated based on these data by the Global Metro Monitor program. Complicated data sources make it very difficult to quantify the overall uncertainty. Although different agencies should use the best available data, uncertainties or errors will inevitably propagate and aggregate. Caution should be exercised when using and interpreting the GDP data for this study. This study used the per capita GDP data for the year 2011, which is the same year as vehicle ownership and fuel economy data (described next).

Appendix A.2.2. Vehicle Ownership
The Vehicles owned per capita (VOPC) data were obtained from World Road Statistics (https: //worldroadstatistics.org/contact.html) [43]. This is a document published by the International Road Federation (IRF), a non-profit global organization with headquarters in Washington DC. Through their network, IRF sends out questionnaires to over 200 countries to collect statistical data related to road networks, traffic, and vehicles. The survey is conducted annually at the national scale as their primary data source. The secondary supplemental data source is the national year book from countries. Data are categorized by vehicle types and time periods, including passenger cars, lorries and vans, buses and motorcycles from 2007 to 2012. This study uses the light duty passenger vehicle counts for the year 2011, which is coincident with the GDP and fuel economy data (next section). According to IRF's documentation, the vehicle ownership data are validated by comparing them to other data sources (which vary by country and are not listed), comparing them with historical data, and checking/confirming outliers with contacts in their network. There hasn't been a quantitative quality assessment on this national vehicle ownership data. The average fleet composition data for each country are based on the vehicle registration records provided by government statistical departments and worldwide third-party agencies (a detailed list of sources for each country can be found in the table Annex I quoted from [42]). The registration data were collected in CY 2005 and 2008 and were comprised of almost 50 million records in each year covering 94% and 88% of vehicles produced, respectively. Market sales data have been used to stratify these data. The market sales data are from 21 countries (for a detailed country list see Table 1 in [42]) covering 88% of the world total vehicle sales in 2008. The sales-weighted vehicle registration data are then summarized into a national fleet composition.
For vehicle models with various age, engine type and fuel type), the fuel economy is tested in a laboratory based on the result of fuel consumed per kilometer in different testing routines. The tested results and national fleet composition data are then compiled into fuel economy by vehicle model and country. This study uses the national average fuel economy across all models vehicle for each country at year 2011.
Cuenot and Fulton [42] acknowledged the caveats of these data such as the difference between the ideal fuel economy tested in lab and actual fuel economy under real-world conditions, not all data are from official government reports, and the testing methods may vary by country. No quantitative uncertainty analysis was done in their reports.

Appendix A.3. Data Sources for on-Road FFCO 2 Emission
This study collected data from 58 global cities with on-road FFCO 2 emission data available for year 2011. Half of the data are derived from FFCO 2 submissions to the C40 project [27], another half were included in the Millennium City Database [37]. Appendix A.3.1. C40 Cities C40 is a network of the world's megacities committed to addressing climate change. The C40 cities are cities for which mayors have committed to reduce greenhouse gas emissions [27]. Annual city-wide greenhouse gas emissions are reported by C40 cities based on guidelines provided by the Intergovernmental Panel on Climate Change (IPCC), Global Protocol for Community (GPC), and other local protocols for emission inventories.
The IPCC guidelines provide methodologies for estimating inventories of greenhouse gas emissions resulting from human activities [72]. For the transportation sector, two methods have been recommended by IPCC. "Top down" refers to an approach that uses fuel sales and an assumption regarding the carbon content of the fuel. "Bottom up" refers to an approach that uses VKT, an estimate of vehicle fuel economy, and the carbon content of fuel. Both methods have been used by Kennedy et al. [73]. They concluded that these methods resulted in similar outcomes. For example, Kennedy reported that for Bangkok's gasoline use in 2006, "the estimate of 2662 million liters based on VKT is 2.9% lower than the estimate of 2741 million liters from fuel sales" [73].
The GPC is a project developed by Local Governments for Sustainability (previously known as International Council for Local Environmental Initiatives, ICLEI), the World Resources Institute (WRI), and C40 cities. GPC advocates four data collection methods: (1) the fuel sales approach; (2) city-induced activity trips that either have their origin or destination in the city (passing through trips are excluded); (3) geographic boundary, includes all traffic occurring within city boundaries, regardless of origin or destination; and (4) resident activity, based on household survey of transportation activity. City induced activity is the methodology recommended by GPC.
The categorical difference in these methodologies and the potential for diverse outcomes is acknowledged. Chavez et al. [74] found that, in the city of Delhi, only 3% of VKT occurred across city boundaries. The authors theorized that "in megacities, VKT values attributed to trans-boundary traffic may be negligible due to the large amounts of concurrent in-boundary traffic". This implies that, at least for the city of Delhi and possibly for other megacities, the result of using the city-induced method may not be significantly different from using the geographic boundary method.
Of the 29 C40 cities, seven cited the IPCC guidelines as the primary methodological source for estimating transportation emission data, with two additional cities stating that they used "other" methodologies but were influenced by the IPCC. Eight cities identified the GPC as the primary methodological source with four additional cities stating that they were influenced by the GPC. Thirteen of the C40 cities stated that sources other than IPCC or GPC guided their transportation CO 2 emissions estimation. For example, Los Angeles obtained transportation data from the Southern California Association of Governments, the regional planning authority. Toronto used the City of Toronto's Transportation Services Division as their data source. Some municipalities used a combination of sources. For example, Rio de Janeiro, while using IPCC as their primary source of methodology, also used input from Academia, the World Resources Institute (WRI), and the World Bank.
Approximately thirty percent of C40 cities reported the detailed methodology used for data collection and FFCO 2 emission estimation. Of those cities reporting specific methodologies, Stockholm, Berlin, Portland and Vancouver used top down method. Stockholm and Berlin disaggregated fuel consumption data based on fuel sales data from road traffic. Portland disaggregated fuel sales data, taken from EIA Energy Information Administration (EIA). Vancouver disaggregated fuel sales data, but did not identify the source. Toronto and London used bottom up method based on traffic activity data. Oslo used a combination of fuel sales and activity data. The Millennium City Database (MCD) is compiled by the International Association of Public Transport (UITP) in collaboration with Murdoch University in Perth, Australia [37]. MCD contains over 100 worldwide cities with data on land use, transportation, economics and energy use for the year 1995/1996. MCD data were collected from published sources (such as national censuses and annual reports) and many emails exchanged with individuals working in various corresponding organizations in each city [37]. To synchronize with C40 data for the year 2011, MCD data were scaled using a growth factor of national-scale CO 2 emissions from the transportation sector in the International Energy Agency greenhouse gas reports [2]. This is a compromise of data quality since the IEA national transportation GHG emission growth rate is used to scale city emission data.