Physical and virtual carbon metabolism of global cities

Urban activities have profound and lasting effects on the global carbon balance. Here we develop a consistent metabolic approach that combines two complementary carbon accounts, the physical carbon balance and the fossil fuel-derived gaseous carbon footprint, to track carbon coming into, being added to urban stocks, and eventually leaving the city. We find that over 88% of the physical carbon in 16 global cities is imported from outside their urban boundaries, and this outsourcing of carbon is notably amplified by virtual emissions from upstream activities that contribute 33–68% to their total carbon inflows. While 13–33% of the carbon appropriated by cities is immediately combusted and released as CO2, between 8 and 24% is stored in durable household goods or becomes part of other urban stocks. Inventorying carbon consumed and stored for urban metabolism should be given more credit for the role it can play in stabilizing future global climate.

Carbon emissions are from official data reported by the of Tokyo. Solid waste data at sector level are then adjusted from big metropolitan area by its proportional GDP by sector.

Toronto, Canada
Material imports/exp orts and stocks in products Imports and exports data are compiled using the sectoral structure in 1999. The material flows of the core urban area are adjusted from metropolitan area with its proportional GDP by sector.
Sahely et al. 83       We recognize some of informal recycling activities of materials could be missed in the model due to a lack of data in many cities (especially cities in developing countries), but this will not have major effect on the total physical inflow. Downscaling IO table for urban economies

Virtual carbon flow
We combine a standardized LQ and CIQ method from applied regional analyses to derive urban input-output tables. Value added (urban GDP) and total income are used as main constrains to better reflect local economies. RAS technique used in balancing urban IO tables

Virtual carbon flow
We apply a refined RAS approach based on the work of Lenzen et al. 92 to cope with conflicts of information. The assumptions of homogeneity and production technology inherent in inputoutput models Virtual carbon flow This is an inherent uncertainty in all inputoutput models. IOA assumes the homogeneity of activities within a sector, which could lead to uncertainties in delineating activities of the economy. Also, the production technology of a sector is often assumed to be constant in the technical structure.

Carbon sinks
We estimate the carbon sequestration rates of urban trees based on their forest coverage and city-specific reference values of carbon sequestration rate from literature. The uncertainties in natural sequestration are given.

Supplementary Note 1
Scientists have developed a range of accounting frameworks to capture material flows through the human economy at multiple scales [93][94][95][96][97][98][99][100][101][102][103][104] . Most of these accounting frameworks and approaches can be adopted to city-scale analysis, albeit some of them are originally designed for economies at larger spatial scales such as regions or countries.
Here we use a metabolism-based framework to account for physical carbon inputs to, stored in and leaving urban areas. It should also be noted that for urban carbon accounting we are using citywide material flow data rather than down-scaled national material flow data in most cases. All  Table 4). They are compiled using a consistent integrated framework ( Figure 1 in the main text).
The recycling of materials includes products such as wood, steel, paper, etc. after their first use (excluding methane emitted from waste due to a lack of data for most cities), which is derived from a survey of recycled solid waste for each city. Household retention of physical carbon (HS) only include carbon stored in households usually for more than one year (such as furniture, book and other durable products). Solid waste accounts for both carbon in industrial waste and that in less durable household products such as foods. Waste data are acquired from multiple sources such as urban MFA studies, city-level statistical yearbooks, or Eurostat environmental database [110][111][112][113][114][115][116][117][118][119][120] . though the electricity use data was collected in this section, it was not considered in the physical carbon flows but was included in the virtual carbon flows.
Among all the material imports, the import of food for residential consumption is derived from city-scale data from the literature, as have been done in many metabolism studies (e.g. [121][122][123][124] ).
For food processing in industrial sector and food consumption by tourists (service sector), Beijing, Hong Kong, London, Vienna, Stockholm, Singapore, Sydney and Paris have official data.
For other cities that do not have this data, the food possessing in the industrial sector and food consumption by tourists (commercial and service sector) are scaled from national data (FAOSTAT database 125 and national statistical sources) using the share of the urban sector's economic output relative to the respective sector's national output 126,127 .
II. Similar to the practices in literatures 128-130 , we convert mass-based flows to carbon flows by multiplying them with the carbon content factor (CCF). In this case, sector-specific CCF ( i CCF ) is calculated from the aggregation of the product-specific CCF ( III. Natural sequestration refers to the sequestration of carbon dioxide from the atmosphere.
Urban vegetation has been reported as a major source for carbon sequestration in cities 142,143 , although others doubt its significance and effectiveness as global carbon sinks 144 . We estimate the capacity for carbon sequestration by trees based on their forest coverage and reference values of carbon sequestration rate for each city [145][146][147][148][149] . Note that urban soils are not considered for natural carbon sequestration in this study. In comparison to vegetation, the carbon sequestration effect by urban soils is more complex and uncertain 150,151 . Other studies have shown its insignificance compared to sequestration by vegetation 152,153 .
IV. Due to the lack of city-level IO tables, there have been studies of coupling traditional methods of urban metabolism (such as MFA) with life cycle analysis (LCA) to advance the understanding of urban carbon flows (e.g. 154,155 ). A number of other studies have proposed a cross-boundary quantification approach for urban metabolism by integrating MFA and LCA into environmental impact assessment of cities 156,121 . We adopted this MFA-LCA integrated method to calculate the carbon emission embodied in the imports to the global cities, with adjustments on the sector categorization according to the data framework of material flows. The carbon emission coefficients of material and energy inputs are mainly derived from EcoInvent 2.01 database 157 and are supplemented with processes from the built-in professional database in Simapro 7 when the EcoInvent data do not match with the cities. In addition, city-specific situations of technology and setting are taken into consideration. The industrial processes of producing agro-products and electronic products, etc. are highly associated with the technology related to each city. For example, different emission factors for coal-power, wind-power and nuclearpower electricity used by cities were used. In order to examine how the embodied emissions are driven by final uses of the urban economy (household and government consumption, capital formation, exports, which is consumption-based emission), we applied input-output analysis (IOA) 158,159 in the allocation process.

Supplementary Note 2
Beijing, Hong Kong, Singapore, Sydney, London, New York and Los Angeles have city-level IO tables that can be readily used (IO tables of New York and Los Angeles are derived from IMPLAN, a regional table complication technique for US cities). We compile urban IO tables for the rest cities in this study. The absence of urban input-output (IO) tables has been a main suppression in modelling virtual carbon flows (or other kinds of embodied flows) at city level. Nonetheless, the need of measuring urban carbon balances from physical and virtual perspectives is huge given the high linkage of urban carbon profile with its external markets (or hinterlands). Some important progresses have been made to disaggregate national IO tables to smaller scales such as regions and cities 160 . Some established approaches include IMPLAN (impact analysis for planning), RIMS I, RIMS II (Regional Impact Modeling System). These approaches often use location quotients (LQ) and cross-industry quotients (CIQ) to derive estimates of regional input coefficients, widely accepted and applied in regional economic and environmental analyses.
Here we combine a standardized LQ and CIQ method from applied regional analyses to derive urban input-output tables for cities lacking such data. There are two reasons for applying this technique: (1) It allows for intensive cell-by-cell adjustments for non-diagonal elements and uniform adjustments for diagonal elements in the monetary flow matrix; (2) The relative weight of both selling sector i and buying sector j in the region and the nation is considered, which is important when the scale of the targeted economy is relatively small (such as a city).
The location quotients (LQ) and cross-industry quotients (CIQ) are defined as 160 : RAS technique is used to balance the urban IO tables. This technique has been widely used as an automatic technique in updating IO tables. The process in RAS can be seen as an iterative scaling of a non-negative matrix until its column sums and row sums equal given vectors. The detailed iterative process has been described in references 92,160, . We use local total outputs and value added in the corresponding year as the main constraints in balancing the tables. pointed out that table disaggregation approaches (such as LQ and CLQ) are frequently used in applied regional analysis, but we are quite clear they should only be used to provide broad insights of problems. We do not intend to establish accurate and fully-verified IO tables for global cities.
Instead, we aim to relate cities' final demands to their different carbon inflows, and to demonstrate the importance of urban virtual carbon flows.

Supplementary Note 3
The uncertainties of the model and findings are estimated when possible (as shown in Regarding cities that already have available urban level input-output tables (i.e. Beijing, Hong Kong, Singapore, London, Sydney, New York and Los Angeles), we assume the uncertainties mainly come from the calculation of direct carbon emission intensities for sectors. For the other 9 cities that do not have official input-output tables, the uncertainties come from the accumulation of two modelling steps, i.e. estimation of carbon intensities calculation and rebalancing of urban IO tables.
These uncertainties are quantified for the 9 cities, while the impact of downscaling national IO tables is only qualitatively described. Finally, we have provided a description of raw data sources in Supplementary Table 4 to report the possible data uncertainty.
In terms of Monte Carlo analyses of input-output systems, standard deviations (SDs) were generally used in literature (e.g. 161,162 ). Lenzen and colleagues 163  Here PCF refers to results related to inflows such as imports from other regions (IM), local supply by urban ecosystems (LS) and recycling of materials (RE), as well as all outflows including household storage (HS), solid waste (SW), and export to external markets (EX) and changes in carbon stock (SC). Gaseous emission (CO 2 ) within urban territory has been verified for all cities, and therefore is considered accurate. VCF refers to results of import carbon emission (ICF), and emissions embodied in household consumption (HG), capital formation (CF) and export (EP). RSD p and RSD v (relative standard deviation, usually in ±%) are the ratios of standard deviations to total value of PCF and VCF, respectively.