of 11
ARTICLE
Physical and virtual carbon metabolism
of global cities
Shaoqing Chen
1,2,3
, Bin Chen
1
*, Kuishuang Feng
4
, Zhu Liu
5
*, Neil Fromer
6
, Xianchun Tan
7
,
Ahmed Alsaedi
8
, Tasawar Hayat
8,9
, Helga Weisz
10,11
, Hans Joachim Schellnhuber
10
&
Klaus Hubacek
12,13,14
*
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
fi
nd 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 ampli
fi
ed by virtual emissions
from upstream activities that contribute 33
68% to their total carbon in
fl
ows. While 13
33%
of the carbon appropriated by cities is immediately combusted and released as CO
2
, 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.
https://doi.org/10.1038/s41467-019-13757-3
OPEN
1
State Key Joint Laboratory of Environment Simulation and Pollution Control, School of Environment, Beijing Normal University, Beijing 100875, Chi
na.
2
School of Environmental Science and Engineering, Sun Yat-sen University, Guangzhou 510275, China.
3
Guangdong Provincial Key Laboratory of
Environmental Pollution Control and Remediation Technology (Sun Yat-sen University), Guangzhou 510275, China.
4
Department of Geographical Sciences,
University of Maryland, College Park, MD 20742, USA.
5
Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System
Science, Tsinghua University, Beijing 100084, China.
6
Resnick Sustainability Institute, California Institute of Technology, Pasadena, CA 91125, USA.
7
Institutes of Science and Development, Chinese Academy of Sciences, Beijing, China.
8
NAAM Research Group, Faculty of Science, King Abdulaziz
University, Jeddah 21589, Saudi Arabia.
9
Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan.
10
Potsdam Institute for
Climate Impact Research, Potsdam 14473, Germany.
11
Department of Cultural History & Theory and Department of Social Sciences, Humboldt-University
Berlin, Unter den Linden 6, D-10117 Berlin, Germany.
12
Center for Energy and Environmental Sciences (IVEM), Energy and Sustainability Research Institute
Groningen (ESRIG), University of Groningen, Groningen 9747 AG, The Netherlands.
13
International Institute for Applied Systems Analysis, Schlossplatz 1-A-
2361, Laxenburg, Austria.
14
Department of Environmental Studies, Masaryk University, Brno, Czech Republic. *email:
chenb@bnu.edu.cn
;
zhuliu@tsinghua.
edu.cn
;
k.hubacek@rug.nl
NATURE COMMUNICATIONS
| (2020) 11:182 | https://doi.org/10.1038/s41467-019-13757-3 | www.nature.com/naturecommunications
1
1234567890():,;
A
t present, more than half of the global population resides
in cities
1
. Cities are important real-life observatories that
provide opportunities to study how human activities
in
fl
uence global biogeochemical cycles
2
,
3
. Carbon, as an essential
input to the economy, is found in fossil fuels, biomass, food,
construction materials for buildings and infrastructure, and all
sorts of products that are concentrated in cities. Carbon
fl
ows
associated with cities need to be systematically measured and
modeled to decrease the huge impact of urban activities on global
climate
4
6
.
To date, the inventories of carbon
fl
ows of cities have con-
centrated on gaseous emissions. A territorial inventory is often
used by local authorities to report CO
2
emissions from within
cities (e.g., refs.
7
,
8
). When accounting for urban carbon foot-
prints,
fl
ows of carbon both within and across urban territories
are often considered because of cities
high demands for goods
and services from other regions
9
,
10
. The importance of appro-
priate de
fi
nitions of system boundaries in carbon accounting has
been emphasized in the Greenhouse Gas Protocol proposed by
Local Governments for Sustainability (ICLEI), the World
Resources Institute (WRI), and the C40 Cities Climate Leadership
Group
11
,
12
. Considering both territorial and upstream (virtual)
carbon, they identi
fi
ed three scopes of community-scale green-
house gas (GHG) emissions: emissions within the adminis-
trative boundary of a community (Scope 1); energy-related
embodied emissions outside the community boundary, such as
purchase of electricity from outside of a city (Scope 2); and all
other upstream emissions outside the city as a result of activities
within a community
s boundary (Scope 3). Several com-
plementary (and partially overlapping) frameworks have been
proposed to measure the carbon footprints of cities, such as
community-wide infrastructure footprint
13
15
, consumption-
based footprint
16
18
, and wider production-based footprint
19
,
20
.
Hybrid approaches of material
fl
ow analysis (MFA) and life-cycle
analysis (LCA) have been used to account for carbon emissions
associated with key urban materials or activities (e.g.,
14
,
21
23
). In
addition, input
output analysis (IOA) has been increasingly used
in urban carbon inventories due to its capability of effectively
capturing emissions embodied in supply chains
16
,
19
,
24
.
On the other hand, physical carbon stocks
25
,
26
, natural
sinks
27
,
28
, and
fl
uxes in products
29
within urban settlements have
been examined in order to understand the role played by cities in
the global carbon cycle, relevant to the carbon models focusing on
sources and sinks in biogeochemical cycles developed at country
level
30
,
31
. The carbon balance of urban economy is usually
investigated through imports, exports, and storage of products
and assets. Analyses of urban carbon
fl
ows are closely linked to
the dynamics of climate change since over time, most carbon
products stored in cities will eventually become waste
25
and later
on partially released as gaseous emissions
32
,
33
. Several studies
have highlighted the importance of managing material stocks in
urban areas
34
,
35
, but there is still a lack of detailed quanti
fi
cation
of these urban stocks relative to the entire carbon balance and
how they can contribute to future reduction of carbon emissions.
A national-scale inventory by Peters et al.
36
quanti
fi
ed the CO
2
related to international trade, including emissions embodied in
import and physical carbon present in various products. Similar
information at city scale is missing and the contribution urban
stocks can make for decarbonization is still unclear.
In this paper, we develop an integrated approach to model the
urban carbon
fl
ows of 16 global cities. In most previous studies,
physical carbon account and urban carbon footprint were kept
separate, albeit the existence of hybrid inventories for carbon
cycle
30
and material metabolism
37
at national scale. Here, we
consider urban carbon metabolism as a whole, where physical
carbon account and fossil fuel-derived gaseous carbon footprint
are combined, through examining the metabolic
fl
ows of both
physical carbon direct input to a city and fossil-fuel derived vir-
tual carbon associated with upstream supply chains over a one-
year accounting period. Physical carbon refers to the real carbon
content in materials and products that is directly consumed,
transformed or re-exported by an urban economy (see similar
de
fi
nitions in refs.
25
,
36
). These
fl
ows include gaseous emis-
sions (in this case, CO
2
) as well as physical carbon trapped in
products that can be emitted during their lifetimes. This physical
carbon is contained in biogenic products such as food and
fi
ber as
well as fossil fuels. Virtual carbon refers to fossil-fuel derived CO
2
that was emitted in upstream supply chains of electricity and
other goods and services imported to a city (see similar de
fi
ni-
tions in refs.
38
,
39
), and it excludes CH
4
and other GHGs
embodied in agriculture, which can be signi
fi
cant. As such, fossil-
fuel related physical and virtual carbon together do not cover all
GHGs related to a city, and the remaining carbon in materials
(e.g., wood burning fuels) may or may not considered as a net
GHG in other studies (e.g.,
31
,
40
).
By applying this approach to 16 global cities, we
fi
nd there is a
wide variation in the total carbon appropriated by urban
economies, in which both physical carbon and fossil-fuel derived
virtual carbon play an important role. It is dif
fi
cult or undesirable
to generate a one-size-
fi
ts-all carbon mitigation approach for all
cities due to signi
fi
cant differences in income level, urban form
and infrastructure scale. But cities do share a need of managing
their stocks, as our model shows the carbon stored as durable
household goods or stocks in industrial sectors amounts to 8
24%
of their total carbon in
fl
ows, comparable to carbon that already
ends up as gaseous emissions for energy uses. These carbon
stocks, especially those linked to investment in housing, pro-
duction facilities and infrastructure will shape future emissions
and could compromise on-going climate change mitigation
efforts. Portraying how carbon is appropriated and stored in cities
may offer an often overlooked policy option for a deep urban
decarbonization, and this is unlikely to be gained from separate
accounting of physical carbon balances and fossil fuel-derived
carbon footprints.
Results
Per capita carbon in
fl
ow of cities
. Figure
1
shows per capita total
carbon in
fl
ow (TCI) and per capita gross domestic product in
purchasing power parity (GDP-PPP) of 16 global cities. Here,
TCI refers to the sum of physical carbon inputs to a city and fossil
fuel combustion-related virtual carbon from upstream supply
chains. TCI integrates two complementary accounts, physical
carbon and fossil fuel-derived gaseous (virtual) carbon, and
quanti
fi
es the scale of a city
s carbon metabolism. We use carbon
(C) as the unit of TCI for consistency in that it includes
fl
ows of
physical carbon content in products (in C) as well as fossil fuel
combustion-related virtual carbon emissions (CO
2
, which is
then converted to C).
In the
fi
gure, four quadrants are separated based on the
magnitude of per capita carbon in
fl
ow and urban income,
showing groups of cities with high-income and high-carbon
in
fl
ows (Q1), low-income but high carbon in
fl
ows (Q2), low-
income and low-carbon in
fl
ows (Q3), and
fi
nally, high-income
but low-carbon in
fl
ows (Q4). These are relative situations applied
within this sample of cities, with quadrants separated by the
average value of per capita TCI and per capita GDP-PPP of these
16 cities. We
fi
nd that per capita TCI of Singapore is the highest
(12.0 t C) in the study cities, which is over 4 times of that in Sao
Paulo (2.7 t C). By and large, TCI is positively correlated with
urban income (represented by per capita GDP-PPP), though a
higher per capita urban income does not necessarily result in a
ARTICLE
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2
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larger per capita carbon in
fl
ow. For example, Moscow and Hong
Kong in Q2 have a relatively high level of carbon in
fl
ow and a
lower urban income than other cities located in Q1 (such as Los
Angeles and New York). In comparison, Vienna and London in
Q4 are able to have a relatively low per capita carbon in
fl
ow and
at the same time, a high urban income. Cities in Q3, in this study,
are mainly located in developing countries, which have a per
capita carbon in
fl
ow less than 5.0 t C to their economies, notably
smaller than the high-income group of cities in Q1 which have a
per capita carbon in
fl
ow of over 6.9 t C.
A higher income may signify a bigger expenditure on products
and services purchased from local or external markets, but
evidently, the carbon in
fl
ow to a city can also be in
fl
uenced by
other socioeconomic factors such as economic structure and
urban form, other than af
fl
uence. There is no single factor that
controls the diversity in the human appropriation of carbon in
cities, albeit it can be partially explained by the increasing effect of
the share of services sector and the decreasing effect of population
density, as identi
fi
ed by the regressions (Supplementary Fig. 1).
For instance, within the income range of $38,600
$42,000/year
and the population density range of 4200
6800 inh km
2
, per
capita TCI of Stockholm is only 58% of that in Singapore,
partially explained by the higher proportion of services (and less
manufacturing) in the former city. In contrast, with an
approximate urban income (around $40,500/year) and a similar
share of services (65%), Toronto is reported to have a bigger per
capita TCI than Tokyo, partially because the former has a lower
urban population density, which is relevant to shorter commuting
distance and more energy-ef
fi
cient infrastructure, such as district
heating systems and public transportation. As counter-examples,
Beijing has the second lowest TCI/capita, although manufacturing
(such as power plants inside the city) is still an important sector
for the city in the investigated year and the share of services in its
economy is much lower than other cities like London and Sydney.
This requires further explanation from the contributions of
physical and virtual
fl
ows as well as the varitions in cities
sectoral
structures.
The variation in the TCIs of cities is explained by the different
contributions of physical carbon as well as fossil-fuel derived
virtual carbon associated with the urban economy (Fig.
2
). We
fi
nd that from 32 to 67% of the total carbon appropriated by cities
is obtained from physical
fl
ows in products. The difference in
physical carbon in
fl
ow explains up to half of the difference of per
capita TCI between two cities. Manufacturing, supply of energy
(such as electricity and gas) and construction sectors play an
important role in physical carbon consumption given their high
demands of fossil fuels (Supplementary Fig. 2). For example, the
physical carbon in
fl
ow to Moscow (4.4 t C/capita) is mainly
contributed by the big manufacturing and construction sectors in
its economy. Transportation contributes more to the physical
carbon in low-population-density cities such as Toronto and Los
Angeles than in compact cities like Tokyo. A national-scale
study
36
estimated that the global average physical carbon was
around 1.2 t C/capita in 2004. Our study
fi
nds the average
physical carbon in
fl
ow of the 16 cities (3.5 t C/capita) nearly
triples this global estimate, albeit differences in study boundaries,
year of inventory and other aspects noted in Methods.
Fossil fuel combustion-related virtual carbon, as part of cities
carbon metabolism via upstream activities, is also found to play
a large part in TCI. Most cities in our study, outsource a
considerable proportion of their carbon emissions by producing
electricity upstream and importing materials, goods and services,
0
5
10
15
20
Bangkok
Beijng
Cape Town
Delhi
Hong Kong
London
Los Angeles
Moscow
New York
Sao Paulo
Singapore
Stockholm
Sydney
Tokyo
Toronto
Vienna
Q1: high income and
large carbon inflow
16,800
13,600
10,400
20,000
7200
4000
40
60
Share of services sector in economy (%)
TCI per capita (t C)
GDP-PPP per capita (US$)
Population density (inh. km
–2
)
80
800
Q2: low income but
large carbon inflow
Q3: low income and
small carbon inflow
Q4: high income but
small carbon inflow
40,000
0
20,000
60,000
Fig. 1 Distribution of 16 global cities by per capita total carbon in
fl
ow (TCI) and per capita GDP-PPP.
TCI encapsulates both the physical carbon in
fl
ow
of a city as well as the fossil fuel combustion-related virtual carbon emissions associated with a city
s upstream supply chains. Note that the modeling of
virtual carbon of Beijing, Hong Kong, Singapore, London, Sydney, New York, and Los Angeles is based on city-level input
output tables, while those of the
remaining cities use downscaled tables of the national economy adjusted by location quotients, as described in Methods. We use per capita GDP-PPP
(purchase power parity) as an index of urban income. The intersection of the
x
-axis and
y
-axis represents the average per capita carbon in
fl
ow and per
capita GDP-PPP of the cities. The impacts of the share of services sector (size scale) and population density (color scale) are also shown in the
fi
gure.
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ARTICLE
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3
signi
fi
cantly amplifying the climatic impact of the urban
economy, similar to observations in prior studies
14
,
19
,
20
. Peters
et al.
36
reported virtual gaseous carbon contributed half of total
carbon related to international trade. Here, we
fi
nd a similar share
of virtual carbon in the TCI of urban economies. These results
manifest that, if upstream activities are excluded, the urban
impact on the carbon metabolism will be highly underestimated.
Nevertheless, the share of virtual emissions among cities is
ranging widely from 33% in Sao Paulo to 68% in Hong Kong.
The small virtual carbon emission embodied in goods and
services purchased by a citizen in Beijing on average (2.4 t C/
capita) largely explains why this city, albeit having many
manufacturing industries and power plants within its boundary in
the study year, has a relatively low per capita carbon in
fl
ow.
In addition to per capita in
fl
ow (Fig.
2
a), the TCIs of cities are
also compared based on per GDP-PPP (Fig.
2
b) and per unit
of urban area (Fig.
2
c). The TCI intensity (meaning carbon in
fl
ow
per unit GDP-PPP) of the cities varied notably, and ranged from
0.1 to 0.5 t C/$1000. The TCI intensity is high in Delhi, Beijing,
and Cape Town, more than 4 times of the city with the lowest
intensity (i.e., Sao Paulo). Of the 16 cities, TCI intensity is
the highest in Delhi, mainly because almost all sectors of the city
used carbon-intensive electricity (either gas- or coal-based power
generation). Next to Delhi, cities like Beijing, Cape Town and
Bangkok also have a high TCI intensity, mainly because of their
material-intensive economies, power plants within boundaries and
roles in global supply chains reliant on industrial production with
relatively low value added and high energy intensity. In contrast,
London and Vienna have a lower TCI intensity with a higher
share of services in their urban economies. Our results show that
the TCI spatial density (meaning carbon in
fl
ow per urban area)
is the highest in Delhi (~96,000 t C km
2
), followed by Singapore
and New York, and is the lowest in Toronto (~7000 t C km
2
).
The difference of TCI density among cities is impacted by both the
magnitude of imported carbon for their urban metabolism and the
density of housing and public infrastructure. It should be noted
that these results may be subject to considerable uncertainty from
different sources, as described in the Methods.
Physical carbon balances of cities
. Using the proposed frame-
work, we quantitatively track the physical carbon
fl
ows of the 16
global cities from sources to economic sectors and then to change
in stocks or out
fl
ows (Fig.
3
). Most of the physical carbon
manipulated by cities is obtained from imports (IM). In the study
cities, between 88 and 92% of the physical carbon is gained from
outside the urban boundary, while only between 2 and 6% is
extracted from urban ecosystems, and between 3 and 8% is
recovered from recycling (RE) of materials. The physical carbon
import captures a very important part of the total carbon meta-
bolism of the cities, whose contribution is 47% on average. All the
cities rely heavily on external markets (domestic or global mar-
kets) to derive the physical carbon that supplies their urban
economies. For cities, such as Moscow, Bangkok, and Cape Town,
carbon imported in products accounts for more than half of their
total carbon balances, while local extraction and recycling only
contribute a very small fraction. The annual recycling of carbon
content in Stockholm, Vienna, and Tokyo contributes around 8%
of the input of physcial carbon (but <5% in terms of total carbon),
still small compared with physcial carbon imports. Research has
shown that much of the carbon emissions associated with con-
sumption in urban areas are outsourced via global supply chains,
and frequently to less-developed areas
15
,
16
. Here, we
fi
nd that a
dominant part of physical carbon used in urban production and
consumption is also outsourced. This could amplify the already
unequal exchange of gaseous emissions in trades, and con-
siderably increase the complexity of managing carbon
fl
ows
across boundaries. Supply of energy and construction of bulidings
and infrastructure present a challenge to achieving low-carbon
economies for cities like Beijing, Bangkok, and Cape Town, as
they account for nearly half of the physical carbon in
fl
ow (Sup-
plementary Fig. 2). In cities like London and Hong Kong service
sectors should receive more attention, as they represent up to 25%
of total physical carbon in
fl
ow.
The physical carbon inputs to cities have different metabolic
fates, ending up as gaseous emissions (GE), solid waste (SW),
household storage (HS), changes in stocks of urban economic
sectors (SC), and physcial export in goods (EX). On average, a
0.00
0.20
0.40
0.60
Sao Paulo
London
Vienna
Los Angeles
New York
Tokyo
Stockholm
Toronto
Sydney
Hong Kong
Singapore
Bangkok
Moscow
Cape Town
Beijng
Delhi
t/US$1000
Physical carbon
Virtual carbon
TCI intensity
(per unit GDP-PPP)
b
0.0
30.0
60.0
90.0
Toronto
Cape Town
Bangkok
Sao paulo
Sydney
Los Angeles
Vienna
Stockholm
London
Tokyo
Moscow
Hong Kong
Beijng
New York
Singapore
Delhi
1000t/km
2
Physical carbon
Virtual carbon
TCI spatial density
(per unit urban area)
c
0.00
5.00
10.00
15.00
Sao Paulo
Beijng
Bangkok
Delhi
Cape Town
Vienna
London
Stockholm
Tokyo
Hong Kong
Toronto
Moscow
Los Angeles
New York
Sydney
Singapore
t/capita
Physical carbon
Virtual carbon
TCI per capita
a
Fig. 2 Contributions of physical and fossil fuel combustion-related virtual carbon to the total carbon in
fl
ow of global cities represented by (a) per
capita (TCI per capita), (b) per GDP-PPP (TCI intensity), and (c) per urban area (TCI spatial density).
The TCIs for the 16 global cities encompassing
physical carbon and virtual carbon are shown by using various indicators. The contributions of physical and virtual carbon associated with urban eco
nomies
vary greatly, resulting in different carbon performances of cities (represented by per capita in
fl
ow, intensity, and spatial density).
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considerable amount of the carbon appropriated by cities
immediately become GE (i.e. CO
2
) from combustion of fossil
fuels by urban energy users. GE are ranging from 13 to 33% of the
total carbon appropriated (23%, on average, or 1.6 t C/capita),
with cities like Toronto, Moscow, and Los Angeles at the higher
end of the spectrum. The energy supply sector dominated in
many cities such as Hong Kong and New York accounting for
about 40% of their total emissions, while transportation
represented around 35% of the CO
2
emission from Sao Paulo
and Delhi.
The carbon stored in households as durable products (such as
wooden furniture, textile, plastics, rubber, papers, and paper-
board, but excluding fuels for cooking and driving) amounts to
between 3 and 13% (or 0.2
0.8 t C/capita) of cities
total carbon.
Much of the difference in this household carbon results from the
contribution of services re
fl
ecting the diverse demand levels and
Bangkok
Beijing
Cape Town
Delhi
Hong Kong
London
Los Angeles
Moscow
New York
Sao Paulo
Singapore
Stockholm
Sydney
Tokyo
Toronto
Vienna
2% LS
5% RE
49% IM
43% ICF
Ag
Mi
Ma
En
Co
Tr
Se
3%
1%
17%
26%
25%
8%
21%
HS 9%
GE 28%
SW 7%
EX 7%
SC 7%
CF 14%
EP 8%
HG 21%
Physical carbon flows
Fossil-fuel derived virtual carbon flows
1% LS
3% RE
50% IM
46% ICF
Ag
Mi
Ma
En
Co
Tr
Se
1%
1%
16%
26%
29%
10%
18%
HS 8%
GE 30%
SW 5%
EX 3%
SC 9%
CF 19%
EP 5%
HG 22%
1% LS
4% RE
47% IM
47% ICF
Ag
Mi
Ma
En
Co
Tr
Se
2%
0%
17%
24%
31%
4%
22%
HS 7%
GE 17%
SW 8%
EX 10%
SC 11%
CF 18%
EP 3%
HG 26%
2% LS
3% RE
45% IM
49% ICF
Ag
Mi
Ma
En
Co
Tr
Se
1%
1%
20%
27%
29%
6%
15%
HS 6%
GE 21%
SW 4%
EX 11%
SC 9%
CF 21%
EP 5%
HG 23%
Inflow
Outflow
Urban sector
3% LS
5% RE
53% IM
40% ICF
Ag
Mi
Ma
En
Co
Tr
Se
3%
0%
14%
27%
26%
6%
24%
HS 11%
GE 22%
SW 6%
EX 14%
SC 7%
CF 16%
EP 5%
HG 19%
2% LS
4% RE
55% IM
40% ICF
Ag
Mi
Ma
En
Co
Tr
Se
1%
1%
24%
23%
24%
5%
22%
HS 5%
GE 19%
SW 9%
EX 19%
SC 7%
CF 15%
EP 9%
HG 17%
3% LS
2% RE
61% IM
33% ICF
Ag
Mi
Ma
En
Co
Tr
Se
3%
2%
26%
16%
28%
10%
15%
HS 13%
GE 13%
SW 14%
EX 15%
SC 12%
CF 14%
EP 3%
HG 16%
1% LS
3% RE
38% IM
58% ICF
Ag
Mi
Ma
En
Co
Tr
Se
1%
1%
15%
31%
28%
6%
18%
HS 7%
GE 20%
SW 3%
EX 3%
SC 9%
CF 22%
EP 6%
HG 30%
2% LS
2% RE
50% IM
47% ICF
Ag
Mi
Ma
En
Co
Tr
Se
1%
1%
21%
26%
26%
9%
16%
HS 6%
GE 28%
SW 5%
EX 4%
SC 10%
CF 17%
EP 6%
HG 23%
1% LS
2% RE
41% IM
55% ICF
Ag
Mi
Ma
En
Co
Tr
Se
1%
1%
19%
27%
23%
8%
20%
HS 5%
GE 28%
SW 3%
EX 3%
SC 6%
CF 20%
EP 8%
HG 27%
1% LS
5% RE
47% IM
47% ICF
Ag
Mi
Ma
En
Co
Tr
Se
3%
1%
14%
28%
24%
7%
23%
HS 8%
GE 25%
SW 5%
EX 4%
SC 11%
CF 15%
EP 7%
HG 25%
2% LS
2% RE
28% IM
68% ICF
Ag
Mi
Ma
En
Co
Tr
Se
1%
1%
17%
27%
28%
5%
22%
HS 3%
GE 18%
SW 4%
EX 3%
SC 5%
CF 21%
EP 20%
HG 26%
2% LS
1% RE
36% IM
61% ICF
Ag
Mi
Ma
Co
Tr
1%
1%
22%
24%
28%
11%
14%
Se
En
HS 5%
GE 19%
SW 3%
EX 2%
SC 10%
CF 24%
EP 8%
HG 29%
4% LS
3% RE
55% IM
38% ICF
Ag
Mi
Ma
En
Co
Tr
Se
2%
2%
24%
20%
27%
14%
12%
HS 8%
GE 30%
SW 8%
EX 5%
SC 12%
CF 17%
EP 6%
HG 15%
4% LS
3% RE
52% IM
41% ICF
Ag
Mi
Ma
En
Co
Tr
Se
2%
2%
22%
22%
24%
13%
15%
HS 6%
GE 33%
SW 6%
EX 4%
SC 10%
CF 16%
EP 9%
HG 16%
2% LS
3% RE
37% IM
58% ICF
Ag
Mi
Ma
En
Co
Tr
Se
2%
2%
32%
23%
25%
6%
10%
HS 7%
GE 24%
SW 3%
EX 2%
SC 7%
CF 27%
EP 10%
HG 22%
Inflow
Outflow
Urban sector
Inflow
Outflow
Urban sector
Inflow
Outflow
Urban sector
Fig. 3 Physical carbon and fossil fuel-derived gaseous virtual carbon
fl
ows (excluding CH
4
) modeled for 16 global cities.
These Sankey diagrams show
the in- and out
fl
ows of physical carbon (in blue) and fossil fuel-derived virtual carbon (in red) associated with urban economic sectors. The numbers
represent the proportions of
fl
ows to the total carbon balance of the respective city. The physical carbon in
fl
ows include: imports from other regions (IM),
local supply by urban ecosystems (LS), and recycling of materials (RE), and physical carbon stocks and out
fl
ows, including household storage (HS),
changes in carbon stock in urban sectors (SC), gaseous emissions (GE), solid waste (SW), and physcial export of carbon in goods (EX). Fossil fuel-deri
ved
virtual carbon embodied in import (ICF) to cities is accounted for, and is then allocated to
fl
ows driven by household and government expenditure (HG),
fi
xed capital formation (CF), and exports as
fi
nal demands (EP). Fossil-fuel derived virtual carbon
fl
ows are modeled using input
output analysis. The
sectors are agriculture (Ag), mining (Mi), manufacturing (Ma), supply of energy (En), construction (Co), transportation (Tr), and services (Se).
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5
lifestyles between cities. Residents in cities like Moscow, Los
Angeles, and Toronto store more carbon than people living in
Delhi and Sao Paulo. This proportion of carbon is accumulated in
durable goods purchased by urban households rather than
immediately discarded or treated as waste. The difference is
mainly in the speed of carbon released to the atmosphere
depending on how long carbon is stored in households. In
addition to household storage, a considerable part of physical
carbon goes into industrial sectors and becomes part of the stock,
which is between 5 and 12% of the total carbon balance (or
0.3
0.9 t C/capita). The construction sector makes a large
contribution to stocks, and can be a huge component in rapidly
expanding cities such as Beijing, Delhi, and Sao Paulo. Adding
household storage and other urban stocks together, we
fi
nd
8
24% (or 0.6
1.5 t C/capita) of the total carbon appropriated by
cities is stored within the year of investigation, which is
comparable to the carbon already emitted to the atmosphere
for energy use in many cities investigated here. The carbon stored
in the form of durable products, infrastructure, buildings, or
production facilities can be emitted after a time delay, depending
on the nature of the stock. This stored carbon in cities is found to
be over two times of the global average per capita physical carbon
stock (in wooden and petroleum products) estimated by Peters
et al.
36
. Albeit with a different system boundary and research
scale from their study, these results may indicate that lives and
production in cities accumulate much more carbon than the rest
of the global economy on a per capita level. Similar
fi
ndings can
also be found in energy and material
fl
ows concentrated in cities
(e.g.,
41
,
42
).
The exports of physical carbon from cities are much smaller
than their imports. Around 6% (or 0.5 t C/capita) of the total
carbon appropriated by cities is exported or re-exported to other
regions as products. A large amount of this exported carbon is
from the service sectors (e.g., wholesale and retail trade) and is
large in cities like Singapore and Hong Kong. In addition, another
6% (or 0.4 t C/capita on average) of the total carbon becomes
solid waste that may be disposed off within or outside the urban
boundary. Given current treatment technologies, this carbon is
rarely recycled back to the urban economy, and may have been
partially released into the atmosphere through waste treatment
processes such as incineration.
Carbon sequestration by urban trees is found to be small in this
study compared to the total urban carbon metabolism (Supple-
mentary Fig. 3). Urban carbon sequestration only offsets, on
average, 2% of the territorial carbon emissions from cities and less
than 1% of their TCI, albeit with considerable uncertainty
introduced by estimating forest land cover and selecting
indicators of sequestration. Even for cities like Sao Paulo and
Bangkok, where urban forests occupy large areas of land, the
possibilities for offsetting through natural sinks are limited. The
low rates of carbon sequestration by trees in cities were also
reported in other studies
27
,
28
. While trees in cities have bene
fi
ts
for improving air quality and regulating microclimates, it may be
a more realistic option to create natural sinks outside urban
boundaries where the opportunity costs would be lower.
Virtual carbon balances of cities
. We also show the fossil fuel
combustion-related virtual carbon of cities and how it is attrib-
uted to urban sectors in terms of different
fi
nal demand categories
(household and government consumption, capital formation, and
export) (Fig.
3
). Studies have reported that upstream emissons
have a considerable in
fl
uence on the urban carbon balance
14
,
15
,
20
.
Our work further articulates that upstream emissions are sig-
ni
fi
cant even when they are accounted for in a broader context of
the carbon metabolism that includes both physical and virtual
carbon streams. We
fi
nd that in the whole balance, 30
53% of
total carbon is driven by local consumption and investment (i.e.,
household and government consumption and capital formation)
of the cities as gaseous upstream emissions (2.8 t C/capita, on
average), while gaseous carbon embodied in export as a
fi
nal
demand contributes a smaller part, varying from 3 to 20% of the
total balance (0.5 t C/capita, on average).
There is a high diversity in the fossil fuel combustion-related
virtual carbon driven by urban demands. Cities with high income
tend to have a bigger share of virtual emissions driven by
household and government consumption (Supplementary Fig. 4).
The supply of energy and services sector make a large
contribution to the virtual carbon emissions of many cities
(Supplementary Fig. 5). For example, household and government
consumption in Tokyo, New York and Los Angeles accounts for
more than 30% of their total carbon balances due to their large
imports of electricity for local consumption and products for
services sector, and this is over half of total virtual carbon
emissions associated with these cities. In comparison, higher
proportions of the virtual emissions are driven by capital
formation and export in Beijing, Bangkok, Delhi, and Sao Paulo.
For example, 45% of Beijing
s virtual emissions are associated
with capital formation because of construction of new buildings
and infrastructure as well as purchase of industrial equipment.
Discussion
Cities, important stores of carbon, play an important part in
the global carbon balance and in tackling climate change
3
,
4
,
25
.
Current frameworks for city-level carbon accounting were mainly
developed to capture gaseous carbon emissions within or across
boundaries (e.g.,
12
,
15
,
23
). They concentrate on determining how
much gaseous emission can be attributed to urban activities and
provide a basis for adopting emissions reduction targets based on
historical and current emission trajectories. In relation to these
efforts, the quanti
fi
cation and modeling of both physical carbon
and virtual carbon associated with an urban economy could be a
new and complementary perspective for decarbonization. Based
on an integrated framework, we can target both what has been
emitted into the atmosphere and what may come in the future
that will in
fl
uence climate change mitigation. The inputs, dis-
tribution, and metabolic fate of carbon appropriated by cities can
be tracked based on a harmonized global urban dataset. A
meaningful comparison between different streams of carbon,
such as carbon imports and exports, or carbon that is trans-
formed into stocks versus gaseous carbon can be made within this
consistent framework.
The proposed indicators could provide new insights into the
carbon impacts of urban areas. The TCIs to global cities vary
widely, regardless of whether they are measured in per capita,
intensity, or spatial density units. Cities such as Vienna, London,
and Tokyo exhibit a comparatively low-carbon pathway con-
sidering the whole supply chain. However, their approach may
not be appropriate for all cities. While it may be, as suggested,
possible for cities to form partnerships or collaborative networks
(e.g.,
43
,
44
) when building a low-carbon future, it is dif
fi
cult or
even counterproductive to have the same one-size-
fi
ts-all miti-
gation approach. Scholars have recognized the construction of
low-carbon roadmap for cities should not only be based on their
existing emissions, but also on socioeconomic pro
fi
le, infra-
structure and other metabolic characteristics
41
,
42
,
45
, all factors
that are important in restraining future carbon budgets shared by
urban economies. But there are no simple correlations between
single urban characteristics (such as population density, share of
services sector and income) and the carbon impact, as found by
our study and other research
42
,
45
. While it is still important to
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analyze the drivers underlying carbon emissions, an equally useful
and straightforward cut-in point could be scrutinizing carbon
fl
ows in the entire urban metabolism, including physical and
virtual carbon, and not just gaseous emissions. Ideally, cities
low-
carbon roadmaps should be based upon carbon
fl
ows at the urban
sector level (or even at the process level) and from a life-cycle
perspective, with their linkages to different metabolic pathways
quanti
fi
ed and mapped.
Both physical carbon appropriated within the urban territory
and virtual emissions occurring outside the urban boundaries
strongly in
fl
uence cities
carbon metabolism, largely consistent
with what has been found at national scale
36
. Although nearly
half of the carbon metabolism is outsourced through production
outside urban boundaries, a large amount of carbon trapped in
imported products and stored in the economy can still be man-
aged within the reach of the city. This stored carbon is found by
this study to be at least twice as big as the global average per
capita, but it is much less studied, especially at city level, than the
existing carbon emissions impacting the climate. The carbon
temporarily stored in households and other urban stocks can
contribute a big potential for mitigation that is comparable to the
amount of annual carbon emissions from within cities. In almost
all study cities, household storage is found to be a signi
fi
cant
carbon stock across different levels of income and stages of
development, mostly because these carbon-containing products
are essential for all societies (for housing, transport and other
important aspects of living). Most of this household-related car-
bon will eventually be released into the atmosphere
25
, albeit this
may take from a few years to many decades. Durable products
and materials stored in households and other sectors (such as
wooden furniture, textiles, plastics, and rubber) usually have a
long service life and may undergo another long period of slow
release to the atmosphere after usage. Therefore, cities can still
take advantage of this time lag to manage, or at least at this
point, regularly monitor their carbon in
fl
ows and carbon stocks.
The so-called asymmetrical effect of changes and lags dependent
on economic scale and carbon emission dynamics has been dis-
cussed in the literature
46
. Taking the carbon retained in urban
durable goods into account, this asymmetrical effect could be
larger and longer lasting than expected. This is because stock-
originated emissions may continue to be released with some
inertia even when economic growth has slowed down or stopped
altogether.
Studies have indicated that committed carbon emissions from
current urban infrastructure account for a big share of future
GHGs
47
,
48
. In addition to the impact from buildings and
updating infrastructure in cities, the less-studied aspect, i.e., the
carbon trapped in these infrastruture and other durable products
has also shown to be important as potential sources of future
emissions. Investments in urban stocks (e.g., housing stock,
production facilities, and infrastructure) have strong implications
for carbon emissions during their lifetime. These stocks should
also be regularly examined as part of the committed responsibility
to decarbonization, and for the nonrecyclable stocks, timely
action should be taken when they are disposed of as waste.
Considerable evidence suggests a large amount of carbon is being
emitted globally caused by solid waste disposed in land
fi
lls or to
incineration
33
,
49
,
50
. In most regions and cities, there is no sorting
system to separate carbon-containing waste (woods, plastics, etc.)
from other waste before they are incinerated
32
. Therefore, a sig-
ni
fi
cant potential for climate change mitigation lies in managing
the urban stocks during their lifetime. Taking the modeling of
carbon metabolism of cities as a
fi
rst step, more research is
needed to track urban durable products and their potential
fates as emissions from land
fi
ll, combustion (either on open lands
or in waste-to-fuel plants), and reuse or recycling. Such research
is critical for pinpointing which stock management options
could be promising for cities in order to stabilize future global
climate.
Methods
Relationship to previous studies
. In this study, an integrated approach is
developed to track various metabolic
fl
ows of physical carbon through cities as well
as
fl
ows of fossil fuel combustion-related virtual carbon emissions attributed to
urban demands. It provides a different perspective from the inventories of gaseous
carbon emissions based on energy consumption and industrial processes (e.g.,
citywide inventories
7
,
8
based on IPCC guidelines
51
) as well as the modeling of
embodied emissions in trade (e.g.,
15
,
19
,
20
). Our approach not only captures the
historical carbon emissions that have already been released to the atmosphere
(either from within or outside urban boundaries), but also identi
fi
es future
potential emissions hidden in carbon
fl
ows such as changes in stock of households
and other economic sectors. This latter point also distinguishes our framework
from other carbon accounting schemes, such as the 3-scope Greenhouse Gas
Protocol proposed by ICLEI, WRI, and C40
11
,
12
, and the wide production-
19
,
infrastructure-,
15
and consumption-based carbon footprints
17
that concentrate
their accounts on fossil-fuel related GHG emissions and target economic activities
causing these emissions.
There has been research that linked the urban metabolic framework to footprint
analysis by combing MFA with life-cycle approaches (such as LCA and IOA) and
evaluated the environmental impacts of cities, for example, the works of Hillman
and Ramaswami
21
, Goldstein et al.
52
, as well as other related models at country
level (e.g., Eco-LCA nitrogen model for the US economy
53
and MFA-IOA material
footprint model for nations
37
). A national-scale study by Peters et al.
36
synthesized
CO
2
embodied in import as well as physical carbon present in materials, with a
focus of quantifying total carbon linked by international trade. The integration of
MFA, LCA, and IOA here has a different focus from the abovementioned studies,
i.e., consistently tracking various metabolic pathways of physical carbon from
in
fl
ows to emissions, changes in urban stocks, solid waste or physcial export as well
as virtual emission from import to
fi
nal demand categories. Hao et al.
54
quanti
fi
ed
several types of urban carbon
fl
ows and stocks for one mountainous Chinese city at
a very aggregate level, different from the detailed sector-based accounting and
modeling of various metabolic pathways conducted in this study, where a
harmonized carbon dataset of global cities is compiled and used. We also illustrate
the linkages to and differences from previous studies in Supplementary Fig. 6.
Integrated framework for carbon metabolism
. The technical framework for
modeling the physical carbon and the fossil fuel combustion-related virtual carbon
metabolism in cities is illustrated in Fig.
4
. All the carbon
fl
ows of the urban
economy are tracked and allocated to seven aggregate economic sectors: agriculture
(Ag); mining (Mi); manufacturing (Ma); supply of electricity, gas, and hot water
(En); construction (Co); transportation (Tr), and services (Se). This integrated
framework allows us to trace the in
fl
ows, stocks, and out
fl
ows of physical carbon
content and virtual emissions associated with these urban sectors. Currently,
city-scale carbon inventories are mainly based on energy
fl
ow analyses, life-cycle
analyses, or hybrid models that track emissions precede urban consumption
(e.g.,
20
22
). By integrating MFA, LCA, and IOA, our approach encompasses both
fl
ows of physical carbon and fossil fuel combustion-related virtual carbon, which
could provide a broader view on the carbon impact of urban activities and which
fl
ows to target for a more systemic and informed carbon emission mitigation.
Scope and consistency
. The
fl
ows of physical carbon in the paper are quanti
fi
ed
based on the carbon content of products and materials, consistent with the de
fi
-
nition in existing urban carbon inventories
25
,
29
and national
fl
ow inventories
30
,
36
.
In addition, the
fl
ows of fossil fuel combustion-related virtual carbon are modeled
based on upstream carbon emission (CO
2
), excluding the upstream carbon content
in products that is indirectly linked to the carbon in
fl
ow, consistent with the
de
fi
nition of virtual carbon commonly used in the majority of literature (e.g.,
38
,
39
).
For example, in terms of food, we consider the carbon content in food products as
well as upstream gaseous virtual carbon for food production and processing, but
exclude other upstream non-gaseous carbon (e.g., the carbon content of fertilizers
used in agricultural production). The same can be extended to the scopes of other
physical carbon
fl
ows. Accounting for the upstream physical carbon content based
on direct urban carbon consumption data and city-level IO table, at this stage, is
dif
fi
cult since some of the physical
fl
ows during the extraction and processing (such
as the loss of carbon during cropping, harvesting, and processing) will not be
captured
55
. Current material extraction datasets are mostly developed at the
national level
37
and no worldwide data exist for cities. We focus our global-city
study on the physical carbon in products in
fl
ows to and fossil fuel combustion-
related virtual carbon with a clearly-de
fi
ned boundary that matches with city-scale
metabolic data. Despite the exclusion of the upstream carbon content, the carbon
inventory in the model is self-consistent in that the physical carbon balance from
in
fl
ows to out
fl
ows is accounted for independently from the balance of virtual
emissions. The city-level energy and materials data compiled meet our research
goal of tracking carbon metabolic pathways through cities.
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7
Linkage of the metabolic framework to climate policy
. In this study, we do not
intend to quantify exactly how much GHG will be emitted from each type of
carbon-containing products. Instead, we aim to unlock the potential of carbon
mitigation hidden in the less-studied carbon
fl
ows attributed to cities. We differ-
entiate what have already become gaseous emissions and what have not yet become
emissions (such as urban stocks) but still hold the potential of releasing carbon into
the atmosphere over their remaining life cycles. Most urban stocks will eventually
end up in waste after the service life of products
25
. Studies have quanti
fi
ed the
GHG emissions from a range of techniques applied in solid waste disposal. The
World Bank reported over 90% of waste is burned or dumped on roads, open land,
or waterways in many low-income countries
32
, contributing to a large amount of
unintended CO
2
or CH
4
emissions
33
,
49
. Cities transport part of the waste outside
their boundaries for land
fi
lling, and in this process a considerable amount of
unaccounted carbon emissions leak into the atmosphere. Incineration (e.g., using
waste for electricity generation or heating) is frequently used for waste disposal,
especially in high-income regions. Evidence shows that from a life-cycle perspec-
tive, incineration will still cause net GHG emissions even when solid waste is
incinerated in modern facilities compared to recycling of these materials
(e.g.,
33
,
56
,
57
). The strong implication of solid waste for climate change has also
been acknowledged by global-scale studies, such as analyses on plastic waste
50
and
food waste
58
. There have already been discussions of including stock management
in climate change mitigation (e.g.,
34
36
). In relevance to these efforts, we portray
the carbon metabolic pathways through cities and identify the potential of dec-
arbonization from managing urban stocks.
Accounting of physical carbon
fl
ows
. The accounting scheme for physical carbon
is guided by standards established in MFA (e.g.,
37
,
59
). They are adapted to city-
scale inventory of physical carbon from in
fl
ows to stock changes and to out
fl
ows at
a detailed sector level. Physical carbon in
fl
ows (PCF
in
) account for the carbon
content in goods and raw materials imported to the urban economy (IM, see
Supplementary Table 1); recycling of carbon content in materials within the urban
economy (through a city
s refuse reclamation); and local supply of carbon from
urban ecosystems (local supplies (LS), such as biomass extracted from urban forests
and parks). At the other end, the physical carbon stock and out
fl
ows (PCF
sto
+
out
)
are represented by
fi
ve
fl
ow categories (or metabolic outputs): household storage
(HS), changes in carbon stock in industrial sectors (SC), gaseous emissions (GE),
solid waste (SW), and physcial export (EX). Territorial carbon emissions mainly
originate from imported fossil fuels and are released during energy uses inside the
city. They are tracked and quanti
fi
ed based on IPCC guidelines for GHG inven-
tory
51
. HS accounts for carbon that is stored in households for more than 1 year
(such as wooden furniture and other durable products), while the carbon in less
durable products such as food becomes part of SW. The change in the carbon
stocks in all urban sectors (in the form of buildings, infrastructure, and capital
goods) excluding household purchases are accounted for by SC. Finally, EX
represents the carbon contents in products that are shipped to other regions.
Similar to prior carbon metabolic studies (e.g.,
26
,
29
,
34
), we convert key
imported products and materials to their corresponding carbon content (i.e., the
amount of carbon they contain). These products and materials, include food, fossil
fuels (e.g. coal, coke, petroleum, and natural gas) for transportation, industrial and
residential use, construction materials (wood, cement, and steel), carbon-intensive
products (plastics, rubber, glass, and paper), furniture, and electronic goods. The
physical carbon in
fl
ow
ð
PCF
in
i
Þ
, and stock change and out
fl
ow
ð
PCF
sto
þ
out
i
Þ
related
to sector
i
of an urban economy are represented as follows
PCF
in
i
¼
IM
i
þ
LS
i
þ
RE
i
;
ð
1
Þ
PCF
sto
þ
out
i
¼
HS
i
þ
GE
i
þ
SW
i
þ
EX
i
þ
SC
i
;
ð
2
Þ
where carbon is appropriated by the cities through IM, LS, and RE, and then
allocated to several changes in stock and out
fl
ows, including HS, SC, GE, SW, and
EX. The total of all physical in
fl
ows is equal to the annual changes in the carbon
stock and out
fl
ows of the urban economy (including all
n
urban economic sectors).
The physical carbon balance is established as
X
n
i
¼
1
PCF
in
i
¼
X
n
i
¼
1
PCF
n
sto
þ
out
i
:
ð
3
Þ
Carbon sequestration by urban trees represents a natural carbon sink in urban
areas. Through this process, the amount of CO
2
released into the atmosphere can
be reduced to varying degrees, depending on land use and vegetation distribution
in the urban area. The
fl
ow of carbon sequestration is analyzed to articulate by how
much urban ecosystems can offset emissions from cities in the context of urban
metabolism. As in previous studies (e.g.,
27
,
28
), we use forest coverage and reference
values of the carbon sequestration rate for each city to estimate the capacity for
carbon sequestration by urban trees.
Modeling of fossil fuel-derived virtual carbon
fl
ows
. The second part of the
urban carbon metabolism involves the tracking of fossil fuel combustion-related
virtual carbon (VCF), including carbon emissions embodied in imports of elec-
tricity and other goods and services to a city. It is important to note that, when
computing gaseous virtual carbon, carbon emissions from in-city energy use and
industrial processes are excluded as they are already included in the physical
carbon (as GE).
Many studies have used IOA to compute virtual (or upstream) carbon
fl
ows
(e.g.,
17
,
19
,
20
). IOA is useful for tracking urban carbon
fl
ows since it captures the
entire supply chains related to the urban economy. However, there are fewer IO
tables complied for cities than for nations. The distinct economic characteristics of
cities are only partly considered when national IO tables are downscaled and used
to estimate the urban footprint. LCA provides an alternative approach for
accounting for emissions from upstream and downstream processes without the
constrains of IO table
14
,
52
. In this study, a hybrid life-cycle analysis is used to
model virtual carbon emission at an urban scale. First, we quantify the import-
related carbon emissions and respective carbon intensities (i.e., carbon emissions
per unit of output) based on LCA. These carbon intensities differentiate production
technologies for supplying products to a city. For example, electricity-related
carbon intensity is calculated from the different energy mixes in a city
s power grid.
On this basis, we are able to quantify the virtual carbon embodied in upstream
production for cities. The import-related virtual emission is further allocated to a
city
s
fi
nal demand categories (VCF
fd
). These
fi
nal demand categories, consistent
with mainstream IO models, include household and government consumption,
capital formation, and exports.
k
i
¼
VCF
im
i
=
X
i
;
ð
4
Þ
VCF
fd
i
¼
k
i
ð
I

A
Þ

1
y
HG
i
þ
k
i
ð
I

A
Þ

1
y
CF
i
þ
k
i
ð
I

A
Þ

1
y
EP
i
;
ð
5
Þ
Local supply (LS)
Recycling (RE)
Household storage (HS)
Change in stocks (SC)
Exports of products (EX)
Solid waste (SW)
Gaseous emissions (GE)
Imports (IM)
Export as final demand (EP)
Upstream
production
(ICF)
Physical carbon
inflow
(
PCF
in
)
Virtual carbon
emission in final
demand
(
VCF
fd
)
Physical carbon
stock or outflow
(
PCF
sto+out
)
Virtual carbon
emission in
import
(
VCF
im
)
Local consumption (HG)
Urban territorial boundary
Capital formation (CF)
Urban economy
Agriculture (Ag)
Mining (Mi)
Manufacturing (Ma)
Supply of energy (En)
Construction (Co)
Transportation (Tr)
Services (Se)
Fig. 4 Framework for tracking urban physical and virtual carbon metabolism.
To capture the broader carbon impact of an urban economy, we combine
physical carbon account and fossil fuel-derived virtual carbon account within a consistent framework of carbon metabolism. First, we track the phys
ical
carbon appropriated by a city as goods or raw materials imported from outside (IM), local supply from urban ecosystems (LS), or recycling of materials
(RE), and how this carbon is distributed within the urban economy and become part of household storage (HS), changes in stock industrial sectors (SC),
gaseous emissions (GE), solid waste (SW), or physical exports as goods (EX). Second, we model the virtual carbon emissions manipulated by a city
through its import of products and further allocate them to local (household and government) consumption (HG), capital formation (CF), and exports a
s
fi
nal demand (EP).
ARTICLE
NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-13757-3
8
NATURE COMMUNICATIONS
| (2020) 11:182 | https://doi.org/10.1038/s41467-019-13757-3 | www.nature.com/naturecommunications