An integrated analysis of input and output flows in an urban carbon metabolism using a spatially explicit network model

Journal of Cleaner Production 239 (2019) 118063

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An integrated analysis of input and output flows in an urban carbon metabolism using a spatially explicit network model Linlin Xia a, b, Yan Zhang a, *, Xiangyi Yu c, **, Chenling Fu a, Yaoguang Li a a State Key Joint Laboratory of Environment Simulation and Pollution Control, School of Environment, Beijing Normal University, Xinjiekouwai Street No. 19, Beijing 100875, China b Guangdong Key Laboratory of Environmental Pollution and Health, School of Environment, Jinan University, Guangzhou 510632, China c Solid Waste and Chemicals Management Center, Ministry of Ecology and Environment of the People's Republic of China, Yuhuinanlu No. 1, Chaoyang District, Beijing, 100029, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 January 2019 Received in revised form 29 June 2019 Accepted 15 August 2019 Available online 16 August 2019

An integrated analysis of urban carbon metabolism from both input and output perspectives can present new insights to support carbon mitigation. In this study, we combined a previously developed spatially explicit network model with an analysis of carbon sequestration and emission by different land use or cover types, and illustrate its use by examining carbon flows in Beijing, China, from 1990 to 2015. The goals were to characterize the temporal changes of the integrated (total direct þ indirect) flow structure by applying ecological network analysis and to identify the structure of the urban metabolism by analyzing temporal and spatial changes of the integrated flows. The results showed that the similarity between input and output trophic structures and their spatial pattern indicate increasingly carbonbalanced urbanization by Beijing. The balanced input and output flows for the transportation and industrial land and cultivated land played key roles in forming a central area of aggregated carbon flows between the city's peripheral plains, which also resulted in similar trophic structures for inputs and outputs. Understanding the evolution of the integrated flows during urban development provides a more solid empirical basis for regulating land-use change, improving land consolidation, and reducing carbon flows. © 2019 Elsevier Ltd. All rights reserved.

Handling Editor: Jun Bi Keywords: Urban carbon metabolism Input and output flows Integrated behaviors Spatially explicit network

1. Introduction Urban areas produce 70% of the global carbon emissions (Seto et al., 2014), so reducing these emissions is essential to mitigate climate change. Urbanization is also the main driver of land use and cover change (LUCC) (Yao et al., 2017), which contributes about one-third of the carbon emissions from urban areas (IPCC, 2006). As LUCC represents the consequences of many socioeconomic and natural activities, this process increasingly affects the interactions between and coevolution of a city's natural and social systems. Large exchanges of energy and resources occur within and between

* Corresponding author. State Key Joint Laboratory of Environmental Simulation and Pollution Control, School of Environment, Beijing Normal University, Xinjiekouwai Street No. 19, Beijing, 100875, China. ** Corresponding author. Solid Waste and Chemicals Management Center, Ministry of Ecology and Environment of the People's Republic of China, Yuhuinanlu No. 1, Chaoyang District, Beijing, 100029, China. E-mail addresses: [email protected] (Y. Zhang), [email protected] (X. Yu). https://doi.org/10.1016/j.jclepro.2019.118063 0959-6526/© 2019 Elsevier Ltd. All rights reserved.

groups of socioeconomic and natural activities (Huang and Ulanowicz, 2014) and these exchanges are complicated by frequent LUCC. Accounting for these interactions would improve the rationality of spatial planning in cities and achieve a winewin solution by simultaneously regulating LUCC and reducing carbon emissions. Applying ecological principles to urban systems accounts for the complex evolutionary development patterns that develop during urbanization (Fath et al., 2010). Similarly, the flows of an element such as carbon through an urban system resemble the flows that occur within an organism's metabolism, and can be modeled by analogy with metabolic flows (Wolman, 1965). Such analyses have been conducted to understand the transformation processes and environmental impacts of carbon from a system perspective (Pataki et al., 2006). In this analogy, cities both import carbon from their external environment, and export carbon to their external environment (i.e., the atmosphere and ecosystems that surround and support the city). An imbalance between these inputs and outputs can cause a “metabolic disorder” that affects the overall structure

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and function of the urban system (Fath and Patten, 1999; Zhang, 2013; Zhang et al., 2015a). Exploring these effects requires an examination of both input and output flows, which can be analyzed using tools such as ecological network analysis, and the results can support efforts to develop a low-carbon city (Kennedy et al., 2011). Carbon metabolic analyses have been frequently applied to support sustainable urban planning and design by integrating the many flows of energy and materials within an urban system (Kennedy et al., 2010; Ye et al., 2011). Examples include studies of carbon emission related to flows of energy and materials in an urban area and the surrounding areas (Krausmann, 2013; Zheng et al., 2016), and studies of functional carbon flows that result from LUCC (Wang et al., 2016; Xia et al., 2016b). In this context, the methods of urban metabolic analysis provide a good analytical framework for examining the temporal and spatial dynamics of processes that involve carbon flows (Chen and Chen, 2017; Conke and Ferreira, 2015; Kennedy et al., 2007; Krausmann, 2013; Wang et al., 2016; Xia et al., 2016b). This makes it possible to assess the evolution of a system and its processes and to determine the resulting structural and functional changes in the input and output flows. Jacobs (1961) stated that the goal of urban planning is to solve the problems that arise from a city's organized complexity and a model of an urban system that could be used to examine the evolution of this complex structure is urgently required. Ecological network analysis provides powerful and broadly applicable analytical tools to explore the behavior of such a complex system by refining traditional black-box models, which do not consider the flows inside a system, into models that describe the network of flows within the system (Fath and Grant, 2007; Ulanowicz, 2004; Zhang et al., 2015b). One of the great contributions of ecological network analysis to urban research is its ability to quantify both the direct and indirect flows that define the relationships between system components (Borrett et al., 2006; Fath and Killian, 2007; Hannon, 1973; Patten, 1982; Schramski et al., 2007). Because these flows are integrated (summed up) to provide a total flow, we have used the term “integrated” to describe these flows; however, some papers on ecological network analysis use the word “integral” instead. In an ecological network, direct flows between two connected components (i.e., flows that do not pass through an intermediate component) are integrated with indirect flows (i.e., flows that pass through at least one intermediate component) to describe both the direct and the indirect relationships between all of the system's components (Fath, 2012). Studies of the indirect flows and their effects have attracted increasing attention from researchers because of the size and importance of these flows in both natural and artificial systems (Borrett et al., 2006; Zhang et al., 2016a). Thus, a comprehensive integrated analysis that accounts for both direct and indirect flows is necessary to reveal the true magnitudes and directions of the input and output flows. Understanding the relationships among a system's components also provides meaningful information that can be used to increase urban sustainability by regulating the interactions among the system's artificial and natural components (Fath, 2015). Researchers have attempted to model and analyze the carbon metabolic networks of cities around the world, including studies of Vienna and Hong Kong (Chen and Chen, 2012a, b). In these analyses, relationships among the interacting components can be considered to be analogous to the relationships among the organisms in a natural food web. These relationships combine the weights of the flows and the resulting system trophic structure to explain the relative status and the functions of the components and thus, the nature of the system (Deehr et al., 2014; Fath et al., 2010; Zhang et al., 2010, 2012). Various trophic structures have been revealed for urban carbon-flow networks: a balanced pyramidal structure (Lu et al.,

2015), a relatively unbalanced spindle shape (Zhang et al., 2014b), and an unbalanced inverted pyramid (Fath et al., 2010). Understanding which structure exists for a city's urban metabolism helps planners understand whether and how the structure must be adjusted to make the system more sustainable (Ulanowicz, 2004). In addition to an overall flow structure, which represents an average for the large physical objects that cities represent, there is often considerable spatial variation in the urban structure. One novelty of the present study is that it characterizes the spatial distribution of land-use changes, thereby allowing policy developers to develop location-specific policies that will constrain land-use change in ways that increase carbon sequestration or decrease carbon emission. The spatial pattern of urban carbon flows (emission and sequestration) that results from this variation is an important research subject, particularly since the development of remote sensing technology and geographic information system software, which together allow analysis over large areas (Gonzalez, 2005; Mitraka et al., 2012). Researchers have applied different definitions of a system's boundaries, such as the administrative boundary versus the boundary between the built-up area and its surroundings, and have defined different land use and cover types (Houghton et al., 2012; Wang et al., 2015). For example, Svirejeva-Hopkins and Schellnhuber (2006) divided a city into “green” areas, slums, and built-up areas, whereas Hutyra et al. (2011) defined the spatial distribution of carbon emission and sequestration based on the distance from the city center. Our research group combined these approaches to analyze the spatial pattern of carbon emission and sequestration (Zhang et al., 2014a). However, that study did not focus on quantifying the integrated flows by means of ecological network analysis. The indirect effects of the carbon flows on the spatial pattern should also be quantified, and that became one of the goals of the present study. The studies conducted thus far have provided good insights into the temporal and spatial dynamics of the urban carbon metabolism using a spatially explicit network model. To build on this research, the present study monitored the evolution of Beijing's carbon metabolism from 1990 to 2015 by combining ecological network analysis with geographical information system software. The study constructed an integrated framework to assess the variations of Beijing's characteristics from both input and output perspectives to reveal how they have been affected by urbanization. The objectives of the research were (1) to reveal the temporal and spatial changes in the integrated flows of carbon (i.e. the sum of the direct and indirect flows); (2) to determine indirect and direct effects of these flows during urbanization; and (3) to characterize the temporal changes in Beijing's trophic structure to reveal problems with the structure of the city's carbon metabolic system. This research provides a theoretical basis for adjustments of the flows among different sectors and urban areas. 2. Materials and methods Details of the analyses are presented in the Supplemental Information. Here, we have summarized the overall process used to create the model. 2.1. Model construction The present study builds on a spatially explicit network model of carbon metabolism constructed in previous studies (Xia et al., 2016b; Zhang et al., 2016b). Sections 1 and 2 of the Supplemental Information provide details of the model. In an ecological network, components link to the world through their input and output environments (Fath and Patten, 1999). The network model was constructed using a 5-year time step to provide enough time for land

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use to change, and the input and output flows were differentiated to define the system's behaviors. Fig. 1 illustrates the changes in storage and flows that occur when land is transferred from component j to component i. For example, when bare land is converted to forest (i.e, when the land is transferred between these two uses), its carbon storage increases, whereas the conversion of forest to bare land represents a loss of that stored carbon, which is equivalent to emission of that carbon into the atmosphere; thus, LUCC can serve as a proxy for carbon sequestration and emission. In our analysis, components of the urban system (each representing a specific area with its own land use or cover type) change over time. If a component changes from land use j to land use i, then the carbon storage of that component changes from Sj to Si (Fig. 1a and b) and the change is defined as DS.

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Carbon sequestration in Si and Sj (xj(t0), xj(t), xi(t0), and xi(t), in kg C yr1) are represented as storage changes in the network. The area that changes from land type j to land type i also triggers changes in carbon storage for the two land use categories. For simplicity, we assumed that the changed area (DS) released all of its carbon stock (xjDS, kg C, Fig. 1a) into the atmosphere when land type j turns into land type i and that land type i then recaptured some or all of this carbon, depending on its carbon sequestration capacity (xiDS, kg C, Fig. 1b). We considered the carbon storage to be homologous with carbon flows, which means that storage in a component became a flow term through turnover (Fath and Patten, 1999); here, “turnover” represents a change to a different land use. Because this form of network flow analysis is conducted in most urban metabolism studies (Chen and Chen, 2012b; Fath et al., 2010), we also used it in

Fig. 1. Description of urban carbon metabolic flows. (a) Land component j in the output environment. (b) Land component i in the input environment. (c) Land component j in the output environment. Variables: fij, flow from component j to component i; i and j, components of the system; S, land area; t, time (t0, the start time); W, carbon metabolic density; x, carbon storage; y, outflow from the system to the environment; z, inflow from the system to the environment.

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the present study. We defined the change in carbon sequestration capacity to represent the network flows (i.e., the change in land use served as a proxy for the actual carbon flow). As shown in Fig. 1c, a change in land use for a given area causes that area to lose the carbon sequestration capacity of its original land type (DS is negative) but gain the carbon sequestration capacity of its new land type (DS is positive); that is, the corresponding sequestration capacity is yj(t), in kg C yr1, and the carbon flow to component i (fij(t), in kg C yr1, is based on the sequestration capacity (zi(t), in kg C yr1). According to IPCC (2006), carbon flows could be calculated at the end of a time period. Then, at time t, network flow can be calculated as follows:

dimensionless inter-component flows from component j to component i are calculated as gij ¼ fij/Tj for input flows and g'ij ¼ fij/Ti for output flows, where Tj and Ti are the total output and input throughflow for components j and i, respectively. We also calculated the system-level indirect flow to direct flow ratio (IDR) to explore the importance of the indirect flows in the 0 0 study system. The indirect flows were calculated as N IF for 0 output flows and as NeIeF for input flows, where F and F represent the direct output and input flow matrices, respectively. IDR equaled the ratio of the sum of the indirect flows to the sum of the direct flows. 2.4. Variations in the integrated structure

fij(t) ¼ jWj(t) Wi(t)j  DS

(1)

zvi(t) ¼ Wi(t)  DS

(2)

yvj(t) ¼ Wj(t)  DS

(3)

where Wj(t) and Wi(t) are the carbon metabolic densities of components j and i, respectively, at time t, and zvi(t) and yvj(t) are the inflow from the external environment to the system and the outflow from the system to the external environment. W, z, y, and fij are used in the analysis described in the rest of section 2. 2.2. Flow inventory Carbon emission and sequestration rates (kg C yr1) were calculated at 5-year intervals from 1990 to 2015. We used government statistical data for Beijing and the empirical coefficients described in Section 4 of the Supplemental Information to calculate carbon emission (including human breathing) and sequestration (Zhang et al., 2014a). For example, the carbon emission accounting for urban land accounted for all of the urban socioeconomic activities that produce carbon emission: energy consumption from the water, electricity, gas supply and production, wholesale, retail and services, and construction industries, as well as urban households and human breathing. Sections 3 and 4 of the Supplemental Information provide details of these processes. 2.3. Integrated flows and indirect effects An integrated flow equals the sum of the inputs and outputs contained in both the direct and indirect flows (Fath and Patten, 0 1999). The integrated output and input flows are given by N and N, respectively:


0   0  0 1  0 2  0 3  0 m 0 0 N ¼ nij ¼ G þ G þ G þ G þ / þ G  0 1 ¼ IG

2.5. Spatial variation of the integrated flows 0

(7)

  N ¼ nij ¼ ðGÞ0 þ ðGÞ1 þ ðGÞ2 þ ðGÞ3 þ / þ ðGÞm ¼ ðI  GÞ1 (8) 0

Integrated structures were defined by using the weights of the flows and the relationships between pairs of components in the system (Yang et al., 2014). Section 5 of the Supplemental Information provides details of this calculation. Relationships defined the positions of nodes (i.e., the level of each component within the integrated structure) and the integrated flows defined its strength at that level (i.e., the contribution of that level to the total flows). Components with high numbers of relationships in which they benefit from flows from other components appear higher in the trophic hierarchy, as described in Section 5 of the Supplemental Information. We quantified the interactions among the components (i.e., their ecological relationships) using ecological network analysis (Xia et al., 2016a). 0 Matrix N maps outputs into the throughflow along all paths. 0 0 0 0 0 The column vector nj ¼ ðn1j ; n2j ; n3j ; /nmj Þ reflects the integrated Pm 0flows that component j contributes to components 1 to m. output n i¼1 ij Pm P m 0 represents the integrated output weight of component j n j¼1 i¼1 ij and defines the output structure. Matrix N maps inputs into throughflows along all paths. The row vector Pm ni ¼ ðni1 ; ni2 ; ni3 ; /; nim Þ then reflects the integrated input flows n j¼1 ij that component i obtains from nodes 1 to m. Pm P represents m n i¼1 j¼1 ij the integrated input weight of component i and defines the input structure. We examined the changes of the output and input structures during 5-year time periods from 1990 to 2015. We determined the influences of the direct and indirect flows on the output and input structures by comparing these flows between consecutive time periods during Beijing's urbanization process. We conducted the sensitivity analyses for selected coefficients to examine the influence of their values on the model's outputs, including ecological relationships, integrated flows and IDR value from both input and output orientation (Tables S4eS8).

where N and N are the dimensionless integrated flow intensity matrices, and G′ and G represent the direct flow intensity matrix. The integrated flow comprises three parts: a component's initial state, which is represented by the identity matrix I, and implies flows of length 0 (i.e., flows within the component), represented by 0 ðG Þ0 and ðGÞ0 , respectively; direct flows to a second component that do not pass through an intermediate component, represented 0 by ðG Þ1 and ðGÞ1 , respectively; and indirect flows, which pass through me1 components before reaching their final destination, 0 represented by ðG Þm and ðGÞm , respectively, for m > 1. The

By examining ðN  IÞ and ðN  IÞ, we calculated the direct and indirect flow matrices for the input and output flows along each path between components. All the paths were tracked using the land transition matrix, and their positions were recorded using version 10.3 of ArcGIS (http://www.esri.com/). The land information for Beijing was obtained from spatially explicit digital land-use data with a 30-m grid resolution for the years 1990, 1995, 2000, 2005, 2010, and 2015, which we obtained from the Institute of Geographic Sciences and Natural Resources Research. The interpretation process is described in previous research (Xu and Min, 2013; Xu et al., 2012). See Section 3 of the Supplemental Information for more details. Using the spatial variations in the input and output structures for the direct and indirect flows, the flows that resulted from LUCC within the urban system were determined by examining all of the paths that contained integrated flows using ArcGIS. These integrated paths differed from the paths that

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originated directly from LUCC because of indirect effects. This distinction let us map the input and output structures. Using the natural breaks method in ArcGIS, we classified the results into eight grades (Fig. 4). The clusters of high and low values were recognized using the hot-spot analysis tool provide by ArgGIS. Based on these results, we described the spatial variability of the input and output structures, and used these maps to discuss the overall structure and hierarchy of Beijing's system.

3. Results and discussion 3.1. Analysis of the integrated flows Table 1 summarizes the integrated output and input flows in Beijing's urban metabolism from 1990 to 2015. (Details of the data used in these calculations is provided in Supplemental Tables S9eS19.) The total output flows decreased slightly and total input flows increased at average annual rates of 0.2% and 1.2%, respectively. The highest output and input values occurred from 1990 to 1995 and from 2010 to 2015, respectively, whereas the lowest output and input values both occurred from 2000 to 2005. The integrated activities in Beijing produced more output flows from 1990 to 1995, when the urban area expanded fastest, at an annual rate of 17.4%, versus an average of 2.8% during the other periods (Zhang et al., 2014a). After 1995, input flows were dominant. The IDR value quantifies the relative importance of the indirect flows during urbanization (Fig. 2 for outputs and Fig. 3 for inputs). The IDR value for output flows was greater than that for input flows in all five periods, but both decreased greatly from 2000 to 2010 because the number of paths decreased as land use patterns stabilized. The land use pattern's stability could be examined by the dynamic degree of land-use transfer, which was calculated by the ratio of the total area of land i that was converted to land j to the n P DSij total land area every 5 years ( S =5  1000%). The degree i¼0;j¼0

was 1.1% and 0.6% from 2000 to 2005 and 2005 to 2010, respectively, and the numbers of paths were 152 and 206, respectively;

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both were smaller than the corresponding degrees and numbers before 2000, when the degree values were 11.2% from 1990 to 1995 and 9.1% from 1995 to 2000, respectively, for 264 and 276 paths. For the output flows, the direct flows from 2000 to 2005 decreased to 29.5% of the direct value from 1990 to 1995, whereas the indirect flows decreased to 15.7% of the indirect value from 1990 to 1995. For the input flows, the direct flows from 2000 to 2005 increased to 1.35 times the value from 1990 to 1995 and the indirect flows decreased to 56.6% of the value from 1990 to 1995. The indirect effects were more sensitive to the number of paths. The IDR was greater than 1 from 2010 to 2015, with values of 1.23 and 1.22 (respectively) for the output and input flows, which reveals the key role played by indirect flows. Higashi and Patten (1989) identified the dominance of indirect effects for a highorder interaction system (an oyster-reef ecosystem), for which the system-level IDR was 3.3. However, indirect effects differ among networks, times, and locations. A previous energy metabolism study by our research group suggested that indirect flows accounted for 80e90% of the total integrated flows (Zhang et al., 2015c). A recent study of nitrogen metabolic data by our research group showed that the component-level IDR ranged from 0 to 4.7 (Zhang et al., 2016a). In the present study, the rate of land transfer and number of transfer paths from 2010 to 2015 were 2.7% and 246, respectively, and infrequent paths that involved large areas were replaced by more frequent paths that involved smaller areas, which increased the number of paths, especially for the input flows. 3.2. Temporal changes in the input and output trophic structures For natural systems, researchers classify species into different functional groups within the trophic structure: producers, consumers, and decomposers. By analogy to these roles within the food web of a natural system (Fath and Killian, 2007), we determined the relationships among the components of the system, and based on this analysis, we treated urban land and transportation and industrial land as tertiary and secondary consumers, and treated the cultivated land and rural land as the primary consumers, with eight sub-types of the natural components functioning as producers and the other five sub-types functioning in recycling and acting as

Table 1 The output and input integral flows in Beijing's urban metabolism from 1990 to 2015. Levels in the trophic hierarchy were defined based on the methods described in Section 5 of the Supplemental Materials. Roles

Components Input integral flows

Output integral flows

1990e1995 1995e2000 2000e2005 2005e2010 2010e2015 1990e1995 1995e2000 2000e2005 2005e2010 2010e2015 Decomposer

B1 B3 F4 G2 W1 Tertiary consumer U Second consumer T Primary consumer R C1 C2 Producer B2 F1 F2 F3 G1 G3 W2 W3 Sum

1.01 1.00 1.35 1.32 1.01 3.21 10.31 1.88 1.04 2.01 1.00 1.18 1.42 1.20 1.02 1.04 1.08 1.15 33.20

1.00 1.11 1.39 1.03 1.01 2.50 12.63 4.54 1.41 1.18 1.00 1.54 1.26 1.18 1.14 1.10 1.19 1.06 37.25

0.00 0.00 1.03 1.00 1.00 4.55 11.98 2.28 1.00 1.12 0.00 1.02 1.00 1.00 1.00 1.00 1.04 1.02 31.04

0.00 1.00 1.00 1.00 1.00 5.99 12.94 1.98 1.00 1.26 1.00 1.02 1.00 1.00 1.09 1.00 1.24 1.23 35.76

1.02 1.00 1.19 1.08 1.10 4.86 14.04 5.49 1.00 3.84 1.00 1.68 1.18 1.18 2.44 1.02 1.12 1.02 45.26

1.00 1.00 1.25 1.05 1.01 2.07 11.26 3.79 1.10 8.07 1.00 1.81 1.33 1.32 1.29 1.11 1.05 1.10 41.60

1.01 1.01 1.63 1.78 1.01 2.35 11.17 2.23 1.27 3.93 1.01 1.33 1.64 1.32 1.03 1.08 1.10 1.28 37.19

0.00 0.00 1.20 1.01 1.00 1.01 2.81 1.30 1.10 3.62 0.00 1.02 1.02 1.04 1.04 1.05 1.16 1.04 20.42

0.00 1.01 1.27 1.05 1.01 1.10 4.25 1.31 1.17 3.35 1.00 1.12 1.22 1.06 1.21 1.08 1.08 1.33 24.61

1.00 1.00 1.40 1.20 1.01 3.28 12.23 2.64 1.13 4.43 1.00 1.35 1.47 1.15 1.42 1.09 1.15 1.16 39.12

B1, sand; B2, barren earth; B3, bare exposed rock; C1, irrigated cultivated land; C2, dry cultivated land; F1, forest; F2, shrub land; F3, open woodland; F4, other woodland; G1, high-coverage grassland (vegetation cover more than 50%); G2, medium-coverage grassland (vegetation cover between 20 and 50%); G3, low-coverage grassland (vegetation cover between 5 and 20%); R, rural; T, transportation and infrastructure; U, urban; W1, rivers; W2, lakes and reservoirs; W3, intermittently flooded land.

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Fig. 2. (Top) The trophic structure of output flows (i.e., the output structure). and bottom left) the weights and (bottom right) the indirect to direct flow ratio (IDR) for each layer from 1990 to 2015. Component definitions: B1, sand; B2, bare earth; B3, bare exposed rock; C1, irrigated cultivated land; C2, dry cultivated land; F1, forest; F2, shrub land; F3, open woodland; F4, other woodland; G1, high-coverage grassland (vegetation cover more than 50%); G2, medium-coverage grassland (vegetation cover between 20 and 50%); G3, lowcoverage grassland (vegetation cover between 5 and 20%); R, rural land; T, transportation and infrastructure land; U, urban land; W1, rivers; W2, lakes and reservoirs; and W3, intermittently flooded land.

Fig. 3. (Top) The trophic structure of the input flows (i.e., the input structure). and (bottom left) the weights and (bottom right) the indirect to direct flow ratio (IDR) for each layer from 1990 to 2015. Component definitions: B1, sand; B2, bare earth; B3, bare exposed rock; C1, irrigated cultivated land; C2, dry cultivated land; F1, forest; F2, shrub land; F3, open woodland; F4, other woodland; G1, high-coverage grassland (vegetation cover more than 50%); G2, medium-coverage grassland (vegetation cover between 20 and 50%); G3, lowcoverage grassland (vegetation cover between 5 and 20%); R, rural land; T, transportation and infrastructure land; U, urban land; W1, rivers; W2, lakes and reservoirs; and W3, intermittently flooded land.

decomposers. (See Section 5 of the Supplemental Information for details.) The classification agreed with previous descriptions of socio-economic systems (Fath et al., 2010; Zhang et al., 2011). The initial states of multiple components represented high weights for producers (27% ± 0.3%, mean ± SD) and decomposers (14% ± 0.08%). The high demand for and consumption of carbon during urbanization produced a large group of secondary consumers (29% ± 0.6%) in the middle of the hierarchy and led to significant changes in the weights of the consumers. From 1990 to 2015, the output structure formed an increasingly regular pyramid for all levels below the decomposer level, with a relatively stable decomposer level (Fig. 2). Outputs of secondary and tertiary consumers increased at average annual rates of 0.6 and 2.1%, respectively, and the same trend was observed in the IDR values. Indirect effects never dominated the secondary consumers (with IDR values ranging from 0.12 to 0.71), but dominated the tertiary consumers from 1995 to 2000 (IDR ¼ 2.15). The outputs of primary consumers decreased at an average annual rate of 1.6%, and their IDR values showed the opposite trend. Indirect effects dominated the outputs of primary consumers from 1990 to 2000 (with IDR values of 2.44 from 1990 to 1995 and 2.68 from 1995 to 2000) and from 2010 to 2015 (IDR ¼ 3.84). The weights of these layers

fluctuated over time. An excessively high weight from primary consumers (31.2%) formed a distinctly different output structure from 1990 to 1995. The output structures from 1995 to 2000 and from 2010 to 2015 were similar, with the strongest layer in the middle (30.0 and 31.3%, respectively) and higher weights for tertiary consumers than in other periods (6.3 and 8.4%, respectively). The output structure formed similar, relatively regular pyramids from 2000 to 2005 and 2005 to 2010, and the IDR value was lower than that in the other three periods. Indirect effects for producers and decomposers were more significant, and were dominant in four of the five periods, excluding the periods from 1990 to 1995 for the producers and from 2000 to 2005 for the decomposers (with values ranging from 1.02 to 4.80 and from 2.56 to 7.41, respectively). During the study, the input structure formed an irregular elliptical structure with increasing strengths for the top and bottom layers and a heavy center (Fig. 3). Inputs of the tertiary and primary consumers increased at annual average rates of 0.4 and 1.7%, respectively, and indirect effects were dominant for tertiary and primary consumers for (respectively) four periods (except from 2000 to 2005), with values of 1.41e3.67, and for all five periods, with values of 1.41e4.48. Secondary consumers had the largest inputs in all five periods, with values ranging between 31.0% and

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38.6%; that is, indirect effects were never dominant for this level of the hierarchy. Tertiary consumers were the only level of the hierarchy that increased over time in both the output and input structures (at annual average rates of 2.1 and 0.4%, respectively) and inputs for the other layers changed in the opposite direction to their outputs. The biggest changes occurred from 2000 to 2010, and the input structure formed a relatively uniform ellipse. The tertiary and secondary consumers had the greatest inputs (16 and 37%, respectively) when the IDR value was lower. Indirect effects for four periods for the producers (excluding 1990 to 1995) and five periods for the decomposers showed dominance by indirect flows, with IDR values between 1.25 and 5.36 for producers and between 2.38 and 5.86 for decomposers. During the study period, Beijing's trophic structure changed in response to urban development. The weights of the levels in the input and output structures changed in opposite directions from 1990 to 1995, from 2000 to 2005, and from 2005 to 2010. The significant differences between these structures during these three periods indicated imbalances in the inputs and outputs for a given layer. Unprecedentedly rapid urbanization that led to excessive carbon emission occurred in these three periods. The areas of urban land and of transportation and industrial land expanded rapidly during these periods, with urban land increasing by 596.4, 264.6, and 118.2 km2, respectively, and the area of transportation and industrial land increasing by 181.0, 42.4 and 31.7 km2, respectively. Beijing's total carbon emission increased by 353.8, 296.9, and 248.4 Gg C yr1 during the corresponding periods, which equaled 2.7 to 3.8 times the increase from 1995 to 2000. The total carbon sequestration decreased by 8.0 Gg C yr1 from 1990 to 1995 and remained nearly unchanged from 2000 to 2010. From 1995 to 2000 and from 2010 to 2015, the input and output structures were similar, with balanced inputs and outputs for a given layer. Carbon emission was relatively low and urban expansion was relatively slow during these periods. From 1995 to 2000, the areas of urban land and of transportation and industrial land decreased by 46.4 and 119.0 km2, respectively. Simultaneously, carbon emission and sequestration increased by 92.8 and 8.0 Gg C yr1. From 2010 to 2015, the area of urban land increased by 131.0 km2 and the area of transportation and industrial land decreased by 41.3 km2; carbon emission decreased by 92.3 Gg C yr1 and carbon sequestration increased by 1.8 Gg C yr1. Zhang et al. (2014a) and Xia et al. (2017) defined the periods from 1990 to 1995 and from 2000 to 2005 as developmental stages, during which urban areas expanded fast and emission increased fast, and the periods from 1995 to 2000 and from 2005 to 2010 as adjustment stages, during which urban areas expanded slowly and emission increased slowly. Based on these results our integrated analysis provided important insights into Beijing's trophic structure. The relatively balanced inputs and outputs and similar structures suggest that urbanization slowed and land adjustments became relatively sustainable. The IDR value provided a new insight into the details of urbanization by revealing the importance of indirect flows. The lower IDR values for urban land and for transportation and industrial land showed that indirect effects were relatively small during the period of fast urbanization. About 83 and 73% (respectively) of the land transferred to these land uses were attributed to primary consumers, and dry cultivated land accounted for 56 and 64% of these transfers, respectively. This may be because highly aggregated networks produce weaker indirect effects because of the highly aggregated inflows and outflows (Higashi and Patten, 1989). The changes of the IDR value for primary consumers reveal that the outputs were mostly transmitted to urban land and to transportation and industrial land from 2000 to 2010. The inputs from components to the primary consumers were distributed more

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uniformly among the components, especially for the natural components, and the high outputs of the producers and decomposers occurred when the IDR value for the primary consumers was relatively high. 3.3. Spatial variability of input and output flows Fig. 4 shows the spatial variability of the direct and indirect output and input flows. We divided these flows into three trends from the center of the study area and the southeast plains towards the northwest mountains, where the main land types are urban land, transportation and industrial land, dry cultivated land, and natural components (of which the F1 category of forest land accounted for 42% of the total land area). From 60 to 80% of the total flows were higher flows (direct þ indirect flows > 0.15), whereas the number of such flows accounted for 8e21% of the total for each period. The spatial allocation of the higher output and input flows was distributed throughout the city from 1990 to 1995, with the areas transferred accounting for 22.0% for the outputs and 15.8% for the inputs; these proportions decreased to 6.5 and 5.3%, respectively, from 1995 to 2000, when the high flows became concentrated in the southeastern part of the city; the smallest proportion (<0.1%) of the transferred areas were found from 2000 to 2010, with small patches scattered in the peripheral plains areas, and the largest portion (35.2 and 27.5% for outputs and inputs, respectively) from 2010 to 2015 because of frequent land adjustments through the whole city during this period. In summary, flows were more concentrated when the system contained fewer paths and the transferred areas of high flows for inputs were always less than the corresponding flows for outputs, but input flows were more common than output flows. The aggregation of input and output flows showed strong spatial heterogeneity (Fig. 5). The hot-spot and cold-spot areas aggregated the high and low flows in the southeastern and northwestern parts of the city, respectively. The flows showed no significant spatial aggregation (yellow areas) in the northwestern part of the study area. The hot-spot areas showed a similar pattern for outputs and inputs in the peripheral plans area from 1990 to 2000 and from 2010 to 2015. The rapid expansion of urban land that replaced dry cultivated land formed a unique output structure, whereas the high output flows produced by dry cultivated land were aggregated in a ring around the urban center from 1990 to 1995; input flows were strongly centralized in the urban center and the input structure exhibited a typical pattern with outward radiation. The same input structure existed from 1995 to 2000, and the output structure changed to a pattern with a unidirectional trend inward from the periphery towards the urban center and outward towards the northwest mountains. In contrast, the input and output structures from 2010 to 2015 were the opposite of the structures before 2000. Meanwhile, the output structures from 1995 to 2000 and from 2010 to 2015 both formed obvious cold-spot areas in the northwestern and northern mountains, respectively. The stable period from 2000 to 2010 gathered high output flows in the peripheral plains area, whereas the high input flows were relatively dispersed, with weak aggregation in parts of the peripheral plains, from 2000 to 2005 and in urban areas in the southeast from 2005 to 2010. A previous spatially explicit analysis of Beijing's carbon metabolism by our research group showed that most of the emission and sequestration were aggregated in the center of the city and the mountainous areas, respectively (Zhang et al., 2014a). The indirect flows gave rise to a different pattern of integrated flows so that most input flows were located in the peripheral plains, and urban areas were not the only dominant beneficiary of these flows. Indirect effects also made the distribution of the carbon flows more uniform because energy and matter are mixed and cycled within

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Fig. 4. Spatial variability in the direct and indirect flows for (aee) the output pattern and (fej) the input pattern from 1990 to 2015. Rectangles indicate the locations of hot-spot areas with the strongest flows (>0.67).

Fig. 5. Spatial aggregation in the direct and indirect (aee) output flows and (fej) input flows from 1990 to 2015.

urban networks (Fath and Patten, 1999). For example, carbon emission by the plains area was about 13 times that in the mountains, and carbon sequestration in the mountains was 10 times that in the plains (Zhang et al., 2014a). The input and output flows in the mountains could be 2 to 4 times the input and output flows in the

plains, whereas the flows in the plains could be 2 to 4 times flows in the mountains. Land adjustments from 2010 to 2015 caused significant changes in the spatial distribution of the flows; the hot-spot areas for input flows first occurred in the peripheral plains, and the urban center

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became a hot-spot area for output flows. Carbon emission in other cities is typically centralized in the urban areas (Chrysoulakis et al., 2013) and decreases with increasing distance from the city center (Hutyra et al., 2011). However, these studies underestimated the contribution of other land uses within urban systems (La Rosa and Privitera, 2013). To clarify the key flows and components of these flows, we have drawn rectangles around the areas with the highest flows (>0.67) in Fig. 4. The areas with the largest flows (>0.67) showed the same trend as the areas with the second-highest flows (>0.15). More concentrated output flows occurred from 2000 to 2010, when only 2 paths (2000e2005) and 4 paths (2005e2010) accounted for 36.9 and 49.6% of the total flows, respectively. Each period had 2 paths that transferred dry cultivated land and transportation and industrial land (respectively, primary and secondary consumers) to urban land (a tertiary consumer). From 1990 to 1995, 1995 to 2000, and 2010 to 2015, we found 9, 7, and 9 paths, respectively, with the highest output flows, which accounted for 34.9, 38.7, and 39.7%, respectively, of the total flows; 7, 7, and 8 of these output flows (respectively) transferred transportation and industrial land to other types of land. From 1990 to 1995, 4 of the 7 flows were from transportation and industrial land to decomposers, 2 were to urban land, and 1 was to a producer. From 1995 to 2000 and from 2010 to 2015, 3 and 4 flows (respectively) were from transportation and industrial land to producers, and each period had 2, 1, and 1 flows from this land to (respectively) primary consumers, decomposers, and urban land. In contrast, the number (6e10) of the highest flows for inputs were distributed evenly among the five periods. The proportion of input flows was largest from 1995 to 2000 (51.2%) and equaled 1.4 times the proportion from 2010 to 2015 (37.8%). In all five periods, all input flows transferred land to transportation and industrial land from producers (50e78% of the transfers) and consumers (10e50% of the transfers). The areas transferred in such input flows were 1.3e9.8 times the areas for output flows from 1990 to 2010 and decreased to 58.9% of the area of output flows from 2010 to 2015. 4. Conclusions and implications Trophic structures can be observed in both natural and artificial systems (Hardy and Graedel, 2002). Trophic theory suggests that a pyramid structure indicates a well-structured and stable system (Elton, 1927; Lindeman, 1942). Some urban research also showed a pyramidal structure, as in the case of Beijing's carbon metabolism (Lu et al., 2015) and Vienna's urban carbon metabolism (Chen and Chen, 2012b). Other studies have reached different conclusions. A study of natural networks found that only 3 of 17 empirical foodwebs had a pyramidal structure and others showed irregular structures (Fath and Killian, 2007). Although these contradictory results could arise from methodological differences or differences in the characteristics of the study systems, this suggests that the traditional pyramid structure may not be the only option for mature systems. This is an important issue for urban planners, since sustainable development requires a well-organized and stable structure. The present study provides a more holistic way to fully understand an urban carbon metabolism by integrating the input and output flows. Beijing's rapid urbanization produced structures that did not always resemble a stable pyramid. Because the decomposers increase a city's sustainability by recycling wastes or treating them before releasing them into the environment, the large decomposer level in the trophic structure during certain periods does not necessarily represent a serious imbalance in the system. The corresponding output and input structures suggest excessive carbon inputs and carbon emission, combined with decreased carbon sequestration (from 1990 to 1995 and from 2000 to 2010).

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However, the similarity of the output and input structures suggests successful urban adjustment, decreasing carbon emission, and increased carbon sequestration (from 1995 to 2000 and from 2010 to 2015). Urban planners will prefer the latter trophic structure for Beijing's future condition. Considering the decrease in urban land from 1995 to 2000, the trophic structure from 2010 to 2015 would be more suitable for a low-carbon future, with a steady increase of sequestration and restructuring leading to optimization of the urban structure. Our results suggest the need to develop similar output and input structures in the future through decreased inputs and outputs for secondary consumers, a shared “producer” for primary consumers and producers, and increased feedback from tertiary consumers and decomposers. Limiting the conversion of cultivated land to constructed land is a fundamental policy in Beijing. Urban land expanded through transfers of cultivated land, which must be replenished to restore the strength of the producer trophic level. The decreased areas transferred through input flows from 2010 to 2015 suggest improving utilization of space as a result of increasing similarity of the input and output flows, which means that less space was used to support urban expansion. By calculating the integrated flows from 25 years of socioeconomic activities (i.e., transportation, industry, commercial, household) and natural activities (i.e., forests, grassland, water), we were able to quantify the spatial and temporal changes in Beijing's urban carbon metabolism. These results provide guidance for policy developers about the types of land-use change that should be encouraged (to promote carbon sequestration) or discouraged (to reduce carbon emission), and because the results are spatially explicit, different policies can be developed for each region of Beijing to address each region's specific needs. However, the empirical coefficients we used to assess carbon emission and sequestration contain numerous sources of uncertainty. Although the calculation relied on published data, it will be necessary to empirically determine the values of the coefficients through field surveys or experiments that provide more accurate local data. In addition, the sensitivity analyses for carbon sequestration and emission coefficients indicated that the estimation on forest, urban land, transportation and industrial land, and dry cultivated land are the main sources of uncertainties for integrated flows and IDR value. Carbon sequestration coefficient of water played an extra influence on IDR value. The composition of ecology relationships was sensitive to the estimation on forest, grass, rural, and transportation and industrial land. Although the present data on aboveground components of carbon flows were reasonably accurate, the knowledge of the flows in belowground biomass and the soil are weak and must be improved. Moreover, definition of the system's boundary and of the flows across the boundary must be improved to allow more accurate assessment of the exchanges between Beijing and the surrounding region. Acknowledgments This work was supported by the Fund for Innovative Research Group of the National Natural Science Foundation of China (no. 51721093), and by the National Natural Science Foundation of China (no. 41871213, 41171068). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jclepro.2019.118063. References Borrett, S.R., Whipple, S.J., Patten, B.C., Christian, R.R., 2006. Indirect effects and

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