Journal of Cleaner Production 112 (2016) 4304e4317
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Development of a spatially explicit network model of urban metabolism and analysis of the distribution of ecological relationships: case study of Beijing, China Yan Zhang a, *, Linlin Xia a, Brian D. Fath b, c, Zhifeng Yang a, Xinan Yin a, Meirong Su a, Gengyuan Liu a, Yanxian 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 Biology Department, Towson University, Towson, MD, 21252, USA c Advanced Systems Analysis Program, International Institute for Applied System Analysis, Laxenburg, Austria
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 April 2014 Received in revised form 3 June 2015 Accepted 11 June 2015 Available online 20 June 2015
In this paper, we develop a spatially explicit model of carbon transfers between regions of an urban area. The carbon transfers represent the metabolic processes due to regional land use changes. We used the model to identify spatial heterogeneity in the carbon metabolic structure, functions, and relationships within the network. Data for Beijing from 1990, 1995, 2000, 2005, and 2010, were combined with empirical coefﬁcients, to construct the network. We used ecological network analysis to analyze the structure and function of the network, and to determine the ecological relationships between the components of the system, their distribution, and their changes over time. The analysis revealed that carbon throughﬂow of the network decreased and positive relations mostly outweighed negative relations. Exploitation relationships were the dominant type in Beijing during most of the study period, particularly in the northwest before 2000, but moved towards the southeast over time, leaving competition relationships with losses of beneﬁts dominant in the northwest. Mutualism relationships with mainly beneﬁcial carbon ﬂows were dominant in the southeast, increasing in frequency in this region throughout the study period. The results provide a theoretical basis for planning adjustments to the city's structure to achieve low-carbon goals. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Urban metabolism Carbon emission Carbon sequestration Ecological network analysis Spatial analysis Ecological relationships
1. Introduction Land use and cover change (LUCC) accounts for one-third of urban carbon emissions (Denman et al., 2007), and because carbon sequestration is closely related to the presence of natural land cover (Houghton, 2003), the balance between carbon emission and sequestration depends on how much natural land is converted to human uses. In addition to the inputs (carbon sequestration) and outputs (carbon emission) between land systems and the atmosphere, carbon transitions occur between socioeconomic systems and the environment. Within a mixed natural and socioeconomic system, these transitions are also directly related to LUCC. For instance, in the United States carbon storage in vegetation generally
* Corresponding author. Tel./fax: þ86 10 5880 7596. E-mail address: [email protected]
(Y. Zhang). http://dx.doi.org/10.1016/j.jclepro.2015.06.052 0959-6526/© 2015 Elsevier Ltd. All rights reserved.
increases by 0.02 PgC yr1 when constructed land (land that has been converted into buildings, roads, and other forms of infrastructure) is transformed into farmland (Imhoff et al., 2004). Similarly, transforming forests near Seattle, Washington into constructed land decreased carbon storage in vegetation by 1.2 Mg C ha1 yr1 (Hutyra et al., 2011). LUCC occurs within developing cities, and can have important effects on a city's carbon balance as the distribution of various land use and cover types change. For example, land uses and cover types in Beijing exhibit strong spatial and temporal variation leading to frequent carbon transition processes. From 1992 to 2008, urban sprawl in Beijing converted 792.7 km2 of cultivated land (20% of the total arable land area in 1990) into constructed land. During the same period, 28% of the forested land was converted to constructed land (Miao et al., 2011). This imbalance caused by construction has led to increasingly signiﬁcant environmental contradictions in Beijing (Beijng Municipal Bureau of Land and Resources, 2010).
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Urban planners must construct an effective and harmonious urban ecological network and a sustainable urban development environment (Zhang and Wang, 2006). As part of the goal of reducing carbon emissions, this paper aimed to identify the key control points required for implementing quantitative adjustments to the overall regional development to improve its carbon balance. Wolman (1965) deﬁned the concept of urban metabolism by describing the city as analogous to an ecosystem. He outlined how materials, energy, food, and other inputs ﬂowed into the system, and how products and wastes are generated by the system. Urban metabolism is a process of resource consumption and waste generation, and accounts for the circulation, emissions, disposal, and use of resources and wastes by the city (Zhang, 2013). Tracking the ﬂow of materials and energy through an entire urban ecosystem can provide a more robust framework for understanding these ﬂows (Pataki et al., 2006). Some scholars have studied key ﬂows of a single material or element within an urban metabolism, such as water (Tambo, 2002; Zhang et al., 2010), energy (Huang, 1998; Zhang et al., 2011), copper (Gordon et al., 2006; Tanimoto et al., 2010), and nitrogen (Forkes, 2007; Saikku et al., 2007). With growing concern about climate change, scholars have adopted the concept to study the urban carbon metabolism (Sovacool and Brown, 2009; Karakiewicz, 2011). Some scholars have focused on the ﬂow of carbon emissions from cities into the atmosphere, and have focused on carbon emissions produced by socioeconomic activities, such as energy and resource consumption by the transportation infrastructure and electricity use (Kennedy et al., 2010, 2011). Others have studied carbon emissions associated with speciﬁc economic activities, such as those produced by transportation in a port city (Villalba and Gemechu, 2011) or by residential energy consumption (Ye et al., 2011). Some scholars have focused on carbon emissions in socioeconomic activities and natural carbon sequestration from the atmosphere by the biosphere. Baccini (1996) considered carbon emissions produced by urban socioeconomic activities, while accounting for agricultural activities, and further focused on carbon sequestration by farmland and forest. Others have focused on carbon transitions embodied in the products of socioeconomic activities, including a consideration of natural activities as a component of the overall system but ignoring the carbon metabolic processes in the natural activities (Chen and Chen, 2012a,b). After ongoing application of urban metabolism in management and design research (Huang et al., 2006; Kennedy et al., 2011), researchers began to study the correlations between an urban metabolism and the spatial distribution of land use within the urban area (Huang and Chen, 2009; Marull et al., 2010). Pauleit and Duhme (2000) studied the interactions between carbon emissions and land use. Christen et al. (2010) focused on the changes in carbon stocks caused by LUCC. Others have looked at the increases in carbon storage caused by transforming cultivated land into woodland and grassland (Dixon et al., 1994), and the decreases in carbon storage caused by the reverse transformation (Houghton and Goodale, 2004). Some studies calculated the carbon ﬂows based on urban metabolism and evaluated the impact of urban form on the pattern of carbon emission and sequestration. Researchers conducted the studies in several European cities like London and Florence and showed that different urban form affected the distribution of carbon ﬂows signiﬁcantly (Blecic et al., 2014; Chrysoulakis et al., 2010, 2013). These studies have provided the basis for a fuller consideration of carbon transition processes, which is the key to building an accurate and useful spatial model of the network's carbon metabolism. Such a carbon ﬂux model has been built based on network environ analysis (Chen and Chen, 2012a,b), which is a form of ecological network analysis (ENA). ENA originated in the economic
analysis of monetary ﬂows and examines the exchanges of materials (i.e., inputs and outputs) between one component of a system and adjacent components. Hannon (1973) ﬁrst applied economic inputeoutput analysis (the Leontief model) to simulate the structural distribution of ecosystem components and the interrelationships among trophic levels. Finn (1976) improved the method and Patten (1982) further reﬁned the method to examine the interdependencies among the components of an ecosystem by describing the ﬂows of materials and energy. This approach establishes a network ﬂow diagram that captures both direct and indirect ﬂows of materials and energy among the components of a system (Levine, 1980; Patten, 1982). Network environ analysis reveals the function and interdependencies within a system (Fath and Killian, 2007; Patten, 1982). This approach has been widely used to study the ﬂows within natural ecosystems and socioeconomic systems (Finn, 1976; Baird et al., 2009; Zhang et al., 2010; Li et al., 2012). However, such studies provide insufﬁcient consideration of the relationships between the natural components of the system. And, because they lacked a spatially explicit expression, urban development plans supported by a network environ analysis could not be implemented with a spatially speciﬁc focus. To solve this problem, some models have adopted the perspective of landscape ecology to reﬂect the interactions created by spatial relationships within an environmental landscape. The idea of landscape networks originated from the national park planning period during the 19th century. After the concept of ecological networks was noted in a government report in the United States (President's Commission on Americans Outdoors, 1987), ecological networks were widely applied, and have played a core role in improving city landscapes and achieving bos, a more rational layout and structure of urban green space (Fa 2004; Jongman et al., 2004). Ecological networks are based on the landscape ecology concepts of “irreplaceable patterns” and “best landscape patterns” (Forman and Godron, 1981). Some landscape components are irreplaceable because no other land use or cover type can replace the services they provide; bodies of water and farmland are two examples. “Best” patterns represent landscape patterns that preserve these irreplaceable elements and represent a potentially optimal use of the available space to achieve both ecological and socioeconomic objectives. Ecological networks consist of landscape-level patterns of green space, including farmland, forest, grassland, water areas, and artiﬁcial green spaces in urban areas (UPDST, 1998; Franco et al., 2003; Liu et al., 2005). Linehan et al. (1995) described the steps to design one such network: assessment of land cover, wildlife, and habitat, followed by node and connectivity analysis, and ﬁnishing with generation and evaluation of the network. They used the resulting network to evaluate forested regions of central New England in the United States. This method allows researchers to weight the interactions between nodes, while determining the potential paths for ﬂows of materials and energy (Kong and Yin, 2008). In constructing landscape ecological networks, these paths can be determined two ways. First, they can be identiﬁed by extracting natural cover and terrain, as in the case of a “blue network” extracted from river corridors (Hoctor et al., 2000) or a “green” network extracted from ecological corridors (Conine et al., 2004). Second, the potential paths between nodes can be determined using a distance-based cost, as described by Zhang and Wang (2006), who determined the minimum distance between two green patches based on minimizing the cost of the ﬂows between them. Socioeconomic activities are regarded as obstacles that disrupt the spread of a network along these paths (Gao et al., 2010), and are difﬁcult to contain within a landscape ecological network. At the same time, all paths represent potential ﬂows (Jim and Chen, 2003), but do not
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reﬂect the quantity of energy or materials that are transferred between pairs of nodes. This means that there is insufﬁcient data to quantitatively evaluate interactions within the network. Although researchers can adjust the spatial structure of an ecological network model, it is also necessary to ﬁnd a way to account for the carbon ﬂows within the network. In this paper, we performed a study in which we answered three research questions: How much have carbon sequestration and emission changed during Beijing's urban development from 1990 to 2010? Will the carbon transitions that result from LUCC lead to more or less harmonious relationships between Beijing's socioeconomic system and the environment that sustains it, and between the natural and artiﬁcial components of the urban system? How can the directions and sizes of the carbon ﬂows be determined based on the spatial distribution of land use types and the ecological relationships between them? These questions can be answered by applying urban metabolism theory to analyze the carbon transition processes that occur in an urban area such as Beijing from the perspective of LUCC, as this approach can track the spatial and temporal variations of carbon ﬂows in a variety of exchange activities, and can explore the interactions between different components of the system. The paper examined the effects of LUCC on carbon transition processes within an urban network, as these transitions are an important part of the urban metabolism. To perform this analysis, we developed a spatially explicit carbon ﬂux network model to link the natural and artiﬁcial components of an urban ecosystem based on their roles in the city's carbon metabolism. The network model focuses on carbon transitions between and within the system's natural and artiﬁcial components. The structure of paper is as follows: First, we develop a spatially explicit network model, and determine the data requirements and theoretical underpinning of the work. To do so, we obtained land-use data for Beijing from 1990 to 2010, and established a land-use transition matrix for 5-year periods using geographical information system software. By combining the matrices with empirical coefﬁcients that represent the carbon ﬂows embodied in LUCC, we constructed a spatial model of the network's carbon metabolism for four different periods based on the carbon transitions that result from LUCC. Next, we analyze the model's structure and the embodied ecological relationships. We then applied ecological network analysis to determine the negative and positive effects of metabolic ﬂows and the spatial distributions of the resulting ecological relationships, and summarize the processes that control the metabolic network through comparative analysis of the different periods. Based on the results of these analyses, we provide strong empirical support for spatial adjustments of the urban pattern to improve the carbon emission and sequestration balance between the socioeconomic and natural components of the system. 2. Principles for constructing a spatially explicit urban carbon metabolic network model A city is a complex network of both socioeconomic and natural activities with a wide range of material and energy exchanges occur within and between their activities. These complex relationships and their spatial structures can be abstracted into a spatial network model. A spatial model of the network's carbon ﬂows that links the system's artiﬁcial and natural components can help these planners to achieve more reasonable urban spatial patterns by controlling key socioeconomic and ecological processes (Yu, 1996). Providing support for these activities is fundamental to the present research, as an improved understanding of the urban metabolism can help planners take measures to adjust urban spatial patterns by changing the amounts of energy consumption and the ﬂows of
energy among the components of the system (Kennedy et al., 2010). Previous networks only modeled the carbon exchanges between the atmosphere and the biosphere from the perspective of carbon emission and sequestration (i.e., by only considering the overall ﬂows), but make it difﬁcult to understand the network's spatial structure. In addition, models based on network environ analysis lacked a spatially explicit component, and therefore could not determine the directions and locations of urban evolution and reveal possible adjustment mechanisms. A landscape ecology network can be used to identify possible paths among components of the system, but can only be used to adjust the structure of the network (Jongman et al., 2004). It was therefore necessary to develop a model that accounted for both the paths and the ﬂows along those paths in a spatially explicit manner. To meet this need, we developed a spatial model of the network's carbon metabolism based on the increases and decreases of carbon stocks along the links among the urban components in response to LUCC. Urban development greatly changes the land surface and land use (Alberti and Marzluff, 2004; Grimm et al., 2008), leading to frequent carbon transitions between the land use and cover types. Carbon transitions throughout the city must be based upon a network of LUCC. In this study, we determined changes in the carbon metabolism capacity, carbon transitions, and transfers of land among land use and cover types using a land-use transfer matrix to support our spatially explicit model. LUCC between any two components can cause changes in the carbon metabolism capacity of the land affected by this change, including its carbon absorption or release capacity. When a landscape type is transformed to a different type, this represents an output of that area of land, which causes the loss of that land type's carbon metabolism capacity. Conversely, that output of land becomes the input (increase in area) for a different land type. The carbon metabolic capacity then changes by the change in carbon metabolic density of the land that receives that input, multiplied by the area of land received as an input. For example, if 10 ha of forest changes to grassland, carbon absorption or release by those 10 ha of land is accounted for using the metabolic capacity of the new land use or cover type (i.e., that of grassland). These LUCC processes cause exchanges of carbon metabolic capacity between landscape components and the external environment (here, the atmosphere) in the form of input ﬂows (z) and output ﬂows (y). The carbon metabolic density (W) is expressed as the change in carbon stock per unit time and per unit area for each component (kg m2 yr1), and the carbon ﬂux along each path in the network results from a difference in the carbon metabolic density (DW) between the two components involved in the exchange, producing the equivalent of a carbon ﬂow along each path from component i to component j (fji). Because the carbon metabolic capacity is divided into carbon release and carbon absorption, ﬂows in the network can be divided into beneﬁcial ﬂows (absorption) that alleviate imbalances in the carbon metabolism (Figs. 1a, c, e) and harmful ﬂows (releases) that aggravate imbalances in the system (Figs. 1b, d, f). Both processes should be considered by a spatial model of the urban network's carbon metabolism that links the system's natural and artiﬁcial components and that expresses the interactions among the different components of the system (Fig. 1). The ﬂow between any two components of the system is driven by the difference in metabolic densities between those components. For example, a given forest area will typically absorb more carbon than the same area of grassland, whereas a given area of transportation and industrial land will release more energy than the same area of urban land. However, the net absorption (a beneﬁcial ﬂow of beneﬁts) or release (a harmful ﬂow of beneﬁts, which represents a loss of carbon) depends on the relative area of
Y. Zhang et al. / Journal of Cleaner Production 112 (2016) 4304e4317
Fig. 1. Examples of urban carbon metabolic processes that represent the ﬂows of energy and material among the components of the system (F, forest; G, grassland; T, transportation and industrial land; U, urban land). (a, b) Exchanges between two natural components of the system. (c, d) Exchanges between two artiﬁcial components of the system. (d, e) Exchanges between natural and artiﬁcial components of the system. Flows are denoted as fij, which represents the carbon ﬂow from component j to component i; zij represents the input ﬂow from component j to component i, and yij represents the output ﬂow from component j to component i. W represents the carbon metabolic density, which is expressed as the change in carbon stock per unit time and per unit area for each component.
each type of land; multiplying this area by its metabolic density per unit area determines the total capacity for carbon absorption or release. Thus, a given LUCC may create beneﬁcial or harmful ﬂows, depending on the results of this calculation. The ﬂows can occur along three types of path: between natural components of the system, between human-constructed components, and between these different types. These ﬂows may be beneﬁcial or harmful. Fig. 1a shows an example of beneﬁcial ﬂows resulting from the carbon transitions between two natural components. When the area of grassland decreases (i.e., an output), its carbon absorption capacity decreases, thereby decreasing its carbon stock and releasing carbon (yFG). When this output of land is converted to forest (i.e., an input), the forest's carbon absorption capacity increases, thereby increasing its carbon stock and resulting in carbon absorption (zFG); that is, a net increase in beneﬁts occurs. In Fig. 1b, the opposite process occurs, with a net increase of grassland area (zGF) and decrease of forest area (yGF). Fig. 1c shows an example of the carbon transition between two artiﬁcial components of the system. The transportation and industrial land changes to urban land (an output), resulting in
carbon absorption (zUT) and a net increase in beneﬁts. Conversely, when urban land changes to transportation and industrial land (Fig. 1d), there is a net carbon release (yUT), resulting in a net loss of beneﬁts. Fig. 1e and f represent LUCC between natural and artiﬁcial components of the system. Because of the different carbon metabolic capacities of the two components, the process differs from those shown in the two previous types of exchanges. When urban land changes to forest (an output), the carbon release capacity decreases, resulting in carbon absorption (zUF) as the forest area increases (an input), thereby increasing carbon absorption capacity (Fig. 1e), resulting in net carbon absorption (zUF), and representing an increase in beneﬁts. Conversely, when forest changes to urban land, the carbon release capacity increases, resulting in a loss of beneﬁts (Fig. 1f). Table 1 summarizes these LUCC processes and the equations used to quantify their effects on carbon ﬂows. We developed a conceptual spatial model of the carbon metabolism of a network that contains both natural and artiﬁcial components as the nodes and that focuses on the carbon ﬂuxes along ﬂow paths between these nodes (Fath and Patten, 1999). Fig. 2 illustrates the connections among the model's eight components: urban land (U), rural land (R), transportation and industrial land (T), cultivated land (C), forest (F), grassland (G), water (W), and bare land (B). Bare land refers to unused land with no vegetation cover and no sign of human activities, and is therefore assumed to have no signiﬁcant carbon ﬂow. Each component is associated with the whole network through several state variables. In this paper, the state variable xk represents the change in carbon storage of component k of the system (Finn, 1980). Each component may absorb a carbon ﬂux from the environment, which is shown as the input ﬂows (zij) in Figs. 1 and 2, and release a carbon ﬂux to the environment, which is shown as the output ﬂows (yij) in Figs. 1 and 2. The state variable (xk) equals inﬂows minus outﬂows for each component. Throughﬂow (Tk) equals the sum of all ﬂows to component k plus or minus the change in state (xk). If xk < 0, Tk equals the sum of all inﬂows minus the state variable; if xk > 0, Tk is equal to the sum of all outﬂows plus the state variable. For the city as a whole, total throughﬂow is the sum of Tk for all eight components. The total inﬂows to the network can be expressed as:
f kj þ
While the total outﬂows from the network can be expressed as:
n X i¼1
n X k¼1
where fkj and fik represent ﬂows from component j to component k and ﬂows from component k to component i, respectively, and n equals the number of components (eight in the present study). The
Table 1 Summary of the key carbon ﬂow paths in the urban network model and the equations used to quantify the ﬂows along each path. Part of Fig. 1
a b c d e f
G/F F/G T/U U/T U/F F/U
þ e þ e þ e
WG < WF WG < WF WT > WU WT > WU W U > WF WU > WF
yFG ¼ WG△S yGF ¼ WF△S yUT ¼ WT△S yTU ¼ WU△S e yFU ¼ (WU þ WF) △S
zFG ¼ WF△S zGF ¼ WG△S zUT ¼ WU△S zTU ¼ WT△S zFU ¼ (WU þ WF) △S e
(WGeWF) △S (WGeWF) △S (WTeWU) △S (WTeWU) △S (WU þ WF) △S (WU þ WF) △S
F, forest; G, grassland; T, transportation and industrial land; U, urban land; W, carbon metabolic density; △S, transferred area; fij, carbon ﬂow from j to i; zij, input ﬂow from j to i; yij output ﬂow from j to i.
Y. Zhang et al. / Journal of Cleaner Production 112 (2016) 4304e4317
Fig. 2. The conceptual model of a city's spatial carbon metabolism network. (B, bare land; C, cultivated land; F, forest; G, grassland; R, rural land; T, transportation and industrial land; U, urban land; W, water; zij, the input ﬂow from j to i; yij the output ﬂow from j to i).
positive sign of subscript of xk represents the storage increases. In contrast, the negative sign represents that the storage decreases. Based on the principle of Conservation of mass, the total inﬂows and total outﬂows are always equal in the network (i.e., Ti ¼ Tj). 3. Methods 3.1. Quantiﬁcation for the spatial model of the urban network's carbon metabolism Quantiﬁcation of the ﬂows through the urban network is based on accounting for the carbon metabolic density. The carbon metabolic density is calculated as the carbon metabolic rate per unit area. The ﬂows through the spatial network are quantiﬁed by calculating the difference in carbon metabolic density between the output and input ends of a component, using the following steps: 1. We obtained spatially explicit digital land-use data at a scale of 1:100 000 for the years 1990, 1995, 2000, 2005, and 2010 (Fig. 3). Each of the ﬁve images was geometrically corrected
to an average positioning error of less than 50 m; the integrated discrimination accuracy for the various land-use types reached 95% or more (Liu et al., 2009; Xu et al., 2012) . The original 16 land-use and cover types in the government databases (Supplemental Table S1) were combined into the eight composite categories shown in Fig. 2. Land-use data from consecutive years was overlaid using version 10.0 of the ArcGIS software (www.esri.com) to create a land-use transition matrix for the four periods from 1990 to 2010. To calculate the carbon metabolic densities, agriculture data were obtained from the China Grain Yearbook (China State Grain Administration, 2012) and the Beijing Statistical Yearbook (Beijing Municipal Bureau of Statistics, 2012), and energy and fuel consumption data were obtained from the China Energy Statistical Yearbook (China National Bureau of Statistics, 1998, 2004, 2007, 2010) and the Beijing Statistical Yearbook (Beijing Municipal Bureau of Statistics, 1992). The data used in our calculations are summarized in Supplemental Tables S2 to S8. 2. Our accounting method for carbon metabolic rates (kgC yr1) includes carbon emission (subscript E) and sequestration (subscript S) by both natural and artiﬁcial components of the system: forest (vSF), grassland (vSG), water (vEW), cultivated land (vSC), urban land (vEU), rural land (vER), and transportation and industrial land (vET). We have excluded bare land from these calculations because, as noted earlier, we consider it emission and sequestration to be insigniﬁcant. The carbon metabolic rate (vk) for a given component (k) is calculated using an empirically derived coefﬁcient:
vk ¼ c$Sk
where c is the coefﬁcient of the carbon metabolism (kgC m2 yr1) and Sk is the area of component k. Supplemental Tables S9 and S10 list the coefﬁcients of carbon sequestration and other accounting items used in the present study. The method of accounting for carbon emission of cultivated land was based on that of West and Matland (2002). 3. The carbon metabolic density (W) includes the carbon sequestration density (WS) and the carbon emission density (WE) for each component. The carbon metabolic difference (DW) between two components for which the land use changed is based on the carbon ﬂow accounting results. For example, for the change from urban to cultivated land, DW ¼ WEU e WSC. This term is calculated as follows:
DW ¼ Wi Wj ¼ ðvi =Si Þ vj Sj
where v is the carbon metabolic rate for components i and j, which includes the carbon emission rate (vE) and the carbon sequestration rate (vS) for these components. The result is used to determine the net direction of the carbon transition: if DW > 0, then carbon storage increases, representing a beneﬁcial ﬂow; if DW < 0, then carbon storage decreases, representing a harmful ﬂow. We multiplied the area that transferred between two land use types by the corresponding DW value to calculate the total carbon ﬂow fji along each path between two nodes:
fji ¼ DW$DS
Fig. 3. Land use map for Beijing in 2010. Maps for 1990 to 2005 are presented as Supplemental Figure S1.
A ﬂow matrix for the spatial model of the urban network's carbon metabolism was built based on the results for carbon ﬂow (fji), and is called the direct ﬂow matrix, F. This matrix is the basis of ecological network analysis (Fath and Patten, 1998).
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4. Calculate the throughﬂow for the whole network (T) and for each component (Tk) using Equations (1) and (2). Then use these values to identify the key components and ecological processes that control the ﬂow changes by analyzing and comparing the throughﬂow during different parts of the study period (i.e., four periods in the present study). 5. Identify and analyze the key ﬂows that create beneﬁcial and harmful effects using the value of DW. If DW > 0, then the process is beneﬁcial because carbon sequestration increases or carbon emission decreases; if DW < 0, the process is harmful because carbon sequestration decreases or carbon emission increases. By analyzing the carbon ﬂows using ArcGIS 10.0, we obtained spatial patterns for the carbon ﬂows with beneﬁcial and harmful effects. We then automatically classiﬁed the optimal results using the Jenks natural breaks optimization calculation method provided by the software. From these results, we identiﬁed the main paths that produced ﬂows with beneﬁcial and harmful effects and the main land use transformations. 3.2. Analysis of ecological relationships in the spatial model of the urban network's carbon metabolism A dimensionless direct utility intensity matrix (D) can be computed based on the direct ﬂow matrix, F. In matrix D, element dij represents the utility of the net ﬂow from compartment j to compartment i, and the net ﬂow between i and j is normalized by the total throughﬂow T at i (see equation (6)). We can then obtain a dimensionless integral utility intensity matrix U ¼ (uji) using Equation (2) from Fath and Patten (1998):
. Ti dij ¼ f ij f ji
U ¼ ðuij Þ ¼ D0 þ D1 þ D2 þ D3 þ ::: þ Dm þ ::: ¼ ðI DÞ1
where the superscript following D represents the number of components an exchange passes through before reaching its ﬁnal component (0 represents exchanges within a component) and I represents the identity matrix. In summary, utility represents the nature of the beneﬁt each component receives from an exchange; positive values represent a net beneﬁt from the relationship, whereas negative values represent a net liability (loss). In this paper, positive signs of the elements in U represented positive utility, and negative signs represented negative utility. Using the positive and negative signs of the elements in U, we can determine the nature of the relationship between any two components (Fath, 2007). According to the signs in the matrix, there are nine possible relationships between pairs of components. The signs in the diagonal of matrix U are positive, which corresponds to selfsymbiosis for each node in the network; this means that it beneﬁts from membership in the network (Patten, 1991). Table 2 summarizes the possible types of ecological relationships. Among the nine theoretically possible relationships, only four relationships are common. Of these, exploitation and control are reciprocal relationships, and because they represent the same sign pair, we have combined them into a single category (exploitation Table 2 The relationships between components of the network. Values in brackets represent the value in the ﬁrst column of table (i) followed by the value in the ﬁrst row of table (j) for ﬂow fji.
þ 0 e
(þ, þ) mutualism (0, þ) commensalism host (, þ) control
(þ, 0) commensalism (0, 0) neutralism (, 0) amensal host
(þ,) exploitation (0,) amensalism (,) competition
relationships). In exploitation, one component beneﬁts from the relationship and the other component suffers. For example, the expansion of urban land into farmland beneﬁts urban land (its area increases) but causes the shrinkage and fragmentation of farmland. This relationship is very common in an expanding city. In mutualism, both components beneﬁt from the relationship, and both depend on each other; as a result, they develop together. For example, farmland and grassland can establish a mutualistic relationship if chemical fertilizer leaching from the farmland can be captured and used to provide nutrients to grassland, whereas the existence of grassland enriches the biodiversity that is typically lost in farmland. Such relationships are less common, but are the most beneﬁcial to a city. In competition, both components suffer from the relationship. For example, where cultivated land and natural vegetation such as grassland must compete for water, both components will have less water available, and both will suffer. This relationship is relatively common in an expanding city, but should be avoided. By classifying all relationships among components into these three categories, we can judge the utility of the relationships among components both for each pair of components and for the system as a whole. To do so, we used a mutualism index (M):
M ¼ Nþ =N
where Nþ is the number of positive signs in matrix U and N is the number of negative signs in the matrix (Zhang et al., 2014a). To analyze the spatial distribution of the ecological relationships, we mapped the transfers of land between land use and cover types during four 5-year periods (1990 / 1995, 1995 / 2000, 2000 / 2005, and 2005 / 2010) using Arcmap 10.0. The land transferred along each path between components for a given period was extracted and then labeled with the corresponding ecological relationship, thereby providing the spatial distribution of the relationships. The ecological relationships should be identiﬁed at an appropriate scale for all transfers of land between components throughout the city. Because the city experiences thousands of land transformation processes in any given period, it would be impractical to calculate all of them, so some degree of aggregation is necessary. In the present study, we aggregated the changes of a certain pair of components. We used the transfer that accounted for the total area of land to represent all the land transformation processes. In this manner, we were able to summarize the changes in the spatial variation of the city's carbon metabolism in a given period. By combining the analysis of carbon throughﬂow and of the ﬂows with beneﬁcial and harmful effects, we were able to identify the key paths that most strongly affected the city's carbon metabolism. This data can be used to improve the carbon metabolism by changing the ﬂow along certain paths in certain locations. 4. Results 4.1. Carbon throughﬂow and its beneﬁcial and harmful effects Fig. 4 shows the changes in total throughﬂow of the network from 1990 to 2010 and the contribution of each land use node to the total. Fig. 5 summarizes the distribution of the carbon ﬂows in each period. During the study periods, total throughﬂow gradually decreased in Beijing. The throughﬂow from 1990 to 1995 was 3.7 times the value from 2005 to 2010, for an average annual decrease of 6.3%. The total throughﬂow of the network was 5174.41 106 kgC yr1 from 1990 to 1995 and 4894.51 106 kgC yr1 from 1995 to 2000. Because the rate of land transfer between components decreased after 2000, the throughﬂow also decreased dramatically.
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Fig. 4. (a) Contribution of each component to the total throughﬂow (T) from 1990 to 2010 and (b) changes in throughﬂow for each component (Tk) during the four periods from 1990 to 2010. The three components with the smallest values are not shown. (B, bare land; C, cultivated land; F, forest; G, grassland; R, rural land; T, transportation and industrial land; U, urban land; W, water).
Fig. 5. Carbon metabolic ﬂows for Beijing during the four study periods. Darker lines represent larger ﬂows; red lines represent a ﬂow that causes a loss of beneﬁts, whereas green lines represent a ﬂow that increases beneﬁts. (B, bare land; C, cultivated land; F, forest; G, grassland; R, rural land; T, transportation and industrial land; U, urban land; W, water; zij, the input ﬂow from component j to component i; yij the output ﬂow from component j to component i). (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.)
The throughﬂow from 2000 to 2005 and from 2005 to 2010 amounted to 33% and 27% of the rate from 1990 to 1995. During the four periods, the net effects of LUCC changed from harmful to beneﬁcial, then to harmful, and ﬁnally to beneﬁcial. The magnitude of the ﬂows with beneﬁcial effects amounted to 0.44, 1.14, 0.22, and 3.53 times the magnitude of the ﬂows with harmful effects during the four periods, resulting in a net beneﬁcial direction from 1990 to 2010. During the study period, transportation and industrial land was the most important contributor to throughﬂow, accounting for 51.1% of total carbon throughﬂow resulting from LUCC (Fig. 4a). Cultivated land was the second-largest contributor, accounting for 22.0% of the total carbon throughﬂow. Carbon throughﬂow from rural land and urban land together accounted for 18.5% of the total, and the other natural components (forest, grassland, water, and bare land) together accounted for only 8.4% of the total. The
throughﬂow of all the areas decreased from 1990 to 2010. Transportation and industrial land followed the same trend as the average annual change for the city as a whole, with an average annual growth rate of 6.3%, but began to decrease rapidly in 2000, at an average annual rate of 12.3%. The average annual rates of decrease for cultivated, rural, and urban land were 7.2, 10.1, and 7.1%, all of which were greater than the average annual rate of change for the city. The throughﬂow for cultivated land decreased rapidly starting in 1995, at an annual average rate of 7.8%. Rural land decreased rapidly starting in 2000, at an annual average rate of 16.9%, which was even greater than the decrease for transportation and industrial land during the same period. The throughﬂow of urban land did not decrease greatly during the study period. The decrease in Beijing's total throughﬂow therefore did not result from changes in a single key land use type, but rather from reduced interactions among all types.
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Throughﬂows with harmful effects dominated the network from 1990 to 1995 and from 2000 to 2005. Flows with harmful effects in the two periods (1966.2 106 and 1388.5 106 kgC yr1, respectively) were 2.3 and 4.6 times the value of beneﬁcial ﬂows in the corresponding periods. The main contributors to harmful carbon ﬂows in the network were transitions between cultivated land and transportation and industrial land (C / T), between rural land and transportation and industrial land (R / T), between cultivated land and urban land (C / U), and between forest and transportation and industrial land (F / T) (Fig. 5a,c). These four interactions accounted for 88.4% of the harmful carbon ﬂows from 1990 to 1995 and 83.4% of the harmful carbon ﬂows from 2000 to 2005. The largest contributor was C / T during both periods, accounting for 59.5% of the harmful carbon ﬂows from 1990 to 1995 and 58.5% of the harmful carbon ﬂows from 2000 to 2005. The second-largest contributor from 1990 to 1995 was R / T, which accounted for 14.7% of the harmful carbon ﬂows. From 2000 to 2005, R / T was the fourth-largest contributor, accounting for 6.2% of the harmful carbon ﬂows. The second-largest contributor from 2000 to 2005 was C / U, which accounted for 10.5% of the harmful carbon ﬂows, equivalent to 1.4 times its value from 1990 to 1995. The main contributors to beneﬁcial carbon ﬂows during these two periods were transitions between transportation and industrial land and the following components: urban land (T / U), cultivated land (T / C), forest (T / F), and rural land (T / R) (Fig. 5a,c). These four paths accounted for 81.2% of the beneﬁcial carbon ﬂows from 1990 to 1995 and 98.2% of the beneﬁcial carbon ﬂows from 2000 to 2005. The largest contributor was T / U during both periods, accounting for 39.8% of the beneﬁcial carbon ﬂows from 1990 to 1995 and 62.6% of the beneﬁcial carbon ﬂows from 2000 to 2005. The second-largest contributors during the two periods were T / C, which accounted for 17.2% of the beneﬁcial carbon ﬂows from 1990 to 1995, and T / R, which accounted for 29.9% of the beneﬁcial carbon ﬂows from 2000 to 2005. During both periods, the main paths were most strongly related to transportation and industrial land, including three of the main harmful paths and all of the main beneﬁcial paths. The main paths were also more strongly related to cultivated land (as output ends) and urban land (as input ends). Flows with beneﬁcial effects dominated the network from 1995 to 2000 and from 2005 to 2010 (1591.1 106 and 555.1 106 kgC yr1, respectively), being 1.1 and 3.5 times the values of the corresponding harmful ﬂows, respectively. The largest contributor was T / C for both periods, accounting for 33.9% of the beneﬁcial carbon ﬂows from 1995 to 2000 and 63.9% of the beneﬁcial carbon ﬂows from 2005 to 2010. The second- and third-largest contributors differed in the two periods. From 1995 to 2000, T / R and T / U accounted for 33.3 and 14.5% of the beneﬁcial carbon ﬂows, respectively. The proportions of these ﬂows decreased to 1.3 and 0.3% from 2005 to 2010, and they were no longer main paths. The second- and third-largest contributors from 2005 to 2010 were T / F and between transportation and industrial land and water (T / W), which accounted for 17.6 and 11.0% of the beneﬁcial carbon ﬂows, respectively. From 1995 to 2000, T / F was the fourthlargest contributor. The fourth-largest contributor from 2005 to 2010 was between transportation and industrial land and grassland (T / G), accounting for 10.0% of the beneﬁcial carbon ﬂows. T / G and T / W were not the main paths in any other period. Flows in the four main paths accounted for 89.3% of the beneﬁcial carbon ﬂows from 1995 to 2000 and 96.7% of the beneﬁcial carbon ﬂows from 2005 to 2010. The main contributors to harmful carbon ﬂows in the network from 1995 to 2000 were C / T, F / T, transfers between urban land and transportation and industrial land (U / T), and R / T (Fig. 5b). Flows in these four paths accounted for 77.2% of the
negative carbon ﬂows during this period. The largest contributor during this period was C / T, which accounted for 36.1% of the harmful carbon ﬂows. C / T was the fourth-largest contributor to harmful carbon ﬂows from 2005 to 2010, when the proportion decreased to 5.7% (Fig. 5d). U / T and R / T accounted for 13.9 and 12.0% of the harmful carbon ﬂows, respectively, from 1995 to 2000. These proportions increased to 63.9% for U / T and 20.7% for R / T from 2005 to 2010, when these two paths were the ﬁrst and second contributors to the harmful carbon ﬂows. The third-largest contributor was G / T, which accounted for 2.2% of the harmful carbon ﬂows from 2005 to 2010. This path is not a main harmful contributor in any other period. During these two periods, the main paths were most strongly related to transportation and industrial land. It is important to note that the main paths during adjacent periods had opposite directions. This illustrates that carbon ﬂows in the network were dynamic processes. During the four periods, transportation and industrial land was the most important output and input component, largely because of its high carbon metabolic density. Cultivated land was the second-largest output component and urban land was the second-largest input component. 4.2. The spatial distribution of carbon relationships The eight components of the spatial network model of Beijing's carbon metabolism formed 28 pairs of ecological relationships (Fig. 2). They could be classiﬁed primarily as mutualism, competition, and exploitation relationships (see Table 1 and Supplemental Tables S11eS14). Neutralism relationships only occurred from 2000 to 2005 (between bare land and other lands that did not change), and because we were mainly concerned with the spatial and temporal variations in relationships that resulted in signiﬁcant carbon ﬂows, we have not analyzed the neutralisms further. Fig. 6a shows the changes in the mutualism index (M) during the study period; M decreased by nearly two-thirds from 1990 to 2005, then recovered slightly. During the study period, the mean value of M was 1.73. However, the system's mutualism level changed greatly, decreasing at a total average rate of 3.8% between 1990 and 2010, illustrating that fewer positive relations existed for the relationships between the components. Because M > 1 throughout the study period, the land use changes were overall resulting in positive relations, which we consider to represent relatively regular and ordered metabolism. However, the positive relations decreased as Beijing's development proceeded (Fig. 6a). During the study period, the proportions of the three main types of relationships changed. The numbers of exploitation and mutualism relationships decreased, while the number of competition relationships increased; however, the number of mutualism relationships increased signiﬁcantly during the last of the four periods. Fig. 6b shows the changes in the proportions of mutualism, competition, and exploitation relationships that were responsible for the changes in M shown in Fig. 6a. Throughout the study period,
Fig. 6. (a) The changes in the mutualism index (M) from 1990 to 2010, and (b) the changes in the proportions of the three dominant ecological relationships that were responsible for the changes in M.
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exploitation relationships were dominant; 24 of the 28 pairs of relationships had an exploitation relationship at least once during the study period, accounting for 85.7% of the total pairs. On average for the four periods, exploitation relationships accounted for about 50% of all relationships. This was followed by mutualism relationships, which accounted for about 30% of all relationships. Last were the competition relationships, accounting for about 20% of all relationships. From 1990 to 1995, exploitation and mutualism relationships both accounted for 46.6% of the total number, and competition relationships accounted for 7.1%. The relations in the network were almost all positive, and M equaled 2.76, its highest value during the four periods. From 1995 to 2000, M decreased to 1.91, at an annual average rate of 7.1%. Competition relationships changed little, whereas exploitation relationships increased greatly (to about 64.2% of the total, at an average rate of 6.7% annually), and mutualism relationships decreased greatly (to about 28.6% of the total, at an average rate of 9.3% annually). The decrease in the number of mutualism relationships was largely responsible for the decrease in M. The exploitation relationships that replaced the mutualism relationships still contributed some positive utility to the network, and therefore slowed the decrease of M. From 2000 to 2005, M continued to decrease dramatically, at an average annual rate of 12.8%, the highest during the study period, reaching 0.96 (its lowest value during the four periods), indicating that negative utilities outweighed positive utilities for the ﬁrst time. During this phase, the numbers of exploitation and mutualism relationships both decreased, and competition increased, at average annual rates of 11.2, 12.9, and 28.5%, respectively. These changes increased the number of negative utilities, causing M to decrease dramatically. From 2005 to 2010, M increased to 1.28, at an average annual rate of 6.0%, largely due to an increase in mutualism relationships (which occurred at nearly 3 times the rate of increase for competition relationships). M was still smaller than during the ﬁrst two periods, but the network had regained a more regular and balanced metabolism. During this phase, exploitation relationships decreased and mutualism and competition relationships increased, at annual average rates of 4.4, 20.9, and 7.4%, respectively. From 2005 to 2010, competition relationships accounted for almost as large a proportion of the total as mutualism relationships, indicating signiﬁcant problems despite the overall improvement in mutualism. During the study period, the spatial distribution of the ecological relationships changed (Fig. 7). White areas represent land that did not transfer between land uses or cover types during a given period. Because white areas increased over time, this suggests that the land use and cover type pattern gradually stabilized in many areas of Beijing. Before 2000, the three ecological relationships clustered together and were distributed throughout Beijing, forming different spatial patterns in the northwestern and southeastern parts of the city. The southeastern plains contained 50% of the total exploitation relationships, as well as 50% of the mutualism relationships and 39% of the competition relationships. The northwestern mountainous area contained scattered exploitation, competition, and mutualism relationships, accounting for 50, 61, and 50% of these relationships. After 2000, LUCC was concentrated in the central and southeastern parts of Beijing. Exploitation, mutualism, and competition relationships in the southeastern plains accounted for 81, 72, and 65% of the total number throughout Beijing, respectively. The northwestern mountainous area contained a relatively small number of competition and mutualism relationships, accounting for 35 and 28% of these types of relationship, respectively. Exploitation relationships mainly occurred between artiﬁcial components of the system, indicating that these were the dominant areas of land use change. Mutualism relationships mainly occurred between the
Fig. 7. Spatial distribution of the ecological relationships from 1990 to 2010. White areas represent areas for which the land use or cover type did not change during the period.
natural and artiﬁcial areas, indicating that both natural and artiﬁcial areas can beneﬁt from LUCC during socioeconomic development. Competition relationships mainly occurred between natural components and between cultivated land and natural components, indicating that the area of natural components decreased as a result of strong competition for land between these two uses. The components that produced exploitation relationships did not change greatly during the study period. Exploitation relationships mainly occurred between transportation and industrial land and other components, and accounted for nearly 50% of the total exploitation relationships in each phase (Table S15eS18). Exploitation relationships existed between transportation and industrial land and both rural land and urban land in every period, and most of these relationships were found at the periphery of the southeastern plains (Fig. 8). Other exploitation relationships were mainly distributed in the northwestern mountainous area. Carbon ﬂows to and from the transportation and industrial land accounted for more than 92% of the total ﬂows by exploitation relationships, half of which were negative ﬂows. Relationships between urban land and other components were usually exploitation relationships, and accounted for 31.7% of the total exploitation relationships in each phase, and these were mainly distributed on the periphery of the southeastern plains (Table S15eS18). Exploitation relationships existed between urban land and transportation and industrial land in all periods, between urban land and rural land in all periods except 1990 to 1995, and between urban land and cultivated land in all periods except 2005 to 2010. These relationships were mainly distributed in the northwestern mountainous area. Carbon ﬂows to and from the urban land accounted for 19.8% of the total ﬂows by exploitation relationships, but more than 97% of these were positive ﬂows. Carbon ﬂows between transportation and industrial land and cultivated land accounted for 47.0% of the total ﬂows in exploitation relationships. Carbon ﬂows between transportation and industrial land and urban land were the second-largest value, accounting for 14.3% of the total ﬂows in exploitation relationships, and carbon ﬂows between urban land and cultivated land accounted for 4.6% of the total ﬂows in exploitation relationships.
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Fig. 8. Spatial distribution of exploitation relationships and associated carbon ﬂows from 1990 to 2010.
Mutualism relationships were also distributed throughout Beijing before 2000, but subsequently shifted to a cluster at the periphery of the southeastern plains (Fig. 9). During the study period, the components that produced mutualism relationships changed dramatically. Mutualism relationships occurred between the natural and artiﬁcial areas, and primarily included rural land, which accounted for more than 30% of the total mutualism relationships (Table S15eS18). Carbon ﬂows in the corresponding paths accounted for 67.4% of the total ﬂows in mutualism relationships, and 61.3% of these ﬂows were positive. Mutualism relationships were identiﬁed between rural land and grassland, water, and bare land in every phase (except for bare land from 2000 to 2005), and
Fig. 9. Spatial distribution of the mutualism relationships and the associated carbon ﬂows from 1990 to 2010.
were mainly distributed at the periphery of the southeastern plains. Mutualism relationships occurred between rural land and forest from 1995 to 2000 and from 2005 to 2010, mainly in the northwestern mountainous area. Mutualism relationships related to urban land accounted for 40% of the total mutualism relationships. Carbon ﬂows along these paths accounted for 56.9% of the total ﬂow in mutualism relationships, and 89.7% of these ﬂows were negative. Mutualism relationships occurred between urban land and grassland after 1995, and were mainly distributed in the center of the southeastern plains. Relationships occurred between urban land and forest and between urban land and water after 2000, and these were mainly distributed in the northwestern mountainous area. Relationships occurred between urban land and bare land from 1990 to 1995 and from 2005 to 2010, and these were mainly distributed on the periphery of the built-up areas in the northwestern mountains. Mutualism relationships related to cultivated land accounted for more than 20% of the total mutualism relationships, and carbon ﬂows in these paths accounted for 27.2% of the total ﬂow in mutualism relationships; 83.7% of these ﬂows which were negative. From 1990 to 1995 and from 2000 to 2005, mutualism relationships occurred between transportation and industrial land and grassland. The carbon metabolic density of transportation and industrial land is large, and carbon ﬂows in these paths were so large that they reduced the proportions of ﬂows in other paths. Mutualism relationships between cultivated land and grassland and between cultivated land and water were replaced by competition relationships (see below), which were mainly distributed in the northwestern mountainous area. Mutualism relationships between cultivated land and urban land and between cultivated land and rural land were mainly distributed in the northern and southern parts of the southeastern plains. As we noted in Section 4.1, cultivated land was the second-largest output, and accounted for a large proportion of the negative ﬂows. Mutualism relationships mainly occurred between rural land and grassland, between rural land and water, between cultivated land and grassland, and between cultivated land and water before 2000; after 2000, they mainly occurred between urban land and forest, between urban land and grassland, and between urban land and water. Competition relationships were distributed throughout Beijing before 1995, but by 1995, they were mostly distributed in the northwestern half of the study area (Fig. 10). Thereafter, they were concentrated in the western, northern, and southern parts of the city. Competition between cultivated land and forest and between cultivated land and rural land were mainly distributed at the periphery of the southeastern plains and in the northwestern mountainous area from 1990 to 1995 (Table S15eS18). Negative carbon ﬂows accounted for 90.4% of the total ﬂows along these paths. Competition relationships between forest and grassland and between water and grassland were mainly distributed in the northwestern mountainous area from 1995 to 2000. Negative carbon ﬂows accounted for 98.1% of the total ﬂows along these paths. After 2000, any pair of forest, grassland, water, and cultivated land produced a competition relationship, and these were mainly distributed in the northwestern mountainous area. Relationships involving cultivated land accounted for 42.1% of the total competition relationships, but carbon ﬂows in the corresponding paths accounted for 60.0% of the total ﬂow in competition relationships. All of these ﬂows had negative effects, and the most signiﬁcant were between cultivated land and forest. Relationships involving grassland accounted for 42.9% of the total competition relationships, but carbon ﬂows along these paths accounted for only 17.2% of the total ﬂow in competition relationships; 97.4% of the ﬂows were negative. The most signiﬁcant ﬂows occurred between grassland and forest. Carbon ﬂows in
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Fig. 10. Spatial distribution of the competition relationships and the associated carbon ﬂows 1990 to 2010.
competition relationships created an imbalanced urban carbon metabolism. 5. Discussion As cities face the difﬁcult task of reducing carbon emissions, researchers have tried various methods to analyze urban carbon transfer processes to support this task. Urban metabolism methods can provide an effective framework to trace a city's ﬂows because they provide more information than alternative methods that analyze carbon ﬂows and stocks due to land transformations (Pataki et al., 2006). The relations between land use types can be revealed by building a spatial model of the network's carbon metabolism using ecological network analysis (Zhang, 2013). In this paper, we identiﬁed the dominant land use types of the urban carbon metabolism by analyzing carbon ﬂows within and between the different natural and artiﬁcial areas. Because the carbon ﬂow processes differed from those in previous research, similarities and differences exist between this research and other studies. The consumption of fossil fuel to generate electricity and support transportation was the main inﬂuence on Vienna's carbon metabolism (Chen and Chen, 2012a). Transportation was also a key factor in a study of the carbon processes in 10 cities (Kennedy et al., 2007, 2009). In the present study, transportation and industrial land was also a dominant feature of the carbon metabolic network. However, it is undesirable for Beijing to guide urban development based only on this, which does not improve the carbon metabolic balance. The carbon metabolic density of transportation and industrial land was nearly 15 times (Table S11) the value of the nextmost-signiﬁcant component (urban land), which had a negative effect on the ability to encourage mutualism relationships. A study of urban metabolism in Hong Kong from 1971 to 1997 (Rhodes and Koeing, 2001) found that the metabolism of all materials, including carbon outputs, increased during the study period. Carbon outputs increased most and have risen up by 245%. Metabolic accounting research in other cities found that the material input and output ﬂuxes usually increased during development (Huang et al., 2006; Marull et al., 2010; Krausmann, 2011; Gingrich et al., 2012),
which was the inevitable result of fast urbanization. In our study, carbon throughﬂow decreased as a result of a decreasing rate of transfers of land between different land use and cover types. When land use changed signiﬁcantly, carbon throughﬂow was large (1990e2000); when land use did not change signiﬁcantly, carbon throughﬂow was small (2000e2010). Monitoring LUCC therefore provides a means to quantitatively adjust the spatial patterns revealed by our analyses. Mutualism within a natural ecological system indicates a steady symbiosis within the network (Fath and Patten, 1998). In contrast, a city is an ecological system dominated by artiﬁcial features, and the metabolic imbalances caused by resource and energy consumption and waste emission are not easily corrected by the natural components of the system (i.e., the internal and external environment). As a result, urban ecosystems sometimes cannot maintain mutualism. The spatial model of the urban network's carbon metabolism that we developed demonstrates this problem. From 2000 to 2005, the mutualism index was low (M < 1), indicating that negative relations outweighed positive relations. In contrast, Chen and Chen found a higher value of M (1.91) in Vienna's carbon metabolic system, indicating that positive relations outweighed negative relations (Chen and Chen, 2012a). This difference may be the result of differences in the maturity of the two cities: Vienna is an old and relatively mature city with a stable development status, whereas Beijing has developed rapidly during the past 20 years and is only slowly beginning to stabilize. The dominant component in Beijing's development has related to transportation and industrial land, creating an unbalanced carbon metabolism. In natural ecosystems, positive relationships typically outnumber negative relationships (Fath, 2007). Our study reached a similar conclusion from 1990 to 1995 with a high value of M (4.00) for only the natural components. In contrast, the natural areas of Beijing's system were dominated by the artiﬁcial ones after 1995, leading to more competition or exploitation relationships than mutualism relationships. As a result, M < 1 for these components from 1995 to 2010. Li et al. (2012) also found that competition relationships outnumbered mutualism relationships in their study of Beijing. There are several possible explanations for this. First, these studies used different time scales. We studied urban carbon metabolism from 1990 to 2010, whereas Li et al. (2012) studied urban carbon metabolism from 1998 to 2007. The time scale in our study captured the period of low-level urbanization in Beijing from 1990 to 2000. Natural components, acting as producers and decomposers, could accommodate the metabolic stress produced by consumers during this period, so the city acquired more mutualism relationships. Second, Li et al. (2012) calculated the relations based on the material ﬂow, and in this study land use and cover change is the basis of the calculation. Li et al. (2012) ignored natural areas within the Beijing's region, and this reduced the number of competition relationships. In our study, we subdivided the environment into several types, resulting in more mutualism relationships. In this analysis, natural components played an indispensable role in improving the city's carbon metabolism. The carbon network model her used a spatially explicit consideration of the land use change. This result provides guidance for plans to adjust the city pattern by identifying speciﬁc land uses in speciﬁc areas that will require additional attention. Other researchers have tried to redesign a city based on efforts to improve its urban metabolism. For example, students at the University of Toronto used the concept of neighborhood metabolism (Engel Yan et al., 2005; Codoban and Kennedy, 2008) to reduce resource inputs and waste outputs by designing closed loops and green buildings. Similarly, redesigning Beijing based on the present results can also focus on the land readjustment. We identiﬁed the key ecological processes by analyzing the spatial variation of three ecological
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relationships based on the carbon ﬂow along each path between components, which would allow us to adjust the spatial pattern quantitatively. Exploitation relationships that mainly occurred between constructed areas are a main characteristic of Beijing's urbanization. Exploitation relationships also controlled the spatial distribution of competition and mutualism relationships. Transportation and industrial land played an overwhelmingly dominant role in the exploitation relationships. The layout of a city's transportation network is a key aspect of urban spatial adjustment because it provides the ﬂows of materials and energy that sustain the city, and because planners can direct the city's population and industrial development to certain areas by providing an attractive transportation infrastructure. Tang and Wang (2007) also considered the layout of the transportation network and tried to improve a city's environmental performance by improving the transportation layout. However, the paths related to transportation and industrial land contributed 35% of the total harmful ﬂows in Beijing in the present study, causing increasing negative ﬂows and unbalancing the urban carbon metabolism. In the future, we should look for ways to decrease the dominance of Beijing's transportation and industrial component of Beijing. Among the exploitation relationships, urban land had the second-largest contribution, so altering urban expansion could potentially improve the city's carbon metabolism. Our results showed that more than 97% of the carbon ﬂows related to conversion to urban land were beneﬁcial ﬂows. Therefore, urban land should become a dominant component in future development to maintain the city's carbon metabolism balance in the future. Similar results were reported for Beijing by Zhang et al. (2014b), who found that adjusting the spatial pattern of urban land was an important strategy to maintain the city's carbon balance. Exploitation relationships also existed between urban and rural land. These relationships mainly resulted from urban exploitation of rural land, represented by transformation of rural land into urban land. Since 53% of the ﬂows in this relationship were beneﬁcial, transformation of rural land into urban land could increase the city's population density, thereby improving the energy consumption efﬁciency and decreasing carbon emission (Ewing and Rong, 2008), both of which would improve the carbon metabolism. However, some studies have shown that an excessively high population density can increase carbon emission (Perkins et al., 2009). This will not likely occur at the edges of urban and suburban areas. Another problem is that loss of agricultural land can create long-term problems with food security, so it may be necessary to implement measures to protect farmland from being converted to urban and other uses. Mutualism relationships often existed between constructed areas that had low carbon emission and natural areas, and these relationships had positive effects on the overall degree of mutualism of the network (M) by increasing the number of positive relations. Especially for mutualism relationships between rural land and forest and between rural land and grassland, more than 60% of the ﬂows were beneﬁcial and improved the city's urban carbon metabolism. Mutualism relationships also existed between cultivated land and the system's natural components; the resulting beneﬁcial ﬂows were 6 times the harmful ﬂows. In the future, Beijing should protect cultivated land. In addition to the abovementioned challenge of food security, the carbon accumulation by agricultural crops can be greater than that by the region's natural vegetation under appropriate management regimes (Chen et al., 2006). Human-managed areas such as cultivated land had a relatively harmonious relationship with natural areas in terms of Beijing's carbon metabolism. Thus, planners can push the region in the direction of increased mutualism by changing the
carbon ﬂows to favor such harmonious relationships. For example, a rooftop or ground-level community gardens may be beneﬁcial to rural areas. With increased urban development, competition relationships become the key to adjusting the spatial structure and function of the urban network's carbon metabolism. The loss of cultivated land in Beijing revealed by the present study is becoming increasingly serious, so preserving cultivated land will be a primary target for reducing competition relationships. Urban development has also limited the space available for natural areas. As a result, competition for the available land is ﬁerce among the natural areas as well as between cultivated and natural land. Farmland protection policies are likely to exacerbate the competition between cultivated land and alternative uses of the land. The competition relationships and the corresponding high proportion of negative ﬂows indicate that protecting farmland within the city should not be achieved at the expense of decreasing the space available for the city's natural components. Meanwhile, the General Plan for the Land Utilization of Beijing city: 2006e2020 (Beijing Municipal Bureau of Land and Resources, 2010) identiﬁed the basic strategies for the Beijing land planning includes that the protection and reasonable utility of cultivated land, scientiﬁc exploitation of unused land, rational distribution of transportation land, and promotion of the intensive development of urban land. These strategies conformed to the outcomes the model in the paper which can be reliability. 6. Conclusions In this study, we constructed a spatial model of an urban network's carbon metabolism, and used the model to examine carbon ﬂows in Beijing during four 5-year periods from 1990 to 2010. This analysis was based on carbon transitions estimated from empirical coefﬁcients for the carbon metabolic density of the main land use and cover types and empirical data on LUCC. We applied ecological network analysis to evaluate the city's carbon metabolism. The changes in carbon ﬂows and in the spatial distribution of the ecological relationships were revealed by comparing the distributions of LUCC during different parts of the study period. We performed a spatially explicit simulation of Beijing's land transformations between natural and artiﬁcial, 2) among natural, and among artiﬁcial areas. Throughﬂow in Beijing's spatial model of the network's carbon metabolism decreased during the study period. Carbon ﬂows between transportation and industrial land and cultivated land was a key factor in these changes in Beijing's metabolic network, and the directions of these ﬂows determined the net effect on the system. The spatial distributions of exploitation and mutualism relationships decreased in the southeastern part of the city, whereas competition relationships expanded gradually in the northwestern and southeastern parts. Increasing competition relationships led to an unbalanced carbon metabolism, and exacerbated the contradictions in land use. The present study demonstrates the importance of research on urban carbon metabolic networks. Previous research has led both researchers and urban planners to pay more attention to land resources and LUCC than in the past. A spatially explicit analysis, such as the one in the present study, can build on previous research by revealing additional interactions among the areas of an urban region and can provide empirical support for spatially explicit adjustments of the urban structure. The present study had some weaknesses that should be addressed in future research. First, the urban system was divided into eight relatively coarse-grained types, resulting in insufﬁcient identiﬁcation of the ecological relationships. The urban system should be divided into ﬁner-grained classiﬁcations in the future, as more data become available, to better identify the ecological relationships and provide ﬁner-grained support for urban planning.
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In addition, the evaluation of the city's carbon metabolic network was relatively coarse. Further analysis using ecological network analysis should be conducted to provide more detailed insights into spatial and temporal variations in the carbon metabolic network. Once these issues have been resolved, it will be interesting to apply the techniques described in this paper to compare several cities, even the built-up areas with similar or different characteristics, since such comparisons can provide additional insights that are not possible from studying a single city, for example the investigation of whether the size of the study area may affect the model results. These comparisons among different areas and different land use types can also provide verify the variation of the outcomes and provide the validation of the proposed model. Acknowledgments This work was supported by the Fund for Innovative Research Group of the National Natural Science Foundation of China (no. 51421065), by the Program for New Century Excellent Talents in University (no. NCET-12-0059), by the National Natural Science Foundation of China (no. 41171068), and by the Fundamental Research Funds for the Central Universities (2015KJJCA09). Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.jclepro.2015.06.052. References Alberti, M., Marzluff, J., 2004. Ecological resilience in urban ecosystems: linking urban patterns to human and ecological functions. Urban Ecosyst. 7 (3), 241e265. Baccini, P., 1996. Understanding regional metabolism for a sustainable development of urban systems. Environ. Manag. Strateg. 3 (2), 108e111. Baird, D., Fath, B.D., Ulanowicz, R.E., Asmus, H., Asmus, R., 2009. On the consequences of aggregation and balancing of networks on system properties derived from ecological network analysis. Ecol. Model. 220 (23), 3465e3471. Beijing Municipal Bureau of Statistics, 1992. Beijing Statistical Yearbook. China Statistics Press, Beijing (in Chinese). Beijing Municipal Bureau of Statistics, 2012. Beijing Statistical Yearbook. China Statistics Press, Beijing (in Chinese). Beijing Municipal Bureau of Land and Resources, 2010. The General Plan for the Land Utilization of Beijing City: 20062020. Beijing Municipal Bureau of Land and Resources Press, Beijing (in Chinese). Blecic, I., Cecchini, A., Falk, M., Marras, S., Pyles, D.R., et al., 2014. Urban metabolism and climate change: a planning support system. Int. J. Appl. Earth Observ. Geoinf. 26, 447e457. Chen, S.Q., Chen, B., 2012a. Network environ perspective for urban metabolism and carbon emissions: a case study of Vienna, Austria. Environ. Sci. Technol. 46, 4498e4506. Chen, S.Q., Chen, B., 2012b. Determining carbon metabolism in urban areas though network environ theory. Procedia Environ. Sci. 13, 2246e2255. Chen, H., Tian, H.Q., Liu, M.L., Melillo, J., Pan, S., Zhang, C., 2006. Effect of land-cover change on terrestrial carbon dynamics in the southern United States. J. Environ. Qual. 35 (4), 1533e1547. China National Bureau of Statistics, 1998. China Energy Statistical Yearbook. China Statistics Press, Beijing (in Chinese). China National Bureau of Statistics, 2004. China Energy Statistical Yearbook (in Chinese). National Bureau of Statistic and Energy Bureau of National Development and Reform Commission. China Statistics Press, Beijing (in Chinese). China National Bureau of Statistics, 2007. China Energy Statistical Yearbook (in Chinese). National Bureau of Statistic and Energy Bureau of National Development and Reform Commission. China Statistics Press, Beijing (in Chinese). China National Bureau of Statistics and Energy Bureau of National Development and Reform Commission, 2010. China Energy Statistical Yearbook. China Statistics Press, Beijing (in Chinese). China State Grain Administration, 2012. China Grain Yearbook. Economy and Management Publishing House, Beijing (in Chinese). Christen, A., Coops, N., Kellett, R., Crawford, B., Heyman, E., Olchovski, I., et al., 2010. A LiDAR-based Urban Metabolism Approach to Neighbourhood Scale Energy and Carbon Emissions Modelling. University of British Columbia, Vancouver. Chrysoulakis, N., Mitraka, Z., Diamantakis, E., Gonz alez, A., Castro, E.A., San Jose_, R., et al., 2010. Accounting for urban metabolism in urban planning. The case of
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