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Ecological Modelling 220 (2009) 2940–2959

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Ecological Modelling

journa l homepage: www.e lsev ier .com/ locate /eco lmodel

ynthesis and spatial dynamics of socio-economic metabolism andand use change of Taipei Metropolitan Region

hun-Lin Leea,∗, Shu-Li Huangb, Shih-Liang Chanc

Department of Landscape Architecture, Chinese Culture University, Taipei 11114, TaiwanGraduate Institute of Urban Planning, National Taipei University, Taipei 10433, TaiwanDepartment of Real Estate & Built Environment, National Taipei University, Taipei 10433, Taiwan

r t i c l e i n f o

rticle history:vailable online 14 July 2009

eywords:ocio-economic metabolismand use changepatial system simulationEMLUCaipei Metropolitan Regionpatial interaction mechanisms

a b s t r a c t

Ever since the concept of metabolism was extended from biological science by social scientists to analyzehuman systems, socio-economic metabolism has been extensively applied to explore resource consump-tion, asset accumulation, waste emissions, and complex processes of land use change in a socio-economicsystem. Current research in socio-economic metabolism and land use change has used accountingapproaches for macroscopic comparisons of countries and regions. However, socio-economic metabolismhas seldom been applied to the analysis of land use change. To simulate the spatial-temporal dynamics ofsocio-economic metabolism and land use change, this study adopts a spatial system modeling method todevelop a Socio-Economic Metabolism and Land Use Change (SEMLUC) model for the Taipei Metropoli-tan Region. The simulation results illustrate that the Taipei Metropolitan Region is highly dependent on
inflows of non-renewable energy and exhibits a spatial hierarchy of non-renewable energy consumptioncentering on Taipei’s Main station. Additionally, urban assets provide feedback to natural and agriculturalsystems to extract additional resource inflows which, driven by the maximum power principle, acceleratethe convergence of energy flows toward urban assets. Accumulating urban assets also facilitates inflowsof non-renewable material to nearby cells thereby enhancing land use conversion to urban areas. Thiswork also demonstrates the capability of ArcGIS software in simulating socio-economic metabolism and
an sy
land use change in an urb
. Introduction

Socio-economic metabolism (alternatively termed “urbanetabolism” or “societal metabolism”) has been extensively

pplied to explore resource consumption, material flows, assetccumulation and waste emissions in socio-economic systemsWolman, 1965; Rappaport, 1971; Boyden et al., 1981; Fischer-owalski, 1998; Huang and Hsu, 2001) since the concept wasrst extended from biological science by social scientists to ana-

yze human systems. A socio-economic metabolism perspectiverovides a useful framework for natural and social scientiststudying interrelationships between human societies and naturalnvironments. Material Flow Accounting (MFA) and Material and
nergy Flow Accounting (MEFA) have been used to compare socio-conomic metabolism in many countries and regions throughouthe world (World Resources Institute, 2000; Eurostat, 2001; Haberlt al., 2004). However, resource consumption, asset accumula-
∗ Corresponding author. Tel.: +886 2 2861 0511x41533; fax: +886 2 2861 7507.E-mail addresses: [email protected], [email protected] (C.-L. Lee),

[email protected] (S.-L. Huang), [email protected] (S.-L. Chan).

304-3800/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.ecolmodel.2009.06.021

stem.© 2009 Elsevier B.V. All rights reserved.

tion and waste emissions aspects of socio-economic metabolisminvolve complex processes of land use change (Turner et al.,1993; Huang et al., 2006). Analyses of socio-economic metabolismconsidering land use factors for a research site are just begin-ning (Haberl et al., 2001). Socio-economic metabolism and landuse change are research themes in the core research projectsof IHDP (The International Human Dimensions Programme onGlobal Environmental Change). The impact of land use change onsocio-economic metabolism and the influence of socio-economicmetabolism on land use change should be investigated care-fully. Krausmann and Haberl (2002) combined MFA with HumanAppropriation of Net Primary Production (HANPP) to analyze socio-economic metabolism and land use change. Further, Krausmann etal. (2003) adopted a Geographical Information System (GIS) to dis-play the results of HANPP in order to elucidate spatial interrelationsbetween land use change and socio-economic metabolism. How-ever, the relationship between land use change and socio-economic
metabolism should be analyzed from a more dynamic and spatialapproach.
In recent decades, advances in GIS technology and efforts ofthe Land Use and Land-Cover Change (LUCC) project of IHDP haveled to the development of various land use models for simu-

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dx.doi.org/10.1016/j.ecolmodel.2009.06.021

odelling 220 (2009) 2940–2959 2941

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ating land use change. These have included empirical statisticalodels, spatial system models, agent-based models and cellu-

ar automata (Serneels and Lambin, 2001; Costanza and Voinov,004; Matthews, 2006). Spatial statistical methods (e.g., spatialegression) are a convenient way to construct the relationshipsetween land use change and the driving factors of land use changeVerburg et al., 2002). However, statistical approaches often ignorehe interactive behavior between factors and between neighboringells during the process of land use change. Integrating cellu-ar automata and agent-based models obviously becomes one ofhe most effective methods for exploring land use change from

bottom-up perspective (Parker et al., 2003). However, spatial-emporal dynamics of land use change in socio-economic systemsepend not only on previous and surrounding states but also onxogenous conditions and driving forces such as renewable energyows and imported goods and services, which affect land usehange in the socio-economic system. The top-down approach ofpatial system modeling, which is based on general system theory,an analyze patterns of land use change systems by emphasiz-ng material and energy flows between system components from

macroscopic perspective (Costanza and Voinov, 2004; Huangt al., 2007). However, spatial system modeling is at present anmerging methodology that still has difficulties dealing with spa-ial heterogeneity and spatial interaction mechanisms. Lee et al.2008) simulated land use change systems from a biophysicalerspective and improved the methodological shortcomings of spa-ial system simulation to establish a basis for exploring spatialnterrelations between land use change, resource consumption,sset accumulation and waste emissions. However, research onpatial-temporal dynamics between socio-economic metabolismnd land use change from biophysical perspectives is still unavail-ble.

Therefore, to investigate spatial patterns and mechanisms ofhe relationship between socio-economic metabolism and land usehange, this study adopts a biophysical approach. A spatial sys-em simulation is used to create a Socio-Economic Metabolismnd Land Use Change (SEMLUC) model for the Taipei Metropoli-an Region based on the procedure for developing spatial system

odels described by Lee et al. (2008). The SEMLUC model is notn explicitly predictive model for predicting land use change butather an explanatory model for investigating spatial-temporal pat-erns and mechanisms of relationships between socio-economic

etabolism and land use change.

. Methodology

.1. System modeling

Based on general system theory and the laws of thermodynam-cs, Odum (1971, 1983) designed a set of energy system symbols

hich can be used to develop system models for simulating tem-oral dynamics of ecological systems. The energy symbols haveinetic and energetic definitions and can describe the interactionsf ecosystem components via energetic flows. Fig. 1 displays thenergy system symbols, which include (a) energy circuit; (b) source;c) tank; (d) heat sink; (e) interaction; (f) producer; (g) consumer;h) transaction; (i) box. In addition to their systemic and ener-etic meanings, these symbols also have mathematical meaningsnd can be transferred into system equations. Fig. 2 summarizeshe mathematical representations used in this study. A description,xplanation and mathematical representation of these symbols can
e found in Odum (1983). Procedures and the applications of energyiagrams for simulating ecosystems of different scales can be found
n Odum and Odum (2000). Further, Huang (1998) also employednergy system diagram and modeling to simulate the evolution ofrban zonation and land use change.

Fig. 1. Odum’s energy system symbols. (a) Energy circuit; (b) source; (c) tank; (d)heat sink; (e) interaction; (f) producer; (g) consumer; (h) transaction; (i) box. (Odum,1983).

2.2. Spatial system modeling

Spatial system modeling (Costanza and Voinov, 2004) is anemerging and synthesized simulation approach based on gen-eral system theory (von Bertalanffy, 1968) and fractal forms(Mandelbrot, 1983). It combines system modeling (Odum, 1983;Ford, 1999), GIS and map algebra (Tomlin, 1990) to explore thespatial-temporal dynamics of an ecosystem (see Fig. 3). Through thedevelopment of the Spatial Modeling Environment (SME) software,Costanza and Voinov (2004) proposed a spatially explicit landscapesimulation model to investigate spatial patterns of ecosystems andlandscape systems. The SME allows the integration with othermodeling software such as Stella to simulate ecological processesboth locally and spatially. Huang et al. (2007) developed a spatialmodel of urban energetics and used the spatial analysis capabil-ity of the raster-based geographic information system to simulatethe spatial dynamics of the Taipei urban landscape system. Froma top-down perspective, spatial system modeling divides a geo-metric area of a system into component grids, each with its ownsimulation model, connected by energetic flows (Odum and Odum,2000). Application of spatial system modeling to spatial patternsof energy consumption, invasive species spread and landscapechange have clearly demonstrated its feasibility (Meinhardt, 1982;Costanza and Voinov, 2004; BenDor and Metcalf, 2006; Huanget al., 2007). However, due to the shortcomings of spatial sys-tem modeling (e.g., spatial homogeneity assumption, difficulties inpresenting spatial interaction, and programming difficulties withthe integration of different software) such models have had alimited following and restricted explanatory power (Parker et al.,2003).

2.3. Spatial system modeling with GIS

In order to eliminate the effort of linking GIS with systemdynamic software, Huang et al. (2007) made use of the arithmeticcapability of a raster-based GIS to develop a spatial system modelbased on energetic principles for simulating land use change. Lee etal. (2008) were able to make use of the spatial variation of systeminflows, storages and coefficients by using the “spatial analyst” and“map algebra” functions in ArcGIS and thereby overcome the homo-
geneous assumption that limited previous spatial system models.In addition, they designed spatial interaction mechanisms basedon carrying capacity of urban assets, urban population and naturalassets to present spatial flows for system models. Their procedurefor developing and simulating spatial system models was done

2942 C.-L. Lee et al. / Ecological Modelling 220 (2009) 2940–2959

Fig. 2. Mathematical representation of system symbols (Huang, 1998, p. 395).

Fig. 3. The spatial simulation idea.

C.-L. Lee et al. / Ecological Modelling 220 (2009) 2940–2959 2943

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sing Model Builder in ArcGIS and therefore avoiding the challengef programming an interface for different software. The procedurencludes nine steps: (1) preliminary analyses for a research site;2) system diagram; (3) data collection; (4) preparation of raster

aps; (5) system equations and parameters; (6) spatial interac-ion mechanisms; (7) construction of the model in Model Builder;8) validation test; and, (9) scenario analyses and hypotheses tests.see Fig. 4). This procedure overcomes the methodological draw-acks of previous spatial system modeling effectively, is adopted inhis paper to develop the spatial system model for simulating socio-conomic metabolism and land use change of Taipei Metropolitanegion.

. The study area: Taipei Metropolitan Region

In building a spatial system model, it is necessary to understandesource consumption, biophysical characteristics, and land use of

system models (Lee et al., 2008).

the research site. The study area, the Taipei Metropolitan Region(2457.13 km2), is the socio-economic center of Taiwan and is locatedin Taipei Basin. Three water ways – Tahan Creek, Hsintein Creekand the Keelung River – intersect and converge in Taipei Basin toform the main branch of Danshui River (Fig. 5). The change in ele-vation from the basin floor to the mountainous areas is dramatic,consequently the slopes of surrounding areas of Taipei Basin oftenexceeds 40%. The soils in the low lying Taipei Basin are alluvialmaking them excellent for agricultural cultivation. Further, rain-fall intensity is greatest in the mountainous northeast areas due inlarge part from northeastern monsoonal effect during part of theyear.

Zoning controls in the Taipei Metropolitan Region have guidedthe spatial location of residential districts, commercial districtsand infrastructure, and provided capacity limits for the densityof urban development in different regions of the basin (Fig. 5).Development of the Taipei Metropolitan Region has therefore


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Fig. 5. The location and biophysical

een constrained by the steep topography and zoning controlsn the basin; and consequently is concentrated in the flatterortions of the Taipei Basin (Fig. 6). The Taipei Metropolitanegion has undergone rapid economic development during theast decades. Large built-up areas now occupy most flatlands

n the basin and sprawl now occurs along the floodplains ofahan Creek and the Keelung River. Further, some of the agri-ultural land in surrounding mountainous area is no longerarmed because of the reduced role of agriculture in the Taipeirea.

Socio-economic metabolism can be defined as resource extrac-ion from the socio-economic system, resource consumption fromhe outer system, asset accumulation in the system and waste emis-ions by the system (World Resources Institute, 2000; Eurostat,001). Fig. 7(a) shows the change in demand for different renewable
roducts from 1971 to 2005. The inflows of goods, non-renewableaterials and energy, particularly sand, rock, electricity and
etroleum are also shown (Fig. 7(d), (b), and (c)). All of these inflowsncreased over this period. Agricultural production in the Taipei

etropolitan Region has decreased rapidly due to the industrial

Fig. 6. Land use of Taipei M

tions of Taipei Metropolitan Region.

transformation during the past 35 years (Fig. 7(e)). Moreover, goodsoutflows and waste emissions increased significantly (Fig. 7(f) and(g)). Population change, however, stabilized after a rapid populationimmigration from 1981 to 1986 (Fig. 7(h)).

In summary, economic growth and urban development in theTaipei Metropolitan Region is concentrated in the low lying areas ofTaipei Basin. Due to industrial transformation, agriculture no longerplays as important role in the Taipei area as it once did. The variousresources, goods and services needed to stimulate asset accu-mulation and socio-economic development are largely imported.Because land use change in the Taipei Metropolitan Region is char-acterized as an urban-driven phenomenon, the basin is filled upwith built-up areas that now extend to the base of the mountain-sides. Growth in the Taipei Metropolitan Region has now stabilizedand the region has become a mature socio-economic system which
requires significant resource inflows in order to maintain itself. Atthe same time, huge amounts of waste emissions are generated.Based on this understanding of material and energy flows, popula-tion change, assets accumulation and land use change in the TaipeiMetropolitan Region, an integrated spatial system model, SEMLUC,
etropolitan Region.


Fig. 7. Socio-economic metabolism of Taipei Metropolitan Region.


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as developed to simulate socio-economic metabolism and landse change of Taipei Metropolitan Region.

. A model of the socio-economic metabolism and land usehange in the Taipei Metropolitan Region

We present the Socio-Economic Metabolism and Land Usehange (SEMLUC) model using the Overview, Design concepts, andetails (ODD) protocol suggested by Grimm et al. (2006). This pro-

ocol includes purpose, state variables and scales, process overviewnd scheduling, design concepts, initialization, inputs, and sub-odels.

.1. Purpose

The SEMLUC model was built for analyzing spatial-temporalatterns and interaction mechanisms between socio-economicetabolism and land use change for the Taipei Metropolitan Region.

he model is an explanatory model for exploring dynamic patternsf resource flows, assets accumulation, waste emission and land usehange for the period from 1971 to 2005.

.2. State variables and scales

The SEMLUC is a top-down model and divides the Taipeietropolitan Region into 9827 cells (cell size, 0.5 km × 0.5 km)

o simulate the spatial dynamics of socio-economic and land usehange in the study area. State variables, codes, and explanation ofhe model are shown in Table 1.

UC system.

4.3. Process overview and scheduling

4.3.1. The SEMLUC systemThe core of SEMLUC model of Taipei Metropolitan Region is com-

prised of natural, agricultural and urban subsystems (see Fig. 8). TheSEMLUC system consists of natural areas (Ln), agricultural areas(La), urban areas (Lu), natural assets (An), agricultural assets (Aa),urban assets (Au) and urban population (Pu). Land use changes inthe system are designed as bi-directional flows between natural,agricultural and urban areas (Ln, La and Lu) based on the rota-tion model proposed by Odum and Odum (2000). Environmentalinflows (E) (e.g., solar and rain), renewable products (R) (e.g., agri-cultural products), non-renewable materials (NM) (e.g., sand, rocksand cement), non-renewable energy (NE) (e.g., electricity, gas andpetroleum) and goods (G) are major inflows to the socio-economicmetabolism and land use change system. Population immigration(P) from the outer system is a significant source of urban popu-lation (Pu) increase. Moreover, system storages are connected bybiophysical flows (J101, . . ., J316; see Fig. 8) marked with coefficients(k101, . . ., k316; see Table 2 ) to represent the SEMLUC process viamaterial and energy flows. Detailed explanation of system equa-tions and each flow for SEMLUC system are described in Section4.7.1.

4.3.2. The process of the SEMLUC modelFig. 9 shows the simulation process performed by the SEMLUC

model. GIS maps, statistics, and other research data are collectedand used to generate initial raster maps of variables, coefficients,inputs and land suitability. Spatial system modeling (Huang et al.,


Table 1State variables of SEMLUC model.

State variables Code Explanation

StoragesNatural area Ln Ln is the storage of natural area, including forest, meadow, wasteland, shrubbery, and wetland.Agricultural area La La is the storage of agricultural area, including farmland, orchard, pasture, and fish farm.Urban area Lu Lu is the storage of urban area, including residential area, commercial area, industrial area, and infrastructure area.Natural assets An An is the storage of natural assets, including animals, plants, and organisms, on Ln.Agricultural assets Aa Aa is the storage of agricultural assets, including grain, vegetables, fruits, livestock, and aquatic products, on La.Urban assets Au Au is the storage of urban assets, including building, infrastructure, goods, and embankment, on Lu.Urban population Pu Pu is the storage of urban population on Lu.

InflowsEnvironmental inflow E E is the inflow of environmental inflow, including sun, wind, rain, and tide, into Taipei Metropolitan Region.Renewable products R R is the inflow of renewable products, including grain, vegetables, fruits, livestock, and aquatic products, into Taipei

Metropolitan Region.Non-renewable material NM NM is the inflow of non-renewable material, including sand, gravel, and cement, into Taipei Metropolitan Region.Non-renewable energy NE NE is the inflow of non-renewable energy, including electricity, petroleum gas, and oil, into Taipei Metropolitan Region.Goods G G is the goods inflow into Taipei Metropolitan Region.Population immigration P P is the population immigration into Taipei Metropolitan Region.

Fig. 9. The process of the SEMLUC model.


Table 2The estimation of initial storages and flows.

Items Mathematical expression Estimation basis (units)

StoragesNatural area Ln Ln is generated by land use map 1971 (km2 cell−1)Agricultural area La La is generated by land use map 1971 (km2 cell−1)Urban area Lu Lu is generated by land use map 1971 (km2 cell−1)Natural assets An Based on land use map in 1971 and natural researches on biomass per area for each

kind of natural area (103 ton cell−1)Agricultural assets Aa Based on land use map in 1971 and agricultural researches on agricultural assets per

area for each kind of agricultural area (103 ton cell−1)Urban assets Au Based on land use map in 1971 and urban researches on urban assets per area for each

kind of urban area (103 ton cell−1)Urban population Pu Based on land use map in 1971 and population researches on population per area for

each kind of urban area (103 pop cell−1)

FlowsEnvironmental use by natural area k101 × Enn × An J101 is estimated by environmental inflow, natural area, and the utility rate, assumed

to be 90% of E (km cell−1)Production of natural asset k102 × Enn × An J102 = An change + J103 + J104 + J105 + J106 + J107 + J108, An change is the average of

natural asset change between 1971 with 2005 (103 ton cell−1)Conversion of natural asset to urban asset k103 × An × Ln × Au J103 = 0.039% × An, which bases on the ratio of timber harvests to the amount of

natural assets in 1971 (103 ton cell−1)Natural use to convert urban area into

natural areak104 × An × Lu J104 is estimated by natural asset per natural area and land use conversion from urban

to natural area, which bases on land use maps in 1971 and 2005 (103 ton cell−1)Natural use to convert agricultural area

into natural areak105 × An × La J105 is estimated by natural asset per natural area and land use conversion from

agricultural to natural area, which bases on land use maps in 1971 and 2005(103 ton cell−1)

Waste emission from natural asset k106 × An × (Ln × Aa + Ln × Au) J106 is estimated by natural asset per natural area and land use conversion fromnatural area to agricultural and urban area, which bases on land use maps in 1971 and2005 (103 ton cell−1)

Conversion of natural assets toagricultural asset

k107 × An × Ln × Aa J107 = 0.014% × An, assumed to be 0.014% of natural asset (103 ton cell−1)

Depreciation of agricultural asset k108 × An J108 = 2.75% × An, assumed depreciation rate of 2.75% (103 ton cell−1)Change of natural area to urban area k109 × Ln × Au J109 is the average of land use conversion from natural to urban area, which bases on

land use maps in 1971 and 2005 (km2 cell−1)Change of natural area to agricultural

areak110 × Ln × Aa J110 is the average of land use conversion from natural to agricultural area, which

bases on land use maps in 1971 and 2005 (km2 cell−1)Environmental use by agricultural area k201 × Ena × Aa J201 is estimated by environmental inflow, agricultural area, and the utility rate,

assumed to be 70% of E (km cell−1)Production of agricultural asset k202 × Ena × Aa J202 = Aa change + J203 + J204 + J205 + J206 + J207 + J208 − J107, Aa change is the average

of agricultural asset change between 1971 with 2005 (103 ton cell−1)Agricultural use to convert natural area

into agricultural areak203 × Ln × Aa J203 is estimated by agricultural asset per agricultural area and land use conversion

from natural to agricultural area, which bases on land use maps in 1971 and 2005(103 ton cell−1)

Agricultural use to convert urban areainto agricultural area

k204 × Lu × Aa J204 is estimated by agricultural asset per agricultural area and land use conversionfrom urban to agricultural area, which bases on land use maps in 1971 and 2005(103 ton cell−1)

Conversion of agricultural asset to urbanasset

k205 × Aa × La × Au J205 = 0.085% × Aa, which bases on the ratio of agricultural production to the amountof agricultural asset in 1971 (103 ton cell−1)

Agricultural products outflow k206 × Aa J206 = 0.021% × Aa, assumed to be 0.021% of agricultural asset (103 ton cell−1)Waste emission from agricultural asset k207 × Aa × (La × An + La × Au) J207 is estimated by agricultural asset per agricultural area and land use conversion

from agricultural area to natural and urban area, which bases on land use maps in 1971and 2005 (103 ton cell−1)

Depreciation of agricultural asset k208 × Aa J208 = 3.5% × Aa, assumed depreciation rate of 3.5% (103 ton cell−1)Change of agricultural area to natural

areak209 × La × An J209 is the average of land use conversion from agricultural to natural area, which

bases on land use maps in 1971 and 2005 (km2 cell−1)Change of agricultural area to urban area k210 × La × Au J210 is the average of land use conversion from agricultural to urban area, which bases

on land use maps in 1971 and 2005 (km2 cell−1)Environmental use by urban area k301 × Enu × NM × (Ln + La) × Au J301 is estimated by environmental inflow, urban area, and the utility rate, assumed to

be 40% of E (km cell−1)Production of urban asset by

non-renewable materialk302 × Enu × NM × (Ln + La) × Au J302 is estimated by the ratio of non-renewable material inflows to the amount of

urban asset in 1971 (103 ton cell−1)Production of urban asset by renewable

resourcesk303 × R × Pu J303 is estimated by the ratio of renewable product inflows to the amount of urban

asset in 1971 (103 ton cell−1)Production of urban asset by

non-renewable energy and goodsk304 × NE × G × Au J304 is estimated by the ratio of goods inflows to the amount of urban asset in 1971

(103 ton cell−1)Urban asset consumed by people k305 × Au × Pu J305 = 0.01% × Au, assumed to be 0.01% of urban asset (103 ton cell−1)Urban asset outflow k306 × Au J306 = 0.162% × Au, which bases on the ratio of goods outflows to the amount of urban

asset in 1971 (103 ton cell−1)Waste emission from urban asset k307 × Au J307 = 0.124% × Au, which bases on the ratio of waste emission to the amount of urban

asset in 1971 (103 ton cell−1)Depreciation of urban asset k308 × Au J308 = 0.5% × Au, assumed depreciation rate of 0.5% (103 ton cell−1)Urban asset use to convert natural area

into urban areak309 × Ln × Au J309 is estimated by urban asset per urban area and land use conversion from natural

to urban area, which bases on land use maps in 1971 and 2005 (103 ton cell−1)Urban asset use to convert agricultural

area into urban areak310 × La × Au J310 is estimated by urban asset per urban area and land use conversion from

agricultural to urban area, which bases on land use maps in 1971 and 2005(103 ton cell−1)


Table 2 (Continued )

Items Mathematical expression Estimation basis (units)

Population growth k311 × Au × Pu J311 = 2.583% × Pu, which bases on the birthrate in 1971 (103 pop cell−1)Population immigration k312 × P × Au J312 is estimated by the immigration of population in 1971 (103 pop cell−1)Population emigration k313 × Pu × Pu J313 = 4.638% × Pu, which bases on the emigration of population in 1971

(103 pop cell−1)Death of population k314 × Pu J314 = 0.415% × Pu, which bases on the death rate in 1971 (103 pop cell−1)Change of urban area to natural area k315 × Lu × An J315 is the average of land use conversion from urban to natural area, which bases

on land use maps in 1971 and 2005 (km cell−1)Change of urban area to agricultural area k316 × Lu × Aa

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Fig. 10. Land use conversion and metabolism.

007; Lee et al., 2008), inflow allocation, constraints on land con-ersion and spatial interaction designs are all integrated in theonstruction of the SEMLUC model. The SEMLUC model is raster-ased and the spatial-temporal simulated results of stock valuesuch as land area (Ln, La, and Lu), asset (An, Aa, and Au) and popu-ation are displayed with a GIS.

.4. Design concepts—land use conversion and metabolism

The energy system diagram developed by Odum and Odum2000) considers land area and land use conversion as stocks (stor-ges) and flows respectively. This stock-and-flow approach to thenvestigation of land use changes and their subsequent materialsnd energy flows is the core concept in the SEMLUC model forhe Taipei Metropolitan Region. Fig. 10 shows an example of landse conversion from a natural area to an urban area, including theelationships between land conversion, resources flows, asset accu-ulation and waste emissions. The accumulation of urban assets

an help stimulate the conversion of land from natural areas torban areas. Additionally, conversion of land from natural areas torban areas accelerates resource inflows, which in turn increaseshe accumulation of urban assets. Moreover, some natural assetutflows occur as waste emissions during the process of land useonversion.

.5. Initialization

To overcome the criticism of spatial homogeneity in spatialystem modeling, each storage and flow in the SEMLUC modelre presented as a raster map to describe local heterogeneity of
ariables and flows. Table 2 summarizes the estimation of initialtorages and flows in the model. Fig. 11 shows the distributionraster maps) of initial storages and flows in urban subsystems.ig. 12 provides an illustration of the estimation process of sys-em coefficients. In this illustration we estimate coefficient k105
J316 is the average of land use conversion from urban to agricultural area, whichbases on land use maps in 1971 and 2005 (km2 cell−1)

to show that k105 distribution can be generated by calculating thesystem equation (k105 = J105/An × La) based on the raster maps ofJ105, An and La generated by Table 2 via map algebra and ArcGIS.Using the estimation process shown in Table 2 and Fig. 12, the initialstorages and coefficients (k101 ∼ k316) of the SEMLUC model weregenerated.

4.6. Input

Environmental inflow (E), renewable products (R), non-renewable materials (NM), non-renewable energy (NE), goods (G)and population immigration (P) are the major inflows into the TaipeiMetropolitan Region from outside systems. Based on the estimationin Table 3, SEMLUC model produces spatial distribution for eachinflow (see Fig. 13) to avoid the homogeneity assumption adoptedby past research on spatial system modeling.

4.7. Sub-models

4.7.1. The SEMLUC system model—system equationsA detailed description of SEMLUC system and its equations are

displayed in Fig. 8 and Table 4. The natural subsystem utilizes envi-ronmental inflows (k102 × Enn × An) to increase the accumulationof natural assets (An) and provides the urban and agricul-tural subsystems with necessary resources (k103 × An × Ln × Au;k107 × An × Ln × Aa). Additionally, natural assets (An) contribute(k104 × An × Lu; k105 × La × An) to the land conversion of agri-cultural areas (La) and urban areas (Lu) into natural areas(Ln) (k209 × La × An; k315 × Lu × An). Moreover, natural assetsflow out of the system as waste emissions during the pro-cess of land use conversion (k106 × An × (Ln × Aa + Ln × Au)). Onone hand, the agricultural subsystem is a producer whichuses environmental inflows (k202 × Ena × Aa) to produce agri-cultural assets (Aa). Conversely, the agricultural subsystemis also a provider of urban subsystem agricultural products(k205 × Aa × La × Au). Agricultural assets (Aa) also contribute(k203 × Ln × Aa; k204 × Lu × Aa) to increasing the conversion ofland from natural areas (Ln) and urban areas (Lu) (k110 × Ln × Aa;k316 × Lu × Aa) and outflow as goods and waste emissions(k206 × Aa; k207 × Aa × (La × An + La × Au)).

The urban subsystem is the major consumer in the SEM-LUC system. To promote the accumulation of urban assets(Au), the urban subsystem extracts environmental inflows, non-renewable materials (k302 × Enu × NM × (Ln + La) × Au), renew-able products (k303 × R × Pu), non-renewable energy and goods(k304 × NE × G × Au) from the outer system. Some urban assets areconsumed by the urban population (k305 × Au × Pu) or are con-verted to output as goods (k306 × Au) and waste (k307 × Au). Urban
assets can also depreciate in the urban subsystem (k308 × Au).Urban assets (Au) stimulate land use conversion from natural andagricultural areas to urban areas (k109 × Ln × Au; k210 × La × Au)via the feedback of urban assets (k309 × Ln × Au; k310 × La × Au).Additionally, population immigration (k312 × P × Au), emigration


orage

(d

4

R(ida

TT

I

ERNNGP

Fig. 11. Distribution of initial st

k313 × Pu × Pu), birth (k311 × Au × Pu) and death (k314 × Pu)etermine the size of urban populations (Pu).

.7.2. Inflow allocationThere are five inflows into SEMLUC system: R, NE, NM, G and P.

and NE are necessary to maintain operation of the urban assetsAu). Therefore, for example, Au(n) (the value of Au at stage n) affectsnflows of non-renewable energy at next stage (NE(n + 1)) and theistribution of NE(n + 1) is allocated by Au(n) (see Fig. 14). Therere also additional urban assets and space which can make use of

able 3he estimation of inflows.

nflows Code Estimation basis (units

nvironmental inflow E Based on rainfall map ienewable products R Allocate the amount ofon-renewable material NM Allocate the amount ofon-renewable energy NE Allocate the amount ofoods G Allocate the amount ofopulation immigration P Allocate the amount of

s and flows (urban subsystem).

NM, G and P when the increase in urban assets (dAu) is positive.Consequently, dAu(n) allocates the total amount of NM, G and Pto generate the distribution of NM(n + 1), G(n + 1) and P(n + 1). TheSEMLUC model adopts the inflow allocation process to reveal thespatial heterogeneity of inflows.

4.7.3. Constraints on land conversionBiophysical conditions and institutional controls on land do

place limitations on land use change. The SEMLUC model consid-ers biophysical characteristics (e.g., slope, soil, land use zoning and

)

n 1971 (km cell−1)renewable products in 1971, which bases on the distribution of Pu (103 ton cell−1)non-renewable material in 1971, which bases on the increase of Au (103 ton cell−1)non-renewable energy in 1971,which bases on the Au (1018 sej cell−1)goods in 1971, which bases on the increase of Au (103 ton cell−1)immigrated population in 1971, which bases on the increase of Au (103 pop cell−1)


on of c

cteca

Fig. 12. Estimati

onservation area) through a land suitability analysis to producehresholds for natural areas, agricultural areas and urban areas inach cell. For example, once the threshold of urban area (Lu) in aell is reached the Lu value in the cell is not allowed to increasenymore.

Fig. 13. Distributio

oefficient k105.

4.7.4. Spatial interactionThe SEMLUC model has two spatial interaction designs for assets

and population. First, natural assets (An) flow from high (more)to low (less) concentrations according to biophysical principles.Second, this study assumes that urban assets (Au) and population

n of inflows.


Table 4System equations of SEMLUC model.

Natural areaEnn: environmental remainder of natural area

Enn = E × Ln/(1 + k101 × An)

An: natural assetsdAn/dt = k102 × Enn × An − k103 × An × Ln × Au − k104 × An × Lu − k105 × La × An − k106 × An × (Ln × Aa + Ln × Au) − k107 × An × Ln × Aa − k108 × An

Ln: natural areadLn/dt = k209 × La × An + k315 × Lu × An − k109 × Ln × Au − k110 × Ln × Aa

Agricultural areaEna: environmental remainder of agricultural area

Ena = E × La/(1 + k201 × Aa)

Aa: agricultural assetdAa/dt = k202 × Ena × Aa + k107 × An × Ln × Aa − k203 × Ln × Aa − k204 × Lu × Aa − k205 × Aa × La × Au − k206 × Aa − k207 × Aa × (La × An + La × Au) − k208 × Aa

La: agricultural areadLa/dt = k110 × Ln × Aa + k316 × Lu × Aa − k209 × La × An − k210 × La × Au

Urban areaEnu: environmental remainder of urban area

Enu = E × Lu/(1 + k301 × NM × (Ln + La) × Au)

Au: urban assetdAu/dt = k302 × Enu × NM × (Ln + La) × Au + k303 × R × Pu + k304 × NE × G × Au + k103 × An × Ln × Au + k205 × Aa × La × Au − k305 × Au × Pu − k306 × Au − k307 × Au

− k308 × Au − k309 × Ln × Au − k310 × La × Au

Lu: urban areadLu/dt = k109 × Ln × Au + k210 × La × Au − k315 × Lu × An − k316 × Lu × Aa

(aflmyuav

Pu: urban populationdPu/dt = k311 × Au × Pu + k312 × P × Au − k313 × Pu × Pu − k314 × Pu

Pu) will diverge into neighboring areas after Au and Pu convergend reach their upper limit (see Fig. 15(a)). Looking at the spatialows of urban assets as an example (see Fig. 15(b)), the SEMLUCodel adopts “Hot Spot Analysis,” a spatial autocorrelation anal-

sis tool (Getis and Ord, 1992), in ArcGIS to locate hot spots forrban assets (Au(n)) with a 90% significance level. Once urbanssets in the hotspot cells are larger than their upper limit (aalue generated by a maximum estimation of urban asset accu-

Fig. 14. Inflow a

mulation based on land use zoning control for Taipei MetropolitanRegion) a map of urban assets urban assets outflows is producedby the “Map Algebra” and “Math Logical” tools. The differencebetween the cell’s Au(n) and upper limit determines the level
of urban assets that flows out of the cell. Additionally, to gener-ate a map of urban assets inflows, the SEMLUC model uses the“Block Statistic” and “Filter” tools to choose which cells, aroundthe cells where urban assets will be outflowing, have urban assets
llocation.


urban

tiflti(

5

5

satatAMse

Fig. 15. Spatial flows of

hat are smaller than their upper limits. The percent differencen cells of urban assets will inflow allocates urban assets out-ows into the neighborhood. Ultimately, Au(n) is adjusted usinghe asset outflow and inflow to Au(n*), which is used as an inputnto the land use change system to calculate Au in the next stageAu(n + 1)).

. Results

.1. Simulation results and validation

Fig. 16 provides the simulation results of the SEMLUC model fortorage of areas, assets, biomass and urban population. Natural andgricultural areas (Ln and La, respectively) reflect the influence ofhe industrial transformation on the reduction of agricultural landnd the growth of natural areas in hillside fields. These spatial pat-
erns also apply to natural assets and agricultural assets (An anda) because land is a necessary resource for accumulating assets.oreover, urban area, assets and population (Lu, Au, and Pu) clearly
how the concentration of development in Taipei Basin and thextension of development to the surrounding hillside fields. These

assets (Lee et al., 2008).

patterns accurately reflect the evolutionary characteristics of TaipeiMetropolitan Region.

To validate the simulation results, the coefficients of determi-nation were used to compare observed data with the simulationresults (see Lee et al., 2008). Because the spatial interaction designis based on of the limits of urban areas and population (that is, thestock of Au and Pu) the simulation results of Au and Pu match wellwith observed data (Table 5). The model also has good explana-tory ability for biomass (B) and natural areas (Ln) and acceptableexplanatory ability for urban areas (Lu) and agricultural areas (La).However, the SSM/SST value of agricultural assets (Aa) is lower thanthat of other storages.

5.2. Spatial patterns of socio-economic metabolism

To explore the spatial-temporal patterns of socio-economic
metabolism and land use change, this study adopts buffer analy-sis (Figs. 17–20) centering on the Taipei Main Station to calculateaverage values for variables in each buffer zone based for simula-tion results from the SEMLUC model for the time period from 1971to 2005.


Fig. 16. Simulation results.

Table 5Validation of SEMLUC model.

Storages SSM (sum of squares model) SSE (sum of squares error) SST = SSM + SSE (total sum of squares) SSM/SST

Urban Assets (Au) 781,586,568 42,302,857 823,889,425 0.949Urban Population (Pu) 22,830 2,678 25,508 0.895Agric. Assets (Aa) 8,642,306 7,114,808 15,757,114 0.548Biomass (B) 44,956 5,458 50,414 0.892Urban Area (Lu) 42.284 14.989 57.273 0.738Agric. Area (La) 18.541 6.222 24.763 0.749Natural Area (Ln) 89.688 7.246 96.933 0.925

odelli

sriurpid


Fig. 17 presents the simulation results and buffer analysis ofocio-economic metabolism. The amount of non-renewable mate-ial (NM) increased rapidly from 1971 to 1991. Since 1991 the NMnflow has decreased substantially due we believe to a stabilizedrban development (Fig. 17(a)). The spatial pattern of NM inflow
epresents a hierarchical pattern centered in a 7.5 km zone. Thisattern shows the important demand for NM in the surround-
ng urban areas which are experiencing rapid urban growth andevelopment. The amount of non-renewable energy inflows (NE)

Fig. 17. Buffer analysis of socio

ng 220 (2009) 2940–2959 2955

has substantially increased during the past 34 years. This reflectsthe high dependence on systems outside the Taipei MetropolitanRegion for energy (Fig. 17(b)). However, the spatial hierarchicalpattern of NE inflow also displays energy convergence and depen-dence. Fig. 17(c) illustrates the contribution from the agricultural
subsystem on the mountainside to the urban subsystem in 1971.The industrial transformation in the Taipei Metropolitan Regionstimulated the abandonment of agricultural lands and assets inthe surrounding areas of the Taipei Basin. Moreover, as Fig. 17(d)
-economic metabolism.


(Cont

sict(

5

5

eaoadmaF

Fig. 17.

hows there is a concentration of waste emissions in the surround-ng area (7.5–12.5 km) from 1971 to 1988 caused by urban land useonversion. As for the spatial patterns of waste emissions in 2005,hey show a hierarchical pattern similar to that of urban assetsAu).

.3. Socio-economic metabolism and land use change analyses

.3.1. Asset accumulation and land use changeAccording to the maximum power principle, urban systems

xtract energy and material from outer systems to increase theccumulation (convergence) of urban assets (Au). Once the stockf urban assets in city center areas reach their upper limit, urban
ssets, led by the spatial interaction mechanism of urban assets,iverge via the spatial feedback process to stimulate asset accu-ulation and increase land conversion (dLu) from natural and
gricultural to urban in surrounding areas (7.5–12.5 km) (Fig. 18).rom the viewpoint of system ecology, the concept (see Fig. 10)

inued ).

that urban assets stimulate land use conversion from natural andagricultural areas to urban areas via the feedback of urban assetshas been convincingly demonstrated (Huang et al., 2007). Further,the buffer analysis for the simulation results of the SEMLUC modelpresents the motion process of the concept on spatial-temporalpatterns.

5.3.2. Land use change and resource inflowsFrom 1971 to 2005, urban area (Lu), assuming Taipei Main

Station as the center, presented a consistent hierarchical patternthat decreases with increased distance from the center (Fig. 19).Although the central urban area (0–5 km) reached their upperlimit in 1971, surrounding areas (7.5–12.5 km) show significantly
increased urban area. Additionally, the spatial patterns of non-renewable material and goods inflows are curves taking the area of7.5 km as concentration core. Therefore, Fig. 19 displays the processwhereby increased urban area attracted inflow of non-renewablematerial and goods.


accum

5

lropT

Fig. 18. Buffer analysis of asset

.3.3. Land use change and waste emissionsBecause of the consideration for waste emissions during the

and conversion (dLu) process in the SEMLUC model, the simulation
esults and buffer analysis can be used to show the concentrationf waste emissions in the surrounding area (7.5–12.5 km) over theeriod from 1971 to 1988 (Fig. 20). When the development of theaipei Metropolitan Region approached a stable maturation status,
Fig. 19. Buffer analysis of land use

ulation and land use change.

waste emissions exhibited a spatial pattern (decreased hierarchyas distance to center increased) similar to that of urban assets. Thisoccurred in 2005. The spatial pattern of waste emissions we believe
depends on the variation in urban area (dLu) during the develop-ment period. As a consequence, it has a hierarchical pattern similarto that of urban assets (Au) when the development approachesmaturation.
change and resource inflows.


d use

6

mmdraa

Fig. 20. Buffer analysis of lan

. Conclusion

The mechanisms of the relationship between socio-economicetabolism and land use change can be elucidated through for-
al analyses. According to the maximum power principle, a
eveloping socio-economic system attracts a large number ofenewable products (R), non-renewable material inflows (NM)nd non-renewable energy inflows (NE), which stimulate theccumulation (convergence) of urban assets (Au) (see Period I

Fig. 21. Spatial interaction m

change and waste emission.

in Fig. 21). When the stock of urban assets reaches its upperlimit (Period II), the urban system outflows some urban assetsto the surrounding areas through a feedback (divergence) path-way, which triggers land use change (Period III). Because of the
conversion of land from natural and agricultural uses to urbanuse, additional waste emissions are produced (Period III). Theincreased urban area (Lu) attracts additional inflows of non-renewable materials (NM) and promotes urban sprawl (Period IV).As the circulation of urban assets converges and diverges, urban
echanism of SEMLUC.

odelli

aV

bbeactBnlMeaniaclsiWurfe

bmStabldsabomiobomt

A

o

R

B

the spatial dynamics of regional land use: the CLUE-S model. Environ. Manage.30, 291–405.

von Bertalanffy, L., 1968. General System Theory. George Braziller, New York.


reas stabilize, and an urban hierarchical pattern emerges (Period).

Socio-economic metabolism provides a useful framework foroth natural and social scientists studying the interrelationsetween human societies and their natural environments. How-ver, the absence of spatial-temporal dynamic research limits andvanced investigation of socio-economic metabolism and land usehange. This study adopts a procedure for developing spatial sys-em models (Lee et al., 2008) to build the SEMLUC model in Modeluilder and successfully explores spatial patterns and mecha-isms of the relationship between socio-economic metabolism and

and use change. The simulation results illustrated that the Taipeietropolitan Region has become dependent on non-renewable

nergy inflows. The spatial pattern of energy consumption hassimilar hierarchical pattern to that of urban assets. However,

on-renewable material inflows tend to concentrate in surround-ng areas undergoing rapid land use conversion from natural andgricultural land to urban land. Additionally, the mountainside agri-ultural system, which was an important producer in study area, noonger plays a significant role. Moreover, given their characteristicpatial convergence, urban assets can extract additional resourcesnflows via feedbacks driven by the maximum power principle.

hen urban development reaches its maximum, the outflows ofrban assets to surrounding areas will result in inflows of non-enewable materials which trigger land use conversion to an urbanorm; and it is this urban system that then becomes the center ofnergy consumption and waste emission.

This research demonstrates that spatial system modeling cane effective in the investigation of spatial patterns of energy andaterial flows that occur during the process of land use change.

patial system modeling therefore can be seen as a novel alterna-ive for simulating land use change from biophysical, systematicnd macroscopic perspectives. The energetic mechanism and theiophysical relationship between socio-economic metabolism and

and use change elucidated in this study can be used as basis foreveloping an interaction theory between land use change andocio-economic metabolism. Additionally, various spatial policiesnd institutions of land use and resource controls can be exploredy scenario analyses using this approach. Finally, the impactf global climate change on spatial patterns of socio-economicetabolism and land use change are expected to be increasingly

mportant. Based on a system approach, an interdisciplinary modelf land use change can be made by integrating sociology, economics,iophysics, and planning into an eco-economic system. Method-logically, considering multi-scales factors, floated parameters, andulti-patterns methods to calibrate parameters for developing spa-

ial system models are the important tasks in the future.

cknowledgement

We would especially like to thank William W. Budd for his thor-ugh editorial assistance and comments on the manuscript.

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