Cosmic emergy based ecological systems modelling

Cosmic emergy based ecological systems modelling

H.Chen a ,G.Q.Chen a,*,X.Ji b,*

a State Key Laboratory of Turbulence and Complex Systems,Department of Mechanics and Aerospace,College of Engineering,

Peking University,Beijing 100871,China

b Center for Human and Economi

c Development Studies,School of Economics,Peking University,Beijing 100871,China

a r t i c l e i n f o Article history:Received 22August 2009Received in revised form 19September 2009Accepted 22September 2009Available online 25September 2009Keywords:Cosmic exergy Emergy Regional economy Urban study Systems ecology

a b s t r a c t

Ecological systems modelling based on the uni?ed biophysical measure of cosmic emergy

in terms of embodied cosmic exergy is illustrated in this paper with ecological accounting,

simulation and scenario analysis,by a case study for the regional socio-economic ecosys-

tem associated with the municipality of Beijing.An urbanized regional ecosystem model

with eight subsystems of natural support,agriculture,urban production,population,

?nance,land area,potential environmental impact,and culture is representatively pre-

sented in exergy circuit language with 12state variables governing by corresponding eco-

dynamic equations,and 60?ows and auxiliary variables.To characterize the regional

socio-economy as an ecosystem,a series of ecological indicators based on cosmic emergy

are devised.For a systematic ecological account,cosmic exergy transformities are provided

for various dimensions including climate ?ows,natural resources,industrial products,cul-

tural products,population with educational hierarchy,and environmental emissions.For

the urban ecosystem of Beijing in the period from 1990to 2005,ecological accounting is

carried out and characterized in full details.Taking 2000as the starting point,systems

modelling is realized to predict the urban evolution in a one hundred time horizon.For sys-

tems regulation,scenario analyses with essential policy-making implications are made to

illustrate the long term systems effects of the expected water diversion and rise in energy

price.

ó2009Elsevier B.V.All rights reserved.1.Introduction

Based on the maximum empower principle,the feedback mechanism in cybernetics,and the universal energy hierarchy in systems ecology [1],Odum’s emergy synthesis [2]is a thermodynamic approach for evaluation of the real wealth of re-sources,products,and services by accounting the total natural work previously involved to generate them.

Heterotrophic and self-regulating as they are in the biosphere,urban ecosystems as super-organisms are apparently cre-ated for the bene?t of human beings and for sustaining their livelihood.Cities cannot be self-regulating without maintaining stable links with their environment,to obtain energy,food,and materials and to release their wastes.Once a city or region is explored in view of systems ecology,it is rigorous to incorporate emergy into its conceptualization and to thread together socio-economic and natural systems with the same thermodynamic measure.Emergy synthesis provides a holistic alterna-tive to many existing methods for urban study,as applicable to combined systems of humanity and nature [3].

Though emergy is conceptually de?ned in ecological energetics as embodied energy in general,solar emergy in terms of embodied solar energy has been prevailing in ecological accounting in particular,as solar energy has been conventionally believed to be the primary driving force for the ecosphere.Solar emergy synthesis has been applied to many cases at regional 1007-5704/$-see front matter ó2009Elsevier B.V.All rights reserved.

doi:10.1016/461fe1492b160b4e767fcf40sns.2009.09.025*Corresponding authors.Tel.:+861062767167;fax:+861062754280.

E-mail addresses:gqchen@461fe1492b160b4e767fcf40 (G.Q.Chen),jixi@461fe1492b160b4e767fcf40 (X.Ji).

Commun Nonlinear Sci Numer Simulat 15(2010)2672–2700

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H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–27002673 or urban scale,such as the West Virginia,Maine,the Jacksonville in Florida,Beijing,Hong Kong,Macao,Taipei and so on[4–65],with the studies on Taipei by Huang and his fellows[9,21–28]highly remarkable in terms of successive series over dec-ades.The most intensive regional or urban studies based on solar emergy appeared in mainland China,covering many prov-inces,municipalities,autonomous regions and cities,including Beijing,Shanghai,Chongqing,Tianjin,Jilin,Liaoning,Qinghai, Hunan,Ningxia,Inner Mongolia,Yunnan,Shandong,Fujian,Guangdong,Jiangxi,Sichuan,Gansu,Xinjiang,Tibet,Hainan, Jiangsu,Harbin,Hangzhou,Nanjing,Xining,Guiyang,Haikou,Wuhan,Urumchi,Taiyuan,Lanzhou,Changsha,Lhasa,Guangz-hou,Fuzhou,Chengdu,Xi’an,Kunming,Yinchuan,Changchun,Shijiazhuang,Shenyang,Zhengzhou,Nanchang,Hefei,Hohhot, Jinan,Nanning,Fushun,Tangshan,Baotou,Xiamen,Qingdao,Shenzhen,Ningbo,Shunde,Nanchong,Chengde,Kaifeng,Da-lian,and Xuzhou[19,20,29–65].

Notwithstanding the wide applications[2,66–69],solar emergy synthesis has many critic encounters(e.g.[70–72]),with the trouble of the double accounting at various ecological stages.As realized[2,73,74],what matters should be available en-ergy,i.e.exergy,and emergy needs to be explained and de?ned as embodied exergy instead of embodied energy,since there is no possibility for anything to embody some energy,as energy is always in conservative cycling and never consumed [75,76].As a modi?cation,emergy has been reformulated as a function of exergy,to associate physical and mathematical validity as the same as that for exergy’s[74].Also,arguments emerged about the relations between emergy evaluation and exergy analysis(e.g.[68,73,75–79]).

As a recent progress,Chen[75,76]developed an updated emergy synthesis with the concept of embodied cosmic exergy, for brevity termed cosmic emergy,with the reference environment surrounding the earth represented by a singularity of the sun and the continuous distribution of the CBM(cosmic background microwave)radiation,corresponding to the unit of cos-mic Joule(Jc)in contrast to the solar Joule(sej)in solar emergy analysis.The updated emergy as embodied exergy is strictly additive in quantity,consistent with the second law of thermodynamics in terms of exergy consumption and entropy cre-ation.Based on the genuine scarcity and usefulness of cosmic exergy as the fundamental natural resource for the earth eco-system,the updated emergy analysis is rooted in the?rm theoretical foundation for exergetical ecology.As a systematic reversion,rephrasing,and updating of Odum’s emergy analysis,concrete diagramming symbols,and calculation schemes for cosmic emergy accounting[75,76]have been fruitfully applied in a variety of studies with national,regional and urban scales[80–83].

This paper is on the ecological systems modelling based on the uni?ed biophysical measure of cosmic emergy in terms of embodied cosmic exergy,with an urban case study of ecological accounting,simulation and scenario analysis for the urban ecosystem associated with the municipality of Beijing.

2.Methodology

2.1.Exergy network model

A typical exergy network model can be diagrammed in Fig.1for a regional or urban ecosystem,based on the exergy cir-cuit symbols[75,76],as revision from the energy circuit symbols[2],illustrated in Fig.2.

As illustrated,there are eight subsystems of natural support,agriculture,urban production,population,?nance,land area, potential environmental impact,and culture.The natural support subsystem includes water,topsoil and ore resources stocks.Agricultural assets stock is calculated as summation of biomass and the others.Urban assets stock from urban pro-duction system consists of building and production equipment as well as transportation roads,vehicles and related facilities. Population stock means residential population with different levels in the education hierarchy.Money?ows are produced via market exchanges,wherein some money?ows into?nancial assets stock and the remaining used to buy necessary raw materials as well as to pay for labor 461fe1492b160b4e767fcf40nd areas are divided into natural,urban,and ecological types.Potential environmental impact as a stock is due to the accumulation of environmental emissions.Most importantly,cultural infor-mation stock comprises cultural heritage and cultural information products,locating in the highest hierarchy of the network with the ability to affect all the other processes.

Details for the12state variables and60?ows and auxiliary variables in the model are given in Table1,and the12eco-dynamic equations governing the state variables are listed in Table2.

2.2.Cosmic emergy based indicators

As in conventional solar emegy synthesis[9,21–28,68],a series of overall indicators based on cosmic emergy are devised for an urban or regional ecosystem.

Ecological wealth is de?ned as summation of various stocks providing ecological service in urban ecosystems,composed of natural resources affording life-support service and necessary production factors,agricultural and urban assets offering useful products,?nancial assets providing money supply,population as an important gatekeeper,and cultural information serving as the monitor for socio-economic activities.To indicate the living standard of the local residents,per capita ecolog-ical wealth is de?ned as the ratio of ecological wealth to the number of local residents.

To indicate the stability of the urban ecosystem,the complexity of ecological stocks is measured by Shannon’s informa-tion entropy as:

D ?àX i W i W

?ln W i W

with D referred as ecological wealth diversity,W i the i th ecological stock and W the ecological wealth.

Capital wealth in unit of the cosmic emdollar (CEm$)is calculated as ecological wealth divided by cosmic emergy/money ratio.Considering that cosmic emergy/money ratio measures the ability of buying real wealth by money,capital wealth could be a better indicator to re?ect the wealth of urban ecosystems than

money.

2674H.Chen et al./Commun Nonlinear Sci Numer Simulat 15(2010)2672–2700

H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–27002675

Table1

Variables for the urban ecosystem.

Item Variable Equation Unit

Stocks

Water resource stock W Jc

Fuels and ore resources stock F&O Jc

Topsoil resource stock TS Jc

Agricultural assets stock AAs Jc

Urban assets stock UAs Jc

Financial assets stock FAs Billion Yuan Population stock P Jc

Cultural information stock CI Jc

Potential environmental impact stock EI Jc

Ecological land area stock NAr1000ha Agricultural land area stock AAr1000ha Urban land area stock UAr1000ha

Other symbols

Jc Agricultural output AO k601?(RS?AAr^2)?(W?TS)?(F&O+Fi&Ei)

?AAs^2?P?CI?UAs

Urban output UO k605?(W?UAs)?(F&O+Fi&Ei)?UAs^2?P?CI Jc

Price(products and service)p1Yuan/billion Jc Price(fuels and electricity)p2Yuan/billion Jc Market price p3p3?(1+p3i)^(nà2000)(n means years)Yuan/billion Jc Price indicator p3i

Immigrants intensity PIi J703/UAs

Investment intensity Ii J602/UAs Billion Yuan/Jc Inward?ows

Local free renewable resources RS Jc/yr

Incoming renewable?ows IF Jc/yr

Fuels and electricity F&E Fi&Ei?(AAs+UAs)Jc/yr

Products and service G&S k602?FAs/p1?10Jc/yr

Immigrants PI PIi?UAs Jc/yr

Investment I Ii?UAs Billion Yuan/yr Internal?ows

1.Water-related?ows

Local free renewable resources J101k101?RS?(NAr+AAr)?W Jc

Incoming?ows J002IF Jc

Water diversion J003CW Jc

Waste water recovery J104k903?EI?W Jc

Agricultural production J105k102?W?AAr Jc

Urban use J106k103?W?UAs Jc

Out?ows J107k104?W Jc

Dissipation J108k105?W Jc

2.Soil-related?ows

Local free renewable resources J201k201?RS?(NAr+AAr)?TS Jc

Consumption as fertilizers J202k202?TS Jc

Erosion J203k203?TS Jc

3.Fuels and ore-related?ows

Local free renewable resources J301k301?RS?(NAr+AAr)?F&O Jc

Agricultural production J302k302?F&O?AAs Jc

Urban use J303k303?F&O?UAs Jc

Dissipation J304k304?F&O Jc

4.AAs-related?ows

Net increase J401k401?RS?AAr?W?TS?(F&O+Fi&Ei?AAs)?

Jc

P?CI?AAs?UAs?AAr

Transformation to UAs J402k402?AAs Jc

Discard J403k403?AAs Jc

5UAs-related?ows

Net increase J501k501?W?(F&O+Fi&Ei?UAs)?UAs?P?CI Jc

Transformation to AAs J402k402?AAs Jc

Products and service J005k602?FAs/p1Jc

Resources recovery J502k504?EI?UAs Jc

Feedback to agricultural production J503k506?UAs Jc

Discard J504k505?UAs Jc

6.FAs-related?ows

Revenue J601(AO+PO)?p3Billion Yuan/yr Investment J602UAs?Ii Billion Yuan/yr

(continued on next page)

2676H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–2700

Table1(continued)

Item Variable Equation Unit

Fuels and electricity J603F&E?p2Billion Yuan/yr Products and service J604k602?FAs Billion Yuan/yr

7.Population-related?ows

Birth population J701k701?(AAs+UAs)?P Jc

Death population J702k702?P?EI Jc

Immigrants J703PIi?UAs Jc

Migrants J704k703?P?P Jc

8.Culture-related?ows

Cultural products J801k801?P?CI Jc

Dissipation J802k802?CI?CI Jc

9.EI-related?ows

Agricultural environmental emission J901k901?AO+k403?AAs Jc

Urban environmental emission J902k902?UO+k505?UAs Jc

Waste solid recovery J104k504?UAs?EI Jc

Waste water recovery J503k903?EI?W Jc

Dissipation J903k904?EI Jc

461fe1492b160b4e767fcf40nd-related?ows

NAr transformed to UAr J1001k1001?NAr?UAs1000ha NAr transformed to AAr J1006k1006?NAr?AAs1000ha UAr transformed to NAr J1002k1002?UAr?W1000ha UAr transformed to AAr J1003k1003?UAr?AAs1000ha AAr transformed to NAr J1005k1005?AAr?W1000ha AAr transformed to UAr J1004k1004?AAr?UAs1000ha

Power index is the ratio of resources consumption to ecological wealth.

Comparative wealth index is de?ned as the ratio of ecological wealth to population stock based on cosmic emergy,to compare the rate of accumulation of wealth with that of population development.

Economic activities not only consume natural resources,but also lead to environmental emissions with potential environ-mental impact.Hence,ecological cost of urban development is de?ned as sum of natural resources input and environmental emissions.Per capita ecological cost is the ratio of ecological wealth to the number of local residents.

Renewable resource ratio indicates the share of renewable resources in the total resources consumption,while resource self-support ratio means the fraction of local resources in the total resources consumption.

The environmental emission diversity is also de?ned by the Shannon’s information entropy.With higher values of this index,environmental restoration would be more dif?cult due to the complexity of environmental emissions.

Resource consumption diversity calculated by Shannon’s information entropy is to re?ect the stability of supply sources of consumed resources.

2.3.Cosmic exergy transformities

According to the cosmic exergy budget for the earth system[75],the total cosmic exergy consumed by the terrestrial earth is45TW,that is,1.38E+21Jc/yr.Due to interaction,each item of the seven basic categories of global?ows is allocated with one seventh of the total exergy[76],resulting in the exergy transformities listed in Table3.

With the exergy of terrestrial heat of0.24TW and tide of0.03TW[75],the transformities for terrestrial heat and tide are estimated as0.00782and0.017Jc/J,respectively[76,80].Transformities for rock and soil are estimated as2.10E+5and 4.21E+5Jc/g[76,80].Exergy transformities of the other geological products are estimated in magnitude of0.21‰of their

Table2

Ecodynamic equations for the urban ecosystem.

dW/dt=k101?RS?(NAr+AAr)?W+IF+CW+k903?EI?Wàk102?W?AAsàk103?W?UAsàk104?Wàk105?W

dF&O/dt=k301?RS?(NAr+AAr)?F&Oàk302?F&O?AAsàk303?F&O?UAsàk304?F&O

dTS/dt=k201?RS?(NAr+AAr)?TSàk202?TSàk203?TS

dAAs/dt=k401?AO/k601àk402?AAs?UAsàk403?AAsàk404?AAs?P

dUAs/dt=k501?UO/k605+k402?AAs+k602?FAs/p1+k504?EI?UAsàk506?UAsàk505?UAsàk603?P?UAs?CI

dFAs/dt=(AO+UO)?p3+UAs?IiàFI&UI?UAs?p1àk602?FAs

dP/dt=k701?(AAS+UAs)?P+PIi?UAsàk702?Pàk703?P?P

dCI/dt=k801?P?CIàk802?CI^2

dEI/dt=k901?AO+k403?AAs+k902?UO+k505?UAsàk504?UAs?EIàk903?EIàk904?EI

NAr=TAàAAràUAr

dAAr/dt=k1006?NAr?AAs+k1003?UAr?AAsàk1005?AAr?Wàk1004?AAr?UAs

dUAr/dt=k1001?NAr?UAs+k1004?AAr?UAsàk1002?UAr?(W+TS)àk1003?UAr?AAs

TA,the total area of three categories of land for the urban ecosystem.

corresponding energy transformities in solar emergy account.Cosmic exergy transformities of organic products are esti-mated just 0.9‰of their energy transformities.Related results are listed in Table 4.

With the population divided into ?ve categories with different education levels as preschool,primary school,junior high school,senior high school,college,and university,corresponding transformities for population are estimated as national averages in China as 1.72E +12,2.11E +12,3.70E +12,1.22E +13,and 4.90E +13Jc/capita,respectively.

Referring to Odum [2,83],cosmic emergy values of cultural products could be gained according to their exergy inputs and corresponding production times.Related average transformities of Chinese cultural products during 1996–2005are listed in Table 5.

Table 4

Transformities of resources.Item

Transformity Unit Terrestrial heat 7.82E à03Jc/J Tide 1.70E à02Jc/J Rock 2.10E +05Jc/g Soil

4.21E +05Jc/g Ore resources Iron

2.10E +05Jc/g Energy sources Coal

1.40E +01Jc/J Petroleum

2.33E +01Jc/J Natural gas 1.23E +01Jc/J Electricity

3.34E +01Jc/J Agricultural products Grain 6.53E +05Jc/g Cotton 1.46E +07Jc/g Oil crop 2.11E +06Jc/g Vegetable 5.59E +04Jc/g Forest products Fruit 2.04E +05Jc/g Wood

2.30E +11Jc/m 3Livestock products Meat 4.24E +07Jc/g Egg 1.11E +07Jc/g Milk

4.48E +06Jc/g Fishery products Fish 1.42E +07Jc/g Others Water

3.13E +03

Jc/g

Table 3

Transformities of global cosmic exergy ?ows.Item

Cosmic exergy (Jc)Exergy ?ow (J)Tranformity (Jc/J)Global ?ows 1.38?1021Surface wind

1.97?1020 6.31?10210.03Physical exergy,rain on the land 1.97?1020 5.605?10200.35Chemical exergy,rain on the land 1.97?1020 3.239?10200.61Physical stream exergy 1.97?1020 3.395?10200.58Chemical stream exergy 1.97?1020 1.948?1020 1.01Waves absorbed on shores 1.97?1020 3.09?10200.64Earth sedimentary cycle

1.97?1020

2.746?1020

0.72

Table 5

Transformities of Chinese cultural products on average.Cultural product

Average amount (Unit)Equivalence coef?cient Average transformity (Jc/Unit)Nationwide exergy consumption (Jc)Newspapers 3.39E +090.01 1.43E +09 4.85E +18Journals 2.71E +090.1 1.43E +10 3.88E +19Books

6.80E +091 1.43E +119.72E +20Audio products 1.66E +040.5

7.15E +10 1.19E +15Video products 1.74E +08507.15E +12 1.24E +21Films

1.89E +02100

1.43E +13

2.70E +15

Total equivalent gross books (Volume)

1.61E +10

Total national exergy consumption

2.26E +21

H.Chen et al./Commun Nonlinear Sci Numer Simulat 15(2010)2672–27002677

2678H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–2700

Table6

Transformities ofenvironmental emissions.

Environmental emission Transformity Unit

Waste gas

SO2à1.23E+06Jc/g Sootà4.55E+06Jc/g

Waste water

Organic matterà2.57E+06Jc/g COD Petroleumà5.67E+07Jc/g Volatile phenolic compoundsà6.30E+08Jc/g Prussiateà8.40E+09Jc/g Mercury and its compoundsà3.28E+11Jc/g Cadmium and its compoundsà1.92E+10Jc/g Hexavalent chromium compoundsà1.25E+09Jc/g Arsenicà2.55E+08Jc/g Leadà1.48E+08Jc/g Suspended substanceà1.54E+05Jc/g

Waste solid

Industrial waste solid

Smelt waste residueà4.55E+06Jc/g Fly ashà4.20E+04Jc/g Slagà1.54E+05Jc/g Coal refuseà1.89E+05Jc/g Tailingsà4.20E+04Jc/g

Household garbage

Spodosolà2.10E+05Jc/g Food residueà1.29E+06Jc/g Paperà2.52E+05Jc/g Plastics and rubberà2.31E+06Jc/g Textile fabricà1.51E+07Jc/g Glassà2.10E+05Jc/g Tileà4.14E+05Jc/g Plantsà1.22E+06Jc/g

Table7

Boundary?ows for Beijing2000.

Boundary?ow Symbol Result Unit

1.Inward?ows

Local free renewable resources J001 1.73E+16Jc/yr Incoming renewable?ows J002 2.23E+15Jc/yr Fuels and electricity J004 2.13E+19Jc/yr Products and service J0057.79E+19Jc/yr Immigrants J7038.20E+17Jc/yr Investment J601 2.21E+01Billion Yuan/yr

2.Outward?ows

Products and service J5057.96E+19Jc/yr Migrants J704 2.69E+17Jc/yr Soil loss J203 5.80E+17Jc/yr Renewable resources out?ows J107 2.43E+15Jc/yr

Table8

Ecological stocks for Beijing2000.

Ecological stock Symbol Result Unit

1.Natural resources stock

Water resource W 5.28E+15Jc

Fuels and ore resources F&O 4.75E+20Jc

Topsoil TS 5.47E+19Jc

2.Agricultural assets stock AAs 2.45E+19Jc

3.Urban assets stock UAs 3.61E+20Jc

4.Financial assets stock FAs 1.61E+03Billion Yuan

5.Population P

6.66E+19Jc

6.Cultural information CI 6.77E+19Jc

7.Potential environmental impact EIà2.77E+19Jc

8.Ecological land area NAr 2.28E+021000ha

9.Agricultural land area AAr 1.13E+031000ha

10.Urban land area UAr 2.80E+021000ha

H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–27002679

With existing solar energy transformities for industrial by-products[84],environmental emissions in atmosphere and water[85,86],as well as organic compounds and toxic ions[87,88],corresponding cosmic exergy transformities could be estimated as listed in Table6,where the negative sign associated with the transformity is due to the negative values asso-ciated with a waste,in magnitude equal to its remediation cost as de?ned in the cosmic emergy based ecological economet-rics[76].

Table9

Internal?ows for Beijing2000.

Internal?ow Symbol Result Unit

1.Water-related?ows

Local free renewable resources J101 4.30E+15Jc

Incoming?ows J002 2.23E+15Jc

Water diversion J0030.00E+00Jc

Waste water recovery J104 1.00E+15Jc

Agricultural production J105 2.17E+15Jc

Urban use J106 3.78E+15Jc

Out?ows J107 2.43E+15Jc

Dissipation J108 1.00E+14Jc

2.Soil-related?ows

Local free renewable resources J201 1.73E+11Jc

Consumption as fertilizers J2027.95E+17Jc

Erosion J203 5.80E+17Jc

3.Fuels and ore-related?ows

Local free renewable resources J301 1.73E+09Jc

Agricultural production J302 3.08E+18Jc

Urban use J3038.92E+18Jc

Dissipation J304 5.00E+17Jc

4.AAs-related?ows

Net increase J401 4.78E+18Jc

Transformation to UAs J402 2.00E+18Jc

Discard J403 3.91E+17Jc

5.UAs-related?ows

Net increase J501 1.81E+19Jc

Transformation to AAs J402 2.00E+18Jc

Products and service J0057.79E+18Jc

Resources recovery J502 1.98E+18Jc

Feedback to agricultural production J503 4.00E+18Jc

Discard J5048.51E+18Jc

6.FAs-related?ows

Revenue J601 1.19E+02Billion Yuan/yr Investment J602 2.21E+01Billion Yuan/yr Fuels and electricity J603 2.79E+01Billion Yuan/yr Products and service J604 1.01E+01Billion Yuan/yr

7.Population-related?ows

Birth population J701 1.59E+17Jc

Death population J702 2.89E+17Jc

Immigrants J7038.20E+17Jc

Migrants J704 2.68E+17Jc

8.Culture-related?ows

Cultural products J801 3.95E+19Jc

Dissipation J802 1.29E+19Jc

9.EI-related?ows

Agricultural environmental emission J901 1.77E+18Jc

Urban environmental emission J9028.21E+18Jc

Waste solid recovery J104 1.98E+18Jc

Waste water recovery J503 1.00E+15Jc

Dissipation J903 2.98E+18Jc

461fe1492b160b4e767fcf40nd-related?ows

NAr transformed to UAr J10017.00Eà011000ha NAr transformed to AAr J1006 1.00E+011000ha UAr transformed to NAr J10020.00E+001000ha UAr transformed to AAr J10030.00E+001000ha AAr transformed to NAr J1005 3.00E+001000ha AAr transformed to UAr J1004 1.00E+011000ha

2680H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–2700

3.Accounting

Systematic accounting is carried out for the urban ecosystem of Beijing in the period from1990to2005.

3.1.Flows and stocks

Associated with the urban system as diagrammed in Fig.1,accounted results for Beijing in the representative year of2000 are listed in Tables7–9for boundary?ows,ecological stocks,and internal?ows,respectively.

3.2.Ecological wealth and related indicators

Presented in Table10are six categories of ecological wealth in Beijing in selected years from1990to2005.

Table10

Ecological wealth of Beijing for selected years.

Ecological wealth(Jc)19901995200020012002200320042005

Natural resources stock 6.28E+20 6.16E+20 5.30E+20 5.13E+20 4.87E+20 4.25E+20 4.06E+20 3.70E+20 Ore resources 5.70E+20 5.60E+20 4.75E+20 4.58E+20 4.33E+20 3.71E+20 3.53E+20 3.17E+20 Topsoil 5.84E+19 5.63E+19 5.47E+19 5.46E+19 5.41E+19 5.37E+19 5.35E+19 5.30E+19 Water resource 1.11E+169.42E+15 5.28E+15 5.02E+15 5.04E+15 5.02E+15 5.06E+15 5.04E+15 Agricultural assets stock 1.65E+19 1.63E+19 2.29E+19 2.45E+19 2.67E+19 2.78E+19 2.88E+19 2.99E+19 Biomass 1.61E+19 1.57E+19 2.15E+19 2.30E+19 2.50E+19 2.46E+19 2.33E+19 2.10E+19 The others 4.25E+17 5.35E+17 1.35E+18 1.44E+18 1.72E+18 3.20E+18 5.47E+188.84E+18 Urban assets stock 1.68E+20 1.93E+20 3.61E+20 3.82E+20 4.54E+20 5.12E+20 5.51E+20 5.60E+20 Building and production equipment 1.40E+20 1.54E+20 2.89E+20 2.86E+20 3.45E+20 3.95E+20 4.19E+20 4.17E+20

2.80E+19

3.86E+197.21E+199.54E+19 1.09E+20 1.18E+20 1.32E+20 1.43E+20

Transportation roads,vehicles and related

facilities

Financial assets stock 1.14E+20 1.63E+20 5.36E+20 5.76E+20 6.93E+207.89E+208.55E+208.85E+20 Population stock 3.60E+19 5.15E+19 6.66E+19 6.60E+19 6.80E+197.08E+197.13E+197.23E+19 Preschool 1.47E+18 1.19E+18 1.61E+18 1.69E+18 3.89E+17 1.80E+17 1.48E+17 6.20E+17 Primary school 1.80E+18 1.98E+18 1.70E+18 1.69E+18 1.49E+18 1.30E+18 1.10E+18 1.01E+18 Junior high school 4.28E+18 5.19E+18 6.10E+18 6.05E+18 6.02E+18 6.12E+18 6.00E+18 6.02E+18 Senior high school8.94E+18 1.09E+19 1.26E+19 1.24E+19 1.11E+19 1.02E+199.55E+188.65E+18 College and university 1.95E+19 3.23E+19 4.46E+19 4.41E+19 4.90E+19 5.30E+19 5.45E+19 5.60E+19 Cultural information stock 1.14E+20 1.31E+20 1.41E+20 1.41E+20 1.48E+20 1.50E+20 1.56E+20 1.58E+20 Cultural heritage9.00E+199.00E+199.00E+199.00E+199.00E+199.00E+199.00E+199.00E+19

Cultural information products 2.40E+19 4.05E+19 5.07E+19 5.14E+19 5.80E+19 6.01E+19 6.61E+19 6.82E+19

H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–27002681

3.2.1.Natural resources stock

Natural resources stock in2005was41.08%lower than that in1990,of which water resource stock decreased by54.59%, ore resources stock decreased by44.38%,and topsoil stock decreased by9.25%.

With residential population increasing from10.86million in1990to15.38million in2005,per capita water resource stock in2005was only one third of that in1990almost.

While the decrease of topsoil cosmic emergy should be attributed to land use change,water loss and soil erosion as well as unreasonable cultivation,land use change was the main contributor of the decrease.From1990to2005,plenty of natural land and ecological land were transformed into construction land to keep up the rapid development of real estate industry and transportation construction.

Accounted ore resources include fuels(e.g.coal,oil,and natural gas)and metallic minerals plus non-metallic minerals (e.g.iron ore,zinc ore,ilmenite,and bauxite).Although Beijing has relied mainly on external resources input,exploitation of local mineral resources can’t be neglected,such as nearly40%of annual coal supply is from local coal mines.

3.2.2.Agricultural assets stock

Agricultural assets stock accounts for animals and plants in cropping,forestry,husbandry,and?shery.Plants consist of forests,crops and rangeland,and animals just consider livestock taking no account of wild animals due to their rarities.In the

2682H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–2700

lower hierarchy of the cosmic emergy network,agricultural production system has to provide a large amount of products for urban production and household use,and hence the share of agricultural assets stock in the total ecological wealth is small in spite of a slow growth trend in recent years.For example,the amount of forests for sustaining water supply rose during last decades,and the green coverage rate increased from28.00%to42.50%from1990to2005.

3.2.3.Urban assets stock

Urban assets stock in2005was2.33times larger than that in1990,of which buildings and production equipment tripled and transportation roads,vehicles and related facilities increased by4.11-fold.

Buildings construction accelerated because of city economic development in recent years.At the end of2004,?oor space amounted to465.00million square meters,of which residual buildings accounted for57.84%,public buildings34.13%and the others8.02%.In fact,average per capita dwelling area was improved remarkably,up to22square meters in2005as com-pared to just14square meters in1990.

Recently,Beijing entered the period of rapid development of infrastructure construction.As the host city of the2008 Olympics,Beijing spent abundant funds of226billion Yuan from2000to2005.Lots of infrastructure projects with respect to water,electricity,gas,heat,and environment were put into operation.

H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–27002683

Table11

Emergy for environmental emission(Unit:Jc).

Item19901995200020012002200320042005

Waste gasà1.40E+18à1.70E+18à7.32E+17à6.58E+17à6.06E+17à5.49E+17à5.59E+17à4.98E+17 SO2à3.87E+17à4.69E+17à2.76E+17à2.48E+17à2.37E+17à2.26E+17à2.36E+17à2.35E+17 Sootà1.01E+18à1.23E+18à4.55E+17à4.10E+17à3.69E+17à3.23E+17à3.23E+17à2.62E+17 Waste waterà1.59E+18à1.70E+18à8.77E+17à8.23E+17à7.62E+17à7.83E+17à8.64E+17à7.67E+17 Industrial sewageà1.27E+18à1.27E+18à4.73E+17à4.32E+17à4.06E+17à4.65E+17à5.60E+17à4.97E+17 Organic matterà1.91E+17à1.74E+17à5.54E+16à4.65E+16à3.67E+16à2.68E+16à2.91E+16à2.83E+16 Petroleumà6.13E+17à5.59E+17à2.63E+16à2.03E+16à1.51E+16à9.75E+15à7.03E+15à6.83E+15

à4.50E+17à5.22E+17à3.82E+17à3.58E+17à3.48E+17à4.23E+17à5.18E+17à4.56E+17 Volatile phenolic

compounds

Prussiateà5.82E+15à5.31E+15à2.90E+15à1.37E+15à7.22E+14à3.36E+14à2.86E+14à2.77E+14 Mercury and its compoundsà4.46E+15à4.40E+15à3.76E+15à3.76E+15à3.76E+15à3.76E+15à3.76E+15à3.76E+15

à7.20E+14à6.88E+14à4.06E+14à4.06E+14à3.68E+14à3.68E+14à3.68E+14à3.68E+14 Cadmium and its

compounds

à1.11E+15à1.02E+15à2.74E+14à2.74E+14à2.99E+14à1.61E+14à2.61E+14à2.57E+14 Hexavalent chromium

compounds

Arsenicà8.31E+12à7.92E+12à3.91E+12à3.91E+12à3.91E+12à3.91E+12à3.91E+12à3.91E+12 Leadà1.02E+14à9.77E+13à1.00E+14à1.04E+14à1.03E+14à7.33E+13à5.99E+13à5.96E+13 Suspended substanceà4.80E+15à4.38E+15à1.44E+15à1.32E+15à1.12E+15à8.16E+14à7.85E+14à7.62E+14 Sanitary wastewaterà3.21E+17à4.34E+17à4.04E+17à3.91E+17à3.56E+17à3.18E+17à3.04E+17à2.70E+17 Waste solidà7.18E+18à8.38E+18à6.46E+18à6.10E+18à5.94E+18à7.25E+18à8.83E+18à8.13E+18 Industrial waste solidà3.49E+18à4.14E+18à3.38E+18à2.89E+18à2.60E+18à3.49E+18à3.72E+18à3.03E+18 Smelt waste residueà1.61E+18à1.91E+18à1.56E+18à1.33E+18à1.20E+18à1.61E+18à1.72E+18à1.40E+18 Fly ashà2.49E+16à2.95E+16à2.41E+16à2.06E+16à1.86E+16à2.49E+16à2.65E+16à2.16E+16 Slagà4.21E+16à4.98E+16à4.07E+16à3.48E+16à3.14E+16à4.21E+16à4.48E+16à3.65E+16 Coal refuseà8.98E+16à1.06E+17à8.69E+16à7.41E+16à6.69E+16à8.98E+16à9.56E+16à7.79E+16 Tailingsà4.34E+16à5.14E+16à4.20E+16à3.59E+16à3.24E+16à4.34E+16à4.63E+16à3.77E+16 Othersà1.68E+18à1.99E+18à1.63E+18à1.39E+18à1.25E+18à1.68E+18à1.79E+18à1.46E+18 Household garbageà3.69E+18à4.24E+18à3.08E+18à3.22E+18à3.34E+18à3.76E+18à5.11E+18à5.10E+18 Spodosolà4.36E+17à5.02E+17à3.08E+17à3.21E+17à3.34E+17à3.76E+17à5.10E+17à4.39E+17 Food residueà1.26E+18à1.45E+18à1.04E+18à1.09E+18à1.13E+18à1.27E+18à1.73E+18à1.67E+18 Paperà3.19E+16à3.68E+16à2.72E+16à2.84E+16à2.95E+16à3.32E+16à4.52E+16à4.66E+16 Plastics and rubberà4.38E+17à5.04E+17à3.74E+17à3.90E+17à4.06E+17à4.57E+17à6.20E+17à6.41E+17 Textile fabricà1.14E+18à1.31E+18à1.03E+18à1.08E+18à1.12E+18à1.26E+18à1.71E+18à1.84E+18 Glassà2.38E+16à2.74E+16à2.15E+16à2.25E+16à2.33E+16à2.63E+16à3.57E+16à3.84E+16 Tileà2.02E+16à2.33E+16à1.57E+16à1.64E+16à1.70E+16à1.91E+16à2.60E+16à2.39E+16 Plantsà3.37E+17à3.89E+17à2.60E+17à2.71E+17à2.82E+17à3.17E+17à4.31E+17à3.98E+17 Total environmental

à1.02E+19à1.18E+19à8.07E+18à7.59E+18à7.31E+18à8.58E+18à1.03E+19à9.40E+18

emission

2684H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–2700

In addition,annual growth rate of transportation roads was3%compared with annual growth rate of vehicles of15%.At the end of2005,traf?c mileage reached4476km,of which rapid transit length rose to114km equal to the thereby total

Table12

Complementary data for Beijing2000.

Item Variable Initial value Unit

Agricultural output AO 1.93E+18Jc

Urban output UO7.76E+19Jc

Price(products and service)p1 1.29E+00Yuan/billion Jc Price(fuels and electricity)p2 1.32Eà01Yuan/billion Jc Market price p3 1.49Eà01Yuan/billion Jc Price indicator p3i 5.00Eà02

Immigrants intensity PIi 2.27Eà03

Investment intensity Ii 6.12Eà04Billion yuan/Jc

H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–27002685 transit construction of Beijing since the foundation of the People’s Republic of China in1949.Moreover,the number of pri-vate cars over3million units mark in year2008has been beyond the reach of the carrying capacity of transportation infra-structure,which made traf?c congestion a daily life in the city.

3.2.

4.Financial assets stock

Financial assets stock is calculated as money supply multiplied by cosmic emergy/money ratio at the same year,repre-senting the amount of?nancial wealth measured by the ecological measure of cosmic emergy.This stock had the highest growth rate among all the stocks,with the amount in2005up to7.76times that in1990.

3.2.5.Population stock

Population stock is the summation of the population with varied education levels measured by cosmic emergy.Popula-tion with advanced-degrees accounted for a dominant share in the population emergy,with a trend of further increase in contrast to that with the preschool education level.In fact,the advanced-degree population stock in2005was1.90times larger than that in1990.

2686H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–2700

This phenomenon should be attributed to the variation of economic structure.In the early period after the foundation of People’s Republic of China,Beijing devoted itself to constructing an industrial system.In the1990s,transition to service-based economy gradually appeared.For the?rst time,the ratio of added value of the tertiary industry to GDP exceeded that of the primary industry and that of the secondary industry in1994,and this ratio even accounted for69.19%in2005.

3.2.6.Cultural information stock

Cultural information stock includes cultural heritage and cultural information products.Cultural heritage means cultural information embodied in historic landmarks and sites as well as that embodied in intangible cultural heritage,while cultural information products stand for books,audio and video products,etc.Cultural information stock rose by0.39times during the 15years,of which cultural information products increased by1.84times while cultural heritage remained stable relative to the long history process.

3.2.7.Ecological wealth related indicators

As shown in Fig.3,ecological wealth diversity rose at the beginning due to accumulation of?nancial and urban assets as complements to natural resources,with a peak value in1999.And then,ecological wealth diversity fell attributed to the con-tinuous increase of?nancial and urban assets and consumption of natural resources.

H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–27002687

As presented in Fig.4,capital wealth rose initially from1990to2002with peak value in20023.82times larger than that in1990,followed by the slight drop in the later years.

In general,power index had an increasing trend from1990to2005,characterized of a special phase in development obey-ing by the maximum power principle for a self-organized system(see Fig.5).

As listed in Fig.6,contrary to comparative wealth index,per capita ecological wealth increased step by step from1990to 2005.Though the number of residents in Beijing rose rapidly,the rate of accumulation of wealth seemed to be quicker,and hence per capita ecological wealth still had an ascending trend.However,from population quality prospect,wealth accumu-lation got slower so that comparative wealth index fell as a whole.

3.3.Ecological cost and related indicators

As illustrated in Fig.7for Beijing1990–2005,ecological cost increased steadily after2000,in2005up to2.83times that of 1995.

Listed in Table11are the accounted emergy results for environmental emissions associated with waste gas,waste water, and waste solid.

2688H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–2700

The accounted waste gas comprised of industrial and household exhaust of SO2and soot.Exhaust of SO2always increased and then?uctuated with a decreasing trend,while exhaust of soot peaked in2000and fell quickly.

The accounted waste water involved principal components in industrial sewage(461fe1492b160b4e767fcf40anic matter,petroleum,volatile phenolic compounds,prussiate,mercury and its compounds,cadmium and its compounds,hexavalent chromium com-pounds,arsenic,lead,and suspended substance)as well as organic matter in sanitary wastewater.In fact,although environ-mental emissions in waste water measured by mass could be ignored compared to waste solid and waste gas,they led to serious potential environmental impact due to their high cosmic emergy transformities.Emergy of industrial sewage de-clined before2002and rose slightly in recent years,whereas cosmic emergy of sanitary wastewater rose?rst and then fell.

The accounted waste solid was consisted of industrial waste solid(i.e.smelt waste residue,?y ash,slag,coal refuse,tail-ings,and others)as well as household garbage(i.e.spodosol,food residue,paper,plastics and rubber,textile fabric,glass,tile, and plants).Cosmic emergy of industrial waste solid rose?rst and then declined,follow by an increasing trend after2003.In general,the emergy of household garbage?uctuated with an increasing trend and accelerated recently.

Both of the renewable resource ratio and resource self-support ratio were lower than10%with degressive trends pre-sented in Fig.8.

H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–27002689

4.Simulation

Taking the accounted results from Tables7–11and complementary information listed in Table12for Beijing2000as ini-tial values,the ecological systems simulation for Beijing are processed with a time horizon spanning from2000to2100,with a similar length in Huang[28].Shown in Table1are the12state variables,60?ows and auxiliary variables,and k values determined by the adopted initial values through the mathematical expressions of symbols as listed in Table13.Details for the variables are given in Table1,and related dynamic equations are presented in Table2.Simulated values of important variables are veri?ed by accounted values for the period2000–2005in Figs.9–23.

As shown in Fig.9,water resource stock would decline to about1.00PJc(almost0.3billion cubic meters)in2050should there be no water diversion engineering,and thereafter keep nearly constant until2100.Though water resource is conven-tionally considered renewable,its stock would decrease quickly in the beginning,before2015,due to insuf?cient rainfall, short incoming amount attributed to overexploitation of upriver cities,and increasing demand attributed to agricultural pro-duction as well as urban use.As time goes by,water supply in terms of rainfall,incoming?ow,and waste water recovery could not make up water demand,and hence water resource would be reduced continuously until some kind of equilibrium between economic activities and water resource reaches,as characterized by the stable water stock level after about2050.

2690H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–2700

As presented in Fig.10,topsoil resource would fall steadily due to land use change,water loss and soil erosion as well as unreasonable cultivation.Drop of land fertility would be an inevitable cost of?eet urban sprawl.

As illustrated in Fig.11,exploitation rate of local ore resources stock would be so high that nearly all of them would be exhausted in two decades.

As indicated in Fig.12,agricultural assets stock would peak at2010and then fall steadily to zero value in about2050. Although feedbacks from urban subsystem and population might promote increase of agricultural assets temporarily,it would be unsustainable owing to biophysical limit from scarcity of water and land.

Accumulation of urban assets stock derives from economic production,input of agricultural subsystem,and external in-put,supported by water and energy resources.As water resource decreased step by step,economic production would be increasingly reduced,leading to the decline of the rate of urban assets accumulation.As a result,urban assets would begin to decay after its peak value around2060.

Financial assets stock derives from money circulated in the market and external investments.As illustrated in Fig.14,?nancial assets stock would rise due to economic development at the beginning,to its peak in around2025,when agricul-

H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–27002691

Table13

k values.

Item Value Item Value Item Value

k101 3.46Eà04k4028.70Eà02k802 1.66Eà06 k102 3.62Eà03k403 1.70Eà02k901 1.23E+00 k103 1.99Eà06k501 1.64Eà29k902 5.10Eà03 k104 4.61Eà01k504 5.91Eà07k903 6.75Eà06 k105 1.89Eà02k505 2.36Eà02k904 1.06Eà01 k201 1.34Eà12k506 1.11Eà02k10018.53Eà09 k202 1.45Eà02k601 6.49Eà38k10020.00E+00 k203 1.06Eà02k602 6.24Eà03k10030.00E+00 k301 1.55Eà15k605 1.46Eà28k1004 2.45Eà08 k302 2.82Eà07k701 6.21Eà09k1005 5.01Eà04 k303 2.29Eà07k702 1.54Eà07k1006 1.91Eà06 k304 1.05Eà02k703 6.06Eà08

k4018.77Eà38k801 4.21Eà06

2692H.Chen et al./Commun Nonlinear Sci Numer Simulat15(2010)2672–2700

tural production and urban production start to fall,which would lead to revenue reduction and?nancial assets stock reduc-tion subsequently.

Population simulation accounts for not only the quantity but the quality with structural variation.As revealed in Fig.15, population stock will increase mildly during the simulating horizon.Variation of cultural information stock has a trend sim-ilar to that with population.As variation of cultural heritage is not remarkable,the contribution of cultural information prod-ucts will be dominant.

As shown in Fig.17,the magnitude of environmental emissions would rise initially to its peak in about2010,then decline quickly to its minimum in around2015,and thereafter remain largely stable.

As shown in Figs.18–20,urban land area would extend at the cost of the reduction of natural and agricultural land area. Urban land area would rise to almost1400thousand hectares by2100,accounted for nearly eighty percent of the total area of Beijing.

Presented in Figs.21–23are simulated values of related indicators.Per capita ecological wealth reached its peak value in 2005and then would decline year by year.Ecological cost is consisted of resources consumption and environmental emis-sions,among which resources consumption would rise for nearly25years and then fall with a lower rate,and the magnitude

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