Appendices
Appendixi. Water footprint accounting
The basic mathematical structure of the IO model and the Leontief inverse matrix
The basic mathematical structure of the input-output system consists of nlinear equations as shown in Eq.S1, depicting how the outputs of an economy depend on inter-sectoral inputs and final demands.
(S1)
wherenis the number of economic sectors; is the total output of sectori;is the inter-sectoral monetary flows from sector ito sectorj; is the final demand of sector i.
The direct input refers to the input provided by a sector for the production of another sector in the last stage of the productionchain and it numerically equals to the elements of the inter-sectoral flow matrix (i.e., is the direct input from sector ito sector j). The direct input coefficientindicates the amount of input from sector i required to increase one monetary unit output of sector j(Eq.S2).
(S2)
Therefore, Eq.1 can be rewritten so as to include the direct input coefficient :
(S3)
which can be transformed as follows in matrix notation:
(S4)
whereX, A and Y are respectively the matrices of output, direct input coefficients and final demand.
Assuming the matrixA of direct input coefficients is constant, it is possible to change Eq.4 into the demand-driven format:
(S5)
whereis known as the Leontief inverse matrix, with element denoting how muchoutputofsectoriisrequiredtomeetonemonetaryunitofthefinaldemand of sectorj. Thus, thefinal demand and its corresponding direct and indirectproduction are linked.
Direct water use coefficient and total water usecoefficient
In order to combine the monetary trade with the associatedwater use, the essential step is to derive direct water use coefficient (DWUC), the amount of direct water intake to produce one monetary unit of output, representing the direct orthe first round effects of the sectoral interaction in the economy (Bouhia, 2001; Hubacek and Sun, 2005). DWUC canbe expressed as Eq. (S6).
, (S6)
where W is the matrix of DWUC (measured inm310−4Yuan−1in this study); is the DWUC of
sectorj ; is calculated by dividing the water use ofsectorjby total output of sectorj (in monetaryterm).
The total water use coefficient (TWUC) (measured inm310−4Yuan−1), an indicator of the total water consumption throughout the whole production chain, can be achievedby multiplying DWUC with the Leontief inverse matrix.
, (S7)
where D is the matrix of TWUC, which links the monetaryproduct trade with their corresponding total amount of water use.
The total water requirements to meet domestic final demand
The water footprint of a region can be derived by multiplying the TWUC with final demand:
, (S8)
whereTis the matrix of the water footprintwhich indicates the total amount of water resources used in meeting thefinalconsumption of the inhabitants in region s.is the water footprint of sectorjin region s; is the TWUC of sector j in region s; is the final demand of sector j in region s.
Virtual water flows accounting
In the virtual water flow analysis, the virtual water exportcan be obtained through Eq. (S9).
, (S9)
where U is the matrix of the virtual water outflow (measuredin 106m3/yr); is the virtual water export of sector j inregion s, including export to domestic and foreignuse; is the TWUC of sector j in region s ; is theexport of sector j in region s.
The virtual water import can be obtainedas:
, (S10)
where V is the matrix of virtual water inflow (measured in106m3/yr);is the virtual water import of sector j inregion s, including import for final demand and intermediate use of sector j in region s; is the import of sector j in region s.
Thus, the net virtual water outflow can be obtained as:
,(S11)
whereF is the matrix of net virtual water outflow (measured in106m3/yr);is the net virtual water outflow of sector j inregion s. A positive value indicates that the sector j in region s export virtual water to outside, and a negative indicates that the sector j in region s dependson virtual water import from outside.
Appendix ii.Structural decomposition analysis approach
Generally, the SDA can be conducted based on either the “base year value” or the “end year value.” In this study, the average value of the decomposition results of the base year and the end year values are adopted. The decomposition based on the “base year value” (0) and “end year value” (1) can be presented as follows:
(12)
(13)
is the change in WF. is the direct water use coefficient of sector i, calculated by dividing the water use of sector i by total output of sector i(in monetary term). is the element of the Leontief inverse matrix. is the summation of the final demand of all the sectors. is the percentages of the final demand of sector i in the total final demand of all the sectors. ,,and represent the changes in ,,and.
The change in water footprint from the base year (0) to the end year (1) can be decomposed into changes in the component driving forces. In the SDA framework, the contributions of the technological effect (), the economic system efficiency effect (), the scale effect (), and the structural effect () are presented as below:
(14)
Each of the four terms in Eq.(14) represents the contribution to the change in WF triggered by one driving force while keeping the rest of the variables constant.
Appendix iii.Illustration of the sectoral WF and net VW flow forBeijing and Tianjin in 2002 and 2007
Table S1a Thesectoral WF and net VW flow forBeijing in 2002 and 2007 (million m3)
Sectors / 2002 / 2007Total WF / Net VW outflow / Total WF / Net VW outflow
1-AGR / Agriculture / 903 / -416 / 929 / -1470
2-MIN / Mining / 9 / -257 / 5 / -280
3-FDP / Manufacture of Food / 498 / -75 / 888 / -311
4-TXT / Manufacture of Textile / 25 / -15 / 39 / -58
5-WAL / Manufacture of Textile Wearing Apparel and Leather / 64 / -11 / 54 / -25
6-PTF / Processing of Timber and Manufacture of Furniture / 38 / -50 / 16 / -38
7-PPP / Manufacture of Paper and Paper Products / 61 / -262 / 12 / -205
8-PPC / Processing of Petroleum and Coking / 4 / 59 / 24 / -161
9-CMP / Manufacture of Raw Chemical Materials and Chemical Products / 142 / -44 / 83 / -328
10-NMP / Manufacture of Non-metallic Mineral Products / 12 / -77 / 3 / -140
11-SPM / Smelting, Pressing and Manufacture of Metals / 25 / -226 / 21 / -588
12-MSM / Manufacture of Special Purpose Machinery / 211 / -145 / 87 / 3
13-TPE / Manufacture of Transport Equipment / 108 / -55 / 57 / 63
14-EME / Manufacture of Electrical Machinery and Equipment / 54 / -31 / 51 / -124
15-CCE / Manufacture of Communication Equipment, Computers and Other Electronic Equipment / 125 / 47 / 54 / -104
16-MMO / Manufacture of Measuring Instruments and Machinery for Cultural Activity and Office Work / 7 / -5 / 7 / -17
17-OMS / Other manufacturing sectors / 8 / -7 / 14 / -23
18-EHP / Production and Supply of Electric Power and Heat Power / 80 / -349 / 141 / -216
19-PSW / Production and Supply of Water / 50 / -1 / 36 / 0
20-CTR / Construction / 845 / -12 / 1200 / -322
21-FTS / Freight Transport and Storage / 42 / 49 / 30 / 130
22-ICS / Information Transmission, Computer Services and Software / 92 / 77 / 191 / 306
23-WRT / Wholesale and Retail Trades / 164 / 303 / 418 / 431
24-HCS / Hotels and Catering Services / 181 / -8 / 229 / 57
25-TSM / Tourism / 4 / 4 / 39 / 10
26-RED / Scientific Research / 58 / -1 / 105 / 357
27-ECE / Education, Culture and Entertainment / 168 / 8 / 278 / 58
28-HSS / Health, Sports and Social Welfare / 66 / 5 / 329 / 5
29-SVH / Service to Households / 245 / -17 / 364 / -18
30-OTS / OtherTechnical Services / 116 / 77 / 43 / 33
Total / 4406 / -1437 / 5748 / -2975
Table S1b Thesectoral WF and net VW flow forTianjin in 2002 and 2007 (million m3)
Sectors / 2002 / 2007Total WF / Net VW outflow / Total WF / Net VW outflow
1-AGR / Agriculture / 396 / 222 / 999 / -286
2-CMD / Coal Mining and Dressing / 0 / -13 / 0 / -17
3-PNE / Petroleum and Natural Gas Extraction / 0 / 35 / 0 / 73
4-MMD / Metals Mining and Dressing / 0 / 0 / 0 / 0
5-NMM / Nonmetal Minerals and Other Minerals Mining and Dressing / 0 / -62 / 0 / -42
6-FDP / Manufacture of Food / 131 / -76 / 342 / -21
7-TXT / Manufacture of Textile / 8 / -8 / 6 / -8
8-WAL / Manufacture of Wearing Apparel and Leather / 30 / 62 / 57 / -9
9-PTF / Processing of Timber and Manufacture of Furniture / 14 / 7 / 46 / -61
10-PPP / Manufacture of Paper and Paper Products / 10 / 1 / 2 / -9
11-PPC / Processing of Petroleum and Coking / 1 / 20 / 2 / 30
12-CMP / Manufacture of Raw Chemical Materials and Chemical Products / 26 / 129 / 49 / -68
13-NMP / Manufacture of Non-metallic Mineral Products / 4 / -26 / 3 / -79
14-SPM / Smelting, Pressing and Manufacture of Metals / 4 / -83 / 3 / -21
15-MSM / Manufacture of Special Purpose Machinery / 80 / -98 / 83 / -14
16-TPE / Manufacture of Transport Equipment / 14 / 27 / 14 / 163
17-EME / Manufacture of Electrical Machinery and Equipment / 20 / 72 / 21 / 56
18-CCE / Manufacture of Communication Equipment, Computers and Other Electronic Equipment / 25 / 137 / 19 / 280
19-MMO / Manufacture of Measuring Instruments and Machinery for Cultural Activity and Office Work / 5 / -7 / 4 / 12
20-OMS / Other manufacturing sectors / 7 / -3 / 3 / -9
21-EHP / Production and Supply of Electric Power and Heat Power / 33 / -102 / 28 / -47
22-PSW / Production and Supply of Water / 73 / -266 / 26 / -181
23-CTR / Construction / 291 / -72 / 747 / -154
24-FTS / Freight Transport and Storage / 9 / 37 / 34 / -170
25-HCS / Hotels and Catering Services / 40 / 12 / 108 / -57
26-OSS / OtherServices Sectors / 634 / -203 / 556 / -244
Total / 1855 / -260 / 3152 / 883
*Zero of WF indicates there is no consumption in such sector in the city.
*In Beijing, primary industry only contains sector 1-AGR.The sectors from 2-MIN to 20-CTR belong to the secondary industry. The remaining sectors belong to the tertiary industry. In Tianjin, primary industry only contains sector 1-AGR. The sectors from 2-CMD to 23-CTR belong to the secondary industry. The remaining sectors belong to the tertiary industry.
Appendixiv. Contribution of four effects to changes in the sectoral WF in Beijing and Tianjin 2002-2007
Table S2aContribution of four effects to changes in the sectoral WF in Beijing 2002-2007(million m3)
Sectors / Change in WF / Technological effects / Economic system efficiency effects / Scale effects / Structural effectsValue / Proportion / Value / Proportion / Value / Proportion / Value / Proportion
1-AGR / Agriculture / 26 / -327 / -21% / 76 / 5% / 715 / 46% / -438 / -28%
2-MIN / Mining / -3 / -7 / -38% / 2 / 9% / 5 / 31% / -4 / -22%
3-FDP / Food processing / 389 / -376 / -26% / 395 / 27% / 521 / 36% / -150 / -10%
4-TXT / Manufacture of textile / 14 / -23 / -31% / -7 / -10% / 29 / 39% / 15 / 20%
5-WAL / Manufacture of wearing apparel and leather / -10 / -43 / -42% / 0 / 0% / 47 / 45% / -13 / -13%
6-PTF / Processing oftimber andManufactureof furniture / -22 / -19 / -25% / 6 / 9% / 20 / 27% / -29 / -39%
7-PPP / Manufactureof paper and paper products / -50 / -26 / -23% / 7 / 6% / 25 / 22% / -55 / -49%
8-PPC / Processing of petroleum and coking / 19 / -18 / -33% / 6 / 11% / 13 / 24% / 18 / 32%
9-CMP / Manufacture of raw chemical materials and chemical products / -58 / -85 / -32% / 21 / 8% / 85 / 31% / -79 / -29%
10-NMP / Manufacture of nonmetallic mineral products / -9 / -5 / -23% / 2 / 9% / 5 / 22% / -11 / -46%
11-SPM / Smelting,pressing and manufacture of metals / -4 / -22 / -40% / 8 / 14% / 18 / 33% / -7 / -14%
12-MSM / Manufacture of specialpurposemachinery / -124 / -119 / -30% / 29 / 7% / 107 / 27% / -142 / -36%
13-TPE / Manufacture of transport equipment / -51 / -68 / -33% / 17 / 8% / 61 / 29% / -61 / -29%
14-EME / Manufacture of electrical machinery and equipment / -3 / -49 / -40% / 18 / 15% / 41 / 34% / -13 / -11%
15-CCE / Manufacture of communication equipment,computers and other electronic equipment / -70 / -69 / -27% / 27 / 10% / 67 / 26% / -94 / -37%
16-MMO / Manufacture of measuring instruments and machinery for cultural activity and office work / -1 / -6 / -37% / 3 / 17% / 5 / 31% / -3 / -15%
17-OMS / Other manufacturing sectors / 6 / -11 / 25% / 17 / 36% / 10 / 21% / -9 / -19%
18-EHP / Production and supply of electric power and heat power / 61 / -114 / -38% / 99 / 33% / 83 / 27% / -7 / -2%
19-PSW / Production and supply of water / -15 / -37 / -44% / -1 / -1% / 34 / 41% / -11 / -13%
20-CTR / Construction / 356 / -1021 / -43% / 541 / 23% / 804 / 34% / 31 / 1%
21-FTS / Freight transport and storage / -13 / -31 / -35% / 11 / 12% / 28 / 31% / -20 / -22%
22-ICS / Information transmission,computer services and software / 100 / -141 / -37% / 62 / 16% / 115 / 30% / 63 / 17%
23-WRT / Wholesale and retail trades / 254 / -275 / -34% / 123 / 15% / 235 / 29% / 171 / 21%
24-HCS / Hotels and catering services / 48 / -143 / -35% / 68 / 17% / 159 / 39% / -36 / -9%
25-TSM / Tourism / 35 / -22 / -28% / 24 / 30% / 12 / 15% / 21 / 27%
26-RED / Research and development / 47 / -77 / -38% / 39 / 20% / 64 / 32% / 20 / 10%
27-ECE / Education,culture and entertainment / 111 / -198 / -39% / 128 / 25% / 170 / 34% / 10 / 2%
28-HSS / Health, sportsand social welfare / 263 / -205 / -30% / 98 / 15% / 162 / 24% / 208 / 31%
29-SVH / Service to households / 119 / -273 / -41% / 106 / 16% / 244 / 37% / 42 / -6%
30-OTS / Other technical services / -73 / -50 / -16% / 47 / 15% / 76 / 24% / -146 / -46%
Total / 1342 / -3862 / -37% / 1972 / 19% / 3961 / 38% / -729 / -7%
Table S2bContribution of four effects to changes in the sectoral WF in Tianjin 2002-2007(million m3)
Sectors / Change in WF / Technological effects / Economic system efficiency effects / Scale effects / Structural effectsValue / Proportion / Value / Proportion / Value / Proportion / Value / Proportion
1-AGR / Agriculture / 604 / 35 / 5% / 41 / 6% / 593 / 81% / -65 / -9%
2-CMD / Coal Mining and Dressing / 0 / 0 / -27% / 0 / 6% / 0 / 26% / 0 / 41%
3-PNE / Petroleum and Natural Gas Extraction / 0 / 0 / -33% / 0 / 2% / 0 / 29% / 0 / 36%
4-MMD / Metals Mining and Dressing / 0 / 0 / 0% / 0 / 0% / 0 / 0% / 0 / 0%
5-NMM / Nonmetal Minerals and Other Minerals Mining and Dressing / 0 / 0 / -29% / 0 / 4% / 0 / 27% / 0 / 39%
6-FDP / Manufacture of Food / 211 / -27 / -7% / 85 / 23% / 204 / 56% / -52 / -14%
7-TXT / Manufacture of Textile / -2 / -2 / -11% / -2 / -12% / 6 / 45% / -5 / -33%
8-WAL / Manufacture of Wearing Apparel and Leather / 27 / -21 / -30% / 6 / 9% / 39 / 57% / 2 / 3%
9-PTF / Processing of Timber and Manufacture of Furniture / 31 / -14 / -23% / 7 / 11% / 25 / 43% / 13 / 22%
10-PPP / Manufacture of Paper and Paper Products / -8 / -4 / -23% / -1 / -4% / 5 / 27% / -8 / -46%
11-PPC / Processing of Petroleum and Coking / 1 / -1 / -37% / 1 / 15% / 1 / 31% / 1 / 17%
12-CMP / Manufacture of Raw Chemical Materials and Chemical Products / 23 / -32 / -37% / 8 / 9% / 36 / 42% / 11 / 13%
13-NMP / Manufacture of Non-metallic Mineral Products / -1 / -4 / -43% / 0 / -2% / 4 / 44% / -1 / -11%
14-SPM / Smelting, Pressing and Manufacture of Metals / -1 / -3 / -40% / -1 / -6% / 3 / 43% / -1 / -11%
15-MSM / Manufacture of Special Purpose Machinery / 2 / -79 / -47% / -3 / -2% / 84 / 51% / 0 / 0%
16-TPE / Manufacture of Transport Equipment / 0 / -13 / -44% / -1 / -4% / 15 / 50% / -1 / -2%
17-EME / Manufacture of Electrical Machinery and Equipment / 1 / -19 / -44% / -2 / -5% / 22 / 49% / 1 / 3%
18-CCE / Manufacture of Communication Equipment, Computers and Other Electronic Equipment / -7 / -17 / -29% / 5 / 9% / 20 / 35% / -15 / -27%
19-MMO / Manufacture of Measuring Instruments and Machinery for Cultural Activity and Office Work / -1 / -4 / -38% / -1 / -8% / 5 / 46% / -1 / -9%
20-OMS / Other manufacturing sectors / -4 / -3 / -27% / -2 / -15% / 4 / 33% / -3 / -25%
21-EHP / Production and Supply of Electric Power and Heat Power / -5 / -53 / -52% / 0 / 0% / 39 / 39% / 9 / 9%
22-PSW / Production and Supply of Water / -47 / -54 / -41% / -8 / -6% / 43 / 32% / -28 / -21%
23-CTR / Construction / 456 / -332 / -30% / 107 / 10% / 474 / 42% / 206 / 18%
24-FTS / Freight Transport and Storage / 25 / -14 / -26% / 13 / 25% / 17 / 32% / 9 / 17%
25-HCS / Hotels and Catering Services / 69 / -7 / -8% / 1 / 1% / 62 / 75% / 13 / 16%
26-OSS / Other Services Sectors / -78 / -438 / -36% / -51 / -4% / 574 / 47% / -163 / -13%
Total / 1297 / -1104 / -30% / 202 / 6% / 2275 / 62% / -76 / -2%