# Water Footprint Calculation on the Basis of Input–Output Analysis and a Biproportional Algorithm: A Case Study for the Yellow River Basin, China

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}/cap/year using input–output methods. They found that water intensity differs significantly among industries and that China is a net exporter of virtual water. Following an interregional IOA framework, Zhang et al. [10] found more than 50% of Beijing’s WF is attributable to imported virtual water. The multi-regional IOA model of Feng et al. [30] assessed the WF transfer in the upper, middle and lower Yellow River Basin. They demonstrated that economic growth and water shortages can be adjusted through virtual water imports and exports. Deng et al. [31] calculated selected regional WFs in China based on IOA. Their results indicated that China must use water more efficiently and readjust trade in virtual water.

**R**and fabrication matrix

**S**for calculating the direct consumption coefficient in the target year, in order to update the input–output table [34]. Dobrescu and Gaftea [35] checked the applicability and accuracy of the RAS based on the statistical series of emerging economy in Romanian. The results provided the superiority of the RAS for updating the input–output coefficients, especially in the short term. The RAS method is effective in revising input–output tables [33,34,35,36,37], and with its help, dynamic changes in the WF can be examined via IOA. Numerous socio-economic factors affect water demand and can be identified through dynamic change analysis [38].

## 2. Study Area and Method

#### 2.1. Study Area

^{3}, approximately 2% of the national total, and its available water resources are 37 billion m

^{3}. Approximately 12% of China’s population, 15% of its farms and more than 50 cities and 420 towns rely on the river for water [39,40]. The Yellow River Basin is a water-scarce region. Per capita water resources are less than one-quarter the world average [41]. Only 17,097 km

^{2}of Sichuan Province is located along this watershed, accounting for 3.5% of the province’s area, and it with draws 400 million m

^{3}from the Yellow River yearly, less than 0.65% of the total runoff of the Yellow River. Therefore, we did not analyse its WF.

#### 2.2. Data

#### 2.3. Method

#### 2.3.1. Water Footprint (WF) Calculation

_{ij}denotes product flow among sectors; x

_{i}denotes the gross output of sector i; x

_{j}denotes the total input of sector j; c

_{j}denotes the added value of sector j during production. f

_{i}denotes the final regional use, which includes final domestic consumption and capital formation. Final domestic consumption is consumption by rural habitants, urban habitants and total capital formation. e

_{i}denotes output, and m

_{i}denotes input. We added a row indicating fresh water consumption (w

_{j}) to the original input–output table, and w

_{j}denotes water consumption of sector j. We classified production sectors into primary, secondary and tertiary industries (i, j = 1, 2, 3).

**A**is expressed as:

_{ij}stands for the amount of product of sector i consumed directly for producing unit product of sector j [29]. With Equation (1), Leontief inverse matrix

**B**is written as:

_{ij}denotes demand of products by sector i to produce unit final product of sector j, which includes direct and indirect demand. Chinese input–output tables are constructed assuming that imported and domestic products are substitutes, so domestic and foreign products are included in interdepartmental flow and final demand. Regional input–output tables also are constructed assuming that imported and domestic products are substitutes. According the concept of WF, virtual water is encompassed in domestic and imported products consumed by inhabitants. We assumed that water consumed per unit of imported products equals that in the input area. Hence, the total water consumption coefficient (TWCC) matrix includes requirements for local and import products. The direct water consumption coefficient (DWCC) vector

**d**is calculated first by dividing water consumed by input of sectors.

_{j}presents water requirement of unit product in sector j. The TWCC vector

**v**can be derived by multiplying

**d**by the total demand coefficient matrix

**B**:

_{j}denotes water requirement of unit final product, also known as total water consumption, and contains the direct and indirect water consumption. Then the indirect water consumption coefficient (IWCC) vector

**i**can be calculated by subtracting

**d**from

**v**.

**wf**) are calculated by multiplying by final demand of sectors.

_{j}is water use of product to meet regional final demand in sector j. Net external WF is equal to net virtual water import, so it can be gotten by multiplying v

_{j}by net import in sector j.

_{j}

^{net}is the net external WF of sector j.

#### 2.3.2. Water Footprint (WF) Dynamic Analysis

**R**and

**S**, respectively [34]. The technology coefficient matrix for the target year t is estimated as follows:

**A**denotes the base year’s matrix,

_{0}**R**and

**S**are diagonal matrices constructed from the vectors of row and column-wise multipliers r

_{i}, (substitution) and s

_{j}, (fabrication), respectively. r

_{i}reflects the degree of structural change in intermediate inputs of sector i. s

_{j}reflects the degree of change in the proportion of intermediate inputs of department j. In Equation (8), only

**A**is known,

_{0}**R**and

**S**can be obtained by iteration.

**U**denotes the total column vector for the intermediate product in the settlement year.

**V**denotes the total row vector for the intermediate input in the settlement year.

**e**denotes a column vector of matrix elements with 1. Superscript

**T**indicates the transpose of a matrix.

**X**is a diagonal matrix of the actual total output in the settlement year.

**y**is an n × 1 vector of the standardized indexes,

**λ**is an n × m factor load matrix,

**f**is an m × 1 vector of the factors,

**ε**is an n × 1 vector of errors. The correlation matrix of

**y**is used to obtain the eigen values. The varimax rotation and factor coefficients are used to facilitate interpretation of factor loadings and obtain factor scores for selected factors respectively. The factors with the eigen values larger than 1 are selected for linear regression.

_{i}are obtained by Least-Squares method [44]. fs

_{i}is the factor score, which of the selected factor is considered as independent variable for predicting of WF, and εf is the error term. There are some regression coefficients are used as the indicators of the quality, such as correlation coefficient and p-value [45]. All data were analysed using statistical packet programs of MATLAB 2015 and SPSS 22.

## 3. Results

#### 3.1. Water Consumption Coefficient

^{3}/10

^{4}Yuan, 697.3 m

^{3}/10

^{4}Yuan and 459.9 m

^{3}/10

^{4}Yuan, respectively. Qinghai, Gansu and Inner Mongolia take second place and others third. TWCCs for primary and secondary industries in Shandong exhibit minimal values: 625.8 m

^{3}/10

^{4}Yuan and 142.0 m

^{3}/10

^{4}Yuan. The tertiary industry TWCC in Henan has the least TWCC: 56.0 m

^{3}/10

^{4}Yuan. TWCC is total water consumption per monetary unit, which can indicate the economic benefits of industry water consumption. By geographic distribution, provinces that exhibit greater values for TWCC occupy the upper reaches of the river and those with lesser values the lower. Therefore, efficiency along the lower reaches of the Yellow River is higher.

#### 3.2. Distribution of Water Footprint (WF)

^{3}/cap/year (161.5 m

^{3}/cap/year). Per capita consumption and consumption patterns influence intra-regional differences between urban and rural per capita WF. Per capita WF of urban inhabitants exceeds that of rural habitants in all provinces except Qinghai. The largest gap is 760.6 m

^{3}/cap/year of Inner Mongolia; elsewhere the gap spans 73.5 m

^{3}/cap/year to 521.4 m

^{3}/cap/year. These findings reveal that consumption by urban habitants greatly exceeds consumption of rural habitants in the basin.

#### 3.3. Total Water Footprint (WF)

^{3}, and the per capita WF was 247.1 m

^{3}/cap/year. Figure 4 reveals that Henan has the greatest WF (16.52 billion m

^{3}) and Qinghai the least (2.90 billion m

^{3}). Industry WFs related to the industry water consumption coefficient and the final consumption. Proportions for the latter among the three industries in this watershed are 6.4%, 44.1% and 49.5%, respectively. The WFs of the three industries are 33.41 billion m

^{3}, 38.39 billion m

^{3}and 7.32 billion m

^{3}, which, respectively, constitute 42.2%, 48.5% and 9.3% of the total WF. Differences in WF among the three industries are notable. The WF of the primary industry is largest, exceeding 50%, in Qinghai, Gansu, Ningxia and Inner Mongolia. Other provinces display similar ratios. WF of the secondary industry exceeds 50%, followed by the primary and tertiary industries, the latter below 15%.

#### 3.4. Net External Water Footprint (WF)

^{3}. They originated mainly in the secondary industry, 3.51 billion m

^{3}or 9.1% of the WF. Net exports of virtual water are concentrated in the primary industry. Qinghai, Gansu and Shaanxi are net importers, with Gansu the largest at 1.30 billion m

^{3}or 10.1% of the total provincial WF. The other provinces are net exporters of virtual water, with Inner Mongolia ranking first at −3.65 billion m

^{3}(Table 3).

#### 3.5. Annual Variation of Water Footprint (WF)

^{3}to 92.9 billion m

^{3}from 1997 to 2001, decreased to 75.2 billion m

^{3}in 2002 and increased to 118.8 billion m

^{3}in 2006. The 4% annual growth during the research period suggests that demand for water in the Yellow River basin grew. The per capita WF can reflect changes in living standards. The trend resembles that for overall WF: 278 m

^{3}/year per person in 1997 and 372 m

^{3}/year per person in 2006, an increase of 3.4%.

^{3}in 1997 to 39.9 billion m

^{3}in 2006 for the primary industry. Variation for the secondary industry increased from 45.4 billion m

^{3}to 61.1 billion m

^{3}. It declined for the territory industry from 19.4 m

^{3}to 17.8 billion m

^{3}. Annual variations for the three industries were 9.6%, 3.5% and −8.8%, respectively. The WF of the primary industry, as a part of the total WF, increased gradually from 23% to 33%. For the secondary industry, it varied between 49% and 53%, as the main subject of water consumption. For the territory industry it fell from 22% to 15%.

^{3}in 1997 and declining gradually. In 2003, exports as a component of WF began rising, peaking in 2009 at 17.95 billion m

^{3}, constituting 13.5% of the total. By industrial distribution, the net volume of exported water for the primary industry rose until 1997 and then declined. The WF became a net importer in 2001. However, the net exported WF increased constantly from 2002 from 5.91 billion m

^{3}to 28.06 billion m

^{3}. In 2006, the WF of the basin’s primary industry was 39.9 billion m

^{3}, and about 41.2% was exported. It suggests that the variation in net imports as a proportion of WF was tied to China’s food policy. The Yellow River basin is China’s food basket, and food production there has grown gradually since 2002, which may lead to the low value of total WF in 2002.

^{3}in 2003 to 6.99 billion m

^{3}in 2006, annual growth of 52.3%. Net imports by the tertiary industry in 2005 and 2006 were 0.2 to 1 billion m

^{3}, and net exports were below 220 million m

^{3}. Compared with the domestic industrial area, the Yellow River basin is less powerful, and exported industrial products were primarily energy and resources (e.g., coal, iron and petroleum). However, imports of finished industrial products were substantial, and the imported WF of the secondary industry was huge.

#### 3.6. Driving Factors of Water Footprint (WF)

#### 3.6.1. Index Selection

#### 3.6.2. Factor Analysis and Linear Regression

## 4. Discussion and Implications

#### 4.1. Discussion

^{3}, and net imports of virtual water were −4.50 billion m

^{3}in our result. Their sum is 76.68 billion m

^{3}, nearly the total WF of 79.12 billion m

^{3}. A number of water footprint studies have been conducted for China in general and for the Yellow River Basin [16,20,29,31,47,48]. The previous studies calculated the WF mainly by IOA method and a summation method based on blue water, green water and grey water WF (BGG). After verification, we found that the results of the researches [20,29,31,48] based on the IOA and its extension methods are almost identical to our results, in the same region (basin or province) and the same period of time. However, the IOAs have certain limitations. The input–output table of China and the provinces is released every 5 years, and in recent years, the economic develops rapidly in each province, the adjustment of industrial structure is obvious. Thus, the study of WF’s variation was limited by using the relative lag data released every five years. In this paper, the IOA/RAS method can be used to expand the input–output table, estimate WF by year, and obtain the dynamic process of WF.

#### 4.2. Implications

^{3}/hm

^{2}and 11,820 m

^{3}/hm

^{2}respectively, and it is 2708 m

^{3}/hm

^{2}and 4485 m

^{3}/hm

^{2}in middle and lower reaches [52]. Crops need more water for dryness, but high agricultural water consumption via flooding irrigation and crops that demand more water (e.g., rice) account for 25% of the seeding area in Ningxia. Thus, it can save much direct water and reduce the water consumption coefficient of the primary industry by heightening agricultural water use efficiency and adjusting plantation structure.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Water consumption coefficients of the Yellow River Basin (m

^{3}/10

^{4}Yuan). Note: 1, 2 and 3 in abscissa stand for the primary, secondary and tertiary industries, respectively.

**Figure 3.**Water footprint (WF) distribution proportion of the Yellow River Basin (m

^{3}/10

^{4}Yuan). Note: 1, 2 and 3 in abscissa stand for the primary, secondary and tertiary industries, respectively.

**Figure 5.**Variation of total WF and per capita WF of consumption in the Yellow River basin from 1997 to 2006.

**Figure 6.**Variation of the net import water footprint (WF) of the Yellow River basin from 1997 to 2006.

**Figure 7.**Comparison between the actual value and the predicted value of WF based on the linear regression.

Output | Intermediate Product | Final Use | Exports | Imports | Gross Output | |
---|---|---|---|---|---|---|

Input | ||||||

Intermediate input | x_{ij} | f_{i} | e_{i} | m_{i} | x_{i} | |

Value added | c_{j} | - | - | - | - | |

Total inputs | x_{j} | - | - | - | - | |

Water consumption | w_{j} | - | - | - | - |

City | Per Capita WF_{rural} | Per Capita WF_{urban} | Per Capita WF_{whole} |
---|---|---|---|

Qinghai | 256.0 | 205.4 | 538.9 |

Gansu | 146.7 | 383.4 | 490.2 |

Ningxia | 396.6 | 918.0 | 1177.4 |

Inner Mongolia | 158.2 | 918.8 | 541.7 |

Shaanxi | 53.2 | 132.8 | 169.0 |

Shanxi | 53.4 | 126.9 | 161.5 |

Henan | 47.7 | 148.8 | 170.0 |

Shandong | 36.7 | 132.9 | 168.7 |

Sum | 71.2 | 225.3 | 247.1 |

_{whole}; and the first two columns include WF of rural and urban habitants consumption denoted as WF

_{rural}and WF

_{urban}, respectively.

City | Primary Industry | Secondary Industry | Tertiary Industry | Sum |
---|---|---|---|---|

Qinghai | 0.18 | −0.06 | 0.22 | 0.35 |

Gansu | −0.21 | 1.58 | −0.07 | 1.30 |

Ningxia | −1.41 | 0.71 | 0.36 | −0.34 |

Inner Mongolia | −5.39 | 1.91 | −0.17 | −3.65 |

Shaanxi | −1.09 | 0.72 | −0.02 | −0.39 |

Shanxi | 0.17 | 0.15 | 0.00 | 0.33 |

Henan | 0.41 | −0.96 | 0.03 | −0.52 |

Shandong | −1.01 | −0.55 | −0.03 | −1.58 |

Sum | −8.35 | 3.51 | 0.34 | −4.51 |

Indexes | Correlation Coefficient |
---|---|

Population | 0.635 * |

GDP | 0.778 ** |

Food output | 0.407 |

Industrial added value | 0.807 ** |

Proportion of the secondary industry | 0.772 ** |

Water consumption per unit grain | −0.658 * |

Water consumption per 10,000 Yuan of incremental industrial value | −0.588 |

Capital formation | 0.821 ** |

Meat consumption per capita | 0.650 ** |

Food consumption per capita | 0.751 * |

Irrigation area | 0.670 * |

Indexes | Main Factor 1 | Main Factor 2 |
---|---|---|

Population | 0.971 | −0.077 |

GDP | 0.896 | 0.436 |

Food output | 0.847 | 0.518 |

Industrial added value | 0.886 | 0.425 |

Proportion of the secondary industry | 0.614 | 0.713 |

Water consumption per unit grain | 0.974 | 0.209 |

Water consumption per 10,000 Yuan of incremental industrial value | 0.829 | 0.545 |

Capital formation | 0.864 | 0.418 |

Meat consumption per capita | 0.844 | 0.513 |

Food consumption per capita | 0.914 | 0.145 |

Irrigation area | 0.971 | −0.077 |

Indexes | Non-Standardized Regression Coefficient | Standardized Regression Coefficient |
---|---|---|

Population | 0.147 | 0.628 |

GDP | 0.007 | 1.461 |

Proportion of the secondary industry | 46.190 | 1.053 |

Water consumption per 10,000 Yuan of incremental industrial value | 8.148 | 3.933 |

Meat consumption per capita | 1.000 | 0.664 |

Irrigation area | 0.213 | 1.008 |

Constant | −11,986.274 | --- |

Correlation Coefficient (R^{2}) | 0.999 | |

Value of F-test | 398.113 | |

p-value | 0.0002 |

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## Share and Cite

**MDPI and ACS Style**

Yin, J.; Wang, H.; Cai, Y.
Water Footprint Calculation on the Basis of Input–Output Analysis and a Biproportional Algorithm: A Case Study for the Yellow River Basin, China. *Water* **2016**, *8*, 363.
https://doi.org/10.3390/w8090363

**AMA Style**

Yin J, Wang H, Cai Y.
Water Footprint Calculation on the Basis of Input–Output Analysis and a Biproportional Algorithm: A Case Study for the Yellow River Basin, China. *Water*. 2016; 8(9):363.
https://doi.org/10.3390/w8090363

**Chicago/Turabian Style**

Yin, Jian, Huixiao Wang, and Yan Cai.
2016. "Water Footprint Calculation on the Basis of Input–Output Analysis and a Biproportional Algorithm: A Case Study for the Yellow River Basin, China" *Water* 8, no. 9: 363.
https://doi.org/10.3390/w8090363