A new input-output-based framework for measuring the active and passive water use

Highlights

• •Construct a dual-perspective framework for measuring water use.
• •Define the water use fluctuating due to macroeconomic condition changes.
• •Introduce a new indicator to measure the rate of passive water use.
• •Estimate the key water use channels from a passive perspective through SPA.
• •Discuss the supply chain's intermediate sector's role for the water use.

1. Introduction

Sustainable development is a popular topic in recent times. Reducing the use of water is aimed at protecting the environment and promoting the sustainable development of the economy. This is particularly relevant in countries like China, which grapple with severe water scarcity and related resource issues [1]. The challenge lies in identifying potentials of reducing water use [2]. At the industrial level, various sectors have been exploring advanced manufacturing processes, such as the adoption of new materials and other proactive strategies, to reduce water use. For instance, the construction industry has been experimenting with high-performance materials to enhance water use efficiency [3]. However, the emergence of sudden phenomena affecting the macroeconomic situation, such as wars, natural disasters, depressions, etc., can also alter the amount of natural resources get used and pollutants emitted [4]. While these events can negatively impact the economy by reducing production, lowering demand, and slowing economic growth, they also inadvertently lead to decreased water use and carbon emissions [5,6].This change in water use is observed both in sectors and households [4,7]. Unlike the proactive efforts made by industries to conserve water through technological advancements, these changes in water use are passively accepted consequences of shifts in macroeconomic conditions.

Considering the aforementioned context, this paper categorizes the water use of an economic system into two types. The first, termed as “active water use”, refers to the water use that can be altered through the deliberate water conservation efforts, such as the enhancement of production processes and implementation of water use restrictions [8]. The second, termed as “passive water use”, refers to the water use that increases or decreases in response to changes in macroeconomic conditions, such as economic depressions, natural disasters, or sector structure shifts [[9], [10], [11]]. For instance, China's water use did not return to post-pandemic levels until 2023 since the end of 2019 [12] It is also crucial to prevent extreme water use increasing as economic conditions recover [13]. Sustainable policies should consider the variability or decline of water use across sectors under changing macroeconomic conditions [14].The overall decrease in water use resulted from both active water use changes due to sectoral upgrades and other measures, and passive water use changes affected by macroeconomic conditions. Notably, passive water use changes included not only decreases in industrial and commercial sectors [15] but also increases in sectors related to residential life [16]. However, there is a gap in understanding

and developing methodologies for identifying the critical sectors of passive water use. To address this, our study innovatively proposes a dual-perspective framework for measuring the critical sectors of both active and passive water use. This novel framework, which measures water use from an active

perspective, will support the economic system in achieving water conservation goals. Simultaneously, the component that measures passive water use can help the system leverage crises as opportunities to reduce water consumption, thereby accelerating sustainable development in the future. As the assessment of passive water use will take into account shifting macroeconomic conditions, Fig. 1 illustrates the real and expected growth rates of sectors in China spanning from 2000 to 2021. A marked slump is evident in 2020, with the majority of sectors registering growth rates that did not meet their anticipations, apart from the primary sector which stood as an outlier.

Fig. 1.

Annual growth rate and expected growth rate in China from 2000 to 2021 (percent).

This paper's objective is to develop a new dual-perspective framework for measuring water use, for identifying the critical sectors of active and passive water use while macroeconomic condition changes. By utilising this new dual-perspective framework, water use is bifurcated into active and passive categories, and key water use sectors are identified from two perspectives. The dual-perspective framework first employs the modified hypothetical extraction method (MHEM) to measure the critical sectors for active water use. And then use the weighted hypothetical extraction method (WHEM) to find the primary components for passive water use. Lastly, the Structural Path Analysis (SPA) is deployed to measure the significant channels of water use within sectors from a passive water use perspective.

To remind the structure of this article, the following contents are: The first section will review the previous articles on associated methodologies. Next part will introduce methods utilised in developing the new dual-perspective water use measurement framework and the data sources of empirical study, and then discuss the empirical results. Through the findings from the dual-perspective water use measurement framework, the last section will present policy implication from novel viewpoint.

2. Literature review

To construct the novel dual-perspective water use pathways measurement framework, this section reviews previous relevant research methodologies. The input-output (IO) model was introduced by Leontief in 1936 for documenting the financial flows between sectors and reflecting the linkage within sectors [[17], [18], [19]]. IO model has a broad application in exploring the sector linkage in terms of agriculture [20], transport sector [21], and construction sector [22,23], etc. In recent years, IO model is applied in measuring key sectors in carbon emission [[24], [25], [26], [27]], identifying other crucial pollutant emission sectors [28,29], and measuring energy consumption [30,31]. Besides the macro perspective, the IO model was also taken to investigate from micro perspectives [32,33]. Except sustainable development topics, IO model has also been used to evaluate labour force and human capital [34]. As the core purpose in this paper, IO model is comprehensively used in previous literature in testing embodied water [35,36], analysing water use in exporting and importing [37].

The hypothetical extraction method (HEM), derived from the IO model, is an econometric method used for assessing sector linkages of individual sectors within the economy. There is a broad application of utilising HEM, such as evaluating economy importance [[38], [39], [40], [41]], revealing carbon emission linkage [[42], [43], [44]], examining energy consumption linkage, and measuring water linkage [45,46]. Building on the logic of HEM, previous papers take MHEM to examine the sector linkage in the system [47,48]. As a widely accepted method in environmental research, using MHEM aligns with the objectives of this paper to measure the key active water use sectors.

There is a natural weak point of HEM. HEM may not accurately reflect the sudden change in the economy, and potentially result in inaccurate sector linkage measurement. Recognizing such potential research gaps, the WHEM has been developed based on HEM for measuring the influence of economic conditions change. Although it is a new method, there are literature using WHEM in measuring emission fluctuation [13,49]. Therefore, WHEM aligns with the objective of measuring passive water use in the dual-perspective measurement framework.

SPA is a method of identifying more precise paths in the supply chain, which was first introduced in 1984 for identifying flow paths at sector level [50]. Previous studies used SPA for discussing the key paths of emissions in economic systems [51,52], critical pathways for water conservation [53], and the critical carbon emission supply chain roads [47,54]. Therefore, SPA is suitable for capturing the critical paths of water use in the dual-perspective measurement framework.

While numerous IO based studies have been conducted on water use, the majority have primarily concentrated on active water use [35,36,55]. Some literature has acknowledged the influence of shifting macro conditions on water use [7,56]. Nevertheless, a notable research gap persists in examining passive water use within the context of an IO based framework. This paper seeks to address this gap by offering a multifaceted analysis within the context of an IO-based framework. Moreover, the majority of studies employing SPA concentrate on upstream and downstream sectors, neglecting the discussion on intermediate sectors. Consequently, a research void exists in exploring the role of intermediate sectors in the supply chain concerning the trade of embodied water use. This paper introduces a novel IO based framework to address two relatively understudied areas: (1) passive water use, and (2) the role of intermediate sectors in embodied water use. Drawing on existing literature, this framework is poised to aid future research in quantifying water use from both active and passive perspectives, and in identifying key channels that consider intermediate sectors within the supply chain.

3. Methods and data

This section will discuss the methods applied in the constructed dual-perspective measurement IO based framework, and then introduce the data used for the empirical research.

3.1. The dual-perspective water use measurement framework

Developing the new dual-perspective framework for measuring critical sectors of water use is the central contribution of this paper. This framework assesses the key sectors of water use in the economic system from two perspectives. This paper's research framework is shown as Fig. 2 illustrating what contents the dual-perspective measurement framework contains.

Fig. 2.

Research framework.

The first perspective is the active perspective. The logic of measuring the active water use key sectors is to measure the structure of water use for both production and consumption process in the economic system through MHEM. This is followed by decomposing the two processes of water use sector linkage to find the key active water use sectors. This paper considers the sectors with higher active water use as the more important active water use sectors. The second perspective is the passive perspective. The logic of passive water use measurement is using WHEM for capturing the alterations in water use resulting from shifts in the macro economy conditions. This is followed by finding out the key sectors of passive water use through sectoral decomposition. Similar with the active perspective, this paper considers the sectors with higher passive water use as the more important passive water use sectors. For further clarity, the analysis of water use from both production and consumption perspectives hinges on whether the water use of an industry serves its own production requirements or those of other sectors, thus investigating the sector linkage of water use. The production and consumption perspective are one aspect of the active water use measurement. Similarly, the passive perspective is analysed from forward and backward viewpoints. Detailed explanations of these perspectives will follow in sections 3.1, 3.1.1.2.

Through the measurement of water use, this paper obtains a coefficient that measures the rate at which the sector's water use changes in response to changes in macroeconomic conditions, termed the passive water use coefficient. Using this coefficient, the developed dual-perspective water use measurement framework will identify the critical paths of water use for important sectors of water use from the passive perspective through SPA.

3.1.1. Active water use measurement

The fundamental methodology used in measuring active and passive water use is IO model. The fundamental equation of IO model can be expressed as:

$$X=AX+Y$$ (1)

where the total output $X$ can be written as an equation associated with $Y$ as follow:

$$X={\left(I-A\right)}^{-1}Y$$ (2)

In Eq. (1), $X$ indicates the total output of sectors. $Y$ refers to the final demand vector. In Eq. (2), ${\left(I-A\right)}^{-1}$ is referred to the Leontief inverse matrix. $I$ is the identify matrix. $A$ symbolizes the matrix of direct consuming coefficients which measures the amount of required input for one unit of output. The direct consuming coefficients can be computed as follow:

$$A=\left\{a_{\theta \iota }\right\}=\left\{\frac{x_{\theta \iota }}{X_{\iota }}\right\}=\left[\begin{array}{ccc}{a}_{11}& \cdots & a_{1\xi }\\ ⋮& \ddots & ⋮\\ a_{\xi 1}& \cdots & a_{\xi \xi }\end{array}\right],\left(\theta ,\iota =1,2,3\dots n\right)$$ (3)

where $x_{\theta \iota }$ is the element of $\theta$ consumed by sector $\iota$. Moreover, $a_{\theta \mathrm{\iota }}$ indicates products from sector $\theta$ consumed by sector $\iota$ to generate a unit of output.

The amount of water used by the economy can be expressed as:

$$Q=qX=q{\left(I-A\right)}^{-1}Y$$ (4)

where $Q$ indicates the sectors' water use amount. $q$ represents to the water use coefficient which can be calculated by $Q$ divided by $X$.

Next, to find the key water use sectors, it is necessary to measure the water use sector linkage which will be measured by MHEM. The fundamental logic of traditional HEM, which serves as the basis for MHEM, involves dividing the entire economic system into two parts and then subtracting them. The first part is the system containing the target sector ${\Omega }_{\xi }$, which is represented by $\Omega$ as follows:

$$\Omega =\left[\begin{array}{cc}{\Omega }_{\xi ,\xi }& {\Omega }_{\xi ,-\xi }\\ {\Omega }_{-\xi ,\xi }& {\Omega }_{-\xi ,-\xi }\end{array}\right]$$ (5)

and $X$ of Eq. (5) can be expressed as:

$$X=\left[\begin{array}{cc}{A}_{\xi ,\xi }& A_{\xi ,-\xi }\\ A_{-\xi ,\xi }& A_{-\xi ,-\xi }\end{array}\right]\left[\begin{array}{c}{X}_{\xi }\\ X_{-\xi }\end{array}\right]+\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]=\left[\begin{array}{cc}{\Phi }_{\xi ,\xi }& {\Phi }_{\xi ,-\xi }\\ {\Phi }_{-\xi ,\xi }& {\Phi }_{-\xi ,-\xi }\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (6)

where the Leontief inverse matrix in Eq. (6) is:

$${\left(I-A\right)}^{-1}=\left[\begin{array}{cc}{\Phi }_{\xi ,\xi }& {\Phi }_{\xi ,-\xi }\\ {\Phi }_{-\xi ,\xi }& {\Phi }_{-\xi ,-\xi }\end{array}\right]$$ (7)

Assuming that everything remains unchanged except for the target sector ${\Omega }_{\xi }$ is no longer connected with other sectors ${\Omega }_{-\xi }$, we can obtain the second hypothetical system, which is isolated ${\Omega }_{\xi }$ from the original economy. In other words, the original supply chain or selling and purchasing relationship between ${\Omega }_{\xi }$ and ${\Omega }_{-\xi }$ does not exist in the hypothetical system. The output of the hypothetical economy is represented by $X^{\ast }$ as follows:

$$X^{\ast }=\left[\begin{array}{cc}{A}_{\xi ,\xi }& 0\\ 0& A_{-\xi ,-\xi }\end{array}\right]\left[\begin{array}{c}{X}_{\xi }^{\ast }\\ X_{-\xi }^{\ast }\end{array}\right]+\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]=\left[\begin{array}{cc}{\left(I-A_{\xi ,\xi }\right)}^{-1}& 0\\ 0& {\left(I-A_{-\xi ,-\xi }\right)}^{-1}\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (8)

Thus, the result of subtracting Eq. (8) from Eq. (6) implicit the economic influence of the target sector ${\Omega }_{\xi }$ to the total output as follows:

$$X-X^{\ast }=\left[\begin{array}{c}{X}_{\xi }-X_{\xi }^{\ast }\\ X_{-\xi }-X_{-\xi }^{\ast }\end{array}\right]=\left[\begin{array}{cc}{\Phi }_{\xi ,\xi }-{\left(I-A_{\xi ,\xi }\right)}^{-1}& {\Phi }_{\xi ,-\xi }\\ {\Phi }_{-\xi ,\xi }& {\Phi }_{-\xi ,-\xi }-{\left(I-A_{-\xi ,-\xi }\right)}^{-1}\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (9)

Then we add water use coefficient into Eq. (9) to get the difference between the water use before and after hypothetically extracting, which indicates the sector linkage of the target sector to the total water use in the economy as follows:

$$Q-Q^{\ast }=\left[\begin{array}{c}{Q}_{\xi }-Q_{\xi }^{\ast }\\ Q_{-\xi }-Q_{-\xi }^{\ast }\end{array}\right]=\left[\begin{array}{c}{q}_{\xi }{X}_{\xi }-q_{\xi }{X}_{\xi }^{\ast }\\ q_{-\xi }{X}_{-\xi }-q_{-\xi }{X}_{-\xi }^{\ast }\end{array}\right]=\left[\begin{array}{cc}{q}_{\xi }\left[{\Phi }_{\xi ,\xi }-{\left(I-A_{\xi ,\xi }\right)}^{-1}\right]& q_{\xi }{\Phi }_{\xi ,-\xi }\\ {q_{-\xi }\Phi }_{-\xi ,\xi }& q_{-\xi }\left[{\Phi }_{-\xi ,-\xi }-{\left(I-A_{-\xi ,-\xi }\right)}^{-1}\right]\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (10)

Now decompose the measured water use sector linkage into five parts shown in Eq. (11), (12), (13), (14), (17) [57]. The first part is the water use for meeting the demand of target sector ${\Omega }_{\xi }$ from ${\Omega }_{\xi }$ in process of supplying internally. This type of water use is named the internal linkage water use (ILW) and calculated as follows:

$$ILW={\hat{u}}_{\xi }{q}_{\xi }{\left(I-A_{\xi ,\xi }\right)}^{-1}{Y}_{\xi }$$ (11)

where ${\hat{u}}_{\xi }$ is the unit vector of ${\Omega }_{\xi }$.

The mixed linkage water use (MLW) measures the amount of water use where the sector ${\Omega }_{\xi }$ produces to meet its own needs, but produces and inputs for intermediate use, and then inputs back to ${\Omega }_{\xi }$. MLW can be calculated as follows:

$$MLW={\hat{u}}_{\xi }{q}_{\xi }\left[{\Phi }_{\xi ,\xi }-{\left(I-A_{\xi ,\xi }\right)}^{-1}\right]Y_{\xi }$$ (12)

The net forward linkage water use (NFLW) measures the water use where ${\Omega }_{\xi }$ produces and exports to ${\Omega }_{-\xi }$ for meeting the demand of ${\Omega }_{-\xi }$ as follows:

$$NFLW={\hat{u}}_{\xi }{q}_{\xi }{\Phi }_{\xi ,-\xi }{Y}_{-\xi }$$ (13)

The net backward linkage water use (NBLW) measures the water use where ${\Omega }_{-\xi }$ produce and export to ${\Omega }_{\xi }$ for meeting the demand of ${\Omega }_{\xi }$ as follows:

$$NBLW={\hat{u}}_{-\xi }{q}_{-\xi }{\Phi }_{-\xi ,\xi }{Y}_{\xi }$$ (14)

where ${\hat{u}}_{-\xi }$ is the unit vector of ${\Omega }_{-\xi }$.

The total amount of ILW, MLW and NFLW is the water used by ${\Omega }_{\xi }$ for producing to meet the needs of the whole economy, which can be called water use in production process as follows:

$$P_{\xi }=ILW+MLW+NFLW$$ (15)

Similarly, the total amount of ILW, MLW and NBLW can represent the water use for satisfying the demand of ${\Omega }_{\xi }$. It can be called water use in consumption process because it is due to that ${\Omega }_{\xi }$ consume products from other sectors, and the destination of products used water in this process is ${\Omega }_{\xi }$ as follows:

$$C_{\xi }=ILW+MLW+NBLW$$ (16)

The difference between the above two water use process indicates the role of ${\Omega }_{\xi }$ whether ${\Omega }_{\xi }$ is water exporter or water importer in economic system. This difference can be called net transferred of water use (NTW) and be calculated as:

$${NTW}_{\xi }=P_{\xi }-C_{\xi }=NFLW-NBLW$$ (17)

When ${NTW}_{\xi }>0$, it means that ${\Omega }_{\xi }$ acts primarily as a water use exporter in economic system, and the processes that use water are mainly to satisfy the needs of ${\Omega }_{-\xi }$ more than importing from other sectors for satisfying its own demand. When ${NTW}_{\xi }<0$, it means ${\Omega }_{\xi }$ acts primarily as an importer of water use. Comparing with ${\Omega }_{\xi }$ producing and using water for ${\Omega }_{-\xi }$, ${\Omega }_{-\xi }$ using more water for the demand of ${\Omega }_{\xi }$.

3.1.2. The passive water use measurement

This section will introduce the part of passive water use in the new dual-perspective measurement framework. The critical passive water use sectors will be measured through WHEM.

WHEM differs from traditional HEM in that it does not completely separate sectors from the economic system hypothetically [13]. Instead, it measures a value as a weight from realistic data, and then partially isolates the target sectors through these weights expressed as follows:

$$W_{\xi }={\left[W_1,W_2,\dots W_{\xi }\right]}^{\prime }$$ (18)

According to Chen, Song, Li and Li [49], the weighted value, which captures the influence of macroeconomic condition changes to the individual sectors, of the sector $\xi$ can be measured by the difference between the real growing ratio and the expected ratio of economic development as follows:

$$W_{\xi }=\left(\sqrt[\alpha -\beta ]{\frac{N_{\alpha }}{N_{\beta }}}\times 100\%-100\%\right)-\left(\frac{{IV}_1-{IV}_0}{{IV}_0}\times 100\%\right)$$ (19)

In Eq. (19), the left part refers to the expected growth rate of sector $\xi$, calculated by the data in a period. And the right part represents the real sectoral growth rate. $N_{\alpha }$ and $N_{\beta }$ denote the economic added value in year $\alpha$ and year $\beta$, respectively. ${IV}_1$ and ${IV}_0$ represents the added value of industry at present time and the same time at last year.

As above mentioned, matrix W measures the influences on sectors of the economic system when macroeconomic conditions change. $W_{\xi }>0$ implies that sector $\xi$ is negatively affected by changes in macroeconomic conditions, resulting in a slowdown in the sector's growth rate. $W_{\xi }<0$ indicates that sector $\xi$ is positively affected by macroeconomic conditions, leading to an accelerated growth rate.

Within matrix $W_{\xi }$, we can derive a new hypothetical economy where the sectors are partially isolated from each other. The passive water use can be classified to three types, including forward, backward, and overall passive water use [13,49]. From the forward perspective, assume that the target sector's downstream of the supply chain reduces its demand from the target sector due to the macroeconomic condition changes, while the target sector and its upstream are not affected. The total output under this assumption is as follows:

$$X_{forward}^{\#}=\left[\begin{array}{cc}{A}_{\xi ,\xi }& \left(1-W_{\xi }\right)A_{\xi ,-\xi }\\ A_{-\xi ,\xi }& A_{-\xi ,-\xi }\end{array}\right]\left[\begin{array}{c}{X}_{\xi }\\ X_{-\xi }\end{array}\right]+\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]=\left[\begin{array}{cc}{\left(I-A_{\xi ,\xi }\right)}^{-1}& \left(1-W_{\xi }\right){\left(I-A_{\xi ,-\xi }\right)}^{-1}\\ {\left(I-A_{-\xi ,\xi }\right)}^{-1}& {\left(I-A_{-\xi ,-\xi }\right)}^{-1}\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (20)

Subtracting the affected economy from the unaffected world, the affected forward economic linkage is:

$$X-X_{forward}^{\#}=\left[\begin{array}{cc}{\Phi }_{\xi ,\xi }-{\left(I-A_{\xi ,\xi }\right)}^{-1}& {\Phi }_{\xi ,-\xi }-\left(1-W_{\xi }\right){\left(I-A_{\xi ,-\xi }\right)}^{-1}\\ {\Phi }_{-\xi ,\xi }-{\left(I-A_{-\xi ,\xi }\right)}^{-1}& {\Phi }_{-\xi ,-\xi }-{\left(I-A_{-\xi ,-\xi }\right)}^{-1}\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (21)

The target sector's forward passive water use linkage can be calculated by combining the affected forward economic linkage and the water use coefficient vector as follows:

$$Q-Q_{forward}^{\#}=\left[\begin{array}{c}{q}_{\xi }\\ q_{-\xi }\end{array}\right]\left[\begin{array}{cc}{\Phi }_{\xi ,\xi }-{\left(I-A_{\xi ,\xi }\right)}^{-1}& {\Phi }_{\xi ,-\xi }-\left(1-W_{\xi }\right){\left(I-A_{\xi ,-\xi }\right)}^{-1}\\ {\Phi }_{-\xi ,\xi }-{\left(I-A_{-\xi ,\xi }\right)}^{-1}& {\Phi }_{-\xi ,-\xi }-{\left(I-A_{-\xi ,-\xi }\right)}^{-1}\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (22)

Next, Assuming the upstream of supply chain is affected, the target sector and its intermediate providers were faced production shortage while the downstream industries are not influenced. The total output of the backward extracted hypothetical system is shown as follows:

$$X_{backward}^{\#}=\left[\begin{array}{cc}\left(1-W_{\xi }\right)A_{\xi ,\xi }& A_{\xi ,-\xi }\\ \left(1-W_{-s}\right)A_{-\xi ,\xi }& A_{-\xi ,-\xi }\end{array}\right]\left[\begin{array}{c}{X}_{\xi }\\ X_{-\xi }\end{array}\right]+\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]=\left[\begin{array}{cc}\left(1-W_{\xi }\right){\left(I-A_{\xi ,\xi }\right)}^{-1}& {\left(I-A_{\xi ,-\xi }\right)}^{-1}\\ \left(1-W_{-\xi }\right){\left(I-A_{-\xi ,\xi }\right)}^{-1}& {\left(I-A_{-\xi ,-\xi }\right)}^{-1}\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (23)

The affected backward economy linkage is:

$$X-X_{backward}^{\#}=\left[\begin{array}{cc}{\Phi }_{\xi ,\xi }-\left(1-W_{\xi }\right){\left(I-A_{\xi ,\xi }\right)}^{-1}& {\Phi }_{\xi ,-\xi }-{\left(I-A_{\xi ,-\xi }\right)}^{-1}\\ {\Phi }_{-\xi ,\xi }-\left(1-W_{-\xi }\right){\left(I-A_{-\xi ,\xi }\right)}^{-1}& {\Phi }_{-\xi ,-\xi }-{\left(I-A_{-\xi ,-\xi }\right)}^{-1}\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (24)

Then the backward passive water use sector linkage can be measured as follows:

$$Q-Q_{backward}^{\#}=\left[\begin{array}{c}{q}_{\xi }\\ q_{-\xi }\end{array}\right]\left[\begin{array}{cc}{\Phi }_{\xi ,\xi }-\left(1-W_{\xi }\right){\left(I-A_{\xi ,\xi }\right)}^{-1}& {\Phi }_{\xi ,-\xi }-{\left(I-A_{\xi ,-\xi }\right)}^{-1}\\ {\Phi }_{-\xi ,\xi }-\left(1-W_{-\xi }\right){\left(I-A_{-\xi ,\xi }\right)}^{-1}& {\Phi }_{-\xi ,-\xi }-{\left(I-A_{-\xi ,-\xi }\right)}^{-1}\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (25)

Similarly, when both the forward and backward are affected by macroeconomic changes, i.e., when the demand from the downstream supply chain and the production from the upstream supply chain both changes, an overall affected economic linkage is formed as follows:

$$X_{overall}^{\#}=\left[\begin{array}{cc}\left(1-W_{\xi }\right)A_{\xi ,\xi }& \left(1-W_{\xi }\right)A_{\xi ,-\xi }\\ \left(1-W_{-\xi }\right)A_{-\xi ,\xi }& A_{-\xi ,-\xi }\end{array}\right]\left[\begin{array}{c}{X}_{\xi }\\ X_{-\xi }\end{array}\right]+\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]=\left[\begin{array}{cc}\left(1-W_{\xi }\right){\left(I-A_{\xi ,\xi }\right)}^{-1}& \left(1-W_{\xi }\right){\left(I-A_{\xi ,-\xi }\right)}^{-1}\\ \left(1-W_{-\xi }\right){\left(I-A_{-\xi ,\xi }\right)}^{-1}& {\left(I-A_{-\xi ,-\xi }\right)}^{-1}\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (26)

The overall affected economic linkage is expressed as follows:

$$X-X_{overall}^{\#}=\left[\begin{array}{cc}{\Phi }_{\xi ,\xi }-\left(1-W_{\xi }\right){\left(I-A_{\xi ,\xi }\right)}^{-1}& {\Phi }_{\xi ,-\xi }-\left(1-W_{\xi }\right){\left(I-A_{\xi ,-\xi }\right)}^{-1}\\ {\Phi }_{-\xi ,\xi }-\left(1-W_{-\xi }\right){\left(I-A_{-\xi ,\xi }\right)}^{-1}& {\Phi }_{-\xi ,-\xi }-{\left(I-A_{-\xi ,-\xi }\right)}^{-1}\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (27)

The overall passive water use of the target sector can be measured as follows:

$$Q-Q_{overall}^{\#}=\left[\begin{array}{c}{q}_{\xi }\\ q_{-\xi }\end{array}\right]\left[\begin{array}{cc}{\Phi }_{\xi ,\xi }-\left(1-W_{\xi }\right){\left(I-A_{\xi ,\xi }\right)}^{-1}& \left(1-W_{\xi }\right){\Phi }_{\xi ,-\xi }-{\left(I-A_{\xi ,-\xi }\right)}^{-1}\\ {\Phi }_{-\xi ,\xi }-\left(1-W_{-\xi }\right){\left(I-A_{-\xi ,\xi }\right)}^{-1}& {\Phi }_{-\xi ,-\xi }-{\left(I-A_{-\xi ,-\xi }\right)}^{-1}\end{array}\right]\left[\begin{array}{c}{Y}_{\xi }\\ Y_{-\xi }\end{array}\right]$$ (28)

Inspired by Ref. [49], this paper introduces a new indicator for reflecting the rate of passive water use as passive water use coefficient. The passive water use coefficient can be calculated by dividing the overall passive water use in Eq. (28) by the total output as follows:

$$pwc=\frac{Q-Q_{overall}^{\#}}{X}$$ (29)

3.1.3. Critical water use channels measurement

As the final section of the dual-perspective water use measurement framework developed, this section will measure the critical path of water use from passive perspective. It will analyse the different sector roles, including the pushing, pulling, and bridging roles. To achieve this, the framework uses SPA to measure key water use channels stimulated by the critical sectors which is measured in section 3.1.2. The logic of SPA is expanding Leontief inverse matrix through a Taylor series approximation. In measuring the key paths of water use, each term in the expansion represents the water use in the supply chain at different production layers. First, expand Leontief inverse matrix shown as follows:

$${\left(I-A\right)}^{-1}=I+A+A^2+A^3+\dots +A^{\tau }where\underset{\tau \to \infty }{\mathit{lim}}{A}^{\tau }=0$$ (30)

where $\tau$ implies the layer of the supply chain. Combining Eqs. (7), (29), (30), the passive water use can be expanded as follows:

$${PW}_{overall}=pwc{\left(I-A\right)}^{-1}Y=pwcIY+pwcAY+pwc{A}^{2}Y+\dots +pwc{A}^{\tau }Y=\left[\begin{array}{c}{pwc}_1{y}_1\\ \begin{array}{c}{pwc}_2{y}_2\\ ⋮\end{array}\\ {pwc}_n{y}_n\end{array}\right]+\left[\begin{array}{c}{pwc}_1\sum _{\iota =1}^n{a}_{1,\iota }{y}_{\iota }\\ \begin{array}{c}{pwc}_2\sum _{\iota =1}^n{a}_{2,\iota }{y}_{\iota }\\ ⋮\end{array}\\ {pwc}_n\sum _{\iota =1}^n{a}_{n,\iota }{y}_{\iota }\end{array}\right]+\left[\begin{array}{c}{pwc}_1\sum _{\iota ,\theta =1}^n{a}_{1,\iota }{a_{\iota ,\theta }y}_{\theta }\\ \begin{array}{c}{pwc}_2\sum _{\iota ,\theta =1}^n{a}_{2,\iota }{a_{\iota ,\theta }y}_{\theta }\\ ⋮\end{array}\\ {pwc}_1\sum _{\iota ,\theta =1}^n{a}_{n,\iota }{a_{\iota ,\theta }y}_{\theta }\end{array}\right]+\left[\begin{array}{c}{pwc}_1\sum _{\iota ,\theta ,\kappa =1}^n{a}_{1,\iota }{a_{\iota ,\theta }{a}_{\theta ,\kappa }y}_{\kappa }\\ {pwc}_2\sum _{\iota ,\theta ,\kappa =1}^n{a}_{2,\iota }{a_{\iota ,\theta }{a}_{\theta ,\kappa }y}_{\kappa }\\ \begin{array}{c}⋮\\ {pwc}_n\sum _{\iota ,\theta ,\kappa =1}^n{a}_{n,\iota }{a_{\iota ,\theta }{a}_{\theta ,\kappa }y}_{\kappa }\end{array}\end{array}\right]+\dots$$ (31)

where $pwc{A}^{\tau }Y$ implies the passive water use transmitted through the production layer $\mathrm{\tau }$ in the supply chain. When $\tau$ = 0, there is only one sectors involved in the supply chain. As $\tau$ = 1, there are two sectors involved in the supply chain. By extension, there are n+1 sectors involved in the supply chain when $\tau$ equals n. In Eq. (31), the larger $\tau$ is, the smaller $pwc{A}^{\tau }Y$ will be. This suggests that when the layer of supply chain is higher, the water use transmitted in the supply chain is smaller [47]. Considering the higher layer of the supply chain will obtain smaller water use representing less important water use paths, this developed framework will measure from layer one to layer three. In further Section 4.3, Table 1 reveals that the first layer has the highest proportion of water use, while the third layer has the lowest proportion of water use.

Table 1.

Water use proportions at different layers of critical passive water use sectors in China 2021.

Sector roles	Level	S1	S10	S13	S14	S15
Pushing	1st	22.79 %	7.93 %	0.63 %	25.26 %	11.43 %
	2nd	20.79 %	6.93 %	0.27 %	15.43 %	6.97 %
	3rd	14.13 %	4.77 %	0.14 %	8.80 %	4.24 %
	Total	57.70 %	19.63 %	1.04 %	49.50 %	22.64 %
Pulling	1st	−1.13 %	13.84 %	28.60 %	6.30 %	16.15 %
	2nd	−0.78 %	11.27 %	16.69 %	1.49 %	7.59 %
	3rd	−0.47 %	7.15 %	8.60 %	0.88 %	3.80 %
	Total	−2.39 %	32.26 %	53.90 %	8.68 %	27.55 %
Bridging	2nd	−1.18 %	2.51 %	0.19 %	4.88 %	3.47 %
	3rd	−0.67 %	2.19 %	0.08 %	2.98 %	2.11 %
	Total	−1.85 %	4.70 %	0.27 %	7.87 %	5.58 %

As one significant innovation point of this paper, in the critical water use channels measurement section, it will discuss the target sector's different roles played in the supply chain in water use through SPA from the passive perspective. The first role is the pushing role when the target sector $\xi$ is the original upstream of the supply chain. This can be considered as an extension of the forward passive water use. The SPA of critical water use paths for layers one to three are shown as Eq. (32), (33), (34):

$${PW}_{L1}^{Pushing}={pwc}_{\xi }\sum _{\iota =1}^n{a}_{\xi \iota }{y}_{\iota },\left(\xi \ne \iota \right)$$ (32)

$${PW}_{L2}^{Pushing}={pwc}_{\xi }\sum _{\iota ,\theta =1}^n{a}_{\xi \theta }{a}_{\theta \iota }{y}_{\iota },\left(\xi \ne \iota \right)$$ (33)

$${PW}_{L3}^{Pushing}={pwc}_{\xi }\sum _{\iota ,\theta ,\kappa =1}^n{a}_{\xi \kappa }{a}_{\kappa \theta }{a}_{\theta \iota }{y}_{\iota },\left(\xi \ne \iota \right)$$ (34)

It's crucial to point out that in the measurement of the critical paths of water use, the primary focus is on the linkage between the target sector and other sectors. Therefore, the target sector will not be the ending sector in the supply chain in analysing the critical paths of passive water use. In Eq. (32), $a_{\xi \iota }{y}_{\iota }$ implies that the target sector $\xi$ produces $a_{\xi \iota }$ products for meeting the needs of sector $\iota$ spending ${pwc}_{\xi }{a}_{\xi \iota }{y}_{\iota }$ units of water. And in Eq. (33), $a_{\xi \theta }{a}_{\theta \iota }{y}_{\iota }$ implies the products produced by the sector $\xi$ for sector $\theta$ to produce $a_{\theta \iota }{y}_{\iota }$ products to meet the requirement of sector $\iota$ in which process sector $\xi$ uses ${pwc}_{\xi }{a}_{\xi \theta }{a}_{\theta \iota }{y}_{\iota }$ units of water.

The second role is the pulling role when the target sector $\xi$ is at the ending point of the supply chain. This can be considered as expanding the backward passive water use, but with a primary focus on the sector linkage between sector $\xi$ and other sectors. The backward passive water use SPA can be expressed as Eq. (35), (36), (37).

$${PW}_{L1}^{Pulling}=\sum _{\iota =1}^n{pwc}_{\iota }{a}_{\iota \xi }{y}_{\xi },\left(\iota \ne \xi \right)$$ (35)

$${PW}_{L2}^{Pulling}=\sum _{\iota ,\theta =1}^n{pwc}_{\iota }{a}_{\iota \theta }{a}_{\vartheta \xi }{y}_{\xi },\left(\iota \ne \xi \right)$$ (36)

$${PW}_{L3}^{Pulling}=\sum _{\iota ,\theta ,\kappa =1}^n{pwc}_{\iota }{a}_{\iota \kappa }{a}_{\kappa \theta }{a}_{\theta \xi }{y}_{\xi },\left(\iota \ne \xi \right)$$ (37)

Taking the two production layers SPA as an example, Eq. (36) implies ${pwc}_{\iota }{a}_{\iota \theta }{a}_{\vartheta \xi }{y}_{\xi }$ water used by sector $\iota$ in creating $a_{\iota \theta }{a}_{\vartheta \xi }{y}_{\xi }$ products for satisfying the final demand of the sector $\xi$. Subsequently, sector $\theta$ produces $a_{\theta \xi }{y}_{\xi }$ intermediate products to sector $\xi$.

The third role is the bridging role when the target sector $\xi$ is not neither at the starting nor ending point. In the supply chain, the sector $\xi$ acts as a bridge sector, only producing intermediate products. If there are only two sectors in the supply chain, it is not satisfied with the requirement of the bridging role. Therefore, the bridging role of passive water use SPA will analyse the critical paths with two and three production layers.

The bridging water use of two layers supply chain is shown as follows:

$${PW}_{L2}^{Bridging}=\sum _{\iota ,\theta =1}^n{pwc}_{\iota }{a}_{\iota \xi }{a}_{\xi \theta }{y}_{\theta },\left(\iota \ne \xi ,\xi \ne \theta \right)$$ (38)

In Eq. (38), the target sector $\xi$ connects the upstream and downstream by receiving $a_{\iota \xi }{a}_{\xi \theta }{y}_{\theta }$ intermediate products from sector $\iota$ and producing $a_{\xi \theta }{y}_{\theta }$ for sector $\theta$. In this process, to meet the final demand $y_{\theta }$, ${pwc}_{\iota }{a}_{\iota \xi }{a}_{\xi \theta }{y}_{\theta }$ unit of water is used.

In the three layers water use bridging role SPA, there are three situations for the target sector: at the first layer which is close to the starting point; at the second layer which is close to ending sector; and simultaneously at both the first and second layers, which directly connects the original producer and final consumer. The three situations of bridging water use for the target sector $\xi$ are shown as follows:

$${PW}_{L3,2}^{Bridging}=\sum _{\iota ,\theta ,\kappa =1}^n{pwc}_{\iota }{a}_{\iota \xi }{a}_{\xi \kappa }{a}_{\kappa \theta }{y}_{\theta },\left(\iota \ne \xi ,\xi \ne \theta ,\xi \ne \kappa \right)$$ (39)

$${PW}_{L3,3}^{Bridging}=\sum _{\iota ,\theta ,\kappa =1}^n{pwc}_{\iota }{a}_{\iota \kappa }{a}_{\kappa \xi }{a}_{\xi \theta }{y}_{\theta },\left(\iota \ne \xi ,\xi \ne \theta ,\xi \ne \kappa \right)$$ (40)

$${PW}_{L3,2\&3}^{Bridging}=\sum _{\iota ,\theta ,\kappa =1}^n{pwc}_{\iota }{a}_{\iota \xi }{a}_{\xi \xi }{a}_{\xi \theta }{y}_{\theta },\left(\iota \ne \xi ,\xi \ne \theta ,\xi \ne \kappa \right)$$ (41)

In Eq. (39), the target sector $\xi$ is closer to the starting sector. This process starts from sector $\tau$ and ends at sector $\theta$ using ${pwc}_{\iota }{a}_{\iota \xi }{a}_{\xi \kappa }{a}_{\kappa \theta }{y}_{\theta }$ units of water. The target sector $\xi$ receives $a_{\iota \xi }{a}_{\xi \kappa }{a}_{\kappa \theta }{y}_{\theta }$ products and then produces $a_{\xi \kappa }{a}_{\kappa \theta }{y}_{\theta }$ for the other sectors. Eq. (40) represent the target sector $\xi$ is at the second layer which close to the downstream. In this process, sector $\xi$ produces $a_{\xi \theta }{y}_{\theta }$ for the downstream sector $\theta$, and ${pwc}_{\iota }{a}_{\iota \kappa }{a}_{\kappa \xi }{a}_{\xi \theta }{y}_{\theta }$ unit of water is used by sector $\iota$. In Eq. (41), the target sector $\xi$ first receives $a_{\iota \xi }{a}_{\xi \xi }{a}_{\xi \theta }{y}_{\theta }$ products from sector $\iota$ and then produces $a_{\xi \xi }{a}_{\xi \theta }{y}_{\theta }$ products to itself. After that, sector $\xi$ produces $a_{\xi \theta }{y}_{\theta }$ products to sector $\theta$ for the final demand $y_{\theta }$. In this process, sector $\iota$ spends ${pwc}_{\iota }{a}_{\iota \xi }{a}_{\xi \xi }{a}_{\xi \theta }{y}_{\theta }$ units of water in producing intermediate products.

3.2. Data

The 2017 IO table and the economy data utilised in this study are sourced from the National Bureau of Statistics [58,59]. Given that the economy structure is unlikely to be significantly changed within several years, and with IO table being updated every five years, it is reasonable for this paper to utilise the former 2017 edition of IO table. The original table comprises 149 sectors, which have been consolidated into 15 sectors based on the standard of GB/T 4754-2017 for the purposes of simplifying calculation [60]. The 15 sectors include the primary (S1), mining (S2), tobacco, food and beverage processing (S3), textile (S4), education and entertainment (S5), fuel-processing (S6), chemical manufacturing (S7), non-metallic manufacturing (S8), metal-processing manufacturing (S9), equipment and other manufacturing (S10), electric, heat, and gas supply (S11), water production and supply (S12), construction (S13), circulation (S14), and other services sector (S15). Details on sectoral combination information can be found in Appendix A. For the sake of readability, sector ID will be used as a substitute for sectors' names in the next section.

The original IO table is a competitive IO table. To construct a closed economic system, eliminate the impact of imports, and ensure the accuracy of water use measurement for the sectors in the empirical

analysis, this paper would prefer a non-competitive IO table. To achieve this purpose, this paper subtracts the value of import from intermediate use and final demand. This adjustment is carried out based on the assumption that proportions of imports in both intermediate use and final demand remain stable within the same sector [47]. Data on sector water used is from the China water resources bulletin 2021 (page 20, part 4.1 Water Resource Development and Utilization: Water Consumption) by the Ministry of Water Resources of the People's Republic of China [61]. Utilising the IO method, the developed framework will measure “embodied water use”, based on the original data pertaining to “blue water” [55]. Undefined water use is distributed based on the proportion of S12 inputs to other sectors in the IO table [47,62]. Detailed information on water use can be found in Appendix B.

4. Results

4.1. Active water use measurement results

Section 4.1 provides an overview of the sector linkages in water use by measuring the structure of active water use, and then further measures the detailed sector linkages of active water use through sector decomposition. Fig. 3 shows the intensity and proportion of active water use of each sector from both the production and consumption processes.

Fig. 3.

Active water use in production and consumption process intensity and proportion in China 2021 (billion Cubic metres).

From Fig. 3, S1 contributes most water use in the production process, accounting for 364.43 billion Cubic Metres (BCM). And S3 has the greatest intensity of water use in consumption process with 137.5 BCM. As shown in Fig. 3(a), water use in the production process is primarily concentrated in S1, accounting for 61.56 % of the total amount, which dominants in water use in the production process. Except S1, the contribution of other sectors to the production process water use does not exceed 8 %. While Fig. 3(b) shows that water use in the consumption process is more dispersed. The sector with the highest water use is S3 at 23.23 %, followed by S1 at 20.31 % (120.26 BCM), and S13 at 15.82 % (93.63 BCM). Notably, S1, the sector with the highest production water use, has about two-thirds less active water use than production, at about 240 BCM.

Fig. 4 depicts the different measured water use linkages for each sector, including ILW, MLW, NFLW, NBLW, and NTW. In terms of the water use of the whole economy, ILW significantly surpasses MLW, with most sectors using less than 1 BCM of MLW. S1 has the highest MLW, but the equivalent value is only the eighth highest of all sectors in terms of ILW. Analysing ILW individually, S1 also has the highest ILW at 111.61 BCM, which is a substantial gap compared to other sectors. The sector with the second highest ILW is S15 with 28.42 BCM, which is almost a quarter of S1's ILW. From the NFLW perspective, S1 has the most active water linkages at 246.63 BCM, almost 16 times more than S14, the second highest sector. However, apart from S1, no other sector's NFLW exceeds 16 BCM, indicating

Fig. 4.

Active water use sector linkage of each sector in China 2021 (billion Cubic metres).

that S1 is the main contributor to economy wide NFLW. In terms of NBLW, S3 leads with 118.5 BCM, and next is S13 with 66.7 BCM, and S15 with 51.6 BCM. Unlike the dominance of S1 in NFLW, the gap between the sectors in NBLW is not substantial. Meanwhile, S1 is at the bottom of the list with only 24.52 BCM of NBLW.

The results of NTW show that S1, S2, S6, S7, S8, S9, S12 are the exporting sectors of active water use, while S3, S4, S5, S10, S13, S14, S15 are the importing sectors of active water use. Xiang et al. [63] also finds that the agriculture, as a water-concentrating sector, spends large amounts of water by providing food other sectors.

Fig. 5 depicts the decomposition of the active production process and consumption process of the water use for each sector. The ILW share of sectors decreases from the outer to the inner circles, meaning the outermost sector has the highest ILW share, while the innermost sector has the lowest.

Fig. 5.

Decomposition of active water use in production process and consumption process in China 2021 (billion Cubic metres).

According to Fig. 5(a), most sectors’ active water use is contributed by NFLW. Apart from S3, S4, and S13, the water use in the production process for these sectors is primarily composed of ILW. The highest percentage of NFLW is found in S2 at almost 99 %, followed by S8, S11, S6 and S9. And S13 has the highest percentage of ILW, which is associated with the findings of Sharma and Chani [64]. Meanwhile, the MLW of all sectors only represents a minor proportion of the water use in the production process.

According to Fig. 5(b), water used in the consumption process in most sectors is made up of NBLW, with only S12, S1, and S11 having more than 50 % of their water use composed of ILW. Similar to Fig. 5(a), there is only a tiny fraction of MLW in the consumption process. The sector with the largest share of MLW in the consumption process is S1, which only accounts for 5.15 %.

Focusing on the shares of NBLW, S4 holds the highest NBLW share of its water use in consumption process with S3 following closely behind. Both S5 and S6 also have over 75 % of NBLW shares in their water use during the consumption process.

Fig. 6 illustrates the sector decomposition of NFLW and NBLW. From Fig. 6(a), S13, S10, and S15 are the primary components of NFLW in each sector. Typically, S13 accounts for more than 80 % of NFLW components in S8. The highest proportion of S10 occurs in S9, where it is second only to S10, reaching a share of 35 %. S15 is the most significant component of NFLW in S13, with a share of about 65 %, which also represents the highest proportion of S15. Notably, S1, which was previously found to have the highest NFLW intensity, has S3 as its most dominant composition, accounting for more than 45 %. S10, S13, and S15 collectively constitute around 30 % of S1's NFLW.

Fig. 6.

Sector shares of net forward and backward water use in China 2021 (billion Cubic metres).

Fig. 6(b) shows the decomposition of NBLW sectors, revealing that the NBLW of all sectors' water use, except S1 itself, is primarily composed of S1, with a minimum share of 35 % in S6.

Typically, more than half of the NBLW in S3, S4, S5, S7, S14, and S15 is composed of S1. The highest composition shares of NBLW for S1 at 95 % occurs in S3, which is the sector with greatest.

NBLW intensity. This finding is consistent with Fig. 6 showing that S1 is the most significant water use“exporter” to other sectors, which aligns with Fan et al. [65].

4.2. Passive water use measurement results

This section presents the results obtained through the passive water use measurement. Fig. 7 displays the intensity and proportion of three types of passive water use including forward, backward, and overall passive water use. From a forward passive water use perspective in Fig. 7(a), S14, S7, S15, S11, and S12 exhibit the highest positive passive water use. Uniquely, S1 shows negative passive water use, reaching a substantial proportion of 32.02 % (5.5 BCM). Among sectors with positive forward passive water use, S14 accounts for 13.5 % (2.32 BCM), followed by S7 contributes 11 % (1.29 BCM), and S15 has 6.68 % (1.15 BCM). S13 has just 0.21 % (35 million Cubic Metres), ranking last among all sectors.

Fig. 7.

Passive water use sector linkage intensity and sector shares in China 2021 (billion Cubic metres).

According to the measurement results of backward passive water use in Fig. 7 and (b), only S1 has negative backward passive water use, while all other sectors exhibit positive backward passive water use. Among sectors with positive backward passive water use, S13 dominants with 30.09 % (6.52 BCM).

Additionally, S15 contributes 20.89 % (4.5 BCM), S10 provides 17.01 % (36.89 BCM), and S14 contributes 8.4 % (18.2 BCM). Those four sectors collectively account for approximately 85 % of the backward passive water use, with the remaining 15 % shared among the other ten sectors, each of which contributes less than 1 %.

Fig. 7 and (c) also illustrates the overall passive water use sector linkage. S13, S15, S10, and S14 exhibit the highest positive passive water use, while only S1 has a negative overall passive water use of 20.22 % BCM (7.86), which is the greatest in absolute terms. Among sectors with positive overall passive water use, S13 contributes 16.87 % (6.56 BCM), followed by S15 with 14.6 % (5.68 BCM), S10 with 11.39 % (4.43 BCM), and S14 with 10.65 % (4.14 BCM). Aside from these sectors, none of the other sectors contribute more than 2 BCM.

Fig. 8(a) provides a sectoral decomposition of forward passive water use. For S1, 2.53 BCM, or nearly 46 % of the forward passive water use, is stimulated by S3. Moreover, S15, S13, and S4 contribute to the forward passive water use of S1 by 0.7 BCM, 0.63 BCM, and 0.56 BCM, respectively. As the mostimportant forward passive water sector with positive value, S14's forward passive water use mainly comes from S13 at nearly 28 % (0.67 BCM) and S15 by 27 % (0.63 BCM).

Fig. 8.

Decomposing sector shares of passive water consumption forward and backward linkage in China 2021 (billion Cubic metres).

Fig. 8(b) displays the sectoral decomposition of backward passive water use. It reveals that all sectors, except S1 itself, positively contribute positive backward passive water use to S1. However, the negative backward water use resulting from S1's own production is too substantial, ultimately resulting in significant negative backward passive water use. Moreover, as the sector with the greatest positive backward passive water use, S13's internal production stimulates 2.86 BCM, or nearly 40 % of its total backward passive water use, a proportion relatively low compared to other sectors. For instance, S15 and S10, the sectors with the second and third highest backward passive water use, have about 62 % (2.85 BCM) and 54 % (1.99 BCM) of their backward passive water use stimulated by their own production, respectively. Overall, we can find that the backward passive water use is mainly stimulated by the sector itself rather than other sectors.

4.3. Critical water use channels measurement results

Based on the perspective of passive water use, this section will measure how the water use are transmitted during the critical sector's supply chain, and finally obtain the critical paths when the focused sector plays different roles including pushing, pulling, and bridging roles. The roles of sectors vary due to their different positions in the supply chain. As a kind reminder, the term ‘pushing role’ refers to the target sector being situated at the upper stream of the supply chain. Conversely, the ‘pulling role’ signifies the target sector being at the end point of the supply chain. The ‘bridging role’, on the other hand, represents a position that is neither at the starting nor at the ending point, but rather, at an intermediate location within the supply chain.

Table 1 presents the water use proportions of each layer, following the measurement of critical paths of water use for key passive water use sectors, including S1, S10, S13, S14, and S15. This table outlines the first, second, and third layers of both pushing and pulling passive water use shares, as well as the second and third layers of bridge passive water use shares.

First, observing the change in the share of passive water use at each layer, a decreasing trend from lower to higher layers is evident, corresponds with the findings of Chen, Liu and Li [47]. This pattern indicates that passive water use is primarily driven by the procedure of the upstream supplying to downstream, with less water use stimulated by production through the intermediate sector. Second, when considering the total shares of the first three layers, the total shares of pushing water use in the first three layers exceed the total shares of pulling water use in S1 and S14. Conversely, the combined shares of pulling water use in the first three layers of S10, S13, and S15 surpass those of the pushing water use. Third, the bridging passive water use of all five sectors, when acting as an intermediate sector, is remarkably low, not exceeding 8 %. Notably, there are two anomalous results. First, the findings in 4.2 about S14 suggest that S14's passive water use is primarily driven by upstream sectors deviate. But the critical paths measurement indicates that S14 is more influenced by the forward, i.e., by the downstream sectors. This discrepancy may arise because the critical paths measurement neglects the contribution of the sector itself, as SPA focuses more on linkages with other sectors. Thus, changes within the sector itself are more crucial for measuring the backward passive water use[66]. Second, the shares of S1 in pulling and bridging water use are negative, which differs from the proportions of other sectors. This is because, in the measurement of S1's backward passive water use, while S1 contributes negative water use, other sectors contribute positively. Now, when focusing on the linkages of other sectors with S1, only the positive composition left, contrasted with the negative overall passive water use, results in the opposite directions of pulling and bridging water use observed in Table 1.

Following the passive water use measurement in section 4.2, we identify S13 as the sector with the most significant potential for passive water use reduction. Consequently, the subsequent section will measure more detailed water use paths of S13.

Fig. 9(a) presents the measured results of S13's critical passive water use paths in pushing role. Analysing from the upstream of the supply chain, S13 primarily uses water to produce products directly for S15, S14, S10, S1, and S11. In the first production layer, S13's supply to S15 accounts for over 80 % of this layer's water use. Subsequently, S15 contributes to over 42 % of the water use in the second layer and 18 % in the third layer. Besides S15, S14 also emerges as a significant intermediate sector in the second layer, accounting for about 10 % of the water use, while S15 dominates the first layer. From this, we can identify that the most critical path of S13's forward water use is S13→S15→S15→S15 (arrows from left to right represents upstream to downstream).

Fig. 9.

Critical passive water use paths of S13's pushing and pulling roles in China 2021.

Fig. 9(b) presents the results of the critical passive water use path measurement for S13 acting as a pulling role. Analysing from the downstream of the supply chain, S13 is the final consumer, with S8, S15, S9, and S14 directly supplying to S13 being critical water use paths. Notably, the water use share from S8 to S13 constitutes 32.63 % of the water use in the third production layer. Apart from S8, S15 accounts for 17.65 %, S14 for 14.8 %, and S9 for 13.03 %. Tracing up the supply chain, in the first production layer, the most crucial path is S8's internal production and consumption, accounting for 10.29 %. The second critical path in this layer is S9 supplying to itself, which accounts for 4.23 %. I In the initial production layer, the situation shifts, with S9's internal cycling having the highest water use shares and S8 being the second highest. Compared with the forward critical paths measurement, S13's backward water use critical paths are connected with more sectors and have more dispersed shares. The relatively critical paths among them are S8→S8→S8→13 and S9→S9→S9→S13.

Fig. 10 presents the measured results of the critical passive water use paths of S13 acting bridging role. Fig. 10(a) illustrates the critical paths of S13 situated in the first production layer of the three-sectors supply chain. Analysing from the downstream, S13 primarily connects with S15 and S14, with S15 accounting for over 88 % of the water use as an intermediate sector for transmitting water use. To meet the high demands of S15 and S14, S13 also connects with upstream sectors, where S8 accounts for 30 % of the water use, and S15, S14, and S9 each account for over 10 %. When S13 acts as the only intermediate sector, S8, S14, S9, S12, and S10 collectively use 75 % of

Fig. 10.

Critical passive water use paths of S13's bridging role in China 2021.

the passive water. Based on the water use shares of each production layer, in this scenario, S8→S13→S15 is the most critical path.

Fig. 10(b)(c)(d) are the measurement illustration of S13 critical passive water use paths as a bridging role in the four-sector supply chain. Fig. 10(b) displays the critical paths when S13 is located at the first layer. Analysing from the starting points of the supply chain, S8, S14, and S9 are the primary upstream sectors, accounting for 5.86 %, 1.36 %, and 1.19 % of S13's bridge water use, respectively. Furthermore, S13 produces products for other intermediate sectors in the second layer, such as S15, which accounts for 7.01 % of the water use, and S14, which accounts for 1.31 %. At the ends, S14, S10, and S15 are the main consuming sectors. S14 and S10 primarily receive their supply from S15, which accounts for 5.54 % and 1.56 % of the water use, respectively. S15 is supplied by S14, which accounts for 1.31 % of the water use. Based on the proportions of water use transmitted, S8→S13→S15→S14 is the most critical path in this scenario.

Fig. 10(c) depicts the critical path measurement when S13 is situated in the second production layer. Analysing from the downstream perspective, S13, serving as an intermediate sector, produces products for the final endpoints, transmitting about 56.74 % of the water use to S15. Before production for the downstream, S13 receives products from the intermediate sectors in the first layer, including S8, which accounts for 28.29 % of the water use, S9, which accounts for 20.83 %, and S14, which accounts for 7.63 %. Tracing up to the starting sectors, S14 supplying to S8 and S9 accounts for 12.11 % and 6.75 % of the water use, respectively. Moreover, S2's supply to S8 and S9 contribute 6.99 % and 6.74 % of the water use, respectively, while S11's supply to S8 and S9 uses 9.19 % and 7.33 %. According to the proportions of each layer, the most critical bridge water use path of S13 at the third layer is S14→S8→S13→S15.

Fig. 10(d) illustrates the critical paths when S13 is located in the first and second layers simultaneously. Following the supply chain from the starting sectors, S8, S15, S14, S9, and S12, as the main producers, supply products to S13, accounting for 4.99 %, 2.7 %, 2.27 %, 1.83 %, and 1.06 % of the water use in the initial layer, respectively. Furthermore, S13 engages in internal production and consumption in the first and second layers and then supplies to S15 and S14 in the third layer, accounting for 12.96 % and 0.83 % of the water use, respectively. According to water use share, the most critical path is S8→S13→S13→S15.

5. Discussion, conclusions, and policy implications

This study introduces a new concept of passive water use and constructs a dual-perspective framework to measure water use. The developed framework measures the corresponding changes in water use in an economic system when macroeconomic conditions change. This study also measures the critical sectors for water use from different perspectives. The dual-perspective framework is composed of three parts: the measurement of critical active water use sectors, the measurement of critical passive water use sectors, and the measurement of critical paths of key water use sector. This study applies this approach to measure the active and passive water use sector linkages for each sector in China in 2021, and from a passive perspective, it measures the critical channels of significant water use sectors in different roles in the supply chain. The main empirical findings are as follows:

First, the active water use measurement finds that the primary sector (S1) stands out as a critical sector in the production process, spending a significant amount of water in meeting the demands of other sectors. On the other hand, the tobacco, food and beverage processing sector (S3), the construction sector (S13), and other services sector (S15) emerge as important sectors in terms of water use in the consumption process, stimulating other sectors to supply to them with products at a high level of water use. In the production process, most sectors are predominantly stimulated by NFLW. Conversely, in the consumption process, the majority of sectors are primarily driven by ILW. After sectoral decomposition, we find the construction sector(S13), the equipment and other manufacturing sector (S10), and other services sector (S15) are the main component of NFLW in the system. And the primary sector (S1) is the critical component of NBLW.

Second, the passive water use measurement finds that the primary sector(S1), the equipment and other manufacturing sector (S10), the construction sector (S13), the circulation sector (S14), and other services sector (S15) are the critical sectors of passive water use. While the primary sector (S1) is the only sector with increasing water use showing negative in quantity, and other sectors show decline in water use. Among the sectors with positive passive water use, the circulation sector (S14) is the most important sectors of forward water use, and the construction sector (S13) is the most important positive backward and overall passive water use sector. After decomposing the water use sector linkages, find that the demand decreasing of the construction sector (S13) and other services sector (S15) is the main stimulation of the decline in forward passive water use. Furthermore, the decomposition also finds sectors’ own production reduction leads to the backward passive water use reduction.

Third, the critical paths measurement of the construction sector (S13) finds that the critical paths of pushing water use role is the construction sector (S13)→other services sector (S15) where other services sector (S15) acts as the downstream and receive products. The critical paths of pulling water use role are more spreadable. The most two important paths are the non-metallic manufacturing sector (S8)→the construction sector (S13) and the metal-processing manufacturing sector (S9)→the construction sector (S13). At the view of bridging water use role, the critical path is the non-metallic manufacturing sector (S8)→the construction sector (S13)→other services sector (S15). In the supply chain with three sectors, the construction sector (S13) plays a bridging role in transmitting water use more in the second layer. There are three critical paths of bridging water use and the most critical path is the circulation sector (S14)→the non-metallic manufacturing sector (S8)→the construction sector (S13)→other services sector (S15).

Based on the findings of this paper, we make the following policy recommendations:

First, policymakers need to focus not only on the amount and influence of active water use, but also, from a different perspective, on the changes in water use that occur in sectors when macroeconomic conditions change. Even some sectors show a relatively low level in active water use, they may have significant in passive water use.

Second, it is important to note that passive water use is not readily measurable. This does not mean that passive water use is unimportant, but rather that it is vital to measure the ‘unstable’ water use that tends to increase or decrease when macroeconomic conditions change. It is also important to avoid excessive water use following changes in macroeconomic conditions, as well as sudden increasing or decreasing water use that may negatively influence the economy and society.

Third, focusing on the sector's bridging water use role in the supply chain could motivate water conservation. Beyond just the original producers and final consumers, sectors within the middle of the supply chain also play a vital role in the transmission of water use. This perspective should not be overlooked.

This study may have some uncertainties about the results and limitations. First, the passive water use measured in this paper only considers economic conditions shifting. We would consider more conditions to measure passive water use in the future work. Second, since the sectoral structure may change after COVID19 pandemic, it is necessary to use more updated IO table to measure the water use sector linkage.

Data availability statement

Data will be made available on request.

CRediT authorship contribution statement

Lingfan Wu: Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Formal analysis, Data curation. Yu Song: Writing – review & editing, Writing – original draft, Supervision, Resources, Methodology, Funding acquisition, Formal analysis, Conceptualization. Yueyang Li: Writing – review & editing, Writing – original draft, Visualization, Methodology, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A.

Appendix I.

Sectoral information

Original sector ID	Original sector name	Combined sector ID	Combined sector name
s1	Agricultural products	S1 (s1-s5)	Primary
s2	Forest products
s3	Livestock products
s4	Fishery products
s5	Agricultural, forestry, animal husbandry and fishery service products
s6	Coal mining and washing products	S2 (s6-s11)	Mining
s7	Oil and gas extraction products
s8	Ferrous metal mining and dressing products
s9	Non-ferrous metal mining and dressing products
s10	Non-metallic mineral mining and dressing products
s11	Mining ancillary activities and other mining products
s12	Grain mill products	S3 (s12-s26)	Tobacco, food and beverage processing
s13	Processed feed products
s14	Processed vegetable oils
s15	Sugar and sugar products
s16	Slaughtering and processed meat
s17	Processed aquatic products
s18	Vegetables, fruits, nuts and other processed agricultural and sideline foods
s19	Convenience food
s20	Dairy product
s21	Condiments, fermented products
s22	Other foods
s23	Alcohol and liquor
s24	Beverage
s25	Refined tea
s26	Tobacco products
s27	Cotton, chemical fiber textiles and printing and dyeing fine products	S4 (s27-s34)	Textile
s28	Wool textiles and finishing products

Original sector ID	Original sector name	Combined sector ID	Combined sector name
s29	Hemp, silk textiles and processed products
s30	Knitting or crochet and the products thereof
s31	Textile manufactured products
s32	Textiles, garments, and apparel
s33	Leather, fur, feathers and articles thereof
s34	Footwear
s35	Wood processing and wood, bamboo, rattan, palm and grass products	S5 (s35-s40)	Education and entertainment
s36	Furniture
s37	Paper and paper products
s38	Reproductions in printed and recording media
s39	Arts and crafts
s40	Cultural, educational, sports and recreational goods
s41	Refined petroleum and nuclear fuel processed products	S6 (s41-s42)	Fuel-processing
s42	Processed coal products
s43	Basic chemical raw materials	S7 (s43-s53)	Chemical manufacturing
s44	Manure
s45	Pesticide
s46	Coatings, inks, pigments and similar products
s47	Synthetic materials
s48	Special chemical products and explosives, pyrotechnics, pyrotechnic products
s49	Daily chemical products
s50	Pharmaceutical products
s51	Chemical fiber products
s52	Rubber products
s53	Plastic products
s54	Cement, lime and gypsum	S8 (s54-s60)	Non-metallic manufacturing
s55	Gypsum, cement products and similar products
s56	Building materials such as bricks and tiles, stones, etc
s57	Glass and glass products
s58	Ceramics
s59	Refractory products
s60	Graphite and other non-metallic mineral products
s61	Steel	S9 (s61-s66)	Metal-processing manufacturing
s62	Steel rolled products
s63	Iron and ferroalloy products
s64	Non-ferrous metals and their alloys
s65	Non-ferrous metal calendered products
s66	Metalwork
s67	Boilers and prime mover equipment	S10 (s67-s97)	Equipment and other manufacturing
s68	Metalworking machinery
s69	Material handling equipment
s70	Pumps, valves, compressors and similar machinery
s71	Cultural and office machinery
s72	Other general purpose equipment
s73	Special equipment for mining, metallurgy and construction
s74	Special equipment for chemical, wood and non-metallic processing
s75	Special machinery for agriculture, forestry, animal husbandry and fishery
s76	Other special equipment
s77	Automobiles
s78	Auto parts & accessories
s79	Railway transport and urban rail transit equipment
s80	Ships and related installations
s81	Other transportation equipment
s82	Motor
s83	Power transmission and distribution and control equipment
s84	Wires, cables, fiber optic cables and electrical equipment
s85	Battery
s86	Household utensils
s87	Other electrical machinery and equipment
s88	Computer
s89	Communication equipment
s90	Radio and television equipment and radar and supporting equipment
s91	Audio-visual equipment
s92	Electronic components
s93	Other electronic devices
s94	Instrumentation
s95	Other manufactured products
s96	Waste resources and waste materials are recycled and processed
s97	Repair services for metal products, machinery and equipment
s98	Electricity, heat production and supply	S11 (s98-s99)	Electric, heat, and gas supply
s99	Gas production and supply
s100	Water production and supply	S12 (s100)	Water production and supply
s101	Housing construction	S13 (s101-s104)	Construction
s102	Civil engineering construction
s103	Construction installation
s104	Building decoration, renovation and other construction services
s105	Wholesale	S14 (s105-s120)	Circulation
s106	Retail
s107	Rail passenger transport
s108	Rail freight transportation and transport support activities
s109	Urban public transport and road passenger transport
s110	Road freight transport and transport ancillary activities
s111	Passenger transportation on the water
s112	Cargo transportation on the water and transport auxiliary activities
s113	Air passenger transportation
s114	Air cargo transportation and transportation ancillary activities
s115	Pipeline transportation
s116	Multimodal transport and transport agency
s117	Loading, unloading, handling and warehousing
s118	Postal
s119	Lodging
s120	Catering
s121	Telecommunications	S15 (s121-s149)	Other services sector
s122	Broadcasting, television and satellite transmission services
s123	Internet and Related Services
s124	Software services
s125	Information technology services
s126	Monetary finance and other financial services
s127	Capital markets services
s128	Insurance
s129	Real estate
s130	Lease
s131	Business services
s132	Research and experimental development
s133	Professional technical services
s134	Science and technology promotion and application services
s135	Water management
s136	Ecological protection and environmental governance
s137	Public facilities and land management
s138	Resident services
s139	Other services
s140	Education
s141	Hygiene
s142	Social work
s143	Press and publishing
s144	Radio, television, film and film sound recordings
s145	Culture and the arts
s146	Physical education
s147	Entertainment
s148	Social security
s149	Public administration and social organization

Appendix B.

Appendix II.

Water use information

Water use type	Original amount	Distributed sector	Distributed amount
Agricultural	364.43	S1	364.43
Industrial	104.96	S2	4.43
		S3	27.94
		S4	4.84
		S5	7.65
		S6	2.01
		S7	14.88
		S8	9.19
		S9	9.01
		S10	25.01
Other types of water use	122.63	S11	11.00
		S12	16.67
		S13	27.25
		S14	25.79
		S15	41.92
Total	592.02	Total	592.02

Note: The original data is from the China water resources bulletin 2021 (page 20, part 4.1 Water Resource Development and Utilization: Water Consumption) (unit: billion Cubic Metres).