Full Domestic Supply Chains of Blue Virtual Water Flows Estimated for Major U.S. Cities

Abstract

Through the trade of products and services, cities indirectly depend on distant water sources to function, prosper, and grow. To fully account for indirect (virtual) water dependencies, virtual water flows need to be known along complex supply chains. To this purpose, we build a new environmental multiregional input–output model for U.S. regions. The model is used to quantify the domestic, blue virtual water flows and analyze the water footprints of 69 major U.S. cities. Our results show a large inequality in the urban water consumed for economic production: just 7 out of the 69 cities included in this study account for 35% of the U.S. national water footprint of production. This is due to the production of water-intensive agricultural products in the metropolitan areas of western cities. The inequality reduces for the urban water footprint of consumption because, through the supply chains of industrialized food sectors, western virtual water is partially transferred to eastern cities as final demand. The water embodied in industrial products and services tends to be higher in western cities than in eastern cities; that is, the water embodied in food services could be several times higher in Los Angeles than in New York City. Trade hub cities attract large inflows of products which are mostly transformed for consumption elsewhere. Thus, the omission of product interdependencies within trade hub cities can increase by several times their water footprints of consumption. Overall, the proposed model is able to enhance subnational estimates of U.S. virtual water flows.

Key Points

• The virtual water associated with agricultural production in western U.S. regions is partially transferred to eastern cities as final demand
• The water embodied in industrial products and services in western cities tends to be higher than in eastern cities
• Ignoring product interdependencies could result in large truncation errors for the water footprint of consumption of U.S. cities

1 Introduction

Cities depend directly and indirectly on water to function and thrive (Diamond, 2005). Direct water dependencies arise from the need to use physical water to meet multiple urban demands—household, government, commercial, industrial, and service sector (Flörke et al., 2018; Renouf et al., 2017). Direct water demands require building and maintaining infrastructure (e.g., reservoirs, pipe networks, treatment plants) to physically transfer water to cities (Porse et al., 2018). These direct dependencies, although critical to city functioning, require less water than indirect water dependencies (Ahams et al., 2017; Chini et al., 2017; Hoff et al., 2014; Lenzen & Peters, 2010; Mahjabin et al., 2018; Paterson et al., 2015; Rushforth & Ruddell, 2016, 2018; Vanham et al., 2017a). Indirect water dependencies arise through the water embodied in the products and services consumed by a city that are produced within and outside a city's boundary.

Embodied or virtual water, the terms are used interchangeably, is the water required for the production of a product or service along its supply chain (Allan, 1992). As cities grow and prosper, so does their demand for traded products and services, resulting in increased demand for virtual water (Lenzen, 2009). In the face of rising concerns for regional and global water scarcity and stress (Djehdian et al., 2019; Marston & Konar, 2017; Vanham et al., 2018), cities need reliable and sustainable virtual water supplies (Kennedy et al., 2015; Renouf & Kenway, 2017; Rushforth & Ruddell, 2015, 2016; Vanham et al., 2017b). This requires knowing the indirect water needs of cities to meet both intermediate and final demand and, therefore, accurately mapping and quantifying virtual water flows (Lant et al., 2019; Lenzen & Peters, 2010).

Environmental multiregional input–output (E-MRIO) models are used to trace and quantify the complex and multiple pathways of virtual water through the economy (Cazcarro et al., 2013; Lenzen, 2009; Wang & Zimmerman, 2016; Yang et al., 2017; Yang et al., 2018). MRIO models link production, intermediate demand, and final demand across economically interrelated sectors and regions to capture the full supply chains of products and services (Miller & Blair, 2009). By further linking MRIO models to satellite accounts for resources (e.g., water and energy) and pollutants (e.g., CO₂, NO_x), E-MRIO analysis enables the comprehensive and systematic quantification of environmental flows embodied in the production of products and services along supply chains (Wiedmann, 2009; Wiedmann et al., 2007).

E-MRIO models of virtual water flows are needed to inform and more comprehensively assess regional water management strategies and policies (Bachmann et al., 2015; Daniels et al., 2011; Marston et al., 2015; Zhao et al., 2015), measure and track water sustainability indicators (Ahams et al., 2017; Cazcarro & Arto, 2019; Hoekstra & Mekonnen, 2012; Hoekstra & Wiedmann, 2014; Hoff et al., 2014), anticipate the impacts of water-related shocks that can propagate through supply chains (Contreras & Fagiolo, 2014; Distefano et al., 2018), and optimize regional flows to be more water efficient (Daniels et al., 2011; Hoekstra, 2014). Daniels et al. (2011) provide a comprehensive review of policy application areas and examples where the geographical mapping of virtual water flows is relevant.

An important application of virtual water flows is in the estimation of water footprints. The water footprint is an indicator of water use that accounts for both the direct and indirect consumptive water use of a consumer or producer (Cazcarro et al., 2019; Hoekstra & Chapagain, 2007; Hoekstra & Mekonnen, 2012; Rushforth & Ruddell, 2018). It is a measure of freshwater appropriation that can be separated into blue, green, and gray water contributions (Hoekstra et al., 2011). Water footprints have been used to assess the water sustainability of countries (Hoekstra & Mekonnen, 2012), cities (Ahams et al., 2017; Rushforth & Ruddell, 2016; Vanham et al., 2017a, 2017b), products (Schyns et al., 2017), and water conservation measures (Haghighi et al., 2018), among other applications.

Here our main objective is to build an E-MRIO model to quantify and analyze the blue virtual water flows of U.S. regions, including major cities. Blue water refers to the consumptive use of water sourced from surface water and groundwater. Although E-MRIO approaches have recently been used to analyze embodied energy (Canning et al., 2017) and CO₂ emissions (Caron et al., 2017) at the U.S. subnational level, we are unaware of any other attempts where E-MRIO analysis is used to determine blue virtual water flows at the U.S. city level. Our E-MRIO model integrates for the first time a comprehensive database of interregional commodity flows, the Freight Analysis Framework version 4 (FAF4) (FAF, 2018), and U.S. national input–output make and use tables (Horowitz & Planting, 2009). We use the E-MRIO model to address the following questions: how does indirect water consumption vary in space, specifically among U.S. cities? How is regional indirect water consumption distributed among broad product categories such as agricultural products, manufactured food, industrial products, and services? What are the hot spot regions and products of U.S. virtual water flows? How do the E-MRIO estimates of virtual water flows compare with estimates that do not account for the full supply chains of products?

Several global E-MRIO databases are available, for example, Eora (Lenzen et al., 2013), EXIOBASE (Tukker et al., 2018), GTAP (Aguiar et al., 2016; Walmsley et al., 2018), and WIOD (Timmer et al., 2015). This has facilitated E-MRIO analyses of virtual water flows at the global level. Although E-MRIO models have been widely used to assess the impacts of international trade on water resources (Distefano et al., 2018; Distefano & Kelly, 2017; Wang & Zimmerman, 2016), approaches have been limited at the U.S. subnational level. This is due to the extensive data requirements and scarce data availability for building E-MRIO models at the subnational level. These data limitation barriers, however, are being surpassed in the United States through improved, open-source subnational data sets (Hwang et al., 2016; Yang et al., 2018) and modeling techniques (Boero et al., 2018; Canning et al., 2017; Caron et al., 2017).

E-MRIO models have been used to analyze subnational virtual water flows in Australia (Lenzen, 2009; Lenzen et al., 2017), China (Chen et al., 2017; Guo & Shen, 2015; Zhao et al., 2015), India (Katyaini & Barua, 2017), Mexico (López-Morales & Duchin, 2011), Spain (Cazcarro et al., 2013), and the UK (Yu et al., 2010), among other countries. For the United States, an open-source state-level E-MRIO model was recently developed (Yang et al., 2018), which includes a satellite account for water use. Rehkamp and Canning (2018) employed an E-MRIO model to measure the blue water embodied in American diets. Others have used regional input–output tables to model a few U.S. subnational regions (Dilekli et al., 2018; Mubako et al., 2013). For example, Mubako et al. (2013) implemented a two-region E-MRIO model to explore virtual water flows between the state of Illinois and California, USA. Besides virtual water flows, E-MRIO models have recently been built to analyze embodied CO₂ emissions at the U.S. state level (Caron et al., 2017) and energy embodied in food flows at the U.S. county level (Canning et al., 2017). In this study, we use E-MRIO modeling to determine virtual water flows for the entire conterminous United States (CONUS), including 69 major cities.

A common approach to determine U.S. subnational virtual water flows is to rely on commodity flow data alone (Ahams et al., 2017; Chini et al., 2017; Dang et al., 2015; Mahjabin et al., 2018; Marston et al., 2015; Marston & Konar, 2017; Rushforth & Ruddell, 2016). In that approach, the virtual water flows are determined by ignoring sectoral interdependencies (intermediate demand), thus omitting downstream and upstream terms of the full supply chains which can lead to substantial truncation errors (Cadarso et al., 2018; Lenzen, 2009). For example, Lenzen (2009) found for Australian provinces that truncation errors for water consumption volumes can be as high as 50%. Virtual water flows need to be accurate and consistent with economic analysis to be an effective and relevant tool for computing water-related consumption-based indicators (Hoekstra & Wiedmann, 2014; Lenzen, 2009), and informing regional water management and policy (Daniels et al., 2011). E-MRIO analysis provides a robust and consistent framework for enhancing subnational estimates of U.S. virtual water flows. Here we demonstrate that relying solely on commodity flow data to estimate the virtual water flows of U.S. cities results in large truncation errors.

MRIO models can be categorized into survey, nonsurvey, and hybrid approaches (Boero et al., 2018; Jensen, 1990). The survey approach relies on observational (survey) data to obtain the regional input–output information. This approach is rarely implemented at the subnational level because observing all of the necessary variables is seldom feasible. Nonsurvey approaches rely on national input–output tables and modeling techniques (e.g., interregional flows are often modeled) to derive regional coefficients. The hybrid approach combines both survey and nonsurvey techniques (Boero et al., 2018; Lahr, 1993). Our E-MRIO model uses the hybrid approach by integrating a semisurvey database of subnational, interregional commodity flows with U.S. national input–output tables. Next, the data used and the steps followed to construct the E-MRIO model are explained. The model is then used to analyze subnational virtual water flows for U.S. regions.

2 Data

We build a new E-MRIO model to determine the domestic blue virtual water flows for 115 U.S. regions (Figure 1a) and 41 different products. The model is described in section 3. We focus on domestic flows by excluding international imports and exports from the analysis. The 41 products consist of the 35 different commodity classes in the FAF4 database (FAF, 2018), which is the source of the commodity flow data used in this study, and 6 service sectors (Table S1 in the supporting information lists the products and service sectors). Hereafter we use the word product to refer both goods and services. Note that the FAF4 consists of 42 products. We use 35 products by aggregating a few of the FAF4 products. This is done to facilitate the linkage between the FAF4 database and national input–output tables.

Figure 1

(a) Map illustrating the 115 FAF4 regions used to build the E-MRIO model, including 69 cities and 46 remainders of states. (b) Hypothetical example illustrating FAF4 commodity flows between cities and a remainder of state.

The 115 regions in the E-MRIO model match the regions in the FAF4 database which cover the entire CONUS (Figure 1a). These 115 regions consist of 69 U.S. metropolitan statistical areas, hereafter cities, and 46 remainders of states (Figure 1b). The 69 metropolitan statistical areas include the largest and major middle-sized cities in the United States, which account for approximately 69% of the total U.S. population. The remainders of states represent the area of a state that is not part of a FAF4 city or the states without a FAF4 city in them.

To build the E-MRIO model, six different data sets are used: national input–output make and use tables, national input–output import matrix, interregional commodity flows, county-level population, national employment by sector, and direct water consumption coefficients. We use national input–output tables to capture product interdependencies. For example, the supply chain of beef production might begin with cereal grains grown in Oklahoma, which are used to feed cattle in Texas. These cattle in turn might be sold and slaughtered in Kansas to be finally consumed by households and restaurants in New York City. By representing product interdependencies (i.e., the input products needed to produce another product), input–output tables allow making the supply chain connections needed to map the production of a product to its final consumption destination.

In this study, the U.S. Bureau of Economic Analysis (BEA) detailed (405 industries), after redefinitions, national input–output make and use tables are used for the 2012 base year (BEA, 2018). The BEA redefinitions consist of moving the output for few secondary products into an industry in the make and use tables in which production of those products is primary (Horowitz & Planting, 2009). To obtain a new use matrix with only domestic inputs, the BEA's after redefinition import matrix is subtracted from the original BEA's use matrix (BEA, 2018). The national input–output make table represents the industries' outputs and the use table the industries' inputs needed to produce the outputs. The make and use tables can be combined to produce a single input–output table (see section 3). We utilize the make and use tables to facilitate the integration with the subnational commodity flow data.

Since the input–output tables are available at the national level (BEA, 2018), we regionalize the tables using subnational commodity flow data for the year 2012 from the FAF4 database (FAF, 2018). The regionalization approach is explained in section 3. The FAF4 integrates various sources of data to create a complete representation of product flows for the entire U.S. economy (Hwang et al., 2016). It is a semisurvey database since it complements the U.S. subnational commodity flow survey (CFS, 2018) with additional data sources and modeling results. Although there are limitations to the FAF4 database, mostly due to the aggregation of products, it is the most comprehensive, publicly available, and consistent data set of U.S. commodity flows.

The FAF4 uses the two-digit Standard Classification of Transported Goods codes to classify products (Hwang et al., 2016) while the benchmark BEA tables use the six-digit North American Industry Classification System. By aggregating industry codes, the detailed BEA North American Industry Classification System industries are mapped onto the FAF4 Standard Classification of Transported Goods classes. This results in the aggregation of the BEA national input–output make and use tables from 405 industry codes into the 35 product codes of the FAF4 database and 6 additional service sectors. Since the FAF4 database does not include separate categories for interregional service flows (e.g., restaurants and government), they are treated as sinks in the E-MRIO model. This means that the embodied water for services is computed based on the local supply chains, not accounting for the supply chains of services purchased from other regions.

Another important data set required by the E-MRIO model is household consumption. Population data for the year 2012 (U.S. Census, 2018) are used to disaggregate the national-level household consumption for each product to the level of the 115 FAF4 regions. National household consumptions are obtained from the BEA national use table. In the E-MRIO model, household consumption is used to compute the final demand. In terms of the supply chains, the final demand represents the final destination where products are consumed and stop circulating within the economy.

The last data set needed to implement the E-MRIO model is a satellite account containing the direct water consumption associated with the production of each product at the level of the FAF4 regions. To compute the direct water consumption, the approach by Ahams et al. (2017) is followed, which utilizes water consumption coefficients from the Water Footprint Network (Mekonnen & Hoekstra, 2011) and other sources (CDM-Smith, 1996). For agricultural and livestock products, the water consumption coefficients are for consumptive blue water at the state level in cubic meters per ton (m³ ton⁻¹) (Mekonnen & Hoekstra, 2011). The coefficients are converted to m³ and disaggregated to the FAF4 level by multiplying the coefficients by the production (i.e., the FAF4 commodity flows) in tons associated with each product and region. The FAF4 data include commodity flows in both tons and dollars (FAF, 2018). Since the agricultural and livestock water consumption coefficients are provided at a higher product resolution than the FAF4 commodity flows, the coefficients are aggregated using a weighted average approach (Ahams et al., 2017).

For industrial products and services, the available data are national-level blue water use coefficients for individual products in m³/employee (CDM-Smith, 1996). These coefficients are converted into national-level water consumption in m³ by multiplying the coefficients by the national number of employees associated with each product, and by a consumption coefficient representing the fraction of water that is consumed. For the consumption coefficient, we use 5% for all industrial and service products. This value represents the average consumption coefficient based on USGS data for industrial water consumption (Ahams et al., 2017). However, we tried other values ranging from 5 to 20% and found that they only had a minimal impact on the model results. The national water consumption for each product is then disaggregated to the level of the FAF4 regions according to the proportion of production associated with each product and region. Further details about the determination of the direct water consumption used to build the water satellite account can be found in Ahams et al. (2017).

3 Methods

3.1 Environmental Multiregional Input–Output Model

To build the E-MRIO model, we start with the basic multiregional input–output relationship (Isard, 1951; Leontief et al., 1953; Moses, 1955)

(1)

where X, A, and Y are the block matrices representing regional gross domestic output (production), direct requirements, and exogenous final demand for products, respectively, in a total number of R U.S. regions, each region capable of producing P number of products. The total number of products m in the economy is then R × P. In this case, R = 115, P = 41, and m = 4,715.

Equation 1 captures all the domestic interregional and intersectoral product flows among the R regions and P different products comprising the U.S. economy. X consists of R column vectors, each vector defined by with being the output (production) of product i in region r to meet (final and intermediate) demand in region s. The m × 1 column vector of total production from region r is x_r = X1 with . denotes the total output of product i in region r, and 1 is an appropriately sized, m × 1 in this case, column vector of 1 s. is the regional direct requirements matrix representing the inputs as a share of the total outputs. is the direct requirement representing the amount of input i from region r necessary per monetary unit of product j produced in region s. Y is the final demand matrix consisting of R column vectors, with each vector given by , where is the final demand in region s of product i produced in region r.

Solving for X in equation 1, one obtains

(2)

where I ∈ ℝ^m × m is the identity matrix and (I − A)⁻¹ is the Leontief inverse. Letting (I − A)⁻¹ be equal to L, we can write

(3)

The Leontief inverse contains, through , the total output of product i in region r directly or indirectly incorporated into the final demand of product j in region s accounting for the full supply chain, that is, accounting for all the regions and products involved in the production process (Miller & Blair, 2009).

To account for the water embodied in the consumption of products by a region, we extend the model in equation 3 using the water satellite account . ω (m³) is a column vector that denotes the direct water consumption associated with the production of domestic products; (m³) is then the direct water consumption of product i in region r. The direct water intensities [m³/USD] (hereafter water intensities) are computed using

(4)

, where (m³/USD) is the water intensity of a product defined as the direct water consumption per unit value of output product i in region r, and is the inverse matrix of the diagonalized total production vector x_r. The water intensity is associated with the production of product i in region r regardless of the destination and type of demander (intermediate or final). For instance, if a region r consumes 1 m³ of locally sourced water for each USD of production of product i, the water intensity is 1 m³/USD independently of whether the water is consumed to meet intermediate or final demand. In the case of industrialized products, which receive primary inputs from other sectors and regions (upstream steps in the supply chain), the water intensity represents the local water directly consumed in region r to transform the raw inputs into the equivalent of 1 USD of output i.

Letting W be equal to the diagonalized vector w, , and the diagonalized vector of total final demand, the virtual water flows are determined as follows:

(5)

such that quantifies the water needed to produce product i in region r, which is in turn directly or indirectly (virtually) used to meet final demand for product j in region s. The matrix WL provides similar information to Q but in the form of water coefficients. The column sums of WL are the total water consumption coefficients, that is, the Leontief multipliers of water consumption (hereafter water multipliers). These multipliers represent the water required to produce all the inputs or products i from different regions needed to directly or indirectly meet final demand for product j in region s. The water multipliers (m³/USD) represent the direct and indirect water accumulated throughout the full supply chain and embodied in the consumption of a product by a final user. A hypothetical example of water multipliers follows below.

Let us assume that product 1 is required to produce product 2, and product 2 is required to produce product 3. Product 3 is also an input to itself. Further, assume that 0.1 USD of product 1 from region A is indirectly needed, while 0.2 USD of product 2 from region B and 0.01 USD of product 3 from region C are directly needed, to produce 1 USD of product 3 in region C. Lastly, suppose that product 3 is consumed in region C as final demand. Letting the water intensities of products 1, 2, and 3 be equal to 10, 5, and 1 m³/USD, respectively, the water multiplier of product 3 in region C would be (0.1 × 10) + (0.2 × 5) + (0.01 × 1) = 2.01 m³/USD. If the final demand for product 3 in region C is 100 USD, the total virtual water consumption would be 201 m³ (2.01 m³/USD × 100 USD).

3.2 Interpretation of the Environmental Multiregional Input–Output Model

The E-MRIO model in equation 5 says that the consumption of products represented by the final demand Y drives the consumption of water within and outside a region's boundary. Ultimately, the final demand Y, together with the water intensities W of the producing sectors, determine the geography or spatial patterns of virtual water flows through complex supply chains captured by L. To implement the model in equation 5, the final demand Y is set equal to the household consumption obtained by disaggregating the national-level household consumption. W is determined from the water satellite account. The direct requirement matrix A is obtained by regionalizing the national input–output make and use tables using the subnational FAF4 commodity flow data. The mathematics of the regionalization approach used to determine A are described in detail in Text S1 in the supporting information.

We illustrate the flows captured by the E-MRIO model using a hypothetical example consisting of a three-region and three-sector economy (Figure 2). In Figure 2, arrow 1 shows an intermediate demand flow from agriculture to industry within region A, that is, an intraregional flow. This flow corresponds to a single transaction in the matrix A in equation 1. Arrow 2 shows another intermediate demand flow but this time the flow crosses from region A to B (interregional flow), and from agriculture to industry (intersectoral flow). This flow corresponds to another single transaction in A. Arrow 3 illustrates a final demand flow from region B to C (Figure 2), where some of the industrial production in region B is consumed by households in region C. Final demand flows are represented in the E-MRIO model by the matrix Y. Lastly, arrow 4 represents a total demand or virtual water flow from region A to C. This flow captures the total amount of water accumulated through the supply chain formed by arrows 2 and 3 linking agricultural products in region A and household consumption in region C. These flows are represented in the E-MRIO model through the matrix Q in equation 5.

Figure 2

Illustration of the E-MRIO model using a three-region and three-sector economy. The regions are labeled A, B, and C. The sectors are agriculture, industry, and services. Arrows 1 and 2 represent intermediate demand flows, arrow 3 a final demand flow, and arrow 4 a total demand or virtual water flow.

3.3 Analysis of Virtual Water Flows

We use equation 5 to quantify and analyze blue virtual water flows within CONUS. Specifically, the virtual water flows are used to compute water footprints of production and consumption representing the producer and consumer perspective, respectively. Since we only account for the blue water contribution, the term water footprint hereafter refers to blue water.

Using the E-MRIO model, the water footprint of production is calculated as follows:

(6)

, (m³) is the water footprint of production of product i in region r, and the total water footprint of production of region r is then . p^r measures the direct blue water consumed in the total production of products in region r.

The water footprint of consumption is calculated using

(7)

, (m³) is the water footprint of consumption of product j in region s, and the total water footprint of consumption of region s is then . c^s measures the water indirectly consumed in region s through the consumption of products. This definition of the water footprint of consumption differs from that of the Water Footprint Network (Hoekstra et al., 2011) since we include in c^s the water indirectly consumed through products produced within the region. In addition, to remove the effect of region size on p^r and c^s, they are divided by the population of r and s, respectively. The net water footprint of region r, η^r (m³), is then given by

(8)

To assess whether some regions have a disproportionate impact on national water use, the inequality of the water footprints is calculated using the Gini coefficient G (Ahams et al., 2017; Seekell et al., 2011),

(9)

where F(b) is the cumulative distribution function of the random variable b and μ_b is the expected value of b. The inequality of the water footprints is computed by setting b = p^r or c^s. G ranges from 0 to 1, with 1 indicating maximum inequality. To visualize G, the Lorenz curve is used (i.e., a plot of F (p^r) or F (c^s) against the cumulative number of regions), where increased deviation from the 1:1 line of perfect equality indicates greater inequality.

To identify hot spot regions and products of virtual water, backward and forward economic linkages are analyzed (Hirschman, 1958; Rasmussen, 1956). The linkages are estimated using the sensitivity of dispersion, φ, and power of dispersion, β, indices (Drejer, 2002; Hazari, 1970; Lenzen, 2003; Sonis et al., 2000; Yu et al., 2010). The sensitivity of dispersion of product i in region r is used to measure the forward linkages. measures the increase in water consumption associated with product i driven by a unit increase in the final demand of all products in the economy.

Letting Λ = WL, where and is the water embodied in the supply chain flow of product i in region r to meet final demand for product j in region s, the sensitivity of dispersion is given by

(10)

quantifies the ability of other regions and products to draw virtual water from product i in region r. The sensitivity of dispersion for a given region or product is calculated as and , respectively. The sensitivity of dispersion is considered low when φ_i < 1 or φ^r < 1 since the value is less than the average sensitivity for the entire economic system, and high when φ_i > 1 or φ^r > 1.

The power of dispersion of sector j in region s is used to measure the backward linkages. measures the total increase in virtual water from the entire economic system of interrelated sectors and regions needed to cope with an unit increase in the final demand of product j. The power of dispersion is calculated using

(11)

quantifies the ability of product j in region s to draw virtual water from other regions and products. The power of dispersion for a given region or product is calculated as and , respectively. For β_j < 1 or β^s < 1, the power of dispersion is considered low since it is less than the expected value for the entire economic system, and vice versa for β_j > 1 or β^s > 1.

4 Results

4.1 Mass Balance Consistency Checks for the E-MRIO Model

Prior to analyzing the virtual water flows, we assess the E-MRIO model by performing the following five different mass-balance consistency checks: (i) the row sums in the regional use matrix should be equal to the corresponding FAF4 outflows; (ii) the column sums in the regional make matrix should be equal to the corresponding FAF4 inflows; (iii) the row sums in the total requirements matrix should be equal to the corresponding FAF4 outflows; (iv) the row sums of the matrix Q should be equal to the water consumed in production obtained by multiplying the corresponding FAF4 flows by the water intensities w; and, finally, (v) the total water consumed in production summed across all products and regions should be equal to the total virtual water of consumption summed across all products and regions. All of these consistency checks were positively corroborated (i.e., the equality required by each consistency check was satisfied), indicating that the E-MRIO model is balanced and suitable for analyzing virtual water flows. In addition, the last consistency check demonstrates that double counting is not occurring because the total volume of water consumed in production is the same as the total volume for the virtual water of consumption.

4.2 Producer Perspective

Using p^r to quantify the producer perspective, we find that regions, both cities and remainders of states, in the eastern United States have a relatively low p^r (Figure 3a), with an average of ~170 m³/yr/cap. As a point of reference, the national average is ~1,000 m³/yr/cap. By eastern United States, we mean the CONUS area east of the Mississippi River. The western regions tend overall to have high p^r values (Figure 3a), with the average being ~1,400 m³/yr/cap. A key reason for the higher p^r values in the western regions is due to the effect of crop irrigation on the water intensities of agricultural products. The warm summer and semiarid climate of most of the West make irrigation necessary for crop production. This increases the water intensity of crop production in the West, resulting in higher water footprints of production. Despite the overall higher p^r values of western regions, some of the cities in the West (e.g., Las Vegas and Austin) have relatively low p^r values compared to their surrounding regions (Figure 3a). These are cities that specialize in less water-intensive economic sectors than their surrounding areas. For instance, Austin's economy specializes in business services and high technology (U.S. Cluster Mapping, 2019). Figure S2 in the supporting information shows the location and name of each of the cities included in the E-MRIO model.

Figure 3

(a) Map of the U.S. water footprint of production (i.e., the blue water consumed in the total production of products by a region). (b) Lorenz curve for the water footprint of production of cities. (c) Share of the water footprint of production associated with self-consumption (lighter colors) and trade (darker colors) for two major product groups: agricultural products and manufactured food. Self-consumption is the blue water consumed by a city in production to meet internal economic demand, and trade is blue water consumed by a city to meet demand elsewhere.

For cities, the range of p^r is from ~9 to 11,400 m³/yr/cap, with only 7 cities having p^r values higher than ~3,000 m³/yr/cap. Nonetheless, these 7 cities account for ~35% of the total national p^r while the lowest 33 cities account for only ~1%. This inequality results in a high G of 0.7 for p^r (Figure 3b). Thus, a few cities with high p^r have disproportionately greater influence on blue water resources than the remainder cities. The source of this inequality are cities whose metropolitan areas include relatively large swaths of irrigated cropland. For example, the metropolitan areas of both Fresno and Sacramento include parts of California's Central Valley, which is the most agriculturally productive U.S. region (USDA, 2019). Fresno and Sacramento are both among the top cities with the highest water footprint of production (Figure S3 in the supporting information).

To better understand how blue water is consumed within cities, we decompose p^r into self-consumption and trade, and group products into four main groups: agricultural products, manufactured food, industrial products, and services (Figure 3c). Table S1 in the supporting information provides a detailed list of the products included in each group. The industrial products and service groups are not visible in Figure 3c because they account for <1% of p^r in any city.

We find that trade accounts for ~26% of the total p^r from all cities (Figure 3c). Cities that trade a high share of the p^r associated with manufactured food (e.g., Columbus, Cincinnati, Salt Lake City, and Washington DC) are food processing and manufacturing hubs (U.S. Cluster Mapping, 2019). These hubs are captured by our E-MRIO model (Figure 3c). Most of the cities (60 out of the 69) retain more than 50% of p^r for self-consumption, indicating that cities tend to satisfy local demand before trading with other regions. Most of the urban blue water used in production for both self-consumption and trade, ~55%, is destined to agricultural products (live animals, cereal grains, fruits and vegetables, and animal feed). Manufactured foods (prepared food, meat, milled grains, and beverages) account for ~44% of the total p^r. The share of p^r associated with agricultural products and manufactured food varies among cities. Cities with high water intensities for agricultural products tend to have a higher share of their total p^r going into this group. For example, this is the case with the cities of Laredo, Austin, and Corpus Christi in Texas and with Fresno and Sacramento in California (Figure 3c). However, the most industrialized city in Texas, Dallas, has a higher share of p^r destined to manufactured food.

4.3 Consumer Perspective

The regions with a high p^r (Figure 3a) tend to have a high c^s (Figure 4a). For our 69 cities, we find that the correlation coefficient between p^r and c^s is ~0.95. This suggests that cities tend to consume the water-intensive products they produce. Thus, if a city produces staple products (i.e., basic food-related products) with higher water intensity than the national average, and since staple products tend to dominate the value of c^s, its c^s value will likely be higher than the national average. The values of c^s for cities, however, are generally smaller and have a narrower range than those of p^r. The range of c^s is from ~64 to 7,400 m³/yr/cap (Figure 4a) and G = 0.5 (Figure 4b). Since G is less for c^s than p^r, this means that virtual water is transferred from western U.S. regions to eastern cities as final demand. For example, the eastern cities have a maximum c^s of ~1,750 m³/yr/cap while a maximum p^r of ~750 m³/yr/cap. This transfer of virtual water from West to East is also visible in the p^r and c^s maps. The c^s map (Figure 4a) shows water footprint values that are more spatially dispersed than the p^s map (Figure 3a).

Figure 4

(a) Map of the U.S. water footprint of consumption (i.e., the blue water indirectly consumed as final demand by a region through products). (b) Lorenz curve for the water footprint of consumption of cities. (c) Share of the water footprint of consumption associated with self-consumption (lighter colors) and trade (darker colors) for four major product groups: agricultural products, manufactured food, industrial products, and services. Self-consumption is the virtual water consumed by a city through products produced in the city and trade is virtual water consumed through traded products from outside the city.

In terms of the separation of c^s into self-consumption and trade, the latter accounts for ~34% of the total c^s from all cities. The cities with the highest c^s tend to have a lower dependence on trade, that is, Houston and Salt Lake City (Figure 4c). In fact, the 10 cities with the highest c^s (Figure S3) account for ~39% of the total national c^s, out of which only 20% is attributed to trade. These cities rely heavily on self-consumption to meet final demand. The share of c^s associated with agricultural products and manufactured food accounts for the majority, ~96%, of self-consumption. In terms of trade, the total c^s from all the cities is divided into ~62% manufactured food and agricultural products that are transformed within the city prior to consumption by final users, 7% (nontransformed) agricultural products, 12% industrial products, and 19% services. This means that the majority of the virtual water in cities is consumed through products that have supply chains with multiple steps rather than as primary products. It suggests that not accounting for product interdependencies could result in large truncation errors when calculating the c^s of U.S. cities.

To examine the truncation errors, the virtual water of consumption is estimated using the trade-alone approach (Figure 5), which is often utilized to estimate U.S. subnational virtual water flows (Ahams et al., 2017; Dang et al., 2015; Marston et al., 2015). For the trade-alone approach, the FAF4 commodity flows are simply multiplied by their corresponding water intensities (the intensity of the region where the flow originates) to obtain the virtual water flows (Ahams et al., 2017), thus ignoring all product interdependencies.

Figure 5

Comparison between the water footprints of consumption of cities obtained using the E-MRIO model and FAF4 commodity flows (trade-alone approach). The cities are ordered from West (left) to East (right) based on longitudinal location.

In comparison to our E-MRIO results, we find that the virtual water of consumption from the trade-alone approach can be 2 to 7 times higher for cities located near inland waterways and ports, such as St. Louis, Lake Charles, and New Orleans (Figure 5). In the trade-alone approach, by omitting the downstream supply chain of primary agricultural products (e.g., cereal grains), the consumption of virtual water is assigned to the immediate destination region of the agricultural flow. This is equivalent to assuming that the entire flow is used to meet final demand in the destination region and none is used to meet intermediate demand, which could allow for a portion of the flow to leave the destination region. In fact, for multiple products (e.g., cereal grains, basic chemical, and plastics/rubber), the national share of virtual water required by intermediate users is more than that of final users (Figure S4 in the supporting information). These products are used as input in the production of other products and circulate in the economy until they are demanded by final consumers. Therefore, by not representing intermediate users, the trade-alone approach can result in large truncation errors.

4.4 Comparison Between the Producer and Consumer Perspective

To compare the producer and consumer perspective, we use the net water footprint as well as the water intensities and multipliers. The net water footprint η^r shows that most cities (57 out of 69) are net importers (consumers) of blue virtual water (Figure 6). The highest net importer cities (i.e., negative n^r values in Figure 6) are Birmingham, Lake Charles, Memphis, and New Orleans. These are cities that meet indirect water demands by relying more on trade than self-consumption (e.g., they are located toward the left in Figure 4c) and tend to export less than 50% of their water footprint of production (Figure 3c). Thus, cities with high trade activity and high levels of self-consumption tend to be high net water importers. An exception is the city of Memphis, whose c^s value is indeed highly dependent on trade, ~97%, but the majority of its p^r is exported, ~70%. This is due to Memphis being a trade hub. It hosts the world's second busiest cargo airport, the country's fourth largest inland river port, and is served by three major U.S. highways (Memphis and Shelby County Regional Economic Development Plan, 2014). This unique role of Memphis is captured well by our E-MRIO model. It shows that the E-MRIO model is able to distinguish a city's unique trading pattern.

Figure 6

Net water footprint, η^r, of cities computed as the difference between the per capita water footprint of production and consumption.

Products have higher water multipliers, Λ_j, than water intensities, w_i (Table 1). This is because the water multipliers account for all the upstream contributions of the supply chain. Table 1 shows the values of Λ_j and w_i for selected products in Los Angeles and New York. These cities have the highest water footprint of consumption in the West and East, respectively. In both cities, the products with the highest water multipliers tend to have the highest water intensities, that is, milled grains and fruits and vegetables (Table 1). However, the water multipliers are higher in Los Angeles than New York. This is the case not only for agricultural products, whose water intensities can be directly influenced by the use of irrigation, but also for industrial products, even though the same national values are used for the water intensities of industrial products in both cities. This is due to product interdependencies that allow transferring virtual water from more water-intensive (agricultural) products to less water-intensive (industrial) ones. For instance, basic chemicals have a relatively high water multiplier in both cities (Table 1). The production of basic chemicals requires agricultural products as inputs (BEA, 2018). Since agricultural products are more water-intensive in Los Angeles than New York, it follows that basic chemicals tend to be more water intensive in Los Angeles. This could in part be influenced by the level of product aggregation in our E-MRIO model (Lenzen, 2011). Further disaggregating products could lessen these product interdependencies. This would require, however, having commodity flows that are more economically disaggregated than the FAF4 data. Assuming that such flows become available, our E-MRIO approach could still be used to obtain more disaggregated virtual water estimates.

Table 1. Comparison of the Producer and Consumer Perspective Using the Water Intensities and Water Multipliers for the Cities of Los Angeles and New York

	Los Angeles		New York City
Product	Water intensity (m^3/USD)	Water multiplier (m^3/USD)	Water intensity (m^3/USD)	Water multiplier (m^3/USD)
Live animals	2.62E−05	1.68E−01	2.62E−05	5.27E−02
Cereal grains	1.31E+00	1.40E+00	6.93E−03	4.01E−02
Fruits and vegetables	1.76E+00	1.80E+00	2.07E−01	2.21E−01
Animal feed	5.99E−04	3.39E−01	5.99E−04	5.20E−02
Meat	2.42E−04	2.33E−02	2.42E−04	6.06E−03
Milled grain products	5.56E+00	6.00E+00	2.68E−02	1.30E−01
Manufactured food	5.01E−04	2.76E−01	5.01E−04	7.80E−02
Alcoholic beverages	1.00E−05	1.92E−02	1.00E−05	4.99E−03
Tobacco products	1.20E−06	9.75E−01	1.20E−06	6.00E−02
Coal	1.00E−07	6.47E−03	1.00E−07	2.01E−03
Basic chemicals	6.20E−06	7.18E−02	6.20E−06	1.39E−02
Pharmaceuticals	1.02E−05	1.95E−03	1.02E−05	1.03E−03
Chemical products	4.80E−06	6.54E−03	4.80E−06	3.53E−03
Plastics/rubber	8.40E−06	7.32E−03	8.40E−06	5.19E−03
Newsprint/paper	3.30E−06	2.53E−02	3.30E−06	6.52E−03
Textiles/leather	5.30E−06	1.06E−02	5.30E−06	6.63E−03
Machinery	1.30E−05	1.36E−03	1.30E−05	9.70E−04
Electronics	4.20E−06	4.73E−04	4.20E−06	3.97E−04
Motorized vehicles	8.00E−07	1.30E−03	8.00E−07	1.10E−03
Precision instruments	5.44E−05	1.87E−03	5.44E−05	1.67E−03
Utilities	1.00E−05	5.85E−03	1.00E−05	1.23E−03
Transportation services	1.00E−05	3.70E−03	1.00E−05	1.01E−03
Accommodation and food services	1.00E−05	9.16E−02	1.00E−05	1.03E−03
Government	1.00E−05	1.95E−02	1.00E−05	3.41E−03

• Note. The list is for the 24 products with the highest water footprint of consumption.

Together with basic chemicals, the following products have a low water intensity but relatively high water multiplier in both cities: live animals, animal feed, manufactured food, tobacco products, and accommodation and food services (Table 1). These are products whose upstream supply chains include water-intensive products. Although milled grains and fruits and vegetables have the highest water multipliers in both cities, the ranking of water multipliers for other products differs between the two cities. In Los Angeles, the next four products with the highest water multipliers are cereal grains, tobacco products, animal feed, and manufactured food (Table 1), while in New York the ranking is manufactured food, tobacco products, live animals, and animal feed (Table 1). This information could be useful for designing consumption-based, water use management strategies that encourage consumers and firms to choose products that are less water-intensive. It shows that, for such strategies to be effective, different products might need to be targeted depending on a city's supply chain.

Furthermore, in both cities, industrialized products with more complex supply chains (i.e., supply chains that contain substantial inputs from multiple sectors) have lower water multipliers than their associated primary sectors. For example, manufactured food in Los Angeles has a water multiplier of 2.76 × 10⁻¹ m³/USD while the multiplier for fruits and vegetables is 1.80 m³/USD (Table 1). This is because the supply chain for manufactured food contains multiple supplying sectors that are less water intensive. Although the results in Table 1 are for the cities of Los Angeles and New York, similar water intensity and multiplier patterns are observed for the other cities.

4.5 Hot Spot Products and Regions of Virtual Water

The hot spot products with high sensitivity of dispersion (φ_i > 1) are milled grains, cereal grains, and fruits and vegetables (Figure 7a). Meat and animal feed have φ_i values that are less than 1 but higher than the values for more industrialized products (Figure 7a). φ_i is high for agricultural products with high water intensities as they are characterized by supply chains with strong downstream linkages to industrialized food sectors. That is, increases in the final demand for food products will draw large amounts of virtual water from the agricultural sectors. The products with high power of dispersion (β_j > 1) or with β_j close to 1 (e.g., basic chemicals, tobacco, paper, and textiles) show more product heterogeneity than the φ_i > 1 products (Figure 7a). These tend to be industrialized products whose upstream supply chains are substantially linked to the agricultural sectors, so that they are able to draw relatively large amounts of virtual water. However, these industrialized products have low φ_i values (e.g., φ_i≈0.25 for textiles) because their water intensities are low. Milled grains is the only hot spot product of virtual water that has both φ_i > 1 and β_j > 1 (Figure 7a). What makes milled grains stand out more than the other high-sensitivity products (e.g., cereal grains) is that its supply chain has strong linkages to both: products with high water intensities and high water multipliers. It is linked upstream to agricultural sectors and downstream to food manufacturing.

Figure 7

(a) Sensitivity of dispersion φ_i versus power of dispersion β_j for products. Only the 24 products with the highest water footprint of consumption are shown. (b) Hot spot regions determined by the intersection of both high sensitivity of dispersion (φ^r > 1) and high power of dispersion (β^s > 1). (c) Sensitivity of dispersion φ^r and (d) power of dispersion β^s for regions.

Based on the intersection of regions with both high sensitivity of dispersion (φ^r > 1) and high power of dispersion (β^s > 1), the hot spot regions of virtual water are in the West (Figure 7b), with the exception of Baton Rouge, New Orleans, St. Louis, the remainder of Georgia, and the state of Mississippi. The regions with the highest sensitivity of dispersion are the states or remainders of Nebraska, California, Arkansas, Texas, and Idaho (Figure 7c). For our 2012 base year, these are the five leading U.S. states in shares of irrigated acres; together they account for ~51% of the total irrigated acres in the United States (USDA, 2012). There are nine cities with high sensitivity of dispersion (Figure 7c). These cities are located in states that rely on irrigation (e.g., Sacramento and Houston) and likely to be exposed to water stress. They could be particularly vulnerable to competing water demands between agricultural and urban users (Flörke et al., 2018), as increases in final demand elsewhere will draw virtual water from them, potentially reducing their ability to meet direct water demands. Some cities have a low sensitivity of dispersion, , even though they are surrounded by regions with φ^r > 1 (e.g., Denver and Seattle in Figure 7c). This may be beneficial to these cites, as it suggests that other regions have a lesser ability to draw large volumes of virtual water from them, potentially ameliorating water competition.

The regions with high power dispersion are in the West (Figure 7d). This indicates that as demand increases for water-intensive products, western regions with high power of dispersion are likely to draw virtual water from neighboring regions. As economic activity intensifies in these western regions, all else being equal (e.g., technical coefficients, water intensities), water stress will likely exacerbate unless adjustments are made to the virtual water flow patterns. This is supported by findings based on complex network analysis which shows that U.S. virtual water flows have a regional structure (Garcia & Mejia, 2019); that is, the density of flows within U.S. regions (e.g., the Southwest or Northeast) is greater than between regions.

5 Discussion

The novelties of our E-MRIO model consist of integrating the FAF4 database of interregional commodity flows with U.S. national input–output accounts, including major U.S. cities, and accounting for virtual water flows into the service sectors. In addition, there are benefits to the way our E-MRIO model is built. To obtain the regional direct requirement matrix A, we adjust the national make and use matrices rather than directly adjusting the national, product-by-product, direct requirements. This avoids having to iteratively rebalance A, which can be an important source of discrepancies (Marto-Sargento, 2009). The utilization of make and use matrices also enhances the interface with available data (Guo et al., 2002). This could be useful in the future when trying to incorporate improved data sets, that is, commodity flows with higher sectoral resolution.

We highlight three different policy and research implications from our results. First, it is increasingly recognized that sustainable urban water management needs to consider both direct and indirect water uses (Renouf & Kenway, 2017). For cities to manage indirect water use efficiently, they need performance and sustainability indicators (e.g., environmental footprints) that can be reliably tracked and benchmarked (Hoff et al., 2014). E-MRIO analysis provides a consistent framework for computing different environmental footprints. Using the E-MRIO model, we have demonstrated the estimation of urban water footprints. This information could be valuable to cities as they begin to pay more attention to their virtual water supplies.

Second, the reduction of food losses and waste has been identified as an important global sustainability goal (FAO, 2011). Our E-MRIO analysis shows that the manufactured food sector has the ability to draw substantial virtual water across U.S. regions. By reducing losses along the food manufacturing supply chain and/or altering manufacturing processes, virtual water flows could be decreased, potentially leading to water savings. Such water savings could be significant in the United States, given that food losses and waste are estimated to be ~30% (Buzby et al., 2014). By allowing the explicit delineation of supply chains, that is, through structural path analysis (Lenzen, 2003), MRIO models are particularly well-suited to identify regions and sectors to target reduction strategies for food losses.

Third, E-MRIO models facilitate linking supply chains to satellite accounts for water-related pollutants, that is, nitrogen and phosphorus. Nutrient pollution is a major and persistent water quality problem in the United States (Shortle & Horan, 2017). Our E-MRIO model could be combined with data sets for subnational nutrient emissions to determine spatially explicit U.S. nutrient footprints (Cazcarro et al., 2016; Moran & Kanemoto, 2016; Sun et al., 2019). These could serve to better inform U.S. consumers and firms about the water quality sustainability of their consumption decisions, helping to engage multiple actors and stakeholders in nutrient pollution management.

The three different sustainability goals previously mentioned—managing virtual water supplies, reducing food losses and waste, and tracking indirect nutrient pollution—could be further integrated using a circular economy approach (Ellen MacArthur Foundation, 2019; Kalmykova et al., 2018). This would allow exploring resource recovery and reuse scenarios for cities. For different embodied resources, E-MRIO could be used to identify key feedback loops between regions and sectors for prioritizing the exploration of circular approaches.

There are limitations to our E-MRIO model, which offer opportunities for expanding in the future the analysis performed along several directions. One possible direction is to use error propagation to assess the effect of different sources of uncertainty on the water footprint estimates (Bachmann et al., 2015; Cazcarro et al., 2013; Lenzen et al., 2010). Three sources of errors are immediately relevant: water consumption coefficients, trade flows, and sectoral aggregation. In this case, errors in the water use coefficients for industrial sectors are large since there are less information available to determine them. However, since water intensities tend to be low for industrial sectors, they have a reduced effect on the accuracy of the water footprints. For instance, when implementing our E-MRIO model, we tried different consumption coefficients (5 and 20%) for the industrial water uses and found that they only had a minimal effect on the water footprints. Similarly, Sargento et al. (2012) tested the effect of trade flow errors on MRIO results and found that they tend to have a limited impact. Sectoral aggregation is likely the most dominant source of error and future efforts should be aimed at increasing sectoral resolution to reduce uncertainty (Cazcarro & Arto, 2019; Lenzen, 2011).

Another future direction is to improve virtual water estimates for the service sectors. The service sectors are treated as sinks in our E-MRIO model but future efforts could try to account for interregional service flows using modeling techniques. The challenge with this is that surveys for subnational service flows are rare, making it difficult to validate any model of service flows. Further, by coupling the E-MRIO model to an existing global E-MRIO database (Bachmann et al., 2015; Rodrigues et al., 2016), the model could be used in the future to link supply chains across spatial scales and explore the virtual water dependencies between specific U.S. regions and different countries. It was recently shown that affluence growth in developed countries tends to depend on foreign water resources (Soligno et al., 2019). It would be interesting to assess the degree to which different U.S. regions follow this pattern.

Lastly, the E-MRIO model could be applied over time to capture the temporal evolution of subnational virtual water flows. This would require, however, modeling commodity flows and interpolating input–output tables for years without data, since U.S. subnational data are only available in five-year increments. Overall, the E-MRIO model enhances subnational estimates of U.S. virtual water flows and serves as a consistent framework for performing in the future different analyses (e.g., structural path and decomposition analysis, feedback analysis, shock propagation) to gain deeper insight about indirect water interactions across spatial scales and sectors.

6 Conclusions

In this study, we build and implement an E-MRIO model to determine the direct and indirect water consumption of U.S. regions. The model is used to analyze virtual water flows by estimating and comparing urban water footprints, and identifying hot spot products and regions through backward and forward economic linkages. This is the first study to compute the water footprints of major U.S. cities while accounting for their full domestic supply chains. Using the E-MRIO model, we find that cities in the eastern United States have relatively low water footprints of production compared to western cities. The high water footprints of production in western cities are largely due to the effect of crop irrigation on the water intensities of agricultural products.

We find that cities with high water footprints of production tend also to have high water footprints of consumption. This is because of the dominance of agricultural products and manufactured food on virtual water flows and a tendency for virtual water to flow regionally. The differences, however, between the water footprints of consumption of eastern and western cities are less pronounced than in the water footprints of production. For instance, the inequality, measured using the Gini coefficient, is equal to 0.7 and 0.5 for the water footprints of production and consumption of cities, respectively. This, together with our water footprint maps, indicates that the supply chains redistribute virtual water toward the East from water-intensive agricultural products produced in the West.

The E-MRIO model captures the West-to-East U.S. redistribution of virtual water through the supply chain linkages between water-intensive agricultural products and industrialized food sectors. Since supply chain linkages are omitted in the trade-along approach, it cannot properly account for this redistribution effect. In the case of trade hub cities, such as St. Louis and New Orleans, the water footprint of consumption from the trade-alone approach can be 2 to 7 times higher than the values obtained with the E-MRIO model. Therefore, the trade-alone approach can lead to substantial truncation errors. A key contribution of our E-MRIO model is to enhance estimates of U.S. subnational virtual water flows compared to the trade-alone approach.

The analysis of forward and backward economic linkages, through the dispersion indices, highlights the role of western regions as sources of virtual water for the U.S. economy and their influence on the overall pattern of U.S. virtual water flows. The analysis also shows that industrialized and service sectors play a key role in dispersing virtual water across products and regions, reinforcing the need to account for the full supply chains of products when determining water footprints. This is even more so for cities since they are more opened to trade than countries.

Acknowledgments

We are thankful to the three anonymous reviewers for their thorough reviews which helped improve the original manuscript. This material is partially based upon work supported by the National Science Foundation (NSF) under grant ACI-1639529. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the view of the NSF. The data used in this study are all publicly available and are described and referenced in section 2. The modeled data are available through the HydroShare system of The Consortium of Universities for the Advancement of Hydrologic Science Inc. at http://www.hydroshare.org/resource/8059b9c24d2e4f1d8bd28d04758b007a.