Decomposition Analysis of Global Water Supply-Demand Balances Focusing on Food Production and Consumption

: Food production and consumption require large amounts of freshwater. There is no literature on the decomposition analysis of the intensities of water supply-demand balances (water balance intensities) for each country worldwide. The aim of this study is to evaluate the water balance intensities and elucidate the promoting factors and offset factors of water balance intensities for each country worldwide, focusing on food supply-demand balances and considering food trade balances on a global scale. The modiﬁed Laspeyres index method is applied to both a production-based water balance index ( WBI PB ) and a consumption-based water balance index ( WBI CB ). The major promoting factor for the WBI PB is the renewable freshwater resources, whereas the major offset factor is the produced item preference. The major promoting factor for the WBI CB is the consumed item preference, whereas the major offset factor is the producing area preference. Improving irrigation efﬁciencies of rice and cereals is effective because rice requires the largest blue water footprint intensities, considering irrigation efﬁciency on a calorie content basis in all of the items, whereas cereals are the largest share of calorie-based production quantities in all of the items worldwide. This study provides the foundation for decreasing water balance intensities regarding food production and consumption.


Introduction
Food production and consumption are essential for human life but require large amounts of freshwater. The agricultural sector consumes the largest amount of water (2658 km 3 /year), accounting for approximately 70% of the global total water withdrawal [1]. However, freshwater resources tend to be unevenly distributed in water-rich regions worldwide. It is said that the direct trade of freshwater resources between waterrich and water-poor regions is impossible due to the costs incurred in long-distance transportation [2]. Thus, trading food could be an important option for water-poor regions to compensate for their food shortage, which leads to an unintentional increase in freshwater requirements for food-producing regions.
The International Organization for Standardization introduced the concept of water footprint, which makes it possible to quantify the potential impact of water use and pollution based on the idea of a life cycle assessment [3]. Most goods and services are consumed by households, businesses, and offices at the final demand stages and finally arrive at the end-of-life stages via raw material, processing, distribution, and retail sale stages. The water requirements of goods and services are estimated by summarizing the water consumption for all stages. The Water Footprint Network proposed three types of water footprint: green, blue, and gray [4]. Green water originates from precipitation, does consuming country i. Raw data of each category are used after calculating the three-year average from 2009 to 2011 to employ as the yearly reference data for each category. Here, IQ ijk and EQ ijk are taken from the food trade balance matrices for each item, which were calculated in our previous study [25]. Before calculating IQ cj and EQ cj , each component of the food trade balance matrices is adjusted by using the RAS method [26] to match the sum of import quantities with that of export quantities for each food item on a global scale.
In the commodity balance sheets of the Food and Agriculture Organization Corporate Statistical Database (FAOSTAT), DSQ cj is the sum of six consumption categories: feed, processed materials, losses, food supply quantities, seeds, and other uses [27]. In this study, feed and processed materials are considered as intermediate demands, whereas food supply quantities and losses are classified into final demands and composed of food consumption. Losses are interpreted as losses caused during storage or technical losses caused when transforming the primary commodities into processed products, excluding losses occurring during the pre-harvest and harvesting stages and deriving from edible or inedible waste in the household [27]. Seeds are the amounts of the commodity used for reproductive purposes, such as seed of sugarcane plant, hatching eggs, and fish bait [27]. Other uses include the amounts of the commodity mainly consumed by tourists and used for manufacturing in non-food purposes such as oil for soap [27].

Production-Based and Consumption-Based Blue Water Requirements
In this study, only blue water is targeted. Surface and ground water play a role of a supply source of blue (irrigation) water to supplement the shortage of green water (rainwater). From this viewpoint, focusing on blue water requirements is suitable to simulate water balance intensities. Thus, green water is excluded from the evaluation target. The blue water requirement is calculated in two manners: a blue water requirement on a production basis and a consumption basis (WR PB and WR CB , respectively) defined as follows: where superscripts PB and CB represent production-based simulation and consumptionbased simulation, respectively. WR PB kj is the WR PB , PRO kj is the production quantity, WFI kj is the water footprint intensity, and IRE kj is the irrigation efficiency of item j for producing country k. In Equation (3), WR CB ijk is the WR CB and COM ijk is the food consumption of item j between consuming country i and producing country k.
COM ijk is classified into two patterns based on the relationship between consuming country i and producing country k, namely, i = k and i = k: where PRO ij is the production quantity, SV ij is the amount of stock variation, FE ij is the amount of feed, PRC ij is the amount of processed materials, SE ij is the amount of seeds, and OU ij is the amount of other uses of item j for consuming country i. Here, (IQ ijk − EQ ijk ) is defined as the net trade quantity calculated by subtracting the export quantity from the import quantity for each country on a per capita basis. The net import and export quantities are defined as (IQ ijk − EQ ijk ) with IQ ijk ≥ EQ ijk and IQ ijk < EQ ijk , respectively. If IQ ijk ≥ EQ ijk , the water footprint intensity of production countries is applied to WFI ijk ; otherwise (IQ ijk < EQ ijk ), that of consumption countries is applied to WFI ijk . The irrigation efficiency is evaluated in the same way as the WR PB . For agricultural crops, only direct water consumption during the cultivation stage is included. For livestock products, direct water consumption during the rearing stage of livestock, such as drinking water and service water to maintain a rearing environment, and feed crops for livestock during the cultivation stage are included. These stages consist of a system boundary for water footprint simulation. Here, the aforementioned types of water consumption are originally included in the water footprint intensities. The intermediate demand composed of feed and processed materials is excluded from our simulation because an overestimation could be caused by a double counting of the water footprint. Thus, the final demand, composed of food supply quantities and losses, is targeted. In addition, seeds and other uses are excluded from the simulation because seeds are considered as a type of upstream indirect water consumption during the cultivation stage for each agricultural crop, and other uses are not inconsistent in the system boundary. Thus, feed, processed materials, seed, and other uses are subtracted from the sum of production quantities and the amount of stock variation in the Equation (4).
WFI kj and IRE kj mainly refer to the literature values (Refs. [28,29], respectively) of item j for the producing country or for area k. Missing data on WFI kj are replaced with the water footprint intensities of neighboring countries for each item, simple average values of 23 regions for each item, calculated using the literature values for the applicable countries, or literature values of the world average for each item [28]. IRE kj for rice is uniformly set as 1.0, whereas IRE kj for non-rice items is set as the irrigation efficiency of non-rice items for each region. IRE kj of Middle Africa and North America are set as irrigation efficiencies on a simple regional average for each applicable area. To avoid overestimation due to transit trades, the exported blue water footprint intensity of item j for consuming country i on a weighted average is defined. The weights are the production and net import quantities of item j for producing country k.

Production-Based and Consumption-Based Water Balances Indices
In this study, water balance intensities are evaluated by using two water balance indices: a production-based water balance index (WBI PB ) and a consumption-based water balance index (WBI CB ). The former can evaluate water balance intensities based on production by assigning water requirements to producing countries, whereas the latter can evaluate water balance intensities based on consumption by assigning water requirements to consuming countries. Consumption is roughly calculated by adding production and subtracting exports from imports. Based on a comparison between the two indices, it is expected that the difference in water balance intensities between the production and consumption sides can be quantitatively evaluated.
The WBI PB and WBI CB are defined as follows: where WBI PB k is the WBI PB of producing country k, and WBI CB i is the WBI CB of consuming country i. TRWR k and TRWR i are the total renewable water resources (TRWR's) of producing country k and consuming country i, respectively. AWW k and AWW i are the agricultural water withdrawal (AWW) of producing country k and consuming country i, respectively. TWW k and TWW i are the total water withdrawal (TWW) of producing country k and consuming country i, respectively. For the TRWR's, AWW, and TWW, missing data are replaced with data from the nearest period of the reference year (2010). Countries with no data for the nearest period are excluded from the target countries of this study.
WBI PB k and WBI CB i are evaluated in terms of five intensity categories as follows: very low intensity (WBI < 0.1), low intensity (0.1 ≤ WBI < 0.2), moderate intensity (0.2 ≤ WBI < 0.4), high intensity (0.4 ≤ WBI < 0.8), and very high intensity (WBI ≥ 0.8). The five intensity categories of both indices follow those of the water stress index in a previous study [30].

Decomposed Factors of Production-Based Water Balance Index
To conduct a decomposition analysis, the difference in the WBI PB between each country's value and the standard value is defined as follows: where subscript zero represents the standard value. ∆WBI PB k is the difference in the WBI PB for producing country k, and WBI PB 0k is the standard value of the WBI PB for producing country k. ∆WBI PB kjn (n = 1, 2, 3, 4, 5, where n is the number of factors) is the decomposed factor of item j for producing country k. Each factor is defined as follows: ∆WBI PB kj1 is a renewable freshwater resources factor (∆F1_PB); ∆WBI PB kj2 is an industrial structure factor (∆F2_PB); ∆WBI PB kj3 is a production scale factor (∆F3_PB); ∆WBI PB kj4 is a produced item preference factor (∆F4_PB); and ∆WBI PB kj5 is a water footprint intensity factor (∆F5_PB). If ∆WBI PB kjn ≥ 0, this factor is seen as a promoting factor for water balance intensities (promoting factor); otherwise (∆WBI PB kjn < 0), this factor is seen as offset for water balance intensities (offset factor).
WBI PB k is decomposed into five factors as follows: where superscript CAL indicates a calorie-based conversion. PRO CAL k is the calorie-based production quantity of producing country k, PRO CAL kj is the calorie-based production quantity of item j for producing country k, and UCF j is the calorie conversion factor of item j. In Equations (9) and (10), all of the right terms except for the third term of Equation (10) are calculated on a per capita basis. Each term in both equations is interpreted as follows: (1/TRWR k ) is the multiplicative number of the TRWR's related to ∆F1_PB; (TWW k /AWW k ) is the multiplicative inverse of the ratio of AWW to TWW (agricultural withdrawal rate) related to ∆F2_PB; PRO CAL k is the calorie-based production quantity related to ∆F3_PB; (PRO CAL kj /PRO CAL k ) is the produced item's share related to ∆F4_PB; and (WFI kj /UCF j /IRE kj ) is the water footprint intensity per calorie content considering the irrigation efficiency related to ∆F5_PB.
Calorie conversion factors for 11 items ("Cereals, Other", "Roots, Other", "Sweeteners, Others", "Pluses, Other and products", "Oilcrops, Other", "Oilcrops Oil, Other", "Vegetables, Other", "Citrus, Other", "Fruits, Other", "Spices, Other", and "Meat, Other" in the FAOSTAT) are set as a median of calorie conversion factors for each applicable item. Calorie conversion factors for meats are set as a weighted average of the calorie conversion factor whose weight is the amount of distribution for each applicable meat. The meat distribution is calculated by multiplying the amount of distribution by cuts of meat by the population of Japan. The calorie conversion factors for mutton and goat meat are calculated by the calorie conversion factor for lamb meat by cuts of a part on a simple average due to the lack of data on the amount of distribution for both items.

WBI PB
0k is calculated as follows: where TRWR 0 is the standard value of TRWR's and calculated by dividing the sum of TRWR's for all countries based on the FAO's Global Information System on Water and Agriculture (AQUASTAT) by the global population. AWW 0 is the standard value of AWW and calculated by dividing the sum of AWW's for all countries based on the AQUASTAT by the global population. TWW 0 is the standard value of TWW and calculated by dividing the sum of the TWW's for all countries based on the AQUASTAT by the global population. PRO CAL 0 and PRO CAL 0jk are the standard values of the calorie-based production quantities and that of item j for producing country k, respectively. The former is calculated by adding the calorie-based production quantities for all countries by the global population, whereas the latter is calculated by that of item j for all countries. WFI 0j refers to the literature values [28]. IRE 0j is the irrigation efficiency on a simple world average and calculated using the literature values for all areas [29]. Here, the correction factor is defined as the ratio of the global population of ∆F3_PB to that of ∆F1_PB, which is multiplied by ∆F1_PB to correct the error of ∆F1_PB. This error could result from the difference in the global population of ∆F1_PB and that of ∆F3_PB. The global population of ∆F4_PB is equal to that of ∆F3_PB. Finally, nearly 70% of all WBI PB 0k exist at 0.079 ± 0.033.

Decomposition Factors of Consumption-Based Water Balance Index
To conduct a decomposition analysis, the difference in the WBI CB for each country's value and the standard value is defined as follows: where ∆WBI CB i is the difference in the WBI CB for consuming country i and WBI CB 0k is the standard value of the WBI CB for producing country k. ∆WBI CB ijkn (n = 1, 2, 3, 4, 5, 6) are six decomposed factors of item j between consuming country i and producing country k. Each factor is defined as follows: ∆WBI CB ijk1 is a renewable freshwater resources factor (∆F1_CB); ∆WBI CB ijk2 is an industrial structure factor (∆F2_CB); ∆WBI CB ijk3 is a consumption scale factor (∆F3_CB); ∆WBI CB ijk4 is a consumed item preference factor (∆F4_CB); ∆WBI CB ijk5 is a producing area preference factor (∆F5_CB); and ∆WBI CB ijk6 is a water footprint intensity factor (∆F6_CB). If ∆WBI CB ijkn ≥ 0, this factor is seen as a promoting factor; otherwise (∆WBI CB ijkn < 0), it is seen as an offset factor. WBI CB i is decomposed into six factors as follows: where COM CAL i is the amount of calorie-based consumption of consuming country i, COM CAL ij is the amount of calorie-based consumption of item j for consuming country i, and COM CAL ijk is the amount of calorie-based consumption of item j between consuming country i and producing country k. In Equations (14) and (15), all of the right terms except for the fourth term of Equation (15) are calculated on a per capita basis. Each factor Sustainability 2021, 13, 7586 7 of 32 term in Equations (14) and (15) is interpreted as follows: (1/TRWR i ) is the multiplicative inverse of the TRWR's related to ∆F1_CB; (TWW i /AWW i ) is the multiplicative inverse of the agricultural withdrawal rate related to ∆F2_CB; COM CAL i is the calorie-based food consumption related to ∆F3_CB; (COM CAL ij /COM CAL i ) is the consumed item's share related to ∆F4_CB; (COM CAL ijk /COM CAL ij ) is the producing country's share related to ∆F5_CB; and (WFI kj /UCF j /IRE kj ) is the water footprint intensity per calorie content considering the irrigation efficiency related to ∆F6_CB.
WBI CB 0i is calculated as follows: where TRWR 0 , AWW 0 , and TWW 0 are calculated in the same manner as in the aforementioned WBI PB simulation. COM CAL 0 is the standard value of calorie-based consumption and calculated by adding the calorie-based consumption for all countries by the global population. COM CAL 0j and COM CAL 0jk are the standard values of the calorie-based consumption of item j and that of item j for consuming country k, respectively. The former is calculated by adding the calorie-based consumption of item j for all countries by the global population, whereas the latter is calculated by that of item j for producing country k.
Here, the error of ∆F1_CB is calculated in the same way as in the aforementioned WBI PB simulation. The global population of ∆F4_CB or ∆F5_CB is equal to that of ∆F3_CB. Finally, nearly 70% of all WBI CB 0i exist at 0.086 ± 0.0015.

Complete Decomposition Analysis
In this study, the MLI method [14,15] is applied to both the WBI PB and WBI CB to consider the residual terms for calculating contribution factors. If the factors of positive change and those of negative change are simultaneously mixed in an interaction term, the interaction term is attributed to only the former term related to them. If an interaction term consists of factors of positive or negative change not simultaneously mixed with each other, the interaction term is attributed to their related factors.
In the case of the WBI CB , first, the MLI method is applied to ∆WR CB ijk = WR CB ijk − WR CB 0jk . Here, ∆WR CB ijk is decomposed into four factors (∆WR CB ijk1 , ∆WR CB ijk2 , ∆WR CB ijk3 , and ∆WR CB ijk4 ) and is equal to the sum of these four factors. Thus, ∆WR CB ijk1 is calculated as follows: Here, ∆x m and a m are defined as follows: where x m is the mth factor for the consuming country, item, and producing country (omitted respective subscripts i, j, and k), and x 0m is the standard value of the mth factor. The value of a m with ∆x m < 0 is set to zero as long as the total number of a m with an allocation coefficient of ∆x m < 0 is less than that of the denominator of the allocation factor. If all of the variables of ∆x m are negative values, each allocation coefficient is replaced with the difference between one and itself, and a m with ∆x m < 0 is not set to zero. For example, allocation coefficients {a 1 /(a 1 + a 2 )}, {a 1 /(a 1 + a 2 + a 3 )}, and {a 1 /(a 1 + a 2 + a 3 + a 4 )} are replaced with {1 − a 1 /(a 1 + a 2 )}, {1 − (1/2) × a 1 /(a 1 + a 2 + a 3 )}, and {1 − (1/3) × a 1 /(a 1 + a 2 + a 3 + a 4 )}, respectively. The same is true for ∆WR CB ijk2 to ∆WR CB ijk4 . It should be noted that each substitution formula of weight coefficients with over three a m is uniquely formulated by referring to the literature [14,15].
Second, ∆WBI CB ijk is decomposed into three factors (∆WBI CB ijk1 , ∆WBI CB ijk2 , and ∆WBI CB ijkWR ; ∆WBI CB ijkWR is a water requirement factor) as follows: ∆WBI CB ijkWR = y 01 y 02 ∆y WR Here, ∆y n and b n are defined as follows: ∆y n = y n − y 0n (n = 1, 2, WR) b n = ∆y n y n +y 0n 2 where y n is the nth factor (n = 1, 2) or factor of the WR CB (n = WR) for the consuming country, item, and producing country (omitted respective subscripts i, j, and k). y 0n is the standard value of the nth factor (n = 1, 2) or factor of the WR CB (n = WR). Each b n is calculated in the same way as in the aforementioned description. If all ∆y n are negative values, each allocation coefficient is replaced with the difference between one and itself, and b n when ∆y n < 0 is not set to zero. In Equation ( respectively. It should be noted that each substitution formula of weight coefficients composed of three b n is uniquely formulated by referring to the literature [14,15]. Finally, substituting ∆WR CB ijk for ∆y WR enables ∆WBI CB ijk to be decomposed into six factors (from ∆F1_CB to ∆F6_CB) by rearranging each term of Equations (21)-(23) to satisfy Equation (13).
In the case of the WBI PB , ∆WBI PB ijk is decomposed into five factors (from ∆F1_PB to ∆F5_PB) by changing from Equation (18) with four factors to an equation with three factors (the same form as Equation (21)) regarding ∆WBI PB ijk1 . The same is true for ∆WBI PB ijk2 and ∆WBI PB ijk3 . For both the WBI PB and WBI CB , the total number of samples is different for each country. The total numbers of samples for the WBI PB and WBI CB are shown in Tables A1 and A2 (Appendix A), respectively. In other words, some of the samples are excluded from the decomposition analysis targets when either their numerators or denominators are equal to zero.

Study Target and Usage Data
In this study, the target year is set to 2010 to use simulation data of import and export quantities obtained from our previous study [15]. In addition, 175 countries and 78 food items are targeted by referring to the commodity balance sheets of the FAOSTAT [31,32]. Only mainland China is embodied as China, and Hong Kong SAR, Macao SAR, and Taiwan Province are handled as trade partner countries. For the water supply-demand balances and decomposition analysis, 156 countries are targeted. Two countries (Maldives and Saint Vincent and the Grenadines) are excluded from both analyses because their AWW's are zero, and therefore, their WBI PB and WBI CB values diverge to positive infinity. In addition, Sustainability 2021, 13, 7586 9 of 32 17 countries are excluded due to the lack of data on any of the TRWR's, AWW's, and TWW's. However, these 19 countries only include the trade partner total of 156 nations.
For the food supply-demand balances, the production and domestic supply quantities for each country and item refer to the commodity balance table of the FAOSTAT [31,32]. The import and export quantities for each country and item refer to the commodity balance sheets [31,32] and the detailed trade matrix of the FAOSTAT [33]. For the WR PB and WR CB , the water footprint intensity and irrigation efficiency for each country and item are the literature values ( [28,29], respectively). For both the WBI PB and WBI CB , the TRWR's, AWW, and TWW for each country refer to AQUASTAT [34]. For the decomposition analysis, the calorie conversion factor mainly refers to the Standard Tables of Food Composition in Japan in the reference year [35], and missing data are replaced with that the data of 2015 [36]. The calorie conversion factors for items applied to the median refer to several statistical databases [35][36][37][38] and the literature value [39]. The amount of distribution by cuts of meat refers to the statistical data [40]. Population data are obtained from the demographic data of the FAOSTAT [41].

Comparing Production-Based and Consumption-Based Water Balance Indices
As shown in Figure 1a, 58 countries from the moderate to very high intensity regions based on the WBI PB tend to be distributed around the mid-latitude regions, such as arid regions, large population regions, and industrialized countries. In contrast, Figure 1b shows that 72 countries from the moderate to very high intensity regions based on the WBI CB tend to be concentrated in Northern Europe, Africa, Central Asia, Western Asia, and several island countries around Africa and the Caribbean region.
A comparison of the intensities between the WBI PB and WBI CB shows that the former is higher for 17 countries, whereas the latter is higher for 36 countries. In addition, 103 countries are approximately the same, including 40 countries from the moderate to very high intensity regions. For example, China's WBI PB is 0.49 and WBI CB is 0.38, and the United States of America's WBI PB is 0.20 and WBI CB 0.096. The intensities of the WBI PB can increase because of food production for export. In contrast, the United Kingdom has a WBI PB of 0.16 and WBI CB of 0.61, and South Africa has a WBI PB of 0.29 and WBI CB of 0.43. The intensities of the WBI CB tend to rise due to their food trade, and they can increase the water balance intensities of producing countries through their food imports. There are 98 countries in the very low or low intensity regions, 16 countries in the moderate intensity region, and 42 countries in the high or very high intensity regions. In the very low or low intensity regions, ∆F1_PB is the major promoting factor for 31 countries, followed by ∆F2_PB for 30 countries, and ∆F4_PB for 19 countries. In the moderate-intensity region, ∆F1_PB and ∆F2_PB are tied for six countries and are relatively large promoting factors, followed by ∆F4_PB and ∆F5_PB for two countries in a tie. In the high or very high intensity regions, 20 countries have ∆F1_PB as the major promoting factor, followed by ∆F5_PB for ten countries, and ∆F2_PB and ∆F4_PB for five countries in a tie. Note: WBI PB is the production-based water balance index, and WBI CB is the consumption-based water balance index. Each color represents as follows: "Red": very high intensity, "Orange": high intensity, "Yellow": moderate intensity, "Green": low intensity, "Blue": very low intensity, and "Gray" is excluded countries from both WBI PB and WBI CB analyses.

Comparing Decomposition of Production-Based and Consumption-Based Water Balance Indices
ΔF4_PB for five countries in a tie. Focusing on offset factors for WBI PB , ΔF4_PB is the major offset factor for 35 countries in the very low or low intensity regions, followed by ΔF1_PB for 33 countries, and ΔF3_PB for 14 countries. In the moderate-intensity region, six countries have ΔF4_PB as the major offset factor, followed by ΔF5_PB for five countries, and ΔF2_PB for the three countries. In the high or very high intensity regions, ten countries have ΔF3_PB as the major offset factors, followed by ΔF5_PB for nine countries, and ΔF2_PB and ΔF4_PB for eight countries in a tie.

Very low or low intensity regions (a)
Very low or low intensity regions (d) Moderate ΔF1_PB is the renewable freshwater resources factor, ΔF2_PB is the industrial structure factor, ΔF3_PB is the production scale factor, ΔF4_PB is the produced item preference factor, and ΔF5_PB is the water footprint intensity factor. Six factor for WBICB are defined as follows: ΔF1_CB is the renewable freshwater resources factor, ΔF2_CB is the industrial structure factor, ΔF3_CB is the consumption scale factor, ΔF4_CB is the consumed item preference factor, ΔF5_CB is the producing area preference factor, and ΔF6_CB is the water footprint intensity factor. Each factor of WBI PB (from ΔF1_PB to ΔF5_PB) and of WBI CB (from ΔF1_CB to ΔF6_CB) is aggregated by the summation of item j for each country and for each n. Vertical axis shows five (from ΔF1_PB_PRO to ΔF5_PB_PRO for WBI PB ) or six (from ΔF1_CB_PRO to ΔF6_CB_PRO for WBI CB ) promoting factors. Explanatory note shows five (from ΔF1_PB_OFF to ΔF5_PB_OFF for WBI PB ) or six (from ΔF1_CB_OFF to ΔF6_CB_OFF for WBI CB ) offset factors.
Figure 2d-f shows the number of countries based on the six promoting factors and six offset factors of the WBI CB . There are 84 countries in the very low or low intensity regions, 23 countries in the moderate intensity region, and 49 countries in the high or very high intensity regions. In the very low or low intensity regions, ΔF4_CB is the major promoting factor for 47 countries, followed by ΔF6_CB for 22 countries, and ΔF1_CB for 11 countries. In the moderate-intensity region, ΔF4_CB is the major promoting factor for and (c,f) in the high or very high intensity regions. Note: Five factors for WBI PB are defined as follows: ∆F1_PB is the renewable freshwater resources factor, ∆F2_PB is the industrial structure factor, ∆F3_PB is the production scale factor, ∆F4_PB is the produced item preference factor, and ∆F5_PB is the water footprint intensity factor. Six factor for WBICB are defined as follows: ∆F1_CB is the renewable freshwater resources factor, ∆F2_CB is the industrial structure factor, ∆F3_CB is the consumption scale factor, ∆F4_CB is the consumed item preference factor, ∆F5_CB is the producing area preference factor, and ∆F6_CB is the water footprint intensity factor. Each factor of WBI PB (from ∆F1_PB to ∆F5_PB) and of WBI CB (from ∆F1_CB to ∆F6_CB) is aggregated by the summation of item j for each country and for each n. Vertical axis shows five (from ∆F1_PB_PRO to ∆F5_PB_PRO for WBI PB ) or six (from ∆F1_CB_PRO to ∆F6_CB_PRO for WBI CB ) promoting factors. Explanatory note shows five (from ∆F1_PB_OFF to ∆F5_PB_OFF for WBI PB ) or six (from ∆F1_CB_OFF to ∆F6_CB_OFF for WBI CB ) offset factors.
Focusing on offset factors for WBI PB , ∆F4_PB is the major offset factor for 35 countries in the very low or low intensity regions, followed by ∆F1_PB for 33 countries, and ∆F3_PB for 14 countries. In the moderate-intensity region, six countries have ∆F4_PB as the major offset factor, followed by ∆F5_PB for five countries, and ∆F2_PB for the three countries. In the high or very high intensity regions, ten countries have ∆F3_PB as the major offset factors, followed by ∆F5_PB for nine countries, and ∆F2_PB and ∆F4_PB for eight countries in a tie. Figure 2d-f shows the number of countries based on the six promoting factors and six offset factors of the WBI CB . There are 84 countries in the very low or low intensity regions, 23 countries in the moderate intensity region, and 49 countries in the high or very high intensity regions. In the very low or low intensity regions, ∆F4_CB is the major promoting factor for 47 countries, followed by ∆F6_CB for 22 countries, and ∆F1_CB for 11 countries. In the moderate-intensity region, ∆F4_CB is the major promoting factor for 11 countries, followed by ∆F1_CB for six countries, and ∆F6_CB for four countries. In the high or very high intensity regions, ∆F4_CB is the major promoting factor for 20 countries, followed by ∆F1_CB for 14 countries, and ∆F5_CB for seven countries.
Focusing on offset factors for WBI CB in the very low or low intensity regions, ∆F5_CB is the major promoting factor for 80 countries, followed by ∆F4_CB for two countries, and ∆F1_CB and ∆F6_CB being equal for one country. In the moderate-intensity region, ∆F5_CB is the major offset factor for 19 countries, followed by ∆F2_CB, ∆F3_CB, ∆F4_CB, and ∆F6_CB being equal for one country. In the high or very high intensity regions, ∆F5_CB is the major offset factor for 34 countries, followed by ∆F1_CB and ∆F2_CB for five countries in a tie, and ∆F4_CB and ∆F6_CB for two countries in a tie.
In summary, based on WBI PB , the renewable freshwater resources factor (∆F1_PB) becomes the major promoting factor in the very low, low-, and high or very high-intensity regions while ∆F1_PB and ∆F2_PB are relatively large promoting factors in the moderateintensity region. The WBI PB is constrained by renewable freshwater resources and industrial structures rather than food production. The major offset factor for WBI PB is ∆F4_PB for countries in the very low-to moderate-intensity regions. The high or very high intensity regions have ∆F3_PB as the major offset factor for WBI PB . Changing high-calorie food into low-calorie food production is expected to lead to a decrease in the intensities of WBI PB . On the other hand, based on WBI CB , the consumed item preference factor (∆F4_CB) becomes the major promoting factor for all regions. The major offset factor for WBI CB is the producing area preference (∆F5_CB) for all regions. Although high-calorie food consumption increases the intensities of WBI CB , food imports from regions with lower water requirements decrease those of WBI CB . The intensities of WBI PB and WBI CB are determined by the balance of the degrees of contribution between the promoting and offset factors.
For example, China belongs to the high or very high intensity regions based on the WBI PB . As shown in Table A1, the major promoting factor is the renewable freshwater resources factor (∆F1_PB_PRO: 0.44), which is mainly offset by the water footprint intensity factor (∆F5_PB_OFF: −6.8 × 10 −2 ). Here, ∆F1_PB_PRO shows that ∆F1_PB is a promoting factor (a positive value), whereas ∆F5_PB_OFF shows that ∆F1_PB is an offset factor (a negative value). The respective interpretation rules are the same as below. This shows that the promoting effect on renewable water resources is offset by the production of items with relatively low water requirements per calorie content. This country is a high-intensity region of WBI PB according to Figure 1a; this is determined by adding ∆F1_PB to ∆F5_PB depending on the balance of degrees of contribution between the three promoting and two offset factors (Table A1). In contrast, this country belongs to the moderate-intensity region based on WBI CB . As shown in Table A2, the major promoting factor is the water footprint intensity factor (∆F6_CB_PRO: 3.4), which is mainly offset by the producing area preference factor (∆F5_CB_OFF: −3.4). This shows that the promoting effect on food production with high water requirements per calorie content is offset by food imports from regions with lower water requirements. China is a moderate-intensity region of WBI CB according to Figure 1b; this is determined by adding ∆F1_CB to ∆F6_CB depending on the balance of degrees of contribution between the four promoting and two offset factors (Table A2). In summary, the water balance intensity of WBI PB in China mainly increases because of the renewable freshwater resources factor and is mainly offset by the water footprint intensity factor. On the other hand, the intensities of WBI CB mainly increase because of the producing area preference factor and is offset by the producing area preference factor.
As another example, the United States of America belongs to the moderate-intensity region based on their WBI PB . As shown in Table A1, the major promoting factor is the industrial structure factor (∆F2_PB_PRO: 8.5 × 10 −2 ), which is mainly offset by the water footprint intensity (∆F5_PB_OFF: −3.0 × 10 −2 ). This occurs because the AWW per capita (282 m 3 /capita) is less than the IWW per capita (101 m 3 /capita). This effect is mainly offset by the consumption of items with relatively low water requirements per calorie content. The United States of America is a moderate-intensity region of WBI PB according to Figure 1a, which is determined by adding ∆F1_PB to ∆F5_PB depending on the balance of degrees of contribution between the two promoting and three offset factors (Table A1). In contrast, this country belongs to the very low or low intensity regions based on their WBI CB . As shown in Table A2, the major promoting factor is the producing item preference factor (∆F4_CB_PRO: 0.66), which is mainly offset by the water footprint intensity factor (∆F5_CB_OFF: −0.87). This shows that the effect of high-calorie content on food consumption is offset by the effect on food imports from regions with lower water requirements. This country is a moderate-intensity region of WBI CB according to Figure 1b, which is determined by adding ∆F1_CB to ∆F6_CB depending on the balance of degrees of contribution between the two promoting and four offset factors (Table A2). In summary, the intensities of WBI PB in the United States of America mainly increase owing to the industrial structure factor and are mainly offset by the water footprint intensity factor. On the other hand, the intensities of WBI CB mainly increase because of the consumed item preference factor and are mainly offset by the producing area preference factor.

Discussion
In 2010, the TRWR per capita is 8036 m 3 /capita, the AWW per capita is 406 m 3 /capita, and the TWW per capita is 583 m 3 /capita, on a global average. The respective values correspond to TRWR 0 , AWW 0 , and TWW 0 , those are used in Equations (11) and (16). The ration of AWW 0 to TWW 0 shows that global AWW accounts for approximately 70% of global TWW. Agricultural water demand is prominent and in danger of increasing water balance intensities. According to Figure 3, rice has a prominent blue water requirement on global average. Its blue water footprint intensity is 5350 m 3 /ton with 356 kcal/100 g of calorie content, the minimum value in all of the items, considering its irrigation efficiency is 0.1. For cereals, maize has the largest share of global calorie-based production (44% of cereals) and requires 155 m 3 /ton of blue water. Wheat follows by 33% and 656 m 3 /ton, showing the largest blue water intensity in all cereals, and 6.8% and 152 m 3 /ton for barley. The respective calorie content are 350 kcal/100 g for maize, 337 kcal/100 g for wheat, and 341 kcal/100 g for barley. For oil crops and oils, olive oil has the largest blue water intensity, requiring 4677 m 3 /ton of blue water with 921 kcal/100 g of calorie content. However, its share of global calorie-based production is 0.77% for oil crops and oils, which is less than that for palm oil (11% of oil crops and oils), followed by 10% for coconuts, 9.5% for soybean oil, 8.2% for rape and mustard seeds, and 5.7% for cottonseed. The respective blue water intensities are 2 m 3 /ton with 921 kcal/100 g of calorie content for palm oil, 4 m 3 /ton with 668 kcal/100 g for coconuts, 263 m 3 /ton with 921 kcal/100 g for soybean oil, 328 m 3 /ton with 500 kcal/100 g for rape and mustard seeds, and 802 m 3 /ton with 506 kcal/100 g for cottonseed. Soybeans have the largest share of global calorie-based production (27% of oil crops and oils) of all the oil crops and oils. Its blue water intensity is 134 m 3 /ton with 417 kcal/100 g of calorie content. For livestock products, "Meat, Other" (already integrating relatively minor meat items except for bovine, pig, poultry, mutton, and goat meat and edible offal in the FAOSTAT) has the largest blue water intensity (1223 m 3 /ton) with 119 kcal/100 g of calorie content. However, its share of global calorie-based production takes the minimum value in all livestock products at only 0.41%. Milk has the largest share of global calorie-based production (28% of livestock products) in all of the livestock products, followed by 18% for pig meat, and 14% for bovine meat. The respective blue water intensities are 165 m 3 /ton with 66 kcal/100 g of calorie content for milk, 622 m 3 /ton with 294 kcal/100 g for pig meat, and 1044 m 3 /ton with 360 kcal/100 g for bovine meat. Poultry meat's share of global calorie-based production is 11%, requiring 601 m 3 /ton of blue water with 194 kcal/100 g of calorie content. It seems that global blue water requirements mainly increase due to the large production of rice and relatively high water-required items with a large share of global calorie-based production rather than because of items with the largest blue water requirement in each item category. In particular, the blue water requirement for producing oil crops and oils increases due to the production of oil crops rather than oils. m /ton with 668 kcal/100 g for coconuts, 263 m /ton with 921 kcal/100 g for soybean oil, 328 m 3 /ton with 500 kcal/100 g for rape and mustard seeds, and 802 m 3 /ton with 506 kcal/100 g for cottonseed. Soybeans have the largest share of global calorie-based production (27% of oil crops and oils) of all the oil crops and oils. Its blue water intensity is 134 m 3 /ton with 417 kcal/100 g of calorie content. For livestock products, "Meat, Other" (already integrating relatively minor meat items except for bovine, pig, poultry, mutton, and goat meat and edible offal in the FAOSTAT) has the largest blue water intensity (1223 m 3 /ton) with 119 kcal/100 g of calorie content. However, its share of global calorie-based production takes the minimum value in all livestock products at only 0.41%. Milk has the largest share of global calorie-based production (28% of livestock products) in all of the livestock products, followed by 18% for pig meat, and 14% for bovine meat. The respective blue water intensities are 165 m 3 /ton with 66 kcal/100 g of calorie content for milk, 622 m 3 /ton with 294 kcal/100 g for pig meat, and 1044 m 3 /ton with 360 kcal/100 g for bovine meat. Poultry meat's share of global calorie-based production is 11%, requiring 601 m 3 /ton of blue water with 194 kcal/100 g of calorie content. It seems that global blue water requirements mainly increase due to the large production of rice and relatively high water-required items with a large share of global calorie-based production rather than because of items with the largest blue water requirement in each item category. In particular, the blue water requirement for producing oil crops and oils increases due to the production of oil crops rather than oils. Note: The target items (78 items) are aggregated in six categories as follows: "Cereals" for 13 items, "Beverages and seasonings" for 13 items, "Fruits and vegetables" for 18 items, "Oil crops and oils" for 22 items, "Livestock products" for 11 items, and "Rice" for one items. The blue water intensity means blue water footprint intensity considering irrigation efficiency on a world average.
The scatter plot in Figure 4a shows a clearly symmetric distribution centered around four on the horizontal axis. There are 98 countries in the very low or low intensity regions, 16 countries in the moderate intensity region, and 42 countries in the high or very high intensity regions. Countries in the very low or low intensity regions have a wide spread ranging from 10 3 to 10 8 . Counties in the high or very high regions spread in the range of 10 to 10 4 . Countries with moderate intensity have a spread between 10 3 to 10 4 . In the very low or low intensity regions, the largest calorie-based production quantity per capita is 48 GJ/capita in Argentina, followed by 40 GJ/capita in Canada, and 39 GJ/capita in Paraguay. In the moderate-intensity region, the largest calorie-based production quantity per capita is 31 GJ/capita in the United States of America, followed by 22 GJ/capita in Bulgaria and Kazakhstan, and 14 GJ/capita in Slovakia and Thailand. In the high or very high intensity regions, the largest calorie-based production quantity per capita is 40 GJ/capita in Demark, followed by 26 GJ/capita in France, and 18 GJ/capita in the Czech Republic, Poland and Austria. China has calorie-based production quantity per capita of 8.8 GJ/capita. In summary, calorie-based production quantities per capita tend to be higher in the very low or low intensity regions than in the moderate to very high intensity regions. is 31 GJ/capita in the United States of America, followed by 22 GJ/capita in Bulgaria Kazakhstan, and 14 GJ/capita in Slovakia and Thailand. In the high or very high inten regions, the largest calorie-based production quantity per capita is 40 GJ/capita Demark, followed by 26 GJ/capita in France, and 18 GJ/capita in the Czech Repub Poland and Austria. China has calorie-based production quantity per capita of GJ/capita. In summary, calorie-based production quantities per capita tend to be hig in the very low or low intensity regions than in the moderate to very high inten regions.
(a)   Figure 4b shows that countries in the high or very high intensity regions concent on net importers. Globally, net importers are dispersed independently of water bala intensities except for several net exporters of the very low or low intensity regions w prominent calorie-based net export quantities per capita. In the high or very high inten regions, the number of net importers is 43, more than that of net exporters (six countr In the moderate-intensity region, the number of net importers is 17, more than that of exporters (six countries). In the very low or low intensity regions, the number of importers (53 countries) is greater than that of net exporters (31 countries). In total, countries depend on food imports from 43 exporter countries. For example, in the hig very high intensity regions, the largest calorie-based net import quantity per capita i GJ/capita in Djibouti, followed by 12 GJ/capita in the United Arab Emirates and Belgi and 10 GJ/capita in Israel and The Netherlands. The United States of America has GJ/capita of calorie-based net export quantities per capita. The largest calorie-based export quantity is 7.1 GJ/capita in France, followed by 5.6 GJ/capita in Denmark, and   Figure 4b shows that countries in the high or very high intensity regions concentrate on net importers. Globally, net importers are dispersed independently of water balance intensities except for several net exporters of the very low or low intensity regions with prominent calorie-based net export quantities per capita. In the high or very high intensity regions, the number of net importers is 43, more than that of net exporters (six countries). In the moderate-intensity region, the number of net importers is 17, more than that of net exporters (six countries). In the very low or low intensity regions, the number of net importers (53 countries) is greater than that of net exporters (31 countries). In total, 113 countries depend on food imports from 43 exporter countries. For example, in the high or very high intensity regions, the largest calorie-based net import quantity per capita is 20 GJ/capita in Djibouti, followed by 12 GJ/capita in the United Arab Emirates and Belgium, and 10 GJ/capita in Israel and The Netherlands. The United States of America has 5.7 GJ/capita of calorie-based net export quantities per capita. The largest calorie-based net export quantity is 7.1 GJ/capita in France, followed by 5.6 GJ/capita in Denmark, and 2.8 GJ/capita in the Republic of Moldova. In the moderate-intensity region, the largest calorie-based net import quantity per capita is 6.3 GJ/capita in the Republic of Korea, followed by 4.8 GJ/capita in Spain, and 4.0 GJ/capita in Saint Lucia and Switzerland. China has 1.1 GJ/capita of calorie-based net import quantities per capita. The largest calorie-based net export quantity per capita is 9.4 GJ/capita in Bulgaria, followed by 4.6 GJ/capita in Kazakhstan, and 1.3 GJ/capita in Slovakia. In the very low or low intensity regions, the largest calorie-based net export quantity per capita is 20 GJ/capita in Paraguay, followed by 19 GJ/capita in Argentina and Australia, and 18 GJ/capita in Uruguay and Canada. The largest calorie-based net import quantity per capita is 8.8 GJ/capita in Portugal, followed by 7.1 GJ/capita in Norway, and 6.6 GJ/capita in Iceland. In summary, most countries are net importers that spread worldwide, whereas food exports are covered by a few net exporters. Figure 5a,b shows that cereals' share of calorie-based production quantities for each intensity of WBI PB is the largest in all of the items. The respective total calorie-based production quantities are 26,000 PJ (0.94 × 10 3 km 3 ) in the very low or low intensity regions, 13,000 PJ (0.54 × 10 3 km 3 ) in the moderate intensity region, and 27,000 PJ (3.1 × 10 3 km 3 ) in the high or very high intensity regions. In the very low or low intensity regions, the largest share of calorie-based production quantities is 35% (9.3 × 10 3 PJ) for cereals, followed by 32% (8.5 × 10 3 PJ) for oil crops and oils, 11% (2.8 × 10 3 PJ) for rice, and 9.0% (2.4 × 10 3 PJ) for livestock products. The respective shares of blue water requirements are 6.5% (61 km 3 ) for cereals, 1.7% (16 km 3 ) for oil crops and oils, 69% (0.65 × 10 3 km 3 ) for rice, and 12% (0.11 × 10 3 km 3 ) for livestock products. In the moderate-intensity region, the largest share of calorie-based production quantities is 57% (7.5 × 10 3 PJ) for cereals, followed by 21% (2.7 × 10 3 PJ) for oil crops and oils, 11% (1.4 × 10 3 PJ) for livestock products, and 4.2% (0.55 × 10 3 PJ) for rice. The respective shares of blue water requirements are 15% (80 km 3 ) for cereals, 6.1% (33 km 3 ) for oil crops and oils, 13% (71 km 3 ) for livestock products, and 53% (0.29 × 10 3 km 3 ) for rice. In the high or very high intensity regions, the largest share of calorie-based production quantities is 43% (11 × 10 3 PJ) for cereals, followed by 18% (4.8 × 10 3 PJ) for oil crops and oils, 14% (3.6 × 10 3 PJ) for rice, and 12% (3.2 × 10 3 PJ) for livestock products. The respective shares of blue water requirements are 22% (0.67 × 10 3 km 3 ) for cereals, 5.3% (0.16 × 10 3 km 3 ) for oil crops and oils, 50% (1.5 × 10 3 km 3 ) for rice, and 11% (0.33 × 10 3 km 3 ) for livestock products. Based on caloriebased production quantities, cereals, rice, livestock products, and oil crops and oils are produced worldwide. However, based on blue water requirements, rice is the most waterintensive item of all because its irrigation efficiency is 0.1, requiring ten times as many water withdrawals as its blue water consumption. In summary, rice and cereals increase global blue water requirements for production because the respective items have the largest share of blue water requirements and calorie-based production quantities in all of the items for all of the regions.
products. The respective shares of blue water requirements are 22% (0.67 × 10 km ) for cereals, 5.3% (0.16 × 10 3 km 3 ) for oil crops and oils, 50% (1.5 × 10 3 km 3 ) for rice, and 11% (0.33 × 10 3 km 3 ) for livestock products. Based on calorie-based production quantities, cereals, rice, livestock products, and oil crops and oils are produced worldwide. However, based on blue water requirements, rice is the most water-intensive item of all because its irrigation efficiency is 0.1, requiring ten times as many water withdrawals as its blue water consumption. In summary, rice and cereals increase global blue water requirements for production because the respective items have the largest share of blue water requirements and calorie-based production quantities in all of the items for all of the regions.  Figure 6a,b depict that the very low and low intensity regions show a net exporter on both bases, whereas the moderate-intensity region shows a net importer. The high or very high intensity regions show a net exporter on a calorie basis in contrast with a net importer region on a blue water requirement basis. In the very low or low intensity regions, the total calorie-based net export quantity is 4.6 × 10 3 PJ, and the total net export quantity of blue water requirements is 11 km 3 with no net import quantities on both bases. In the moderate-intensity region, the total calorie-based net import quantity is 2.2 × 10 3 PJ, and the total net import quantity of blue water requirements is 35 km 3 . The total calorie-based net export quantity is 22 PJ with no net export quantities of blue water requirements. In the high or very high intensity regions, the total calorie-based net import quantity is 1.9 × 10 3 PJ, and the total net import quantity of blue water requirements is 0.38 km 3 . Meanwhile, the total calorie-based net export quantity is 56 PJ, and the total net export quantity of blue water requirements is 21 km 3 . Based on blue water requirements, rice is largely exported to Western Africa (24 km 3 and 16 PJ), followed by Western Asia (23 km 3 and 31 PJ), and Eastern Africa (23 km 3 and 11 PJ). These are offset by rice imports from Southern Asia (43 km 3 and 36 PJ), followed by South-Eastern Asia (11 km 3 and 42 PJ), and North America (6.8 km 3 and 8.1 PJ). Four items (e.g., rice, cereals, livestock products, and oil crops and oils) in particular show net importers on a calorie basis, in contrast with showing net exporters on a blue water requirement basis. This contrast could be caused by the stacked difference of blue water requirements because the blue water intensity for each item is different between producing countries. The calorie conversion factor for each item is constant and not separately set among producing countries. In summary, oil crops and oils have the largest share of calorie-based net trade worldwide. However, blue water requirements for oil crops and oils are less than those for rice and as much as those of cereals. Thus, rice trade increases global blue water requirements.  Figure 6a,b depict that the very low and low intensity regions show a net exporter on both bases, whereas the moderate-intensity region shows a net importer. The high or very high intensity regions show a net exporter on a calorie basis in contrast with a net importer region on a blue water requirement basis. In the very low or low intensity regions, the total calorie-based net export quantity is 4.6 × 10 3 PJ, and the total net export quantity of blue water requirements is 11 km 3 with no net import quantities on both bases. In the moderate-intensity region, the total calorie-based net import quantity is 2.2 × 10 3 PJ, and the total net import quantity of blue water requirements is 35 km 3 . The total calorie-based net export quantity is 22 PJ with no net export quantities of blue water requirements. In the high or very high intensity regions, the total calorie-based net import quantity is 1.9 × 10 3 PJ, and the total net import quantity of blue water requirements is 0.38 km 3 . Meanwhile, the total calorie-based net export quantity is 56 PJ, and the total net export quantity of blue water requirements is 21 km 3 . Based on blue water requirements, rice is largely exported to Western Africa (24 km 3 and 16 PJ), followed by Western Asia (23 km 3 and 31 PJ), and Eastern Africa (23 km 3 and 11 PJ). These are offset by rice imports from Southern Asia (43 km 3 and 36 PJ), followed by South-Eastern Asia (11 km 3 and 42 PJ), and North America (6.8 km 3 and 8.1 PJ). Four items (e.g., rice, cereals, livestock products, and oil crops and oils) in particular show net importers on a calorie basis, in contrast with showing net exporters on a blue water requirement basis. This contrast could be caused by the stacked difference of blue water requirements because the blue water intensity for each item is different between producing countries. The calorie conversion factor for each item is constant and not separately set among producing countries. In summary, oil crops and oils have the largest share of calorie-based net trade worldwide. However, blue water requirements for oil crops and oils are less than those for rice and as much as those of cereals. Thus, rice trade increases global blue water requirements.

Conclusions
This study aims to evaluate the intensities of water supply-demand balances (water balance intensities) and elucidate the promoting factors of water balance intensities (promoting factors) or offset factors of water balance intensities (offset factors) for each country, focusing on food supply-demand balances and considering food trade balances on a global scale. A complete decomposition analysis is applied to both the WBI PB and the WBI CB to analyze the promoting and offset factors of both WBI's. The WBI PB is decomposed into five factors as follows: a renewable freshwater resources factor, an industrial structure factor, a production scale factor, a produced item preference factor, and a water footprint intensity factor. The WBI CB is decomposed into six factors as follows: a renewable freshwater resources factor, an industrial structure factor, a consumption scale factor, a

Conclusions
This study aims to evaluate the intensities of water supply-demand balances (water balance intensities) and elucidate the promoting factors of water balance intensities (promoting factors) or offset factors of water balance intensities (offset factors) for each country, focusing on food supply-demand balances and considering food trade balances on a global scale. A complete decomposition analysis is applied to both the WBI PB and the WBI CB to analyze the promoting and offset factors of both WBI's. The WBI PB is decomposed into five factors as follows: a renewable freshwater resources factor, an industrial structure factor, a production scale factor, a produced item preference factor, and a water footprint intensity factor. The WBI CB is decomposed into six factors as follows: a renewable freshwater resources factor, an industrial structure factor, a consumption scale factor, a consumed item preference factor, a producing area preference factor, and a water footprint intensity factor. The elucidation of the promoting and offset factors of both WBIs is expected to provide essential knowledge for decreasing water balance intensities regarding food production and consumption based on water resource management. In this study, the following three results are revealed: (1) The water balance intensity for each country is evaluated using five intensity categories: very low, low, moderate, high, and very high. 58 countries from moderate to very high intensity regions on a WBI PB basis tend to be distributed around midlatitude regions including arid regions, large population regions, and industrialized countries. In contrast, 72 countries from moderate to very high intensity regions on a WBI CB basis are spread worldwide. Comparing intensities between WBI PB and WBI CB , the former is higher for 17 countries, whereas the latter is higher for 36 countries.
In addition, 103 countries are approximately the same, including 40 countries from moderate to very high regions. (2) Each country is classified into one of three regions: the very low or low intensity region, the moderate intensity region, and the high or very high intensity region. Based on WBI PB , the renewable freshwater resources factor is the major promoting factor in the very low or low and the high or very high intensity regions, while the renewable freshwater resources and industrial structure factors are relatively large promoting factors in the moderate-intensity region. The major offset factor of WBI PB is the consumed item preference factor for countries in the very low to moderate-intensity regions. The high or very high intensity regions have the production scale factor as the major offset factor of the WBI PB . Based on WBI CB , the consumed item preference factor is the major promoting factor for countries from the very low to moderate regions, and the renewable freshwater resources factor is the major promoting factor for countries in the high or very high intensity regions. In contrast, the major offset factor of WBI CB is the producing area preference for all regions. The water balance intensities of WBI PB and WBI CB are determined to balance the degrees of contribution between the promoting and offset factors. (3) This study reviews two countries (China and the United States of America) in more detail. In China, the renewable freshwater resources factor is mainly offset by the water footprint intensity factor based on WBI PB . In contrast, the water footprint intensity factor is mainly offset by the producing area preference factor based on WBI CB . In the United States of America, the water balance intensity of WBI PB mainly increases because of the industrial structure factor, which is offset by the water footprint intensity factor. In contrast, the water balance intensity of WBI CB increases because of the consumed item preference factor, which is offset by the producing area preference factor.
A discussion focusing on food production and trade is provided. Calorie-based production quantities tend to be higher for countries in the very low or low intensity regions than for those in the moderate to very high regions. Most countries are net importers that spread worldwide, whereas food exports are covered by a few net exporters. Rice and cereals increase global blue water requirements for production because the respective items have the largest share of blue water requirements and calorie-based production quantities in all of the items for all of the regions. Oil crops and oils have the largest share of caloriebased net trade worldwide. However, blue water requirements for oil crops and oils are less than those for rice and as much as those for cereal. Thus, rice trade increases global blue water requirements. It is effective to improve irrigation efficiency for rice and cereals because rice has the largest blue water footprint intensity considering irrigation efficiency in all of the items, whereas cereals show the largest share of calorie-based production quantities in all of the items for all of the regions.
Several problems need to be addressed in future studies. This study in particular analyzes water balance intensities, focusing on the elucidation of a global distribution tendency of degrees of promoting and offset factors for each country. Therefore, this study could not refer to the relationship between countries in detail. For this reason, more detailed analyses at the regional or country level are necessary. In addition, the standard value of this study differs for each country to apply the complete decomposition analysis to spatial data. The standard value for each factor, the renewable freshwater resources, industrial structure, production (for WBI PB ), and consumption scale (for WBI CB ) factors are set by using world average values per capita while the water footprint intensity factor is set by using the world average values. In contrast, the produced and consumed item preferences (for WBI PB and WBI CB , respectively) and producing area preference (for only WBI CB ) factors are set by using distinct values for each country. Additional analyses from various points of view are necessary. Using time series data as degrees of contribution factors can easily change depending on the method of taking standard values and selecting parameters and indices.
This study quantifies water balance intensities based on macroeconomic statistics, such as FAOSTAT and AQUASTAT when calculating food supply-demand factors (food production, consumption, and net trade) and water-related factors (total renewable water resources, agricultural withdrawal rate, and water footprint intensity) to evaluate the effect of these factors on water balance intensities. Therefore, this study could not consider accelerating changes in water footprint, such as various irrigation technology, cultivation methods, and agricultural activities. In addition, green water is excluded from the evaluation target of this study. However, green water could become an indirect effect on water balance intensities because decreasing the availability of green water causes additional blue water use. Additional analysis is necessary to develop this study for the future. For example, creating a new decomposition formula for water requirements incorporating the ratio of virtual water to real water and that for food production incorporating crop yield could adopt appropriate policies to conserve water resources and increase crop productivity, respectively. In addition, analyzing the value of virtual water enables to evaluate the effect of trade dependence between countries on water balance intensities, and therefore, could add economic viewpoint to this study.
It should be noted that this study is based on the FAOSTAT, and therefore the quality of all results of this study highly rely on the data limitation and drawbacks of this statistics. This study could not consider the input-output balances between raw materials and processed goods because the FAOSTAT does not refer to the relationship between two. In addition, this study could not cover unreported data of the FAOSTAT. This statistics' quality depends on the quality of received data, supplied by national statistical authorities or by other international organizations [42]. In future work, the analysis combined with input-output tables is desirable.