Outline of agricultural water scarcity modelling
According to Bayart et al. (2010) and Kounina et al. (2013), excessive freshwater consumption will lead to irrigation water scarcity and result in health damage from malnutrition. Malnutrition may also result from infectious diseases that decrease nutrient absorption (World Water Assessment Programme 2009; Boulay et al. 2011). On the other hand, only malnutrition damage from food deprivation was considered in this study as a straightforward and robust endpoint resulting from agricultural water scarcity. The cause-effect chain in this modelling process is defined as shown in Fig. 1.
Freshwater consumption will potentially lower water availability for agriculture and agricultural production, but the severity of this depends on irrigation intensity and societal capacity for compensation. Depending on absolute levels of water scarcity, a shortage of irrigation water might be compensated for by inputting additional water from other available freshwater resources and food stocks. In this context, alternative freshwater resources and food stocks can represent physical and socio-economic vulnerability to water scarcity, respectively, and were therefore included in characterisation factors (CFs) at the midpoint.
On the other hand, food production shortages may not be fully compensated for within a local system. Any local production shortages may also be spread through international food trade. As a result, food supply shortages due to agricultural water scarcity can cause health damage as a major endpoint impact. However, the spread effects of shortages in food production will depend on the commodity balance of water consumers, the vulnerability of economy and food stocks in food-importing countries. In addition, the significance of food supply shortages will also be controlled by overall nutritional conditions and their variability in each region. Suitable characterisation factors at the endpoint were developed by integrating these parameters.
As mentioned above, physical factors such as freshwater resources and social factors relating to food production and consumption were included in the modelling at both the midpoint and endpoint. However, the availability of statistical data for many socio-economic indices is often limited to the national level. Therefore, the geographic resolution of both the midpoint and endpoint was set at the scale of individual countries, even if some factors could be analysed at higher spatial resolution. Details of the modelling methodology are described in the following sections.
Midpoint modelling
While current midpoint indicators can be applied in different types of formulation, they commonly express the relationship of freshwater use (withdrawal or consumption) to the total amount of available freshwater resources (Kounina et al. 2013). However, agricultural water scarcity is not only determined by the total amount of water consumed. The severity of agricultural water scarcity will also be influenced by the level of dependency on irrigation for agricultural production. Agricultural food production losses may also be compensated for by additional food stocks from the viewpoint of social vulnerability. In this context, characterisation factors for agricultural water scarcity at the midpoint (CFAgr_Midpoint,i
) should be defined by combining physical compensation capacity with the extent of agricultural water demand, dependency on irrigation water and social compensation capacity as follows:
$$ {\mathrm{CF}}_{\mathrm{Agr}\mathrm{Midpoint},i}=\underset{\kern1em \left(\mathrm{Irrigated}\kern0.5em \mathrm{crop}\kern0.5em \mathrm{production}\kern0.5em \mathrm{vulnerability}\right)}{\underbrace{R_{\mathrm{Agr},i}\cdot {\mathrm{IDR}}_i}}\cdot \underset{\kern1em \left(\mathrm{Physical}\kern0.5em \mathrm{vulnerability}\right)}{\underbrace{\left(1-{\mathrm{PCF}}_i\right)}}\cdot \underset{\begin{array}{l}\kern1em \mathrm{Social}\\ {}\mathrm{vulnerability}\end{array}}{\underbrace{\left(1-{\mathrm{SCF}}_i\right)}} $$
(1)
where R
Agr,i
[dimensionless] is the ratio of agricultural water use to total water withdrawal in country i, IDR
i
[dimensionless] is the irrigation dependency ratio for crop production in country i, PCF
i
[dimensionless] expresses the physical compensation capacity of country i, and SCF
i
[dimensionless] expresses the social compensation capacity of country i.
The meaning of the CFs at the midpoint is the ratio of potential “net” production loss of irrigated crops resulting from freshwater consumption. Based on the hypothesis that all water users are proportionally affected and that production loss is proportional to irrigation loss, the product of R
Agr,i
and IDR
i
expresses the potentially lost share of agricultural production. The gross value is converted to the net loss by considering vulnerability of physical (in terms of water resources) and social (in terms of food stocks) aspects.
R
Agr,i
was calculated based on the amount of agricultural water use and total water withdrawal for each country (FAO 2010a). The dependence of agriculture on irrigation IDR
i
was quantified by calculating the weighted average of the ratio of irrigation water volume to total water volume consumed (evapotranspiration) by commodity group (based on the metric of dietary energy). For physical vulnerability (1 − PCF
i
), midpoint indicators (the so-called water scarcity index (WScI)) expressing water scarcity at the national level developed by previous studies (Frischknecht et al. 2006; Pfister et al. 2009; Boulay et al. 2011) can be applied without any modifications. For the compensation capacity (SCF) using additional food stocks, the ratio of average surplus food stocks and total production for the last 10 years (to derive more robust results) was calculated for each commodity. Target commodities for calculating crop production loss (45 items) were determined (the specific lists in Tables S1 and S2 of the Electronic Supplementary Material) in accordance with the agricultural commodity classification in FAOSTAT (FAO 2013). The weighted average of the ratio by commodity production (based on the metric of dietary energy) was applied as SCF
i
.
$$ {\mathrm{IDR}}_i={\displaystyle {\sum}_j\left\{{\mathrm{AID}}_{ij}/{\displaystyle {\sum}_j{\mathrm{ATD}}_{ij}}\cdot \underset{\mathrm{Weighting}\ \mathrm{on}\ \mathrm{production}}{\underbrace{\left({\mathrm{AFP}}_{ij}/{\displaystyle {\sum}_j{\mathrm{AFP}}_{ij}}\right)}}\right\}} $$
(2)
$$ {\mathrm{PCF}}_i = 1-{\mathrm{WScI}}_i $$
(3)
$$ {\mathrm{SCF}}_i = \kern1em \left\{\begin{array}{l}\kern1em 1\kern19em ,{\mathrm{AFP}}_{ij}<{\mathrm{AFS}}_{ij}\hfill \\ {}1-{\displaystyle {\sum}_j\left\{\left({\mathrm{AFP}}_{ij}-{\mathrm{AFS}}_{ij}\right)/{\mathrm{AFP}}_{ij}\cdot \underset{\mathrm{Weighting}\kern0.5em \mathrm{on}\kern0.5em \mathrm{production}}{\underbrace{\left({\mathrm{AFP}}_{ij}/{\displaystyle {\sum}_j{\mathrm{AFP}}_{ij}}\right)}}\right\},{\mathrm{AFP}}_{ij}\ge {\mathrm{AFS}}_{ij}}\hfill \end{array}\right. $$
(4)
where WScI
i
is the scarcity index expressing a function of the ratio of water use to available water resources, AID
ij
[m3/year] expresses the annual demand of irrigation water for producing commodity j in country i, ATD
ij
[m3/year] expresses the annual total demand (including irrigation and rain) of water for producing commodity j in country i, AFP
ij
[kcal/year] means the average annual production of commodity j in country i for 10 years (from 2000 to 2009), and AFS
ij
[kcal/year] is the average annual stock of commodity j in country i for 10 years (from 2000 to 2009). For calculating AFP
ij
and AFS
ij
, the amounts of annual production and stocks in metric tons were converted into dietary energy based on FAOSTAT data (FAO 2013). Details of calculation of AID
ij
, ATD
ij
, AFP
ij
and AFS
ij
are described in Section 2.3.1.
Endpoint modelling
Malnutrition damage at the endpoint will occur when agricultural water scarcity causes losses of crop production and food supply cannot be locally compensated for. Consequences of crop production loss may be spread to other countries through international trade in food. Any resulting shortage of food in each country (not only water consumer but also food-importing countries) may cause malnutrition damage. For these reasons, the modelling incorporates three modules (food production loss assessment, food supply shortage assessment and health damage assessment) as described in the following sections.
The food production loss assessment module
The extent of agricultural water scarcity due to freshwater consumption was assessed based on the agricultural water use share. However, the vulnerability of crop production relevant to freshwater consumption needs to be distinguished among individual commodities, because irrigation water demand for each unit amount of crop production depends on the nature of specific commodities. In addition, the commodity balance of production and consumption in each country will control the types of agricultural commodities influenced by agricultural water scarcity. Thus, agricultural water scarcity needs to be allocated to each commodity by considering commodity balances in each country. Crop yield per unit of irrigation water should also be identified for specific commodities and countries. In this context, crop production loss (CPL
ij
) for each commodity was calculated by modifying the midpoint CFs (Eq. (1)) for each country and commodity to reflect the differences in water demand and food stock capacity of each commodity j:
$$ {\mathrm{CPL}}_{ij}={R}_{\mathrm{Agr},i}\cdot {\mathrm{IDR}}_{ij}\cdot \left(1-{\mathrm{PCF}}_i\right)\cdot {\mathrm{CY}}_{ij}\cdot \left(1-{\mathrm{SCF}}_{ij}\right) $$
(5)
where CPL
ij
[ton/m3] indicates the amount of production loss of commodity j in country i, IDR
ij
[dimensionless] expresses the demand ratio of irrigation water for commodity j to total irrigation water demand in country i, CY
ij
[ton/m3] means the crop yield of commodity j in country i per unit irrigation water input, and SCF
ij
[dimensionless] is the social compensation capacity of commodity j in country i.
The relationship IDR
ij
allocates a unit volume of agricultural water scarcity to each commodity based on the ratio of the annual irrigation water demand of each commodity to the total annual agricultural water demand. The annual agricultural water (irrigation and rain) demand for each commodity was calculated by dividing the annual production amount of all crops produced in each country (FAO 2013) by the crop yield per unit volume of water consumption (CY
ij
) based on Mekonnen and Hoekstra (2010). AID
ij
was calculated by multiplying ATD
ij
with the ratio of irrigation water to total water consumption. IDR
ij
and SCF
ij
are described by the following:
$$ {\mathrm{IDR}}_{ij}={\mathrm{AID}}_{ij}/{\displaystyle \sum_j}{\mathrm{ATD}}_{ij} $$
(6)
$$ {\mathrm{SCF}}_{ij}=\kern1em \left\{\begin{array}{l}1\kern9.5em ,{\mathrm{AFP}}_{ij}<{\mathrm{AFS}}_{ij}\hfill \\ {}1-\left({\mathrm{AFP}}_{ij}-{\mathrm{AFS}}_{ij}\right)/{\mathrm{AFP}}_{ij},\ {\mathrm{AFP}}_{ij}>{\mathrm{AFS}}_{ij}\hfill \end{array}\right. $$
(7)
The amount of crop production loss in terms of dietary energy supply is not necessarily the same for all crops, because the dietary energy obtained from the same unit weight of production can be different for different crops. In addition, some part of each produced crop may be used as feed for producing animal food commodities which leads on average to a 7.22 times lower dietary energy supply (Boulay et al. 2011). Conversion factors for each commodity from weight to dietary energy and feed production ratio to total crop production were calculated based on data supplied by FAOSTAT (FAO 2013). Dietary energy loss of each crop production was separated into food and feed. Dietary energy loss of feed was allocated to each animal food commodity (ten types of meat and dairy products in accordance with the classification of FAOSTAT shown in Table S3 of the Electronic Supplementary Material), based on the ratio of the annual production amount of each animal food in dietary energy to the total annual animal food production. The food production loss of agricultural and animal food commodities was determined using the following equations:
$$ {\mathrm{FPL}}_{ij}=\left\{\begin{array}{l}{\mathrm{CPL}}_{ij}\cdot \underset{\begin{array}{l}\mathrm{Conversion}\kern0.5em \mathrm{t}\mathrm{o}\\ {}\mathrm{dietary}\kern0.5em \mathrm{energy}\end{array}}{\underbrace{{\mathrm{DEC}}_{ij}}}\cdot \underset{\begin{array}{l}\mathrm{Allocation}\kern0.5em \mathrm{t}\mathrm{o}\\ {}\mathrm{agricultural}\kern0.5em \mathrm{food}\end{array}}{\underbrace{\left(1-{\mathrm{FPR}}_{ij}\right)}}\kern3.1em ,j: agricultural\kern0.5em \mathrm{food}\kern0.5em \mathrm{commodities}\hfill \\ {}{\mathrm{CPL}}_{ij}\cdot \underset{\begin{array}{l}\mathrm{Conversion}\kern0.5em \mathrm{t}\mathrm{o}\\ {}\mathrm{dietary}\kern0.5em \mathrm{energy}\end{array}}{\underbrace{{\mathrm{DEC}}_{ij}}}\cdot \underset{\begin{array}{l}\mathrm{Allocation}\kern0.5em \mathrm{t}\mathrm{o}\\ {}\mathrm{animal}\kern0.5em \mathrm{food}\end{array}}{\underbrace{{\mathrm{FPR}}_{ij}\cdot {\mathrm{AFPR}}_{ij}}}\kern1em ,j:\mathrm{animal}\kern0.5em \mathrm{food}\kern0.5em \mathrm{commodities}\hfill \end{array}\right. $$
(8)
where FPL
ij
[kcal/m3] expresses the food production loss of commodity j in country i (in terms of dietary energy), DEC
ij
[kcal/ton] means the unit conversion factor of food from metric weight to dietary energy, FPR
ij
[dimensionless] is the ratio of feed production amount to total crop production amount, and AFPR
ij
[dimensionless] is the ratio of each type of animal food commodity to total animal food (both in terms of dietary energy).
Food supply shortage assessment module
These losses in food production may result in a shortage of food supplies inside the water consumer country. However, the water consumer country can avoid these by decreasing food exports (in case of a net exporter of a commodity) or by importing food. Therefore, the shortages in food supplies will differently affect water consumer countries based on the dependency ratio of domestic food supplies to total supplies (including the net amount of imports). If the water consumer country is a net exporter of a particular commodity, all of the food production loss is assumed to affect the net importers. Net importer countries share a part of the food shortage based on their individual ratios of net imports of each commodity to total net imports in the world. In international trade, economic power for purchasing commodities can be the biggest determining factor for decreasing the sharing ratio of food supply shortage. Thus, economic adaptation capacity is considered in the estimation of the sharing ratio. The actual food supply loss for each commodity in water consumer and other importer countries can be described using the following equations, respectively:
$$ {\mathrm{FSL}}_{ij}=\left\{\begin{array}{l}{\mathrm{FPL}}_{ij}\cdot {\mathrm{DSR}}_{ij}\cdot \underset{\begin{array}{l}\mathrm{Economic}\\ {}\mathrm{vulnerability}\end{array}}{\underbrace{\left(1-{\mathrm{EAC}}_i\right)}}\kern2em ,i:\mathrm{water}\kern0.5em \mathrm{consumer}\kern0.5em \mathrm{coutnry}\hfill \\ {}\underset{\begin{array}{l}\mathrm{Trade}-\mathrm{induced}\kern0.5em \mathrm{food}\kern0.5em \mathrm{loss}\\ {}\mathrm{in}\kern0.5em \mathrm{importer}\kern0.5em \mathrm{countries}\end{array}}{\underbrace{\left({\mathrm{FPL}}_{\mathrm{WC},j}-{\mathrm{FSL}}_{\mathrm{WC},j}\right)}}\cdot {\mathrm{ISR}}_{ij}\kern1em ,i:\mathrm{other}\kern0.5em \mathrm{importer}\kern0.5em \mathrm{countries}\hfill \end{array}\right. $$
(9)
where FSLWC, j
[kcal/m3] expresses the supply shortage of commodity j in the water consumer country, DSRWC, j
[dimensionless] indicates the ratio of the domestic supply amount of commodity j to the total supply in the water consumer country, EACWC [dimensionless] describes the economic adaptation capacity in the water consumer country, FPLWC, j
[kcal/m3] is the production loss of commodity j in the water consumer country, FSL
ij
[kcal/m3] is the supply shortage of commodity j in country i, ISR
ij
[dimensionless] is the import sharing ratio of commodity j in country i, and EAC
i
[dimensionless] is the economic adaptation capacity in country i.
For the calculation of the import sharing ratio for each commodity ISR
ij
, data on the net import amount of each commodity j in country i was obtained from FAOSTAT for all countries (FAO 2013):
$$ {\mathrm{ISR}}_{ij}=\left\{\left({\mathrm{NIA}}_{ij}\cdot \left(1-{\mathrm{EAC}}_i\right)\right)/{\displaystyle \sum_i}\left({\mathrm{NIA}}_{ij}\cdot \left(1-{\mathrm{EAC}}_i\right)\right)\right\} $$
(10)
where NIA
ij
[kcal] expresses the net import amount of commodity j in country i.
The economic adaptation capacity EAC
i
was defined by referring to the method by Boulay et al. (2011) based on income level classifications supplied by the World Bank (World Bank 2014a). Equations for calculating ISR
ij
and EAC
i
are as follows:
$$ {\mathrm{EAC}}_i=\left\{\begin{array}{l}1\kern12.5em ,\ \mathrm{G}\mathrm{N}\mathrm{I}\ \mathrm{per}\ \mathrm{capita}>12,615\kern0.5em \mathrm{US}\$\hfill \\ {}\left({\mathrm{GNI}}_i-1035\right)/\left(12,615-1035\right)\kern1em ,1035<\mathrm{G}\mathrm{N}\mathrm{I}\ \mathrm{per}\ \mathrm{capita}<12,615\kern0.5em \mathrm{US}\$\hfill \\ {}0\kern12.4em ,\mathrm{G}\mathrm{N}\mathrm{I}\ \mathrm{per}\ \mathrm{capita}<1035\kern0.5em \mathrm{US}\$\hfill \end{array}\right. $$
(11)
where GNI
i
[current US$;] is the per-capita gross national income of country i reported by the World Bank (2014b).
The health damage assessment module
Loss of food supplies will result in a prevalence of undernourished populations. While the size of the undernourished population also depends on many aspects of nutrition in each country, we chose average dietary energy supply per capita as the main parameter for describing fundamental nutrient conditions at the national level. Additionally, a gap in nutrient conditions in each country was assumed to be a potential factor in the creation of an undernourished population (Thompson and Meerman 2010). Therefore, the level of the undernourished population in each country was modelled using two parameters of nutrient conditions (average dietary energy supply per capita and the Gini coefficient of dietary energy consumption). Non-linear multiple regression analysis was applied to model the relationship between the undernourished population and the above two parameters in accordance with the procedures described in Motoshita et al. (2010). Details of the analysis procedure and results are found in the Electronic Supplementary Material of this paper. Fundamental data on the above two explanatory variables was collected from the FAO database (FAO 2010b, 2013).
The following equation was obtained from the multiple regression analysis as follows (R
2* = 0.92, N = 171):
$$ {\mathrm{RUP}}_i=\begin{array}{lll}\underset{\begin{array}{l}\mathrm{Undernourished}\kern0.5em \mathrm{population}\\ {}\kern3em \mathrm{o}\mathrm{wing}\kern0.5em \mathrm{t}\mathrm{o}\\ {}\mathrm{average}\kern0.5em \mathrm{dietary}\;\mathrm{condition}\end{array}}{\underbrace{1.53\times {10}^3\cdot {e}^{-0.193\cdot {\mathrm{ADES}}_i}}}+\hfill & \underset{\begin{array}{l}\mathrm{Undernourished}\kern0.5em \mathrm{population}\\ {}\kern4em \mathrm{o}\mathrm{wing}\kern0.5em \mathrm{t}\mathrm{o}\\ {}\mathrm{gap}\kern0.5em \mathrm{condition}\kern0.5em \mathrm{o}\mathrm{f}\kern0.5em \mathrm{dietary}\kern0.5em \mathrm{energy}\end{array}}{\underbrace{0.878\cdot {\mathrm{GC}}_i}}\hfill & -20.1\hfill \end{array} $$
(12)
where RUP
i
[%] expresses the rate of undernourished population in country i, ADES
i
[kcal/capita/day] is the average daily dietary energy supply per capita in country i, and GC
i
[dimensionless] is the Gini coefficient of dietary energy consumption per capita in country i.
The response factor (RF) describes changes in the undernourished population rate caused by changes in unit average daily dietary energy supply and can be described by deviating Eq. (12) in terms of ADES
i
as follows:
$$ {\mathrm{RF}}_i=\varDelta {\mathrm{RUP}}_i/\varDelta {\mathrm{ADES}}_i=-2.96\times {10}^2\cdot {e}^{-0.193\cdot {\mathrm{ADES}}_i} $$
(13)
The level of health damage (disability adjusted life years (DALYs)) from malnutrition on a per case basis (HDM
i
[DALY/case]) was calculated for each country by dividing total health damage from malnutrition in each country by the level of undernourished population (WHO 2008; FAO 2010b). By multiplying predicted undernourished population increases due to food supply shortages with the level of health damage of malnutrition per individual case, any increases in health damage from undernourishment caused by food supply shortages can be estimated. A point of notice is the limitation that the shortages in food supply are assumed to affect all population equally without considering the depth of lacking dietary energy for a specific part of the population. Thus, health damage calculated from Eq. (13) only describes the impact on all population at an average nutrient condition in each country.
The characterisation factor at the endpoint level
The characterisation factor [DALY/m3] of agricultural water scarcity on human health inside water consumer countries (national damage) and other influenced countries (trade-induced damage) can be separately calculated by integrating the above equations as follows:
$$ \begin{array}{l}{\mathrm{CF}}_{\mathrm{Agr}\_\mathrm{Endpoint}\_\mathrm{H}\mathrm{H},i}=\\ {}\left\{\begin{array}{ll}\kern1em \left({\displaystyle {\sum}_j{\mathrm{FSL}}_{ij}}\right)/\left({P}_i\cdot 365\right)\cdot {\mathrm{RF}}_i\cdot {\mathrm{HDM}}_i\hfill &, \mathrm{damage}\kern0.5em \mathrm{in}\kern0.5em \mathrm{water}\kern0.5em \mathrm{consumer}\kern0.5em \mathrm{country}\hfill \\ {}{\displaystyle {\sum}_i\left\{{\displaystyle {\sum}_j{\mathrm{FSL}}_{ij}}/\left({P}_i\cdot 365\right)\cdot {\mathrm{RF}}_i\cdot {\mathrm{HDM}}_i\right\}}\hfill &, \mathrm{trade}\hbox{-} \mathrm{induced}\kern0.5em \mathrm{damage}\kern0.5em \mathrm{in}\kern0.5em \mathrm{other}\kern0.5em \mathrm{countries}\hfill \end{array}\right.\end{array} $$
(14)
where P
i
[capita] expresses the population of country i.
The impact on freshwater consumption from agricultural water scarcity can be separately identified for national and trade-induced damage by using these characterization factors at the endpoint (specific characterisation factors are shown in Annex A2 in the Electronic Supplementary Material).