*2.3. Virtual Water Contents*

The virtual water trade between the country/region of production to the country/region of consumption through product trade is the volume of water that is being transferred in virtual form. In this study, the virtual water flows related to Pakistan's agricultural trade have been calculated by multiplying commodity trade flows (ton/year) by their associated virtual water content (m3/ton). The virtual water content (VWC) of a commodity is the quantity of water required to produce one ton of crop biomass, estimated as Equation (1).

$$\text{VWC}\_{i, \text{g.t.}} = \frac{ETTOTAL\_{i, \text{g.t.}}}{Yield\_{i, \text{g.t.}}} \tag{1}$$

where *ETTOTAL* is the total evapotranspiration during the cropping period (m3/ha); yield is crop yield (ton/ha) and *i, g, t* denote crop, grid cell and year, respectively. *ETTOTAL* is further formulated as follows:

$$ETTOTAL\_{i, \mathbb{g}, t} = \sum\_{day = p}^{h} ET\_{\mathfrak{c}\_r \mathfrak{g}\_r \text{ day}} \tag{2}$$

where ET is daily evapotranspiration (m3 ha−<sup>1</sup> day−1) and *doy*, *p* and *h* denote the day of year, the planting date and the harvesting date, respectively. *ETTOTAL* is divided into blue and green water as follows:

$$ETTOTAL\_{i, \text{g.f.}} = ETOTAL\_{\text{BLLE}, i, \text{g.f.}} + ETOTAL\_{\text{GREEN}, i, \text{g.f.}} \tag{3}$$

Based on the type of water used in *ETTOTAL*, *VWC* can be split into green and blue types, where green and blue water in the context of VW are water consumed by crop vegetation that originated from precipitation and irrigation, respectively [46]. Blue and green VWC have substantially different opportunity costs associated with them (for a more detailed discussion of the method see Hanasaki [46]. Pakistan's virtual water export is the volume of water used to produce export commodities. Similarly, the virtual water import of Pakistan is the volume of water used to produce commodities in the trading partners imported by Pakistan.

The data on VWC of rice, wheat, maize, beef, mutton and poultry are taken from Reference [46] throughout 1990–2005. The original data in the study [46] are based on the H08 model and runs from 1986 to 2005 (The data can be downloaded from the link: https://sites.google.com/site/naotahanasaki/ english-contents/data/vwc). Here, we note that in the absence of national estimates of virtual water contents, our study uses assessments from global models, which might contain discrepancies in the results due to the differences in modelling assumptions, input data and parameters adopted by local and global models (see Zoumides et al. [47] for a detailed discussion of these discrepancies). For the period after 2005, where VWC data are unavailable, we make use of the finding that VWC (or water productivity) has a strong inverse (or direct) relationship with crop yield [22]. This method has also been used in other studies like [8,48,49]. Specifically, we employ yield data from Reference [39] in Equation (4) to update the country-specific VWC of these crops and livestock as:

$$\text{VWC}\_{w,j,r,t} = \text{VWC}\_{w,i,r,2005} \times \text{Y}\_{w,i,r,2005} / \text{Y}\_{w,i,r,t} \tag{4}$$

where *w* represents water type (blue and green), *i* denotes commodity, *r* means country/region and t represents the years, that is, 2006 to 2016.

For updating the VWC for livestock sectors, we extrapolated the VWC values from Reference [46] to future years by assuming a 1% improvement in water productivity every five years for livestock production, which is in the spirit of Reference [27]. For fruits and vegetables, we used VWC for apples and tomatoes, respectively, from Reference [10], which is also in the spirit of Reference [50], which used VWC for apples and tomatoes as representative crops for fruits and vegetables, respectively. The VWC for cotton, palm oil, tea, tobacco, other cereals and oilseeds are from Reference [10], who reported country-wise blue and green VWC of these crops for the period 1996–2005. We applied the method described in Equation (3) to update respective VWCs.

For the future VWC values of rice, wheat, maize, cotton, tea, tobacco, oilseeds, other cereals, sugar and palm oil, from 2017 to 2030, we make use of the forecasts on water productivity from Reference [51]. The study uses IMPACT-WATER model to examine water and food policy and investment issues. Based on the assumptions of enhancements in area and yield growth; decrease in water consumption per hectare and improvement in water supply between 1995 and 2025, the study suggests that over the 30 years, the water productivity of non-rice cereals will improve by 66% (from 0.6 to 1.0 kg/m3) for developing countries and 40% (from 1.0 to 1.4 kg/m3) for developed countries. The water productivity for irrigated rice is projected to increase by 33% and 10% for developing and developed countries, respectively. We used these figures to estimate the average annual improvement in the water productivities for developing and developed countries (e.g., 66/30 = 2.2% per annum improvement in water productivity for developing countries) and then the annual change in country-specific VWCs for all the crops mentioned above. The future values of VWC for fruits and vegetables were updated by incorporating 0.5% yearly improvement in water productivity; which is based on [27]. Table 1 contains a full summary of the sources and assumptions for the VWC values used in this study for all the commodities over various periods.


**Table 1.** Summary of sources and assumptions used for virtual water content (VWC) data.
