*2.4. Virtual Water Flows*

We calculated the virtual water imports (*VWIw*,*i*,*r*,*t*) and virtual water exports (*VWEw*,*i*,*r*,*t*) of Pakistan for both blue and green water by multiplying the blue and green VWC with import and export quantities of the commodities, as follows:

$$V\text{V}\mathbf{M}\_{w,i,r,t} = \mathbf{M}\_{i,r,t} \times V\text{V}\mathbf{C}\_{w,i,r,t} \tag{5}$$

$$V\text{W}I\_{w,i,r,t} = M\_{i,r,t} \times V\text{W}C\_{w,i,PAK,r,t} \tag{6}$$

where *Mi*,*r*,*<sup>t</sup>* denotes the quantity of commodity *i* imported by Pakistan from country/region *r* during year *t*. *Xi*,*r*,*<sup>t</sup>* represents Pakistan's export of commodity *i* to destination *r* in year *t*. *VWCw*,*i*,*r*,*<sup>t</sup>* is the partner countries' virtual water content (blue and green) of the particular commodity in the respective year (unit: m3/ton). *VWCw*,*i*,*PAK*,*<sup>t</sup>* is Pakistan's virtual water content (blue and green) of the particular commodity in the respective year (unit: m3/ton). Subtracting VWE from VWI gives us net virtual water imports (NVWI) of Pakistan, as under:

$$NVWI\_{w,i,PAK,t} = VWI\_{w,i,r,t} - VWE\_{w,i,r,t} \tag{7}$$

Pakistan's domestic saving of blue/green water (*DSAVw*,*i*,*PAK*,*t*) through imported commodities is the amount of blue/green water needed to produce the same commodities at home. This is estimated by replacing *VWCw*,*i*,*r*,*<sup>t</sup>* of the partner country, with *VWCw*,*i*,*PAK*,*<sup>t</sup>* of Pakistan in Equation (5) and then using it in Equation (7).

Pakistan can also contribute to global water saving if it saves more domestic water (*DSAVw*,*i*,*PAK*,*t*) than its net virtual water import (*NVWIw*,*i*,*PAK*,*t*). Specifically, the global saving (or loss) of blue and green water is the difference between the amount of water which Pakistan saves domestically through its food trade and the amount of *NVWIw*,*i*,*PAK*,*t*, which it imports from other countries Equation (8).

$$GSAV\_{w,j,t} = DSBV\_{w,j,PAK,t} - NVVMI\_{w,j,PAK,t} \tag{8}$$

Pakistan's food trade would save (waste) water at the global level if we get a positive (negative) value from Equation (8). Total national and global water savings are the sum of respective savings from all commodities and all trading partners.
