During a rainstorm, only a part of rainfall is retained in the soil and plants that used by crop for growing. This amount of rainfall is called effective rainfall (R_eff, mm). When effective rainfall exceeds potential evapotranspiration of plant ETc, the total amount of potential evapotranspiration is green evapotranspiration. However, when potential evapotranspiration is greater than the total effective rainfall, the amount of green water evapotranspiration is equal by effective rainfall:

Replacing Eq.2 and 3 to Eq.1, green water footprint is calculated as following equation.

Blue water footprint

As mentioned above, blue water footprint is surface and ground water consumed in cropping which is also estimated as total blue water used for one unit of crop yield (m³/ton).

Where, CWR_blue is blue water requirement (m3/ha);

Y is crop yield (tons/ha);

10 is transform coefficient from mm to m³/ha;

ET_blue: Green evapotranspiration (Eq.7);

W_loss water loss in irrigation system that do not return to surface and ground water;

Lgp length of growth period of crops.

ET_blue only has meaningful when in case of identifying the influence of evapotranspiration from rainfall or irrigation system. In case of calculation of water footprint for crop, in order to simplify calculation process, blue water footprint can be calculated directly from total irrigation water requirement, and it is not necessary classify ET_blue and W_loss.

Grey water footprint

Grey water calculation equation is based on method of Hoekstra and Chapagain:

Where:

- α: permeability coefficient;

- AR (kg/ha): The amount of fertilizer used for 1 hectare;

- c_max, c_nat(kg/m³): the maximum concentration allowed and natural concentration of chemical pollutants;

- Y (ton/ha): crop yield.

The contaminants are usually found in fertilizers (nitrogen, phosphorus, etc.) insecticides and herbicides. In order to simplify the calculation process, assuming there is only a "waste stream" flowing into freshwater resources that is constant proportion of total amount of fertilizer or pesticide use in the field. Then, it is only need to calculate for the most serious pollutants that has highest grey water footprint

2.2 Calculation virtual water in products processing

Water footprint of the output of a production processing is as following:

Where:

- WF_prod[p] the water footprint of output product p (volume/mass);

- WF_prod[i] is the water footprint of inputs i that is calculated as total virtual water used for cropping (volume/mass);

 - WF_proc[p] is water footprint that used in processing of input products that derived for each unit of output products (volume/mass);

- f_p­[p] : is the ratio of output achieved per unit of input products

- f_v­[p] : the percentage value of product p in total value of outputs (Outputs can be more than 1 type of products)

In this study, each component is identified as following:

- WF_prod[p] is water footprint to produce 1 ton of white rice, corn or coffee (m³/ton);

- WF_prod[i] applies only to calculate the virtual water used for rice production, is water footprint of 1 ton of paddy (m³/ton);

- WF_proc[p] is equal zero (m³/ton);

- f_p­[p]: is equal 0.8 with rice processing from paddy to Brown rice (content bran) and 0.85 with rice processing from brown rice to white rice.

- f_v­[p]: is equal 0.95 with rice processing from paddy to Brown rice (content bran) and 0.86 with rice processing from brown rice to white rice.

3. APPLICATION AND RESULTS

The proposed method is applied to calculate virtual water for three main crops in seven economic zones of Vietnam. For each zone, the data used for calculation are: meteorological data at 100 stations (NCHMF, 2013), statistics data of residence and agriculture [5-6]. The information of agricultural water consumption and fertilizer use are obtained from [7] and [8], respectively.