Optimal virtual water flows for improved food security in water-scarce countries

Crop production, water productivity, and virtual water

A method to calculate the water needed for crops is the water footprint (WF). The WF has a color-based classification: green water (precipitation), blue water (ground and surface water), and grey water (water to dilute polluted water to accepted water quality standards). A manual on how to calculate WFs has been published¹². Calculations of WFs integrate green and blue crop water use (evapotranspiration by crops) over the growing period of specific crops and express results per unit of yield (m³ kg⁻¹). The difference between crop-water use and effective rainfall is applied as a proxy for blue WFs when no data on actual irrigation water supply are available. WFs of specific crops vary greatly among countries, and even within countries⁴⁵. This means that water can be saved when crops are smartly traded. This may also be possible within a country if crops are grown where water productivity is the highest.

Calculation of the water footprint

Water footprints (WFs) are calculated as green and blue water footprints (WF_green, WF_blue, respectively) adopting the method from the WF manual¹². This study assumes that the difference between crop water requirement and evapotranspiration of green water (ET_Green) in crops is equal to the evapotranspiration of blue water (ET_blue); therefore, crop water requirements are met with irrigation water. The crop water requirements are estimated with the Food and Agriculture Organization’s CROPWAT model⁴⁶. The selected methods for calculating the reference evapotranspiration (ET₀) and effective precipitation (P_eff) are the FAO Penman–Monteith method^47,48 and the USDA’s SCS method⁴⁸, respectively. Calculations were performed at the provincial scale for each crop. Equations (1) through (4) are applied to calculate WF_green and WF_blue for the crops included in this study:

Actual crop evapotranspiration from reference evapotranspiration:

Reference evapotranspiration:

where ETc denotes the actual crop evapotranspiration (mm) during the growth period (t), ET₀ represents the reference evapotranspiration (mm day⁻¹), and K_c denotes the crop coefficient based on crop type and development stages (initial, middle, and late stages). In Eq. (2) e_a (kPa), e_d (kPa), Δ (kPa °C⁻¹), G (MJ m⁻² day⁻¹), T (°C), R_n (MJ m⁻² day⁻¹), U₂ (m s⁻¹), and γ (kPa °C⁻¹) denote the saturation vapor pressure, the actual vapor pressure, the slope of the saturation-vapor pressure curve, the soil heat flux, the average air temperature, the net radiation on the crop surface, the wind speed measured at a height of 2 m above ground level, and the psychrometric constant, respectively. Equations (3) and (4) calculate the green and blue water footprints (m³ ton⁻¹), in which P_eff (mm), Y (ton ha⁻¹), and 10, are represent effective precipitation, the crop yield, and a conversion factor from mm to m³ ha⁻¹, respectively. WF_green and WF_blue occur in irrigated cultivation; however, there is only WF_green in rainfed cultivation.

Optimization of crop production

All the steps of the methods used in this work were coded in MATLAB for use by decision-makers, planners, and interested organizations.

Balancing the agricultural system

An internal trade network was created to organize and remedy the weaknesses of the trade network. The lack of a comprehensive trade network has caused the crops to be exported regardless of the country’s demands, which eventually leads to the import of the same crops. The production and demand amounts of each crop in each province and their WF_green and WF_blue are determined with the following equations applied to N = 51 crops in J = 31 provinces:

where (i=1, 2,ldots , N;j=1, 2, ldots, J,) CP_(i,j) (ton), ICP_(i,j) (ton), RCP_(i,j) (ton), BCY_(i,j) (ton.ha⁻¹), GCY_(i,j) (ton.ha⁻¹), ICA_(i,j) (ha), RCA_(i,j) (ha), CD_(i,j) (ton), PCD_i (ton.person⁻¹), POP_j (person), TWF_blue(i,j) (m³), and TWF_green(i,j) (m³) denote the production of crop i in province j, crop production of irrigated land, crop production in rainfed cultivation, irrigated crop yield, rainfed crop yield, irrigated acreage, rainfed areas acreage, demand for crop i in province j, per capita diet, population of province j, the blue WF of crop i in province j corresponding to irrigated cultivation, and the green WFs of crop i in province j corresponding to irrigated cultivation, respectively.

TWF_blue(i,j) equals zero in rainfed cultivation, and TWF_green(i,j) is calculated with Eq. (10) based on RCP_(i,j). The deficit or surplus over the demand of the provinces were determined by comparing CP_(i,j) and CD_(i,j) for each crop in each province. Equation (11) implies that CS_(i,j) is the amount of crop i supplied in province j (ton), which involves the export and import of crops:

where (i=1, 2,ldots , N;j=1, 2, ldots, J) .The internal trade network is formed once the deficit and surplus for each crop in the provinces is determined, and crops are traded based on the shortest distance between the provinces. The developed trade network would improve the country’s agricultural system and reduce transportation costs between the provinces. Each province adds to or subtracts T_i,j (ton) from its crop amounts, where imports imply an addition and exports a subtraction of crop amounts. The internal exports and imports of WFs and the net water footprints trade (NWFT) in each province are calculated as follows:

where (i=1, 2,ldots , N;j, x=1, 2, ldots, J, r=x-1), WFT_(x,r,i) (m³), T_(x,r,i) (ton), (WF_green + WF_blue)_(x,i) (m³ ton⁻¹), EWF_(x) (m³), IWF_(r) (m³), and NWFT_(j) (m³) denote the WFs traded for crop i from exporting province x to importing province r, the amount of crop i exported from province x to province r, the blue and green WFs related to crop i in exporting province x, the WFs exported from province x by the trade of crops, the WFs imported into province r by the trade of crops, and the net water footprints trade in province j, respectively.

The positive and negative values ​​of NWFT_(j) represent the import and export of WFs to province j, respectively. The calculation of the internal trade between provinces with Eq. (11) permits determining the deficits and surpluses for each crop in the provinces nationally. At this juncture the provinces may resort to international trade to cope with deficits and surpluses. However, from this work’s premise of improving food security and self-sufficiency the cropping patterns of surplus crops in the provinces are modified as described in the next section.

Modifying exports to optimize the cropping pattern

The multi-objective optimization approach to increase food security and self-sufficiency redirects the resources to be used to cultivate export crops to the cultivation of crops that are in deficit (i.e., whose production is less than demand). This modification of cropping patterns in the provinces is based on their traditional cropping patterns. For this purpose, the internal trade network is linked to the optimization method to manage cropping patterns of the regions based on the output of the trade network, and on the goals of achieving food security and preventing water crisis. These two goals are pertinent in many countries where water scarcity is a limiting factor to achieve food security⁴⁹. Therefore, concerning available agricultural water it is imperative to pay attention to the type of water (green or blue) used. Specifically, WF_blue can be used in several areas of consumption; however, WF_green is not controllable in the same manner. The usage of WF_green by crops depends on the growing season, and the maximum use can be achieved by choosing the optimal crops. Therefore, this work treats WF_green and WF_blue as indicators of water crisis and food security, which were chosen as objective functions. In other words, controlling and managing WFs prevent its waste (thus reducing the water deficit and crisis). Selecting optimal crops based on WFs will increase production and food security. The water crisis and food security serve as the benchmark for comparison between the reference situation (without optimization) and the results of this new method. The reference situation refers to the initial state of food security and water crisis, which occurs before optimizing the cropping patterns.

The food-security objective function is expressed as follows:

The water-crisis objective function is written as follows:

where (i=1, 2,ldots, N=51;j=1, 2, ldots, J=31,) FS_i, CP_(i,j) (ton), CD_(i,j) (ton), WC_j, TWF_blue(i,j) (m³), and RWR_j (m³) denote the food security for crop i, production of crop i in province j, the demand of crop i in province j, the water crisis in province j, the blue WFs of crop i in province j, and the renewable water resources in province j, respectively.

Maximizing the FS index and minimizing the WC index represent the ideal situation. The maximizing function was converted to a minimization function for the purpose of multiobjective optimization. The final form of the objective functions i given by the following equations:

where (i=1, 2,ldots , N=51;j=1, 2, ldots, J=31.) The objective function Z₁ is calculated based on the food security index expressed as an average for all crops, and the objective function Z₂ is calculated as the average of the water crisis indexes in the 31 provinces. Both objective functions are affected by cropping patterns and cultivation areas. The water and land used must be calculated prior to modifying the cropping patterns. The amounts of surplus crops in the provinces and their equivalent water and land are calculated using the following equations:

where (i=1, 2,ldots, N;j=1, 2, ldots, J,) SCP_(i,j), (X_{1(i,j)}), (X_{2(i,j)}) denote the surplus crop i in province j (ton) determined based on demand and trade in the province, and the percentage of crop i in province j that must be removed from irrigated and rainfed cultivation, respectively. The amount of water and land available for new cultivation are calculated as follows:

where (i=1, 2,ldots , N;j=1, 2, ldots, J,) ICA_j^free and RCA_j^free denote the total available area of ​​irrigated and rainfed cultivation (ha) in province j, respectively, and TWF_blue,j^free represents the total amount of blue WFs available in province j (m³). It is noteworthy that the water and land available in irrigated cultivation can be altered. On the other hand, only the available land is controllable under rainfed cultivation.

The objective functions of the proposed method [Eqs. (18) and (19)] were subjected to a set of constraints introduced next.

1. (i)

   Modification of the cropping patterns

The available land in each province is allocated to crops that feature a deficit in the country and are part of the traditional cropping patterns of the provinces. The set of cultivable crops is determined using the following equation:

where p denotes the set of crops with deficit conditions in the country and SCP_(i,j) was defined above. Letting traditional irrigated and rainfed cropping patterns be denoted by A_j and B_j in province j, respectively, the set of irrigated and rainfed crops cultivable in province j was calculated as follows:

where (j=1, 2, ldots, J), IC_j and RC_j denote the irrigated and rainfed crops cultivable in province j, respectively.

1. (ii)

   Constraint on cultivation area

A fraction of ICA_j^free can be used in irrigated lands:

where (j=1, 2, ldots, J), and M denotes the fraction of blue water available.

1. (iii)

   Constraint on water use

The amount of water used to modify the cropping pattern in the provinces is limited:

where (left(j=1,2,3,ldots,Jright),) TWF^m_blue(i,j) denotes the blue WFs used to modify the cultivation in province j, and TWF_blue(i,j) represents the initial blue WFs consumed in province j to cultivate crops before changing the cropping pattern.

Ideal solution and pareto optimality

This work applied the multi-objective optimization Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The NSGA is based on the Genetic Evolutionary Algorithm and the Selection, Crossover, and Mutation operations⁵⁰. The NSGA was introduced by Deb et al.⁵¹,Srinivas and Deb⁵², then improved to the NSGA-II⁵¹. The NSGA-II has been widely studied in water resources management^53,54,55.

The NSGA-II produces a Pareto front of solutions, in which, each point represents a management scenario. The decision-maker selects a scenario based on the objective functions and situational analysis. Multi-criteria decision-making methods (MCDM) can be applied to select an efficient point on the Pareto front curve^56,57. This work implements the technique for order preference by similarity to ideal solution (TOPSIS) as the MCDM employed for that purpose. A description of the TOPSIS method is presented in the appendix.

The NSGA-II parameters were determined based on a trial-and-error process. Multiple runs of the algorithm were used to adjust the parameters to reduce uncertainty. For this purpose, the population size and maximum iteration were set equal to 400 and 500, respectively, and the crossover and mutation rates were set equal to 0.8 and 0.1, respectively. The flowchart of the proposed approach is displayed in Fig. 1.

Source: Ecology - nature.com