Irrigation

Two water management systems are implemented for agricultural land: irrigation and rain-feeding. The percentage of total agricultural land under irrigation is a non-linear function of GDP per capita:

 FeliX formula for irrigated area  σ , expressed as  a fraction of agricultural area.  σMIN  and   σMAX  represent lower and upper (a priori) limits on irrigated area, and are defined to be 0 and 1, respectively.  GDPpc  is global productivity per capita (variable), and  GDP†  is a reference value calibrated to 120,000 (US$2005 per capita).

FeliX formula for irrigated area σ, expressed as a fraction of agricultural area. σMIN and σMAX represent lower and upper (a priori) limits on irrigated area, and are defined to be 0 and 1, respectively. GDPpc is global productivity per capita (variable), and GDP† is a reference value calibrated to 120,000 (US$2005 per capita).

The plot below traces the expansion of irrigation systems through 2100, explicitly displaying the percentage of agricultural land under irrigation (σ). This high-efficiency water management strategy is predicted to expand over 300% by the end of the century. Also shown is rain-fed area, which oscillates within a smaller range over the same period.

water_Agricultural_Water_Demand.png

For simplicity, average areal water consumption is primarily dependent on management system (binary) and secondarily linked to GDP per capita. Water use is not dependent on agricultural land subclassifications. Areal water demand is parameterized by GDP, growing with agricultural intensification according to the following equation:

 FeliX formula for areal water demand (  
  
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   ω )  of irrigated ( I ) and rain-fed ( R ) land. Demand is scaled between   ω  MIN (I,R)  = (0.005, 0.005) and   ωMAX (    I,R)  = (0.05, 0.1), representing minimum and maximum water demand, respectively.    GDP†(I,R)  are  r  eference values calibrated to (4,000, 8,000) (US$2005 per capita).

FeliX formula for areal water demand (ω) of irrigated (I) and rain-fed (R) land. Demand is scaled between ω MIN (I,R) = (0.005, 0.005) and ωMAX (I,R) = (0.05, 0.1), representing minimum and maximum water demand, respectively.  GDP†(I,R) are reference values calibrated to (4,000, 8,000) (US$2005 per capita).

otal demand through 2100 is in the lower half of the plot above. Over this period, intensification and expansion lead to a 60% increase in total agricultural water demand.

Water & Agricultural Yields

One section of the FeliX model deals with water availability and usage, which carries consequences for agricultural yields and places exogenous limits on global (absolute) food production. The factor (γ) linking water availability to cropland yields is defined by the equation at right, where:

  • (Agricultural Water Withdrawal Fulfillment Factor) = 3.5 : a factor defining the strength of infrastructural limitations on agricultural water demand fulfillment.
  • σ (Maximum Water Withdrawal Rate: a variable function equivalent to Available Water Resources
  • θ (Agricultural Water Demand) : total agricultural water demand, based on extent of rainfed & irrigated land
SI_Agricultural_Water_Demand.png

In the above plot, annual Agricultural Water Demand is shown in green. Industrial and Domestic Water Demand (orange) are grouped together. Historical data from the UN International Hydrological Programme (IHP) is used to calibrate demand. The blue line represents IHP historical data on global annual supply, including withdrawals from surface and groundwater and non-conventional sources such as desalination [1].

Despite anticipated improvements in water use efficiency (due especially to irrigation), agricultural water demand grows 62% by 2100. Overall, water demand grows 75%, while supply is projected to grow only 54%. Unaddressed, this deficit limits the Maximum Water Withdrawal Rate for agricultural activities, with a double-digit negative impact on agricultural yields, as shown by the factors at the bottom of the plot.

[1] Shiklomanov, I.A., Rodda, J.C.: World water resources at the beginning of the twenty-first century. Technical report, International Hydrological Programme (IHP) of UNESCO (2003)