*2.3. AquaCrop Model*

The AquaCrop model is a crop water-driven productivity model developed by the FAO in 2009. A detailed description is presented in [49]. Water is the key limiting factor for crop production in this model [74]. Inputs for the AquaCrop model consist of weather data, crop, and soil characteristics (soil profile and groundwater), and field management practice or irrigation management practices [49].

Canopy cover is a crucial feature of AquaCrop [49]. Under unstressed condition, the exponential growth equation to simulate canopy development for the vegetative stage is

$$\text{CC} = \text{CC}\_0 \text{e}^{\text{CCC} \times \text{t}} \tag{1}$$

where CC is the canopy cover at time t and is expressed as fraction of ground covered, CCo is initial canopy cover size (at t = 0) as a fraction (%), and CGC is the canopy growth coefficient in fraction per growing degree day (GDD), a constant for a crop under optimal conditions, but modulated by stresses.

In the condition of water stress, the CGC is multiplied by a water stress coefficient of expansive growth (Ksexp) (Equation (2)).

$$\text{CGC}\_{\text{adj}} = \text{Ks}\_{\text{exp}} \text{CGC} \tag{2}$$

where Ksexp ranges from 1 to 0, canopy growth begins to slow down below the maximum rate when soil water depletion reaches the upper threshold, and stops completely when the depletion reaches the lower threshold.

Crop transpiration is proportional to the canopy cover and given by

$$\text{Tr} = \text{K} \text{s}\_{\text{sto}} \text{K} \text{cr}\_{\text{Tr}} \text{ET}\_{\text{o}} \tag{3}$$

Kssto is the stress coefficient for stomatal closure. KcTr is the crop transpiration coefficient (determined by canopy cover and KcTr,x), KcTr,x is the coefficient for maximum crop transpiration, and ETo is reference evapotranspiration (mm).

Biomass production is computed from crop transpiration and crop water productivity normalised for ETo and CO2 (Equation (4)). The extreme effect of low temperature on crop phenology, biomass accumulation, and harvest index, is considered with adjustment factors [67,75].

$$\mathbf{B} = \mathbf{K}\_{\mathbf{s}\_b}.\mathbf{f}\_{\text{WP}}.\mathbf{WP}^\*.\frac{\text{Tr}}{\text{ETo}}\tag{4}$$

where B is biomass, Tr is crop transpiration (mm day−1), ETo is reference evapotranspiration (mm day−1), and Ksb is the stress coefficient for low-temperature effects on biomass production. fWP is the adjustment factor to account for differences, if any exist, in the chemical composition of the vegetative biomass and harvestable organs. WP∗ is normalised crop water productivity, defined as the ratio of biomass produced to water transpired, normalised for the evaporative demand and CO2 concentration of the atmosphere.

The AquaCrop stress indicators include water storage (not enough water), waterlogging (too much water), air temperature (too high or too low), and soil salinity stress (too high).
