## 2 Materials and Methods
### Description of the AquaCrop Model  
AquaCrop is a multi-crop model developed by the Land and Water Division of the Food and Agriculture Organization (FAO). The model estimates the crop productivity decrease in response to water stress [52]. The AquaCrop model evolved from the proportionality factor between the relative yield decline and the relative reduction in evapotranspiration (Ky) [26] by (1) separating  
Figure 2: Flowchart showing the methodology used in this study. See text for full details.  
non-productive soil evaporation (E) from productive crop transpiration (Tr); and (2) estimating biomass production directly from actual crop transpiration using a water productivity parameter. These changes lead to the following equation, which is at the core of the AquaCrop model [53]:  
\[\text{B}=\text{WP}\cdot\Sigma\text{Tr} \tag{1}\]  
where \(B\) is the biomass, produced cumulatively (kg per m\({}^{2}\)), \(Tr\) is the crop transpiration (either mm or m\({}^{3}\) per unit surface) summed over the period in which the biomass is produced and \(WP\) is the water productivity parameter (either kg of biomass per m\({}^{2}\) and per mm or kg of biomass per m\({}^{3}\) of water transpired).  
For most crops, only part of the biomass produced is partitioned to the harvested organs to produce yield (Y) and the ratio of yield to biomass is known as the harvest index (HI), hence:  
\[\text{Y}=\text{HI}\cdot\text{B} \tag{2}\]  
The underlying processes culminating in B and HI are largely distinct from each other. Therefore, separation of Y into B and HI makes it possible to consider the individual effects of environmental conditions and stresses on B and HI separately. The normalized WP (designated as WP*) remains virtually constant over a range of environments. This has fundamental implications for the robustness of the model, which is further enhanced by the daily quantification of HI over the yield formation period. Improved knowledge of plant responses to water stress on short time scales as well as enhanced computational capacity and more accurate procedures to determine daily soil water status, make it possible to simulate yield in daily time steps. This enabled the important transition from a static approach to a dynamic growth model [23; 53; 54].  
It assumes relative evapotranspiration as the key to simulating the yield of a given environment. It divides evapotranspiration into soil evaporation and crop transpiration and integrates a canopy growth and senescence model as the basis for estimating transpiration. The crop yield is computed as a function of the final biomass and the harvest index, while the effects of water stress are isolated to canopy growth, canopy senescence, transpiration and the harvest index [9; 54; 55].  
AquaCrop includes the major components of the soil-plant-atmosphere continuum and the parameters driving phenology, canopy cover, transpiration, biomass production and final yield [54; 55]. To run the model, five daily weather input variables are required, including maximum and minimum air temperatures, evapotranspiration, rainfall, annual mean carbon dioxide concentrations of the soil root zone's water balance and air CO\({}_{2}\) concentration, which affects water productivity and leaf growth [53; 55]. The specific features of AquaCrop that distinguish it from other crop models are its emphasis on water and the use of ground canopy cover instead of the LAI, as well as the use of both water productivity values normalized for atmospheric evaporative demand and carbon dioxide concentration, which gives the model an extended extrapolation capacity [54; 55]. Compared with other models, AquaCrop is relatively simple to operate by those with little or no research experience. It produces a high level of accuracy and requires only a limited set of input parameters, most of which are rather easy to acquire [20].