## 2 Materials and Methods
### Method
#### 2.3.3 Crop Irrigation Requirement Modelling  
Crop irrigation requirements (CIRs) are defined as the total amount of water, expressed in water height (mm), applied to the crop throughout the entire irrigation season to fully satisfy the crop water requirements. CIRs were computed in this study according to the FAO 56 approach [13] using the IrrigRotation soil water balance simulation model [22].  
The IrrigRotation (Figure 4) model simulates the soil water balance for crop rotations, performing this simulation with a daily time step, and computes \(ET_{c}\) according to the dual crop coefficient approach proposed by [13; 14; 35], as defined in Equation (3):  
\[ET_{c}=(K_{s}\times K_{cb}+K_{e})\times ET_{o} \tag{3}\]  
where \(ET_{c}\) is the crop evapotranspiration (mm\(\cdot\) day\({}^{-1}\)), \(K_{cb}\) is the basal crop coefficient, \(K_{e}\) is the soil evaporation coefficient, \(K_{s}\) is the water stress coefficient and \(ET_{o}\) is the reference crop evapotranspiration (mm\(\cdot\) day\({}^{-1}\)). \(K_{s}\) describes the effect of water stress on crop transpiration. For soil water-limiting conditions, \(K_{s}<1\), and when there is no soil water stress, \(K_{s}=1\). In this study, no water stress is assumed when simulating the soil water balance. The \(K_{cb}\)-NDVI retrieved from EO data provides \(K_{cb}\) values adjusted to the field conditions, already incorporating water stress, in contrast to the standard tabulated \(K_{cb}\) values.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Crop Type** & **No. of Training Parcels** & **No. of Validation Parcels** & **Total of Parcels** \\ \hline Maize & 12 & 16 & 28 \\ Soybean & 5 & 8 & 13 \\ Pasture & 2 & 3 & 5 \\ Bean & 2 & 3 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Ground truth parcels used to train the classifier and to validate the classification results.  
Figure 4: Flowchart of the IrrigRotation soil water balance model [22].  
\(ET_{o}\) is computed from meteorological data using the FAO Penman-Monteith (FAO-PM) method [13; 14]. The required meteorological data variables include solar radiation (\(R_{s}\)) (MJ: m\({}^{-2}\cdot\) day\({}^{-1}\)), maximum air temperature (\(T_{max}\)) (\({}^{\circ}\)C), minimum air temperature (\(T_{min}\)) (\({}^{\circ}\)C), maximum relative humidity (\(HR_{max}\)) (%), minimum relative humidity (\(RH_{min}\)) (%), average wind speed at a height of 2 m (\(u_{2}\)) (m\(\cdot\) s\({}^{-1}\)) and precipitation (mm\(\cdot\) day\({}^{-1}\)).  
The estimation of \(K_{e}\) requires a daily water balance computation for the calculation of the soil water content remaining in the upper topsoil [13; 14; 35]. The soil water balance equation adopted in IrrigRotation model is defined as [36]:  
\[\Delta R=\left(P-ET_{c}+R_{g}-E_{s}+A_{c}-D_{r}\right)_{\Delta t} \tag{4}\]  
where \(\Delta R\) is the variation of the volume of water stored in the root zone (mm), \(\Delta t\) is the time step (day), \(P\) is the precipitation (mm\(\cdot\) day\({}^{-1}\)), \(R_{g}\) is the irrigation (mm\(\cdot\) day\({}^{-1}\)), \(A_{c}\) is the capillary rise (mm\(\cdot\) day\({}^{-1}\)), \(ET_{c}\) is the crop evapotranspiration (mm\(\cdot\) day\({}^{-1}\)), \(E_{s}\) is the runoff (mm\(\cdot\) day\({}^{-1}\)) and \(D_{r}\) is the drainage and deep percolation (mm\(\cdot\) day\({}^{-1}\)). In this model, the soil profile is divided into three different layers. In the top soil layer, soil evaporation occurs with plant transpiration. The second layer corresponds to the portion of the soil that is occupied by the roots and where water is only withdrawn by plant transpiration. The thickness of this layer increases during crop growth. The bottom layer lies between the crop root depth \(Z_{r}(t)\) on day \(t\) and the maximum root depth. The irrigation requirements are calculated based on the values of the available soil water (ASW) in the second layer and on the irrigation management options [22; 37]. In the present study, an irrigation strategy of no water restrictions was evaluated.