## 2 Materials and Methods
### Data Collection
#### 2.2.3 Estimation of Crop Water Requirements and Evapotranspiration Models  
To estimate the water requirements of the avocado orchard during the 2021 and 2022 growing seasons, crop coefficients (Kc) were derived independently from the NDVI, SAVI, and NDWI. Crop coefficients are dimensionless factors that adjust ETo to reflect the actual water use of the crop (ETc), varying with the crop's growth stage and canopy development, and are able to capture the dynamic water needs throughout the season. The reference evapotranspiration was calculated daily using three meteorological models: the Hargreaves-Samani model, a simplified Priestley-Taylor model, and the Blaney-Criddle model. This framework provided a detailed understanding of crop water dynamics under varying environmental conditions. The crop coefficients were calculated using empirical equations tailored for perennial crops, ensuring relevance to avocado orchards. The equations for each vegetation index were as follows:NDVI:  
\[\text{Kc}=1.2\cdot\text{NDVI}-0.15 \tag{4}\]  
where 1.2 is a coefficient reflecting the sensitivity of \(\text{Kc}\) to the NDVI, emphasizing its strong correlation with canopy cover and the leaf area index (LAI), and \(-0.15\) is an intercept that adjusts \(\text{Kc}\) for sparse vegetation conditions where NDVI values are low. SAVI:  
\[\text{Kc}=1.0\cdot\text{SAVI}-0.1 \tag{5}\]  
where 1.0 is a coefficient capturing the soil-adjusted dynamics of \(\text{Kc}\), which is particularly relevant for partial canopy cover conditions, and \(-0.1\) is an intercept to account for soil reflectance under sparse vegetation. NDWI:  
\[\text{Kc}=0.85\cdot\text{NDWI}+0.05 \tag{6}\]  
where 0.85 is a coefficient reflecting the relationship between the canopy water content and \(\text{Kc}\), making the NDWI particularly sensitive to changes in water availability, and 0.05 is an intercept ensures that \(\text{Kc}\) remains positive despite low NDWI values. The differences in the coefficients and intercepts reflect each vegetation index's unique sensitivities to biophysical characteristics, such as vegetation cover, soil influences, and water contents. The reference evapotranspiration (ETo) was calculated using three meteorological models chosen for their compatibility with the available meteorological inputs:  
Hargreaves-Samani model:  
\[\text{ETo}=0.0023\cdot\text{Rs}\cdot\left(\text{T}_{\text{max}}-\text{T}_{ \text{min}}\right)\cdot 0.5\cdot\left(\text{T}_{\text{avg}}+17.8\right) \tag{7}\]  
where Rs is the solar radiation at the surface (MJ/m\({}^{2}\)); \(\text{T}_{\text{max}}\), \(\text{T}_{\text{min}}\), and \(\text{T}_{\text{avg}}\) are the maximum, minimum, and average daily temperatures (\({}^{\circ}\)C); and 0.0023 is a coefficient specific to the Hargreaves-Samani model. Simplified Priestley-Taylor model:  
\[\text{ETo}=0.23\cdot\text{Rs} \tag{8}\]  
where 0.23 is a coefficient suited for energy-driven evapotranspiration in humid or energy-limited conditions. Blaney-Criddle model:  
\[\text{ETo}=\text{p}\cdot\left(0.46\cdot\text{T}_{\text{avg}}+8\right) \tag{9}\]  
where p is the proportion of annual daytime hours for each day of the year (unitless), \(\text{T}_{\text{avg}}\) is the average daily temperature (\({}^{\circ}\)C), and 0.46 and 8 are constants derived from the original Blaney-Criddle formulation. These models were selected to accommodate the available meteorological inputs, which included the daily temperature (\(\text{T}_{\text{max}}\), \(\text{T}_{\text{min}}\), \(\text{T}_{\text{avg}}\)), solar radiation (Rs), and estimated daylight hours (p). The derived \(\text{Kc}\) values for the NDVI, SAVI, and NDWI and the ETo values for each meteorological model were calculated independently. This separation allowed for a robust assessment of each index's relative performance without introducing aggregation biases.