## 1 Introduction  
To improve irrigation water management in agricultural fields and attain sustainability, it is critical to define the optimal irrigation time and irrigation amounts to replenish the soil vadose layers, where crop roots develop, to conserve water and soil resources. Irrigation water management practices are often based on the soil water balance (SWB) approach for irrigation scheduling development [1, 2]. The SWB approach for irrigation provides a soil water volume balance that accounts for the inflow and outflow of water fluxes in the crop root zone to define the temporal changes in the soil volumetric water content [3]. The simplified daily SWB approach is given by Equation (1):  
\[D_{r,i}=D_{r,i-1}\ -\left(P-RO\right)_{i}-I_{i}-CR_{i}+ET_{c,i}+DP_{i} \tag{1}\]  
where \(\mathrm{D_{r,i}}\) is the water depleted in the root zone at the end of day \(\mathrm{i^{th}}\); \(\mathrm{D_{r,i-1}}\) is the water in the root zone in the previous day \(\mathrm{(i-1)^{th}}\); \(\mathrm{P_{i}}\) is the rainfall water depth; \(\mathrm{RO_{i}}\) is the surface water runoff; \(\mathrm{I_{i}}\) is the net irrigation water depth; \(\mathrm{CR_{i}}\) is the capillary rise from shallow water table (groundwater); \(\mathrm{ET_{c,i}}\) is the daily crop evapotranspiration; \(\mathrm{DP_{i}}\) is the deep percolation (vertical water loss beyond the root zone). All variables in Equation (1) are given as water depth units (e.g., mm or in). Better irrigation strategies are often related to an SWB approach that accounts for an accurate \(\mathrm{ET_{c}}\) estimate through the actual crop evapotranspiration (\(\mathrm{ET_{a}}\)) rates determination. This is the correct amount of water depleted in the soil throughout the plant root zone that would be replenished with irrigation when \(\mathrm{ET_{c}}\) (through \(\mathrm{ET_{a}}\)) has been properly determined. In general, throughout this process, water and nutrient savings or conservation are achieved because common irrigation practices tend to over-irrigate, promoting water, soil, and agro-chemical losses through land surface runoff and deep percolation, potentially contaminating groundwater and/or surface water bodies. At the local farm scale, accurate crop \(\mathrm{ET_{a}}\) estimation is critical to support quasi-real-time decision-making approaches for water allocation and optimization of irrigation water management [4; 5]. Modeling advancements in remote sensing (RS) of the environment have facilitated the quasi-real-time mapping of crop water requirements or \(\mathrm{ET_{a}}\) for irrigation on a spatio-temporal basis, using multispectral and thermal imagery from different sensor types [6; 7] since the early 1970s. Remote sensing involves the scientific measurement of emitted and reflected light across various spectral ranges, including visible, invisible, and longwave infrared (LWIR), without direct contact with the target area [8]. Optical devices mounted on aerial platforms (e.g., small aircraft or automated aerial vehicles), spaceborne systems (e.g., satellites), and proximal instruments (e.g., handheld roaming or stationary radiometers) have generated data at different temporal, spectral, and spatial resolutions, benefiting applications like irrigation water management, soil nutrient monitoring, crop growth assessment, and yield mapping [9; 10; 11]. The use of RS techniques to support sustainability of irrigation scheduling practices has been investigated for more than 50 years [12; 13]. Remote sensing of crop \(\mathrm{ET_{a}}\) approaches that use multispectral and thermal data to map crop \(\mathrm{ET_{a}}\) are fundamentally based on the land surface energy balance (SEB) concept. The SEB approach for estimating \(\mathrm{ET_{a}}\) calculates the energy required for evaporating water (latent heat flux, LE) as the residual term of the simplified SEB (Equation (2)).