Mathematical Modeling of the Evapotranspiration of Common Crops in Different Latitudes of Iran

The population is growing at an unprecedented rate, leading to a surge in food demand. This surge is coinciding with scarcity of water resources and intensifying competition among various sectors for water consumption and therefore there is an urgent need to precisely assess the water requirements of crops. Numerous studies have been conducted so far to determine water demand by considering various factors. Among these approaches, the FAO-Penman-Monteith equation has emerged as a widely recognized method. However, this equation entails extensive data requirements and involves lengthy calculations. The objective of this study was to develop a model for estimating the cumulative water requirement of common crops (wheat, barley, corn, and forage corn) on various latitudes within a specific region (the western vertical strip of Iran). Remarkably, the model only considers time as the input variable (growth period duration). Since the relationship between the cumulative water requirement of various crops and the length of the growth period follows a sigmoidal pattern, three mathematical models were employed to capture this trend; three-parameter logistic models, Gaussian functions, and third-order polynomials, all used for the purpose of modeling. The findings indicated that all three models exhibited high accuracy in estimating the cumulative water requirement for the crops during the growth period. The logistic model, in particular, demonstrated superior performance when evaluated using R2, RMSE, and NSE indices. Unlike the Gaussian and polynomial models, the logistic model preserved its original shape within the range of the growth period length, making it more appropriate for modeling the cumulative water demand from physical and biological standpoints. By utilizing this model, the water requirement for the intended product can be effortlessly estimated at any given point and within any desired time interval throughout the growth period, spanning from seconds and minutes to days, weeks, months, and beyond. As per the findings of this study, an equation with exceptional precision was introduced for each product in a homogeneous region, where the length of the growth period is consistent. This equation allows for the straightforward and precise estimation of crop water requirements.