Inverse Modeling for Crop Coefficient Optimization in Thornthwaiteand Mather and FAO-56 Dual-Kc Models for Daily and 10-day Estimation of Actual Evapotranspiration and Soil Water Content in Rainfed Sugarcane

Abstract Reliable soil water balance models are needed for sugarcane water management under rainfed and non-standard field conditions. This study optimized crop coefficients and assessed the Thornthwaite and Mather Crop (ThM) and FAO-56 dual-Kc models for estimating daily and 10-day soil water content (θ) and actual evapotranspiration (ET a ) in rainfed sugarcane in Alagoas State, Brazil. Field θ was measured with a reflectometry probe, and ET a was determined using the Bowen ratio-energy balance method. The Metropolis-Hastings algorithm implemented in OpenModel was used to optimize the mid-season crop coefficient (K c_mid ) for ThM, and the mid-season basal crop coefficient (K cb_mid ) and soil water depletion fraction (p) for dual-Kc, using measured ET a or θ as the optimization reference. The ET a -based optimized K c and K cb values were 0.89–0.90, lower than the FAO-56 tabulated values and close to the experimental K c (0.79 ± 0.11), whereas θ-based optimization resulted in a K cb of 1.04, and a very low K c (0.38), suggesting parameter compensation. Daily ET a estimates improved mainly under soil water recharge (P – ET c ≥ 0), whereas both models performed poorly under soil water extraction (P – ET c < 0), indicating limitations in representing water stress and short-term soil water redistribution. Soil water content was simulated more consistently than ET a , especially after optimization. Aggregation to 10-day intervals improved model robustness, with dual-Kc performing better for ET a and ThM providing the best soil water estimates. Thus, the optimized models are useful for medium-term water balance assessment and irrigation scheduling but should be used cautiously for daily ET a estimation under water-stress conditions.