RESEARCH ARTICLE Application of hybrid ANN-whale optimization model in evaluation of the field capacity and the permanent wilting point of the soils Babak Vaheddoost 1 & Yiqing Guan 2 & Babak Mohammadi 2 Received: 8 August 2019 /Accepted: 24 January 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract Field capacity (FC) and permanent wilting point (PWP) are two important properties of the soil when the soil moisture is concerned. Since the determination of these parameters is expensive and time-consuming, this study aims to develop and evaluate a new hybrid of artificial neural network model coupled with a whale optimization algorithm (ANN-WOA) as a meta-heuristic optimization tool in defining the FC and the PWP at the basin scale. The simulated results were also compared with other core optimization models of ANN and multilinear regression (MLR). For this aim, a set of 217 soil samples were taken from different regions located across the West and East Azerbaijan provinces in Iran, partially covering four important basins of Lake Urmia, Caspian Sea, Persian Gulf-Oman Sea, and Central-Basin of Iran. Taken samples included portion of clay, sand, and silt together with organic matter, which were used as independent variables to define the FC and the PWP. A 80–20 portion of the randomly selected independent and dependent variable sets were used in calibration and validation of the predefined models. The most accurate predictions for the FC and PWP at the selected stations were obtained by the hybrid ANN-WOA models, and evaluation criteria at the validation phases were obtained as 2.87%, 0.92, and 2.11% respectively for RMSE, R 2 , and RRMSE for the FC, and 1.78%, 0.92, and 10.02% respectively for RMSE, R 2 , and RRMSE for the PWP. It is concluded that the organic matter is the most important variable in prediction of FC and PWP, while the proposed ANN-WOA model is an efficient approach in defining the FC and the PWP at the basin scale. Keywords Hybrid model . Hydropedology . Meta-heuristic algorithm . Soil moisture Introduction Field capacity (FC) and permanent wilting point (PWP) are usually evaluated as two vital parameters in irrigation, agri- culture, and study of the water and the minerals within the soil (Rab et al. 2011). The definition of the FC is slightly modified in the glossary of the soil science (SSSA 1984) as the amount of moisture or the remained water in the soil sample after which 2–3 days of excessive water is drained from the soil or as the water content when the soil suction is - 33 kPa. This can usually be reached when several days from the precipitation or irrigation within a uniformly structured soil are passed. On the other hand, PWP is defined as the water content in the soil which plants cannot extract from the soil profile. It represents a lower limit of water available for the plant which is retained by the soil particles under a tension of 1500 kPa (Slatyer 1967). Thereby, the FC and the PWP are two parameters in evaluation of the moisture in calculation of the available water for irrigation. Hence, for a relatively small area with an acceptable homogeneity, in terms of soil physicochemical properties, it would be possible to gain a good approximation of the moisture by performing an adequate number of costly and time-consuming field and lab experiments (Veihmeyer and Hendrickson 1949; Keshavarzi et al. 2012). On the other hand, other properties related to textural character- istics of the soil are valuable in defining hydraulic prop- erties, and simulation of the deep and subsurface flow in modeling the movement of the water in the soil. In this respect, characteristics like the amount of water in the soil sample, as the difference between FC and PWP, can be evaluated to describe the ability of water retention which is an Responsible editor: Marcus Schulz * Babak Mohammadi Babakmohammadi@aol.com 1 Department of Civil Engineering, Bursa Technical University, Bursa, Turkey 2 College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China Environmental Science and Pollution Research https://doi.org/10.1007/s11356-020-07868-4