Detailed information of the field experiments.

Accurate prediction of crop phenological stage is essential for evaluating management strategies and assessing crop responses to environmental changes. In this work, we modified Non-dominated Sorting Genetic Algorithm with the core algorithm of PEST (MNSGA-II) and compared it to two other algorithms of Generalized Likelihood Uncertainty Estimation (GLUE) and Differential Evolution (DE) to calibrate the cultivar-specific parameters (CSPs) of CROPGRO-Soybean phenological model (CSPM) so as to exactly simulate the soybean phenology using the multi-source datasets of multi-site, multi-year, and multi-cultivar. Independent experimental data are used to validate the CSPM with the optimized parameters. The root means square error (RMSE), the mean absolute error (MAE), and coefficient of determination (R2) are used to evaluate the effects of different algorithms on calibrating the CSPs. The RMSEs (MAEs, R2) between all observed data and simulated data based on MNSGA-II, GLUE and DE are 4.28 (3.53, 0.9445) days, 4.76 (4.05, 0.9438) days and 5.17 (4.85, 0.9336) days, respectively, with little difference among the three algorithms. MNSGA-II has a certain advantage in calibration effect, and GLUE is the most stable during the repetition of each calibration. The MNSGA-II can be considered as a relatively ideal algorithm for estimating the crop model parameter. Which algorithm should be selected to calibrate the parameters of crop model according to the actual requirements. These results provide a reference to choose the suitable algorithm for estimating crop model parameter.