Abstract Crop phenological development models are fundamental tools that can be used for scheduling agricultural practices and predicting crop yields. In previous research, different crop phenology models were compared, and different parameterization methods for crop model calibration were evaluated, which revealed that both model structures and parameterization methods were important for crop modeling. However, few studies have considered the combination of both factors and compared these influences simultaneously. Therefore, information regarding the extent of variation in model accuracy and uncertainty depending on model structure and parameterization method is lacking. In this study, we developed three winter wheat phenology models with different structures, i.e., the Agricultural Production System Simulator model for wheat (APSIM-wheat), Wang and Engel model, and sigmoid and exponential function based model, to predict the heading date as a case study. We calibrated these models using three different parameterization methods (augmented Lagrange multiplier method, Nelder-Mead method, and Bayesian optimization with Gaussian process) to investigate their effects on model accuracy and uncertainty. Six-fold cross validation of nine combinations of model calibration (3 models × 3 parameterizations) and their validation revealed that accuracies ranged mostly from 2 to 7 days in the root mean square error (RMSE). The coefficient of variation of RMSE varied widely in among model structures and parameterization methods (∼0.01–0.6). Furthermore, the coefficient of variation of model parameters also varied substantially depending both on model structure and parameterization method. Especially for the model with more parameters, we found that the prediction and parameter stability varied depending on parameterization methods. These findings suggest that both prediction and parameter uncertainty varied with model structure and parameterization method and emphasize the importance of which models and parameterization methods modelers use for robust crop phenology model.

中文翻译：

---

冬小麦物候模型的预测和参数不确定性取决于模型和参数化方法的差异

摘要 作物物候发育模型是可用于安排农业实践和预测作物产量的基本工具。在以往的研究中，比较了不同的作物物候模型，评估了用于作物模型校准的不同参数化方法，表明模型结构和参数化方法对于作物建模都很重要。然而，很少有研究同时考虑这两个因素的组合并比较这些影响。因此，缺乏关于取决于模型结构和参数化方法的模型精度和不确定性变化程度的信息。在本研究中，我们开发了三种不同结构的冬小麦物候模型，即小麦农业生产系统模拟器模型（APSIM-wheat），Wang 和 Engel 模型，以及基于 sigmoid 和指数函数的模型，以预测航向日期作为案例研究。我们使用三种不同的参数化方法（增强拉格朗日乘数法、Nelder-Mead 法和贝叶斯优化高斯过程）校准这些模型，以研究它们对模型精度和不确定性的影响。九种模型校准组合（3 个模型 × 3 个参数化）及其验证的六倍交叉验证表明，均方根误差 (RMSE) 的准确度主要在 2 到 7 天之间。RMSE 的变异系数在模型结构和参数化方法之间变化很大（~0.01-0.6）。此外，模型参数的变异系数也随着模型结构和参数化方法的不同而发生很大变化。特别是对于参数较多的模型，我们发现预测和参数稳定性取决于参数化方法。这些发现表明，预测和参数不确定性都因模型结构和参数化方法而异，并强调了建模者使用哪些模型和参数化方法来建立稳健的作物物候模型的重要性。