基于非线性参数优化的水稻花前生育期参数估计

Parameter Estimation in Pre-flowering Rice Phenological Models Using Nonlinear Parameter Optimization

水稻生育期模型为复杂的非线性模型,其参数的合理标定是模型应用的重要环节。本文采用两种不同温度响应函数的花前生育期模型(MBETA和MBILN),利用基于GML(Gauss-Marquardt-Levenberg)算法的模型独立参数优化程序PEST(model-independent parameter estimation)对模型参数进行优化,并在优化中引入参数先验信息和参数初始值扰动方法,以提高参数优化结果的可靠性。结果显示,参数先验信息有效降低了待优化参数的不确定性。最优参数值的95%置信区间较初始值域显著缩小。在优化得到的参数相关系数矩阵中也未显现出高度相关的参数。从目标函数值(Φ)序列看,MBETA和MBILN的Φ值最终收敛至相当接近的最小值,分别为11.71和11.82。但该最小值下两个模型的温度、光周期效应等参数值存在一定差异。这种差异平衡了不同温度响应方程与模型其它方程对水稻生育期模拟误差的贡献。在最优参数值组合下,两个模型验证结果表现一致。其中,抽穗开花期模拟值与实测值的相关性均通过了0.01水平的显著性检验。模拟误差主要来自幼穗分化期,与缺少对水稻光周期敏感始期的观测有关。本文优化方法降低了待优化参数收敛于局部小值的几率,对稳定参数优化和提高优化结果的可靠性具有重要作用。

Rice phenological model contains a nonlinear dependence between rice phenological prediction and model parameters and thus estimation of these parameters from measurements is the most critical step for the model application. These parameters include critical temperatures,critical photoperiod,and photoperiod sensitivity. For transplanting rice,the transplanting shock is another parameter should be adjusted,which is used to introduce the influence of transplanting on rice development. Previous reports showed that the critical temperatures and two photoperiod-related parameters are strongly correlated and their calibration is still unsuccessful. In this paper,the model-independent parameter estimation software PEST was used to estimate these parameters. We try to improve the calibration by introducing a method to find optimal values in their parameter space. This method firstly introduces prior information for each parameter and then adjusts initial parameter values by overall ± 1% recursive changes to their prior values. With all combinations of initial parameter values,PEST calculates objective function values and looks for an optimal combination of parameter values according to the objective function value is the lowest or not. Here,phenological observations of rice variety Liangyoupeijiu were used to parameter estimation. And,for simplicity,the parameter estimation for pre-flowering phenological model was tested as an example. The pre-flowering model was performed applying two different temperature response functions,i. e. BETA function and a bilinear function（ BILN）.Hence,the model with BETA function was called as MBETA and the model with BILN was named as MBILN. The results showed that the parameters uncertainties were effectively reduced through introducing the prior information. The obtained 95% confidence intervals of parameter values were significantly reduced. Highly correlated parameters were not perceived in the parameters correlation matrix. By adjusting initial parameter values,a series of objective function values were obtained through each calculation. In these series,the objective function values of MBETA and MBILN finally converged at similar minima,i. e. 11. 71 and 11. 82,respectively. Under the minima,optimal combination of parameter values for each model was obtained and used in validation. It shows that the optimal parameter values are different between models,but the validation results are consistent. The difference between optimal values was mainly attributed to the different temperature response functions which compete with photoperiod effect in minimizing objective function values. From the validation,flowering stages simulated by the two models are all correlated with that observed at a significance of 0. 01. While,the panicle initiation stages simulated by MBILN showed a correlation with that observed at the 0. 05 level. The simulation errors were caused by the estimation of panicle initiation stages. This is due to the great difficulty in estimating the beginning of rice photoperiod. However,the above results indicate that the incorporation of prior information obviously enhanced the reliability and efficiency of optimization. This approach not only improves the estimation for insensitive parameters,but also depresses the high correlation between parameters.Meanwhile,the method by adjusting initial parameter values significantly reduced the probability in converging at local minima and improved the reliability in optimization. As a result,the optimization method presented in this paper is able to improve the efficiency and reliability in phenological parameters estimation. The method is promising in application for calibration of parameters in crop models and models in agricultural ecology.