关键词: 模型, BETA方程, 参数反演, 先验信息, 光周期

Abstract: 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.

Key words: Model, BETA equation, Parameter inversion, Prior information, Photoperiod