Monte Carlo 法在多元肥效模型参数估计和推荐施肥中的应用

针对多元肥效模型大量存在非典型式的事实，本文应用“3414”田间试验结果，详细介绍Monte Carlo法的原理以及在多元肥效模型参数估计、非典型肥效模型推荐施肥等方面的应用方法和步骤。结果表明，采用最小二乘法回归建模，67个二元和59个三元肥效模型的典型式出现机率分别为23.1%和16.9%；而改用Monte Carlo法参数寻优，典型式出现机率分别提高到56.7%和37.3%，是最小二乘法的2.5倍和2.2倍。与最小二乘法相比，Monte Carlo法是在参数寻优时牺牲数学上偏差平方和最小的最优性，使待估参数达到专业上最优而数学上较优，从而提高典型肥效模型的出现机率。对Monte Carlo法也不能得到典型式的晚稻磷钾非典型肥效模型，用产量频率分析法计算推荐施肥量，表明只有一组磷钾肥用量组合入选，导致磷肥推荐用量偏高而钾肥偏低。在相同目标产量下，改用Monte Carlo法，平均推荐用量介于相同试验地所建立的氮磷、氮钾和氮磷钾典型肥效模型的推荐用量之间，结果明显优于产量频率分析法。因此，Monte Carlo法为多元肥效模型参数估计和非典型肥效模型推荐施肥提供了一种新方法，提高了当前测土配方施肥田间试验的成功率。

Using Monte Carlo method for parameter estimation and fertilization recommendation of multivariate fertilizer response model

Multivariate fertilizer response models are often non–representative models for recommending fertilization. The Monte Carlo’s principle and its applications for estimating parameters of multivariate fertilizer response models, and for fertilization recommendation method of non–representative models were studied using the ‘3414’ field fertilizer experiment design. About 67 two-nutrients and 59 three-nutrient second degree polynomial models are developed using the least square method. Among these models, the representative fertilizer response models only account 23.1% and 16.9%, respectively. While the rates increased to 56.7% and 37.3% by using the Monte Carlo method to estimate the model parameters. Compared to the least square method, the Monte Carlo method may obtain the best parameters in plant nutrition and fitting sum of square in error mathematically by abandoning properly best character in sum of square in error in the least square method. Therefore, the rates are increased. As a case in this study, there is a non–representative PK duality model which adopts the least squares method or even the Monte Carlo method to estimate their parameters. Using yield frequency analysis to recommend fertilization, only a group of P and K coenobium, the sixth treatment, meets the conditions of goal yield. It stands that the coenobium number is not enough as a basis for fertilization recommendation, and results in the P recommending application rate on the high side and K on the low side. Under the same goal yield, the Monte Carlo method may obtain the average P and K recommending application amounts which are within the P and K optimum application rates based on NP, NK and NPK multivariate representative models in the same experiment sites. These results are obvious better than those of yield frequency analysis method. Therefore, the Monte Carlo method provides a new technique to estimate parameters and fertilization recommendation for multivariate fertilizer response models.