单产提升潜力衰减模型法在河南粮食单产中长期预测中的应用研究

粮食单产水平的提高是河南粮食增产的主要原因,准确预测粮食单产水平,对科学判断河南粮食生产能力、制定粮食生产战略意义重大。论文针对目前直接以单产为变量建立的预测模型未能反映出单产增长的有限性和增速的减缓性之不足,研究提出了一种基于单产提升潜力衰减过程的单产预测方法。该方法利用河南耕地的平均单产潜力和历年实际单产数据,计算得到河南历年单产可提升潜力值;依据单产提升潜力理论上呈逐渐衰减之变化特点,可采用指数衰减函数建立单产提升潜力回归模型,以达到间接预测单产之目的。结果表明：1）单产提升潜力对数值与时间t之间具有高度负线性相关关系,适宜建立指数回归模型;2）回归模型V_q-V_t=e^{-0.009 5t+9.464 7}拟合优度R²=0.973 1,在0.01置信水平上回归显著;3）预测模型反映出了单产提升潜力的有限性和衰减性,即单产潜力对单产水平的限制性,模型理论诠释清晰;4）利用河南1978—2000年的单产数据作为样本建立预测模型,用样本以外2001—2015年的实际单产作为观测值,对预测单产进行模型预测检验,结果表明该模型预测单产绝对误差均值为129.15 kg/hm²,仅为现有方法的0.17~0.82倍,且误差平稳,适宜于单产中长期预测;5）预测得河南2020、2025、2030年的平均单产分别为6 375、6 765、7 155 kg/hm²,年均增幅为85.20~74.55 kg/hm²,增速呈逐渐减缓趋势。

Forecasting the Promotion Potential of Grain Yield per Unit in Mid-long Term with a Decay Model:A Case Study in Henan Province

The increase of grain output mainly depends on the improvement of grain per unit yield. To scientifically determine grain production capacity in the future and make food production strategy, it has great significance to accurately forecast the grain yield per unit. At present, the prediction models based on grain yield per unit could not reflect the limited growth and the slowing down of growth rate well. Therefore, a new prediction method of grain yield per unit based on the decaying of the promotion potential is proposed and its application in Henan Province is carried out in this paper. With this method, the promotion potential of grain yield per unit can be calculated with the average potential yield and the actual yield in past years. Due to the year-by-year decrease of the promotion potential of yield per unit, a model of promotion potential for grain yield can be established and the grain yield can be predicted with an exponential decay function. The results are as follows: 1) There is a linear decrease of the logarithm of the promotion potential of grain yield per unit during 1978-2015, and an exponential regression model can be established. 2) The regression model, V_q-V_t=e^{-0.009 5t+9.464 7}, is significant at the confidence level of 0.01. 3) The model has a clear theoretical meaning which shows the finite and the attenuation of the yield potential, that is, the limitation to the yield per unit caused by the promotion potential. 4) To test the model’s accuracy, the grain yields per unit in Henan during 1978-2000 are taken as samples to forecast the grain yields during 2001-2015, and the actual grain yields during 2001-2015 are used to test the predicated results. The result shows the average absolute error of predication is 129.15 kg/hm², which is 0.17-0.82 times of the errors of other methods. So it is more precise. Furthermore, the error of this method is more stable than errors of other models, so this new method is more suitable to forecast grain yield per unit in mid-long term. 5) The forecasted grain yields per unit in 2015, 2020, 2030 in Henan are 6 375, 6 765 and 7 155 kg/hm², respectively, and the annual increase is 85.20-74.55 kg/hm² during 2016-2030 with decreasing increment rate.