三元非结构肥效模型提高水稻施肥推荐的可靠性
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摘要
【目的】针对三元二次多项式肥效模型的设定偏误和多重共线性危害导致建模成功率低的问题,研发三元非结构肥效模型,扩大模型适用性。【方法】在福建省平和县和仙游县选择了13个水稻氮磷钾田间肥效试验结果作为研究案例。田间试验均采用"3414"设计方案,即:1) N_0P_0K_0;2) N_0P_2K_2;3) N_1P_2K_2;4) N_2P_0K_2;5)N_2P_1K_2;6) N_2P_2K_2;7) N_2P_3K_2;8) N_2P_2K_0;9) N_2P_2K_1;10) N_2P_2K_3;11) N_3P_2K_2;12) N_1P_1K_2;13) N_1P_2K_1;14)N_2P_1K_1。其中,"2"水平为试验前当地氮磷钾推荐施肥量,"0"水平表示不施肥,"1"水平和"3"水平的施肥量分别为"2"水平的50%和150%。在一元非结构肥效模型基础上,利用氮磷钾田间肥效试验结果,在每个试验点分别构建了三元二次多项式肥效模型和三元非结构肥效模型。利用已有的668个水稻"3414"田间试验结果,比较验证了两种模型的拟合效果和推荐施肥量的可靠性。【结果】在构建的13个三元二次多项式肥效模型中,有2个模型的结果未达到统计显著水平,3个肥效模型属于非典型式,而构建的13个三元非结构肥效模型均得到了典型式。通过668个水稻氮磷钾田间肥效试验结果验证表明,三元二次多项式肥效模型未能通过显著性检验的比例达到30.1%,而三元非结构肥效模型未能通过的比例下降到23.4%。在推荐施肥量外推的非典型式中,三元二次多项式肥效模型的比例为4.0%,而三元非结构肥效模型则提高到30.7%。在系数符号不合理和无最高产量点的两种非典型式类型中,三元二次多项式肥效模型的比例分别达到32.3%和14.4%,而三元非结构肥效模型则分别降低到6.9%和0。三元二次多项式肥效模型的典型式比例仅为19.5%,而三元非结构肥效模型典型式比例则提高到39.1%,是前者的2.0倍,明显提高了田间试验结果的建模成功率。【结论】大样本田间试验充分证明,相比三元二次多项式肥效模型,采用三元非结构肥效模型进行早、中、晚稻推荐施肥,提高了建模的成功效率和模型的实用性,是可靠性更高的模型。
【Objectives】Ternary quadratic polynomial fertilizer response model(TPFM) has low success rate due to setting bias and multicollinearity. A ternary non-structural fertilizer response model(TNFM) was established to expand the model applicability and precision of fertilizer recommendation in rice production.【Methods】Thirteen rice field NPK fertilizer experiments were chosen in Pinghe County and Xianyou County, Fujian Province. Design of "3414" was used in all the thirteen experiments, the treatments were as following: 1) N_0P_0K_0;2) N_0P_2K_2;3) N_1P_2K_2;4) N_2P_0K_2;5)N_2P_1K_2;6) N_2P_2K_2;7) N_2P_3K_2;8) N_2P_2K_0;9) N_2P_2K_1;10) N_2P_2K_3;11) N_3P_2K_2;12) N_1P_1K_2;13) N_1P_2K_1;14)N_2P_1K_1. Of them, "2" represented current recommended nutrient levels, "1" and "3" represented 50% and 150% of those, and "0" represented no nutrient input. The TPFM and TNFM were established for each experiment. Extra 668 rice field results were collected all over Fujian Province, and used for the verification of the fitting effect and the reliability of fertilization recommendation of the two kinds of models. 【Results】Among the established 13 TPFMs, two failed to achieve statistical significance levels and three resulted in non-typical model. While all the 13 TNFMs were typical models, showing less setting bias and multicollinearity. The TPFMs recommended higher nutrient rates than the practical ones,while the TNFMs verified with the 668 field experiments results, 30.1% of the TPFMs failed to pass the significance test, but 23.4% of the TNFMs did not. In the non-typical model that made the recommended fertilization rate by extrapolation, the proportion of the TPFMs was only 4.0%, while that of the TNFMs was increased to 30.7%. In the two types of non-typical models of unreasonable coefficient symbol and without maximum yield point, the proportion of the TPFMs reached to 32.3% and 14.4%, respectively. However, the TNFMs were reduced to 6.9% and zero, respectively, and the proportion of typical model by the TPFMs was only19.5%. In contrast, using the TNFMs made the proportion of the typical model increase to 39.1%, which was twice of the TPFMs. Hence, the new model significantly improved the modeling success rate. 【Conclusions】The ternary non-structural fertilizer response model(TNFM) has a higher fitting accuracy and wider application scope in the modeling of nitrogen, phosphorus and potassium fertilization response of paddy rice.
【Objectives】Ternary quadratic polynomial fertilizer response model(TPFM) has low success rate due to setting bias and multicollinearity. A ternary non-structural fertilizer response model(TNFM) was established to expand the model applicability and precision of fertilizer recommendation in rice production.【Methods】Thirteen rice field NPK fertilizer experiments were chosen in Pinghe County and Xianyou County, Fujian Province. Design of "3414" was used in all the thirteen experiments, the treatments were as following: 1) N_0P_0K_0;2) N_0P_2K_2;3) N_1P_2K_2;4) N_2P_0K_2;5)N_2P_1K_2;6) N_2P_2K_2;7) N_2P_3K_2;8) N_2P_2K_0;9) N_2P_2K_1;10) N_2P_2K_3;11) N_3P_2K_2;12) N_1P_1K_2;13) N_1P_2K_1;14)N_2P_1K_1. Of them, "2" represented current recommended nutrient levels, "1" and "3" represented 50% and 150% of those, and "0" represented no nutrient input. The TPFM and TNFM were established for each experiment. Extra 668 rice field results were collected all over Fujian Province, and used for the verification of the fitting effect and the reliability of fertilization recommendation of the two kinds of models. 【Results】Among the established 13 TPFMs, two failed to achieve statistical significance levels and three resulted in non-typical model. While all the 13 TNFMs were typical models, showing less setting bias and multicollinearity. The TPFMs recommended higher nutrient rates than the practical ones,while the TNFMs verified with the 668 field experiments results, 30.1% of the TPFMs failed to pass the significance test, but 23.4% of the TNFMs did not. In the non-typical model that made the recommended fertilization rate by extrapolation, the proportion of the TPFMs was only 4.0%, while that of the TNFMs was increased to 30.7%. In the two types of non-typical models of unreasonable coefficient symbol and without maximum yield point, the proportion of the TPFMs reached to 32.3% and 14.4%, respectively. However, the TNFMs were reduced to 6.9% and zero, respectively, and the proportion of typical model by the TPFMs was only19.5%. In contrast, using the TNFMs made the proportion of the typical model increase to 39.1%, which was twice of the TPFMs. Hence, the new model significantly improved the modeling success rate. 【Conclusions】The ternary non-structural fertilizer response model(TNFM) has a higher fitting accuracy and wider application scope in the modeling of nitrogen, phosphorus and potassium fertilization response of paddy rice.
引文
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[3]章明清,李娟,孔庆波,严芳.作物肥料效应函数模型研究进展与展望[J].土壤学报,2016, 53(6):1143-1156.Zhang M Q, Li J, Kong Q B, Yan F. Progress and prospect of the study on crop-response-to-fertilization function model[J]. Acta Pedologica Sinica,2016, 53(6):1143-1156.
[4] Valkama E, Uusitalo R, Turtola E. Yield response models to phosphorus application:a research synthesis of Finnish field trials to optimize fertilizer P use of cereals[J]. Nutrient Cycling in Agroecosystems,2011,91(1):1-15.
[5]Gregoret M C, Zorita M D, Dardanelli J, et al. Regional model for nitrogen fertilization of site-specific rainfed corn in haplustolls of the central Pampas, Argentina[J]. Precision Agriculture, 2011, 12(6):831-849.
[6] Petersen J, Thomsen I K, Mattsson L, et al. Estimating the crop response to fertilizer nitrogen residues in long-continued field experiments[J]. Nutrient Cycling in Agroecosystems, 2012, 93(1):1-12.
[7] Thole H, Richter C, Ehlert D. Strategy of statistical model selection for precision farming on-farm experiments[J]. Precision Agriculture,2013, 14(4):434-449.
[8]王兴仁.二元二次肥料效应曲面等产线图在科学施肥中的位置(一)[J].土壤通报,1985,16(1):30-34.Wan X R. The positions of contour map of yield of binary quadratic fertilizer response curve in scientific fertilization(part 1)[J]. Chinese Journal of Soil Science,1985, 16(1):30-34.
[9]王兴仁.二元二次肥料效应曲面等产线图在科学施肥中的位置(二)[J].土壤通报,1985, 16(2):86-88.Wan X R. The positions of contour map of yield of binary quadratic fertilizer response curve in scientific fertilization(part 2)[J]. Chinese Journal of Soil Science,1985, 16(2):86-88.
[10]章明清,林仁埙,林代炎,姜永.极值判别分析在三元肥效模型推荐施肥中的作用[J].福建农业学报,1995, 10(2):54-59.Zhang M Q, Lin R X, Lin D Y, Jiang Y. Function of distinguish analysis on extreme value in recommendatory fertilization for threefertilizer efficiency model[J]. Fujian Journal of Agricultural Sciences,1995, 10(2):54-59.
[11] Zhang M Q, Li J, Chen F, Kong Q B. Unary non-structural fertilizer response model for rice crops and its field experimental verification[J]. Scientific Reports, 2018, 8(1):2792.
[12]李娟,章明清,孔庆波,等.福建早稻测土配方施肥指标体系研究[J].植物营养与肥料学报,2010, 16(4):938-946.Li J, Zhang M Q, Kong Q B, et al. Soil testing and formula fertilization index for early rice in Fujian Province[J]. Plant Nutrition and Fertilizer Science, 2010, 16(4):938-946.
[13]鲁如坤.土壤农业化学分析方法[M]北京:中国农业科技出版社,2000. 146-196Lu R K. Soil and agricultural chemistry analysis method[M]. Beijing:China Agricultural Science and Technology Press, 2000. 146-196.
[14] Montgomery D C, Peck E A,Vining G G.北京:(王辰勇译).线性回归分析导论(第5版)[M].北京:机械工业出版社,2016.Montgomery D C, Peck E A, Vining G G(Translated by Wang C Y).Introduction to linear regression analysis(5th edition)[M]. Beijing:China Machine Press, 2016.
[15]马昌凤,柯艺芬,谢亚君.最优化计算方法及其MATLAB程序实现[M].北京:国防工业出版社,2015. 31-45.Ma C F, Ke Y F, Xie Y J. Optimization calculation method and MATLAB program implementation[M]. Beijing:National Defence Industry Press, 2015. 31-45.
[16]薛毅,陈立萍.实用数据分析与MATLAB软件[M].北京:北京工业大学出版社,2015.Xue Y, Chen L P. Practical data analysis and MATLAB software[M].Beijing:Beijing University of Technology Press, 2015.
[17]徐明岗,姚其华,吕家珑.土壤养分运移[M].北京:中国农业科学出版社,2000. 159-226.Xu M G, Yao Q H, Lu J L. Soil nutrients migration[J]. Beijing:Chinese Agricultural Science Press, 2000. 159-226.
[18]陈新平,周金池,王兴仁,等.小麦-玉米轮作制中氮肥效应模型的选择-经济和环境效益分析[J].土壤学报,2000, 37(3):346-354.Chen X P, Zhou J C, Wang X R, et al. Economic and environmental evaluation on models for describing crop yield response to nitrogenfertilizers at winter-wheat and summer-corn rotation system[J]. Acta Pedologica Sinica, 2000, 37(3):346-354.
[19]何晓群,刘文卿.应用回归分析[M].北京:中国人民大学出版社,2013. 158-170.He X Q, Liu W Q. Applied regression analysis[M]. Beijing:Renmin University Press, 2013. 158-170.
[20]李仁岗.肥料效应函数[M].北京:农业出版社,1987.Li R G. Fertilizer response function[M]. Beijing:Agriculture Renmin Press, 1987.
[21] Valkama E, Uusitalo R, Turtola E. Yield response models to phosphorus application:a research synthesis of Finnish field trials to optimize fertilizer P use of cereals[J]. Nutrient Cycle Agroecosystem, 2011, 91:1-15.
[22] Gregore M C, Diaz Zorita M, Dardanelli J, Bongiovanni R G.Regional model for nitrogen fertilization of site-specific rainfed corn in haplustolls of the central Pampas, Argentina[J]. Precision Agriculture, 2011, 12:831-849.
[23] Neeteson J J, Wadman W P. Assessment of economically optimum application rates of fertilizer N on the basis of response curves[J].Fertilizer Research, 1987, 12:37-52.
[24] Cerrato M E, Blackmer A M. Comparison of models for describing corn yield response to nitrogen fertilizer[J]. Agronomy Journal, 1990,82(1):138-143.
[25]杨靖一,Wadsworth G A,Greenwood D J.三种蔬菜N肥效应曲线的比较研究[J].植物营养与肥料学报,1995, 1(1):71-78.Yang J Y, Wadsworth G A, Greenwood D J. Comparative study on three kinds of vegetables response to N fertilizer curve[J]. Plant Nutrition and Fertilizer Science, 1995, 1(1):71-78.
[26]毛达如,张承东.推荐施肥技术中施肥模型与试验设计的研究[J].土壤通报,1991,22(5):216-218.Mao D R, Zhang C D. Fertilization model and the experiment design of fertilization recommendation technology[J]. Chinese Journal of Soil Science, 1991, 22(5):216-218.
[27]王惠文,吴载斌,孟洁.偏最小二乘回归的线性和非线性方法[M].北京:国防工业出版社,2006.Wang H W, Wu Z B, Meng J. Partial least-squares regression-linear and nonlinear methods[M]. Beijing:National Defence Industry Press,2006.
[28]李娟,章明清,许文江,等.提高三元肥效模型建模成功率的主成分回归技术研究[J].土壤学报,2018,55(2):207-218.Li J, Zhang M Q, Xu W J, et al. Principal component regression technology of ternary fertilizer response model for improving success rate of modeling[J]. Acta Pedologica Sinica, 2018, 55(2):207-218.
[2]王兴仁,陈新平,张福锁,等.施肥模型在我国推荐施肥中的应用[J].植物营养与肥料学报,1998, 4(1):67-74.Wang X R, Chen X P, Zhang F S, et al. Application of fertilization model for fertilizer recommendation in China[J]. Plant Nutrition and Fertilizer Science,1998, 4(1):67-74.
[3]章明清,李娟,孔庆波,严芳.作物肥料效应函数模型研究进展与展望[J].土壤学报,2016, 53(6):1143-1156.Zhang M Q, Li J, Kong Q B, Yan F. Progress and prospect of the study on crop-response-to-fertilization function model[J]. Acta Pedologica Sinica,2016, 53(6):1143-1156.
[4] Valkama E, Uusitalo R, Turtola E. Yield response models to phosphorus application:a research synthesis of Finnish field trials to optimize fertilizer P use of cereals[J]. Nutrient Cycling in Agroecosystems,2011,91(1):1-15.
[5]Gregoret M C, Zorita M D, Dardanelli J, et al. Regional model for nitrogen fertilization of site-specific rainfed corn in haplustolls of the central Pampas, Argentina[J]. Precision Agriculture, 2011, 12(6):831-849.
[6] Petersen J, Thomsen I K, Mattsson L, et al. Estimating the crop response to fertilizer nitrogen residues in long-continued field experiments[J]. Nutrient Cycling in Agroecosystems, 2012, 93(1):1-12.
[7] Thole H, Richter C, Ehlert D. Strategy of statistical model selection for precision farming on-farm experiments[J]. Precision Agriculture,2013, 14(4):434-449.
[8]王兴仁.二元二次肥料效应曲面等产线图在科学施肥中的位置(一)[J].土壤通报,1985,16(1):30-34.Wan X R. The positions of contour map of yield of binary quadratic fertilizer response curve in scientific fertilization(part 1)[J]. Chinese Journal of Soil Science,1985, 16(1):30-34.
[9]王兴仁.二元二次肥料效应曲面等产线图在科学施肥中的位置(二)[J].土壤通报,1985, 16(2):86-88.Wan X R. The positions of contour map of yield of binary quadratic fertilizer response curve in scientific fertilization(part 2)[J]. Chinese Journal of Soil Science,1985, 16(2):86-88.
[10]章明清,林仁埙,林代炎,姜永.极值判别分析在三元肥效模型推荐施肥中的作用[J].福建农业学报,1995, 10(2):54-59.Zhang M Q, Lin R X, Lin D Y, Jiang Y. Function of distinguish analysis on extreme value in recommendatory fertilization for threefertilizer efficiency model[J]. Fujian Journal of Agricultural Sciences,1995, 10(2):54-59.
[11] Zhang M Q, Li J, Chen F, Kong Q B. Unary non-structural fertilizer response model for rice crops and its field experimental verification[J]. Scientific Reports, 2018, 8(1):2792.
[12]李娟,章明清,孔庆波,等.福建早稻测土配方施肥指标体系研究[J].植物营养与肥料学报,2010, 16(4):938-946.Li J, Zhang M Q, Kong Q B, et al. Soil testing and formula fertilization index for early rice in Fujian Province[J]. Plant Nutrition and Fertilizer Science, 2010, 16(4):938-946.
[13]鲁如坤.土壤农业化学分析方法[M]北京:中国农业科技出版社,2000. 146-196Lu R K. Soil and agricultural chemistry analysis method[M]. Beijing:China Agricultural Science and Technology Press, 2000. 146-196.
[14] Montgomery D C, Peck E A,Vining G G.北京:(王辰勇译).线性回归分析导论(第5版)[M].北京:机械工业出版社,2016.Montgomery D C, Peck E A, Vining G G(Translated by Wang C Y).Introduction to linear regression analysis(5th edition)[M]. Beijing:China Machine Press, 2016.
[15]马昌凤,柯艺芬,谢亚君.最优化计算方法及其MATLAB程序实现[M].北京:国防工业出版社,2015. 31-45.Ma C F, Ke Y F, Xie Y J. Optimization calculation method and MATLAB program implementation[M]. Beijing:National Defence Industry Press, 2015. 31-45.
[16]薛毅,陈立萍.实用数据分析与MATLAB软件[M].北京:北京工业大学出版社,2015.Xue Y, Chen L P. Practical data analysis and MATLAB software[M].Beijing:Beijing University of Technology Press, 2015.
[17]徐明岗,姚其华,吕家珑.土壤养分运移[M].北京:中国农业科学出版社,2000. 159-226.Xu M G, Yao Q H, Lu J L. Soil nutrients migration[J]. Beijing:Chinese Agricultural Science Press, 2000. 159-226.
[18]陈新平,周金池,王兴仁,等.小麦-玉米轮作制中氮肥效应模型的选择-经济和环境效益分析[J].土壤学报,2000, 37(3):346-354.Chen X P, Zhou J C, Wang X R, et al. Economic and environmental evaluation on models for describing crop yield response to nitrogenfertilizers at winter-wheat and summer-corn rotation system[J]. Acta Pedologica Sinica, 2000, 37(3):346-354.
[19]何晓群,刘文卿.应用回归分析[M].北京:中国人民大学出版社,2013. 158-170.He X Q, Liu W Q. Applied regression analysis[M]. Beijing:Renmin University Press, 2013. 158-170.
[20]李仁岗.肥料效应函数[M].北京:农业出版社,1987.Li R G. Fertilizer response function[M]. Beijing:Agriculture Renmin Press, 1987.
[21] Valkama E, Uusitalo R, Turtola E. Yield response models to phosphorus application:a research synthesis of Finnish field trials to optimize fertilizer P use of cereals[J]. Nutrient Cycle Agroecosystem, 2011, 91:1-15.
[22] Gregore M C, Diaz Zorita M, Dardanelli J, Bongiovanni R G.Regional model for nitrogen fertilization of site-specific rainfed corn in haplustolls of the central Pampas, Argentina[J]. Precision Agriculture, 2011, 12:831-849.
[23] Neeteson J J, Wadman W P. Assessment of economically optimum application rates of fertilizer N on the basis of response curves[J].Fertilizer Research, 1987, 12:37-52.
[24] Cerrato M E, Blackmer A M. Comparison of models for describing corn yield response to nitrogen fertilizer[J]. Agronomy Journal, 1990,82(1):138-143.
[25]杨靖一,Wadsworth G A,Greenwood D J.三种蔬菜N肥效应曲线的比较研究[J].植物营养与肥料学报,1995, 1(1):71-78.Yang J Y, Wadsworth G A, Greenwood D J. Comparative study on three kinds of vegetables response to N fertilizer curve[J]. Plant Nutrition and Fertilizer Science, 1995, 1(1):71-78.
[26]毛达如,张承东.推荐施肥技术中施肥模型与试验设计的研究[J].土壤通报,1991,22(5):216-218.Mao D R, Zhang C D. Fertilization model and the experiment design of fertilization recommendation technology[J]. Chinese Journal of Soil Science, 1991, 22(5):216-218.
[27]王惠文,吴载斌,孟洁.偏最小二乘回归的线性和非线性方法[M].北京:国防工业出版社,2006.Wang H W, Wu Z B, Meng J. Partial least-squares regression-linear and nonlinear methods[M]. Beijing:National Defence Industry Press,2006.
[28]李娟,章明清,许文江,等.提高三元肥效模型建模成功率的主成分回归技术研究[J].土壤学报,2018,55(2):207-218.Li J, Zhang M Q, Xu W J, et al. Principal component regression technology of ternary fertilizer response model for improving success rate of modeling[J]. Acta Pedologica Sinica, 2018, 55(2):207-218.