Share This Article:

Sources of inaccuracy when estimating economically optimum N fertilizer rates

Full-Text HTML XML Download Download as PDF (Size:526KB) PP. 331-338
DOI: 10.4236/as.2012.33037    5,955 Downloads   8,621 Views   Citations


Nitrogen rate trials are often performed to determine the economically optimum N application rate. For this purpose, the yield is modeled as a function of the N application. The regression analysis provides an estimate of the modeled function and thus also an estimate of the economic optimum, Nopt. Obtaining the accuracy of such estimates by confidence intervals for Nopt is subject to the model assumptions. The dependence of these assumptions is a further source of inaccuracy. The Nopt estimate also strongly depends on the N level design, i.e., the area on which the model is fitted. A small area around the supposed Nopt diminishes the dependence of the model assumptions, but prolongs the confidence interval. The investigations of the impact of the mentioned sources on the inaccuracy of the Nopt estimate rely on N rate trials on the experimental field Sieblerfeld (Bavaria). The models applied are the quadratic and the linear-plus-plateau yield regression model.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Bachmaier, M. (2012) Sources of inaccuracy when estimating economically optimum N fertilizer rates. Agricultural Sciences, 3, 331-338. doi: 10.4236/as.2012.33037.


[1] Lambert, D., Lowenberg-DeBoer, J. and Bongiovanni, R. (2002) Spatial Regression, an alternative statistical analysis for landscape scale on-farm trials: Case study of variable rate nitrogen application in Argentina. Proceedings of the 6th International Conference on Precision Agriculture, ASA/CSSA/SSSA, Madison.
[2] Hernandez, J.A. and Mulla, D.J. (2008) Estimating Uncertainty of economically optimum fertilizer rates. Agronomy Journal, 100, 1221-1229. doi:10.2134/agronj2007.0273
[3] Wagner, P. (1999) Produktionsfunktionen und Precision Farming (Response functions in the context of Precision Farming). Zukunftsorientierte Betriebswirtschaft und Informationstechnologien in der Agrarwirtschaft. Gie?ener Schriften zur Agrarund Ern?hrungswirtschaft, 29, 39-66.
[4] Lark, R.M. and Wheeler, H.C. (2003) A method to investigate within-field variation of the response of combinable crops to an input. Agronomy Journal, 95, 1093-1104. doi:10.2134/agronj2003.1093
[5] National Academy of Sciences, National Research Council (1961) Statistical methods of research in economic and agronomic aspects of fertilizer response and use. Committee on economics of fertilizer use of the agricultural board, NAS-NRC Pub. 918, NAS-NRC, Washington DC.
[6] Cerrato, M.E. and Blackmer, A.M. (1990) Comparison of models for describing corn yield response to nitrogen fertilizer. Agronomy Journal, 82, 138-143. doi:10.2134/agronj1990.00021962008200010030x
[7] Bullock, D.G. and Bullock, D.S. (1986) Quadratic and quadratic-plus-plateau models for predicting optimal nitrogen rate of corn: A comparison. Agronomy Journal, 86, 191-195. doi:10.2134/agronj1994.00021962008600010033x
[8] Le Bail, M., Jeuffroy, M.-H., Bouchard, C. and Barbottin, A. (2005) Is it possible to forecast the grain quality and yield of different varieties of winter wheat from Minolta SPAD meter measurements? European Journal of Agronomy, 23, 379-391. doi:10.1016/j.eja.2005.02.003
[9] Colwell, J.D. (1994) Estimating fertilizer requirements: A quantitative approach. CAB International, Wallingford.
[10] Lehmann, E.L. (1986) Testing statistical hypothesis. John Wiley & Sons, Inc., New York.
[11] Weisberg, S. (2005) Applied linear regression. John Wiley & Sons, Inc., New York. doi:10.1002/0471704091
[12] Bachmaier, M. (2009) A confidence set for that x-Coordinate where the quadratic regression model has a given gradient. Statistical Papers, 50, 649-660. doi:10.1007/s00362-007-0104-1
[13] Bachmaier, M. (2011) Fortran programs: 1. Confidence set for the economically optimum nitrogen fertilization in the quadratic model: VINO.EXE. 2. Confidence set for that x-coordinate where the quadratic regression model has a given gradient (incl. special case: confidence set for the x-coordinate of the parabola’s vertex): CIGIGRAD. EXE and CIVERTEX.EXE.
[14] Fieller, E.C. (1954) Some problems in interval estimation. Journal of the Royal Statistical Society, B16, 175-185.
[15] Koziol, D. and Zielinski, W. (2003) Comparison of confidence intervals for maximum of a quadratic regression function. Biometrical Letters, 40, 57-64.
[16] Mittelhammer, R.C., Judge, G.G. and Miller, D.J. (2000) Econometric foundations. Cambridge University Press, Cambridge, 183-185.
[17] Casella, G. and Berger, R.L. (2002) Statistical inference. Duxbury Press, Belmont.
[18] Cook, R.D. and Weisberg, S. (1990) Confidence curves in nonlinear regression. Journal of the American Statistical Association, 85, 544-551. doi:10.2307/2289796
[19] Boyd, D.A., Yuen, L.T.K. and Needham, P. (1976) Nitrogen requirement of cereals. Journal of Agricultural Science, 87, 149-162. doi:10.1017/S0021859600026708
[20] Waugh, D.L., Cate, R.B. and Nelson, L.A. (1973) Discontinuous models for rapid correlations, interpretation und utilization of soil analysis and fertilizer response data. International Soil Fertility Evaluation and Improvement Program, North Carolina Sate University, Raleigh.
[21] Motulsky, H.J. and Christopoulos, A. (2003) PRISM, Version 4.0. Fitting models to biological data using linear and nonlinear regression. A practical guide to curve fitting, GraphPad Software Inc., San Diego.
[22] Liebler, J. (2003) Feldspektroskopische messungen zur ermittlung des stickstoffstatus von winterweizen und mais auf heterogenen schl?gen. Herbert Utz Verlag, Munich.
[23] Hurley, T.M., Malzer, G.L. and Kilian, B. (2004) Estimating site-specific nitrogen crop response functions: A conceptual framework and geostatistical model. Agronomy Journal, 96, 1331-1343. doi:10.2134/agronj2004.1331
[24] Hurley, T.M., Oishi, K. and Malzer, G.L. (2005) Estimating the potential value of variable rate nitrogen applications: A comparison of spatial econometric and geostatistical models. Journal of Agricultural and Resource Economics, 30, 231-249.
[25] Anselin, L., Bongiovanni, R. and Lowen-berg-DeBoer, J. (2004) A spatial economic approach to the economics of site-specific nitrogen management in corn production. American Journal of Agricultural Economics, 86, 675- 687. doi:10.1111/j.0002-9092.2004.00610.x
[26] Bullock, D.S., Lowenberg-DeBoer, J. and Swinton, S.M. (2002) Adding value to spatially managed inputs by understanding site-specific yield response. Agricultural Economics, 27, 233-245. doi:10.1111/j.1574-0862.2002.tb00119.x
[27] Bachmaier, M. and Gandorfer, M. (2009) A conceptual framework for judging the precision agriculture hypothesis with regard to site-specific nitrogen fertilization. Precision Agriculture, 10, 95-110. doi:10.1007/s11119-008-9069-x
[28] Abraham, T.P. and Rao, V.Y. (1965) An investigation on functional models for fertilizer response studies. Journal of the Indian Society of Agricultural Statistics, 18, 45-61.
[29] Anderson, R.L. and Nelson, L.A. (1975) A family of models involving intersecting straight lines and concomitant experimental designs useful in evaluating response to fertilizer nutrients. Biometrics, 31, 303-318. doi:10.2307/2529422
[30] Barreto, H.J. and Westermann, R.L. (1987) YIELDFIT: A computer program for determining economic fertilization rates. Journal of Agronomical Education, 16, 11-14.
[31] Nelson, L.A., Voss, R.D. and Pesek, J.T. (1985) Agronomic and statistical evaluation of fertilizer response. In: Engelstad, O.P., Ed., Fertilizer Technology and Use, ASA, Madison, 53-90.

comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.