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International Journal of Agronomy
Volume 2012, Article ID 580294, 10 pages
Research Article

Estimating Uncertainty of Economically Optimum N Fertilizer Rates

Center of Life Sciences, Technische Universität München, Weihenstephan, 85354 Freising, Germany

Received 13 August 2011; Revised 4 December 2011; Accepted 6 December 2011

Academic Editor: M. Ali Tabatabai

Copyright © 2012 Martin Bachmaier and Markus Gandorfer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 is commonly used to estimate the modeled functions and the economic optimum rate, 𝑁 o p t . However, computer programs do not calculate confidence intervals for 𝑁 o p t derived from quadratic yield response model or other commonly used models. The objective was to develop a method for computing and interpreting confidence intervals for 𝑁 o p t . These confidence intervals can be estimated using an online program VINO.EXE. For the N rate trials on the experimental field Sieblerfeld (Bavaria), confidence intervals were computed for a range of wheat and N fertilizer prices and for selected N rates for quadratic and linear plateau models. The latter concerns the comparison with confidence intervals based upon the linear-plus-plateau yield regression model. All intervals were found to be unexpectedly wide and their ranges were affected by N rates used in the calculations and by the choice of yield response model.