Abstract
Several methods were developed for the redistribution of nitrogen (N) fertilizer within fields with winter wheat (Triticum aestivum L.) based on plant and soil sensors, and topographical information. The methods were based on data from nine field experiments in nine different fields for a 3-year period. Each field was divided into 80 or more subplots fertilized with 60, 120, 180 or 240 kg N ha−1. The relationships between plot yield, N application rate, sensor measurements and the interaction between N application and sensor measurements were investigated. Based on the established relations, several sensor-based methods for within-field redistribution of N were developed. It was shown that plant sensors predicted yield at harvest better than soil sensors and topographical indices. The methods based on plant sensors showed that N fertilizer should be moved from areas with low and high sensor measurements to areas with medium values.
The theoretical increase in yield and N uptake, and the reduced variation in grain protein content resulting from the application of the above methods were estimated. However, the estimated increases in crop yield, N-uptake and reduced variation in grain protein content were small.
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Acknowledgements
The algorithm development is based on field experiments and data analysis funded by the research programmes ‘Applied crop research’ financed by the Danish Agricultural Advisory Service and ‘Agriculture from a holistic resource perspective’ financed by the Danish Ministry of Food, Agriculture and Fisheries.
We wish to thank the following farmers and estates that have hosted the field experiments for their outstanding cooperation: Knud Gasbjerg, Carsten Jensen, Svend Laier, Egeskov Gods, Østergård Hovedgård, Ove Christoffersen, Geert H. de Lichtenberg, H.C. Neergård and Niels Balle. We also wish to thank Margit Schacht for greatly improving the readability of the paper.
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Appendix A
Appendix A
This appendix describes how to maximize yield (Eqs. 5, 6) given a fixed N application rate (Eq. 7). From Eq. 7 it can be seen that the N ij ’s depend on each other. Thus, simultaneous maximization of Eqs. 6, 7 is not immediately possible. However, Eq. (6) can be rearranged to
Eqs. 5, 6 can now be reduced to
This equation is simplified by setting \(\alpha _{ij} = \left( {b_i + f_i S_{ij} + g_i S_{ij}^2 + h_i S_{ij}^3 } \right)\):
In this equation the N ij ’s are independent and \(Y_i^* \) can be maximized by setting the partial derivative of \(Y_i^* \) with respect to N ij to zero:
Eq. (15) is now differentiated and inserted into Eq. (16):
This equation is solved with respect to N ij using Eq. (13).
Combining this equation with Eq. (13) gives
This equation is then solved with respect to \(N_{ik_i } \)
Finally, this is inserted into Eq. (18)
Expanding \(\alpha _{ij} \) gives
To obtain a global model of how to redistribute N based on a sensor measurement (S ij ), it is evident from the above equation that a i , f i , g i and h i cannot be estimated for each field but must be determined as common factors for all experiments. It is also noted that b i and the sum are constants within a single field, which implies that Eq. (22) can be rewritten as
Under field conditions \(\gamma _i \) can be determined by noting that
and by combining Eqs. 6, 22 the following expression is obtained:
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Berntsen, J., Thomsen, A., Schelde, K. et al. Algorithms for sensor-based redistribution of nitrogen fertilizer in winter wheat. Precision Agric 7, 65–83 (2006). https://doi.org/10.1007/s11119-006-9000-2
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DOI: https://doi.org/10.1007/s11119-006-9000-2