Precision Agriculture

, Volume 19, Issue 1, pp 79–92 | Cite as

Nitrogen fertilizer recommendations based on plant sensing and Bayesian updating

  • Brandon R. McFadden
  • B. Wade Brorsen
  • William R. Raun


Methods are available to predict nitrogen needs of winter wheat based on plant sensing, but adoption rates by producers are low. Current algorithms that provide nitrogen recommendations based on plant sensing implicitly assume that parameters are estimated without error. A Bayesian updating method was developed that can incorporate precision plant sensing information and is simple enough that it could be computed on-the-go. The method can consider producers prior information and can account for parameter uncertainty. Bayesian updating gives higher nitrogen recommendations than plant sensing recommendations using a plug-in method. These recommendations increase net returns over the previous recommendations, but not enough to make plant sensing profitable in this scenario.


Bayesian updating Nitrogen response Stochastic plateau Winter wheat 



The research was partially funded by the Oklahoma Agricultural Experiment Station and USDA National Institute of Food and Agriculture, Hatch Project number OKL02939.


  1. Alchanatis, V., Scmilovitch, Z., & Meron, M. (2005). In-field assessment of single leaf nitrogen status by spectral reflectance measurement. Precision Agriculture, 6, 25–39.CrossRefGoogle Scholar
  2. Babcock, B. A. (1992). The effects of uncertainty on optimal nitrogen applications. Review of Agricultural Economics, 14, 271–280.CrossRefGoogle Scholar
  3. Baquet, A. E., Halter, A. N., & Conklin, F. S. (1976). The value of frost forecasting: A Bayesian appraisal. American Journal of Agricultural Economics, 58, 511–520.CrossRefGoogle Scholar
  4. Begiebing, S., Schneider, M., Bach, H., & Wagner, P. (2007). Assessment of in-field heterogeneity for determination of the economic potential of precision farming. In J. V. Stafford (Ed.), Proceedings of the 6th European conference on precision agriculture (pp. 811–818). Wageningen, The Netherlands: Wageningen Academic Publishers.Google Scholar
  5. Biermacher, J. T., Brorsen, B. W., Epplin, F. M., Solie, J. B., & Raun, W. R. (2009). The economic potential of precision nitrogen application with wheat based on plant sensing. Agricultural Economics, 40, 397–407.CrossRefGoogle Scholar
  6. Boyer, C. N., Brorsen, B. W., Solie, J. B., & Raun, W. R. (2011). Profitability of variable rate nitrogen application in wheat production. Precision Agriculture, 12, 473–487. doi: 10.1007/s11119-010-9190-5.CrossRefGoogle Scholar
  7. Boyer, C. N., Lambert, D. M., Velandia, M., English, B. C., Roberts, R. K., Larson, J. A., et al. (2016). Cotton producer awareness and participation in cost-sharing programs for precision nutrient-management technology. Journal of Agricultural and Resource Economics, 41, 81–96.Google Scholar
  8. Boyer, C. N., Larson, J. A., Roberts, R. K., McClure, A. T., Tyler, D. D., & Zhou, V. (2013). Stochastic corn yield response functions to nitrogen for corn after corn, corn after cotton, and corn after soybeans. Journal of Agricultural and Applied Economics, 45(4), 669–681.CrossRefGoogle Scholar
  9. Bullock, D., & Mieno, T. (2017). An assessment of the value of information from on-farm field trials. Unpublished Working Paper, University of Illinois, Champaign, IL.Google Scholar
  10. Bushong, J. T., Mullock, J. L., Miller, E. C., Raun, W. R., Klatt, A. R., & Arnall, D. B. (2016). Development of an in-season estimate of yield potential utilizing optical crop sensors and soil moisture data for winter wheat. Precision Agriculture, 17(4), 451–469.CrossRefGoogle Scholar
  11. Byerlee, D. R., & Anderson, J. R. (1982). Risk, utility and the value of information in farmer decision making. Review of Marketing and Agricultural Economics, 50, 231–246.Google Scholar
  12. Doll, J. P. (1971). Obtaining preliminary Bayesian estimates of the value of a weather forecast. American Journal of Agricultural Economics, 53, 651–655.CrossRefGoogle Scholar
  13. Doye, D., Sahs, R., & Kletke, D. (2014). Oklahoma Farm and Ranch Custom Rates, 20132014. Stillwater, OK, USA: Oklahoma Cooperative Extension Service Fact Sheet CR-205 0214 Rev.Google Scholar
  14. Duda, R. O., Hart, P. E., & Stork, D. G. (2001). Pattern classification. New York, NY, USA: Wiley.Google Scholar
  15. Ehlert, D., Schmerler, J., & Voelker, U. (2004). Variable rate nitrogen fertilization of winter wheat based on a crop density sensor. Precision Agriculture, 5, 263–273.CrossRefGoogle Scholar
  16. El-Hout, N. M., & Blackmer, A. M. (1990). Nitrogen status of corn after alfalfa in 29 Iowa fields. Journal of Soil and Water Conservation, 45, 115–117.Google Scholar
  17. Erickson, B., & Widmar, D. A. (2015). 2015 precision agricultural services dealership survey results. West Lafayette, IN, USA: Department of Agricultural Economics and Department of Agronomy, Purdue University. Retrieved September 14, 2016, from
  18. Franzen, D., Kitchen, N., Holland, K., Schepers, J., & Raun, W. (2016). Algorithms for in-season nutrient management in cereals. Agronomy Journal, 108, 1775–1781.CrossRefGoogle Scholar
  19. Havránková, J., Rataj, V., Godwin, R. J., & Wood, G. A. (2007). The evaluation of ground based remote sensing systems for canopy nitrogen management in winter wheat—Economic efficiency. Agricultural Engineering International: The CIGR Ejournal. Manuscript CIOSTA 07 002, 9.Google Scholar
  20. Huang, W., McBride, W., & Vasavada, U. (2009, March). Recent volatility in U.S. fertilizer prices causes and consequences. Amber Waves, pp. 28–31.Google Scholar
  21. Krause, J. (2008). A Bayesian approach to German agricultural yield expectations. Agricultural Finance Review, 68, 9–23.CrossRefGoogle Scholar
  22. Large, E. C. (1954). Growth stages in cereals: Illustration of the Feekes Scale. Plant Pathology, 3(4), 128–129.CrossRefGoogle Scholar
  23. Marshall, G. R., Parton, K. A., & Hammer, G. L. (1996). Risk attitude, planting conditions and the value of seasonal forecasts to a dryland wheat grower. Australian Journal of Agricultural Economics, 40, 211–233.CrossRefGoogle Scholar
  24. McMaster, G. S., & Wilhelm, W. W. (1997). Growing degree-days: One equation, two interpretations. Agricultural and Forest Meteorology, 87(4), 291–300.CrossRefGoogle Scholar
  25. National Agricultural Statistics Service (NASS). (2017a). Wheat-price received, measured in $/BU. National. US Total 2013. Annual Marketing Year. Retrieved January 3, 2017, from
  26. National Agricultural Statistics Service (NASS). (2017b). Price paid. Nitrogen, urea 44–46%—Price paid, measured in $/ton. National. US Total 2013. Retrieved January 3, 2017, from
  27. Norwood, F. B., Lusk, J. L., & Brorsen, B. W. (2004). Model selection for discrete dependent variables: Better statistics for better steaks. Journal of Agricultural and Resource Economics, 29, 404–419.Google Scholar
  28. Oklahoma State University. (2016a). Experiment 222: Long-term application of N, P, and K in continuous winter wheat, est. 1968. Retrieved June 28, 2016, from
  29. Oklahoma State University. (2016b). Experiment 502: Wheat grain yield response to nitrogen, phosphorus, and potassium fertilization. Lahoma, OK. Retrieved June 28, 2016, from
  30. Ouédraogo, F. B., Brorsen, B. W., & Arnall, D. B. (2016). Changing nitrogen levels in cotton. Journal of Cotton Science, 20, 18–25.Google Scholar
  31. Pautsch, G. R., Babcock, B. A., & Breidt, F. J. (1999). Optimal information acquisition under a geostatistical model. Journal of Agricultural and Resource Economics, 24, 342–366.Google Scholar
  32. Rajsic, P., & Weersink, A. (2008). Do farmers waste fertilizer? A comparison of ex post optimal nitrogen rates and ex ante recommendations by model, site, and year. Agricultural Systems, 97, 56–67.CrossRefGoogle Scholar
  33. Raun, W. R., Solie, J. B., Johnson, G. V., Stone, M. L., Mullen, R. W., Freeman, K. W., et al. (2002). Improving nitrogen use efficiency in cereal grain production with optical sensing and variable rate application. Agronomy Journal, 94, 815–820.CrossRefGoogle Scholar
  34. Raun, W. R., Solie, J. B., Stone, M. L., Martin, K. L., Freeman, K. W., Mullen, R. W., et al. (2005). Optical sensor-based algorithm for crop nitrogen fertilization. Communications in Soil Science and Plant Analysis, 36, 2759–2781.CrossRefGoogle Scholar
  35. Rodriguez, D. G. P., & Bullock, D. S. (2015). An empirical investigation of the Stanford’s “1.2 Rule” for nitrogen fertilizer recommendation. Selected Paper. San Francisco, CA, USA: Agricultural and Applied Economics Association.Google Scholar
  36. Schimmelpfennig, D., & Ebel, R. (2016). Sequential adoption and cost savings from precision agriculture. Journal of Agricultural and Resource Economics, 41, 97–115.Google Scholar
  37. Tembo, G., Brorsen, B. W., Epplin, F. M., & Tostão, E. (2008). Crop input response functions with stochastic plateaus. American Journal of Agricultural Economics, 90, 424–434.CrossRefGoogle Scholar
  38. Tumusiime, E., Brorsen, B. W., Mosali, J., Johnson, J., Locke, J., & Biermacher, J. T. (2011). Determining optimal levels of nitrogen fertilizer using random parameter models. Journal of Agricultural and Applied Economics, 43, 541–552.CrossRefGoogle Scholar
  39. Zellner, A. (1971). An introduction to Bayesian inference in econometrics. New York, NY, USA: Wiley.Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Food and Resource EconomicsUniversity of FloridaGainesvilleUSA
  2. 2.Department of Agricultural EconomicsOklahoma State UniversityStillwaterUSA
  3. 3.Department of Plant and Soil SciencesOklahoma State UniversityStillwaterUSA

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