Precision Agriculture

, Volume 16, Issue 3, pp 275–296 | Cite as

A probabilistic Bayesian framework for progressively updating site-specific recommendations

  • Patrick G. LawrenceEmail author
  • Lisa J. Rew
  • Bruce D. Maxwell


The goal of this research was to create an agricultural adaptive management framework that enables the probabilistic optimization of N fertilizer to achieve maximized net returns under multiple uncertainties. These uncertainties come in the form of bioclimatic variables that drive crop yield, and economic variables that determine profitability. Taking advantage of variable rate application (VRA), spatial monitoring technologies, and historical datasets, we demonstrate a comprehensive spatiotemporal modeling approach that can achieve optimal efficiency for the producer under such uncertainties. The utility of VRA fertilizer research for producers is dependent upon a localized accurate understanding of crop responses under a range of possible climatic regimes. We propose an optimization framework that continuously updates by integrating annual on-site experiments, VRA prescriptions, crop prices received, input prices, and climatic conditions observed each year under a dryland spring wheat (Triticum aestivum) cropping system. The spatio-temporal Bayesian framework used to assimilate these data sources also enables calculation of the probabilities of economic returns and the risks associated with different VRA strategies. The results from our simulation experiments indicated that our framework can successfully arrive at optimum N management within 6–8 years using sequential Bayesian analysis, given complete uncertainty in water as a driver of crop yield. Once optimized, the spatial N management approach increased net returns by $23–25 ha−1 over that of uniform N management. By identifying small-scale targeted treatments that can be merged with VRA prescriptions, our framework ensures continuous reductions in parameter uncertainty. Thus we have demonstrated a useful decision aid framework that can empower agricultural producers with site-specific management that fully accounts for the range of possible conditions farmers must face.


Site-specific experimentation Bayesian statistics Input optimization Simulation experiment Dryland agriculture Spatial variation 



This material is based on work supported by the Montana Institute on Ecosystems’ award from the National Science Foundation EPSCoR Track-1 Program under Grant #EPS-1101342 (INSTEP 3). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. This work is also supported by the Montana Fertilizer Advisory Committee and graduate student Grant GW12-004 from the Western Sustainable Agriculture Research and Education Program.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Patrick G. Lawrence
    • 1
    Email author
  • Lisa J. Rew
    • 1
  • Bruce D. Maxwell
    • 1
  1. 1.Land Resources and Environmental Sciences DepartmentMontana State UniversityBozemanUSA

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