Bayesian hybrid analytics for uncertainty analysis and real‐time crop management

Dynamic, deterministic agricultural models, and current machine learning technologies based on sensor data, enable and support decision making for on-farm management. However, their predictions are subject to various sources of uncertainty. Hybrid analytics that leverage both modelled and sensor data provide predictive information that makes the best of both approaches in a timely fashion to inform operational decision making and enable inclusive uncertainty quantification. We describe and evaluate a probabilistic Bayesian data assimilation tool that combines the state variables from the Sirius wheat (Triticum aestivum L.) development model with time-series environmental and leaf count data. Additionally, the uncertainty associated with input parameters is quantified via expert opinion. The Bayesian approach obtained point estimates through time that were accompanied by inclusive, probabilistic, 95% credible intervals. At the end of simulation, a typical model predicted a final leaf number of 6.6 leaves, Sirius alone predicted seven leaves and the mean of the observed data was 6.7 leaves. The 95% credible interval was estimated as 5.1-8.4 leaves. Importantly, the tool was able to "redirect" simulated outputs if input parameters such as minimum leaf number or base phyllochron were incorrectly specified, with the implication that on-farm decision makers would have advance warning of variation in expected harvest date. Relatively few plants with time-intensive data were sufficient to fit the model, however, more plants would be desirable to reduce the rather wide range of credible intervals. Nevertheless, the tool shows potential and could be readily implemented with low resource requirements, providing more finely tuned harvest date information, with probabilistic uncertainty quantification built-in, for on-farm decisions.