A Bayesian sequential updating approach to predict phenology of silage maize

Crop models are tools used for predicting year-to-year crop development on field to regional scales. However, robust predictions are hampered by uncertainty in crop model parameters and in the data used for calibration. Bayesian calibration allows for the estimation of model parameters and quantification of uncertainties, with the consideration of prior information. In this study, we used a Bayesian sequential updating (BSU) approach to progressively incorporate additional data at a yearly time-step in order to calibrate a phenology model (SPASS) while analysing changes in parameter uncertainty and prediction quality. We used field measurements of silage maize grown between 2010 and 2016 in the regions of Kraichgau and the Swabian Alb in southwestern Germany. Parameter uncertainty and model prediction errors were expected to progressively be reduced to a final, irreducible value. Parameter uncertainty was reduced as expected with the sequential updates. For two sequences using synthetic data, one in which the model was able to accurately simulate the observations, and the other in which a single cultivar was grown under the same environmental conditions, prediction error was mostly reduced. However, in the true sequences that followed the actual chronological order of cultivation by the farmers in the two regions, prediction error increased when the calibration data were not representative of the validation data. This could be explained by differences in ripening group and temperature conditions during vegetative growth. With implications for manual and automatic data streams and model updating, our study highlights that the success of Bayesian methods for predictions depends on a comprehensive understanding of the inherent structure in the observation data and of the model limitations.