Winter wheat phenological development model with a vernalization function using sigmoidal and exponential functions

Wheat is one of the world’s most important crops, and its phenological model is useful for scheduling agricultural practices such as fungicide or fertilizer application. Although various wheat phenological models have been developed throughout the world, a conventional model-mostly used for Japanese cultivars-is one wherein temperature and daylength responses are expressed as sigmoidal and exponential functions that do not have a vernalization function. Since a gradual rise in daily development rate is expressed as an increase in mean temperature in the conventional model, the model may potentially miscalculate the wheat development when used to predict the phenology of a cultivar with a strong vernalization requirement. In this study, we proposed a modified model that combines the conventional model and a vernalization function that expressed the daily vernalization rate using an inverse sigmoid function. Cultivation data for five winter wheat cultivars with relatively strong vernalization requirement were collected for several years (more than 4 years), and the model for flowering date prediction was calibrated based on the sowing date for each cultivar. Six-fold cross-validation was conducted to calibrate and validate the models. We found that the proposed model predicted the flowering date of the wheat cultivars more accurately in the median of root mean square error (RMSE: 1-2 days) than the conventional model (RMSE: 2-5 days). Although the accuracy of the model varies with the cultivar, our results indicated the advantage of using the proposed model compared with that of using the conventional model for describing winter wheat phenology. These findings can contribute to further studies on the crop models of winter wheat and would be an example of combining the vernalization function expressed by an inverse sigmoidal function with the crop model.