Bayesian multi-level calibration of a process-based maize phenology model

Plant phenology models are important components in process-based crop models, which are used to assess the impact of climate change on food production. For reliable model predictions, parameters in phenology models have to be accurately known. They are usually estimated by calibrating the model to observations. However, at regional scales in which different cultivars of a crop species may be grown, not accounting for inherent differences in phenological development between cultivars in the model and the presence of model deficits lead to inaccurate parameter estimates. To account for inherent differences between cultivars and to identify model deficits, we used a Bayesian multi-level approach to calibrate a phenology model (SPASS) to observations of silage maize grown across Germany between 2009 and 2017. We evaluated four multi-level models of increasing complexity, where we accounted for different combinations of ecological, weather, and year effects, as well as the hierarchical classification of cultivars nested within ripening groups of the maize species. We compared the calibration quality from this approach to the commonly used pooled approach in which none of these factors are considered. The pooled model led to over-confident process model parameter estimates and comparatively poor calibration quality. The mean value of the unexplained residual error standard deviation reduced from 5.5 BBCH (phenological development units) in the pooled model case (BM-0) to 5.3 BBCH when eco-region and year effects (BMM-1) were considered. Additionally accounting for weather effects (BMM-2a) resulted in a mean value of 5.2 BBCH. Calibration quality especially improved when the hierarchical classification of cultivars within ripening groups of maize was incorporated. Including the hierarchical classification with eco-region and year effects (BMM-2b) led to a mean residual error of 4.4 BBCH while additionally considering weather effects in the full model case (BMM-3) resulted in a value of 4.3 BBCH. Our findings have implications for regional model calibration and data-gathering studies, since it emphasizes that ripening group and cultivar information is essential. Furthermore, we found that if this information is not available, at least weather, eco-region and year effects should be taken into account. Accounting for only the eco-region and year effects led to parameter-compensation of the missing weather effects. Our results can facilitate model improvement studies since we identified possible model limitations related to temperature effects in the reproductive (post-flowering) phase and to soil-moisture. We demonstrate that Bayesian multi-level calibration of a phenology model facilitates the incorporation of hierarchical dependencies and the identification of model limitations. Our approach can be extended to full crop models at different spatial scales.