Full-Bayesian multi-level models for crop phenology in Germany

Full-Bayesian multi-level models for crop phenology in Germany

Friedrich Busch – Potsdam Institute for Climate Impact Research

Effective adaptation of agriculture to climate change requires detailed insights into all components of the agricultural system. Understanding the phenological development of crops is crucial not only for making informed management decisions, such as the timing of fertilizer or pesticide application and harvest but also for assessing future weather-related risks. With climate change, the timing and duration of phenological phases are expected to shift, and the likelihood of weather extremes during these phases may increase. Therefore, comprehensive phenological models with robust representations of uncertainties are essential.
Most current phenological models rely primarily on temperature-driven development units to predict crop phenology while neglecting other potential predictors. Since phenological observations are often limited, data is typically pooled to obtain seemingly robust parameter estimates. This structural decision, in combination with neglect of input data uncertainty, can lead to overconfidence in parameter estimates.
Hierarchical Bayesian models can address these issues. By employing a multi-level interpretation of the data (partial pooling), parameter estimates for varying groups within the data can be improved. In phenological data, one critical group level is the cultivar level, which is often omitted due to the limited availability of such data. For historical phenological observations of maize grown in Germany, cultivar data is partially available. To maximize the use of this data and minimize bias caused by missing information, a data imputation scheme is applied to reconstruct missing cultivar data. Subsequently, a full Bayesian statistical phenology model is calibrated, incorporating cultivar information and individual farm location as hierarchical levels.
Since phenological observations are typically collected by the local farmers, based on visual judgment, considerable uncertainty is inherent in the data. Incorporating this uncertainty into the model structure allows for more realistic parameter estimates. Furthermore, enhancing the development unit concept by incorporating additional predictors, such as radiation and soil moisture alongside temperature, has the potential to reduce unexplained variance in the data.
Model comparison and evaluation of the trade-off between predictive power and complexity are conducted using information criteria such as WAIC and Pareto-smoothed importance sampling. This work builds on recent advances in hierarchical Bayesian phenological modeling, providing new insights into key driving factors and relevant model structures. The models are developed using the Stan programming language, optimized for Bayesian analysis, and employ state-of-the-art Bayesian parameter sampling algorithms. In conjunction with climate scenarios these models can be used to estimate future changes in the phenological development of crops.