Statistical regression models for assessing climate impacts on crop yields: A validation study for winter wheat and silage maize in Germany

• Three statistical models are validated for yield projections of wheat and maize.
• Inter-annual changes of climate and management variables are combined in the models.
• The usage of relative climate changes in the crop models allows biased climate data.
• Spatial parameter distributions capture climate impacts on growth phases.
• The separate time series models perform best when validated for Germany.

For agriculture in Germany and generally all around the world, yield variability due to uncertain climate conditions represents an increasing production risk. Regional assessments of future yield changes can diminish this risk. For Germany's two most important crops winter wheat (Triticum aestivum L.) and silage maize (Zea mays L.), we investigate three regression models estimating relative climate impacts on relative crop yield changes: the separate time series model (STSM), the panel data model (PDM) and the random coefficient model (RCM). These regression models use the Cobb–Douglas function to capture climatic and non-climatic impacts on yields (e.g., changing prices or inventory management). The yield influencing climatic impacts contain the potential growth and stress factors during vegetative and reproductive plant development. The models are estimated and validated at the county scale. To improve the robustness and goodness of fit, the models are aggregated at the scale of German federal states, river basins and at the national scale. The observed yield changes are satisfactorily reproduced by all models for all aggregated scales (measured by the Nash–Sutcliffe efficiency (NSE)). According to their NSE values, the methodically simple STSMs reproduce extreme yield changes better (0.85) than the RCMs (0.79) and PDMs (0.72) at the national scale. This order can be also found across all scales when considering the models’ goodness of fit. Generally, spatial aggregation increases the goodness of fit by +0.16 for federal states and river basins and by +0.29 for entire Germany compared to the county scale. The mean NSE increase is lowest for STSMs (+0.11), followed by RCMs (+0.13) and PDMs (+0.25) for federal states and river basins, which is opposite to the goodness of fit order. The model parameters show clear spatial patterns, which reflect regional differences of climate and soil. Within its methodological limits, our approach can directly be combined with the output of climate models and is suitable for assessing short- and medium-term yield effects for the current agronomic practice. It requires neither bias correction of the climate variables nor explicit modeling of crop yield trends.