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We apply an empirical, data-driven approach for describing crop yield as afunction of monthly temperature and precipitation by employing generativeprobabilistic models with parameters determined through Bayesian inference. Ourapproach is applied to state-scale maize yield and meteorological data for theUS Corn Belt from 1981 to 2014 as an exemplar, but would be readilytransferable to other crops, locations and spatial scales. Experimentation witha number of models shows that maize growth rates can be characterised by atwo-dimensional Gaussian function of temperature and precipitation with monthlycontributions accumulated over the growing period. This approach accounts fornon-linear growth responses to the individual meteorological variables, andallows for interactions between them. Our models correctly identify thattemperature and precipitation have the largest impact on yield in the sixmonths prior to the harvest, in agreement with the typical growing season forUS maize (April to September). Maximal growth rates occur for monthly meantemperature 18-19$^\circ$C, corresponding to a daily maximum temperature of24-25$^\circ$C (in broad agreement with previous work) and monthly totalprecipitation 115 mm. Our approach also provides a self-consistent way ofinvestigating climate change impacts on current US maize varieties in theabsence of adaptation measures. Keeping precipitation and growing area fixed, atemperature increase of $2^\circ$C, relative to 1981-2014, results in the meanyield decreasing by 8\%, while the yield variance increases by a factor ofaround 3. We thus provide a flexible, data-driven framework for exploring theimpacts of natural climate variability and climate change on globallysignificant crops based on their observed behaviour. In concert with otherapproaches, this can help inform the development of adaptation strategies thatwill ensure food security under a changing climate.

An empirical, Bayesian approach to modelling the impact of weather on crop yield: maize in the US