Abstract: Increasing crop productivity while simultaneously reducing the environmental footprint of crop production is considered a major challenge for the coming decades. Even short episodes of heat stress can reduce crop yield considerably causing low resource use efficiency. Studies on the impact of heat stress on crop yields over larger regions generally rely on temperatures measured by standard weather stations at 2 m height. Canopy temperatures measured in this study in field plots of rye were up to 7 degrees C higher than air temperature measured at typical weather station height with the differences in temperatures controlled by soil moisture contents. Relationships between heat stress and grain number derived from controlled environment studies were only confirmed under field conditions when canopy temperature was used to calculate stress thermal time. By using hourly mean temperatures measured by 78 weather stations located across Germany for the period 1994-2009 it is estimated, that mean yield declines in wheat due to heat stress during flowering were 0.7% when temperatures are measured at 2 m height, but yield declines increase to 22% for temperatures measured at the ground. These results suggest that canopy temperature should be simulated or estimated to reduce uncertainty in assessing heat stress impacts on crop yield.

Abstract: Highlights • Regularization techniques for regression outperformed the classical regression techniques in predicting crop yields. • Different regression techniques with similar prediction accuracy showed different responses of major climatic variables to crop yield. • The regression models showed some responses of crop yield to climatic conditions that is mostly absent in process based crop models. Abstract Statistical regression models represent alternatives to process-based dynamic models for predicting the response of crop yields to variation in climatic conditions. Regression models can be used to quantify the effect of change in temperature and precipitation on yields. However, it is difficult to identify the most relevant input variables that should be included in regression models due to the high number of candidate variables and to their correlations. This paper compares several regression techniques for modeling response of winter oilseed rape yield to a high number of correlated input variables. Several statistical regression methods were fitted to a dataset including 689 observations of winter oilseed rape yield from replicated field experiments conducted in 239 sites in Denmark, covering nearly all regions of the country from 1992 to 2013. Regression methods were compared by cross-validation. The regression methods leading to the most accurate yield predictions were Lasso and Elastic Net, and the least accurate methods were ordinary least squares and stepwise regression. Partial least squares and ridge regression methods gave intermediate results. The estimated relative yield change for a +1°C temperature increase during flowering was estimated to range between 0 and +6 %, depending on choice of regression method. Precipitation was found to have an adverse effect on yield during autumn and winter. It was estimated that an increase in precipitation of +1 mm/day would result in a relative yield change ranging from 0 to −4 %. Soil type was also important for crop yields with lower yields on sandy soils compared to loamy soils. Later sowing was found to result in increased crop yield. The estimated effect of climate on yield was highly sensitive to the chosen regression method. Regression models showing similar performance led in some cases to different conclusions with respect to effect of temperature and precipitation. Hence, it is recommended to apply an ensemble of regression models, in order to account for the sensitivity of the data driven models for projecting crop yield under climate change.