Abstract: Highlights • The larger simulated attainable yield for a specific crop season, the larger the yield gap. • Average size of the yield gap is not affected by the inter-annual variability of attainable yield. • Technology levels (resource input and accessibility) determine average yield gap. • To reduce yield gaps in rainfed environments, farmers need to improve season-specific crop management. Abstract Provision of food security in the face of increasing global food demand requires narrowing of the gap between actual farmer’s yield and maximum attainable yield. So far, assessments of yield gaps have focused on average yield over 5–10 years, but yield gaps can vary substantially between crop seasons. In this study we hypothesized that climate-induced inter-annual yield variability and associated risk is a major barrier for farmers to invest, i.e. increase inputs to narrow the yield gap. We evaluated the importance of inter-annual attainable yield variability for the magnitude of the yield gap by utilizing data for wheat and maize at ten sites representing some major food production systems and a large range of climate and soil conditions across the world. Yield gaps were derived from the difference of simulated attainable yields and regional recorded farmer yields for 1981 to 2010. The size of the yield gap did not correlate with the amplitude of attainable yield variability at a site, but was rather associated with the level of available resources such as labor, fertilizer and plant protection inputs. For the sites in Africa, recorded yield reached only 20% of the attainable yield, while for European, Asian and North American sites it was 56–84%. Most sites showed that the higher the attainable yield of a specific season the larger was the yield gap. This significant relationship indicated that farmers were not able to take advantage of favorable seasonal weather conditions. To reduce yield gaps in the different environments, reliable seasonal weather forecasts would be required to allow farmers to manage each seasonal potential, i.e. overcoming season-specific yield limitations.

Abstract: Highlights • The parameters to be fixed were consistent across sites. • Model calibration must be performed separately for each specific case. • Possible to reduce model parameters from 66 to 45. • Strong model reductions must be avoided. • The error term for the training data were characterised by timing (phase shift). Abstract Proper parameterisation and quantification of model uncertainty are two essential tasks in improvement and assessment of model performance. Bayesian calibration is a method that combines both tasks by quantifying probability distributions for model parameters and outputs. However, the method is rarely applied to complex models because of its high computational demand when used with high-dimensional parameter spaces. We therefore combined Bayesian calibration with sensitivity analysis, using the screening method by Morris (1991), in order to reduce model complexity by fixing parameters to which model output was only weakly sensitive to a nominal value. Further, the robustness of the model with respect to reduction in the number of free parameters were examined according to model discrepancy and output uncertainty. The process-based grassland model BASGRA was examined in the present study on two sites in Norway and in Germany, for two grass species (Phleum pratense and Arrhenatherum elatius). According to this study, a reduction of free model parameters from 66 to 45 was possible. The sensitivity analysis showed that the parameters to be fixed were consistent across sites (which differed in climate and soil conditions), while model calibration had to be performed separately for each combination of site and species. The output uncertainty decreased slightly, but still covered the field observations of aboveground biomass. Considering the training data, the mean square error for both the 66 and the 45 parameter model was dominated by errors in timing (phase shift), whereas no general pattern was found in errors when using the validation data. Stronger model reduction should be avoided, as the error term increased and output uncertainty was underestimated.