Abstract: We compared the precision of simple random sampling (SimRS) and seven types of stratified random sampling (StrRS) schemes in estimating regional mean of water-limited yields for two crops (winter wheat and silage maize) that were simulated by fourteen crop models. We found that the precision gains of StrRS varied considerably across stratification methods and crop models. Precision gains for compact geographical stratification were positive, stable and consistent across crop models. Stratification with soil water holding capacity had very high precision gains for twelve models, but resulted in negative gains for two models. Increasing the sample size monotonously decreased the sampling errors for all the sampling schemes. We conclude that compact geographical stratification can modestly but consistently improve the precision in estimating regional mean yields. Using the most influential environmental variable for stratification can notably improve the sampling precision, especially when the sensitivity behavior of a crop model is known.

Abstract: unless local adaptation can ameliorate these impacts. Ensembles of crop simulation models can be useful tools for assessing if proposed adaptation options are capable of achieving target yields, whilst also quantifying the share of uncertainty in the simulated crop impact resulting from the crop models themselves. Although some studies have analysed the influence of ensemble size on model outcomes, the effect of ensemble composition has not yet been properly appraised. Moreover, results and derived recommendations typically rely on averaged ensemble simulation results without accounting sufficiently for the spread of model outcomes. Therefore, we developed an Ensemble Outcome Agreement (EOA) index, which analyses the effect of changes in composition and size of a multi-model ensemble (MME) to evaluate the level of agreement between MME outcomes with respect to a given hypothesis (e.g. that adaptation measures result in positive crop responses). We analysed the recommendations of a previous study performed with an ensemble of 17 crop models and testing 54 adaptation options for rainfed winter wheat (Triticum aestivwn L.) at Lleida (NE Spain) under perturbed conditions of temperature, precipitation and atmospheric CO2 concentration. Our results confirmed that most adaptations recommended in the previous study have a positive effect. However, we also showed that some options did not remain recommendable in specific conditions if different ensembles were considered. Using EOA, we were able to identify the adaptation options for which there is high confidence in their effectiveness at enhancing yields, even under severe climate perturbations. These include substituting spring wheat for winter wheat combined with earlier sowing dates and standard or longer duration cultivars, or introducing supplementary irrigation, the latter increasing EOA values in all cases. There is low confidence in recovering yields to baseline levels, although this target could be attained for some adaptation options under moderate climate perturbations. Recommendations derived from such robust results may provide crucial information for stakeholders seeking to implement adaptation measures.

Abstract: This study explored the utility of the impact response surface (IRS) approach for investigating model ensemble crop yield responses under a large range of changes in climate. IRSs of spring and winter wheat Triticum aestivum yields were constructed from a 26-member ensemble of process-based crop simulation models for sites in Finland, Germany and Spain across a latitudinal transect. The sensitivity of modelled yield to systematic increments of changes in temperature (-2 to +9°C) and precipitation (-50 to +50%) was tested by modifying values of baseline (1981 to 2010) daily weather, with CO2 concentration fixed at 360 ppm. The IRS approach offers an effective method of portraying model behaviour under changing climate as well as advantages for analysing, comparing and presenting results from multi-model ensemble simulations. Though individual model behaviour occasionally departed markedly from the average, ensemble median responses across sites and crop varieties indicated that yields decline with higher temperatures and decreased precipitation and increase with higher precipitation. Across the uncertainty ranges defined for the IRSs, yields were more sensitive to temperature than precipitation changes at the Finnish site while sensitivities were mixed at the German and Spanish sites. Precipitation effects diminished under higher temperature changes. While the bivariate and multi-model characteristics of the analysis impose some limits to interpretation, the IRS approach nonetheless provides additional insights into sensitivities to inter-model and inter-annual variability. Taken together, these sensitivities may help to pinpoint processes such as heat stress, vernalisation or drought effects requiring refinement in future model development.