Abstract: Multi-model forecasting has drawn some attention in crop science for evaluating effect of climate change on crop yields. The principle is to run several individual process-based crop models under several climate scenarios in order to generate ensembles of output values. This paper describes a simple Bayesian method – called Bayes linear method- for updating ensemble of crop model outputs using yield observations. The principle is to summarize the ensemble of crop model outputs by its mean and variance, and then to adjust these two quantities to yield observations in order to reduce uncertainty. The adjusted mean and variance combine two sources of information, i.e., the ensemble of crop model outputs and the observations. Interestingly, with this method, observations collected under a given climate scenario can be used to adjust mean and variance of the model ensemble under a different scenario. Another advantage of the proposed method is that it does not rely on a separate calibration of each individual crop model. The uncertainty reduction resulting from the adjustment of an ensemble of crop models to observations was assessed in a numerical application. The implementation of the Bayes linear method systematically reduced uncertainty, but the results showed the effectiveness of this method varied in function of several factors, especially the accuracy of the yield observation, and the covariance between the crop model output and the observation. (C) 2015 Elsevier B.V. All rights reserved.

Abstract: • This study combines crop, livestock and economic models.
• Models interaction is through use of relevant input and output variables.
• Future climate change will result in increased grass and wheat dry matter yields.
• Changes in grass, wheat and milk yields in future reduce farm emissions intensity.
• Changes in future dry matter yields and emissions lead to increased profitability.
There is a scientific consensus that the future climate change will affect grass and crop dry matter (DM) yields. Such yield changes may entail alterations to farm management practices to fulfill the feed requirements and reduce the farm greenhouse gas (GHG) emissions from dairy farms. While a large number of studies have focused on the impacts of projected climate change on a single farm output (e.g. GHG emissions or economic performance), several attempts have been made to combine bio-economic systems models with GHG accounting frameworks. In this study, we aimed to determine the physical impacts of future climate scenarios on grass and wheat DM yields, and demonstrate the effects such changes in future feed supply may have on farm GHG emissions and decision-making processes. For this purpose, we combined four models: BASGRA and CSM-CERES-Wheat models for simulating forage grass DM and wheat DM grain yields respectively; HolosNor for estimating the farm GHG emissions; and JORDMOD for calculating the impacts of changes in the climate and management on land use and farm economics. Four locations, with varying climate and soil conditions were included in the study: south-east Norway, south-west Norway, central Norway and northern Norway. Simulations were carried out for baseline (1961–1990) and future (2046–2065) climate conditions (projections based on two global climate models and the Special Report on Emissions Scenarios (SRES) A1B GHG emission scenario), and for production conditions with and without a milk quota. The GHG emissions intensities (kilogram carbon dioxide equivalent: kgCO2e emissions per kg fat and protein corrected milk: FPCM) varied between 0.8 kg and 1.23 kg CO2e (kg FPCM)− 1, with the lowest and highest emissions found in central Norway and south-east Norway, respectively. Emission intensities were generally lower under future compared to baseline conditions due mainly to higher future milk yields and to some extent to higher crop yields. The median seasonal above-ground timothy grass yield varied between 11,000 kg and 16,000 kg DM ha− 1 and was higher in all projected future climate conditions than in the baseline. The spring wheat grain DM yields simulated for the same weather conditions within each climate projection varied between 2200 kg and 6800 kg DM ha− 1. Similarly, the farm profitability as expressed by total national land rents varied between 1900 million Norwegian krone (NOK) for median yields under baseline climate conditions up to 3900 million NOK for median yield under future projected climate conditions.