Abstract: Livestock directly contribute to greenhouse gas (GHG) emissions mainly through methane (CH4) and nitrous oxide (N2O) emissions. For cost and practicality reasons, quantification of GHG has been through development of various types of mathematical models. This chapter addresses the utility and limitations of mathematical models used to estimate enteric CH4 emissions from livestock production. Models used in GHG quantification can be broadly classified into either empirical or mechanistic models. Empirical models might be easier to use because they require fewer input variables compared with mechanistic models. However, their applicability in assessing mitigation options such as dietary manipulation may be limited. The major driving variables identified for both types of models include feed intake, lipid and nonstructural carbohydrate content of the feed, and animal variables. Knowledge gaps identified in empirical modeling were that some of the assumptions might not be valid because of geographical location, health status of animals, genetic differences, or production type. In mechanistic modeling, errors related to estimating feed intake, stoichiometry of volatile fatty acid (VFA) production, and acidity of rumen contents are limitations that need further investigation. Model prediction uncertainty was also investigated, and, depending on the intensity and source of the prediction uncertainty, the mathematical model may inaccurately predict the observed values with more or less variability. In conclusion, although there are quantification tools available, global collaboration is required to come to a consensus on quantification protocols. This can be achieved through developing various types of models specific to region, animal, and production type using large global datasets developed through international collaboration.

Abstract: The accurate estimation of crop grain nitrogen (N; N in grain yield) is crucial for optimizing agricultural N management, especially in crop rotations. In the present study, 12 process-based models were applied to simulate the grain N of i) seven crops in rotations, ii) across various pedo-climatic and agro-management conditions in Europe, under both continuous simulation and single year simulation, and for iv) two calibration levels, namely minimal and detailed calibration. Generally, the results showed that the accuracy of the simulations in predicting grain N increased under detailed calibration. The models performed better in predicting the grain N of winter wheat (Triticum aestivum L.), winter barley (Hordewn vulgare L.) and spring barley (Hordeum vulgare L.) compared to spring oat (Avena saliva L.), winter rye (Secale cereale L.), pea (Piswn sativum L.) and winter oilseed rape (Brassica napus L.). These differences are linked to the intensity of parameterization with better parameterized crops showing lower prediction errors. The model performance was influenced by N fertilization and irrigation treatments, and a majority of the predictions were more accurate under low N and rainfed treatments. Moreover, the multi-model mean provided better predictions of grain N compared to any individual model. In regard to the Individual models, DAISY, FASSET, HERMES, MONICA and STICS are suitable for predicting grain N of the main crops in typical European crop rotations, which all performed well in both continuous simulation and single year simulation. Our results show that both the model initialization and the cover crop effects in crop rotations should be considered in order to achieve good performance of continuous simulation. Furthermore, the choice of either continuous simulation or single year simulation should be guided by the simulation objectives (e.g. grain yield, grain N content or N dynamics), the crop sequence (inclusion of legumes) and treatments (rate and type of N fertilizer) included in crop rotations and the model formalism.

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.