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: Problems related to food security and sustainable development are complex (Ericksenet al., 2009) and require consideration of biophysical, economic, political, and social factors, as well as their interactions, at the level of farms, regions, nations, and globally. While the solution to such societal problems may be largely political, there is a growing recognition of the need for science to provide sound information to decision-makers (Meinke et al., 2009). Achieving this, particularly in light of largely uncertain future climate and socio-economic changes, will necessitate integrated assessment approaches and appropriate integrated assessment modeling (IAM) tools to perform them. Recent (Ewertet al., 2009; van Ittersumet al., 2008) and ongoing (Rosenzweiget al., 2013) studies have tried to advance the integrated use of biophysical and economic models to represent better the complex interactions in agricultural systems that largely determine food supply and sustainable resource use. Nonetheless, the challenges for model integration across disciplines are substantial and range from methodological and technical details to an often still-weak conceptual basis on which to ground model integration (Ewertet al., 2009; Janssenet al., 2011). New generations of integrated assessment models based on well-understood, general relationships that are applicable to different agricultural systems across the world are still to be developed. Initial efforts are underway towards this advancement (Nelsonet al., 2014; Rosenzweiget al., 2013). Together with economic and climate models, crop models constitute an essential model group in IAM for large-area cropping systems climate change impact assessments. However, in addition to challenges associated with model integration, inadequate representation of many crops and crop management systems, as well as a lack of data for model initialization and calibration, limit the integration of crop models with climate and economic models (Ewertet al., 2014). A particular obstacle is the mismatch between the temporal and spatial scale of input/output variables required and delivered by the various models in the IAM model chain. Crop models are typically developed, tested, and calibrated for field-scale application (Booteet al., 2013; see also Part 1, Chapter 4 in this volume) and short time-series limited to one or few seasons. Although crop models are increasingly used for larger areas and longer time-periods (Bondeauet al., 2007; Deryng et al., 2011; Elliottet al., 2014) rigorous evaluation of such applications is pending. Among the different sources of uncertainty related to climate and soil data, model parameters, and structure, the uncertainty from methods used to scale-up crop models has received little attention, though recent evaluations indicate that upscaling of crop models for climate change impact assessment and the resulting errors and uncertainties deserve attention in order to advance crop modeling for climate change assessment (Ewertet al., 2014; R¨ otteret al., 2011). This reality is now reflected in the scientific agendas of new international research projects and programs such as the Agricultural Model Intercomparison and Improvement Project (AgMIP; Rosenzweiget al., 2013) and MACSUR (MACSUR, 2014). In this chapter, progress in evaluation of scaling methods with their related uncertainties is reviewed. Specific emphasis is on examining the results of systematic studies recently established in AgMIP and MACSUR. Main features of the respective simulation studies are presented together with preliminary results. Insights from these studies are summarized and conclusions for further work are drawn. No Label

Abstract: The complexity of risks posed by climate change and possible adaptations for crop production has called for integrated assessment and modelling (IAM) approaches linking biophysical and economic models. This paper attempts to provide an overview of the present state of crop modelling to assess climate change risks to food production and to which extent crop models comply with IAM demands. Considerable progress has been made in modelling effects of climate variables, where crop models best satisfy IAM demands. Demands are partly satisfied for simulating commonly required assessment variables. However, progress on the number of simulated crops, uncertainty propagation related to model parameters and structure, adaptations and scaling are less advanced and lagging behind IAM demands. The limitations are considered substantial and apply to a different extent to all crop models. Overcoming these limitations will require joint efforts, and consideration of novel modelling approaches. No Label