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: Even brief periods of high temperatures occurring around flowering and during grain filling can severely reduce grain yield in cereals. Recently, ecophysiological and crop models have begun to represent such phenomena. Most models use air temperature (Tair) in their heat stress responses despite evidence that crop canopy temperature (Tc) better explains grain yield losses. Tc can deviate significantly from Tair based on climatic factors and the crop water status. The broad objective of this study was to evaluate whether simulation of Tc improves the ability of crop models to simulate heat stress impacts on wheat under irrigated conditions. Nine process-based models, each using one of three broad approaches (empirical, EMP; energy balance assuming neutral atmospheric stability, EBN; and energy balance correcting for the atmospheric stability conditions, EBSC) to simulate Tc, simulated grain yield under a range of temperature conditions. The models varied widely in their ability to reproduce the measured Tc with the commonly used EBN models performing much worse than either EMP or EBSC. Use of Tc to account for heat stress effects did improve simulations compared to using only Tair to a relatively minor extent, but the models that additionally use Tc on various other processes as well did not have better yield simulations. Models that simulated yield well under heat stress had varying skill in simulating Tc. For example, the EBN models had very poor simulations of Tc but performed very well in simulating grain yield. These results highlight the need to more systematically understand and model heat stress events in wheat.