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: Crop models can be sensitive to climate input data aggregation and this response may differ among models. This should be considered when applying field-scale models for assessment of climate change impacts on larger spatial scales or when coupling models across scales. In order to evaluate these effects systematically, an ensemble of ten crop models was run with climate input data on different spatial aggregations ranging from 1, 10, 25, 50 and 100 km horizontal resolution for the state of North Rhine-Westphalia, Germany. Models were minimally calibrated to typical sowing and harvest dates, and crop yields observed in the region, subsequently simulating potential, water-limited and nitrogen-limited production of winter wheat and silage maize for 1982-2011. Outputs were analysed for 19 variables (yield, evapotranspiration, soil organic carbon, etc.). In this study the sensitivity of the individual models and the model ensemble in response to input data aggregation is assessed for crop yield. Results show that the mean yield of the region calculated from climate time series of 1 km horizontal resolution changes only little when using climate input data of higher aggregation levels for most models. However, yield frequency distributions change with aggregation, resembling observed data better with increasing resolution. With few exceptions, these results apply to the two crops and three production situations (potential, water-, nitrogen-limited) and across models including the model ensemble, regardless of differences among models in simulated yield levels and spatial yield patterns. Results of this study improve the confidence of using crop models at varying scales.

Abstract: We assessed the weather data aggregation effect (DAE) on the simulation of cropping systems for different crops, response variables, and production conditions. Using 13 process-based crop models and the ensemble mean, we simulated 30 yr continuous cropping systems for 2 crops (winter wheat and silage maize) under 3 production conditions for the state of North Rhine-Westphalia, Germany. The DAE was evaluated for 5 weather data resolutions (i.e. 1, 10, 25, 50, and 100 km) for 3 response variables including yield, growing season evapotranspiration, and water use efficiency. Five metrics, viz. the spatial bias (Delta), average absolute deviation (AAD), relative AAD, root mean squared error (RMSE), and relative RMSE, were used to evaluate the DAE on both the input weather data and simulated results. For weather data, we found that data aggregation narrowed the spatial variability but widened the., especially across mountainous areas. The DAE on loss of spatial heterogeneity and hotspots was stronger than on the average changes over the region. The DAE increased when coarsening the spatial resolution of the input weather data. The DAE varied considerably across different models, but changed only slightly for different production conditions and crops. We conclude that if spatially detailed information is essential for local management decision, higher resolution is desirable to adequately capture the spatial variability for heterogeneous regions. The required resolution depends on the choice of the model as well as the environmental condition of the study area.