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Wallach, D., Thorburn, P., Asseng, S., Challinor, A. J., Ewert, F., Jones, J. W., et al. (2016). Estimating model prediction error: Should you treat predictions as fixed or random. Env. Model. Softw., 84, 529–539.
Abstract: Crop models are important tools for impact assessment of climate change, as well as for exploring management options under current climate. It is essential to evaluate the uncertainty associated with predictions of these models. We compare two criteria of prediction error; MSEPfixed, which evaluates mean squared error of prediction for a model with fixed structure, parameters and inputs, and MSEPuncertain(X), which evaluates mean squared error averaged over the distributions of model structure, inputs and parameters. Comparison of model outputs with data can be used to estimate the former. The latter has a squared bias term, which can be estimated using hindcasts, and a model variance term, which can be estimated from a simulation experiment. The separate contributions to MSEPuncertain(X) can be estimated using a random effects ANOVA. It is argued that MSEPuncertain(X) is the more informative uncertainty criterion, because it is specific to each prediction situation.
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Zhao, G., Siebert, S., Enders, A., Rezaei, E. E., Yan, C., & Ewert, F. (2015). Demand for multi-scale weather data for regional crop modeling. Agricultural and Forest Meteorology, 200, 156–171.
Abstract: A spatial resolution needs to be determined prior to using models to simulate crop yields at a regional scale, but a dilemma exists in compromising between different demands. A fine spatial resolution demands extensive computation load for input data assembly, model runs, and output analysis. A coarse spatial resolution could result in loss of spatial detail in variability. This paper studied the impact of spatial resolution, data aggregation and spatial heterogeneity of weather data on simulations of crop yields, thus providing guidelines for choosing a proper spatial resolution for simulations of crop yields at regional scale. Using a process-based crop model SIMPLACE (LINTUL2) and daily weather data at 1 km resolution we simulated a continuous rainfed winter wheat cropping system at the national scale of Germany. Then we aggregated the weather data to four resolutions from 10 to 100 km, repeated the simulation, compared them with the 1 km results, and correlated the difference with the intra-pixel heterogeneity quantified by an ensemble of four semivariogram models. Aggregation of weather data had small effects over regions with a flat terrain located in northern Germany, but large effects over southern regions with a complex topography. The spatial distribution of yield bias at different spatial resolutions was consistent with the intra-pixel spatial heterogeneity of the terrain and a log-log linear relationship between them was established. By using this relationship we demonstrated the way to optimize the model resolution to minimize both the number of simulation runs and the expected loss of spatial detail in variability due to aggregation effects. We concluded that a high spatial resolution is desired for regions with high spatial environmental heterogeneity, and vice versa. This calls for the development of multi-scale approaches in regional and global crop modeling. The obtained results require substantiation for other production situations, crops, output variables and for different crop models. (C) 2014 Elsevier B.V. All rights reserved.
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