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Crop models are increasingly used to simulate crop yields at the global scale, but so far there is no general framework on how to assess model performance. Here we evaluate the simulation results of 14 global gridded crop modeling groups that have contributed historic crop yield simulations for maize, wheat, rice and soybean to the Global Gridded Crop Model Intercomparison (GGCMI) of the Agricultural Model Intercomparison and Improvement Project (AgMIP). Simulation results are compared to reference data at global, national and grid cell scales and we evaluate model performance with respect to time series correlation, spatial correlation and mean bias. We find that global gridded crop models (GGCMs) show mixed skill in reproducing time series correlations or spatial patterns at the different spatial scales. Generally, maize, wheat and soybean simulations of many GGCMs are capable of reproducing larger parts of observed temporal variability (time series correlation coefficients (r) of up to 0.888 for maize, 0.673 for wheat and 0.643 for soybean at the global scale) but rice yield variability cannot be well reproduced by most models. Yield variability can be well reproduced for most major producing countries by many GGCMs and for all countries by at least some. A comparison with gridded yield data and a statistical analysis of the effects of weather variability on yield variability shows that the ensemble of GGCMs can explain more of the yield variability than an ensemble of regression models for maize and soybean, but not for wheat and rice. We identify future research needs in global gridded crop modeling and for all individual crop modeling groups. In the absence of a purely observation-based benchmark for model evaluation, we propose that the best performing crop model per crop and region establishes the benchmark for all others, and modelers are encouraged to investigate how crop model performance can be increased. We make our evaluation system accessible to all c

Aircraft collision avoidance systems assist in the resolution of collision threats from nearby aircraft by issuing avoidance maneuvers to pilots. Encounters where more than one aircraft poses a threat, though rare, can be difficult to resolve because a maneuver that might resolve a conflict with one aircraft might induce conflicts with others. Recent efforts to develop robust collision avoidance systems for single-threat encounters have involved modeling the problem as a Markov decision process, discretizing the model, and applying dynamic programming to solve for the optimal avoidance strategy. Because the direct application of this methodology does not scale well to multiple threats, this paper evaluates a variety of decomposition methods that leverage the optimal avoidance strategy for single-threat encounters.