Evaluation of multimodel averaging approaches for ensembling evapotranspiration and yield simulations from maize models

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Combining multi-model simulations can reduce the uncertainty in model structure and increase the accuracy of agricultural systems modeling results. This improvement is essential for supporting better decision making in irrigation planning and climate change adaptation strategies. Besides the commonly used arithmetic mean and median, many multi-model averaging approaches (MAA), widely examined in groundwater and hydrological modeling, but these additional MAA have not been examined in agricultural system modeling to improve the simulation accuracy. Therefore, the objective of this study is to evaluate the performance of seven MAA: two equal weighted approaches (Simple Model Averaging (SMA) and Median) and five weighted approaches (Inverse Ranking (IR), Bates and Granger Averaging (BGA), and Granger Ramanathan A, B, and C (GRA, GRB, and GRC)) in combining results of multiple agricultural system models. The Granger Ramanathan methods differ in their constraints: GRA employs conventional least squares, GRB requires non-negative weights that total to one, and GRC reduces absolute errors for robustness against outliers. The evaluation was conducted using maize yield and daily ETa simulations for both blind (uncalibrated) and calibrated phases of data from two groups of maize sites (Group A and Group B) across North America. The modeling results from the blind and calibrated phases were combined for all maize models and group maize models. Overall, all MAA performed better than individual crop models for blind and calibration phases. Specifically, the GRB model averaging method provided the closest match to measured values for daily ETa, while GRA was the most accurate for maize yield in most cases across all sites and phases. GRB improved daily ETa estimation over the median by an average of 4 % and 8.5 % in terms of RRMSE, while GRA enhanced maize yield estimation over the median by 7.5 % and 10.9 % for Group A and Group B sites, respectively. Notably, the improvement was greater in the blind phase for both groups of maize sites. An ensemble of group maize models with varied structures performed nearly as well as an ensemble of all maize models in simulating daily ETa and yield for Group A and Group B sites. Based on the results, we recommend GRA for crop yield and GRB for ETa simulations for maize, but both methods require observed yield and ETa data for their application; however, in the absence of observed data, we recommend the SMA method as it performs better than the median. However, the performance of these MAA methods may differ for other crops (e.g., soybean, wheat, canola, potato, alfalfa) or regions, and it should be evaluated in future studies.

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