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

Authors: NAND, VIVEKA - McGill University - Canada; QI, ZHIMING - McGill University - Canada; Ma, Liwang; HELMERS, M - Iowa State University; MADRAMOOTOO, C - McGill University - Canada; SMITH, W - Agriculture And Agri-Food Canada; ZHANG, T - Agriculture And Agri-Food Canada; WEBER, T - University Of Kassel; PATTEY, E - Agriculture And Agri-Food Canada; LI, Z - McGill University - Canada; WANG, JIAXIN - McGill University - Canada; Jin, Virginia; JIANG, QIANJING - Zhejiang University; TENUTA, MARIO - University Of Manitoba; Trout, Thomas; CHANG, HAOMIAO - Yangzhou University; Harmel, Robert; Kimball, Bruce; Thorp, Kelly; BOOTE, KENNETH - University Of Florida; STOCKLE, CLAUDIO - Washington State University; SUYKER, ANDREW - University Of Nebraska; Evett, Steven; Brauer, David; Coyle, Gwen; Copeland, Karen; Marek, Gary; Colaizzi, Paul; ACUTIS, MARCO - University Of Milan; ALIMAGHAM, SEYYED - Gorgan University Of Agricultural Sciences And Natural Resources; ARCHONTOULIS, SOTIRIOS - Iowa State University; BABACAR, FAYE - Institute Of National Research For Agriculture; BARCZA, ZOLTÁN - Czech University Of Life Sciences Prague; BASSO, BRUNO - Michigan State University; BERTUZZI, PATRICK - Inrae; CONSTANTIN, JULIE - Inrae; MIGLIORATI, MASSIMILIANO - Queensland Department Of Environmental Science; DUMONT, BENJAMIN - University Of Liege; DURAND, JEAN-LOUIS - Inrae; FODOR, NÁNDOR - Hungarian University Of Agriculture And Life Science; GAISER, THOMAS - University Of Bonn; GAROFALO, PASQUALE - Consiglio Per La Ricerca In Agricoltura E L'Analisi Dell'economia Agraria, Unita Di Ricerca Per I S; GAYLER, SEBASTIAN - University Of Hohenheim; GIGLIO, LUISA - Consiglio Per La Ricerca In Agricoltura E L'Analisi Dell'economia Agraria, Unita Di Ricerca Per I S; GRANT, ROBERT - University Of Alberta; GUAN, KAIYU - University Of Illinois Urbana-Champaign; HOOGENBOOM, GERRIT - University Of Florida; KIM, SOO-HYUNG - University Of Washington; KISEKKA, ISAYA - University Of California, Davis; LIZASO, JON - Universidad Politécnica De Madrid; MASIA, SARA - Ihe Delft Institute For Water Education; MENG, HUIMIN - China Agricultural University; MEREU, VALENTINA - Mediterranean Centre On Climate Change; MUKHTAR, AHMED - University Of Arid Agriculture; PEREGO, ALESSIA - University Of Milan; PENG, BIN - University Of Illinois Urbana-Champaign; PRIESACK, ECKART - Helmholtz Centre; SHELIA, VAKHTANG - University Of Florida; SNYDER, RICHARD - University Of California, Davis; SOLTANI, AFSHIN - US Department Of Agriculture (USDA); SPANO, DONATELLA - University Of California, Davis; SRIVASTAVA, AMIT - University Of Bonn; THOMSON, AIMEE - University Of Alberta; Timlin, Dennis; TRABUCCO, ANTONIO - Mediterranean Centre On Climate Change; WEBBER, HEIDI - Leibniz Centre; WILLAUME, MAGALI - Inrae; WILLIAMS, KARINA - Met Office; VAN DER LAAN, MICHAEL - University Of Alberta; VENTRELLA, DOMENICO - Iowa State University; VISWANATHAN, MICHELLE - University Of Pretoria; XU, XU - China Agricultural University; ZHOU, WANG - University Of Illinois Urbana-Champaign

Submitted to: Journal of Hydrology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 5/30/2025
Publication Date: 6/3/2025
Citation: Nand, V., Qi, Z., Ma, L., Helmers, M.J., Madramootoo, C.A., Smith, W.N., Zhang, T.Q., Weber, T.K., Pattey, E., Li, Z., Wang, J., Jin, V.L., Jiang, Q., Tenuta, M., Trout, T.J., Chang, H., Harmel, R.D., Kimball, B.A., Thorp, K.R., Boote, K.J., Stockle, C., Suyker, A.E., Evett, S.R., Brauer, D.K., Coyle, G.G., Copeland, K.S., Marek, G.W., Colaizzi, P.D., Acutis, M., Alimagham, S.M., Archontoulis, S., Babacar, F., Barcza, Z., Basso, B., Bertuzzi, P., Constantin, J., Migliorati, M., Dumont, B., Durand, J., Fodor, N., Gaiser, T., Garofalo, P., Gayler, S., Giglio, L., Grant, R., Guan, K., Hoogenboom, G., Kim, S., Kisekka, I., Lizaso, J., Masia, S., Meng, H., Mereu, V., Mukhtar, A., Perego, A., Peng, B., Priesack, E., Shelia, V., Snyder, R., Soltani, A., Spano, D., Srivastava, A., Thomson, A., Timlin, D.J., Trabucco, A., Webber, H., Willaume, M., Williams, K., Van Der Laan, M., Ventrella, D., Viswanathan, M., Xu, X., Zhou, W. 2025. Evaluation of multimodel averaging approaches for ensembling evapotranspiration and yield simulations from maize models. Journal of Hydrology. 661(Part B). Article e133631. https://doi.org/10.1016/j.jhydrol.2025.133631.
DOI: https://doi.org/10.1016/j.jhydrol.2025.133631

Interpretive Summary: Due to the uncertainty in model structure, ensemble of simulation results from multiple models have been recently proposed to increase the accuracy of agricultural systems models. However, besides the commonly used arithmetic mean and median, there exist several other multi-model averaging approaches (MAAs) that have not been used in ensembling simulation results. Therefore, the objective of this study is to evaluate the performance of seven MAAs [i.e. Simple Model Averaging (SMA), Median, Inverse Ranking (IR), Bates and Granger Averaging (BGA), and Multilinear Regression A, B, and C (MLR A, MLR B, and MLR C)] in ensembling results from multiple agricultural systems models. Simulated maize yield and daily actual evapotranspiration (ETa) from multiple models were evaluated at both blind (uncalibrated) and calibrated phases with data from maize studies across North America. As expected, ensemble of results from multiple models performed better than individual crop models at both the blind and the calibration phases, regardless of MAA used. In particular, the MLR C provided the best simulation of daily ETa, while MLR A was the most accurate representation for maize yield across all study sites and calibration phases. MLR C improved daily ETa estimation over the median by an average of 7%, while MLR A enhanced maize yield estimation over the median by about 9%. In addition, the improvement was greater at the blind phase than at the calibration phase. Based on these results, we recommend MLR A for crop yield and MLR C for ETa simulations, if observed yield and ETa data are known. However, in the absence of observed data, we recommend the SMA method as it performs better than the median.

Technical Abstract: Averaging multi-model simulations can reduce the uncertainty in model structure and increase the accuracy of agricultural systems modeling results. However, besides the commonly used arithmetic mean and median, there exist several additional multi-model averaging approaches (MAAs) whose performance in improving the modeling accuracy has not been examined. Therefore, the objective of this study is to evaluate the performance of seven MAAs [i.e. Simple Model Averaging (SMA), Median, Inverse Ranking (IR), Bates and Granger Averaging (BGA), and Multilinear Regression A, B, and C (MLR A, MLR B, and MLR C)] in combining results of multiple agricultural systems models. The evaluation was conducted using maize yield and daily actual evapotranspiration (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 MAAs performed better than individual crop models for blind and calibration phases. Specifically, the MLR C model averaging method provided the closest match to measured values for daily ETa, while MLR A was the most accurate for maize yield in most cases across all sites and phases. MLR C improved daily ETa estimation over the median by an average of 6.5% and 8.7% in terms of RRMSE, while MLR A enhanced maize yield estimation over the median by 9.8% and 9.2% 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 these results, we recommend MLR A for crop yield and MLR C for ETa simulations, 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 median.