Climate change, driven by increasing greenhouse gas concentrations, poses a significant threat to global crop production and food security. Rising temperatures and altered precipitation patterns increase the risk of major crop failures in key agricultural regions worldwide, potentially pushing a substantial portion of food production areas beyond suitable climatic conditions. The growing global population and increasing food demand further exacerbate this challenge, jeopardizing the UN's Sustainable Development Goal of eradicating hunger by 2030. Process-based biophysical crop models, coupled with climate data from multiple Global Climate Models (GCMs), are crucial tools for projecting crop yield changes and informing agricultural decision-making. The Agricultural Model Intercomparison and Improvement Project (AgMIP)'s Global Gridded Crop Model Intercomparison (GGCMI) provides valuable data for analyzing global crop yield responses to climate change. Recent studies using the latest generation of GCMs (CMIP6) show largely negative impacts on crop yields in many regions, but also some positive changes at higher latitudes. However, considerable uncertainty persists in GCM-GGCM yield projections, stemming from both GCM and GGCM structural and parameter uncertainties. Previous research has explored GCM and GGCM uncertainty at global scales for various crops, finding GGCMs to be a major source of uncertainty, although this variance decreased in CMIP6 compared to CMIP5. The dominant source of uncertainty can also be site-specific, as demonstrated for wheat yield changes. Optimizing the sample size for GCM-GGCM projections is vital but computationally challenging, given the demands of process-based crop models. The existing CMIP6-based GGCMI Phase 3 projections, with 60 combinations of 12 GGCMs and five GCMs, represent a significant dataset but may not fully capture uncertainty. While studies have examined minimum ensemble sizes for capturing model uncertainty in other fields, guidance for global-scale crop yield projections remains limited. This study focuses on wheat, maize, rice, and soybean—crops providing two-thirds of global caloric intake—to develop a framework for optimizing ensemble design and extracting information from large model pools. Using GGCM emulators driven by climate change data from 32 CMIP6 GCMs and GGCM Phase 3 simulations, the study investigates the influence of ensemble configurations on crop yield projections and modeling uncertainty under future climate change (specifically the SSP585 high emissions scenario). The aim is to improve the accuracy of crop yield projections and contribute to global food security.

The literature extensively documents the impacts of climate change on agriculture, highlighting the risks to global food security. Studies using coupled climate and crop models have shown varying impacts across regions and crops, with significant uncertainties in projections. Several research efforts have focused on quantifying the sources of these uncertainties, often finding that the choice of both Global Climate Models (GCMs) and Global Gridded Crop Models (GGCMs) significantly contributes to the overall variance. Studies using large ensembles of models have demonstrated that including more models can improve the accuracy of projections, particularly in regions where model results are most divergent. There is a recognized need to optimize the selection of models to balance computational cost with the representation of the full range of uncertainty. Previous studies have explored strategies for reducing ensemble sizes, such as using a subset of models that best represents the full range of behaviors. However, a clear strategy for choosing an optimal model ensemble size and composition for global-scale crop yield projections, particularly for climate change impacts, has remained elusive.

This study employed two main methodologies: 1) Cluster analysis of crop-growing regions and 2) Cluster analysis of future yield change. For the first methodology, a k-means cluster analysis was performed to divide the global cropping regions into sub-regions based on environmental variables, climate conditions, and management practices, including temperature, solar radiation, precipitation, humidity, wind speed, latitude, longitude, and nitrogen application rate. Twelve sub-regions were identified for each crop. The second methodology involved agglomerative-hierarchical clustering analysis to group crop yield projections from GCM-GGCM combinations into clusters based on spatial patterns and magnitudes of percentage yield changes. The Canberra distance metric was used to compute the initial cluster distance between ensemble members. Three clusters were identified for each crop, representing distinct yield change scenarios. For both methodologies, the analysis was performed separately for GGCM emulators (GGCMI Phase 2) and for GGCM Phase 3 simulations. The GGCM emulators used a change factor method to generate future climate data by applying future climate changes (from GCMs) to historical daily data from AgMIP's Modern-Era Retrospective Analysis for Research and Applications (AgMERRA). The GGCM Phase 3 simulations used bias-adjusted daily GCM data downscaled to a 0.5° x 0.5° grid. Analysis of variance (ANOVA) was used to quantify the uncertainty in crop yield changes due to GGCMs and GCMs, and to determine the least number of models needed to represent the full ensemble. The proportion of uncertainty attributed to individual GGCMs was assessed by sequentially removing each model and comparing the resulting GGCM-induced uncertainty to the full ensemble. The study used data for four major crops (wheat, maize, rice, and soybean) and a single high greenhouse gas emission scenario (SSP585) for the end of the 21st century.

The study's key findings include: 1) Cluster analysis revealed distinct groups of GGCM-GCM combinations with unique yield projection patterns and uncertainty levels, emphasizing the importance of model composition. The clustering often grouped results by GGCM, suggesting that differences between GGCMs were a primary driver of differences between clusters, although GCMs also contributed to diversity within each GGCM group. 2) The dominant source of uncertainty varied among clusters and spatial scales, with GGCMs being a larger source of uncertainty than GCMs in most cases. Different model combinations impacted the sources of modeling uncertainty, demonstrating the significance of model selection. 3) An analysis of ensemble size indicated that approximately six GGCMs and 9-12 GCMs were sufficient to capture the uncertainty in yield changes compared to the full model set. For GGCM Phase 3 simulations, 6-7 GGCMs were sufficient. The minimum effective ensemble size varied regionally, but typically fell within a range of 4-6 GGCMs and 6-14 GCMs. Spatial patterns of GGCM-induced uncertainty changed little when more than five models were used. 4) Using a cluster-based model selection strategy, 3-4 GGCMs were sufficient to capture the overall variance of the GGCMs, except potentially for wheat yield in Phase 3 simulations. 5) Individual GGCMs contributed differently to overall uncertainty, with some models consistently increasing uncertainty across most regions, while others showed regionally varying impacts. This highlights the importance of local-scale model selection.

The findings highlight the critical role of model composition and ensemble size in accurately representing uncertainty in crop yield projections. The cluster analysis effectively revealed distinct groups of models with varying yield predictions, showcasing the limitations of relying solely on multi-model ensemble means, which can obscure important details. The identification of minimum effective ensemble sizes for GGCMs and GCMs provides valuable guidance for optimizing computational resources in climate-crop modeling studies. The regionally and crop-specific variation in the contribution of individual GGCMs emphasizes the need for careful model selection when conducting local-scale impact assessments. The study's framework offers a more comprehensive understanding of uncertainty than previous approaches that often focused solely on the overall variance. The results could improve the design of future GCM-GGCM ensembles and contribute to more robust and reliable crop yield projections under climate change. The different yield projections resulting from various ensemble members highlight the importance of considering model diversity for creating robust adaptation strategies.

This study demonstrates a novel framework for optimizing ensemble configurations in climate-crop modeling. The findings provide clear guidance on the minimum number of GGCMs and GCMs necessary to capture modeling uncertainty in crop yield projections while accounting for model composition. The results show the variability of individual model contributions to uncertainty, highlighting the need for tailored model selection in local applications. Future research should focus on integrating additional sources of uncertainty (e.g., soil data, management practices, pest and diseases) and refining model structures to further enhance the accuracy and robustness of climate change impact assessments. The development of more sophisticated modeling techniques that account for extreme weather events and other variables will be crucial for improving future projections.

The study has several limitations. First, several factors influencing crop yields were not considered in the GGCM simulations, such as soil data variability, management options (e.g., fertilization rates), pest and diseases. Second, model parameterization uncertainty was not explicitly considered. Third, some GGCMs may underestimate yield losses under extremely wet conditions. Fourth, using the change factor method to generate future climate might not fully capture uncertainty in extreme climate events and within-season variability. Finally, the emulators may not perfectly reproduce raw GGCM simulations. Addressing these limitations will be crucial for improving the reliability of future crop yield projections under climate change.