I n the global gridded crop model (GGCM) approach, the world is divided into grid cells defined by latitude and longitude, and crop yield for the landmass in each grid cell is simulated 1-4 . To estimate the potential impact of climate change on food produc tion, researchers aggregate simulated results into nations, regions or the world to aid economic analysis and inform policymaking at different scales 5,6 . To be deemed trustworthy, GGCM results must provide accurate estimates of yield-climate relationships, or other wise give explicit information of the uncertainty of projections. Current crop models produce different results due to underlying differences in climate projections, model structure, inputs and parameterization, so overall there is a large degree of uncertainty in crop yield projections 1 . An effective way to quantify this uncer tainty is to compare multiple climate-crop simulations of the same climate change problem 7,8 . Most current impact assessments are conducted for just a few wellcharacterized sites 9-12 , so while model accuracy can be improved through understanding where and how uncertainty arises in a multimodel ensemble 13 , the uncertainty of predictions across the mass of diverse arable lands around the world is difficult to estimate.Estimating impact consistently across the globe by applying a GGCM ensemble is expensive and difficult in terms of labour, tim ing, computational ability and resources, and expertise. Compared with crop modelling at individual sites, GGCMs introduce additional sources of uncertainty such as those that arise from geospatial data and data processing. For example, recent GGCM ensemble studies compared simulation results from different research groups 14 . Even when committed to following a common simulation protocol 15 , groups adopted their unique ways of processing data and param eterizing the models for the globe. A further aspect that has received insufficient attention in GGCMs is model parameterization and how it can affect the uncertainty of globalscale predictions, par ticularly for parameters describing localscale spatial variation in the use and performance of cultivars, varieties or hybrids.Here we present a range of global wheat yield responses to future warming scenarios based on a large simulation ensemble. The ensemble was composed of 1,440 global simulations, with combina tions of 20 climate projections (5 climate models under 4 representa tive concentration pathways (RCPs) for greenhouse gas emissions), 3 crop models, 4 parameterization strategies and 3 management inputs of sowing date ( Supplementary Fig. 1). We linked the uncer tainty of gridded predictions to the latitude of grid cells. To include the uncertainty of crop yield predictions due to CO 2 fertilization, we conducted two sets of simulations: the first accounted for the effects of both increased CO 2 as projected by the RCPs and changes in climate (CC w/CO 2 ); the second accounted for changes in climate at 360 ppm CO 2 , assuming CO 2 concentration would remain constant at its...