Heat stress as an emerging constraint on global dairy systems: global gridded CMIP6 projections and national-scale milk loss exposure

Dairy production is a key component of global food systems, providing essential nutrients and supporting rural livelihoods, but it is increasingly exposed to heat stress under climate change. Here, we present a spatially explicit global assessment of heat-stress exposure and potential milk-yield losses using bias-corrected CMIP6 climate projections at 0.25° resolution combined with gridded livestock distribution data. Daily Temperature--Humidity Index (THI) is computed from maximum air temperature and mean relative humidity using five CMIP6 models at 0.25° resolution. Heat-stress exposure is quantified through exceedance metrics of established physiological thresholds (THI~$\geq$~72 and higher values for sensitivity analysis). Milk-yield losses are estimated using an empirical quadratic loss function and aggregated spatially using FAO Gridded Livestock of the World (GLW3) cattle densities. National-scale losses are calibrated against FAOSTAT milk production, and results are reported for OECD countries using both absolute and per-capita indicators based on a fixed population baseline. Results show that heat stress is already a structural feature of dairy production in many regions, with recurrent THI exceedances under present-day climate. Future warming leads to a pronounced intensification and seasonal extension of heat stress, particularly in extratropical dairy systems. By the end of the century under SSP5--8.5, projected milk-yield losses become non-marginal for several major dairy producers, while per-capita indicators reveal strong heterogeneity in potential exposure across OECD countries. In tropical regions, THI exceedances exhibit saturation behaviour, whereas mid-latitude systems experience a marked lengthening of the heat-stress season. By combining climate projections with spatial livestock data and national production statistics, this study provides a consistent framework to translate biophysical heat stress into food-system-relevant exposure metrics. While not accounting for adaptation or structural change, the results highlight heat stress as an emerging systemic constraint on dairy productivity and provide a quantitative baseline for evaluating future adaptation strategies and food-system resilience.