Irreversible glacier change and trough water for centuries after overshooting the Paris Agreement temperature goal

Mountain glaciers significantly impact sea level rise and water availability during droughts. Models project continued glacier mass loss in the 21^st century due to past and future rising temperatures. Our study delves into the repercussions of overshooting the 1.5°C Paris Agreement target and returning to it afterwards. For the first time, we explore the effects of these peak-and-decline overshoot scenarios on glacier volume and runoff using the Open Global Glacier Model (OGGM) framework. We apply novel climate simulations from 2000 to 2500  conducted with a  comprehensive  Earth System Model. These simulations either stabilise at global warming levels of 1.2°C (current warming), 1.5°C and 3°C, or temporally overshoot 1.5°C peaking at 3°C before declining and stabilising at 1.5°C after 2300. Although some glacier regions regrow within a century after the overshoot, the slow global glacier response results in irreversible ice loss over centuries. In 2500, overshooting the 1.5°C scenario temporarily by a peak at 3°C results in 10% more global glacier loss than directly stabilising at 1.5°C. While glacier runoff may temporarily increase in some basins in the coming decades, all basins will see a reduced contribution of glacier runoff to streamflow by the end of the 22^nd century under global stabilisation scenarios at 2°C or higher. In regions where glaciers regrow within the simulation period to reach a new equilibrium after a temporal temperature overshoot, glacier runoff contribution reduces temporally further than if temperature stabilises ("trough water"). The consequences of this newly documented "trough water" will depend on local conditions such as the local temperature overshoot magnitude, volume response time, future precipitation shifts, and melt versus precipitation seasonality. This study lays the first conceptual groundwork for overshoot scenarios on glaciers and introduces the potential of trough water risks. Additional Earth System Model realisations are needed for a detailed regional analysis and adaptation planning.