Evaluating local climate in global storm-resolving models with the K\"oppen-Geiger classification

Global storm-resolving models aspire to become digital twins of the Earth, delivering information at the local scale at which humans experience climate. We evaluated how well two such models, ICON and IFS-FESOM, reproduce the climate as classified by the K\"oppen-Geiger system, using 30-year (2020-2049) simulations from the nextGEMS project at 9~km global resolution under SSP3-7.0 scenario. Both models capture the global distribution of the five main climate categories, encouraging given the infancy of storm-resolving climate modelling. Substantial regional biases nonetheless remain. Both underestimate tropical rainforest (Af) extent due to insufficient dry-month precipitation in Amazonia and equatorial Africa. ICON almost eliminates hot arid desert (BWh) across Australia through excessive precipitation, while IFS-FESOM reproduces it well. The two models show opposing biases along the temperate--continental boundary: IFS-FESOM winters are too cold in western Europe, ICON winters too warm. Substituting observed temperature or precipitation into the model fields reveals that precipitation errors dominate misclassification, while temperature biases play a secondary role confined to mid-latitude climate zone boundaries. Under climate change, the two models and CMIP6 projections agree on the direction of climate zone shifts: expansion of tropical savanna and hot desert at the expense of subarctic, tundra, and ice cap zones. However, inter-model differences in present-day climate exceed the 30-year climate change signal for many zones, calling for caution in regional projections and adaptation planning. Our results expose where local-scale climate representation still falls short of the digital twin ambition, while confirming that storm-resolving models already perform well across many regions. We propose K\"oppen-Geiger classification as a standard diagnostic to help track further progress.