Many current-generation climate models have land components that are too shallow. Under climate change conditions, the long-term warming trend at the surface propagates deeper into the ground than the commonly used 3-10m. Shallow models alter the terrestrial heat storage and distribution of temperatures in the subsurface, influencing the simulated land-atmosphere interactions. Previous studies focusing on annual timescales suggest that deeper models are required to match subsurface-temperature observations and the classic analytical heat conduction solution. However, for a systematic investigation of land-model deepening in the frame of anthropogenic climate change, the classic analytical solution is inaccurate because it does not mimic the timescale and amplitude of the simulated warming trend. This study intends to bridge the gap between analytical and simulation-based estimates of the subsurface thermodynamic state by adapting the classic analytical framework to mimic long-term anthropogenic warming. The analysis shows that a land-model depth of at least 170m is recommended for a proper simulation of the post-1850 ground climate, which differs up to 30% from the estimate of the classic approach. Compared to previous studies, this provides an accurate estimate of the required land model depth for long-term climate-change simulations and indicates the relative bias in insufficiently deep land models.

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