Agreement of Analytical and Simulation-Based Estimates of the Required Land Depth in Climate Models

Previous analytical and simulation-based analyses suggest that deeper land surface models are needed to realistically simulate the terrestrial thermal state in climate models, with implications for land-atmosphere interactions. Analytical approaches mainly focused on the subsurface propagation of harmonics such as the annual temperature signal, and a direct comparison with climate-change model output has been elusive. This study addresses the propagation of a harmonic pulse fitted to represent the timescale and amplitude of anthropogenic warming. Its comparison to land model simulations with stepwise increased bottom boundary depth leads to an agreement between the simulation-based and analytical frameworks for long-term climate trends. Any depth increase gradually decreases the relative error in the subsurface thermodynamics, and a minimum depth of 170 m is recommended to simulate the ground climate adequately. The approach provides an accurate estimate of the required land-model depth for climate-change simulations and assesses the relative bias in insufficiently deep land models. Plain Language Summary 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 3-10 m. 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 170 m 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. Key Points Heat conduction from analytical and numerical estimates suggests a required land-model depth of 170 m for climate change simulations Agreement between numerical and analytical estimates on climate change timescales gives more confidence for the required land-model depth Stepwise land-model depth increase gradually reduces the relative error of shallow models in climate-change simulation