Data supplement for: Agreement of analytical and simulation-based estimates of the required land depth in climate models

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.