Simulating heat transport of harmonic temperature signals in the Earth's shallow subsurface: Lower-boundary sensitivities

We assess the sensitivity of a subsurface thermodynamic model to the depth of its lower‐boundary condition. Analytic solutions to the one‐dimensional thermal diffusion equation demonstrate that boundary conditions imposed at shallow depths (2–20 m) corrupt the amplitudes and phases of propagating temperature signals. The presented solutions are for: 1) a homogeneous infinite half‐space driven by a harmonic surface‐temperature boundary condition, and 2) a homogeneous slab with a harmonic surface‐temperature boundary condition and zero‐flux lower‐boundary condition. Differences between the amplitudes and phases of the two solutions range from 0 to almost 100%, depending on depth, frequency and subsurface thermophysical properties. The implications of our results are straightforward: the corruption of subsurface temperatures can affect model assessments of soil microbial activity, vegetation changes, freeze‐thaw cycles, and hydrologic dynamics. It is uncertain, however, whether the reported effects will have large enough impacts on land‐atmosphere fluxes of water and energy to affect atmospheric simulations.