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.