Considerations in determining thermal diffusivity from temperature time series using finite difference methods

Abstract

The apparent thermal diffusivity, D, of the active layer and permafrost can be determined using finite difference methods provided that the heat flow is conductive, appropriate space ( Δx) and time ( Δt) intervals have been selected, accurate ( ± 0.01°C) temperature measurements have been obtained, and phase change does not occur in the volume of interest. Selection of values for Δx and Δt must take into account the accuracy of the temperature measurements, duration and amplitude of the temperature changes, depth, and the expected values for D. In general, Δx ⪡ X (the depth of interest) and Δt ⪡ P (period or duration of the surface temperature changes). The usual numerical expression for D was extended to include higher order terms and an analytical expression was derived for D when unfrozen water is present in frozen soils and permafrost. This extension reduces truncation errors and alleviates a problem with spikes (large positive and negative values in the calculated D at times when the ground temperatures are near a maximum or minimum). However, it increases the effects of measurement errors and the requirements for accurate temperature data.