An analysis of the annual temperature wave propagating through an alluvial soil

The physical processes by which heat is transferred through a soil depend upon the mineral, organic matter, and moisture contents of the soil and physical parameters as porosity and bulk density were analyzed. Heat transfer has a strong effect on matric potential in an unsaturated soil and on the movement of water and impurities. In dry, relatively homogeneous soils conduction is the dominant mode of heat transfer. Under these conditions, the Fourier equation of heat conduction in a semi-infinite solid body with a constant thermal diffusivity can be used. A cosine wave solution of the Fourier equation is presented which describes temperature as a function of both depth and time. Annual temperature waves recorded at several depths in an alluvial soil were modeled using a least squares estimate based on the cosine function. It is found that the amplitudes and phase angles of the models vary with depth in the same manner as described by the solution to the Fourier equation. It is concluded that this solution describes the propagation of the actual annual temperature wave and thus the thermal diffusivity of the soil can be estimated.