Improved models of thermal diffusion in the soil

It is shown that the non‐homogeneous case of soil‐heat conduction, that is, when soil‐heat conductivity and capacity are functions of depth, can be treated rigorously. An exact formula is derived which gives the thermal diffusivity of the soil as a function of depth, on the basis of Fourier coefficients of diurnal courses of soil temperature at a variety of depths. By employment of the new model of soil‐heat diffusion one avoids misleading results which are obtained when the classical model of heat diffusion in a solid conductor is applied to natural soil indiscriminately. The case of depth‐time varying thermal diffusivity can only be solved in approximate form. The practical application of the classical and the two new models is discussed with the aid of soil‐temperature data obtained by the Johns Hopkins Laboratory of Climatology, Seabrook, N.J.