DETERMINATION OF SOIL APPARENT THERMAL DIFFUSIVITY FROM MULTIHARMONIC TEMPERATURE ANALYSIS FOR NONUNIFORM SOILS

Abstract

This paper presents a new method for combining the individually determined harmonic by harmonic values of thermal diffusivity obtained from a multiharmonic analysis of temperature observations into a single combined value of thermal diffusivity for each soil layer or depth. The new method uses Fourier analysis and variance fractioning of soil temperature observations. First, temperature observations are described by Fourier series. Next, soil apparent thermal diffusivity for each harmonic is calculated by using nonuniform soil heat-transfer analysis. Finally, the harmonic-associated values of soil apparent thermal diffusivity are combined by using a weighted average approach into a single overall composite value of apparent diffusivity. The weighted average thermal diffusivity is determined by weighting individual harmonic values according to the variance fraction of the temperature observations described by the associated harmonic. The variance fraction of soil temperature observations described by a given harmonic can be calculated as the ratio of half the squared amplitude (the square of the amplitude for the last harmonic) to the total variance. Thus, the method is general in that n-harmonics (where n implies a variable number) can be used. This paper presents applications of the method for determining soil apparent thermal diffusivity by analyzing field-temperature observations from nonuniform soil profiles.