Estimation of Soil Thermal Diffusivity and Heat Flux Using Fractional Derivatives of Soil Temperature Variation.

Soil temperature and heat flux near the ground surface are essential to evaluate surface water and energy balances. Thermal properties of soil are required to estimate the heat flux and to predict the temperature variation; however, in-situ measurement of the properties is time-consuming and impractical to execute for large scale. First, we investigated the characteristics of half order fractional derivatives (semi-derivatives) of soil temperature variation. The semi-derivatives of temperature change in relatively homogeneous soils were almost linearly related to temperature gradients. The coefficient of linearity agreed well with a square root of the soil thermal diffusivity. Initial condition had limited effects on the result. For the soil layer in which thermal diffusivity increased with depth, a little larger than half order of derivatives found to be appropriate. Based on the characteristics of the fractional derivatives, soil thermal diffusivity in-situ was estimated using soil temperature gradients, and conductivity and heat capacity were obtained using measurement values of heat flux. Application of the fractional derivatives to assimilate temperature data will also be discussed.