Appendix

Details of the weighting factor Ki formulation in Section 3.

Details of the formulation of Ki are given as

Thermal Inertia-Based Method for Estimating Soil Moisture http://dx.doi.org/10.5772/intechopen.80252 23

$$K\_{i} = \frac{1}{3} \sum\_{j=1}^{3} \left[ 1 + \left( \frac{\lambda\_{i}}{\lambda\_{0}} - 1 \right) g\_{ij} \right]^{-1} \tag{20}$$

where λ<sup>0</sup> is the conductivity of the medium and gij is a shape factor that takes into account the shape and orientation of the granules. Since P<sup>3</sup> <sup>j</sup>¼<sup>1</sup> gij <sup>¼</sup> 1 and a spheroidal shape is assumed gi<sup>1</sup> ¼ gi<sup>2</sup> � �, the above equation reduces to:

$$K\_{i} = \frac{2}{3\left[1 + \left(\frac{\lambda\_{i}}{\lambda\_{0}} - 1\right)g\_{i}\right]} + \frac{1}{3\left[1 + \left(\frac{\lambda\_{i}}{\lambda\_{0}} - 1\right)\left(1 - 2g\_{i}\right)\right]}.\tag{21}$$
