0286+0.02435��?0.0003421��2+0.00000237��3.(5)Permittivity based on capacitance measurement was investigated by [20]. They proposed an empirical model from experiment using a type of quartz sand with particle sizes in the range 0.15�C0.9mm:��=A(11+(��(1?��))n)1?(1/n)+B,(6)where A = 33, B = www.selleckchem.com/products/jq1.html 2, �� = 1.5, and n = 14.2.2. Model with Two or More ParametersSome relationship equations for permittivity and soil water content were also influenced by other parameters such as porosity and bulk density. By using the concept of mixing models and using data from other studies (e.g., [34�C36]), Wang and Schmugge [30] proposed the following equations: ��=��(��i+(��w?��i)�Ȧ�t��)+(��?��)��a+(1?��)��r.

(7a)Equation (7a) is used for �� �� ��t, while for �� > ��t the following equation is used:��=��t(��i+(��w?��i)��)+(��?��t)��w+(��?��)��a+(1?��)��r,(7b)where ��i, ��w, ��a, and ��r are the permittivity of ice, water, air, and rock, respectively (i.e., ��i = 3.2, ��w = 80, and ��a = 1), while ��t is the transition moisture (0.16�C0.33), �� is the porosity of soil (0.5), and �� is the fitting parameter (0.3�C0.5) [30].Roth et al. [28] proposed the equation based on the dielectric mixing model which has been described by [24]. The experiments were carried out by measuring a wide range of soil types using TDR with the error value of soil water content, no more than 0.013cm3cm?3 [28], with forms of the following equation: ��=1,(8b)where?��=?1,(8a)��=�Ŧ�?(1?��)��s��?�Ǧ�a�æ�w��?��a��;?��=�Ŧ�?(1?��)��s��?�Ǧ�a�æ�w��?��a��; �� = ?1 for three phases in series and �� = 1 for three phases in parallel.

Another model was proposed by [23]. They conducted experiments using TDR and 62 kinds of soil samples consisting of mineral soils, organic soil, standard pot soils, artificial peat-loess and peat-sand, sea and river sand, forest litter, and so forth, which differ in terms of texture and bulk density, which gives an uncertainty of soil water content of 0.03 [23]:��=��?3.47+6.22��?3.82��27.01+6.89��?7.83��2.(9)Gardner et al. [19] used capacitance measurement methods to obtain soil water content with soil dry bulk density values ranging rom 1.08 to 1.49 and then used multiple linear regression analysis to best fit the measurement data, resulting in the following equation:��=��+1.208?2.454��9.93,(10)where �� is dry bulk density.Robinson et al.

[14] developed an equation for coarse textured, layered soils by using TDR and coarse-grained, glass bead, and quartz grains:��=��(��?��dry��sat??��dry),(11)where ��dry and ��sat are the permittivity values for dry and saturated soil, respectively.Table 1 shows the 11 proposed equations of the ��-�� relationship for one and two or more parameters. It provides a brief Entinostat explanation, including the experimental method, soil type, properties of the soil, and the sources information for each proposed equation.Table 1Summary of all equations of ��-�� relationship.