This parameter is permittivity. Most of these models are defined using empirical methods. Models with two or more parameters have other parameters besides permittivity, selleck chemical KPT-330 such as porosity and bulk density. 2.3. Secondary DataIn this study, reference data are needed to test the ability of all these models. For this purpose, secondary data obtained from previous experimental studies that showed the relationship between soil water content and permittivity were used. Overall, there are 44 secondary data, and the data sources and soil porosity used in this study can be seen in Table 2. These data were generated from experiments using different methods such as TDR (e.g., [14, 21, 22, 26, 28, 31, 32]), capacitance probe [20], and frequency domain [27] and also from varying types of soil.

Table 2Source of secondary data and porosity.The value of relative permittivity air, water, dry soil, and saturated soil can be seen in Table 3. Relative permittivity of dry soil and saturated soil is obtained from the study of the previous researches [14]. Relative permittivity of material is affected by the chemical components of its constituent and can be calculated by using the mixture model [37]. Table 3Relative permittivity of material properties.3. Results and DiscussionThe effects of porosity on the ��-�� relationship are shown in Figure 1. Four secondary data samples which have porosity ranging from 0.30 to 0.66 are highlighted.Figure 1Secondary data of volumetric water content and permittivity as a function of porosity.

Figure 1 shows that the smaller the soil porosity, the greater the value of permittivity for a given value of volumetric water content. In this condition, the pores in the soil will be filled by water and air. Therefore when the porosity is large, then the rest of the pores are filled by air. This corresponds to the concept of dielectric mixing used in models by [24]. When most of the volume fraction of soil pores is filled by air, it donates a small value of the total permittivity of the soil. This figure also shows that the spread of data does not occur significantly for small water content (0�C0.1). In this condition, the value of permittivity is in the range of 1�C5. Otherwise, when the water content begins to increase, it produces scattered data values.3.1. Model with One ParameterFigure 2 shows curves for (1a) to (6), which have one parameter.

All equations Cilengitide appeared to cover all of the available data. However, each equation appears in a certain position within the data. Equations (1a), (1b), (1d), (3), and (5) are quite close to each other and tend towards the upper part of the data which have relatively small porosity (<0.5). On the other hand, the larger porosity (>0.6) is occupied by (4). Figure 2Comparisons using all data for (1a) to (6).Almost all of the curves show a similar trend, except for (2a) and (6).