4, while the curve for (6) www.selleckchem.com/products/MDV3100.html gives a constant permittivity value when the water content is greater than 0.4. Wu et al. [20] explain that this reduction in the increase of permittivity is due to the effect of saturation in the soil. Equations (1c) and (2b) occupy the central part of data distribution. These curves provide a reasonably safe prediction of the ��-�� relationship for equations with one parameter or without any parameters of porosity. Table 4 shows the R-square of each curve to data and also the Root Mean Square Error (RMSE) of each equation to data. Equation (2b) gives a better result for R-square and RMSE compared with other equations with one parameter.Table 4R-square and root mean square error (RMSE) of the equations to data.3.2. Model with Two ParametersFigure 3 shows the effect of porosity (�� = 0.

3 to �� = 0.7) on the suitability of (7a) to (11) with data and also displays some of the data with a value of porosity (0.33, 0.44, and 0.62) in order to see the fit between data with a curve based on the value of porosity. In Figure 3(a), it can be seen that (7a) only fits in a certain small area of the data, though with different porosity. In this equation, the effect of changing porosity is not significant. Figures 3(b) and 3(c), with all the possible values of porosity, show that neither of these equations is quite enough to follow the pattern of the data. In these equations, the trend is linear for both of the graphs.Figure 3Comparison of (7a) to (11) with all data and different porosity.A better plot is shown in Figure 3(d), where the equation occupies all of the data well.

This figure shows that (9), which was proposed by [23], has a significant effect on changing porosity. The figure also shows that curves merge very well in the range of the secondary data. Overestimated results are produced in Figure 3(e). Curves with small porosity parameters can not even cover the area of data. There are only two curves passing through the area of data. Nevertheless, these curves are inconsistent with the position of the porosity of the data.Figure 3(f) shows a wide spread of curves for changes of porosity as the water content increases. Almost all areas are covered except data for water content values smaller than 0.2. However, when viewed in terms of the porosity data, the curves in this figure do not look quite as good because they spread without following the porosity data.

4. ConclusionA comparison of some equations for the ��-�� relationship was performed to provide an overview of the efficacy and ability of each equation in describing the ��-�� relationship GSK-3 and its correlation to the porosity of soil. In this study, secondary data were used as a reference to compare the equations. Secondary data with porosity values were plotted in one graph to show the effect of soil porosity on the relationship between water content and permittivity.