2.5 Modeling and statistics of the data
The soil water content at saturation (θs), residual moisture (θr), soil S index (slope at the inflection point), potential at the inflection point, water content at field capacity (FC) and permanent wilting point (PWP) were derived from SWRC.
The SWRC was adjusted considering the following parameterization of the van Genuchten model (Van Genuchten, 1980); according to Equation 1:
\(\theta(h)=\theta r+\frac{\theta s-\theta r}{{(1+exp\{n\left(\alpha+h\right)\}}^{1-1/n}}\)(1)
where \(\theta\) is the volumetric soil moisture content (m3 m-3), h is the log base 10 of the applied matric potential (kPa), \(\theta\)r is the residual moisture (lower asymptote), \(\theta\)s is the saturation moisture (upper asymptote), and α and n are empirical parameters of the shape of the water retention curve. The model was fitted to the data using the least squares method with the Newton-Raphson algorithm to obtain estimates for the parameters.
The SWRC parameters were used towas also applied to calculate the S index (Dexter, 2004) and the matric potential at the SWRC inflection point (Mello et al., 2002). according to Equations 2 and 3. The field capacity (FC) value was obtained considering the moisture corresponding to the matric potential of the SWRC at the inflection point (Silva et al., 2014) according to Equation 4. The plant available water capacity (AWC) was computed as the difference between the FC and the PWP at 1500 kPa of the SWRC.
\(S=-n.\ \frac{\theta s-\theta r}{{(1+1/m)}^{m+1}}\ \) (2)
\(I=-\alpha-log(m)/n\) (3)
\(\theta i=\theta(h=I)\) (4)
In the equations, S is the slope at the inflection point, which is an index that uses the pore distribution volume function for assessment of the physical quality of soil, and I correspond to the log of the matric potential at the inflection point of the soil water retention curve. The moisture corresponding to the potential at the inflection point is represented by θI.
For each response variable, a sequence of three models, ranging from the most complex to the simplest model, was tested. Firstly, the polynomial models of the second degree were tested for the three layers, and the models, which did not show a significance for the second-order term were then reduced to a simple model with only first-order terms. The significant models (p<0.05) are presented in the figures, and for the nonsignificant soil properties related to productivity, the model of the layer that showed the best fit above the null model is presented. The figures contain the adjusted models with confidence bands (p> 0.95), and the horizontal dashed lines in the figures represent the average of the productivity observations. If the confidence bands do not contain the dashed line, a significant relationship between the variable and the soybean yield in the specific layer was obtained. The clay, AWC, PR and S index properties were also tested based on the FLF, OLF, HF and SOM in L1.