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.