3.3. Correlation Analysis
In order to detect significant linear correlations between the model parameters and the investigated soil properties, Pearson coefficients were calculated for all variables (
Table 4).
A
1 and A
2 showed significant and positive correlations with OC (0.29 **), while A
2 had a negative correlation with BD (−0.38 **). These results are expected because organic carbon is effective in increasing the porosity at the pore sizes investigated and decreasing the bulk density. However, BD seems to be more influenced by structural porosity than by matrix porosity, at least according to Dexter’s model. h
1 was negatively correlated with KS (r = −0.22 **), which reflects the fact that high matrix pore water suction has a negative impact on KS. With regard to the relationships between the model parameters, it is worth emphasizing the negative correlation of θ
r with A
1 and h
1 and partly with h
2, which shows that soils with a high proportion of residual water have a low proportion of matrix pores. Additionally, other significant observations are as follows: the positive correlation between A
1 and h
1 (0.60 **); the higher the pore water suction at which the matrix pore spaces starts to empty, the higher the proportion of matrix pores; the positive correlation (0.40 **) between the two suctions related to the two sizes of pores. Concerning the significant correlations between soil properties, the positive correlation (0.23 *) of OC with TS is explained because OC increases the soil’s resistance to being crushed. Saturated hydraulic conductivity and OC were negatively correlated with BD (−0.29 **), which was as expected because OC increases porosity, improves KS and reduces BD [
38].
It can be deduced from the above results that, although some correlations are significant, there are no strong relationships between the investigated soil properties and the parameters of Dexter’s model. However, these are linear correlations that do not take into account the spatial correlations of the observations. The spatial analysis could confirm these results.
An isotropic LMC was fitted to the matrix of both the direct and cross-experimental variograms of all Gaussian transformed variables, including the following basic spatial structures: (S0) nugget effect, (S1) spherical model (range = 508.64 m) and (S2) spherical model (range = 3000 m) (
Figure 8a,b). The proportions of the total spatial variance explained by each spatial component were as follows: S0 50%, S1 13% and S2 37%, which shows that most spatial variation is due to the nugget effect, i.e., spatially uncorrelated error. One way to reduce this spatial component might be to intensify sampling because at the scale at which it was performed, it proved incapable of resolving micro-variability due to both intrinsic soil properties and anthropogenic activities.
From
Figure 8a of the LMC, some considerations can be made as follows: all direct variograms show a high nugget, as already noted in general above, which can be attributed to the adopted sampling scale, which should be reduced, as well as the measurement error associated with the measurement of soil properties and parameter estimation error. In addition, all direct variograms clearly show a short-range structure (around 500 m), which can be attributed to intrinsic soil variation within the field and the effects of anthropogenic operations, and a long-range structure (around 3000 m), causing the sill to exceed the sampling variance, which can be attributed to the study area belonging to soil map units extending beyond the field size [
13]. Deviating from the characteristics stated above, there is a KS variogram, which is similar to the pure nugget effect, most likely determined by the low precision of its measurement marked by high stochasticity; and that of BD, in which the long-range component prevails since BD is generally closely linked to the type of map unit to which the soil belongs at a scale greater than that of the field (
Figure 8a).
Regarding the cross-variograms between the model parameters and soil properties, it can be said that in general the spatial relationships are quite low. This can be ascertained from the large distance of the model curve of the cross-variograms from the dashed line (
Figure 8b) representing the intrinsic correlation, i.e., the maximum obtainable spatial correlation between the two variables considered [
32]. The only soil properties that show spatial correlations of some significance with the model parameters are OC, which is positive with A
1 and A
2 due to the positive effect already noted for OC on both matrix and structural porosity; and BD, which is negative with θ
r and A
2 but positive with h
1, meaning that an increase in density causes a reduction in structural porosity and the amount of residual water, but an increase in the suction at which matrix pores become empty. Regarding the spatial relationships between the various parameters of the model, from the cross-variograms, it can be seen that θ
r is negatively correlated with all but A
2; A
1 is positively correlated with h
1 and, to a lesser extent, with h
2. It is noteworthy that A
1 and A
2 are not significantly correlated; that is, there is no significant spatial relationship between the two types of porosity (
Figure 8b). This is probably attributable to the different origins of the two types of porosity; A1 (matric porosity) is intrinsically linked to the granulometric characteristics of the soil (texture), whereas A2 (structural porosity) is mostly related to the type of tillage carried out in the field. Moreover, A2, similarly to the other parameters of Dexter’s model, shows a high degree of stochasticity (nugget effect) and is the one that appears least correlated with the other parameters (
Figure 8b).
There is a positive relationship between h1 and h2 and between h1 and A1; therefore, higher porosity, at least matrix porosity, is associated with higher suction, at which pores (of both types) begin to empty.
Finally, with regard to the spatial relationships among the soil properties investigated, KS appears to be poorly correlated with all of them, mostly due to its essentially stochastic nature. It shows a slight negative correlation with BD, which is quite expected since the densest soils are those with the lowest porosity and, therefore, with low hydraulic conductivity. TS is spatially uncorrelated with the other soil properties, except for a somewhat positive correlation with OC. Therefore, it can be said that both of these properties (OC and TS) contributed to improving the soil structure and consequently its hydraulic characteristics.
Summarising the previous results concerning (1) the high nugget effect for direct variograms, and (2) the general low sill of cross-variograms, denoting low spatial correlation between the curve parameters and between these and the soil variables, it can be stated that this is attributable to two main causes. The first is related to the insufficient sampling density, as already noted; the second is to the uncertainty inherent in the measurements of the soil variables (especially KS) and to the fact that the parameters of Dexter’s model are not directly measurable physical variables but are estimated parameters with an estimation error that may also be high. However, despite the imprecision associated with the measurement and estimation procedures, we believe that it is possible to disclose interesting spatial relationships among variables related to the soil’s capability of transmitting water.
The goodness of fit of the LMC for any Gaussian transformed variable was evaluated through cross-validation, and the results are shown in
Table 5. The
ME and
RMSE were quite close to 0, and the
RMSSE fell within the tolerance interval [0.58–1.42] for all variables.
The maps of soil attributes display that higher KS and OC values were localized in the central parts of the field, whereas lower values were in the south and south eastern corner (
Figure 9a,b). Thus, the OC and KS showed a positive degree of association, and their higher values were associated with higher clay contents as reported elsewhere [
13].
Conversely, BD was higher in the southeastern part of the field, where the soils were mostly sandy (
Figure 9c) [
13]. In the north and central parts, the presence of more OC enhanced the formation of larger soil pores, which reduced BD and improved permeability. Very low KS (0.05–1 cm/h) in the south part of the field, which might cause regular runoff under rainfall and irrigation, is likely to be inefficient. In contrast, in the central part of the field and the north, with hydraulic conductivity greater than 6 mm per hour, superficial water flow would rarely occur, and the soil might be too permeable for irrigation [
36].
The aggregate tensile strength map showed a different trend in the field, which is more similar to that of BD (
Figure 9d). The lowest values of TS were observed in the central and southeastern parts of the field, probably due to an increase in OC, which might decrease the tensile strength because it might increase the size of the aggregates [
39]. Smaller aggregates are stronger because they contain fewer surface cracks [
40] and are denser [
2]. However, the relationship between OC and TS is not always so direct as it appears to be reversed in some southern parts of the field. This would induce one to think that the resistance of aggregates to the disintegrating action of water actually depended on multiple interrelated factors.
The increase in sand in the southeastern part [
13] reduced the tensile strength of aggregates, probably because sand acted as the main nucleus to connect the particles to each other and form larger aggregates, which were more unstable, thereby causing soil fragility to increase [
41].
Greater θ
r values were localized in the central part of the field, whereas smaller values of these parameters were observed in the north and south (
Figure 10a). Moisture retention at greater suctions (θ
r) strongly depends on the particle size distribution [
42]; therefore, a finer texture in the central part of the field might have caused an increase in θ
r.
A
1 showed the lowest values in the southern part of the field, whereas the highest values were observed in the central and northern parts of the field, probably due to the silt content, which is mostly responsible for the pores of the soil matrix [
43]. A
2 map shows a very similar pattern to A
1 map with the exception of the northern part, where the structural porosity is reduced (
Figure 10c) due, as already noted, to the higher silt content in soils to the north. However, throughout the field, the proportion of structural pores prevails over that of matrix pores; that is, the larger pores between the soil aggregates can favour water flow and avoid water logging.
However, a correct proportion between macro- and micro-porosity is fundamental for rational water management in an agricultural field because, while the former facilitates water flow and avoids waterlogging, the latter increases water availability to crops. This critical balance can be achieved by adopting, for example, conservation agriculture techniques [
44] that improve the sustainable use of water resources. The higher OC content in the central part has a positive effect, especially on structural pores (A
2,
Figure 10c), which improves the hydraulic properties and, in particular, promotes the water flow near soil-saturated conditions (KS,
Figure 9a). Therefore, from the above discussion, the central part seems to have water characteristics that make it suitable for irrigation. In contrast, the greater values of sand and BD (smaller values of total porosity) in the southern part of the field would have caused a loss of structural and matrix porosity, which explains the reduction in A
1 and A
2. Therefore, the plants in this part of the field might be more frequently susceptible to water stress than elsewhere.
The maps of h
1 and h
2 (
Figure 10d,e) show a somewhat opposite trend to that of A
1 and A
2, whereby greater (both structural and matrix) porosity generally corresponds to lower suctions. The highest values of h
1 and h
2 are observed in the south, with larger contents of sand. However, the relationship between porosity and suction is not so direct and is greatly influenced by the variations in texture and pore size variation spectra that occur in the field. For example, loam sandy soils (sands and sandstones) located in the northeast and southwest have a very narrow distribution of pore sizes; therefore, they empty over a very narrow range of suctions [
45]. Furthermore, tillage management can affect porosity and suction at which pores become empty because soils under conventional tillage produce higher structural porosity (large and medium pores) and lower matrix porosity (small pores) than soils under no tillage or conservative agriculture [
46,
47], thus reducing the risk of water stress. Therefore, more conservative and less energy-demanding techniques should be promoted, as the field was only subjected to conventional tillage at least until the sampling date.
The maps in
Figure 9 can also be used to derive SWRC curves at each point in the field. As an example, the curves at three locations in the field (
Figure 9a) that clearly differed in their hydraulic properties, as discussed above, are shown (
Figure 9a).
The hydraulic differences among the three zones are also well shown by the SWRC curves; in fact, at equal suction, the highest values of water content occur in the middle zone, the lowest in the southeast zone and the intermediate in the north zone (
Figure 11a). These variations, as discussed above, can clearly be interpreted in terms of textural variations (higher content of silt in the north, clay in the center and sand in the south-east) and OC (higher content in the central zone), which have an impact on bulk density and porosity and, thus, on water availability to plants.
3.4. Factorial Cokriging
To synthesize the spatial relationships shown above between Dexter’s model parameters and soil properties, and simultaneously arrive at a delineation of the field into hydraulically homogeneous areas, a factor analysis was carried out. Only the first factor (F1 short) at the shorter range (508.64 m) and the first and second factors (F1 long and F2 long) at a longer range (3000 m) were retained, with eigenvalues greater than 1, thereby explaining a larger percentage of the variance than that explained by each variable standardized to variance 1. The percentages of spatial variance at the corresponding scale explained by F1 short, F1 long and F2 long were 73.72%, 68.79% and 24%, respectively (
Table 6).
On F1 short, the Gaussian variables were as follows: gh
1, gh
2, gTS and gOC, and to a less extent gA1 and gA
2 weigh negatively, whereas gθ
r weighs positively. Therefore, this factor may be considered an indirect “porosity indicator” associated with higher values of OC and TS. It is worth underlining that, at this scale, the porosities and suctions of both types are positively correlated. Therefore, low values of F1 short are an indicator of soils with high total porosity, greater content of OC, more stable aggregates and low content of residual water. On F1 long, gOC, gA
2, gKS and gθ
r weigh more and positively,
, whereas BD weighs negatively, as expected. Therefore, at this scale, the structural porosity and the content of OC significantly affect the flow of water in the soil. This factor can then be considered a direct “hydraulic indicator” of the properties of the soil. F2 long, although it explains only 24% of the variance at a 3000 m scale, it was nevertheless retained because it can be assumed as an indirect “aggregate stability indicator”, as TS weighs much more negatively than the other variables (
Table 6).
Therefore, from the composition of the retained factors, it is evident how the relationships between the variables change depending on the scale, as they are linked to processes that occur in the soil over different scales [
12]. It is, therefore, expected that the maps of the three factors also have a different pattern and, thus, produce a different partition of the field into homogeneous areas. To stress the differences among the structures of spatial dependence, three classes of equal frequency, i.e., of the same spatial extension, were used, which could be defined as follows: low, medium and high classes of total porosity, water flow and aggregate stability for F1 short, F1 long and F2 long, respectively, taking into account the particular composition of these regionalized factors (
Figure 12).
The F1 short map (
Figure 12a) appears to be divided into several micro-areas characterized by different porosity and consequent permeability, and aggregate stability, to be associated with local variations in texture and OC, but without a clear overall trend. The high areas are those particularly suited to mechanical tillage and irrigation (especially the wide blue coloured area in the south).
The geometric pattern changes markedly in the map of F1 long, in which one can recognize a large central zone, which also extends partly to the south in a narrower form, characterized by good water flow conditions favored by high structural porosity. These properties, determined by pedological characteristics and higher OC content at a longer scale, should reduce the risk of flooding or waterlogging in the occurrence of extreme weather events.
The map of F2 long (
Figure 12c) also appears rather fragmented, as shown in
Figure 11a, with numerous areas characterized by higher aggregate stability, which improves resistance to the destructive action of water, extending from the center of the field towards the south (blue coloured areas). Summarizing the above, it is evident that there is no single partition of the field into homogeneous areas based on the hydraulic properties, but this depends significantly on the scale. Nevertheless, it can be said that there is a large central zone, which is more suitable for irrigation, whereas the northern and southern zones are more variable. In particular, the southern zone with a coarser texture might cause problems for irrigation, so it would be advisable to intervene with smaller but more frequent irrigation volumes and more substantial organic fertilization.