The results of the study were prepared based on the literature, considering the applicability and potential of the resulting dimensionless indexes. The Table (4) presents the two groups of indexes, the established nomenclatures and the equations obtained in the solution matrix Table (2).
3.2.1 Applicability of dimensionless indexes associated with relational analysis of soil management áreas
GIS QGis 3.16.5 was considered to analyze Group 1 of indexes based on the classification of land use in the watershed Córrego da Roseira located in the watershed from Rio Jundiaí-Mirim, Water Resources Management Unit 05, São Paulo, Brasil. The divisions and subdivisions of the watershed Córrego da Roseira in high course, medium course and low course were considered from the elaboration of the elevation profile of the main river with the altimetric database from Geographic and Cartographic Institute of the State of São Paulo (GCI-SP) 1:10.000 scale. Figure (1) presents the results for the two spatial dimensionless indexes of Group 1 Table (4).
The first dimensionless index IRNA Eq. (3) applied in watershed Córrego da Roseira demonstrates that as the index moves away from zero (0) there is a reduction in environmental fragility due to the increase in natural cover (NC) compared to management areas (AMA), indicating greater environmental conservation. The opposite demonstrates that as the index approaches zero, it results in increased environmental fragility in the basin due to the intensification of agrosilvopastoral management activities (AMA) and the pressure they exert on areas of natural vegetation (NC).
In this regard, Santoro et al. (2020) claim that, in addition to the abandonment of traditional management techniques, the main threat to native vegetation and agroforestry systems is the growing separation between natural forests and agricultural practices, often observed in watersheds. In this sense, the advance of agrosilvopastoral management (AMA) activities over natural cover areas (NC) in a disorderly and inadequate way is a worldwide problem, which needs to be solved under the bias of sustainable development in agricultural activities.
IRNA, from this perspective, it can be used to monitor the expansion of agrosilvopastoral management areas (AMA) over natural areas (NC) and, thus, contribute to the management of the fragility promoted by anthropic activities in these scenarios.
Another relevant factor in agrosilvopastoral practices is the increase in areas of exposed soil, as a result of inadequate land use management, mainly conventional agricultural techniques that quickly promote the depletion of the land over time compared to conservationist methods, which aim to make agricultural practices that have less impact on the environment (Sharma et al. 2018; Lojka et al. 2021).
That Said, IRES Eq. (4) exposes the existence of an inverse relationship with the IRNA, because when approaching zero (0), as it is possible to notice in Fig. (1), the reduction of the exposed soil area (ESA) is visualized in relation to the management area (AMA), on the other hand, as it approaches one (1) the amount of exposed soil (ESA) in the studied area increases.
The increase in areas of exposed soil may be related to the decrease in native vegetation that originally protects the soil and also to agricultural activities, the slope of the terrain and animal trampling on the banks of rivers that contribute to its silting up (Sileshi et al. 2020; Santos e Guerra 2021). From this perspective, the IRES dimensionless index allows analyzing the proportion between the areas of exposed soil (ESA) over the management area (AMA) and can contribute to the management of the fragility promoted by agrosilvopastoral management activities in watersheds.
In this sense, the dimensionless spatial indexes of management areas, IRNA and IRES, can be useful for monitoring the environmental fragility of watersheds, helping public authorities, managers, researchers and civil society in the management of agrosilvopastoral activities at local levels, municipal, state or even global, depending on the need of the researcher or manager, making visible the improvement of these activities, in order to reduce the environmental impact of anthropic activities in land use for soil protection.
3.2.2 Applicability of dimensionless indexes associated with soil management activities
Group 2 of dimensionless indexes generated Table (4) were four and the variables attributed to them influence soil characteristics as a result of the intensive use of agricultural machinery in management activities, these dimensionless indexes must be applied experimentally in order to obtain satisfactory results. for the study area to be analyzed. In this topic, however, simulations by quartiles of these four indexes are presented considering the extreme values of the indicators that compose them Table 3(b). The dimensionless index (SDAM) presents the proportion between the geometric average diameter of soil aggregates (MGD) by the square root of an area (AMA), as exposed Eq. (5). The MGD range goes from 0,001 meter (m) to 0,005 m and considers the highest and best values to identify soil structure (Jensen et al. 2020; Mamedov et al. 2021). The Fig. (2 a) expresses the simulation of the relationship between the MGD (m) Table (3 b) for one unit area (AMA) 1 m². And Fig. (2 b) expresses the simulation of the relationship between the ESD (m) Table (3 b) for one unit area (AMA) 1 m².
In the Fig. (2 a) it is noticed that the higher the value of the index, the better the soil aggregation condition on the management area (AMA). This relationship exists, since the MGD enables the analysis of agrosilvopastoral soil aggregation and, therefore, the quality of its structure. Soil structure, mainly agricultural soil in watersheds, is considered a valuable property to verify its quality, as it directly interferes with other soil attributes capable of evaluating agrosilvopastoral activities and the preservation condition of these soils, such as: permeability, aeration, root growth, biota, etc. (Lintemani et al. 2020).
The dimensionless index (EDSM), in turn, consists of the ratio between the effective soil depth (ESD) under the management area (AMA) expressed by Eq. (6) and simulated according to Fig. (2 b). ESD may vary from 0.1 m to 2.2 m depending on the use employed in management and in natural areas (Chatterjee et al. 2018; Kauffman et al. 2020).
Studying these variables through an index can contribute to the analysis of the quality of root depth (ESD) in agrosilvopastoral practices in relation to the area (AMA) and, thus, favor management based on the model of development and quality of agrosilvopastoral production in basins watersheds (Freitas et al. 2020; Mayer et al. 2020).
The PQAM is a more complex dimensionless index, as it involves the relationship between three variables, soil permeability (k), soil organic matter (SOM) and mechanical resistance to soil penetration (MRP), thus allowing to verify the quality of soil permeability (k) in relation to the proportion of organic matter (SOM) by the mechanical resistance to penetration (MRP) in the agrosilvopastoral soil, as shown Eq. (7). Figure (3) presents the relationships established by quartiles for the indicators SOM (kg/m³) and MRP (Pa) (a) and for the PQAM index (b and c), which also involves soil permeability (k).
The simulation of the relationship between organic matter indicators (SOM) and mechanical resistance to penetration (MRP) in Fig. (3 a), shows that the SOM and MRP indicators act in opposite condition, as it is observed that the increase in the amount of SOM contributes to the reduction of the MRP and vice versa. Therefore, the highest values in the two graphs indicate a higher SOM content and the lower values are related to the increase in MRP.
It is important to work on these relationships, since intensive (conventional) management activities constantly affect the soil structure, promoting the rapid decomposition and destruction of SOM, and this situation can cause soil compaction, negatively contributing to the root growth of plants and with soil permeability, these circumstances may promote a reduction in crop yields (Thomé et al. 2021).
The variation of k goes from \({10}^{-7}\)cm/s to \({10}^{-2}\) cm/s varying between permeable clay and sandy soils, respectively (Elhakim 2016). Figure (3 b) presents the relationships in quartiles for the indicators SOM (kg/m³) and MRP (Pa) in clayey soils (kVmin. in m/s) and Fig. (3 c) sandy soils (kQ2 in m/s), using the displayed values in Table (3).
By entering the soil permeability indicator (k) being clayey soils (kVmin. in m/s) and sandy soils (kQ2 in m/s) according to Table (3 b) and Fig. (3 c), in this equation, a slower variation of the index can be seen due to the low value of the indicator for both sandy and clayey soils compared to the simulations between the SOM and the MRP Fig. (3 a). Soil permeability (k) fulfills ecological functions in agricultural activities, being an appropriate indicator to verify changes in the soil under management due to its sensitivity to changes in the porous system and soil density and these changes can interfere negatively in MRP (Gürsoy 2021).
The SOM, which is related to the availability of soil water, helps explain the increase in yield in agrosilvopastoral activities (Wiesmeier et al. 2019). Regarding the MRP, the high mechanical load, monocultures, intensive grazing, little amount of SOM and soil preparation under high humidity can increase its values, which are assigned critical limits to root growth between 2 MPa to 4 MPa, promoting the reduction of agricultural soil porosity and forming furrows on its surface (Khorsand et al. 2021). Thus, the PQAM has the potential to contribute to the determination of the weakening of areas, based on the contribution of the SOM and the MRP to the condition of permeability (k) in the soil aimed at agrosilvopastoral management. Thus, under an organizational purpose, managers and agricultural producers can seek more sustainable production in agrosilvopastoral management using this index.
And, finally, the AAAM dimensionless index is analogous and the anthropic pressure (AAP) corroborates an analogy to the pressure exerted by man (Pa) in agrosilvopastoral management activities and this performance can have negative or positive consequences, considering the influence of MRP values (Pa), as expressed by Eq. (8). The simulation of this index from the direct and inverse relationship between the quartiles with the values from the Table (3 b) is presented in Fig. (4).
The Fig. (4) shows that in a direct relationship between the quartiles of anthropogenic pressure (AAP) by the mechanical strength of the soil (MRP), the smaller values of AAP and MRP according to Table (3 b), normally, they will indicate the best results in the study of the fragility of the environment and this occurs due to the constancy of the relationship expressed by the indicators in the simulation curve. The literature shows that the use of machinery, the type of crop and the practices applied in management can influence the values resulting from the MRP, which can contribute, positively or negatively, to the weakening of these environments due to the increase or decrease in the AAP, this situation will depend on the practices and types of agrosilvopastoral management used in land use (Manoel 2020).
Thus, the use of AAAM aims to provide the best management in agrosilvopastoral management activities within hydrographic basins. The intention is to seek a more sustainable use in agricultural management activities, in this sense, this index may be able to assist managers in adapting and monitoring agricultural and urban expansion over natural areas. The four dimensionless indexes related to agricultural soil management activities (SDAM, EDSM, PQAM and AAAM) have the ability to be used to determine the fragility in agrosilvopastoral management areas. Despite this, although the simulations have helped in understanding the potential applicability and sensitivity of these indexes in the study of the fragility of areas, emphasis is placed on the need for experimentation in specific areas of analysis.