Analysis of Interrelations Structure in Agro-Systems Using the Factor Analysis Technique (FA)

Abstract

A model is not an exact copy of its original, but only its idealised reproduction that is simpler, more understandable, more accessible and easier, safer and more effective to work with. In the presented study, we used the technique of factor analysis (FA). We used 44 parameters to describe an agroecosystem, which proportionally describe the main components of the study agroecosystem. Based on Malinowsky error analysis, we extracted a 6-factor solution. We found out that Factor 1 [Climate factor] had primary factor loads in [average temperatures TIII-TIX (0.99) and [average atmospheric precipitation ZIII-ZIV (0.99)] variables. Factor 2 [Chemical parameters of geological foundation] was mainly saturated by [SiO₂-G (0.92), Al₂O₃-(0.82), (CaO-G (0.83)] variables and secondary loads were observed in soil [SiO₂-P (0.61], [CaO-P (0.64], [Al₂O₃-P (0.32)], [soil skeleton SKEL (0.47)] and [granularity GRN (0.39)] variables. Factor 3 [Phytomass production potential factor] had primary factor loads in [depth of soil profile DSP (0.76)], [quality of organic substances Q_4/6 (0.63)], [slopeness SL (0.67)] and [potential phytomass production PROD (0.65)] variables. In factor 4 [Physical-chemical soil properties factor] variables [Al₂O_3, (0.81)], [granularity GRN (0.69)] and [SiO₂ (0.61)] have significant loads. Factor 5 [Erosion by water potential factor] has the highest primary loads in [large-scale arable land ALL (0.70)] and [soil loss as a result of erosion EROS (0.67)] variables, and secondary loads in the [continuous length of plot of land slope LS (0.53)] variable. Factor 6 [Biochemical properties factor] has the highest factor load values in the content of organic substances in soil [content of organic substances in soil H (0.69)]. Secondary loads can be seen in the properties of soil [GRN (0.35)], [SiO₂ (0.32)], [Al₂O₃-P (0.38)] and [depth of groundwater surface GWS (0.39)]. We determined the weight coefficients for the individual factors with the aim of quantifying ecological criteria with the obtained factor structure. The factor score F₀ determines the projections of the extracted factors for the individual elements of the selection (it is the value soil-ecological units—VSEU). Row vectors in this matrix represent the distribution of the individual factors for the specific realisation of the selection (spatial distribution). We re-scaled the obtained values of the factor score into seven categories and projected them into VSEU units. We could propose a sustainable agroecosystem management based on quantifying the ecological criteria for each VSEU unit.

1. Introduction

From the point of view of an ecosystem, an agroecosystem can be seen as a multilevel, hierarchical system and an interactive area of biotic, abiotic and socioeconomic elements of a landscape that form a unified complex (system-agroecosystem). It is a complex system of interactive relations between the individual landscape elements where it is suitable to use modelling simulation. Each modelling is connected with a certain projection, where one entity, the so called original, is attributed to another entity, the so-called model, which represents in a generalised form only those aspects of the original which are essential to the pre-set aim.

There is a wide spectrum of opinions on basic questions of modelling, however, there is a consensus among the model theory specialists, and it is predominantly the fact that each modelling is connected with a certain projection. This enables studying the original indirectly, through its model, while the results obtained on this level can be transposed back onto the level of the original. As a result of the aforementioned, these models are suitable for understanding the interactive relations in agroecosystems and quantifying ecological criteria for evaluating their sustainability.

Agroecosystems are actually derived from natural ecosystems. Of all ecosystems, agricultural land is the one most intensively utilised (water, forest and other ecosystems) and is spatially located in the most potentially productive segments of the landscape [1].

The combination of climate change, population growth and soil threats including carbon loss, biodiversity decline and erosion increasingly challenge the global community [2]. A major scientific challenge in understanding processes involved in soil threats, landscape resilience, ecosystem stability, sustainable land management and economic consequences is that it is an interdisciplinary field [3], requiring more openness between scientific disciplines.

Soil heterogeneity has been recognised for many years as due to factors operating and interacting at various spatial and temporal scales. The characterisation of the spatial variability of soil attributes is essential to achieving a better understanding of the complex relations between soil properties and environmental factors [4] and to determine the appropriate management practices for soil resource use [5]. It also has practical implications for sampling design for ecological, environmental and agricultural studies [6].

Agricultural land is a typical example where unprofessional interventions of man into landscape are very perceptibly manifested. Concentrating certain agricultural activities increases manifold the risk of non-functionality of the natural system, and thresholds at which a non-reversible degradation process begins are lower than with non-specialised ecosystems. The result is higher landscape vulnerability.

Agricultural production is therefore a potential source of control of dynamic processes ongoing in the landscape.

The following resulting problems arise for agricultural land:

(a)

Environmental problems caused by unfavourable impacts of other industries (expanding urbanisation) on agricultural land resources;

(b)

Problems caused by unfavourable impact of intensive agriculture on agricultural land resources and other natural resources, and on landscape biodiversity;

(c)

Endangering agricultural land resources (ALR)—as a means of its own production process;

(d)

Endangering other natural resources;

(e)

Endangering the environment (residential and recreational), endangering the health of the inhabitants.

The impacts of agricultural intensification in Slovakia and other eastern European countries in the 1970s–1980s on the environment are alarming. They are characterised by the continuous ascending character of the productivity level, extensive agro-ameliorative and agro-technical impacts, to which a negative impact on landscape diversity is connected. A solution to this serious situation is creating a concord between the natural potential of the landscape and intensification of agricultural production on the condition of economic efficiency of producing agricultural products. Due to the aforementioned reasons, a systematic approach towards assessing the suitability of already existing ways of use in the agricultural landscape and proposal of optimal way of use in relation with natural and cultural-historical potential is essential.

The agricultural landscape does not only fulfil the function of biomass production, but it has landscape-forming functions and functions in residence development. Various negative phenomena are a manifestation of improper agroecosystem management such as erosion by water and wind that, as a consequence, damages not only the soil for agricultural production, but also other natural resources of the landscape [7,8,9,10,11,12].

The point of view of sustainable agriculture is which they [13,14,15,16] characterise as the management and use of agroecosystem in a way that preserves its biological diversity, productivity, regeneration capacity, vitality and functionality so that the agriculture fulfils significant ecological, economic and social functions on local, national and global levels in a way that does not damage other ecosystems not only in the present, but also in the future.

Anthropogenous pressure on agroecosystems has been present as an extensive and uncoordinated construction in the past few decades, which can be seen in several countries and to which population growth and demand for living outside of cities and municipalities is connected.

Constructing the agricultural landscape in Mediterranean mountain areas was a long and laborious process that created several types of field or land use patterns. In the Spanish Pyrenees, for example, at the time of low demographic pressure, agricultural land occupied the most fertile areas: plains and gentle slopes (valley floors, watershed and level areas mid-slope) and land close to population centres. Population growth and pressures different than that of farming, led to the use of the steeper and less productive slopes [17,18,19]. Some hillsides were changed by building agricultural terraces on the slopes [20,21].

In recent years, many models of system simulation were developed in order to explore various aspects of agroecosystem sustainability [22,23,24,25,26].

From the point of view of applied methodical means, we see the agroecosystem as a system of diagnostic properties of geocomponents and their relations (traditionally goecomponentially explained as a sum total of geological, hydrogeological and soil-substrate layers in an area with a specific use). The relations in this system represent energetic-material flows in the scope of singled out homogenous elements that are indirectly evaluated through their impact on the change of state of the individual properties [12,26,27].

A manifestation of anthropogenous impact in the landscape is the current land use, configuration and spatial distribution, shape, size, location of plots of land, erosion etc. The impact of human activity on the environment is the quality of agroecosystem function that emphasises the need to take into consideration the interactions between human activities and soil cover [28].

When evaluating interactive relations in the system man-agroecosystem it is crucial to analyse this relation as a unified system unit (ecosystem). For this purpose, a technique of mathematical modelling is suitable, more specifically the variants of explorative techniques of models with latent variables [29,30].

Factor analysis is used in evaluating various landscape-ecological conditions, for example [31], used it in identifying landscape structure. They reduced 55 variables to 26 and 6 of them showed approximately 87% variance. Thirteen variables used by [32] showed significant correlations and they identified three factors that explain approximately 82.3% of the variance. Monitoring of certain aspects of landscape-ecological state on the state level using a long-distance land survey and indicators of landscape cover was dealt with by [33]. Factor analysis was used by [34] for connections of countryside sources with its sustainability. Twenty-one weighted variables were grouped into two categories: high and low sustainability areas. Five factors were taken into consideration in both cases.

Factor analysis is used also in the research of landscape transformation in economically dynamic regions based on space analysis of unchanged areas of soil use over a given time period [35]. Suitable indicators of soil quality using factor analysis were identified by [29]. This can be used in evaluating the sustainability of soil use and soil management in agroecosystems.

Selecting meaningful metrics to describe landscapes is difficult due to our limited understanding of the links between landscape patterns and ecological process, the numerous indices available and the interaction between the spatial characteristics of the system and metric behaviour [36].

The main aim of our work was to analyse the structures of interrelation in systems (mathematical modelling) to find functional links between the individual properties of the system parts, that can be used in optimal management of an agroecosystem.

In our study we concentrated on the anthropogenous impact on agroecosystem and accompanying negative impact(s); not only on the problems caused by unfavourable agricultural influence on soil, but also on other natural resources and the biodiversity of the landscape.

When modelling interactive relations, we used factor analysis that is aimed at creating new latent variables and reducing the extent of input analytical data with the lowest possible information loss. During the evaluation, different possibilities of the factor analysis techniques for the following outputs were used:

• The abstract explorative model of an agroecosystem;
• The possibility of quantifying the selected ecological criteria;
• The application of quantified ecological criteria in the evaluation process;
• The proposal for optimising agroecosystem use.

The present approach to evaluating optimal agroecosystem use utilises the system analysis of relations between abiotic and biotic elements of the landscape, and the impact of man on this system. Using the models of factor analysis and their possibilities we can propose more effective proposals for sustainable management of agroecosystems.

2. Methodological Approaches and Devices

While a theoretical explanation of models with latent variables and the technique of factor analysis is relatively complex, it is appropriate to introduce at least the most basic characteristics of factor analysis models in relation to the issue at hand on account of the small extent of use of these techniques [7,8,9,10,37,38,39].

It is appropriate to apply the selected methodological approaches of the factor analysis technique in modelling the interrelations of structures in the man-agroecosystem system, and in the scope of agroecosystem itself on wider model areas with typologically varied geomorphology, to which varied soil cover and varied land use are connected. It is exactly the variety of natural conditions and management that determines the emergence of various environmental problems of varying importance and scope. This enables processing extensive information material from the selected model area.

2.1. Model Area

Our model areas are cadastral areas of towns and municipalities Skalica, Kátov, Mokrý Háj, Vradište, Prietržka and Koválec.

The mentioned model area is located on the western border of the Slovak Republic and belongs to the Skalica municipality, which is the northernmost municipality of Trnava region. The model area mentioned extends over 87.88 km². It borders the Myjava municipality to the east and the Senica municipality to the south. The western and north-western borders are identical with the state border with the Czech Republic. From the geomorphological point of view, in the west it extends into the Dolnomoravská floodplain, traverses the Chvojnícka upland and in the east it extends into the White Carpathians.

The area of interest is intensively used agriculturally in the form of conventional agriculture with a high ratio of large-scale arable plots, mainly in the more productive segments of agroecosystem in the western, north-western, central and partially the eastern part of the area. Alluvial forests are prevalent in the Dolnomoravská floodplain in the east. Large-scale fields significantly decrease the quality and stability of the area because they are characteristic of a low degree of biodiversity (agrocenose monocultures) and landscape heterogeneity, and simultaneously they represent a real source of environmental problems in the non-vegetative period that endanger the soil resources themselves and their environmental functions, as well as other natural resources. The surface of large-scale arable plots in the area of interest is 65.47% of the total area of Skalica cadastral area (Figure 1).

The representation of the mosaic of small-scale vineyards, orchards, gardens and small-scale plots is more extensive in the southern and south-eastern part of Skalica, in municipalities Mokrý Háj, Koválec and Prietržka. It is a well-known wine-making region. From the point of view of landscape-ecological quality, the vineyards, orchards and gardens mosaic, together with the landscape part of the Chvojnícka upland, with Skalický hájik, Kopečnica, Skalické vinohrady, represent a higher value of landscape-ecological significance (Figure 1 and Figure 2).

Value soil ecological units (VSEU), basic spatial units, were the elements of the se-lected set (Figure 3). They can be considered relatively homogenous from the point of view of abiotic properties. It is also possible to derive other basic characteristics of soil and landscape from the VSEU, such as climatic region, soil type, soil-forming substrate, inclination and exposure of the slope, depth and skeleton of the soil and the sort of soil [40].

2.2. Mathematical-Statistical Nature of Modelling

The main aim of mathematical modelling when analysing structures of interrelation in the systems is to find functional links between anthropogenous action and its impact on agroecosystem in conditions of global bioclimatic changes and analyse them as a unified systematic unit. This role can be formally recorded:

$$Impact=f^{*}\left(Action, Agroecosystem\right)$$

(1)

where the dependent variable Impact stands for the environmental impact of the action, the independent variable Action stands for the basic characteristics of agrochemical and agrotechnical activities (in the paper it is presented in the form of land use, where there is an assumption of a specific set of agrotechnical and agrochemical specialised procedures with regard to a specific form of land use), the Agroecosystem parameter stands for basic properties of the physical state of the agroecosystem, and the mathematical function $f^{*}$ stands for the model. In general, all variables are of statistical character, their randomness is caused by various factors that are related to the following problems:

(a)

The problem of measurability of the variables—quantification and potential re-quantification of the variables;

(b)

The problem of system structuralisation—setting the system limits and selection of suitable variables, and its implementation;

(c)

The problem of interrelated dependence of the variables—we cannot ensure the independence of the variables on their manifest level;

(d)

The problem of approximate reduction—the approximate character of the mathematical model.

These problems give rise to a certain deviation of obtained results from true values. On that account, a detailed statistical multivariance analysis has to be performed in order to choose the most optimal regression function of $f^{*}$ as possible and, therefore, to obtain the most efficient estimates of the results followed by an appropriate statistical verification. In this way, problems of the type (a), (b) and (d), may often be successfully minimized.

Problems of the type (c) are handled in a different, specific way. Mostly, the procedures are based on a certain more or less subjective choice of assessing criteria which differ from each other in weighting and evaluating particular variables (indicators). The uncertainty factor of making this is frequently overlooked, despite the lack of detailed objective analysis of mutual interactions between the basic indicators.

The statistical nature of mathematical model use in analysing interrelations in agroecosystems requires the application of multivariate statistical procedures and formalism of mathematical statistics in creating suitable models, with the help of which we look for “the amplest” solutions with their subsequent statistical verification [30,41,42,43,44].

2.3. Latent Variables Models

Type problems are solved by methodologies in various ways. Basically, these solutions are based on a certain subjective selection of significance and means of evaluating the individual variables without a detailed objective analysis of their interrelated dependence.

In the scope of mathematical modelling, it is possible to solve this problem using latent variables modelling class. Formally, such a model can be obtained by rewriting the model (1) into:

$$Latent={\overline{\mathbf{f}}}^{*}\left(Impact,Action,Environment\right)={\overline{\mathbf{f}}}^{*}\left(X\right) \mathrm{or}$$

$$X={\mathbf{f}}^{*}\left(Latent\right)={\mathbf{f}}^{*}\left(\Phi \right),$$

where the Latent variable stands for a new, theoretical variable or a set of variables Φ, which meet the condition of independence. The axiom of local independence is the basic attribute of the latent variables models. The set of variables X encompasses all manifest variables on one level regardless of them being indicators of physical properties of the environment or indicators of human activity impact intensity on an agroecosystem.

By the term latent variables models (LVM) we mean a group of statistical variables that describe and, in a way, explain the observed data with the help of their dependence on unobserved characteristics that can be mathematically constructed [45]. In the terminology of the general model with latent variables, we can describe these ideas with the help of:

1.

Manifest variables $x_j$, j = 1, 2, …, n, where n is the number of variables, therefore, representing measurable or observable empirical quantities;

2.

Latent variables $\Phi$, that are in the background, are not measurable or directly observable and explain the nature of the phenomenon.

The observed values of x_j and their interrelations can be explained with the help of the set of theoretical variables $\Phi$ that are defined in McDonald’s form [39,46,47,48].

Therefore, the aim of the model is to describe and, in a way, explain manifest variables and their interrelations.

The latent variables model is basically a model of data and their interrelations. It is a statistical model. The data to which it is applied are simultaneous observations of random quantity vector character.

The classic linear explorative factor analysis is the most used method; it is the base of the proposed technique of mathematical modelling [37].

A multi-criteria approach to spatial quantification of ecosystem services connected with a socio-economic indicator (the area units for statistical purposes (VSEU)) will enable us to explicitly assess the potential of agriculturally used soil ecosystem to provide agroecosystem services as well as to adapt the soil management for local conditions.

2.4. Values of Factor Score as a Possibility of Ecological Criteria Quantification for the Purposes of Optimal Agricultural Landscape Use

Each factor is determined by a linear combination of input manifest variables, where weight coefficients (factor structure) are obtained in a way that two criteria are fulfilled:

• The condition of local factor independence;
• The condition of a simple structure.

These two characteristics of latent variables predetermine their very advantageous use in quantifying ecological, or environmental criteria and limits, and their use for the proposals of ecologically optimal functional landscape systems. The obtained factor structure thus determines weight coefficients for the individual factors with the aim to quantify ecological limits. The factors are mutually independent and there is no need to deal with their interrelations when used (applied) as complex criteria in ecological decision-making.

If we thus use the extracted factors as ecological or environmental limits, we obtain the values of these limits for the individual elements of the landscape systems by determining a so-called factor score [29,49,50].

Projections of the extracted factors for the individual elements of the selection (quasi-homogenous areas of the landscape system) are determined by the factor score F₀. The row vectors in this matrix represent the distribution of the individual factors for a specific realisation of the selection (spatial distribution, time development, and so on, according to the mode of analysis used). The factor model of the existing agroecosystem can then be formulated mathematically:

$$X_0=A_0{F}_0+E_0,$$

where A₀ stands for the matrix of factor loads, F₀ is the factor score, E₀ is the matrix of errors.

If needed, it is possible to analogically construct models of higher order for the real agroecosystem (Figure 4).

In the following step, the values of factor score were re-scaled into seven categories and their projection for the individual elements of VSEU is in the following

Table 1. Categories of factor score.

Number of Categories	Scope of the Interval
1st category	x < −0.1
2nd category	−0.1 ≤ x < −0.06
3rd category	−0.06 ≤ x < −0.02
4th category	−0.02 ≤ x < 0.02
5th category	0.02 ≤ x < 0.06
6th category	0.06 ≤ x < 0.1
7th category	x ≥ 0.1

.

2.5. Quantification of Input Variables (Indicators)

Using quantitative variables with the scale of interval type as input variables is essential in any factor analysis (FA) when using input variables. Not following this strict condition can severely damage the analysis results. In cases where it is necessary to use qualitative indicators, there is a possibility for their requalification into variables with a nominal type of scale (quasi-quantitative type) that can then be used for the analysis.

Differentiation of scale type of the variable:

• Nominal variables (quasi-quantitative variables);
• Ordinal variables (qualitative variables);
• Interval variables (quantitative variables).

2.6. The Structure of Input Data Matrix

The data structure in the input matrix is closely related to quantification because it enables us to:

• Quantify information that cannot be directly quantified;
• Quantify ordinal data that cannot be directly used in ecosystem model analysis;
• Modify measured data into standard forms (multi-sized matrices) suitable for synthesis of data sets of various character (data sets describing the physical environment and, therefore, the land use and data of other character).

The most used data structure:

$$X\left(n,N\right)=\left[\begin{array}{ccc}{x}_{11},& x_{12}...........& x_{1n}\\ x_{21},& x_{22}...........& x_{2n}\\ \begin{array}{l}\\ x_{N1},\\ \end{array}& x_{N2}...........& x_{Nn}\end{array}\right]\mathrm{set\; of} n variables, which are indicators$$

N—elements (selected set)

2.7. Selection of Input Indicators and the Means of Their Quantification

For the purpose of mathematically modelling interactive relations between the agroecosystem elements or changes as a result of anthropogenous activities, we use all accessible data that could be related to this issue, while the condition of quantitative or quasi-quantitative data use has to be met. In the majority of cases, we can divide the selection into four basic sets (arrays) of indicators:

Indicators of physical state of the environment or natural potential of the landscape: We describe the properties or functionality of the landscape elements in the form of quantitative or quasi-quantitative data type (soil-ecological units (VSEU) are considered a homogenous landscape element with identical environmental behaviour and identical attributes). We also used indicators of climatic relations (ambient temperature, atmospheric precipitation [51] and morphometric properties of the terrain, which are given in VSEU numerical code in the GIS computer environment.

Indicators of soil site productivity while keeping the basic condition of data quantification: In productivity potential of VSEU calculation [52], we proceeded according to the [14,15,53,54] methodology. The nature of the methodological procedure in evaluating the productivity was the correction of exact calculations of potential phytomass production with the help of point values of quality units in kg.m⁻². To calculate the potential production (PP), we used the following calculation of mathematical relation:

$$\mathit{P}\mathit{P}=\frac{\mathrm{EFAR} .\mathrm{QFAR}}{\mathrm{Qp}.100}, \mathrm{where}$$

EPAR = the coefficient of photosynthetically active radiation use;

QPAR = the photosynthetically active radiation measured in biologically active period for the growth and development of the plant/kWh.m⁻²/;

Qp = energetic value of produced biomass/kcal.g⁻¹ of the mass/.

We proceeded from groundwork about spatial and time distribution of photosynthetically active radiation in the Skalica area, where detailed data about sun radiation in this area are expressed in monthly and annual values of photosynthetically active radiation/QPAR, EPAR/ [51]. Energetic values of produced biomass Qp for the following crops are: grains 4.2 kcal.g⁻¹, sugar beet and grain corn 4.0 kcal.g⁻¹, oilseed rape 6.0 kcal.g⁻¹ [13,14,53].

In calculating the real productive potential (RPP) of VSEU, we proceeded from the relation:

$$\mathit{R}\mathit{P}\mathit{P}=\mathit{P}\mathit{P}. \mathit{V}\mathit{S}\mathit{E}{\mathit{U}}_{\mathit{i}\mathit{n}\mathit{d}\mathit{e}\mathit{x},}$$

where VSEU_index stands for the relative relationship between VSEU quality of the specific model area and the most productive VSEU in the area of Slovakia (GJ.ha⁻¹).

Indicators of anthropogenous activity: Describing other areas where there is a significant human impact on the landscape via suitable indicators—elements of land cover obtained from aerial images, interpretation of ortophotos (LAND COVER) according to the key of the CORINE Land Cover Technical Guide—Addendum 2000 [55].

Indicators of specific character: Describing other areas where there is an assumption of correlation with anthropogenous activity via suitable indicators—e.g., indicators of the degree of potential soil erosion by water. Complex physical models and automated approaches were used in the papers of [56,57,58,59] and other authors and basically apply the procedures of erosion and accumulation modelling based on a modified universal soil loss equation (USLE) in various scales and complexities in the GIS computer environment [60]. In the paper, we used erosion by water on agricultural soils modelling with the use of an empirical model of a universal soil loss equation (USLE), which is a useful tool in managing and planning soil protection.

Indicators of results of monitored cycles and agrochemical examination: That also monitored the content of particulate organic carbon (POC) and quality of organic mass according to Q _4/6 indicator [52,61].

Indicators of chemical composition of soil cover and soil-forming substrate (chemical composition): Derived according to % of the content of basic chemical composition of magmatic rocks SiO₂, Al₂O₃, Fe₂O_3, CaO, MgO [62].

2.8. Standardisation of Data Matrix

Various units and scales of used input data cause harder conditions for factor solution interpretation. When processing the experiment data, it is wise to modify the original data set into a specific standard form which would maintain data equivalency from the point of view of quantification.

The basic matrix, to which we apply the FA technique, can be modified as follows:

(a)

Data centralisation (C), when we get values with zero average value in rows;

(b)

Data normalisation (N), when we get norm values to 1 in rows.

These modifications can be combined. Data standardisation determines the form of the covariant matrix, which is a starting point of each factor analysis.

Each evaluated element (VSEU) was described by 44 parameters whose detailed description and quantification means are in

Table 2. The list of used indicators in describing elements of the selected agroecosystem and means of their quantification.

	Morphometric parameters
1.	[LS]	continuous length of plot of land slope	[m]
2.	[SL]	average slopeness	[grad]
3.	[GWS]	depth of groundwater surface under the terrain	[m]
	Physical parameters of soil cover
4.	[SKEL]	skeletal %—representation of hard skeleton	[vol. %]
5.	[DSP]	Depth of soil profile	[cm]
6.	[GRN]	granularity—% clay fraction< 0.01 mm	[vol. %]
	Energetic potential of real production
7.	[PROD]	energetic potential of real phytomass production	[GJ.ha−1]
	Chemical parameters of soil cover
8.	[SiO2-P]	soil-forming component SiO2	[vol. %]
9.	[Al2O3-P]	soil-forming component Al2O3	[vol. %]
10.	[Fe2O3-P]	soil-forming component Fe2O3	[vol. %]
11.	[CaO -P]	mineral component CaO	[vol. %]
12.	[MgO -P]	mineral component MgO	[vol. %]
	Biochemical parameters of soil cover
13.	[Q4/6]	quality of organic substances	[Q4/6]
14.	[H]	content of organic substances	[vol. %]
	Calculated water erosion according to
15.	[EROS]	erosion by water	[t.ha−1. year]
	Chemical parameters of geological foundation
16.	[SiO2-G]	soil-forming component SiO2	[vol. %]
17.	[Al2O3-G]	soil-forming component Al2O3	[vol. %]
18.	[Fe2O3-G]	soil-forming component Fe2O3	[vol. %]
19.	[CaO -G]	mineral component CaO	[vol. %]
20.	[MgO -G]	mineral component MgO	[vol. %]
	Climatic parameters
21–25.	[ZIII-ZIX]	average precipitation for each month in a vegetative period	[mm]
26.	[SP]	sum of precipitation in a vegetative period	[mm]
27–33.	[TIII-TIX]	average air temperature in a vegetative period for each individual month	[grad]
34.	[ST]	sum of air temperatures in a vegetative period	[grad]
	Categories of land use
35.	[ALS]	small-scale arable land	[bin]
36.	[ALL]	large-scale arable land	[bin]
37.	[MOSFO]	mosaic of small-scale fields and orchards	[bin]
38.	[XGRS]	xerophilous grassland	[bin]
39.	[VIN]	vineyards	[bin]
40.	[MOSOV]	mosaic of orchards, gardens and vineyards	[bin]
41.	[FOR]	forests	[bin]
42.	[BUILT]	built-up area	[bin]
43.	[MGRS]	mesophilic grassland	[bin]
44.	[RECR]	recreational possibilities of use	[bin]

. The indicators were selected in such a way so that they proportionally describe abiotic and socioeconomic elements of the agroecosystem (CLS), and the indicators related to the biomass production and negative anthropogenous phenomena (erosion processes).

The obtained factor solution was rotated into a simple structure using the VARIMAX criterion during the initial analyses. The rotated matrix of factor loads obtained via analysis of real existing agroecosystem will be A₀. Factor loads determined in a simple structure increase the interpretability of the obtained factors. Using the VARIMAX method, we derived several orthogonal rotated solutions (from the original solution) for various number(s) of common factors from the original solution. Each of these alternative solutions was first evaluated based on empirical knowledge. The most suitable was the solution with six common factors, as opposed to four common factors.

The obtained results and the interpretability of the factor solution were compared with the results from similar studies applied on similar data matrices from the point of view of selection and parameter structure and with similar aims [63]. The factor solution structure results can be considered the structure model of the analysed agroecosystem because they describe and quantify the interactive relations between the input parameters (indicators) and the extracted factors.

3. Results

3.1. Agroecosystem Model Based on Factor Loads Structure Interpretation of Input Variables

Using vector loads in columns of the factor loads matrix enables the identification and interpretation of the individual extracted factor significance. The interpretation enables us to carry out two crucial steps:

• Verification of obtained factor structure with regard to the known empirical experience and gained theoretical rules;
• Usage of extracted factors as evaluation criteria in subsequent evaluation of properties and environmental problems in the scope of agroecosystems with regards to favourable orthogonal properties of latent variables.

Table 3. Factor loads matrix for six significant factors.

	Measurable Parameters	F1 Climate	F2 Bedrock Chemistry	F3 Phytomass Production Potential	F4 Physical-Chemical Soil Properties	F5 Potential Erosion	F6 Bio-Chemical Soil Properties
1	LP	0.38516	−0.0428	−0.2822	0.17746	0.53505	−0.0417
2	SL	0.19441	−0.0201	−0.6687	0.27199	−0.0286	0.01949
3	GWS	0.45593	0.38719	0.12578	0.09412	0.13601	0.38989
4	SKEL	0.43088	0.46778	−0.5235	−0.0699	−0.0268	0.0311
5	DSP	−0.4833	−0.2698	0.75812	−0.0642	−0.0474	0.0018
6	GRN	−0.1019	0.06279	−0.4998	−0.6891	−0.3358	−0.3547
7	PROD	−0.3413	−0.222	0.64722	0.46869	0.01722	0.071
8	SiO2 P	0.11108	−0.6143	0.15431	0.607	0.01213	−0.3207
9	AL2O3 P	−0.0451	0.32319	−0.0501	−0.8104	0.02075	0.37844
10	CaO P	0.3665	0.6445	−0.4298	−0.2425	0.08473	0.29551
11	MgO P	−0.2695	0.27354	0.29003	−0.1178	−0.0191	0.02391
12	Q4/6	0.21044	0.25431	−0.6293	−0.3927	−0.0637	−0.0031
13	H%	0.09312	0.09141	0.03073	0.04204	0.045	−0.6875
14	EROS	0.33608	−0.0894	−0.2204	0.10534	0.66982	−0.1106
15	Si02 G	−0.3203	−0.9207	0.05553	0.10352	0.0067	0.0572
16	AL2O3 G	0.23397	0.82191	−0.1212	−0.3566	−0.0302	−0.1008
17	CaO G	0.19456	0.74697	0.26151	0.39799	0.00741	0.07623
18	MgO G	0.46341	0.82702	−0.2574	0.00489	0.03452	−0.0454
19	ZIII	0.9856	0.126	−0.1043	0.01052	0.03301	0.01152
20	ZIV	0.9856	0.126	−0.1043	0.01052	0.03301	0.01152
21	ZV	−0.9856	−0.126	0.10425	−0.0105	−0.033	−0.0115
22	ZVI	−0.9856	−0.126	0.10425	−0.0105	−0.033	−0.0115
23	ZVII	−0.9856	−0.126	0.10425	−0.0105	−0.033	−0.0115
24	ZVIII	0.9856	0.126	−0.1043	0.01052	0.03301	0.01152
25	ZIX	0.9856	0.126	−0.1043	0.01052	0.03301	0.01152
26	SP	0.9856	0.126	−0.1043	0.01052	0.03301	0.01152
27	TIII	−0.9856	−0.126	0.10425	−0.0105	−0.033	−0.0115
28	TIV	−0.9856	−0.126	0.10425	−0.0105	−0.033	−0.0115
29	TV	−0.9856	−0.126	0.10425	−0.0105	−0.033	−0.0115
30	TVI	−0.9856	−0.126	0.10425	−0.0105	−0.033	−0.0115
31	TVII	−0.9856	−0.126	0.10425	−0.0105	−0.033	−0.0115
32	TVIII	−0.9856	−0.126	0.10425	−0.0105	−0.033	−0.0115
33	TIX	−0.9856	−0.126	0.10425	−0.0105	−0.033	−0.0115
34	ST	−0.9856	−0.126	0.10425	−0.0105	−0.033	−0.0115
35	ALS	0.01151	0.12203	0.01623	0.1369	−0.1682	0.1044
36	ALL	0.00208	−0.0674	0.36786	−0.0287	0.7047	0.10101
37	MOSFO	0.13856	0.04155	−0.0356	−0.0281	0.1004	−0.6383
38	XGRS	0.15158	0.05808	−0.1031	0.10936	−0.2058	−0.1172
39	VIN	0.13907	−0.2108	−0.0426	0.02872	−0.1005	0.07131
40	MOSOV	−0.0835	−0.0421	−0.4581	0.10999	0.00208	0.12459
41	FOR	0.02122	0.08088	−0.0476	−0.0804	−0.0983	0.00575
42	BUILT	0.02367	0.20273	0.14299	0.09731	−0.1839	0.04214
43	MGRS	−0.2958	−0.1461	0.15403	−0.4412	−0.2063	−0.0793
44	RECR	0.05487	−0.0172	−0.136	−0.0088	−0.0827	0.05642

Legend: LS—continuous length of the plot of land slope, SL—slopeness of VSEU, GWS—depth of groundwater surface, SKEL—soil skeleton, DSP—depth of soil profile, GRN—granularity (% representation of soil clay fraction), PROD—potential phytomass production (GJ.ha⁻¹), SiO₂ P— % representation in soil, Al₂O₃-P—% representation in soil, CaO-P—% representation in soil, MgO- P—% representation in soil, Q_4/6—quality of organic substances in soil, H%—content of organic substances in soil, EROS—soil loss as a result of erosion by water in t.ha⁻¹, SiO₂-G—% representation in geological bedrock, Al₂O₃-G—% representation in geological bedrock, CaO-G—% representation in geological bedrock, MgO-G—% representation in geological bedrock, ZIII, ZIV, ZV, ZVI, ZVII, ZVIII, ZIX—average amount of atmospheric precipitation for months (vegetative period), SP—sum of atmospheric precipitation for a vegetative period, TIII, TIV, TV, TVI, TVII, TVIII, TIX—average temperatures for given months (vegetative period), ST—average temperatures for a vegetative period, ALS—small-scale arable land, ALL—large-scale arable land, MOSFO—mosaic of small-scale arable land and orchards, XGRS—xerophilous grassland, VIN—vineyards, MOSOV—mosaic of small-scale soil, orchards and vineyards, FOR—forest covers, BUILT—built-up areas, MGRS—mesophilous grassland, RECR—recreational areas.

shows the structure of factor loads value (structure) of six factors, while primary (significant) relations, (and) secondary (less significant) relations are considered as follows:

• Primary correlation relations between the factors and input indicators are considered the values of factor loads in the interval 0.6–1.0;
• Secondary correlation relations are considered the values of factor loads in the interval 0.3–0.6;
• The threshold of significance of correlation relations is considered the values of factor loads in the interval 0.2–0 [37].

Six basic elements of the system based on differentiation level were extracted by reproducing 44 variables in the input data matrix describing the agroecosystem via factor analysis, i.e., the physical components of the geographical sphere. The factor loads matrix (Table 3) describes interrelations between variables in the scope of the individual system elements and latent factors.

3.2. Agroecosystem Model Creation Conditions—Model Calibration

The role of model calibration is to determine the calibration coefficients in the factor loads matrix or matrices A₁, A₂, … in the case of using a factor model of a higher order. Knowledge of complete input data matrix is crucial for their determination. It is possible to use the factor structure obtained in FA application performed in the evaluation of other equivalent systems, in which sets of manifest indicators were used identically.

3.3. Agroecosystem Model Creation Conditions—Model Factorisation

Model factorisation is based on disintegrating a reduced selection correlation matrix created from the data matrix of indicators into a system of Eigenvalues and Eigenvectors

According to Malinowsky error analysis [64], the next step is to determine the number of significant own values, i.e., the number of extracted factors (Figure 5).

In the graph we can see that the breaking point in the graph is somewhere between a 4-factorial solution and a 6-factorial solution, which stand for the number of Eigenvalues. From the point of view of explained cumulative variance, we decided to consider m = 6 as the suitable number of explaining factors.

3.3.1. F1 Climate Factor

The primary factor loads of this factor are [TIII–TIX—(0.98)] and [ZIII–ZIX—(0.99)] variables, which are in mutual negative correlation, which means that with the increase of average monthly temperatures the amount of atmospheric precipitation decreases; in the studied area, the spatial distribution of various precipitation and temperatures is dominantly dependent on the vertical heterogeneity of the area, which is the result of three geomorphologically different elements present—the mountain unit of the White Carpathian Mts., lowlands of the Dyjsko-moravská floodplain and the Chvojnícka upland. The agricultural area extends into only two geomorphological elements. Since the aforementioned geomorphological elements are created by different rock composition, differing also in the content of alkaline elements, it showed on the value of factor loads in variables % representation [MgO-G—(0.46)], [CaO-G—(0.19)] in bedrock and % and [CaO-P—(0.37)].

There is a high variability of morphometric properties of the terrain in the mentioned geomorphological unit, which is manifested in the variability of different depths of the soil profile, erosion processes and groundwater surface, which is confirmed by variables with secondary factor loads [DSP—(0.48)], [GWS—(0.46)] and [EROS—(0.34)], [SKEL—(0.43)] (Figure 6).

3.3.2. F2 Chemical Properties of Bedrock Factor

The F2 factor is primarily saturated by [SiO₂-G], [Al₂O₃-G], [MgO-G], [CaO-G] variables, (in order 0.92, 0.82, 0.83, 0.75), secondary loads can be seen in [SiO₂-P], [CaO-P], [Al₂O₃-P] variables (0.61, 0.64, 0.32) and also [SKEL (0.47)], [GRN (0.39)]. It can be loosely interpreted as the mineralogical composition of geological bedrock and its chemical properties are primarily dependent on mineralogical soil composition and its chemical properties. The origin of the geological bedrock and its mineralogical composition is determined by dispersion and soil chemical properties and the whole process of its development [65,66]. By increasing the dispersion of the mineral proportion, the SiO₂ content decreases and the content of aluminium oxide, calcium oxide, magnesium oxide and other oxides is relatively increased. This fact is also confirmed by a negative correlation between the % of SiO₂ representation and other oxides in the input data matrix. Another fact that was confirmed was that the mineralogical composition of the bedrock, soil and their chemical properties significantly influence soil granularity and its skeleton, e.g., sandy soils are rich in primary minerals, mainly quartz, which erodes only with difficulty, and in clayey-loamy soils the number of secondary minerals increases, mainly from the clayey and loamy group (Figure 7).

3.3.3. F3 Phytomass Production Potential Factor

The third factor is primarily saturated by [DSP (0.76)], [Q_4/6 (0.63)], [SL (0.67)], [PROD (0.65)] variables. Secondary factor loads are in [SKEL (0.52)], [GRN (0.50)], [CaO P (0.43)] variables. In other words, factor load values of the individual variables determine the order of significance of indicators on the production of agricultural crops. On the level of primary factor loads values, variables that have a character of stable soil properties with relation to agricultural crops production (difficult for man to modify landscape properties) are extracted, it is mainly soil depth and slopeness, on the level of secondary factor loads, variables that can be partially modified by man, i.e., skeleton, granularity and calcium content in the soil, are extracted. The parameter of organic substances quality that indicates the balance of climatic, physical, chemical and biochemical properties of the soil environment in relation to phytomass production also has a character of a stable soil property. The variable [H% (0.03)] was not significant in the given factor. The impact of climate is not distinctive either, since the analysed agricultural area is not large enough (Figure 8).

3.3.4. F4 Physical-Chemical Soil Properties Factor

In this factor, the [Al₂O₃ (0.81)], [GRN (0.69)] and [SiO₂ (0.61)] variables have significant loads in the soil, secondary factor loads are in [PROD (0.47)], [Q_4/6 (0.40)], [CaO-G (0.40)] and [Al₂O₃ (0.36)] variables. On one hand, this factor load structure indicates interactive relations between the granularity and proportional representation of Al₂ O₃ and SiO₂ in the soil, and on the other hand, it indicates interactive relations between the CaO bedrock content and quality of organic substances in the soil in relation to potential productivity of the area. The FA used detected correlations between the aforementioned variables and the latent variable—physical–chemical soil properties. Rocks and soil-forming substrates are not only a condition for developing a certain soil type and subtype, but they also influence soil reaction, organic substances content, texture and depth of soil profile with its stratigraphy and morphology [65,66,67,68].

Rocks, from which soils of a correspondent mineral strength originate, understandably influence also the degree of saturation of sorption soil complex by alkaline cations Ca²⁺, Mg², K⁺, Na⁺ and therefore, also the amount of nutrients accessible in the soil. Parent material also influences chemical soil reaction. One of the traditional divisions of igneous rocks according to the silicon dioxide content (SiO₂) divides rocks into acidic rocks with high content of SiO₂ (granite, granodiorite, rhyolite, dacite) and alkaline or ultra-alkaline rocks with low content of SiO₂, but usually with higher magnesium and iron content (basalt, gabbro, peridot, pyroxenite, green marble) [65,69].

The erosion process is a very complex process, where the degree of chemical compound and mineral erosion is an indicator of erosion of a certain type in specific climatic-geographical conditions (Figure 9).

The ratio of SiO₂ or Al₂O₃ or both minerals in soil and soil-forming substrates are used for this purpose.

3.3.5. F5 Erosion by Water Potential Factor

The F5 factor has the highest primary loads in [ALL (0.70)], [EROS (0.67)] variables and secondary loads in the [LS (0.53)] variable. The aforementioned structure of the factor loads values of this factor’s variables indicates the fact that disproportionate plot of land length, unsuitable means of plot of land use in combination with unsuitable management with regard to the soil attributes (granularity) highly participated in erosion processes—surface erosion by water in the analysed area. The relations of soil complexes on individual terrain elements also create other relations between the components of the natural environment and the terrain. The relative height of the geomorphological form over other forms can be significant. Gradient and convex forms of normal curvature in the direction of continuous gradient curvatures (the length of plot of land slope) accelerate gravitationally conditioned processes and surface outflow of water on inclined terrain elements. They increase its kinetic energy and transport capacity. Concave forms of normal curvature in the direction of gradient curvatures slow down the outflow. Concave horizontal forms and thalweg lines in them concentrate the outflow. Depression concave positions accumulate water from the whole gradient area and do not permit it to flow away. Convex horizontal forms diffuse the outflow. The ridge positions form the border of outflow areas. Naturally formed or man-modified terrain skeletons predetermine the system of gradient curvatures and, therefore, the preferred routes of water outflow and rock material movement [69] Figure 10.

3.3.6. F6 Biochemical Properties Factor

This factor has the highest factor loads values in the content variable [H% (0.69)]. Secondary loads can be seen in [GRN (0.35)], [SiO₂ (0.32)], [Al₂O₃-P (0.38)] and [GWS (0.39)], variables, the [CaO-P (0.30)] variable is on the limit of significance. Biochemical soil properties that are conditioned by physical soil properties (granularity) have a decisive role in plant and animal remains decomposition and creation of specific soil organic substances. These immediately condition the water-air regime as well as the pH character of the soil environment. Based on the obtained factor loads value structure, the results of the analysis confirm that higher values of significance in factor 6 are assigned to variables that immediately condition the character of the water–air regime, i.e., soil granularity and the height of groundwater surface, therefore, the prevalence of oxidation or reduction processes in which the organic matter is made. Proportional representation of soil-forming components—% representation of minerals SiO₂ and Al₂O₃ in the bedrock subsequently conditions the character of physical soil properties because the aforementioned oxides are dominant in the creation of secondary alumoferosilicates minerals [65,69] Figure 11.

3.4. Proposals of Functionality Optimisation and Agroecosystem Sustainability

Based on the interpretation of the FA results and the calculations of their factor scores, we propose changes in the use of the agricultural land fund in the model area, which should, at least to some extent, eliminate the adverse effects of agricultural production on the soil and on the overall ecological stability of the country.

3.5. Proposal for Optimising Land Use in the Geomorphological Lowland of the Dyjsko-Moravská Floodplain

The Holocene floodplain of the river Morava is an area in a semiarid climatic area with alluvial soils, which are characteristic for high groundwater level, which seasonally rises close to the surface and, locally in depression positions, even above its level. The soil type representation in the scope of the given geomorphological unit is predominantly Gleyic Fluvisols cultivated, clay-loam, locally clayey and Eutric Fluvisols cultivated. Loamy is less represented. Locally we can find Mollic Fluvisols cultivated. The means of use within the given part of the area is in the form of large-scale arable land with cultivation of highly and medium demanding agricultural crops in crop rotation, i.e., winter wheat, corn. In the parts of the area with a lower groundwater level, in more humid locations, maize for silage, or lucerne, is more dominant in crop rotation. A drainage system in the area is not functional as a result of clogging by various sedimentary material. A part of the area is in a sanitary protection zone, and thus due to high probability of seepage and possible contamination of groundwater it is crucial to propose a change in land use. In the evaluated part of the model area on a wide river floodplain with predominantly developed Fluvisols and Mollic Gleysols cultivated, on fluvial sediments with an average inclination in the interval 0–3° and with the use of large-scale plots of land, the values of factor score for the fifth factor are in the interval from −0.1 ≤ x < −0.06 to −0.06 ≤ x < −0.02, which corresponds to no or low erosion by water. From the point of view of agricultural crops production, and based on the factor score values of the third factor in the interval −0.1 ≤ x < −0.06, the given soil sites are classified into the category of soils with lower production potential. The mentioned soil sites are soils with unfavourable technological properties, i.e., with higher or high representation of clayey fraction (45–60%) (the number of coexistences for the loamy-clayey to clayey soils is in the interval from 40–48.8%).

From the point of view of the mentioned ecological and environmental criteria, we propose introducing fodder crop rotation in the mentioned location, or at least to introduce crop rotation with higher 30–50% proportion of fodder plants (lucerne is suitable) in combination with mulching intercrop (e.g., oilseed rape, sunflower). These can be found in the north-western part of the area on older alluvial fans with developed Mollic Fluvisols and in the south-western part of the area.

A drainage system was introduced in depressed parts of the area with higher groundwater level, in moister locations, which has been, however, not functional for over a decade, due to clogging by various sedimentary material, where original mesophilic meadows and alluvial forests developed naturally. A measure according to the Nitrates Directive 91/676/EEC and classification into vulnerable areas of the Slovak Republic was introduced in ALR. It is a part of the directive of the European Union (EU) about water (directive 2000/60/EC) and is closely connected to other EU policies that deal with air quality, environmental changes and agriculture.

From the point of view of the aforementioned ecological and environmental criteria, we propose to keep the alluvial forests in the given location and to introduce fodder plant crop rotation, or at least to introduce crop rotation with a higher ratio of fodder plants 30–50% (lucerne) in combination with mulching intercrop (e.g., oilseed rape, sunflower). The aforementioned intercrops are used in modern technologies in sanitary protection zones of water resources because they are able to drain accumulated inorganic nitrogen and eliminate the impact of agrochemical seepage into groundwater.

3.6. Proposal for Land Use Optimisation in the Scope of the Chvojnícka Upland Geomorphological Unit

In the given geomorphological unit in early and late alluvial fans with Chernozems cultivated, Luvi-Haplic Chernozems cultivated in semiarid climatic area, the usage is in the category of large-scale arable land with dominant winter wheat and corn. These change into Haplic Luvisols and Albi-Haplic Luvisols with relation to mild slopes that are made up by loess sediments in a humid climatic area. Crop rotations in this area specialise in production of winter wheat as the natural conditions are very good and in common agro-technology, stable crops with adequate economic effect are achieved.

Based on the calculated values of the factor score for the fifth factor in the interval 0.02 ≤ x < 0.06 to 0.06 ≤ x < 0.1, it is an area of mostly medium to higher erosion risk as a result of unsuitable shape, size and the location of the plot of land with regards to contour lines. From the point of view of producing a factor score value for the third factor in the interval 0.02 ≤ x < 0.06, soil sites with higher and high production potential, and with good technological soil properties (content of clay fraction of soils found in the northern part of the area is 30–45%) are indicated.

It is important to mention mainly the technical modifications of the shape and size of the plots of land in the proposals because the intensity of water surface erosion is dominantly conditioned by disproportionate length of plots of land slopes, that means division of each parcel into two or three plots. On patches of land with disproportionate slope length in more sloped segments of the landscape is it suitable to divide groves with the help of the so-called infiltration belts, which slow down the outflow of water and, therefore, enable settling of soil particles in depressions on the soil surface. Moreover, it is crucial to maintain natural obstacles (groves, shrubs in the vicinity of roads, etc.,). From the point of view of crop rotation structure, it is crucial to incorporate intercrops with medium-good anti-erosion effects (lucerne, oilseed rape, peas), i.e.,

• Trifolium incarnatum, if its summer sowing was successful and a continuous growth was created in autumn;
• Autumn fodder blends and grains, if they root well and create a continuous growth before winter;
• Spring grains with underseeding of lucerne;
• Representation of grains 50%, 33.3% of perennial fodder plants, 16.7% of annual fodder plants.

Fluvisols cultivated and Gleyic are in the southern part of the area; in some places, on younger alluvial fans there are Mollic cultivated, of mainly more granular composition. These compounds are not threatened by erosion by water and technological properties of these soils are more favourable than in Fluvisols in the floodplain of the Morava river. From the point of view of crop rotation, we propose to concentrate on malt barley as the dominant crop.

The south-eastern part of the area and the western part of the Chvojnícka upland in the proximity of Skalica town is on loess sediments, with predominant Haplic cultivated and Haplic Luvisols and cultivated. It is used mainly in accordance with natural potential in the form of mosaics of small-scale vineyards, orchards and gardens, where quite good production potential is appropriately used and thus there is no significant soil erosion risk.

3.7. Proposal for Land Use Optimisation in the Scope of the White Carpathians Geomorphological Unit

On foothill locations of the White Carpathians, on transition areas of hilly terrain and deluvia, Haplic Luvisols are cultivated alternately with Calcaric Cambisols and Calcaric Cambisols are cultivated with a relatively significant representation of skeleton soils on plateau surfaces. Stagni Eutric Cambisols and Stagni Eutric Cambisols are developed on the bottoms and foothills of valleys or less steep slopes with impermeable bedrocks of calcareous shales. These soil sites are used in various ways. Large-scale arable land is dominant in transitional parts of two geomorphological units. Small-scale fields, partially represented pastures, forest covers and cottage-recreational area are the categories of land use in foothill locations of the White Carpathian Mts.

Factor score values for the third factor in the interval −0.1 ≤ x < −0.06 describe soil sites with a relatively lower production potential. The factor score values for the fifth factor in the interval from 0.02 ≤ x < 0.06 to 0.06 ≤ x < 0.1 indicate higher local erosion by water in places with unsuitable soil use. Locally, where the combination of variables the length of the plot of land slope and the way of use in the category large-scale arable land was unfavourable, the values of factor score were in the interval x ≥ 0.1, which corresponds to high soil transport from a hectare per year. It is a matter of very varied land use with varied substrate base and soils with links to a very broken terrain.

From the aforementioned it is evident that it is crucial to incorporate low to less demanding crops into the crop rotation. The limiting factor is the soil depth, skeleton and ties to steeper slopes where it is necessary to include crops with good anti-erosion effect in the crop rotation, i.e., natural grassy covers, perennial fodder plants, autumn fodder mixtures and grains with underseeding of lucerne. In the places of identified high erosion potential, it is necessary to single out the plots of land, or VSEU, from the categories of the agricultural soil and preferably use them for eco-stabilising precautions by planting tree species, shrubs or forest covers.

The aforementioned changes in agricultural land use and its management are closely related to the improvement in many ecosystems services, the increase of retention capacity of the landscape, the increase of biodiversity in the landscape, the optimisation of production abilities, the maintaining of soil and water quality, the reduction of climate impact using suitable sowing crops, the mosaic structure of the cultivated plots of land, the sowing of non-forest woody vegetation elements, the completion of elements of the territorial system of ecological stability in the monitored area, etc.

4. Discussion

Factor analysis grouped 44 measured attributes into six factors. All six factors related to more soil functions, e.g., high production in soil profile depth, skeleton, quality organic substances content (O ₄/₆), favourable water–air conditions given by favourable granularity and the presence of alkaline cations (% representation of CaO, MgO), etc.

In factor 1 (climate factor) there is a high variability of the morphometric properties of the relief, which is manifested in the variability of different depths of the soil profile, erosion processes and groundwater surface. According to [29], the soil aeration and soil aggregation factors (with different depths of soil profile) influence soil structure and water transmission properties of soil.

Factor 2 (chemical properties of bedrock factor) interprets the characteristic that the mineralogical composition of the geological bedrock and its chemical properties is primarily dependent on the mineralogical soil composition and its chemical properties. The fact that was confirmed was that mineralogical composition of the bedrock, soil and their chemical properties significantly influence soil granularity and its skeleton. According to [29], clay concentration and soil organic carbon influence aggregation and mean weight diameter of aggregates, which affect water storage and movement in soil, as well as productivity. An increase in soil organic carbon could also reduce environmental pollution.

Correlation analysis and main component analysis indicated that a minimal data set about soil parameters including content soil density, pH of soil environment, C, P and Na elements, would detect many differences in soil state between the studied means of soil use. The authors [9] propose to use these parameters as a minimal data set of indicators for evaluating soil state on this type of soils in this region. They came to the opinion that the set of soil properties did not show any significant difference between soil use and it then could be dismissed as an indicator. However, there were significant differences in soil use and the depth of soil for a whole range of other given soil parameters (content density, C, N, P and Na).

According to factor 3 (phytomass production potential factor), parameter of soil depth, slopeness and organic substances quality have a character of stable soil properties with relation to agricultural crops production. The parameter of organic substances quality that indicates the balance of climatic, physical, chemical and biochemical properties of the soil environment in relation to phytomass production also has a character of a stable soil property. According to [29], the most dominant measured attribute for soil depths was soil organic carbon, which can be monitored over time to determine if soil quality is degrading or stable.

Other authors [70] also dealt with the effect of intensifying soil use on soil carbon and ecosystem services (productivity, retaining abilities, infiltration, etc.,). They state that soil organic mass is an effective indicator of the state of soil resources, which reflects functional properties such as aggregation and infiltration, and plays a decisive role in production sustainability and ecosystem service in agricultural landscapes. Agricultural activities usually decrease soil carbon via disrupting the soil and mineralisation. According to [71] the size of soil buffer capacity is significant in relation to chemical properties of the geological bedrock which was confirmed using multilateral linear gradient analysis with the help of CANOCO software. The production functions of soils determine the soil subtype to some extent, which is confirmed by significant correlation between the variables of soil subtype and C_ox variable.

Rocks and soil-forming substrates influence soil reaction, organic substances content, texture and depth of soil profile with its stratigraphy and morphology [67]. In our assessment, factor 4 (physical–chemical soil properties factor) indicates interactive relations between the granularity and proportional representation of Al₂O₃ and SiO₂ in the soil and, on the other hand, it indicates interactive relations between the CaO bedrock content and quality of organic substances in the soil in relation to potential productivity of the area.

Factor 5 (erosion by water potential factor) indicates the fact that disproportionate plot of land length, unsuitable means of plot of land use in combination with unsuitable management with regards to the soil attributes (granularity) highly participated in erosion processes.

According to [65], proportional representation of soil-forming components to % representation of minerals SiO2 and Al2O3 in the bedrock subsequently conditions the character of physical soil properties. The higher values of significance in factor 6 are assigned to variables that immediately condition the character of the water–air regime.

Other useable similar methods of multi-criteria decision-making for the evaluation of agroecosystems sustainability include MCDM, TOPSIS [72], ANP [73], AHP [74] and ELECTRE [75].

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a multi-criteria decision analysis method. It is based on the concept that the chosen alternative should have the shortest geometric distance from the positive ideal solution (PIS) and the longest geometric distance from the negative ideal solution (NIS). Multiple-criteria decision-making (MCDM) is a sub-discipline of operations research that explicitly evaluates multiple conflicting criteria in decision-making (e.g., solving complex real-world problems like the 2030 Agenda (United Nations)).

The analytic network process (ANP) is a more general form of the analytic hierarchy process (AHP) used in multi-criteria decision analysis. AHP structures a decision problem into a hierarchy with a goal, decision criteria and alternatives, while the ANP structures it as a network. Both then use a system of pairwise comparisons to measure the weights of the components of the structure, and finally to rank the alternatives in the decision. The judgments may be inconsistent, and there is a mathematical way to measure inconsistency so that the outlying judgments may be revised by the decision-maker in an acceptable way, or a decision may be delayed until more consistent information is obtained.

ELECTRE (ELimination Et Choix Traduisant la REalité) is a family of multi-criteria decision analysis (MCDA). As a preference model, an outranking relation on the set of actions is used—it is constructed as a result of concordance and nondiscordance tests involving a specific input preference in-formation.

In multivariate statistics, factor analysis (FA) is a statistical method used to uncover the underlying structure of a relatively large set of variables. FA works efficiently and produces fewer factors to describe the relationship if the variables under study are highly correlated.

It should be noted here that MCDM methods cannot be compared in a way that one of them would outperform the rest, as accuracy in prediction depends on the nature of the problem, as well as the data collection and processing in a way that best fits each individual method and application.

It is crucial for data to include substantial information about what is being researched in multivariate analysis. The amount of information in data depends on how well the problem of research is formulated and how well the observations or measurements are collected. These are the weak and strong sides of the statistical processing and use of various statistical programs. The choice of a suitable statistical program with regard to the object of research and correct interpretation of acquired results is no less important. In our study, with regards to the results of the applied FA technique, we opted for a suitable set of indicators trying to proportionally describe all elements of the agroecosystem, to which the results of matrix factor loads and factor score corresponded, since they were well interpretable.

Recent research is based on long-term quantitative soil monitoring in determining agricultural soil changes and ecosystem processes over time. During long-term application of organic fertilisers, a statistically significant impact of the year-long experiment on all monitored soil parameters was detected, which was confirmed by analysis variance [76].

An unsuitable selection of indicators is a weak side of the used technique of factor analysis. If we analyse any landscape system consisting of abiotic, biotic and socioeconomic elements, the selection of indicators should meet the condition of proportional description and the selection of the number of suitably selected indicators of these elements.

5. Conclusions

It is necessary to obtain the necessary data relevant to the issue at hand in order to apply the selected methodological procedures of factor analysis in modelling structures of interrelations in the system man-agroecosystem. The data are usually of varying physical dimension, they cause difficult conditions for factor solution interpretation. It is suitable to modify the original data set into a specific standard form which would maintain data equivalency from the point of view of quantifying experimental data processing. High values of factor loads can be detected in man-agroecosystem impact, where erosion by water occurs as a result of unsuitable management. For example, primarily in factor 5, the variable [LS (0.53)] was detected on arable soil with disproportionate size and unsuitable orientation with regard to thalwegs and location of the plot of land on the slope. In factor 3, primary saturation of this factor is [PROD (0.65)], [DSP—(0.76)], [Q_4/6—(0.63)], [SL—(0.67)]. Secondary loads were in [SKEL (0.52)], [GRN (0.50)], [CaO P (0.43)] variables, which can be loosely interpreted as physical and biochemical soil properties, such as granularity, organic substances quality, depth of soil and skeleton, but also presence of calcium being dominant impacts on the amount of biomass production. Physical–chemical and bio-chemical soil properties were connected with rock composition and its chemical properties. We further calculated the factor score values for the individual factors (mainly for factors 5 and 3) for proposing optimal agroecosystem use, and their projection for the individual elements of quasi-homogenous areas of the landscape (VSEU). This way we obtained the information about the present agroecosystem use that indicated unsuitable management and use, and enabled us to formulate a proposal of a sustainable functional agroecosystem.