Management Zones Delineation, Correct and Incorrect Application Analysis in a Coriander Field Using Precision Agriculture, Soil Chemical, Granular and Hydraulic Analyses, Fuzzy k-Means Zoning, Factor Analysis and Geostatistics

Abstract

The objective of our investigation was to study the various effects of correct and incorrect application of fuzziness exponent, initial parameterization and fuzzy classification algorithms modeling on homogeneous management zones (MZs) delineation of a Coriandrum sativum L. field by using precision agriculture, soil chemical, granular and hydraulic analyses, fuzzy k-means zoning algorithms with statistical measures like the introduced Percentage of Management Zones Spatial Agreement (PoMZSA) (%), factor and principal components analysis (PCA) and geostatistical nutrients GIS mapping. Results of the exploratory fuzzy analysis showed how different fuzziness exponents applied to different soil parameter groups can reveal better insights for determining whether a fuzzy classification is a correct or incorrect application for delineating fuzzy MZs. In all cases, the best results were achieved by using the optimal fuzziness exponent with the full number of parameters of each soil chemical, granular and hydraulic parameter group or the maximum extracted PCAs. In each case study where the factor analysis and PCA showed optimal MZs > 2, the results of the fuzzy PoMZSA clustering metric revealed low, medium and medium to high spatial agreement, which presented a statistically significant difference between the soil parameter datasets when an arbitrary or commonly used fuzziness exponent was used (e.g., φ = 1.30 or φ = 1.50). Soil sampling and laboratory analysis are tools of major significance for performing exploratory fuzzy analysis, and in addition, the FkM Xie and Benny’s index and the introduced fuzzy PoMZSA clustering metric are valuable tools for correctly delineating management zones.

1. Introduction

Water accounts for approximately 70% of our planet’s area [1,2,3], but just 2.5% is fresh water [4]. The Earth’s most confined freshwater resources are valued to be 35,000,000 km². Low proportions of these fresh water supplies are directly accessible to mankind in river bodies, reachable lakes and groundwater, soil moisture or precipitation [5]. Humanity is overusing the confined freshwater resources [3], resulting in water scarcity that endangers several regions of the world, with approximately 800 million humans not having adequate access to potable water and 2,500,000 million lacking appropriate sanitation, indicating that the problem is expected to intensify in the coming years [6]. Agriculture is the biggest freshwater user on Earth, absorbing almost two-thirds of overall withdrawals [3,7]. The agricultural segment represents 70% of Earth’s freshwater abstractions [3,8,9], 59% of overall freshwater usage in Europa (EU), and around 284,000 million m³ are pumped yearly in order to serve EU requirements [10]. Presently, many nations across the world are confronted with a shortage of fresh water [3,6,7,8,9,10,11,12] for drinking and irrigational purposes. Data analysis have revealed that climate change will have detrimental consequences for Earth’s water supplies, food productivity and yields, resulting in a high extent of inter-regional variation and deficit [13,14,15,16,17]. The global cropping productivity has considerably risen in the last century, boosting the irrigated land by a factor of almost six and raising the pressures on the irrigation water requirements [15].

The frantic rising and growing demand for the world’s diminishing water reserves and the continuously escalating consumption of agricultural products, the challenge of enhancing the effectiveness and capacity of irrigation water consumption by crops, guaranteeing the future security of food and crop commodities and addressing the ambiguities arising from climate change have never seemed so critical [18]. A promising way forward to relieve the growing worldwide water shortage could be to exploit existing irrigation water supplies (precipitation, surface and subsurface water and effluents) in a more viable, wise and eco-friendly manner [19,20,21,22,23].

The above objectives could be accomplished by optimizing farm, soil, irrigation and crop zones management. Precision agriculture (PA), management zones and deficit irrigation (DI) are agricultural and irrigation management practices that assist growers to increase the yield of their crops and optimize the effectiveness and capacity of water, soilbed, farm supplies and other inputs (pesticides, grains, manures, chemical fertilization products, etc.).

The PA industry is projected to increase from EUR 8.1 billion in 2022 to EUR 14.8 billion by 2030 as a result of the increasing acceptance of technologies like auto-steering, positioning systems (GPS), remote sensing, various sensors, GIS, agrodrones, PA software and smartphone apps and variable rate application (VRA) [19]. Variable deficit irrigation (VDI) or “regulated deficit irrigation” (RDI) and management zones are recognized as core components that help to enhance water usage efficiencies (WUE), soil and crop management and yields [3,19,20,21,22,23]. In PA, the most broadly applied interpolation model of the kriging method for predicting the spatial allocation pattern of soil, water and crop’s features is the ordinary kriging (OKr) interpolation model [3,14,19,21,23].

Furthermore, aromatic plants and spices sectors have been undergoing rapid expansion for many decades due to rising consumption in developing economies, in conjunction with growing recognition of the health and culinary virtues of aromatic plants and spices [14,24]. The global herb and spice market with miscellaneous products nowadays represents a multi-billion US dollar industry which is thriving thanks to global sales and the spread of production areas with a strong requirement for international standardization [24]. An extremely valuable aromatic herb-spice is coriander (Coriandrum sativum L.), which belongs to the Apiaceae (Umbellifera) family and is recognized as a plant indigenous to the Mediterranean countries, West Europa and Asia. It is also commonly mentioned as “cilantro”, while cultivated for its herbalism, which is utilized in various food recipes.

As far as cilantro’s soil moisture is concerned, it is the water content of the soil which is retained in the cavities among the soil particles. The presence of soil moisture is regarded as vital for the recycling of nutrients, a precondition for prime plant growth [3], so the hydraulic parameters of the soil that affect water movement, infiltration and moisture retention are regarded as key components to plant growth and should be considered as important factors to management zone delineation. In addition, soil moisture influences evapotranspiration, which is a fundamental mechanism in the climatic cycle and a link between the water, energy and carbon chains [9,11,14,18,19,25,26,27,28,29,30].

Conventional agricultural farming practice employs the entire-field management method, in which every farm field is managed as a homogeneous crop-area, and does not take into account the variability of soil chemical, granular and hydraulic parameters, field’s topography, local prevailing climatic conditions and land use practice. The various field inputs (irrigational water, fertilizers, agrichemicals, etc.) are evenly spread over the entire field. This management method is considered appealing to farmers because it is quite fast, and simple to implement, but it results in inefficient application of inputs, increased cultivation costs and various inherent environmental costs.

Any unspent soil nutrients that are not captured in the soil material are released into the environment through leaching, run-off and air emissions. Abusive application of fertilizers raises up the levels of soil and groundwater pollution and is a concealed cost to the community [31]. In addition, inadequate fertilizer application negatively affects crop growth and consequently yield. Tailored and spatially accurate nutrient practices can significantly decrease these agronomic, financial and environmental costs [3,9,11,20,21,22,23,26,27,28,29,32,33]. The precision agriculture methods have been employed by the farmers without realizing it for thousands of years.

The familiarization with their fields enabled farmers to detect distinct sites in a field that were consistently producing high or low yields [34]. In the past, but also nowadays, the agronomic experience is regarded by the farmers as the main component of farming management and yield success. Nevertheless, a far greater targeting approach could be applied by reducing soil variability by sorting a field into categories (zones) of wide homogeneity. These categories can be termed management zones (MZs) and can be utilized as a basis for proper agricultural decision-making.

The MZ can be described as a sub-area of a field that is sufficiently homogeneous in terms of soil-landscape characteristics [35]. Another definition according to Vrindts et al., 2005 [36] is that the MZs are designated as sub-areas of a field that have a fairly homogeneous mixture of yield constraint factors, for which a single factor of a particular crop input is adequate to achieve the highest efficiency of the farming inputs.

Therefore, many different zones within individual fields can be treated in spite of the existence of spatial variability in a number of yield-limiting drivers, and the correct delineation of MZs is one of the major factors in the effective implementation of farm inputs (water or wastewater, fertilizers, agrochemicals, etc.).

Regarding management zones delineation, using classification algorithms [37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53] is considered as an appropriate counterpart to correlation and regression. Soil data may be classified, together or apart from additional data, such as spectral or yield, to “cluster” these data into feasible management zones (MZs).

Towards this goal, grouping methods are widely adopted in precision agriculture, especially the fuzzy k-means algorithms and their variations [39,40,41,42,43,44,45,46,48,49,50,51]. The k-means algorithm presupposes that these different sources of spatial and other data are situated in a single location. Doing so frequently necessitates proper interpolation as a pretreatment stage, as data gathered at different time periods and/or with different measuring systems are infrequently collected at the same place.

Nevertheless, the benefits of fuzzy k-means algorithms are that they create classes (MZs) with a much better homogeneous performance in each MZ, which can be considered as functional management zones [48,49,50,51,52]. In reviewing many research studies on management zone delineation for various crops using fuzzy classification algorithms, it appears that most researchers for convenience use an arbitrary or commonly used fuzziness exponent, e.g., φ = 1.30 or φ = 1.50, without even considering to perform an exploratory fuzzy analysis to determine whether their classification is a correct or incorrect application to fuzzy management zone delineation. The most likely result of not applying the correct fuzziness exponent and the correct initial parameters to the fuzzy algorithm use is incorrect management clustering (zoning), which leads to further incorrect farm management and to drawing incorrect conclusions.

The objective of the present study was to research the various effects of correct and incorrect application of fuzziness exponent, initial parameterization and fuzzy classification algorithms modeling on homogeneous management zones delineation of a coriander (Coriandrum sativum L.) field using precision agriculture, soil chemical, granular and hydraulic data analyses, fuzzy k-means zoning algorithms, factor and PCA analysis and geostatistical soil nutrients mapping, aiming to be adopted as a correct management zone delineation protocol to the specific climate prevailing in Central Greece and in the areas around the Mediterranean. Adopting this MZs protocol, farmers can improve crop management and increase the yield of the picked seeds and the essential oil while maintaining the desired quality.

2. Materials and Methods

2.1. Study Area, Design of the Trial Plots, Management Zones, Irrigation and Variable Rate Application, Soil Sampling, Laboratory Soil and Hydraulic Analysis

Study area: This study was carried out on a farm located in the municipal unit of Krannonas of the Municipality of Kileler, in the valley “Thessaly” of the Central Greece Region. The climatic data for the study area were obtained from the local weather station. The area studied is dominated by a standard Mediterranean climate [3,9,11,14,21,23,26] with a mild autumn with medium to high precipitation, a cold winter with high precipitation, a mild spring with low to medium precipitation and a hot and dry summer with frequent hot temperatures and poor rainfall.

Soil samples of the plots after the laboratory analysis were found to be Sandy Clay Loam (SCL) soil [30,54]. The soil and crop data of the analysis were collected in two cultivation seasons from trial plots with a specific area of 0.055 ha.

Design of the trial plots, management zones, and soil laboratory analysis: The coriander’s experimental plot design was a plot sub-plot design with four management zones as de facto treatments (MZx where x = 1…4) obtained by a Fuzzy k-means clustering algorithm, with two irrigation sub-treatments [MZx-IR1: full drip irrigation (>90% of ${\theta }_{fc}$) where x = 1…4, MZx-IR2: variable deficit drip irrigation (60–75% of ${\theta }_{fc}$) where x = 1…4].

The overall cultivated area was 546.72 m². The area and dimensions of the 144 sub-plot units were 3.80 m² (1.70 m width × 2.23 m length). The dimensions and configuration of the 48 plots having 3 sub-plots each were designed in such a form that they are appropriate for the proper treatment of the management zones, the drip irrigation scheme, as well as the water purification system and the fertilization system, in order to achieve good application uniformity of irrigation water distribution and easier harvesting.

Effective coriander roots grow at 0–30 cm [14], at which point in a standard water extraction scheme the roots uptake approximately 90% of the soil moisture and the beneficial nutrients present in the soil-water solution.

Thus, to define the soil’s chemical, physical and hydraulic characteristics in the actual root zone (0–30 cm depth), a systematic sampling was conducted in the sub-plots’ units. A GPS (Global Positioning System) detector was employed to locate the positions of soil samples collected and then analyzed in the department’s applied soil science laboratory. The 144 soil samples were air-dried and sieved through a 2 mm grid to define the soil texture (clay, silt and sand contents) [30,54] using the Bouyoucos hydrometer method [55,56].

Soil pH was assessed in a 1:2 soil/water solution using a glass, H⁺ sensing (indicator) electrode paired with a reference electrode connected to a pH monitor meter.

The organic matter (OM) was assayed by chemical oxidation with 1 mol·L⁻¹ of K₂Cr₂O₇ and by titration of the residual reagent with 0.5 mol·L⁻¹ of FeSO₄ [29,30,57].

Soil inorganic nitrogen content was retrieved with 0.5 mol L⁻¹ of CaCl₂ and assessed by means of distillation in the presence of an MgO and Devarda alloy, correspondingly. Available phosphorus P (Olsen method) was retrieved with 0.5 mol L⁻¹ of NaHCO₃ and measured by spectroscopy [30]. The exchangeable forms of potassium K⁺ were extruded with 1 mol L⁻¹ of CH₃COONH₄ and quantified using a flame spectrophotometer.

The exchangeable magnesium Mg⁺⁺ and calcium Ca⁺⁺ cations were obtained by displacement of those elements from the soil colloids with ammonium (NH₄) by shaking the soil sample with 1.0 N ammonium acetate (NH₄OAc) adjusted to pH ‘7.0 with ammonium hydroxide (NH₄OH) and determined by atomic absorption spectrophotometer (AAS Spectroscopy Varian Spectra AA 10 plus, Victoria, Australia) using a flame and air-acetylene mixture [30,58]. The calcium carbonate was determined with a Bernard calcimeter. The assay consists of quantifying the CO₂ released when the sample is treated with 6N HCL. In a closed system, the quantity of CO₃²⁻ is directly proportional to the volumetric increase resulting from the release of the CO₂ [59,60].

The θ_fc (field capacity) and θwp (wilting point) were both obtained by the ceramic porous plate process, with 0.33 Atm for θ_fc and 15 Atm for θwp [3].

Dry bulk soil density was determined by weighting volumetric soil samples (taken with a 45 mm diameter hydraulic undisturbed soil core sampler) from the plots, that were dried at 105 °C for 48 h and then the results were estimated in dry soil g·cm⁻³ of the overall undisturbed soil bulk volume.

Planting period: The optimum period for planting the cilantro is the latter week of October to the early week of November [14,61]. So, the seeding for both years took place on the first week of November by application of 20 kg·ha⁻¹ of Cilantro (Coriandrum sativum var. microcarpum L.) seeds.

2.2. Farm Machines, Irrigation Pipeline System, Soil-Crop Management

The field was ploughed in early October in both cultivation seasons with a four-row reversible mounted plough. A row spring-steel tines cultivator (with inverting points and wheels with floating wings) was deployed into the plots soil in late October. This kind of cultivator is engineered to cultivate the soil between crop rows, aerating the topsoil, uprooting and destroying any existing weeds.

The irrigation pipeline system was composed of a header module with a hydro-cyclone, a screening water filter, a fertigation device, several fittings, a master water supply pipeline and main and secondary aluminum pipelines (Φ = 90 mm/16.21 bar), and drip polyethylene lateral pipes (Φ = 20 mm/6.08 bar) with integrated pressure compensation drippers. Finally, in both cultivation years the coriander plots were harvested in late June at the full maturity phase, when there were only brown colored fruits on plants.

2.3. Climate Data Sensors’ Readings, Net Irrigation Requirements; Reference, Crop, and Actual Evapotranspiration; Soil–Water–Crop–Atmosphere (SWCA) Model, Soil Moisture Depletion Model and the Water Stress Coefficient Ks-Weighted Average

Day-to-day climate inputs were acquired from sensor readings from a weather station located near the field. The monitored climate variables were temperature, relative humidity, atmospheric pressure, wind force, precipitation and solar radiation.

Net irrigation requirements (NIR) were computed by applying a day-to-day SWCA (soil-water-crop-atmosphere) model [3,14,18,19,26,32]. The effective precipitation was computed based on the USDA-SCS (1970) [62]. The reference evapotranspiration ETo was calculated according to the F.A.O. Penman-Monteith methodology [3,14,18,19,26,32].

The crop evapotranspiration (ETc) and the actual crop evapotranspiration (ETa) were computed according to the F.A.O. Penman-Monteith methodology [3,14,18,19,26,32].

The exhaustion of available moisture in the root zone was assessed by applying a day-to-day Available Soil Moisture Depletion model (ASMD) at field’s management zones scale [3,14,18,19,22,26]. The water stress coefficient Ks_{weighted ave} [19] for every coriander growth stage was calculated according to Filintas et al., 2022 [19]. A K_s coefficient score of 1 implies that plants are not subjected to water stress, while K_s < 1 implies plants are under water stress [18,19,26].

2.4. Statistical Data Analysis of Management Zones

Statistics analysis of the data and unbalanced one-way ANOVA were conducted using the statistics software IBM SPSS v.27 [3,14,19,26,32,63,64,65]. The outcomes reflect the averages of the sampled and measured datasets. The means were separated using the Tuckey and Games-Howell statistic tests as a control criterion when significantly different scores occurred (p = 0.05) between treatments (management zones) [3,19,26].

The descriptive statistics [64,65,66] (range, minimum, maximum, mean, standard deviation, variance, and coefficient of variation (CV)) were calculated and the Pearson correlation coefficient matrix [63,64,65] was computed on each dataset.

2.5. Data Preparation, Exploratory Geostatistics Analysis and Modelling, Spatial Interpolation Methods and Models Validation Measures

The sampled, measured and analyzed-in-the-lab soil data were digitized, modelled, geo-mapped in a GIS environment and stored in a digital geodatabase according to the samples’ locations and attributes.

To obtain the several GIS soil parameters variability maps of the plots (twenty parametric maps in total), spatial interpolation was applied using several ordinary kriging geostatistical models, in order to assess an approximate estimate of the unknown location rate, based on the observed values of soil parameters in the sample plots [3,9,14,19,21,23,26,29,32,37,57] using exploratory geospatial analyses, geostatistical analysis and modelling. Regarding the existence of a univariate pattern of normality, this can be verified graphically with the use of normal QQ plots and boxplots and numerically with the use of skewness and kurtosis statistic measures [63,66,67]. So, the next step in the analysis, was to check the chemical, granular and hydraulic data groups of the trial plots by using the normal QQ Plots, data boxplots, skewness and kurtosis statistic measures in order to clarify which datasets of soil properties had an abnormal distribution. After normalizing the distribution of data points, several semivariogram models were tested and evaluated from a library of mathematic models featuring spatial relationships, in the geostatistical modelling. To interpret the spatial variation of soil characteristics, semivariogram analysis and interpolation methods are mainly used.

There are many kriging interpolation methods. These methods consist of Simple Kriging, Cokriging, Ordinary Kriging, Universal Kriging and further spatial models [3,9,14,19,21,23,26,29,32,37,57,67,68,69,70,71,72,73,74,75,76]. The most broadly applied interpolation model of the kriging method for predicting the spatial allocation pattern of soil, water and crop’s features is the ordinary kriging (OKr) interpolation model [3,14,19,21,23,26,29,32,37,57,67,70,71,72,73,74,75,76]. In the Ordinary Kriging, spatial features and patterns of soil attributes related to further environmental components are not considered [76,77]. The kriging methodology is built on the presumptions that the parameters’ attribute rates (in our study: soil’s chemical, granular and hydraulic parameters, of the management zones) in the non-sampled areas of the plots are a well-weighted mean of the values in the sampled areas of the trial plots. The OKr is one of the most utilized kriging methods. In the field site X0 in which no sample was taken, the Z value of the soil or other parameter is estimated utilizing Formula (1):

$$Z_{\left(X0\right)}=\sum _{m=1}^n{\mathsf{\lambda }}_m{Z}_{\left(Xm\right)}$$

(1)

where $Z_{\left(X0\right)}$ = the value that is estimated by the OKr formula of the random variables (RV) Z at the unsampled site X0; λ_m = the n weights ranked to the site points $Z_{\left(Xm\right)}$.

The weights λ_m are equal to one to ensure unbiased conditioning and are obtained by minimizing the variance of the estimate. The random variables $Z_{\left(X\right)}$ can be split into 2 parts, that is, trend tr_(X) and residual R_(X) as it is defined in Formula (2):

$$Z_{\left(X\right)}={tr}_{\left(X\right)}+R_{\left(X\right)}$$

(2)

The OKr supposes data mean stationarity and assumes that the trend part tr_(X) is a fixed, but unidentified, value. The non-stationary constraints are obtained by restricting the stationarity to a locally located neighborhood and rolling it throughout the study field area. The residual part R_(X) is modeled as a constant random variable with zero mean and subject to the assumption of endogenous stationarity; its spatial dependence is specified by the semi-variance ${\gamma }_{\left(h\right)}$ by assuming a stationary mean tr_(X), given in Formula (3):

$${\gamma }_{\left(h\right)}=\frac{1}{2}E⌊{\{Z\left(x+h\right)-Z(x\left)\right\}}^2⌋$$

(3)

where h = an “approximate distance” that is implemented using a certain tolerance.

In order to explore and assess the spatial variability of soil parameters for the 144 subplots of the field, semivariograms were computed within the ordinary kriging interpolation method for each soil’s chemical, granular and hydraulic parameter. The twenty final precision agriculture field maps of soil’s chemical, granular and hydraulic parameter groups were modelled and developed using the best-fitted semivariogram models which described the spatial patterns of the various soil properties. In the present research, for each soil parameter dataset of the field subplots, seven semivariogram models were evaluated. These semivariogram models were Gaussian, Exponential, Stable, Pentaspherical, Tetraspherical, Spherical and Circular, mirroring the varying spatial variability induced by the nature of soil parameters, which was also associated with the field’s prevailing environmental conditions. The various model performances tested with the ordinary kriging methodology were evaluated employing cross-validation, calculation of statistical metrics (prediction errors) and model performance tests with training and validation data. Furthermore, the validity of the outputs of geostatistical models necessitates statistics analyses of residual errors, the differences that exist within the forecasted and the observable values, and the classification of the forecast among overestimates and underestimates. For this purpose, various statistical metrics outlined by previous studies [3,9,14,19,21,23,26,29,32,37,57] were employed. These statistical metrics are the MPE (mean prediction error), the RMSE (root-mean-square error), the MSPE (mean standardized prediction error) [3,9,14,19,21,23,26,29,32,37,57,78,79,80] as a metric of unbiased forecasts, the RMSSE (root-mean-square standardized error) as a benchmark for a proper assessment of the forecast variability [3,9,14,19,21,23,26,29,32,57,78,79,80] and ASE (average standard error) as a measure of the accuracy of the true population mean [3,26]. MSPE and RMSSE metrics were employed to evaluate unbiasedness and uncertainty, accordingly. MPE and MSPE metrics should approximate to zero value for an optimum forecast, RMSSE should be close to unity, the lower RMSE value the better for an optimum forecast and a lower ASE indicates higher accuracy of the model. Moreover, during the validation process, a model performance simulation with 1000 iterations was performed for each soil parameter dataset, in order to achieve the best fit of the training (50% of the entire dataset) and the validation (50% of the entire dataset) data, taking into account the average fit, the best R-square, the RMSE, etc.

2.6. Factor Analysis, Principal Components Analysis, Delination of Management Zones Using Fuzzy k-Means Clustering and Validation Measures

Prior to the delineation of management zones (MZs), correlation analysis (Pearson correlation) [3,63,65] was used to explore the correlation relationships between soil chemical, granular and hydraulic parameters. In multivariate statistics, factor analysis is a powerful explanatory mechanism that can be employed to uncover and explain relationships between interacting parameters or to examine assumptions [3,9,63,65]. In our case, firstly multivariate factor analysis and finally rotated (R-mode) factor analysis were performed to extract the factors (components) governing the soil’s chemical, granular and hydraulic parameters of the experimental field.

The R-mode multivariate factor analysis [9,63,65,81] was performed using as an extraction method the principal components analysis (PCA) [9,63,81] and as a rotation method the varimax method with Kaiser Normalization [3,9,63,65,81,82,83] by utilizing the measured and analyzed-in-the-lab data (soil’s chemical, granular and hydraulic parameters) on GIS parametric maps in order to extract the factors or components (management zones) of the experimental field. Principal components analysis was conducted to group the datasets of soil chemical, granular and hydraulic parameters in statistic components and generate linear independent variables which eliminate multicollinearity and provide a description of the spatial-temporal information obtained. The results of the PCA of each parameters’ group were plotted in an eigenvalue diagram, and in a three-dimensional (3D) component diagram (PCA 1, PCA 2 and PCA 3) in rotated space aiming to uncover and explain relationships graphically between the interacting soil parameters, and to show trends of soil data in rotated 3D space.

The field’s management zones optimal number was obtained based on factor and PCA R-mode analyses of the various soil parameter groups, eigenvalue diagrams, 3-D and 2-D component diagrams in rotated space and the realistic potential of management zones application in the trial plots pattern. Then, Fuzzy k-means clustering [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,84] was performed with the FuzME 3.5c software [49] and the Management Zone Analyst (MZA) 1.01 software [50] in order to cluster the soil parametric data into potential factors (MZs).

Firstly, grouping was carried out with soil’s chemical parameters data (“soil chemical group”), then with soil’s granular data (“soil granular group”), then with soil’s hydraulic parameters data (“soil hydraulic group”) and finally with all the soil chemical, granular and hydraulic parameters data. An exploratory Fuzzy k-means clustering [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,84] analysis was conducted to clarify which distance metric, fuzziness exponent φ and maximum iterations were best used with the available field soil data. Multiple runs of the software were performed in order to evaluate the results and select the best distance metric, fuzziness exponents φ and maximum iterations for further use in the analysis. The final step was termed the “soil All parameters” group data and was regarded as the “reference” for MZs maps. The output MZ map of the “soil All parameters” (20 parameters) data clustering was compared with the generated MZ maps clustered outputs of “soil All parameters” with various fuzziness exponents. The “soil chemical group” map (from a total of 8 soil parameters), the “soil granular group” map (from a total of 6 soil parameters) and the “soil hydraulic group” map (from a total of 6 soil’s hydraulic parameters) were compared with the generated MZ maps clustered outputs with various fuzziness exponents in order to determine the introduced fuzzy metric of the Percentage of Management Zones Spatial Agreement (PoMZSA) (%) between the reference (‘soil All parameters’) map and the rest of the MZ output goal (target) maps, i.e., the percentage of map cells which belong to the same clade in the reference map and the goal maps. This method gives a percentage approximation of the spatial correlation of each management zone of the goal map with the corresponding zone of the reference (‘soil All parameters’) map and the percentage of cells summation agreement of all the zones in the goal map give a percentage approximation of the spatial correlation of the compared maps. The metric of the Percentage of Management Zones Spatial Agreement (PoMZSA) (%) is presented in Formula (4):

$${\mathrm{P}\mathrm{o}\mathrm{M}\mathrm{Z}\mathrm{S}\mathrm{A}}_{\left(k\right)}=\sum _{\begin{array}{c}k=1,\\ l=1\end{array}}^{\begin{array}{c}n,\\ j\end{array}}{Cn}_{l,k}\times 100/\sum _{\begin{array}{c}k-ref=1,\\ l=1\end{array}}^{\begin{array}{c}n,\\ j\end{array}}{Cn}_{l,k-ref}$$

(4)

where ${Cn}_{l,k}$ = number of map cells belonging to each cluster (MZ) k in location l, in the goal (target) map that are in spatial agreement [classified in the same spatial cluster as the cell in location l of the reference (All parameter) map];

${Cn}_{l,k-ref}$ = number of cluster cells belonging to each cluster (MZ) k-ref in location l, in the reference (All parameter) map;

k = number of clusters (MZ), k = 1…n, n = maximum cluster (MZ) number of the goal (target) map;

k-ref = number of clusters (MZ), k-ref = 1…n, n = maximum cluster (MZ) number of the reference (All parameter) map;

l = number of cell locations, l = 1…j, j = maximum number of cell locations of the goal (target) map and of the reference (All parameter) map;

The unbalanced one-way ANOVA (Analysis of variance) [3,9,63] was applied to examine how adequately the variability of each soil parameter group is attributed to the different MZs maps of the specific soil groups. The management zones of the field were the de facto “treatments” and since they were not equal in magnitude, an unbalanced one-way ANOVA statistical analysis [3,9,63] was conducted and the outputs of R-squared and adjusted R-squared values were logged. The R-squared value depicts how effective the performance of the regression model is and how accurately it is predicting the output of the dependent variable. The adjusted R-squared reflects how much the addition of further predictors does or does not improve the regression model [3,26,63]. The significance threshold level (p-value) of the statistical analyses was set at 0.05 [3,9,26,63]. For every soil parameter, an individual statistical analysis was performed against the various soil’s group management zones goal maps utilizing the unbalanced one-way ANOVA statistical analysis [3,63,65,85].

3. Results and Discussion

3.1. Results of Climate Studied

In the last 10 years, the mean annual rainfall of the study area was 456.91 mm, the mean air temperature was 17.36 °C, the mean maximum air temperature was 30.10 °C, the maximum air temperature was 45.50 °C, the mean minimum air temperature was 7.39 °C and the minimum air temperature was −12.70 °C.

Considering the climate data recordings from the weather station during the two growing seasons (each growing season counted from November to June), the mean precipitation was 290.90 mm, the mean precipitation of the first and second growing seasons were 360.20 mm and 221.60 mm, respectively.

3.2. Results and Discussion of Soil’s Chemical, Granular and Hydraulic Analyses

The complete soil data analytics results as descriptive statistical measures [63,64] are reported in

Table 1. Descriptive statistics of soil chemical, granular and hydraulic parameters of the 144 subplots.

SN	Parameter	Range	Minimum	Maximum	Mean	Std. Deviation *	Variance	CV (%)
1	Phosphorus P-olsen (mg·Kg−1)	12.470	8.960	21.430	15.955	2.290	5.242	14.351
2	Potassium K (mg·Kg−1)	520.007	238.500	758.507	409.427	81.036	6566.865	19.793
3	Calcium Ca (mg·Kg−1)	2282.002	1190.841	3472.843	2236.163	427.379	182,653.088	19.112
4	Magnesium Mg (mg·Kg−1)	1775.510	1100.817	2876.327	1900.579	304.554	92,753.405	16.024
5	pH [1:2 soil/water solution]	0.680	7.450	8.130	7.820	0.095	0.009	1.220
6	Nitrogen inorganic (mg·Kg−1)	53.500	47.500	101.000	68.092	10.343	106.985	15.190
7	Organic matter (%)	2.743	1.327	4.070	1.790	0.331	0.109	18.489
8	Calcium carbonate CaCO3 (%)	3.853	0.366	4.219	1.572	0.827	0.684	52.581
9	Clay (size: <0.002 mm) (%)	6.540	22.180	28.720	24.832	1.131	1.279	4.553
10	Silt (size: 0.002–0.02 mm) (%)	8.700	13.610	22.310	19.664	1.694	2.870	8.615
11	Very fine sand (size: 0.02–0.2 mm) (%)	2.337	20.719	23.056	21.943	0.162	0.026	0.738
12	Sand pr (size: 0.2–2 mm) (%)	5.566	30.127	35.693	33.372	1.318	1.736	3.948
13	Gravel (%)	0.235	0.011	0.246	0.077	0.034	0.001	43.661
14	Soil Erodibility [Kfactor] (Mg·ha·h·ha−1·MJ−1·mm−1)	0.009	0.025	0.034	0.031	0.001	0.000	4.734
15	Wilting point θwp (m3·m−3)	4.607	13.365	17.972	15.981	0.672	0.451	4.204
16	Field capacity θfc (m3·m−3)	5.344	25.124	30.468	27.663	0.923	0.852	3.337
17	Saturation θsat (m3·m−3)	13.252	37.295	50.547	46.678	2.215	4.905	4.745
18	Plant available water PAW (cm·cm−1)	0.049	0.085	0.134	0.111	0.007	0.000	6.106
19	Sat. Hydraulic conductivity Ks (mm·hr−1)	18.283	4.656	22.939	16.275	4.226	17.855	25.964
20	Bulk density (g·cm−1)	0.351	1.311	1.662	1.415	0.055	0.003	3.904

Note: * Std. Deviation or SD = standard deviation of the data points.

. The soil properties of the experimental field differed widely (Table 1) and the closer examination of the outcome of the chemical, granular and hydraulic analysis of the soil in the laboratory showed that the field’s soil was appropriate for the growth of coriander [14,18,30,54]. Taking into account the chemical, granular and hydraulic analysis of the overall soil samples (144 in total), it was found that the average values of the examined properties varied from 0.031 (soil erodibility) to 2236.163 (Calcium Ca⁺⁺). The calcium Ca⁺⁺ (mg·Kg⁻¹), magnesium Mg⁺⁺ (mg·Kg⁻¹), potassium K⁺ (mg·Kg⁻¹), nitrogen inorganic (mg·Kg⁻¹), saturation θsat (m³·m⁻³), sand pr (size: 0.2–2 mm) (%) and field capacity θ_fc (m³·m⁻³) presented high average values (≥27.66), while the other attributes had low average values (<27.66).

Soil texture refers to the mixture of sand (sand pr (0.2–2 mm) + very fine sand (0.02–0.2 mm)), silt and clay, and affects nearly any aspect of soil management and especially tillage. Soil texture was classified as sandy clay loam (SCL) [3,18,26,30,54,86] with a low level of clay, a low level of silt and a high level of sand. It is noted that for the experimental plots, the mean soil texture consists of sand (Sand pr + Very fine sand) = 55.31% (±1.50), clay = 24.83% (±1.13) and silt = 19.66% (±1.69). Soil organic matter (OM) contents were classified as low to high level and varied from 1.327 to 4.070% with a mean OM of 1.79% (±0.33), which is regarded as a moderate OM level [3,29,30,57] indicating average structural conditions in soil and average structural stability. These results could be attributed to the high temperatures which occurred in spring and summer in the study area, the low vegetation cover and probably to the lack of organic fertilizer utilization. OM is broadly recognized as a fundamental element of soil fertility due to its significant contribution to the chemical, physical and biological activities that occur throughout the growing stages and provide plants with a variety of nutrients.

The mean pH at (1:2) soil–water extract was found to be 7.82 (±0.095) and it was categorized as alkaline. Soil’s pH is a metric of the concentration of hydrogen ions, and the optimal rate for cilantro is 7.0 [14]. This pH rate for cilantro is regarded as a well-tolerated limit [3,14].

The information majority on nitrogen fertility is addressed to agronomic crops. In principle, 112 to 336 mg·kg⁻¹ should be considered adequate for proper grass growth [86]. Over-supply of nitrogen causes a delay in ripening, triggers growth in turn, increases insect infestations and promotes diseases. The mean nitrogen inorganic of the plots was found to be 68.09 mg·kg⁻¹ (±10.34), which is characterized as a low to medium level of nitrogen [3,14,37]. An adequate amount for proper coriander growth would be 150 to 250 mg·kg⁻¹ [14]. It is necessary and environmentally friendly to implement nitrogen based on the needs of the crop in such a way as to minimize the residual soil nitrogen at the close of the growing season and ensure that there is minimal nitrogen left for losses.

The mean phosphorus P-Olsen of the plots was found to be 15.95 mg·kg⁻¹ (±2.29) (a moderate level [3,14,37]). Regarding phosphorus in soil, there is limited mobility and the risk of leaching phosphorus is not regarded as a concern [3,14,19,30,32,37].

The exchangeable potassium K⁺ of the plots reached high concentration levels with a mean of 409.43 mg·kg⁻¹ (±81.04). The mobilization of potassium in soils is at the intermediate level from nitrogen and phosphorus, but it is not leached out because it has a positive charge (K⁺), so it is attracted to the negatively charged colloids in the soil [3,14,30,32].

The mean calcium carbonate CaCO₃ of the plots was found to be 1.57% (±0.82), which is a medium level [3,30,32]. The mean calcium Ca⁺⁺ of the plots was found to be 2236.16 mg·kg⁻¹ (±427.38), which is a high level [3,30,32,86]. The mean magnesium Mg⁺⁺ of the plots was found to be 1900.58 mg·kg⁻¹ (±304.55), which in accordance with the clay percent content [clay = 24.83% (±1.13)] of the soil is considered as a high Mg⁺⁺ level [3,30,32,86].

The results of hydraulic analysis of the plots’ soil obtained: a mean field capacity θ_fc = 0.277 m³·m⁻³ (±0.0092), a mean wilting point θwp = 0.160 m³·m⁻³ (±0.0067), a mean saturation θsat = 0.467 m³·m⁻³ (±0.0221), a mean plant available water PAW = 0.111 cm·cm⁻¹ (±0.007) and a mean soil’s bulk density (bulk specific gravity) BD = 1.41 g·cm⁻¹ (±0.06), which is classified as a moderate level.

The hydraulic conductivity of the soil is helpful for forecasting water runoff from precipitation, drainage of soil’s root horizons, irrigation amounts and deep drainage, which is contributing to salinity [3,26,68,69]. The saturated hydraulic conductivity results of the plots were classified as slow to moderate level and varied from 4.66 to 22.94 mm·hr⁻¹ with a mean saturated hydraulic conductivity Ks = 16.27 mm·h⁻¹ (±4.23).

The mean soil erodibility of the field plots was found as Kfactor = 0.0306 Mg·ha·h·ha⁻¹·MJ⁻¹·mm⁻¹ (±0.0014), which is a moderate soil erodibility based on the USLE (Universal Soil Loss Equation) [26,57,87,88,89,90].

It is remarked that the experimental plot results for θ_fc and θwp obtained from the hydraulic analysis of the soil are within the normal limits given by Allen et al. (1998) [18].

Soil properties variability as a number is depicted by the coefficient of variation (CV) and it is categorized into three main classes [91]:

(a)

Low coefficient of variation (CV < 15%);

(b)

Moderate coefficient of variation (CV = 15–35%);

(c)

High coefficient of variation (CV > 35%).

In the present study, the coefficient of variation differed from variable to variable and varied from 0.738 to 52.581% between all soil properties. The CV percentages revealed that the variability classification attributed twelve out of twenty examined soil properties as low class (CV < 15%) ranging from 0.738 to 14.351% (Table 1). The nitrogen inorganic (mg·Kg⁻¹), magnesium Mg⁺⁺ (mg·Kg⁻¹), organic matter (%), calcium Ca⁺⁺ (mg·Kg⁻¹), potassium K⁺ (mg·Kg⁻¹) and saturated hydraulic conductivity Ks (m·hr⁻¹) were classified as moderate CV class (CV = 15–35%) ranging from 15.190 to 25.964%.

Finally, the CV percentages of the gravel content (%) and the calcium carbonate CaCO₃ (%) were ranging from 43.661 to 52.581% and resulted as high CV class (CV > 35%) (Table 1). Anthropogenic and/or environmental drivers, like farming management, soil texture, soil chemical, granular and hydraulic properties, soil processes and climate change effects could potentially all be contributors to the moderate and high variability of the above-mentioned parameters (eight out of twenty examined soil properties) of the experimental plots.

3.3. Results and Discussion of Exploratory Data and Correlations Analysis of Soil’s Chemical, Granular and Hydraulic Parameters

Prior to geostatistical modelling an exploratory data and correlation analysis had to be performed. Two important statistic measures of the examined soil properties in the experimental plots are skewness and kurtosis [63]. Skewness is a statistic metric employed to indicate if a data distribution is asymmetric, and points in the direction of possible outliers [63,65,92]. The statistic measure of skewness was varied positively (right-tailed skewness) from 0.240 to 2.860 for the following soil properties (in ascending order): nitrogen inorganic (mg·Kg⁻¹), field capacity θ_fc (m³·m⁻³), clay (%), calcium carbonate CaCO₃ (%), calcium Ca⁺⁺ (mg·Kg⁻¹), magnesium Mg⁺⁺ (mg·Kg⁻¹), gravel content (%), potassium K⁺ (mg·Kg⁻¹), bulk density (g·cm⁻¹) and organic matter (%).

On the contrary, skewness was varied negatively (left-tailed skewness) from −1.837 to −0.111 for the following soil properties (in ascending order): saturation θsat (m³·m⁻³), silt (%), plant available water PAW (cm·cm⁻¹), saturated hydraulic conductivity Ks (m·hr⁻¹), very fine sand (size: 0.02–0.2 mm) (%), sand pr (size: 0.2–2 mm) (%), soil erodibility (Mg·ha·h·ha⁻¹·MJ⁻¹·mm⁻¹), phosphorus P-Olsen (mg·kg⁻¹), wilting point θwp (m³·m⁻³) and pH (-). After evaluating the skewness and kurtosis scores, a similarly occurring outcome for both statistic measures indicated that eight out of a total of twenty parametric datasets of soil chemical, granular and hydraulic properties needed to be transformed to normalize their distribution before applying the geostatistical modelling [92]. The above outcomes pointed out that these datasets of soil properties had an abnormal distribution [63,66,92]. Taking into consideration the above findings, these datasets were transformed employing a logarithmic transformation [66,92]. These eight transformed parametric datasets were calcium Ca (mg·Kg⁻¹), magnesium Mg (mg·Kg⁻¹), gravel (%), potassium K (mg·Kg⁻¹), organic matter (%), bulk density (g·cm⁻¹), nitrogen inorganic (mg·Kg⁻¹) and soil erodibility [Kfactor] (Mg·ha·h·ha⁻¹·MJ⁻¹·mm⁻¹).

The relations between soil characteristics of the chemical, granular and hydraulic data groups were investigated through exploratory correlation analysis. The correlation coefficients (Pearson correlation) among the examined soil characteristics of the chemical group parameters are presented in

Table 2. Statistical results of correlation coefficients (Pearson correlation) matrix of soil’s chemical group parameters.

SN	Parameter	Phosphorus P-Olsen	Potassium K+	Calcium Ca++	Magnesium Mg++	pH	Nitrogen Inorganic	Organic Matter	Calcium Carbonate CaCO3
1	Phosphorus P-olsen	1	0.281 **	0.145	0.202 *	0.011	−0.234 **	0.145	0.400 **
2	Potassium K+	0.281 **	1	−0.047	−0.054	−0.421 **	−0.253 **	0.724 **	0.266 **
3	Calcium Ca++	0.145	−0.047	1	0.953 **	0.470 **	0.241 **	−0.117	0.540 **
4	Magnesium Mg++	0.202 *	−0.054	0.953 **	1	0.491 **	0.217 **	−0.158	0.548 **
5	pH [1:2 soil/water solution]	0.011	−0.421 **	0.470 **	0.491 **	1	0.613 **	−0.269 **	0.428 **
6	Nitrogen inorganic	−0.234 **	−0.253 **	0.241 **	0.217 **	0.613 **	1	0.062	0.340 **
7	Organic matter	0.145	0.724 **	−0.117	−0.158	−0.269 **	0.062	1	0.286 **
8	Calcium carbonate CaCO3	0.400 **	0.266 **	0.540 **	0.548 **	0.428 **	0.340 **	0.286 **	1

Notes: **. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed).

. Phosphorus P-olsen has a significant positive correlation at the 0.01 level (2-tailed) with calcium carbonate CaCO₃, potassium K⁺ and at the 0.05 level (2-tailed) with magnesium Mg⁺⁺, while having significant negative correlation at the 0.01 level (2-tailed) with nitrogen inorganic.

The potassium K⁺ shows a significant positive correlation at the 0.01 level (2-tailed) with organic matter, calcium carbonate CaCO₃ and phosphorus P-olsen, while having significant negative correlation at the 0.01 level (2-tailed) with pH and nitrogen inorganic.

Calcium Ca shows a significant positive correlation at the 0.01 level (2-tailed) with magnesium Mg⁺⁺, calcium carbonate CaCO₃, pH and nitrogen inorganic. Magnesium Mg⁺⁺ presents a significant positive correlation at the 0.01 level (2-tailed) with calcium Ca⁺⁺, calcium carbonate CaCO₃, pH and nitrogen inorganic, and at the 0.05 level (2-tailed) with phosphorus P-olsen.

Additionally, the pH shows a significant positive correlation at the 0.01 level (2-tailed) with nitrogen inorganic, magnesium Mg⁺⁺, calcium Ca⁺⁺ and calcium carbonate CaCO₃, while having significant negative correlation at the 0.01 level (2-tailed) with Potassium K⁺ and organic matter.

Nitrogen inorganic presents a significant positive correlation at the 0.01 level (2-tailed) with pH, calcium carbonate CaCO₃, calcium Ca⁺⁺, and magnesium Mg⁺⁺, while having significant negative correlation at the 0.01 level (2-tailed) with potassium K⁺ and phosphorus P-olsen.

Organic matter shows a significant positive correlation at the 0.01 level (2-tailed) with potassium K⁺ and calcium carbonate CaCO₃, while having significant negative correlation at the 0.01 level (2-tailed) with pH.

Finally, calcium carbonate CaCO₃ presents a significant positive correlation at the 0.01 level (2-tailed) with magnesium Mg⁺⁺, calcium Ca⁺⁺, pH, phosphorus P-olsen, nitrogen inorganic, organic matter and potassium K⁺.

The correlation coefficients (Pearson correlation) among the examined soil characteristics of the granular group parameters are presented in

Table 3. Statistical results of correlation coefficients (Pearson correlation) matrix of soil’s granular group parameters.

SN	Parameter	Clay	Silt	Sand pr	Very Fine Sand	Gravel	Soil Erodibility [Kfactor]
1	Clay	1	−0.508 **	−0.650 **	−0.493 **	−0.203 *	0.693 **
2	Silt	−0.508 **	1	−0.182 *	−0.079	0.400 **	−0.594 **
3	Sand pr	−0.650 **	−0.182 *	1	0.595 **	−0.058	−0.335 **
4	Very fine sand	−0.493 **	−0.079	0.595 **	1	0.137	−0.318 **
5	Gravel	−0.203 *	0.400 **	−0.058	0.137	1	−0.301 **
6	Soil Erodibility [Kfactor]	0.693 **	−0.594 **	−0.335 **	−0.318 **	−0.301 **	1

Notes: **. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed).

.

Clay at the 0.01 level (2-tailed) presents significant positive correlation with soil erodibility [Kfactor] (Mg·ha·h·ha⁻¹·MJ⁻¹·mm⁻¹) and significant negative correlation with sand pr (size: 0.2–2 mm) (%), silt (size: 0.002–0.02 mm) (%), very fine sand (size: 0.02–0.2 mm) (%) and gravel (%). Silt (size: 0.002–0.02 mm) (%) at the 0.01 level (2-tailed) presents significant positive correlation only with gravel (%), and significant negative correlation with soil erodibility [Kfactor] (Mg·ha·h·ha⁻¹·MJ⁻¹·mm⁻¹), clay (size: <0.002 mm) (%) and at the 0.05 level (2-tailed), significant negative correlation with sand pr (size: 0.2–2 mm) (%).

Considering that the sum of the four fractional parts (clay, silt, sand pr and very fine sand) of soil particles is equal to a constant number (100%), they are related in inverse proportion to each other except sand pr and very fine sand. Therefore, it was an expected outcome that sand pr (size: 0.2–2 mm) (%) and very fine sand (size: 0.02–0.2 mm) (%) were found to be negatively correlated with clay (%) and silt (%).

Finally, soil erodibility [Kfactor] (Mg·ha·h·ha⁻¹·MJ⁻¹·mm⁻¹) at the 0.01 level (2-tailed) presents significant positive correlation only with clay (size: <0.002 mm) (%), and significant negative correlation with all the other parameters (silt, sand pr, very fine sand and gravel).

The correlation coefficients (Pearson correlation) among the examined soil characteristics of the hydraulic group parameters are presented in

Table 4. Statistical results of correlation coefficients (Pearson correlation) matrix of soil’s hydraulic group parameters.

SN	Parameter	Wilting Point θwp	Field Capacity θfc	Saturation θsat	Plant Available Water PAW	Saturated Hydraulic Conductivity Ks	Bulk Density BD
1	Wilting point θwp	1	0.720 **	−0.174 *	−0.218 **	−0.604 **	0.201 *
2	Field capacity θfc	0.720 **	1	0.476 **	0.395 **	−0.060	−0.460 **
3	Saturation θsat	−0.174 *	0.476 **	1	0.867 **	0.825 **	−0.991 **
4	Plant available water PAW	−0.218 **	0.395 **	0.867 **	1	0.768 **	−0.866 **
5	Saturated Hydraulic conductivity Ks	−0.604 **	−0.060	0.825 **	0.768 **	1	−0.825 **
6	Bulk density BD	0.201 *	−0.460 **	−0.991 **	−0.866 **	−0.825 **	1

Notes: **. Correlation is significant at the 0.01 level (2-tailed). *. Correlation is significant at the 0.05 level (2-tailed).

. Field capacity θ_fc at the 0.01 level (2-tailed) presents significant positive correlation with wilting point θwp, saturation θsat and plant available water PAW, while having a significant negative correlation with bulk density BD, which is a logical outcome. Saturation θsat at the 0.01 level (2-tailed) presents significant positive correlation with plant available water PAW, saturated hydraulic conductivity Ks and field capacity θ_fc, while having a significant negative correlation with bulk density BD (0.01 level (2-tailed)) and θwp (0.05 level (2-tailed)). Plant available water PAW at the 0.01 level (2-tailed) presents significant positive correlation with saturation θsat, saturated hydraulic conductivity Ks and field capacity θ_fc, while having a significant negative correlation with bulk density BD and wilting point θwp.

Data transforms were implemented to the chemical, granular and hydraulic group soil parameter datasets that had an abnormal distribution, to verify that their datapoints were normally distributed, and that the assumption of variance equality of the data values was satisfied. Among the tested data transforms, the logarithmic transform was implemented in order to achieve normal datapoints distribution for those datasets that presented scatter datapoints far away from the diagonal line of the normal QQ Plot, high value outliers in boxplots, high skewness and abnormal kurtosis [92]. Examples of soil parameters datasets that had an abnormal distribution are Nitrogen inorganic and potassium K⁺. Their normal QQ Plot diagrams and Boxplot diagrams are presented in Figure 1a–d.

Out of a total of twenty parametric datasets of soil chemical, granular and hydraulic properties, the logarithmic transformation was applied only to eight datasets. These eight transformed parametric datasets were calcium Ca (mg·Kg⁻¹), magnesium Mg (mg·Kg⁻¹), gravel (%), potassium K (mg·Kg⁻¹), organic matter (%), bulk density (g·cm⁻¹), nitrogen inorganic (mg·Kg⁻¹) and soil erodibility [Kfactor] (Mg·ha·h·ha⁻¹·MJ⁻¹·mm⁻¹).

3.4. Results and Discussion of Precision Agriculture Geostatistical Modelling of Soil’s Chemical, Granular and Hydraulic Parameters

In agroecosystems, the geostatistical analysis and modelling are importantly implemented to assess the spatial variability of various soil characteristics [3,14,19,21,23,26,29,32,37,57,68,69]. The choice of the kriging model to be applied is dictated by the properties and statistic measures of the data and the preferred spatial model [3,14,19,21,23,26,29,32,37,57,67,70,71,72,73,74,75,76]. The Ordinary Kriging is a spatial forecasting method which decreases the remaining variance [93]. The OKr modelling method was used to predict the soil characteristic parameters for the non-sample areas [3,14,19,23,26,29,32,37,57,66,94] of the experimental plots. This geostatistical method, due to its straightforwardness and preciseness [67], was employed in the present research. The plots design pattern with their number (pn = 1…48) and the subplots pattern with the subplots’ number (sn = 1…144) used in the present study are presented in precision agriculture plot maps of the results on soil nitrogen inorganic (N-in) (Figure 2a) and potassium K⁺ (Figure 2b), respectively.

In Figure 2c,e are depicted the diagrams of Nitrogen inorganic Model and Potassium K⁺ Model, respectively. Additionally, in Figure 2d,f are depicted the Normal QQ Plots of Nitrogen inorganic with Log transformation and Potassium K⁺ with Log transformation, respectively. The modelled precision agriculture spatial variability maps of the soil’s “Chemical Group” parameters are depicted in the various resulted final maps in Figure 3a–h. The created precision agriculture’s spatial variability maps of soil “Chemical Group” parameters uncovered that inorganic nitrogen, pH and calcium carbonate CaCO₃ were similar in their spatial variability across the field plots. Such consistent spatial variability occurs because those soil attributes are associated with each other (at the 0.01 level) and have high (r_pH = 0.613) and moderate (r_CaCO3 = 0.340) positive correlations. In addition, the southwestern and northeastern parts of the precision agriculture’s spatial variability maps of nitrogen inorganic (Figure 3a), pH (Figure 3f) and calcium carbonate CaCO₃ (Figure 3h) showed the highest values of these parameters, while the central-northern and central-southern regions showed the lowest, and the northern part, in the case of calcium carbonate CaCO₃.

Likewise, the modelled PA spatial variability maps revealed that organic matter (Figure 3g) and potassium K⁺ (Figure 3e) had matching spatial variability patterns throughout the field plots area, possibly because they are associated with each other (at the 0.01 level) and have high (r = 0.724) positive correlation. The created PA’s spatial variability maps of soil magnesium Mg⁺⁺ (Figure 3d) presented an almost identical pattern (r = 0.953) of spatial variability with the calcium Ca⁺⁺ (Figure 3b), a relatively high similarity (r = 0.548) with calcium carbonate CaCO₃ (Figure 3h), and was partly similar (r = 0.491) to the pH (Figure 3f) pattern. The generated PA’s spatial variability map of soil calcium carbonate CaCO₃ (Figure 3h) depicted a relatively highly similar spatial variability pattern with the magnesium Mg⁺⁺ (r = 0.548) and calcium Ca⁺⁺ (r = 0.540), and a moderately similar spatial variability pattern with pH (r = 0.428) and phosphorus P-olsen (r = 0.400) in Figure 3c.

An agronomist can be greatly assisted in recognizing and locating field sites of low, medium and high soil fertility by studying and analyzing the precision agriculture’s spatial variability maps of soil “Chemical Group” parameters and comprehending the effect of each parameter on crop growth.

The accurate prediction of these soil parameters is, therefore, driven by the presence of spatial dependence among the plots sample observations, as estimated by the correlogram or semivariogram [67,94].

The modelled precision agriculture spatial variability maps of the soil’s “Granular Group” parameters are depicted in the various resulted final maps in Figure 4a–f. The created precision agriculture’s spatial variability maps of soil “Granular Group” parameters uncovered that the sand fraction (size: 0.2–2 mm) and the very fine sand fraction (size: 0.02–0.2 mm) were similar in their spatial variability across the field plots. Such consistent spatial variability occurs because these two soil attributes are strongly associated with each other by nature and have high positive correlation (r = 0.595) at the 0.01 level (2-tailed).

Furthermore, the spatial variability of sand (size: 0.2–2 mm) was in contrast to the variability of clay (size: <0.002 mm) and silt (size: 0.002–0.02 mm) due to their inversely related nature, with an increase in one decreasing the content in the other. Likewise, the modelled granular PA spatial variability maps revealed that soil’s silt content map (Figure 4e) had a moderately similar spatial variability pattern with the gravel content map (Figure 4f) pattern associated with each other (at the 0.01 level) with a positive correlation (r= 0.400).

The generated PA’s spatial variability map of soil erodibility [Kfactor] (Figure 4d) depicted a relatively highly similar spatial variability pattern with the clay fraction (size: <0.002 mm) associated with each other (at the 0.01 level) with a positive correlation (r = 0.693).

On the contrary, soil erodibility [Kfactor] presented low to moderate negative correlational patterns with the sand (size: 0.2–2 mm) pattern (r = −0.335), very fine sand (size: 0.02–0.2 mm) pattern (r = −0.318) and gravel (r = 0.301), and a relatively high negative correlational pattern with silt (r = −0.594).

The various modelled PA spatial variability maps of soil’s “Hydraulic Group” parameters are depicted in Figure 5a–f. The generated PA’s spatial variability map of saturation θsat (Figure 5a) depicted a highly congruent spatial variability pattern with the plant available water PAW (Figure 5b) map pattern (r = 0.867), and with saturated hydraulic conductivity Ks (Figure 5d) map pattern (r = 0.825), whereas it presented a highly negative correlation (r = −0.991) similar pattern with soil’s bulk density (Figure 5f).

The created field capacity θ_fc (Figure 5c) spatial variability map depicted a relatively highly similar spatial variability pattern with the wilting point θwp (Figure 5e) map pattern, associated with each other (at the 0.01 level) with a positive correlation (r = 0.720). It also presented a negative correlation (r = −0.460), moderately similar spatial variability pattern with soil’s bulk density map (Figure 5f).

The developed PA’s spatial variability map of plant available water PAW (Figure 5b) presented a highly congruent spatial variability pattern with the saturation θsat (Figure 5a), and with a saturated hydraulic conductivity Ks (Figure 5d) map pattern (r = 0.768), whereas it presented a highly similar negative correlation (r = −0.866) pattern with soil’s bulk density (Figure 5f).

The produced saturated hydraulic conductivity Ks spatial variability map (Figure 5d) depicted a highly similar spatial variability pattern with the saturation θsat (Figure 5a) map pattern (r = 0.825), and the plant available water PAW (Figure 6b) map pattern (r = 0.768). On the contrary, it presented a highly similar negative correlation (r = −0.866) pattern with soil’s bulk density (Figure 5f), and with the wilting point θwp (Figure 5e) map pattern (r = −0.604).

The developed twenty precision agriculture field maps of soil’s chemical, granular and hydraulic parameter groups (Figure 2, Figure 3, Figure 4 and Figure 5) illustrate the spatial variability of each soil parameter, identifying which field’s plots and subplots are appropriate for cropping without major restrictions and which ones need cautious management. Therefore, these modelled PA maps depict precisely the soil attributes spatial variability of the field and can be utilized on site-specific management zones farming.

3.5. Results and Discussion of Best-Fitted Semivariogram Models, Spatial Dependence of Soil’s Chemical, Granular and Hydraulic Parameters, and Models Cross-Validation

For the best-fitted semivariogram models, their range, nugget, partial sill, sill, nugget to sill ratio (N:S ratio) and spatial dependence modelling results of soil’s chemical, granular and hydraulic parameters of the studied field plots are presented in

Table 5. Best-fitted semivariogram models, their modelling parameters and spatial dependence of chemical, granular and hydraulic parameters of the studied field plots.

SN	Parameter	Model	Range (m)	Nugget (C0)	Partial Sill (C)	Sill (C0 + C)	N:S Ratio	Spatial Dependence
1	Phosphorus P-olsen	Gaussian	19.1587	1.6796	4.4169	6.0965	0.2755	Medium
2	Potassium K	Circular	8.3288	0.0037	0.0301	0.0338	0.1096	Strong
3	Calcium Ca	Exponential	25.4364	0.0003	0.0384	0.0387	0.0069	Strong
4	Magnesium Mg	Exponential	61.7036	0.0030	0.0360	0.0390	0.0774	Strong
5	pH [1:2 soil/water solution]	Exponential	38.6096	0.0001	0.0110	0.0111	0.0090	Strong
6	Nitrogen inorganic	Exponential	39.8639	0.0001	0.0341	0.0342	0.0029	Strong
7	Organic matter	Exponential	25.1485	0.0005	0.0345	0.0350	0.0149	Strong
8	Calcium carbonate CaCO3	Gaussian	16.5986	0.0745	0.7586	0.8332	0.0895	Strong
9	Sand	Pentaspherical	34.9317	0.3900	1.8638	2.2538	0.1730	Strong
10	Silt	Exponential	11.0822	0.7449	1.1814	1.9263	0.3867	Medium
11	Clay	Pentaspherical	61.7036	0.1000	1.9934	2.0934	0.0478	Strong
12	Very fine sand	Exponential	6.4629	0.0006	0.0262	0.0268	0.0235	Strong
13	Gravel	Spherical	20.6936	0.1267	0.1415	0.2682	0.4724	Medium
14	Soil Erodibility (K factor)	Exponential	4.8323	0.0008	0.0003	0.0011	0.7555	Weak
15	Wilting point θwp	Gaussian	41.6026	0.1340	0.6104	0.7444	0.1800	Strong
16	Field capacity θfc	Circular	25.7388	0.1799	0.9026	1.0825	0.1662	Strong
17	Saturation θsat	Gaussian	13.3309	1.0133	4.3668	5.3801	0.1883	Strong
18	Plant available water PAW	Circular	11.9197	0.00001	0.00004	0.00005	0.1323	Strong
19	Sat. Hydraulic conductivity Ks	Circular	17.8573	0.0075	0.1143	0.1217	0.0614	Strong
20	Bulk density	Exponential	18.9880	0.0001	0.0033	0.0034	0.0292	Strong

.

Based on the modelling results presented in Table 5, the best-fitted semivariogram models found for the chemical parameters group were the Gaussian, Circular and Exponential. The Gaussian model was found to be the best-fitted semivariogram model for a quarter (25.00%) of the group’s parameters, i.e., phosphorus P-olsen (Figure 3c) and calcium carbonate CaCO₃ (Figure 3h). The Exponential model was found to be the best-fitted semivariogram model for 62.50% of the group’s total parameters, i.e., nitrogen inorganic (Figure 3a), calcium Ca⁺⁺ (Figure 3b), magnesium Mg⁺⁺ (Figure 3d), pH (Figure 3f) and organic matter (Figure 3g).

Finally, the Circular model was found to be the best-fitted semivariogram model only for 12.50% of the group’s total parameters, i.e., only for potassium K⁺ (Figure 3e). Based on the modelling results presented in Table 5, the best-fitted semivariogram models found for the granular parameters group were the Pentaspherical, Exponential and Spherical.

The Pentaspherical model was found to be the best-fitted semivariogram model for 33.33% of the group’s total parameters, i.e., sand content (Figure 4a) and clay content (Figure 4b). The Exponential model was found to be the best-fitted semivariogram model for 50.00% of the group’s total parameters, i.e., silt content (Figure 4c), very fine sand content (Figure 4d) and soil erodibility K factor (Figure 4e). Finally, the Spherical model was found to be the best-fitted semivariogram model only for 16.67% of the group’s total parameters, i.e., soil’s gravel content (Figure 4f).

Based on the modelling results presented in Table 5, the best-fitted semivariogram models found for the hydraulic parameters group were the Gaussian, Circular and Exponential. The Gaussian model was found to be the best-fitted semivariogram model for 33.33% of the group’s total parameters, i.e., saturation θsat (Figure 5a) and wilting point θwp (Figure 5e). The Circular model was found to be the best-fitted semivariogram model for 50.00% of the group’s total parameters, i.e., field capacity θ_fc (Figure 5c), plant available water PAW (Figure 5b) and saturated hydraulic conductivity Ks (Figure 5d). Finally, the Exponential model was found to be the best-fitted semivariogram model only for 16.67% of the group’s total parameters, i.e., soil’s bulk density (Figure 5f).

In addition, the range values exhibited significant variability between the measured parameters fluctuating from 4.83 m (Soil Erodibility) to 61.70 m (magnesium Mg⁺⁺ and clay), which indicates a spatial affinity that can connect different spatial entities on the parametric map.

Taking into consideration the modelling results presented in Table 5 and the criterion that the N:S ratio is a metric of the parameters’ spatial dependence, much of the change in variance of the 20 overall parameters of the chemical, granular and hydraulic parameter groups is integrated spatially. According to [94], the N:S designates discrete categories of the soil parameters’ spatial dependence. An N:S ratio ≤ 0.25 designates the parameter to the strong class of spatial dependence, an N:S ratio that is within the range 0.25 to 0.75 designates the parameter to the medium class of spatial dependence and an N:S ratio ≥ 0.75 designates the parameter to the weak class of spatial dependence.

The modelling results of soil’s chemical parameters group revealed strong spatial dependence among nitrogen inorganic (Figure 3a), calcium Ca⁺⁺ (Figure 3b), magnesium Mg⁺⁺ (Figure 3d), potassium K⁺ (Figure 3e), pH (Figure 3f), organic matter (Figure 3g) and calcium carbonate CaCO₃ (Figure 3h), and medium spatial dependence of phosphorus P-olsen (Figure 3c).

The modelling results of soil’s granular parameters group identified strong spatial dependence among sand content (Figure 4a), clay content (Figure 4c) and very fine sand content (Figure 4b), whereas medium spatial dependence was attributed to silt content (Figure 4e) and gravel content (Figure 4f).

In addition, weak spatial dependence was assigned only to soil erodibility K factor (Figure 4d). Exogenous alterations, such as conventional soil tillage, fertilizer applications and intrinsic variations such as clay and organic matter content may control the variability of this weak spatially dependent parameter. The modelling results of soil’s hydraulic parameters group revealed strong spatial dependence among all the hydraulic group parameters [saturation θsat (Figure 5a), field capacity θ_fc (Figure 5c), wilting point θwp (Figure 5e), plant available water PAW (Figure 5b), saturated hydraulic conductivity Ks (Figure 5d) and soil’s bulk density (Figure 5f)]. Taking into consideration the 20 overall soil parameters, 80.00% of the analyzed soil parameters exhibited strong spatial dependence, 15.00% presented medium spatial dependence, and only 5.00% was attributed to weak spatial dependence. Semivariogram models designated a strong spatial dependence to 16 out of the 20 overall soil parameters examined. Parameters that are classified to strong spatial dependence may be driven by intrinsic variations in soil properties, such as textures and minerals [94]. In order to check the performances and the validity of the outputs of the various geostatistical models, required were statistics analyses of residual errors, the differences that exist within the forecasted and the observable values and the classification of the forecast among overestimates and underestimates. MSPE and RMSSE metrics were employed to evaluate unbiasedness and uncertainty, accordingly. Lower MSPE values indicate that the predicted values of soil parameters are closer to the estimated. MPE and MSPE metrics should approximate to zero value for an optimum forecast, RMSSE should be close to unity, the lower RMSE value the better for an optimum forecast and a lower ASE indicates higher accuracy of the model.

In the ongoing research, the models that generated the best results were selected, characterized as the best-fitted semivariogram models and are presented in

Table 6. Modelling validation results of prediction errors for soil’s chemical, granular and hydraulic parameters of the plots.

SN	Parameter	Model	MPE	RMSE	MSPE	RMSSE	ASE
1	Phosphorus P-olsen	Gaussian	0.00648	1.31122	0.00232	0.91665	1.42204
2	Potassium K	Circular	−0.03741	51.16382	0.01199	0.98210	48.91566
3	Calcium Ca	Exponential	3.26177	134.16611	0.03086	0.67445	212.20118
4	Magnesium Mg	Exponential	−0.59038	137.54021	0.00512	0.86182	161.58264
5	pH [1:2 soil/water solution]	Exponential	0.00014	0.02740	0.00242	0.67115	0.03993
6	Nitrogen inorganic	Exponential	0.06161	4.20908	0.01265	0.82269	4.76968
7	Organic matter	Exponential	−0.00189	0.22948	−0.01692	1.25388	0.16409
8	Calcium carbonate CaCO3	Gaussian	−0.00038	0.29917	−0.00057	0.94818	0.31009
9	Sand	Pentaspherical	−0.00223	0.87267	−0.00224	1.06389	0.81605
10	Silt	Exponential	−0.01460	1.16042	−0.01170	0.95974	1.20448
11	Clay	Pentaspherical	0.00294	0.52318	0.00484	1.05010	0.49190
12	Very fine sand	Exponential	−0.00114	0.15055	−0.00802	1.07931	0.13837
13	Gravel	Spherical	0.00057	0.03041	−0.01923	1.00337	0.03430
14	Soil Erodibility (K factor)	Exponential	−0.00001	0.00106	−0.01127	1.02658	0.00104
15	Wilting point θwp	Gaussian	−0.00479	0.39571	−0.01089	1.00732	0.39309
16	Field capacity θfc	Circular	0.00003	0.50707	−0.00157	0.90904	0.55344
17	Saturation θsat	Gaussian	0.02077	1.03674	0.01423	0.88580	1.14763
18	Plant available water PAW	Circular	0.00011	0.00386	0.02377	0.93844	0.00408
19	Sat. Hydraulic conductivity Ks	Circular	0.08167	1.84392	0.01604	0.98314	2.67589
20	Bulk density	Exponential	−0.00028	0.02808	−0.00722	0.89908	0.03092

along with the modelling validation results of prediction errors for soil’s chemical, granular and hydraulic parameters of the plots.

Out of the seven semivariogram kriging models tested for each soil parameter, not one unique model was found to be suitable for all soil characteristics; nevertheless, the final model selected as the best-fitting model varied depending on the soil parameter. In addition, Table 6 also uncovers how different models can produce better insights into several soil characteristics. Regarding the chemical parameters group, the Gaussian model was found to be the best-fitted semivariogram model for a quarter (25.00%) of the group’s parameters, i.e., phosphorus P-olsen and calcium carbonate CaCO₃, presenting the best MPE and best MSPE in calcium carbonate CaCO₃ modelling.

The Exponential model was found to be the best-fitted semivariogram model for 62.50% of the group’s parameters, i.e., nitrogen inorganic, calcium Ca⁺⁺, magnesium Mg⁺⁺, pH and organic matter, presenting the best RMSE and best ASE in pH modelling. Finally, the Circular model was found to be the best-fitted semivariogram model only for 12.50% of the group’s parameters, i.e., only for potassium K⁺, presenting the best RMSSE in potassium K⁺ modelling. Regarding the granular parameters group, the Pentaspherical model was found to be the best-fitted semivariogram model for 33.33% of the group’s parameters, i.e., sand content and clay content, presenting the best MSPE in sand content modelling. The Exponential model was found to be the best-fitted semivariogram model for 50.00% of the group’s parameters, i.e., silt content, very fine sand content and soil erodibility K factor, presenting the best MPE, best RMSE and best ASE in soil erodibility K factor modelling. Finally, the Spherical model was found to be the best-fitted semivariogram model only for 16.67% of the group’s parameters, i.e., soil’s gravel content, presenting the best RMSSE in soil’s gravel content modelling (Table 6).

Regarding the hydraulic parameters group, the Gaussian model was found to be the best-fitted semivariogram model for 33.33% of the group’s parameters, i.e., saturation θsat and wilting point θwp, presenting the best RMSSE in wilting point θwp modelling. The Circular model was found to be the best-fitted semivariogram model for 50.00% of the group’s parameters, i.e., field capacity θ_fc, plant available water PAW and saturated hydraulic conductivity Ks. It presented the best MPE, and best MSPE in field capacity θ_fc modelling, and the best RMSE and best ASE in plant available water PAW modelling. Finally, the Exponential model was found to be the best-fitted semivariogram model only for 16.67% of the group’s parameters, i.e., soil’s bulk density, presenting the group’s second best MPE, second best RMSE, second best MSPE and second best ASE in soil’s bulk density modelling.

Regarding performance of modeling, example outputs of model performance (average fit, best fit, best R-square) using soil organic matter training data (50% of the entire dataset) and SOM validation data (50% of the entire dataset) are depicted in Figure 6a,b.

The results of model performance showed that the data fitting of the selected model for each soil parameter was very satisfactory for training and validation data and the stability of the models was robust, as indicated by the statistical results (Table 6) and also by the graphical results (examples in Figure 6a,b).

In conclusion, the results demonstrated that the chosen semivariogram models are the best adapted ordinary kriging models for the prediction and mapping of spatial variability of the measured soil parameters.

A primary conclusion of practical importance is that the use of soil analyses in crop production offers a reliable way to produce meaningful and useful soil’s chemical-nutrient, granular and hydraulic parameters field maps and operational homogenous management zones by using PA, geostatistics, factor analysis and fuzzy clustering. As many soil analyses laboratories make special offers, in order to acquire a bigger piece of the market, raising competition and diminishing costs, many farmers can engage soil analyses and consultancy services to their production procedure.

3.6. FactorAnalysis Results and Discussion of Soil’s Chemical, Granular and Hydraulic Groups

Factor analysis endeavors to discover a way to detect the hidden parameters that may explain the correlational structure of a set of initial (observable) parameters. This modelling approach is commonly employed to compact the existing information within the initial parameters and further decrease the set of parameters in a dataset with minimal information losses, but it may equally be deployed to investigate the latent structure of parameters in a raw data stream [26]. In our study, firstly multivariate factor analysis and finally multivariate R-mode (rotated) factor analysis were performed to extract the factors governing the soil’s chemical, granular and hydraulic parameters of the experimental field.

The R-mode multivariate factor analysis [9,63,65,81] was performed using as an extraction method the principal components analysis (PCA) [63,65,81] and as a rotation method the varimax method with Kaiser normalization [3,9,63,81,82,83] by utilizing the measured and analyzed-in-the-lab data (soil’s chemical, granular and hydraulic parameters) on GIS parametric maps in order to extract the factors or components (management zones) of the experimental field. The data matrix of twenty parameters (phosphorus P-olsen (mg·Kg⁻¹), potassium K (mg·Kg⁻¹), calcium Ca (mg·Kg⁻¹), magnesium Mg (mg·Kg⁻¹), pH (-), nitrogen inorganic (mg·Kg⁻¹), organic matter (%), calcium carbonate CaCO3 (%), clay (size: <0.002 mm) (%), silt (size: 0.002–0.02 mm) (%), very fine sand (size: 0.02–0.2 mm) (%), sand pr (size: 0.2–2 mm) (%), gravel (%), soil erodibility [Kfactor] (Mg·ha·h·ha⁻¹·MJ⁻¹·mm⁻¹), wilting point θwp (m³·m⁻³), field capacity θ_fc (m³·m⁻³), saturation θsat (m³·m⁻³), plant available water PAW (cm·cm⁻¹), saturated hydraulic conductivity Ks (mm·hr⁻¹) and bulk density (g·cm⁻¹)) of 144 data observations were utilized in this factor analysis.

The results of the statistical PCA analysis for the “soil All Parameters group” are reported in

Table 7. R-mode factor matrix results of the principal components analysis (n = 144).

		R-Mode Factor (Component) Loading Matrix
SN	Parameter	Factor 1	Factor 2	Factor 3	Factor 4	Factor 5
1	Phosphorus P-olsen	0.249	−0.419	0.303	0.297	0.325
2	Potassium K	−0.042	−0.222	0.069	0.891	−0.014
3	Calcium Ca	0.838	−0.192	−0.103	−0.055	0.070
4	Magnesium Mg	0.852	−0.238	−0.065	−0.087	0.073
5	pH [1:2 soil/water solution]	0.726	0.292	−0.015	−0.374	0.015
6	Nitrogen inorganic	0.475	0.803	−0.099	−0.062	−0.063
7	Organic matter	−0.041	0.201	0.127	0.918	−0.049
8	Calcium carbonate CaCO3	0.776	−0.005	0.130	0.380	0.126
9	Sand	0.772	−0.175	0.317	0.122	−0.258
10	Silt	0.239	0.872	−0.249	−0.205	0.149
11	Clay	−0.753	−0.491	−0.136	0.004	0.154
12	Very fine sand	−0.567	−0.350	−0.064	−0.013	0.505
13	Gravel	0.017	0.337	−0.143	−0.054	0.784
14	Soil Erodibility (K factor)	0.644	−0.502	0.203	−0.363	−0.232
15	Wilting point θwp	−0.227	0.920	−0.194	0.098	0.113
16	Field capacity θfc	0.022	0.855	0.460	0.075	0.130
17	Saturation θsat	0.003	0.016	0.985	0.071	0.038
18	Plant available water PAW	0.206	0.016	0.894	0.110	−0.328
19	Saturated hydraulic conductivity Ks	−0.044	−0.490	0.838	0.036	−0.107
20	Bulk density	−0.034	0.007	−0.984	−0.062	−0.049
	Variance (%)	28.798	22.725	17.693	9.976	5.815
	Cumulative variance (%)	28.798	51.523	69.216	79.192	85.006

Notes: Extraction Method: principal components analysis. Rotation Method: Varimax with Kaiser normalization. The bold numbers denote the higher coefficients of the main parameters for each factor.

, and depicted graphically in an eigenvalue diagram (Figure 7a), and in a three-dimensional (3D) component diagram (Figure 7b) in rotated space aiming to uncover and explain relationships numerically and graphically between the 20 interacting soil parameters, and to show trends of soil data in rotated 3D space.

As can be seen in Figure 7a, the low (red circles) and medium (green circles) contribution PCs were found to be 11 and 4, respectively.

As for main PCs (high contribution PCs in blue circles), which can be seen in the extracted diagram of matrix’s eigenvalues (Figure 7a), they aided in determining the optimum total of components (factors), that initially was found to be the number of five components, or in our case, management zones. The 3D component diagram in rotated space (Figure 7b) depicts the spatial distribution and loadings of the 20 examined parameters in rotated three-dimensional space showing the trends and loadings of the data centroids of the primary three PCs (factors) that account for 69.216% of the overall variance in the data matrix (Table 7).

• Factor-1 contains significant loadings of eight parameters, which are magnesium Mg⁺⁺, calcium Ca⁺⁺, calcium carbonate CaCO₃, sand pr (size: 0.2–2 mm), pH, soil erodibility [Kfactor], very fine sand (size: 0.02–0.2 mm) and clay (size: <0.002 mm). Factor-1 can be considered as an ‘Mg-Ca-CaCO₃-Sand-pH-K factor-Vfs-Clay’ component that explains the synergistic soil chemistry interactions between the above-mentioned eight parameters as the dominating chemical processes in the field’s soil. Factor-1 stands for 28.798% of the data matrix’s variance. The presence of high levels of calcium Ca⁺⁺ and magnesium Mg⁺⁺ in the soil is associated with the intensive farming activities taking place in the area. The soil of the experimental plots was categorized as alkaline with pH values between 7.45 and 8.13;
• Factor-2 accounts for 22.725% of the variance and consists of five parameters, which are wilting point θwp, silt (size: 0.002–0.02 mm), field capacity θ_fc, nitrogen inorganic and phosphorus P-olsen. Factor-2 may be considered as a ‘θwp-silt-θ_fc-nitrogen inorganic-Polsen’ component that explains hydraulic and chemical interactions between the above-mentioned five parameters. This factor is mainly represented by positive high θ_fc and nitrogen inorganic loadings and shows negative loading of phosphorus P-olsen. Inorganic nitrogen of this factor does not have a significantly lithologic origin in the site and may be related to the agricultural activities of the region and the surface runoff of nitrogen fertilizers;
• Factor-4 accounts for 9.976% of the variance in the data matrix and is mainly represented by two parameters, and may be considered as an ‘organic matter and potassium K‘ component that exhibits high loadings of OM and potassium K⁺;
• Factor-5 is less significant and accounts for only 5.815% of the overall variance in the data matrix. This factor is considered as a ‘gravel‘ component that exhibits high loading of gravel content, indicating that this factor is rock weathering.

The primary four main factors accounted for 79.192% of the overall variance in the data matrix and dominated against the rest of the components in the control of soil chemistry of the trial plots. The remaining one main factor accounted for 5.815% of the variance, and the overall five factors loadings sum together explains 85.006% of the total variance in the data matrix.

The field’s management zones optimal number was obtained based on factor and PCA R-mode analyses of the various soil parameters groups, eigenvalue diagrams (Figure 7a and Figure 8a,c,e), 3D and 2D component diagrams in rotated space (Figure 7b and Figure 8b,d,f), and the realistic potential of management zones application in the trial plots pattern.

The factor analysis results of “soil All parameters” group data indicated that the suggested optimum total of components (factors) was initially five components or, in our case, five management zones (Figure 7a). The factor analyses outcomes of individual “chemical parameters group”, “granular parameters group” and “hydraulic parameters group” data indicated that the suggested optimum total of components (MZs) were found to be three, two and two, respectively (Figure 8a,c,e).

Taking into account the above outcomes, we had to choose between five, three and two management zones in the trial plots; however, since Factor-5 is less significant than the others and accounts for only 5.815% of the overall variance in the data matrix and for reasons of realistic potential of management zones application in the trial plots, it was finally chosen to apply four management zones in the trial plots.

3.7. Delineating Field’s Management Zones Results and Discussion

The widespread diversity of soil nutritional parameters, and soil granular and hydraulic parameters justifies the classification of these parameters into various categories to detect and delineate homogenous field zones (MZs) for their proper management. They were clustered into various categories based on their extent, represented by their magnitude and the extent of each category was assessed. The Fuzzy k-means clustering [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,84] was performed initially with the FuzME 3.5c software [49] and with the Management Zone Analyst (MZA) 1.01 software [50] in order to cluster the various soil parametric data into potential factors (MZs) and compare them. Finally, it was chosen to use the FuzME 3.5c software [49] because of its better options. First, an exploratory Fuzzy k-means clustering [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,84] analysis was conducted to clarify which distance metric, fuzziness exponent φ and maximum iterations were best used with the available field soil data. Multiple runs of the software were performed in order to evaluate the results and select the best distance metric, fuzziness exponents φ and maximum iterations for further use in the analysis. Based on the nature and characteristics of the field data, the results of the software’s multiple runs and the structure of each variance-covariance matrix, the Mahalanobis similarity distance metric was selected for multivariate clustering. Then, multiple runs of the Fuzzy k-means clustering algorithm [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,84] with varying fuzziness exponent φ from 1.10 to 2.00 and varying maximum iterations from 300 to 600 were performed. Based on the performance of the Fuzzy k-means multivariate clustering algorithm results, it is concluded that 300 maximum iterations were sufficient when we clustered 2 to 12 spatial soil parameters. In contrast, when clustering 13 to 20 soil parameters, the maximum iterations required for optimal results by the Fuzzy k-means algorithm were up to 500 iterations. Furthermore, based on the multivariate clustering results, the calculated indices of fuzzy performance index (FPI), modified partition entropy (MPE) [38,42,49], Xie and Benny’s k-means fuzzy index (FkM Xie and Benny’s index) [46] and Wilks lambda [3,49,64] vs. the varying fuzziness exponent φ were utilized to identify the optimal fuzziness exponent φ and the number of management zones (MZs). The various indexes result of the fuzziness exponent φ evaluation are depicted in Figure 9a–d. In Figure 9a is depicted the FPI and modified partition entropy vs. Fuzzy management class (k), for various fuzziness exponents (φ = 1.10 to 1.21) of “soil All parameters group” (20 parameters). In Figure 9b is depicted the FkM Xie and Benny index and Wilks lambda vs. Fuzzy management class (k), for various fuzziness exponents (φ = 1.10 to 1.21) of “soil All parameters group”. The results of the exploratory Fuzzy k-means clustering [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,84] analysis and the various indexes reveal that the tested fuzziness exponent φ from 1.10 to 2.00 of the group data “soil All parameters” was found valid only in the range between 1.10 and 1.21 (Figure 9a,b) for the data group structure. Over this valid range of values of fuzziness exponent φ, the optimal φ found was φ = 1.14 (Figure 9c,d), and the optimal number of MZs found was k = 4 (Figure 10a). Similar results on fuzziness exponent φ have been reported by other studies [42,43,44,45,46,47].

The combination of the lower values of FPI and MPE [38,42,49] are considered as the best. Moreover, the lower values of Xie and Benny’s k-means fuzzy index (FkM Xie and Benny’s index) [46] and Wilks lambda [3,42,49,63] are considered as the best. When FPI and MPE values were confusing, the FkM Xie and Benny’s index (lowest value) was proven to be robust and pointed clearly to the optimal fuzziness exponent. Next, the Fuzzy k-means clustering algorithm [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,84] was run with parameter settings as follows: Metric distance the Mahalanobis similarity method for multivariate clustering, fuzziness exponent φ = 1.14, maximum iterations = 500, stopping criterion = 0.0001 and random start with membership variance = 0.1. Based on the fuzzy clustering results, the “soil All parameters group” (20 parameters) output maps with four, three and two fuzzy clustering-based MZs were produced and the extent (in %) of each MZ was assessed (Figure 10a,c,e).

Another Fuzzy k-means grouping was carried out with soil’s chemical and nutritional parameters data (“soil chemical group” consisted of eight parameters) using a fuzziness exponent φ = 1.14 (found to be the optimal φ for the group’s structure), which resulted in three fuzzy MZs as the optimal number of classes, and the output MZs map and the extent (in %) of each MZ are depicted in Figure 10b. Based on the soil’s granular data (“soil granular group” consisted of 6 parameters), the Fuzzy k-means clustering algorithm with a fuzziness exponent φ = 1.16 (found to be the optimal φ for the group’s structure), yielded an output map with two fuzzy MZs as the optimal number of classes (Figure 10d). Finally, based on the soil’s hydraulic parameters data (“soil hydraulic group” consisted of six parameters), the Fuzzy k-means clustering algorithm with a fuzziness exponent φ = 1.16 (found to be the optimal φ for the group’s structure) resulted in an output map with two fuzzy MZs as the optimal number of classes (Figure 10f). Taking into consideration the statistical factor analysis and PCA results, the fuzzy k-means algorithm results and the above presented fuzzy management zone maps of the various soil parameter groups, we had to choose in practice between four, three, two and two management zones to apply in the trial plots. By analyzing the data, the MZ output maps of the field and the various evaluation indexes (fuzzy performance index (FPI), modified partition entropy (MPE) [38,42,48], Xie and Benny’s k-means fuzzy index (FkM Xie and Benny’s index) [46] and Wilks lambda [3,42,49,63]), we concluded that the four MZ output map “soil All parameters group” (20 parameters) was supplying the higher clustering insight of the field soil data and nutrients and for reasons of realistic potential of management zones application in the trial plots also, it was finally chosen to apply the four management zones pattern (Figure 10a) in the trial plots.

In order to verify whether or not the use of an arbitrary or commonly used fuzziness exponent, e.g., φ = 1.30 or φ = 1.50 is a correct application practice, we performed two separate Fuzzy k-means clusterings [38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,84] with parameter settings as follows: Metric distance the Mahalanobis similarity method for multivariate clustering, fuzziness exponent firstly φ = 1.30 and secondly φ = 1.50, maximum iterations = 500, stopping criterion = 0.0001 and random start with membership variance = 0.1. Analyzing the results in

Table 8. Fuzzy clustering Percentage of Management Zones Spatial Agreement.

SN	Soil Parameters Group		Fuzzy Clustering Percentage of Management Zones Spatial Agreement (PoMZSA) (%) between Soil Groups
		Fuzziness Exponent φ	* MZ 1	MZ 2	MZ 3	MZ 4	All MZs
1	“soil All parameters group” (20 parameters), 4 MZs	1.14	100.00	100.00	100.00	100.00	100.00
2	“soil All parameters group” (20 parameters), 4 MZs	1.30	35.29	11.43	8.82	0.00	13.19
3	“soil All parameters group” (20 parameters), 4 MZs	1.50	2.94	5.71	5.88	0.00	3.47
4	“soil All parameters group” (20 PCAs), 4 MZs	1.14	100.00	100.00	100.00	100.00	100.00
5	“soil All parameters group” (5 PCAs), 4 MZs	1.56	40.00	60.00	20.59	2.44	29.86
6	“soil chemical group” (8 parameters), 3 MZs	1.14	100.00	100.00	100.00	--	100.00
7	“soil chemical group” (8 parameters), 3 MZs	1.30	74.36	87.23	74.14	--	78.47
8	“soil chemical group” (8 parameters), 3 MZs	1.50	82.05	93.62	77.59	--	84.03
9	“soil chemical group” (8 PCAs), 3 MZs	1.12	100.00	100.00	100.00	--	100.00
10	“soil chemical group” (3 PCAs), 3 MZs	1.69	35.90	25.53	70.69		46.53
11	“soil granular group” (6 parameters), 2 MZs	1.16	100.00	100.00	--	--	100.00
12	“soil granular group” (6 parameters), 2 MZs	1.30	98.70	97.01	--	--	97.92
13	“soil granular group” (6 parameters), 2 MZs	1.50	97.40	95.52	--	--	96.53
14	“soil granular group” (6 PCAs), 2 MZs	1.16	100.00	100.00	--	--	100.00
15	“soil granular group” (2 PCAs), 2 MZs	1.61	80.52	95.52			87.50
16	“soil hydraulic group” (6 parameters), 2 MZs	1.16	100.00	100.00	--	--	100.00
17	“soil hydraulic group” (6 parameters), 2 MZs	1.30	98.51	98.70	--	--	98.61
18	“soil hydraulic group” (6 parameters), 2 MZs	1.50	98.51	96.10	--	--	97.22
19	“soil hydraulic group” (6 PCAs), 2 MZs	1.16	100.00	100.00	--	--	100.00
20	“soil hydraulic group” (2 PCAs), 2 MZs	1.15	85.07	81.82	--	--	83.33

* Background colors associate each MZ with the MZ color of the map in Figure 10a.

, it is shown how different fuzziness exponents applied to different data groups of soil parameters can reveal better insights for determining whether a fuzzy classification is a correct or incorrect application for delineating fuzzy MZs.

In reviewing many research studies on management zone delineation for various crops using fuzzy classification algorithms, it appears that most researchers, for convenience, use an arbitrary or commonly used fuzziness exponent, e.g., φ = 1.30 or φ = 1.50, without even considering to perform an exploratory fuzzy analysis to determine whether their classification is a correct or incorrect application to fuzzy MZ delineation.

The results of applying various fuzziness exponents with the Fuzzy k-means clustering algorithm are presented in Table 8 using the fuzzy clustering metric: Percentage of Management Zones Spatial Agreement (PoMZSA) (%) between soil groups [the “soil All parameters group” (20 parameters), “soil All parameters group” (20 PCAs), “soil All parameters group” (five PCAs), “soil chemical group” (eight parameters), “soil chemical group” (eight PCAs), “soil chemical group” (three PCAs), “soil granular group” (six parameters), “soil granular group” (six PCAs), “soil granular group” (two PCAs), “soil hydraulic group” (six parameters), “soil hydraulic group” (six PCAs), and “soil hydraulic group” (two PCAs)].

The most likely result of not applying the correct fuzziness exponent and the correct initial parameters to the fuzzy algorithm use is incorrect MZ clustering (zoning), which leads to further incorrect farm management and to drawing incorrect conclusions.

In all cases, the best results were achieved by using the optimal fuzziness exponent with the full number of parameters of each soil parameter data group or the maximum extracted PCAs of each soil parameter data group. When applying the factor analysis and PCA that indicated optimal MZs = 2, the results of the PoMZSA fuzzy clustering metric revealed high spatial agreement with no statistically significant difference between the full soil parameter datasets, regardless of the fuzziness exponent used.

In each case study where the factor analysis and PCA showed optimal MZs above 2, the results of the fuzzy PoMZSA clustering metric revealed low, medium and medium to high spatial agreement, which presented a statistically significant difference between the soil parameter datasets when an arbitrary or commonly used fuzziness exponent was used (e.g., φ = 1.30 or φ = 1.50).

Based on the fuzzy algorithm clustering results and the results of the fuzzy PoMZSA clustering metric, it is strongly recommended to use the full number of parameters of each soil parameter data group or the maximum extracted PCAs of each soil parameter data group; moreover, prior to the final fuzzy clustering, it is strongly recommended to perform an exploratory fuzzy analysis in order to determine the optimal fuzziness exponent for each dataset, especially when MZs > 2. In exploratory fuzzy analysis, it is also recommended to use the FkM Xie and Benny’s index (lowest value) when FPI and MPE values are confusing, because the FkM Xie and Benny’s index was proven to be robust and pointed clearly to the optimal fuzziness exponent.

4. Conclusions

The various generated MZ maps showed that data collected from field’s soil did provide different information for decision making, which would lead to different spatial management of the field. Farmers of aromatic, medicinal and other plants should prioritize soil chemical, granular and hydraulic laboratory analyses, modelling and field mapping for differential field management zones. An agronomist can be greatly assisted in recognizing and locating field sites of low, medium and high soil fertility by studying and analyzing the precision agriculture’s spatial variability maps of soil “Chemical Group” parameters. The modelling results of soil’s chemical parameters group revealed strong spatial dependence of nitrogen inorganic, calcium Ca⁺⁺, magnesium Mg⁺⁺, potassium K⁺, pH, organic matter, and calcium carbonate CaCO₃ and medium spatial dependence of phosphorus P-olsen. Out of the seven semivariogram kriging models (Gaussian, Exponential, Stable, Pentaspherical, Tetraspherical, Spherical and Circular) tested for each soil parameter, not one unique model was found to be suitable for all soil characteristics; nevertheless, the final model selected as the best-fitting model varied depending on the soil parameter. The kriging Exponential model was found to be the best-fitted semivariogram model for 62.50% of the chemical group’s parameters, i.e., nitrogen inorganic, calcium Ca⁺⁺, magnesium Mg⁺⁺, pH and organic matter, presenting the best RMSE and best ASE in pH modelling. Based on the nature and characteristics of the field data, the results of Fuzzy k-means algorithm multiple runs and the structure of each variance-covariance matrix, the Mahalanobis similarity distance metric was found as the best for MZ multivariate clustering. Based on the performance of the fuzzy k-means algorithm results, it was concluded that 300 maximum iterations were sufficient when 2 to 12 spatial soil parameters were used, while up to 500 iterations were required when 13 to 20 parameters were clustered. In reviewing many research studies on MZ delineation for various crops using fuzzy classification algorithms, it appears that most researchers, for convenience, use an arbitrary or commonly used fuzziness exponent, e.g., φ = 1.30 or φ = 1.50, without even considering to perform an exploratory fuzzy analysis to determine whether their classification is a correct or incorrect application to fuzzy management zone delineation.

The results of the exploratory Fuzzy k-means clustering analysis and the various indexes reveal that the optimal φ found was φ = 1.14, and the optimal number of MZs found was k = 4. The most likely result of not applying the correct fuzziness exponent and the correct initial parameters is an incorrect MZ zoning, which leads to further incorrect farm management and to drawing incorrect conclusions. The exploratory fuzzy analysis showed how different fuzziness exponents applied to different soil data groups can reveal better insights for determining whether a fuzzy classification is a correct or incorrect application for delineating fuzzy management zones.

In all cases, the best results were achieved by using the optimal fuzziness exponent with the full number of parameters of each soil data group or the maximum extracted PCAs. In each case study where the factor analysis and PCA showed optimal MZs > 2, the results of the fuzzy PoMZSA metric revealed low, medium and medium to high spatial agreement, which presented a statistically significant difference between the soil parameter datasets, when an arbitrary or commonly used fuzziness exponent was applied (e.g., φ = 1.30 or φ = 1.50). Based on the fuzzy algorithm clustering results and the results of the fuzzy PoMZSA metric, it is strongly recommended to use the full number of parameters of each soil data group or the maximum extracted PCAs; moreover, prior to the final fuzzy clustering, it is strongly recommended to perform an exploratory fuzzy analysis in order to determine the optimal fuzziness exponent, especially when MZs > 2. Additionally, it is also recommended to use the FkM Xie and Benny’s index (lowest value) when FPI and MPE indexes values are confusing, because the FkM Xie and Benny’s index was proven to be robust and pointed clearly to the optimal fuzziness exponent.