# 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

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}. 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 m

^{3}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].

## 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.

**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].

^{2}. The area and dimensions of the 144 sub-plot units were 3.80 m

^{2}(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.

^{+}sensing (indicator) electrode paired with a reference electrode connected to a pH monitor meter.

^{−1}of K

_{2}Cr

_{2}O

_{7}and by titration of the residual reagent with 0.5 mol·L

^{−1}of FeSO

_{4}[29,30,57].

^{−1}of CaCl

_{2}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 NaHCO

_{3}and measured by spectroscopy [30]. The exchangeable forms of potassium K

^{+}were extruded with 1 mol L

^{−1}of CH

_{3}COONH

_{4}and quantified using a flame spectrophotometer.

^{++}and calcium Ca

^{++}cations were obtained by displacement of those elements from the soil colloids with ammonium (NH

_{4}) by shaking the soil sample with 1.0 N ammonium acetate (NH

_{4}OAc) adjusted to pH ‘7.0 with ammonium hydroxide (NH

_{4}OH) 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 CO

_{2}released when the sample is treated with 6N HCL. In a closed system, the quantity of CO

_{3}

^{2−}is directly proportional to the volumetric increase resulting from the release of the CO

_{2}[59,60].

_{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].

^{−3}of the overall undisturbed soil bulk volume.

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

#### 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

**A**vailable

**S**oil

**M**oisture

**D**epletion 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

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

_{m}= the n weights ranked to the site points ${Z}_{\left(Xm\right)}$.

_{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):

_{(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):

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

**P**ercentage

**o**f

**M**anagement

**Z**ones

**S**patial

**A**greement (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

**P**ercentage

**o**f

**M**anagement

**Z**ones

**S**patial

**A**greement (PoMZSA) (%) is presented in Formula (4):

## 3. Results and Discussion

#### 3.1. Results of Climate Studied

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

^{++}). The calcium Ca

^{++}(mg·Kg

^{−1}), magnesium Mg

^{++}(mg·Kg

^{−1}), potassium K

^{+}(mg·Kg

^{−1}), nitrogen inorganic (mg·Kg

^{−1}), saturation θsat (m

^{3}·m

^{−3}), sand pr (size: 0.2–2 mm) (%) and field capacity θ

_{fc}(m

^{3}·m

^{−3}) presented high average values (≥27.66), while the other attributes had low average values (<27.66).

^{−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.

^{−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].

^{+}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].

_{3}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].

_{fc}= 0.277 m

^{3}·m

^{−3}(±0.0092), a mean wilting point θwp = 0.160 m

^{3}·m

^{−3}(±0.0067), a mean saturation θsat = 0.467 m

^{3}·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.

^{−1}with a mean saturated hydraulic conductivity Ks = 16.27 mm·h

^{−1}(±4.23).

^{−}

^{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].

_{fc}and θwp obtained from the hydraulic analysis of the soil are within the normal limits given by Allen et al. (1998) [18].

- (a)
- Low coefficient of variation (CV < 15%);
- (b)
- Moderate coefficient of variation (CV = 15–35%);
- (c)
- High coefficient of variation (CV > 35%).

^{−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%.

_{3}(%) 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

^{−1}), field capacity θ

_{fc}(m

^{3}·m

^{−3}), clay (%), calcium carbonate CaCO

_{3}(%), 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 (%).

^{3}·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 (m

^{3}·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}).

_{3}, 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.

^{+}shows a significant positive correlation at the 0.01 level (2-tailed) with organic matter, calcium carbonate CaCO

_{3}and phosphorus P-olsen, while having significant negative correlation at the 0.01 level (2-tailed) with pH and nitrogen inorganic.

^{++}, calcium carbonate CaCO

_{3}, pH and nitrogen inorganic. Magnesium Mg

^{++}presents a significant positive correlation at the 0.01 level (2-tailed) with calcium Ca

^{++}, calcium carbonate CaCO

_{3}, pH and nitrogen inorganic, and at the 0.05 level (2-tailed) with phosphorus P-olsen.

^{++}, calcium Ca

^{++}and calcium carbonate CaCO

_{3}, while having significant negative correlation at the 0.01 level (2-tailed) with Potassium K

^{+}and organic matter.

_{3}, calcium Ca

^{++}, and magnesium Mg

^{++}, while having significant negative correlation at the 0.01 level (2-tailed) with potassium K

^{+}and phosphorus P-olsen.

^{+}and calcium carbonate CaCO

_{3}, while having significant negative correlation at the 0.01 level (2-tailed) with pH.

_{3}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

^{+}.

^{−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) (%).

^{−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).

_{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.

^{+}. Their normal QQ Plot diagrams and Boxplot diagrams are presented in Figure 1a–d.

^{−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

^{+}(Figure 2b), respectively.

^{+}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 CaCO

_{3}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 CaCO

_{3}(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 CaCO

_{3}.

^{+}(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 CaCO

_{3}(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 CaCO

_{3}(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.

_{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).

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

_{3}(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).

^{+}(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.

_{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).

^{++}and clay), which indicates a spatial affinity that can connect different spatial entities on the parametric map.

^{++}(Figure 3b), magnesium Mg

^{++}(Figure 3d), potassium K

^{+}(Figure 3e), pH (Figure 3f), organic matter (Figure 3g) and calcium carbonate CaCO

_{3}(Figure 3h), and medium spatial dependence of phosphorus P-olsen (Figure 3c).

_{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.

_{3}, presenting the best MPE and best MSPE in calcium carbonate CaCO

_{3}modelling.

^{++}, 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).

_{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.

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

^{−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 (m

^{3}·m

^{−3}), field capacity θ

_{fc}(m

^{3}·m

^{−3}), saturation θsat (m

^{3}·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.

- Factor-1 contains significant loadings of eight parameters, which are magnesium Mg
^{++}, calcium Ca^{++}, calcium carbonate CaCO_{3}, 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-CaCO_{3}-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.

#### 3.7. Delineating Field’s Management Zones Results and Discussion

**P**ercentage

**o**f

**M**anagement

**Z**ones

**S**patial

**A**greement (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)].

## 4. Conclusions

^{++}, magnesium Mg

^{++}, potassium K

^{+}, pH, organic matter, and calcium carbonate CaCO

_{3}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.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Küppers, M.; O’Rourke, L.; Bockelée-Morvan, D.; Zakharov, V.; Lee, S.; Von Allmen, P.; Carry, B.; Teyssier, D.; Marston, A.; Müller, T.; et al. Localized sources of water vapour on the dwarf planet (1) Ceres. Nature
**2014**, 505, 525–527. [Google Scholar] [CrossRef] [PubMed] - Siddique, K.H.M.; Bramley, H. Water Deficits: Development; CRC Press: Boca Raton, FL, USA, 2014; pp. 1–4. [Google Scholar] [CrossRef]
- Filintas, A. Land Use Evaluation and Environmental Management of Biowastes, for Irrigation with Processed Wastewaters and Application of Bio-Sludge with Agricultural Machinery, for Improvement-Fertilization of Soils and Crops, with the Use of GIS-Remote Sensing, Precision Agriculture and Multicriteria Analysis. Ph.D. Thesis, University of the Aegean, Mitilini, Greece, 2011. [Google Scholar]
- Gleick, P.H.; Palaniappan, M. Peak water limits to freshwater withdrawal and use. Proc. Natl. Acad. Sci. USA
**2010**, 107, 11155–11162. [Google Scholar] [CrossRef] [PubMed] - Shiklomanov, I.A. Appraisal and assessment of world water resources. Water Int.
**2000**, 25, 11–32. [Google Scholar] [CrossRef] - Schiermeier, Q. The parched planet: Water on tap. Nature
**2014**, 510, 326–328. [Google Scholar] [CrossRef] [PubMed] - Gan, Y.; Siddique, K.H.M.; Turner, N.C.; Li, X.-G.; Niu, J.-Y.; Yang, C.; Liu, L.; Chai, Q. Ridge-furrow mulching systems—An innovative technique for boosting crop productivity in semiarid rain-fed environments. Adv. Agron.
**2013**, 118, 429–476. [Google Scholar] [CrossRef] - FAO. Coping with Water Scarcity: An Action Framework for Agriculture and Food Security; FAO: Rome, Italy, 2012; p. 100. [Google Scholar]
- Stamatis, G.; Parpodis, K.; Filintas, A.; Zagana, E. Groundwater quality, nitrate pollution and irrigation environmental management in the Neogene sediments of an agricultural region in central Thessaly (Greece). Environ. Earth Sci.
**2011**, 64, 1081–1105. [Google Scholar] [CrossRef] - EEA. Use of Freshwater Resources in Europe, CSI 018; European Environment Agency (EEA): Copenhagen, Denmark, 2019.
- Koutseris, Ε.; Filintas, A.; Dioudis, P. Antiflooding prevention, protection, strategic environmental planning of aquatic resources and water purification: The case of Thessalian basin, in Greece. Desalination
**2010**, 250, 318–322. [Google Scholar] [CrossRef] - Κoutseris, Ε.; Filintas, A.; Dioudis, P. Environmental control of torrents environment: One valorisation for prevention of water flood disasters. WIT Trans. Ecol. Environ.
**2007**, 104, 249–259. [Google Scholar] [CrossRef] - Islam, S.M.F.; Karim, Z. World’s Demand for Food and Water: The Consequences of Climate Change. In Desalination-Challenges and Opportunities; Farahani, M.H.D.A., Vatanpour, V., Taheri, A.H., Eds.; IntechOpen: London, UK, 2019; Chapter 4; pp. 1–27. [Google Scholar] [CrossRef]
- Filintas, A.; Wogiatzi, E.; Gougoulias, N. Rainfed cultivation with supplemental irrigation modelling on seed yield and oil of Coriandrum sativum L. using Precision Agriculture and GIS moisture mapping. Water Supply
**2021**, 21, 2569–2582. [Google Scholar] [CrossRef] - Siebert, S.; Kummu, M.; Porkka, M.; Döll, P.; Ramankutty, N.; Scanlon, B.R. A global data set of the extent of irrigated land from 1900 to 2005. Hydrol. Earth Syst. Sci.
**2015**, 19, 1521–1545. [Google Scholar] [CrossRef] - Garrote, L.; Iglesias, A.; Granados, A.; Mediero, L.; Martin-Carrasco, F. Quantitative assessment of climate change vulnerability of irrigation demands in Mediterranean Europe. Water Resour. Manag.
**2015**, 29, 325–338. [Google Scholar] [CrossRef] - Kreins, P.; Henseler, M.; Anter, J.; Herrmann, F.; Wendland, F. Quantification of climate change impact on regional agricultural irrigation and groundwater demand. Water Resour. Manag.
**2015**, 29, 3585–3600. [Google Scholar] [CrossRef] - Allen, R.; Pereira, L.; Raes, D.; Smith, M. Crop Evapotranspiration; Drainage & Irrigation Paper No. 56; FAO: Rome, Italy, 1998. [Google Scholar]
- Filintas, A.; Nteskou, A.; Kourgialas, N.; Gougoulias, N.; Hatzichristou, E. A Comparison between Variable Deficit Irrigation and Farmers’ Irrigation Practices under Three Fertilization Levels in Cotton Yield (Gossypium hirsutum L.) Using Precision Agriculture, Remote Sensing, Soil Analyses, and Crop Growth Modeling”. Water
**2022**, 14, 2654. [Google Scholar] [CrossRef] - Kalavrouziotis, I.K.; Filintas, A.T.; Koukoulakis, P.H.; Hatzopoulos, J.N. Application of multicriteria analysis in the Management and Planning of Treated Municipal Wastewater and Sludge reuse in Agriculture and Land Development: The case of Sparti’s Wastewater Treatment Plant, Greece. Fresenious Environ. Bull.
**2011**, 20, 287–295. [Google Scholar] - Dioudis, P.; Filintas, A.; Koutseris, E. GPS and GIS based N-mapping of agricultural fields’ spatial variability as a tool for non-polluting fertilization by drip irrigation. Int. J. Sustain. Dev. Plan.
**2009**, 4, 210–225. [Google Scholar] [CrossRef] - Dioudis, P.; Filintas, A.; Papadopoulos, A. Corn yield response to irrigation interval and the resultant savings in water and other overheads. Irrig. Drain.
**2009**, 58, 96–104. [Google Scholar] [CrossRef] - Filintas, A.; Dioudis, P.; Prochaska, C. GIS modeling of the impact of drip irrigation, of water quality and of soil’s available water capacity on Zea mays L, biomass yield and its biofuel potential. Desalination Water Treat.
**2010**, 13, 303–319. [Google Scholar] [CrossRef] - FAO. New Quality Criteria to Be Developed for Booming Spice and Herb Sector; Food and Agriculture Organization of the United Nations: Rome, Italy, 2018; Available online: https://www.fao.org/news/story/en/item/213612/icode/ (accessed on 5 February 2021).
- Wan, S.; Norby, R.J.; Ledford, J.; Weltzin, J.F. Responses of soil respiration to elevated CO
_{2}, air warming, and changing soil water availability in a model oldfield grassland. Glob. Chang. Biol.**2007**, 13, 2411–2424. [Google Scholar] [CrossRef] - Filintas, A. Study and Mapping of Biomass Yield with the Use of Spatial Statistics and Geoinformation. Master’s Thesis, Dept. of Natural Resources Management and Agricultural Engineering, Agricultural University of Athens, Athens, Greece, 2008. (In Greek with English Abstract). [Google Scholar]
- Garten, C.T., Jr.; Classen, A.T.; Norby, R.J. Soil moisture surpasses elevated CO
_{2}and temperature as a control on soil carbon dynamics in a multi-factor climate change experiment. Plant Soil**2009**, 319, 85–94. [Google Scholar] [CrossRef] - Falloon, P.; Jones, C.D.; Ades, M.; Paul, K. Direct soil moisture controls of future global soil carbon changes: An important source of uncertainty. Glob. Biogeochem. Cycles
**2011**, 25, GB3010. [Google Scholar] [CrossRef] - Dioudis, P.; Filintas, A.; Papadopoulos, A.; Sakellariou-Makrantonaki, M. The influence of different drip irrigation layout designs on sugar beet yield and their contribution to environmental sustainability. Fresenious Environ. Bull.
**2010**, 19, 818–831. [Google Scholar] - Page, A.L.; Miller, R.H.; Keeney, D.R. Methods of Soil Analysis Part 2: Chemical and Microbiological Properties; Agronomy, ASA and SSSA: Madison, WI, USA, 1982; p. 1159. [Google Scholar]
- Rodriguez, H.G.; Popp, J.; Gbur, E.; Chaubey, I. Environmental and economic impacts of reducing total phosphorous runoff in an agricultural watershed. Agric. Syst.
**2011**, 104, 623–633. [Google Scholar] [CrossRef] - Filintas, A. Soil Moisture Depletion Modelling Using a TDR Multi-Sensor System, GIS, Soil Analyzes, Precision Agriculture and Remote Sensing on Maize for Improved Irrigation-Fertilization Decisions. Eng. Proc.
**2021**, 9, 36. [Google Scholar] [CrossRef] - Geerts, S.; Raes, D. Deficit irrigation as an on-farm strategy to maximize crop water productivity in dry areas. Agric. Water Manag.
**2009**, 96, 1275–1284. [Google Scholar] [CrossRef] - Fleming, K.L.; Westfall, D.G.; Collins, F. Evaluating management zone technology and grid soil sampling for variable rate nitrogen application. In Proceedings of the 5th International Conference on Precision Agriculture, Minneapolis, MN, USA, 16–19 July 2000; Robert, P.C., Rust, R.H., Larson, W.E., Eds.; ASA, CSSA, and SSSA: Madison, WI, USA, 2000. [Google Scholar]
- Haghverdi, A.; Leib, B.G.; Washington-Allen, R.A.; Ayers, P.D.; Buschermohle, M.J. Perspectives on delineating management zones for variable rate irrigation. Comput. Electron. Agric.
**2015**, 117, 154–167. [Google Scholar] [CrossRef] - Vrindts, E.; Mouazen, A.M.; Reyniers, M.; Maertens, K.; Maleki, M.R.; Ramon, H.; De Baerdemaeker, J. Management zones based on correlation between soil compaction, yield and crop data. Biosyst. Eng.
**2005**, 92, 419–428. [Google Scholar] [CrossRef] - Filintas, A.; Gougoulias, N.; Hatzichristou, E. Modeling Soil Erodibility by Water (Rainfall/Irrigation) on Tillage and No-Tillage Plots of a Helianthus Field Utilizing Soil Analysis, Precision Agriculture, GIS, and Kriging Geostatistics. Environ. Sci. Proc.
**2023**, 25, 54. [Google Scholar] [CrossRef] - Bezdek, J.C. Cluster validity with fuzzy sets. J. Cybern.
**1974**, 3, 58–73. [Google Scholar] [CrossRef] - Bezdek, J.C. A convergence theorem for the fuzzy ISODATA clustering algorithm. IEEE Trans. Pattern Anal. Mach. Intell.
**1980**, 2, 1–8. [Google Scholar] [CrossRef] - Bezdek, J.C. Pattern Recognition with Fuzzy Objective Function Algorithms; Plenum Press: New York, NY, USA, 1981. [Google Scholar]
- Bezdek, J.C.; Trivedi, M.; Ehrlich, R.; Full, W. Fuzzy clustering: A new approach for geostatistical analysis. Int. J. Syst. Meas. Decis.
**1981**, 2, 13–23. [Google Scholar] - Filintas, A.; Gougoulias, N.; Kourgialas, N.; Hatzichristou, E. Management Soil Zones, Irrigation, and Fertigation Effects on Yield and Oil Content of Coriandrum sativum L. Using Precision Agriculture with Fuzzy k-Means Clustering. Sustainability
**2023**, 15, 13524. [Google Scholar] [CrossRef] - McBratney, A.B.; Moore, A.W. Application of fuzzy sets to climate classification. Agric. For. Meteorol.
**1985**, 35, 165–185. [Google Scholar] [CrossRef] - De Gruijter, J.J.; McBratney, A.B. A modified fuzzy k-means method for predictive classification. In Classijkation and Related Methods of Data Analysis; Bock, H.H., Ed.; Elsevier: Amsterdam, The Netherlands, 1988; pp. 97–104. [Google Scholar]
- Odeh, I.O.A.; McBratney, A.B.; Chittleborough, D.J. Design of optimal sample spacings for mapping soil using fuzzy k-means and regionalized variable theory. Geoderma
**1990**, 47, 93–122. [Google Scholar] [CrossRef] - Xie, X.L.; Beni, G. A validity measure for fuzzy clustering. IEEE Trans. Pattern Anal. Mach. Intell.
**1991**, 13, 841–847. [Google Scholar] [CrossRef] - McBratney, A.B.; de Gruijter, J.J. A continuum approach to soil classification by modified fuzzy k-means with extragrades. J. Soil Sci.
**1992**, 43, 159–175. [Google Scholar] [CrossRef] - Halkidi, M.; Batistakis, Y.; Vazirgiannis, M. On clustering validation techniques. J. Intell. Inf. Syst.
**2001**, 17, 107–145. [Google Scholar] [CrossRef] - Minasny, B.; McBratney, A.B. FuzME Version 3.0. Australian Centre for Precision Agriculture; The University of Sydney: Sydney, Australia, 2002; Available online: http://www.usyd.edu.au/sulagriclacpa (accessed on 16 May 2006).
- Fridgen, J.J.; Kitchen, N.R.; Sudduth, A.K.; Drummond, S.T. Management Zone Analyst (MZA): Software for subfeld management zone delineation. Agron. J.
**2004**, 96, 100–108. [Google Scholar] [CrossRef] - Steinley, D. K-means clustering: A half-century synthesis. Br. J. Math. Stat. Psychol.
**2006**, 59, 1–34. [Google Scholar] [CrossRef] - Luz López García, M.; García-Ródenas, R.; González Gómez, A. K-means algorithms for functional data. Neurocomputing
**2015**, 151, 231–245. [Google Scholar] [CrossRef] - Taylor, J.A.; Dresser, J.; Hickey, C.C.; Nuske, S.T.; Bates, T.R. Considerations on spatial crop load mapping. Aust. J. Grape Wine Res.
**2019**, 25, 144–155. [Google Scholar] [CrossRef] - Soil Survey Staff. Soil Taxonomy: A Basic System of Soil Classification for Making and Interpreting Soil Surveys; USDA Natural Resources Conservation Service: Washington, DC, USA, 1975.
- Bouyoucos, J.G. Hydrometer method improved for making particle size analysis of soils. Agron. J.
**1962**, 54, 464–465. [Google Scholar] [CrossRef] - Beretta, N.A.; Silbermann, V.A.; Paladino, L.; Torres, D.; Bassahun, D.; Musselli, R.; García-Lamohte, A. Soil texture analyses using a hydrometer: Modification of the Bouyoucos method. Cien. Investig. Agr.
**2014**, 41, 263–271. [Google Scholar] [CrossRef] - Filintas, A.; Nteskou, A.; Katsoulidi, P.; Paraskebioti, A.; Parasidou, M. Rainfed and Supplemental Irrigation Modelling 2D GIS Moisture Rootzone Mapping on Yield and Seed Oil of Cotton (Gossypium hirsutum) Using Precision Agriculture and Remote Sensing. Eng. Proc.
**2021**, 9, 37. [Google Scholar] [CrossRef] - Varian “Flame Atomic Absorption Spectroscopy”, Analytical Methods; Publ. No: 85-100009-00; Varian Techtron Pty. Ltd.: Springvale, Australia, 1989; Available online: https://www.agilent.com/cs/library/usermanuals/Public/0009.pdf (accessed on 17 May 2018).
- Muller, G.; Gatsner, M. Chemical analysis. Neues Jahrb. Mineral. Monatshefte
**1971**, 10, 466–469. [Google Scholar] - Lamas, F.; Irigaray, C.; Oteo, C.; Chacon, J. Selection of the most appropriate method to determine the carbonate content for engineering purposes with particular regard to marls. Eng. Geol.
**2005**, 81, 32–41. [Google Scholar] [CrossRef] - Meena, S.S.; Singh, B.; Singh, D.; Ranjan, J.K.; Meena, R.D. Pre and post harvest factors effecting yield and quality of seed spices: A review. Int. J. Seed Spices
**2013**, 3, 1–11. [Google Scholar] - USDA-SCS. Irrigation Water Requirements; Technical, R. No. 21; USDA Soil Conservation Service: Washington, DC, USA, 1970.
- Norusis, M.J. IBM SPSS Statistics 19 Advanced Statistical Procedures Companion; Pearson: London, UK, 2011. [Google Scholar]
- Hatzigiannakis, E.; Filintas, A.; Ilias, A.; Panagopoulos, A.; Arampatzis, G.; Hatzispiroglou, I. Hydrological and rating curve modelling of Pinios River water flows in Central Greece, for environmental and agricultural water resources management. Desalination Water Treat.
**2016**, 57, 11639–11659. [Google Scholar] [CrossRef] - Davis, J.C. Statistics and Data Analysis in Geology; Wiley: New York, NY, USA, 1986. [Google Scholar]
- Hatzopoulos, N.J. Topographic Mapping, Covering the Wider Field of Geospatial Information Science & Technology (GIS&T); Universal Publishers: Irvine, CA, USA, 2008. [Google Scholar]
- Webster, R.; Oliver, M.A. Geostatistics for Environmental Scientists, 2nd ed.; John Wiley & Sons: Chichester, UK, 2007; p. 271. Available online: https://onlinelibrary.wiley.com/doi/book/10.1002/9780470517277 (accessed on 5 February 2023).
- Bogunovic, I.; Mesic, M.; Zgorelec, Z.; Jurisic, A.; Bilandzija, D. Spatial variation of soil nutrients on sandy-loam soil. Soil Tillage Res.
**2014**, 144, 174–183. [Google Scholar] [CrossRef] - Cass, A. Interpretation of some soil physical indicators for assessing soil physical fertility. In Soil Analysis: An Interpretation Manual, 2nd ed.; Peverill, K.I., Sparrow, L.A., Reuter, D.J., Eds.; CSIRO Publishing: Melbourne, Australia, 1999; pp. 95–102. [Google Scholar]
- Soropa, G.; Mbisva, O.M.; Nyamangara, J.; Nyakatawa, E.Z.; Nyapwere, N.; Lark, R.M. Spatial variability and mapping of soil fertility status in a high-potential smallholder farming area under sub-humid conditions in Zimbabwe. SN Appl. Sci.
**2021**, 3, 396. [Google Scholar] [CrossRef] - Lu, G.Y.; Wong, D.W. An adaptive inverse-distance weighting spatial interpolation technique. Comput. Geosci.
**2008**, 34, 1044–1055. [Google Scholar] [CrossRef] - Zhang, H.; Zhuang, S.; Qian, H.; Wang, F.; Ji, H. Spatial variability of the topsoil organic carbon in the Moso bamboo forests of southern China in association with soil properties. PLoS ONE
**2015**, 10, e0119175. [Google Scholar] [CrossRef] - Yang, P.G.; Byrne, J.M.; Yang, M. Spatial variability of soil magnetic susceptibility, organic carbon and total nitrogen from farmland in northern China. Catena
**2016**, 145, 92–98. [Google Scholar] [CrossRef] - Tang, X.L.; Xia, M.P.; Pérez-Cruzado, C.; Guan, F.Y.; Fan, S.H. Spatial distribution of soil organic carbon stock in Moso bamboo forests in subtropical China. Sci. Rep.
**2017**, 7, 42640. [Google Scholar] [CrossRef] - John, K.; Abraham, I.I.; Kebonye, N.M.; Agyeman, P.C.; Ayito, E.O.; Kudjo, A.S. Soil organic carbon prediction with terrain derivatives using geostatistics and sequential Gaussian simulation. J. Saudi Soc. Agric. Sci.
**2021**, 20, 379–389. [Google Scholar] [CrossRef] - Qu, M.K.; Li, W.D.; Zhang, C.R.; Wang, S.Q. Effect of land use types on the spatial prediction of soil nitrogen. GISci. Remote Sens.
**2012**, 49, 397–411. [Google Scholar] [CrossRef] - Ferreiro, J.P.; Pereira De Almeida, V.; Cristina Alves, M.; Aparecida De Abreu, C.; Vieira, S.R.; Vidal Vázquez, E. Spatial variability of soil organic matter and cation exchange capacity in an Oxisol under different land uses. Commun. Soil Sci. Plant Anal.
**2016**, 47 (Suppl. 1), 75–89. [Google Scholar] [CrossRef] - Loague, K.; Green, R.E. Statistical and graphical methods for evaluating solute transport models: Overview and application. J. Contam. Hydrol.
**1991**, 7, 51–73. [Google Scholar] [CrossRef] - Isaaks, E.H.; Srivastava, R.M. Applied Geostatistics; Oxford University Press: New York, NY, USA, 1989. [Google Scholar]
- Goovaerts, P. Geostatistics for Natural Resources Evaluation; Oxford University Press: New York, NY, USA, 1997. [Google Scholar]
- Jolliffe, I.T. Principal Component Analysis; Springer: Berlin, Germany, 1986. [Google Scholar] [CrossRef]
- Kaiser, H.F. The Application of Electronic Computers to Factor Analysis. Educ. Psychol. Meas.
**1960**, 20, 141–151. [Google Scholar] [CrossRef] - Manly, B.F.J.; Navarro Alberto, J.A. Multivariate Statistical Methods: A Primer, 4th ed.; CRC Press: Boca Raton, FL, USA, 2016. [Google Scholar]
- Bezdek, J.C.; Ehrlich, R.; Full, W. FCM: The fuzzy c-means clustering algorithm. Comput. Geosci.
**1984**, 10, 191–203. [Google Scholar] [CrossRef] - Friedrich, S.; Konietschke, F.; Pauly, M. Resampling-based analysis of multivariate data and repeated measures designs with the R Package MANOVA.RM. R J.
**2019**, 11, 380–400. [Google Scholar] [CrossRef] - Johnson, G.V.; Raun, W.R.; Zhang, H.; Hattey, J.A. Oklahoma Soil Fertility Handbook; OK Agricultural Experiment Station and Oklahoma Cooperative Extension Service, Oklahoma State University: Stillwater, OK, USA, 2000. [Google Scholar]
- Wischmeier, W.H.; Smith, D.D. Predicting Rainfall Erosion Losses–A Guide to Conservation Planning; Agriculture Handbook 537; U.S. Department of Agriculture (Science and Education Administration): Washington, DC, USA, 1978.
- Renard, K.; Foster, G.; Weesies, G.; McCool, D.; Yoder, D. Predicting soil erosion by water: A guide to conservation planning with the Revised Universal Soil Loss Equation (RUSLE). In Agricultural Handbook; United States Government Printing: Washington, DC, USA, 1997; pp. 65–100. [Google Scholar]
- USDA Department of Agriculture—Agricultural Research Service: Revised Universal Soil Loss Equation. 2002. Available online: http://www.sedlab.olemiss.edu/rusle (accessed on 22 April 2022).
- Panagos, P.; Meusburger, K.; Alewell, C.; Montarella, L. Soil erodibility estimation using LUCAS point survey data of Europe. Environ. Model. Softw.
**2012**, 30, 143–145. [Google Scholar] [CrossRef] - Wilding, L.P. Spatial variability: Its documentation, accommodation and implication to soil survey. In Soil Spatial Variability; Nielsen, D.R., Bouma, J., Eds.; Pudoc: Wagenigen, The Netherlands, 1985; pp. 166–189. [Google Scholar]
- Yamamoto, J.K. Comparing ordinary kriging interpolation variance and indicator kriging conditional variance for assessing uncertainties at unsampled locations. In Application of Computers and Operations Research in the Mineral Industry; Gan, D., Guli, N.P., Dwyer, K., Eds.; Balkema: Kalamazoo, MI, USA, 2005. [Google Scholar]
- Goovaerts, P. Geostatistical tools for characterizing the spatial variability of microbiological and physico-chemical soil properties. Biol. Fertil. Soils
**1998**, 27, 315–334. [Google Scholar] [CrossRef] - Cambardella, C.A.; Moorman, T.B.; Novak, J.M.; Parkin, T.B.; Turco, R.F.; Konopka, A.E. Field-scale variability of soil properties in central Iowa soils. Soil Sci. Soc. Am. J.
**1994**, 58, 1501–1511. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Normal QQ Plot diagram of Nitrogen inorganic, (

**b**) Boxplot diagram of Nitrogen inorganic, (

**c**) Normal QQ Plot diagram of potassium K

^{+}, (

**d**) Boxplot diagram of potassium K

^{+}.

**Figure 2.**Precision agriculture plot maps for: (

**a**) Nitrogen inorganic with the plots’ number, (

**b**) Potassium K

^{+}with the subplots’ number, (

**c**) Model of N-in, (

**d**) Normal QQ Plot of N-in with Log transformation, (

**e**) Model of Potassium K

^{+}and (

**f**) Normal QQ Plot of K

^{+}with Log transformation.

**Figure 3.**Various precision agriculture plot maps of soil’s “Chemical Group” variability: (

**a**) Nitrogen inorganic, (

**b**) Calcium Ca, (

**c**) Phosphorus P-olsen, (

**d**) Magnesium Mg, (

**e**) Potassium K, (

**f**) pH, (

**g**) Organic matter and (

**h**) Calcium carbonate CaCO

_{3}.

**Figure 4.**Various PA plot maps of soil’s “Granular Group”: (

**a**) Sand content, (

**b**) Clay content, (

**c**) Silt content, (

**d**) Very fine sand content, (

**e**) Soil erodibility K factor and (

**f**) Soil’s Gravel content.

**Figure 5.**Various PA spatial variability plot maps of soil’s “Hydraulic Group”: (

**a**) Saturation θsat, (

**b**) Plant Available Water PAW, (

**c**) Field capacity θ

_{fc}, (

**d**) Sat. Hydraulic conductivity Ks, (

**e**) Wilting point θwp and (

**f**) Soil’s Bulk Density.

**Figure 6.**Example diagrams of model performance modeling (average fit, best fit, best R-square) by using: (

**a**) SOM dataset (Training data) and (

**b**) SOM dataset (Validation data).

**Figure 7.**Diagrams of “soil All parameters group”: (

**a**) Eigenvalue diagram, and (

**b**) 3D Component diagram.

**Figure 8.**Factor Analysis Diagrams of: “soil chemical group”—(

**a**) Eigenvalue diagram, (

**b**) 3D Component diagram in rotated space, “soil granular group”—(

**c**) Eigenvalue diagram, (

**d**) 2D Component diagram in rotated space, and “soil hydraulic group”—(

**e**) Eigenvalue diagram, (

**f**) 2D Component diagram in rotated space.

**Figure 9.**(

**a**) Fuzziness performance index and Modified partition entropy vs. Fuzzy management class (k), (

**b**) FkM Xie and Benny index and Wilks lambda vs. Fuzzy management class (k), (

**c**) Fuzziness performance index and Modified partition entropy vs. Fuzziness exponent φ and (

**d**) FkM Xie and Benny index and Wilks lambda vs. Fuzziness exponent φ.

**Figure 10.**Various PA maps of field’s fuzzy MZs clustered with correct fuzzy exploratory analysis: (

**a**) 4 Fuzzy MZs based on soil All parameters group (20 parameters), (

**b**) 3 Fuzzy MZs based on chemical-nutrients group (8 parameters), (

**c**) 3 Fuzzy MZs based on All parameters group, (

**d**) 2 Fuzzy MZs based on granular group (6 parameters), (

**e**) 2 Fuzzy MZs based on All parameters group, and (

**f**) 2 Fuzzy MZs based on hydraulic group (6 parameters).

**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 CaCO_{3} (%) | 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 (m^{3}·m^{−3}) | 4.607 | 13.365 | 17.972 | 15.981 | 0.672 | 0.451 | 4.204 |

16 | Field capacity θ_{fc} (m^{3}·m^{−3}) | 5.344 | 25.124 | 30.468 | 27.663 | 0.923 | 0.852 | 3.337 |

17 | Saturation θsat (m^{3}·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 |

**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 CaCO_{3} |
---|---|---|---|---|---|---|---|---|---|

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 CaCO_{3} | 0.400 ** | 0.266 ** | 0.540 ** | 0.548 ** | 0.428 ** | 0.340 ** | 0.286 ** | 1 |

**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 |

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

SN | Parameter | Wilting Point θwp | Field Capacity θ _{fc} | 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 θ_{fc} | 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 |

**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 CaCO_{3} | 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 θ_{fc} | 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 |

**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 CaCO_{3} | 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 θ_{fc} | 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 |

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 CaCO_{3} | 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 θ_{fc} | 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 |

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 |

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## Share and Cite

**MDPI and ACS Style**

Filintas, A.; Gougoulias, N.; Kourgialas, N.; Hatzichristou, E.
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. *Water* **2023**, *15*, 3278.
https://doi.org/10.3390/w15183278

**AMA Style**

Filintas A, Gougoulias N, Kourgialas N, Hatzichristou E.
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. *Water*. 2023; 15(18):3278.
https://doi.org/10.3390/w15183278

**Chicago/Turabian Style**

Filintas, Agathos, Nikolaos Gougoulias, Nektarios Kourgialas, and Eleni Hatzichristou.
2023. "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" *Water* 15, no. 18: 3278.
https://doi.org/10.3390/w15183278