Mapping Soil Properties at a Regional Scale: Assessing Deterministic vs. Geostatistical Interpolation Methods at Different Soil Depths

Abstract

To determine which interpolation technique is the most suitable for each case study is an essential task for a correct soil mapping, particularly in studies performed at a regional scale. So, our main goal was to identify the most accurate method for mapping 12 soil variables at three different depth intervals: 0–5, 5–10 and >10 cm. For doing that, we have compared nine interpolation methods (deterministic and geostatistical), drawing soil maps of the Spanish region of Extremadura (41,635 km² in size) from more than 400 sampling sites in total (e.g., more than 500 for pH for the depth of 0–5 cm). We used the coefficient of determination (R²), the mean error (ME) and the root mean square error (RMSE) as statistical parameters to assess the accuracy of each interpolation method. The results indicated that the most accurate method varied depending on the property and depth of study. In soil properties such as clay, EBK (Empirical Bayesian Kriging) was the most accurate for 0–5 cm layer (R² = 0.767 and RMSE = 3.318). However, for 5–10 cm in depth, it was the IDW (Inverse Distance Weighted) method with R² and RMSE values of 0.689 and 5.131, respectively. In other properties such as pH, the CRS (Completely Regularized Spline) method was the best for 0–5 cm in depth (R² = 0.834 and RMSE = 0.333), while EBK was the best for predicting values below 10 cm (R² = 0.825 and RMSE = 0.399). According to our findings, we concluded that it is necessary to choose the most accurate interpolation method for a proper soil mapping.

1. Introduction

The interpolation methods have been a breakthrough in soil science, expanding the interest of study areas and saving time and money on complex field works. Many of them have been developed particularly for mapping soil properties [1,2,3,4] such as texture [2], nitrogen [5], phosphorus [6] and organic matter content [7] through different techniques [8,9,10]. They can be divided into two main groups: deterministic and geostatistical. Deterministic methods include Inverse Distance Weighting (IDW), Radial Basis Function (RBF), Global Polynomial Interpolation (GPI), Local Polynomial Interpolation (LPI) or Splines. On the other hand, kriging and its variants such as ordinary, simple, empirical, universal, etc., are included in the group of geostatistical techniques. In recent years, however, so-called hybrid techniques have been used, which consist of the fusion of a linear model and a non-linear interpolation model (e.g., Regression Kriging (RK), or Geographically Weighted Regression (GWR)) [11,12].

Given the variety of available interpolation methods, choosing one is a complex and critical task that entails variations in study results, as also do the nature and context of the data (e.g., experimental design, sampling density or topographic characteristics) [13]. Therefore, working on the identification of the most appropriate interpolation method in each case is essential for a proper soil mapping.

Currently, there is much controversy about which interpolation method is ideal for different properties and case studies. In this regard, the working spatial scale is one of the most important issues when it is used in one method or another. At the regional scale, many studies applied interpolation techniques and obtained different results depending on the variables interpolated [14,15,16,17,18,19]. Shen et al. [12], for example, found that ordinary kriging provided the best results for predicting total soil phosphorus content, while Chen et al. [20] identified IDW as the best method for predicting and monitoring soil moisture at regional scale. In other cases in which soil carbon [21] or soil moisture content [22] are predicted, hybrid methods such as RK and GWR were preferred.

The application of these techniques has not been used only to surface soil properties but also to map them at different depth intervals [23,24,25]. The most common depth interval is 0–10 cm, even when in some environments with shallow soils the adequate interval should be 0–5 cm in depth [26,27]. For those works that used different depth intervals, a large variety of methods have been used so far [28]. However, geostatistical techniques are the most widely used [2,29,30].

In addition, there is not yet a clear consensus about which technique is the most appropriate to reflect properties at different depths, frequently depending on individual cases. In some studies, for example, IDW seems to be an appropriate method for mapping variables such as P, K or SOM in the subsoil [31,32], while in others it is the kriging technique that works the best for topsoil [33]. Conversely, in some cases RBF reported better results than IDW or kriging techniques [34].

In regions such as Extremadura (SW Spain), shallow soils occupy 70% of the total area. This characteristic implies that soil mapping at different depth intervals is considered necessary. Nevertheless, so far in this region, there are no works focused on mapping soil properties at different depths. Beyond the soil mapping developed by the European Soil Data Centre (ESDAC) [35,36,37], there are no studies that focus on mapping soil properties. Some of these studies were focused on mapping quality indices at fixed 0–30 cm intervals, mainly using geostatistical techniques [38]. Some studies compared different interpolation techniques but focused on the quantification of soil losses or on some specific properties without considering different depths and at restricted spatial scales [39,40]. Other studies at a regional scale produced maps of soil aridity [41], bioclimatic indices [42] or sensitivity to land degradation [43].

The scarcity of investigations attending the mapping of soil properties at regional scales is evident. This highlights the need to provide accurate mapping techniques for soil properties. Therefore, the main objective of this work was to identify the most suitable interpolation method for the studied variables at different depths.

2. Materials and Methods

2.1. Study Area

The study has been carried out in the Autonomous Region of Extremadura, located in the southwest of Spain (Figure 1). Extremadura has a surface area of 41,635 km², which represents 8.25% of the total area of Spain. The orography of Extremadura is characterised by the presence of two large river basins (the Tagus and Guadiana rivers) and three parallel mountain ranges (Sistema Central, Montes de Toledo and Sierra Morena), which interrupt the dominance of the extensive peneplains. Precambrian and Paleozoic slates and granites are the dominant rocks on which our soils are developed. Cambisol, Leptosol and Regosol soil types occupy 70% of the total surface area, which is mainly used for livestock rearing. On the other hand, Fluvisol or Luvisol soil types predominate in the river valleys, mainly dedicated to agricultural activities [35]. The climate is Mediterranean, with mild winters and hot and dry summers. Yearly total average rainfall is below 600 mm, except in the mountain ranges where values over 1000 mm are reached. The average temperature in the region is around 16–17 °C with lower values in the vicinity of the mountain ranges.

2.2. Dataset Characteristics and Variables Selection

Various data sources contributed to the dataset used in this study. For all sources, data available for any of the three studied soil depths (0–5, 5–10 and >10 cm, respectively) were considered, disregarding depth intervals that do not comply with those proposed in the study. The >10 cm class refers to soils mostly not exceeding 35 or 40 cm depth. This region is dominated by Cambisol and especially Leptosol soils, most of which are less than 40 cm in depth. Data have been structured as a point soil-sample database, where most of the records come from different research projects developed by the Geo-Environmental Research Group (GIGA) of the University of Extremadura over the last 20 years, to whom authors belong. Some data from the book “Estudio de los Suelos de la Tierra de Barros” [36] have also been used. Additionally, other data come from the Spanish Soil Properties Database, created by the Centre for Energy, Environmental and Technological Research (CIEMAT), from the Soil Catalogue of Extremadura in soil profiles carried out at the end of the 1990s, as well from the Soil Grids platform [37]. In one of the data sources used, it was not possible to verify which analysis method was used. However, in the other sources, the method was found to be the same. The total number of sampling points varied depending on the soil property and the depth where soil samples were taken (Figure 2,

Table 1. Methods used for the analysis of the studied properties and distribution of the number of samples by property and soil depth interval.

Soil Property	Depth (cm)	n *	Unit	Method
	0–5	495	%	Soil Survey Laboratory Methods Manual [38]
Clay	5–10	393
	>10	326
	0–5	424
Silt	5–10	392
	>10	328
	0–5	333
Sand	5–10	294
	>10	239
	0–5	509		1:2.5 soil/water
pH	5–10	449
	>10	349
	0–5	445	Cmol kg−1	MAPA [39]
CEC	5–10	402
	>10	306
	0–5	314
Calcium	5–10	262
	>10	171
	0–5	319
Magnesium	5–10	226
	>10	178
	0–5	284
Sodium	5–10	262
	>10	185
	0–5	265	%	Dumas [40]
Available N	5–10	254
	>10	205
	0–5	176	ppm	Olsen et al. [41]
Available P	5–10	155
	>10	94
	0–5	296	Cmol kg−1	Ammonium acetate at pH 7 (USDA) [42]
Potassium	5–10	243
	>10	190
	0–5	420	%	Walkley and Black wet combustion [43]
SOM	5–10	419
	>10	303

* n corresponds to the total number of samples for each property.

). For instance, more than 500 sampling points are available for some properties, such as pH at 0–5 cm depth and 94 for >10 cm depth phosphorus.

2.3. Data Preprocessing and Statistical Analysis

The first step of the analysis consisted of filtering the outliers from the original dataset. In order to do this the cluster and outlier analysis tool (Anselin Local Moran’s I) integrated in ArcGIS 10.5 software was applied [44,45]. This analysis provides a simple and adequate identification of statistically significant outliers, with 95% confidence in relation to neighbouring data.

Once the outliers were identified and removed from the original dataset, the remaining data were randomly partitioned into training and validation datasets, amounting, respectively, to 80% and 20% of the data available for each one of the interpolation methods selected. This sequence of work was carried out for the 12 soil properties and three depths considered.

Statistical parameters such as mean, minimum, maximum and coefficient of variation were calculated to characterise the filtered dataset. In order to reflect the differences observed between some statistics among interpolation methods, bar and whisker plots were used. All the statistical analyses were carried out using Statistica v. 6.0 (StatSoft, Tulsa, OK, USA) [46] and Microsoft Office Excel software packages.

2.4. Interpolation Methods

Nine interpolation methods were considered as spatially predictive techniques for each of the variables selected in the study. Six deterministic and three geostatistical methods were chosen, all of them integrated into the Geostatistical Analyst extension of ArcGIS 10.5 (ESRI, Redlands, CA, USA) [47].

The deterministic methods were:

• Inverse Distance Weighting (IDW), which works on the assumption that closer points are more similar to each other than those further away. This method uses the values surrounding some unmeasured point to predict, giving greater weight to the closer points [48].
• Four Radial Basis Functions: Completely Regularized Spline (CRS), Spline With Tension (SWT), Multiquadric (M-Q) and Inverse Multiquadric (IM-Q). These are exact interpolation techniques, i.e., the surface must pass through each of the measured values. Each function will give an interpolation surface with a different shape and different results [49].
• Local Polynomial Interpolation (LPI), which works by fitting many polynomials within the specified overlapping neighbourhoods as opposed to Global Polynomial Interpolation (GPI) [50].

Contrariwise, the geostatistical techniques assume spatial autocorrelation as part of the interpolation process. The geostatistical methods used in this study were:

• Ordinary Kriging (OK), which works on the assumption that a constant mean is unknown throughout the process [51].
• Simple Kriging (SK), which assumes stationarity from the beginning of a known mean. Hence, mathematically speaking, it is the simplest but least general method [52].
• Empirical Bayesian Kriging (EBK) tends to maximum likelihood estimation. This allows us to measure the evidence and the uncertainty of the emulator [49].

It should be noted that in each of the interpolation methods used, the parameters of the model were modified in order to obtain the lowest mean square error as the output result.

2.5. Assessment of the Interpolation Methods Reliability

From the cross-validation, the mean error (ME), the coefficient of determination (R²) and the root mean square error (RMSE) were used to assess the accuracy of the interpolation methods. In order to consider the most reliable method, the lowest RMSE and the highest R² were taken into account [53]. In some cases, where these parameters were equal, the ME value closest to 0 was used to determine the most reliable method.

ME gives an absolute value that determines the degree of bias obtained in the estimates. Higher values indicate larger differences between predicted and observed values [54]. ME values are calculated as follows:

$$ME=\frac{{{\displaystyle \sum }}_{i=1}^n(\widehat{Z }\left(s_i\right)-z \left(s_i\right))}{n}$$

(1)

where, z ($s_i$) is the observed value at point$s_i$, $\widehat{Z }$($s_i$) is the predicted value at point $s_i$ and n the number of samples.

The coefficient of determination or R-squared (R²) assesses the ability of a model to predict an outcome of a regression. Thus, the coefficient of determination indicates how well the data fit the model. Values vary between positive 1 and 0, values close to 1 indicate a better fitness of the model [55]. The equation is given as follows:

$$R^2=\frac{{[{{\displaystyle \sum }}_{i=1}^n\left(P_i-P_{ave}\right)\left(Q_i-Q_{ave}\right)]}^2}{{{\displaystyle \sum }}_{i=1}^n{(P_i-P_{ave})}^2{{\displaystyle \sum }}_{i=1}^n{(Q_i-Q_{ave})}^2}$$

Being P_ave the average of the estimated value; Q_ave is the average of measured value; and n is the points number used for estimation.

The root mean square error (RMSE) was used to quantify the accuracy of the interpolation model used. Low RMSE values indicate higher reliability of the model. The RMSE is calculated as follows:

$$RMSE=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{[\widehat{Z }\left(s_i\right)-z \left(s_i\right)]}^2}{n}}$$

(2)

Being, z ($s_i$) the observed value at point$s_i$, $\widehat{Z}$ $(s_i)$ the predicted value at point $s_i$, and n the number of samples.

3. Results

3.1. Descriptive Statistics

Table 2. Descriptive statistics of the studied variables.

Variable	Depth	N	Mean	Min.	Max.	CV (%)
Clay (%)	0–5 cm	495	15	1	50	55
	5–10 cm	393	19	2.	81	65
	>10 cm	326	22.811	3	77	59.
Silt (%)	0–5 cm	424	33	1	70	46
	5–10 cm	392	33	1	71	49
	>10 cm	328	31	3	74	54
Sand (%)	0–5 cm	333	47	6	91	27
	5–10 cm	294	43	4	89	32
	>10 cm	239	41	2	85	38
pH (1:2.5)	0–5 cm	509	5.93	4.00	8.20	14
	5–10 cm	449	6.01	3.70	9.1	15
	>10 cm	349	6.14	4.20	9.30	16
CEC (Cmol kg−1)	0–5 cm	445	15.52	0.81	80.46	67
	5–10 cm	402	15.57	2.00	69.66	76
	>10 cm	306	16.34	2.00	61.60	70
Ca (Cmol kg−1)	0–5 cm	314	6.78	0.41	61.87	116
	5–10 cm	262	6.90	0.17	62.00	142
	>10 cm	171	8.85	0.18	55.59	137
Mg (Cmol kg−1)	0–5 cm	319	1.80	0.07	12.30	87
	5–10 cm	226	1.77	0.05	25.00	93
	>10 cm	178	2.29	0.03	16.62	104
Na (Cmol kg−1)	0–5 cm	284	0.65	0.07	2.92	100
	5–10 cm	262	0.40	0.04	2.13	144
	>10 cm	185	0.43	0.02	2.54	129
N (%)	0–5 cm	265	0.23	0.02	0.95	87
	5–10 cm	254	0.13	0.01	0.38	85
	>10 cm	205	0.09	0.00	0.26	97
P (ppm)	0–5 cm	176	22.10	0.40	69.00	53
	5–10 cm	155	15.12	0.40	67.00	44
	>10 cm	94	11.84	0.40	48.30	51.
K (Cmol kg−1)	0–5 cm	296	0.57	0.03	3.40	77.
	5–10 cm	243	0.42	0.02	2.12	87
	>10 cm	190	0.42	0.02	2.91	95
SOM (%)	0–5 cm	420	3.62	0.10	20.80	76
	5–10 cm	419	1.86	0.10	14.50	98
	>10 cm	303	1.21	0.10	6.00	82

shows the descriptive statistics of each of the studied variables. A trend can be observed of clay, silt, and sand content, as well as pH, cation exchange capacity, calcium, and magnesium to increase with depth, showing other variables, i.e., nitrogen, phosphorus, potassium and organic matter, an opposite behaviour. The coefficient of variation (CV) reflects the variability of soil properties was low for pH, with values not exceeding 17%, being high for clay and silt content, as well as for some chemical properties such as cation exchange capacity, phosphorus, potassium, or soil organic matter. The CV was particularly high for calcium, magnesium, sodium, and nitrogen.

3.2. Optimal Interpolation Method by Soil Property

3.2.1. Particle Size Distribution

Model statistics for the three studied soil depths, obtained with the validation dataset when modelling particle size distribution, are shown in

Table 3. Model validation statistics for the different interpolation methods used when modelling particle size distribution at the three studied soil depths. In bold is the optimal method.

		0–5 cm			5–10 cm			>10 cm
Variable	Method	ME	R2	RMSE	ME	R2	RMSE	ME	R2	RMSE
Clay (%)	IDW	−0.249	0.723	3.554	0.265	0.689	5.131	1.393	0.648	5.205
	CRS	0.239	0.725	3.505	1.119	0.663	5.313	1.870	0.639	5.800
	SWT	0.223	0.731	3.456	1.123	0.638	5.321	1.822	0.642	5.771
	M-Q	0.200	0.721	4.002	0.147	0.575	6.357	0.740	0.580	6.503
	IM-Q	3.964	0.650	3.964	0.690	0.641	5.569	2.524	0.562	6.590
	LPI	0.223	0.663	4.046	0.970	0.584	5.799	2.077	0.607	6.153
	OK	0.220	0.728	3.523	0.570	0.625	5.480	1.946	0.578	6.376
	SK	0.390	0.674	4.157	0.388	0.603	5.865	2.367	0.591	6.101
	EBK	0.198	0.767	3.318	0.238	0.639	5.525	1.807	0.613	5.972
Silt (%)	IDW	0.267	0.831	6.222	−0.486	0.897	5.103	1.168	0.905	6.595
	CRS	−0.163	0.823	6.363	−1.365	0.895	5.287	−0.564	0.923	6.438
	SWT	−0.110	0.825	6.331	−1.357	0.895	5.280	−0.418	0.919	6.344
	M-Q	0.489	0.807	6.775	−0.627	0.889	5.494	0.239	0.908	5.804
	IM-Q	−0.416	0.734	7.835	−1.629	0.847	6.375	−2.209	0.761	10.051
	LPI	−0.423	0.793	7.234	−1.415	0.856	6.158	−1.823	0.862	8.939
	OK	−0.264	0.820	6.458	−1.420	0.882	5.626	−0.609	0.921	5.605
	SK	−0.094	0.815	6.563	−1.537	0.884	5.582	0.244	0.923	6.020
	EBK	−0.329	0.820	6.488	−1.040	0.892	5.383	−0.444	0.929	5.725
Sand (%)	IDW	0.847	0.657	5.290	0.200	0.816	5.217	−1.818	0.750	7.039
	CRS	0.290	0.739	4.627	0.730	0.804	5.459	−1.703	0.748	7.072
	SWT	0.204	0.723	4.727	0.832	0.810	9.637	−1.706	0.748	7.069
	M-Q	0.884	0.608	6.406	0.280	0.826	5.729	−1.392	0.732	7.544
	IM-Q	−0.740	0.535	6.233	0.664	0.700	6.680	−2.077	0.514	9.782
	LPI	1.065	0.602	6.279	1.164	0.738	6.881	−0.247	0.615	8.851
	OK	0.471	0.680	5.094	1.460	0.720	6.790	−1.505	0.780	6.586
	SK	0.719	0.677	5.133	0.740	0.693	6.878	−1.437	0.799	6.354
	EBK	1.083	0.637	5.602	0.759	0.816	5.258	−1.794	0.764	6.906

. In Appendix A, Figure A1 shows the regional cartographic representation of the best performing methods for clay, sand, and silt content. Regarding the clay content, the more accurate methods were EBK for 0–5 cm soil depth and IDW for larger depths. RMSE values were below the average reflected in Table 1, showing an increasing trend with depth (3.554%, 5.131% and 5.205%). In turn, R² values decreased (0.767, 0.689 and 0.648). It is worth noting that the differences in RMSE between the most and least accurate methods were about 1% or higher being R² differences minor. In the case of silt content, IDW was the most accurate method for 0–5 and 5–10 cm depth, performing the OK method better for greater depths. As in the case of clay content, RMSE values were below the average measured for the reference dataset. Model accuracy decreased when increasing soil depth (6.22%, 5.103% and 5.605%), showing an opposite behaviour to that observed for clay content, while R² increased (0.831, 0.897 and 0.921). With regards to the sand content, the best performing methods were CRS at 0–5 cm depth, IDW for 5–10 cm depth and SK at >10 cm depth. RMSE data increased in this case with increasing soil depth (4.627%, 5.217% and 6.354%), and the same is true for R² values (0.739, 0.816 and 0.799), contrasting with the trend observed in the clay model.

3.2.2. Selected Chemical and Sorption Complex Properties

Table 4. Model validation statistics for the different interpolation methods used when modelling the chemical properties selected at the three studied soil depths. In bold is the optimal method.

		0–5 cm			5–10 cm			>10 cm
Variable	Method	ME	R2	RMSE	ME	R2	RMSE	ME	R2	RMSE
pH (1:2.5)	IDW	−0.030	0.809	0.350	0.071	0.808	0.349	0.015	0.803	0.413
	CRS	−0.031	0.834	0.333	0.069	0.826	0.331	0.034	0.803	0.412
	SWT	−0.006	0.794	0.364	0.068	0.827	0.330	0.033	0.804	0.411
	M-Q	−0.033	0.726	0.413	0.030	0.803	0.356	0.007	0.796	0.443
	IM-Q	0.013	0.720	0.424	0.070	0.767	0.381	0.061	0.730	0.487
	LPI	−0.064	0.772	0.399	0.028	0.744	0.837	−0.014	0.761	0.455
	OK	−0.029	0.806	0.352	0.041	0.823	0.328	0.021	0.782	0.441
	SK	−0.043	0.813	0.362	0.054	0.804	0.348	0.030	0.757	0.465
	EBK	−0.018	0.823	0.335	0.064	0.816	0.342	0.024	0.825	0.399
CEC (Cmol kg−1)	IDW	1.396	0.854	3.778	1.741	0.683	4.676	0.706	0.690	4.470
	CRS	1.444	0.823	3.990	2.019	0.713	4.555	1.025	0.671	4.625
	SWT	1.438	0.825	3.976	2.018	0.713	4.553	1.021	0.671	4.620
	M-Q	1.402	0.744	5.706	1.893	0.665	5.188	0.418	0.641	4.763
	IM-Q	1.508	0.760	4.436	1.720	0.704	4.538	1.405	0.601	5.239
	LPI	1.158	0.670	5.015	1.819	0.700	4.560	0.575	0.646	4.901
	OK	1.296	0.821	4.108	1.690	0.702	4.533	0.804	0.679	4.583
	SK	1.866	0.770	4.486	1.649	0.703	4.576	1.120	0.704	4.637
	EBK	1.441	0.819	4.199	1.833	0.728	4.567	0.864	0.697	4.415
Ca (Cmol kg−1)	IDW	0.006	0.833	2.263	0.639	0.973	1.879	−0.521	0.959	2.326
	CRS	0.254	0.960	1.153	0.451	0.952	2.280	0.040	0.905	2.610
	SWT	0.178	0.964	1.078	0.469	0.956	2.137	0.056	0.904	2.621
	M-Q	0.105	0.963	1.078	0.368	0.897	3.305	−0.812	0.968	2.254
	IM-Q	0.235	0.964	1.093	0.369	0.911	3.208	0.232	0.830	3.664
	LPI	−0.079	0.819	2.509	0.169	0.912	3.217	−0.665	0.961	2.473
	OK	0.053	0.967	1.055	0.325	0.917	2.744	−0.272	0.959	2.241
	SK	0.298	0.970	1.010	0.332	0.901	3.614	0.075	0.905	2.727
	EBK	0.084	0.977	0.864	0.676	0.947	2.233	−0.400	0.964	1.955
Mg (Cmol kg−1)	IDW	0.112	0.439	0.907	0.147	0.605	0.539	0.347	0.708	0.781
	CRS	0.268	0.448	0.814	0.246	0.554	0.613	0.417	0.688	0.822
	SWT	0.265	0.422	0.872	0.251	0.551	0.618	0.417	0.694	0.816
	M-Q	0.224	0.291	1.183	−0.052	0.432	0.577	0.370	0.365	1.186
	IM-Q	0.294	0.360	0.995	0.222	0.551	0.661	0.429	0.754	0.782
	LPI	0.303	0.413	0.827	0.229	0.485	0.650	0.362	0.659	0.833
	OK	0.135	0.504	0.789	0.102	0.770	0.534	0.553	0.605	0.988
	SK	0.301	0.569	0.741	0.274	0.333	0.724	0.370	0.535	0.939
	EBK	0.158	0.395	0.955	0.027	0.534	0.561	0.398	0.449	1.105
Na (Cmol kg−1)	IDW	0.069	0.828	0.210	0.074	0.505	0.142	0.105	0.044	0.196
	CRS	0.030	0.888	0.167	0.064	0.511	0.138	0.110	0.104	0.198
	SWT	0.040	0.891	0.169	0.067	0.503	0.138	0.116	0.089	0.201
	M-Q	0.008	0.801	0.227	0.040	0.400	0.174	0.085	0.077	0.239
	IM-Q	0.087	0.904	0.202	0.055	0.369	0.175	0.134	0.039	0.227
	LPI	0.048	0.755	0.248	0.102	0.107	0.203	0.139	0.011	0.226
	OK	0.016	0.865	0.178	0.050	0.369	0.137	0.130	0.004	0.234
	SK	0.048	0.855	0.190	0.111	0.303	0.174	0.130	0.103	0.201
	EBK	0.036	0.820	0.213	0.096	0.071	0.200	0.120	0.011	0.218

shows the main model statistics of the interpolation methods used for the selected chemical variables. The maps that represent the regional pattern of these variables with the more accurate interpolation methods are shown in Figure A2. For the pH, the best performing method at 0–5 cm depth was CRS (R² = 0.834 and RMSE = 0.333). The EBK algorithm provided very similar results to the former, but with slightly higher RMSE and lower R². At 5–10 cm depth, OK method performed better (R² = 0.823 and RMSE = 0.328), followed by SWT with slightly higher R² and RMSE. At soil depths greater than 10 cm, EBK was the most accurate method (R² = 0.825 and RMSE = 0.399). Overall, results obtained at each of the three depths were comparable, with RMSE values that varied below 0.07.

Regarding the Cation Exchange Capacity (CEC), IDW was the most accurate method at 0–5 cm depth, with RMSE of 3.778 and R² of 0.854. At 5–10 cm, OK was the method that provided the best results, with RMSE and R² accounting to 4.533 and 0.702, respectively. The same was true at soil depths greater than 10 cm, where EBK was the best performing method, with RMSE of 4.415 and an R² of 0.697. In the case of Calcium (Ca), unlike the previous variables, it was a geostatistical method, EBK, that provided the best results at 0–5 cm depth, with RMSE of 0.864 and R² of 0.977. At 5–10 cm depth, on the other hand, it was the IDW method that showed better results, with RMSE of 1.879, one point higher than the topmost soil layer, but still showing a good fitness with an R² of 0.973. The RMSE increased at deeper depths (>10 cm), where EBK was identified as the most accurate method but still retaining a high R² value of 0.964. Magnesium (Mg) models for the 0–5 cm soil depth showed the SK method as the best performing one with RMSE of 0.741 and an R² of 0.569, indicating poor model fitness. Nevertheless, with increasing depths, results improve considerably, with the OK method being better at 5–10 cm that reduced the RMSE to 0.534 and improved the R² to 0.770. The same was true at >10 cm depth, where the IDW method provided an RMSE that increased again to 0.781 while still maintaining a good R² value of 0.708. Finally, for Sodium (Na) content, it was the CRS method that produced the best results at 0–5 cm depth, with RMSE and R² that amounted to 0.167 and 0.888, respectively. For the 5–10 cm soil layer, CRS was also the method showing the best results, although both RMSE and R² decreased to 0.138 and 0.511, respectively. At >10 cm soil layer, although IDW was the most accurate method, the model validation statistics obtained were poor (RMSE = 0.196 and R² = 0.044) indicating a very poor model fitness.

3.2.3. Selected Elements Content

The statistics obtained as a result of the validation of the selected interpolation methods used for some of the main so-called soil fertilisers are presented in

Table 5. Model validation statistics for the different interpolation methods used when modelling nitrogen (N), phosphorus (P), potassium (K) and soil organic matter (SOM) at the three studied soil depths. In bold is the optimal method.

		0–5 cm			5–10 cm			>10 cm
Variable	Method	ME	R2	RMSE	ME	R2	RMSE	ME	R2	RMSE
N (%)	IDW	0.010	0.577	0.058	−0.003	0.128	0.039	0.002	0.685	0.024
	CRS	0.006	0.590	0.056	−0.001	0.119	0.039	0.005	0.645	0.026
	SWT	0.006	0.597	0.056	−0.001	0.116	0.039	0.005	0.649	0.026
	M-Q	0.006	0.362	0.076	−0.009	0.064	0.051	0.002	0.541	0.031
	IM-Q	0.010	0.598	0.060	−0.009	0.064	0.051	0.002	0.545	0.029
	LPI	0.010	0.463	0.067	0.003	0.039	0.045	0.009	0.587	0.032
	OK	0.004	0.603	0.056	0.000	0.142	0.038	0.005	0.595	0.028
	SK	0.006	0.634	0.053	0.004	0.161	0.033	0.008	0.442	0.034
	EBK	0.005	0.584	0.060	−0.003	0.038	0.040	0.004	0.495	0.032
P (ppm)	IDW	−1.741	0.836	6.917	−0.780	0.739	5.508	5.518	0.319	14.143
	CRS	0.840	0.840	6.726	1.557	0.519	6.911	7.561	0.590	14.615
	SWT	0.705	0.838	6.710	1.727	0.582	7.024	7.433	0.587	14.374
	M-Q	1.131	0.841	10.297	−0.630	0.673	8.475	12.242	0.584	27.097
	IM-Q	2.255	0.523	10.859	2.975	0.278	9.382	6.655	0.625	8.811
	LPI	−0.731	0.780	7.672	3.034	0.411	8.716	4.663	0.243	12.556
	OK	−0.006	0.811	7.378	0.616	0.745	5.366	7.387	0.151	17.555
	SK	−0.355	0.850	7.336	0.929	0.685	6.385	7.141	0.420	17.683
	EBK	1.145	0.831	8.679	0.929	0.685	6.385	8.544	0.579	16.123
K(Cmol kg−1)	IDW	−0.015	0.729	0.170	0.041	0.547	0.147	0.001	0.617	0.146
	CRS	0.000	0.723	0.173	0.040	0.582	0.133	0.032	0.571	0.158
	SWT	0.013	0.686	0.185	0.050	0.522	0.150	0.033	0.575	0.158
	M-Q	−0.032	0.657	0.192	0.002	0.444	0.158	0.004	0.637	0.143
	IM-Q	0.023	0.642	0.203	0.052	0.366	0.194	0.046	0.552	0.185
	LPI	−0.005	0.666	0.188	0.042	0.529	0.159	0.032	0.584	0.140
	OK	−0.020	0.716	0.174	0.027	0.512	0.154	0.021	0.557	0.146
	SK	0.052	0.690	0.187	0.049	0.578	0.141	0.038	0.586	0.145
	EBK	−0.012	0.719	0.172	0.020	0.524	0.139	0.017	0.579	0.140
SOM (%)	IDW	0.105	0.754	0.957	0.31	0.704	0.754	0.109	0.662	0.548
	CRS	−0.041	0.67	1.033	0.268	0.631	0.784	0.083	0.577	0.557
	SWT	−0.078	0.673	1.043	0.267	0.627	0.776	0.084	0.578	0.555
	M-Q	−0.07	0.683	1.072	0.175	0.441	0.881	0.043	0.506	0.630
	IM-Q	−0.052	0.46	1.287	0.264	0.449	0.888	0.022	0.267	0.667
	LPI	0	0.454	1.343	0.318	0.435	0.945	0.131	0.402	0.628
	OK	0.001	0.707	0.97	0.175	0.624	0.79	0.082	0.588	0.531
	SK	−0.07	0.680	1.006	0.199	0.474	0.852	0.091	0.598	0.548
	EBK	−0.008	0.684	1.001	0.221	0.657	0.715	0.046	0.492	0.565

, and their cartographic representation is shown in Figure A3.

At the 0–5 cm soil layer, the most accurate method predicting nitrogen content was the SK, showing an R² of 0.634 and an RMSE of 0.053. SK was also optimal for the 5–10 cm soil layer. However, although the RMSE value of 0.033 is acceptable, the R² value obtained at this depth (0.161) indicates poor model fitness. At the depth >10 cm, IDW provided the best results, with R² of 0.685 and RMSE of 0.024.

As it is seen in Table 5, when the phosphorus content is interpolated, the optimal methods were the CRS for the uppermost soil layer (R² = 0.840 and RMSE = 6.726), the OK at 5–10 cm soil depth (R² =0.745 and RMSE = 5.366) and the IM-Q for the deepest layer (>10 cm) (R² = 0.625 and RMSE = 8.811).

Regarding the potassium, the IDW was the most accurate method at 0–5 cm (R² = 0.729 and RMSE = 0.170). In this case, model accuracies were considerably reduced with depth, with the CRS method being better at 5–10 cm with an R² of 0.582 and an RMSE of 0.133, and at >10 cm soil layer, EBK revealed the most accurate results, very similar to those obtained for the above layer.

For soil organic matter (SOM), IDW was the most accurate method for the 0–5 cm layer, with an R² of 0.754 and RMSE of 0.957. The model accuracy was also reduced when modelling SOM at deeper layers, with R² values of 0.657 at 5–10 cm, where the EBK was the optimal model, and 0.588 at >10 cm layer, with the OK as the best performing method.

3.3. General Assessment of the Interpolation Methods

The general performance of the different interpolation methods considered in this study, attending to the whole set of modelled variables, was evaluated considering their average R² and RMSE statistics, as reflected in Figure 3.

As expressed in Figure 3a, attending to the model accuracies, as expressed by the R², the interpolation methods with the best general performance were IDW, CRS and SWT, reaching, respectively, 0.739, 0.755 and 0.747 on average. The geostatistical methods, on the other hand, showed lower accuracies in general, OK being the one with the highest R², as compared to the similar values obtained with EBK and SK methods.

As for the average RMSE (Figure 3b), again the IDW, followed by CRS and SWT, were the more accurate methods. In this case, the geostatistical methods yielded similar or slightly higher values, with SK producing the highest mean RMSE overall.

When the analysis was performed as a function of the soil depth, the IDW was the method more repeatedly observed as more accurate. It was more reliable at 0–5 cm depth for properties such as silt, cation exchange capacity, potassium, and soil organic matter. At the 5–10 cm layer, it was also preferred when modelling clay, silt, sand, and calcium content. Finally, at depth >10 cm, it was also better when modelling clay, magnesium, sodium, and nitrogen content. Alternatively, CRS was more reliable for variables such as sand, pH, sodium, and phosphorus at the uppermost soil layer, also being good to express sodium and potassium content at 5–10 cm depth. Among the deterministic methods, IM-Q showed the best results when predicting phosphorus content at >10 cm.

As for the geostatistical methods, OK yielded the best results in six cases. At 5–10 cm depth, it was the most reliable method for variables such as pH, cation exchange capacity, and magnesium and phosphorus contents, and also for silt content and soil organic matter at the >10 cm soil layer. SK was the optimal method to model magnesium and nitrogen content at 0–5 cm and for nitrogen content at 5–10 cm and sand content at >10 cm. Finally, the EBK was selected as more accurate in seven cases.

4. Discussion

The lithological and land use characteristics existing in the region under study show a low variability. This highlights that the degree of variation observed was highly dependent on the property itself. The mineral fraction of the soil showed less variability than the selected elements content. In this sense, due to the illuviation process, the clay content showed greater variability as compared with silt and sand content. Those results agree with the findings of Keshavarzi et al. [56] and Addis et al. [57]. In turn, soil nutrients showed a higher variability, since more than 80% of them are concentrated in the upper and shallower soil layers. However, other chemical properties such as pH showed the opposite behaviour, with less variability and higher values at the deepest layers [34].

Currently, geostatistical methods are the most widely used methods for predicting and mapping soil properties [2,58]. However, in this study both deterministic and geostatistical methods have been used to ascertain the more accurate methods. The results of the interpolation analysis in this study showed the deterministic methods as having more potential to interpolate soil particle size distribution as compared to the geostatistical ones. The best results of deterministic methods in the topsoil layers are determined by a sufficiently dense data set. In this way, deterministic functions can capture the extent of local surface variation needed for the analysis and report more accurate results. In contrast to the findings of other authors such as Gozdowski et al. [59] or Radocaj et al. [60], in our study it was the IDW method that provided the best results. However, particularly when interpolating clay content at 0–5 cm or silt and sand content at the >10 cm layer, geostatistical methods were identified as more accurate, as found also by Li et al. [2].

Attending to the chemical variables, it was difficult to identify a unique optimal interpolation technique. The models generated for pH showed adequate fitness and acceptable mean square errors. Although other studies [61] found OK as the best performing method, our analysis showed the CRS as the most accurate for the topsoil, in agreement with Zandi et al. [34]. At the same time, also according with Zandi et al. [34] but contrasting with that observed by Robinson and Metternicht [62], the error and reliability statistics of the subsoil models indicate that kriging techniques were more accurate.

When studying CEC, models showed good performance, even when the average errors obtained were relatively high for two of the three depths. Our results showed that, when interpolating the cation exchange capacity at the 0–5 cm layer, IDW was the best method. Those results are in agreement with the findings of other authors [62,63]. Nevertheless, several works preferred geostatistical techniques, in concordance with the results obtained for the deeper layers, where OK and EBK proved to be more accurate [64,65,66,67,68].

In the case of calcium, models showed good results in general, even though the mean square error increased in depth due to the higher variability of the data. In this case, EBK was the most accurate method for predicting calcium at the shallowest (0–5 cm) and deepest (>10 cm) layers. Our results agree with other authors [69,70], although they disagree with the findings of others [62] that identified IDW as more accurate for interpolating calcium at 5–10 cm depth.

For magnesium, model results improve with depth. When interpolating the shallowest soil layers (0–5 and 5–10 cm), according to John et al. [9], geostatistical methods such as SK and OK were found to be the most accurate. However, IDW was the best method when interpolating Mg at more than 10 cm. This agreed with Schloeder et al. [71], who found no differences between IDW and OK models.

Sodium models provided good results at 0–5 cm depth, with CRS being the most accurate method. Even when at 5–10 cm depth results were less accurate, CRS was also the best method. At >10 cm soil depth, the model showed a weak fitness, indicating the difficulties for mapping Na at this soil depth. In this case, the better accuracy of deterministic vs. geostatistical methods for the first two soil depths coincides with the findings of Fu et al. [72]. However, it differs from Cruz-Cárdenas et al. [70] and Keshavarzi and Sarmadian [73], who found kriging methods as the most accurate.

When interpolating N, P, K and SOM, the results indicate that any of the interpolation techniques dominate in terms of the model’s accuracy, i.e., depending on the property and soil depth, the results vary. Good results were observed for nitrogen at 0–5 cm and >10 cm layers, where SK and IDW, respectively, were the most accurate methods. The usefulness of SK coincides with Wang et al. [15]. Nevertheless, the adequacy of IDW at deeper layers in our case differs from the findings of other works [27,74,75]. However, the results of N models at 5–10 cm depth showed poor fitness, which does not allow for accurate predictions for the study area.

When interpolating phosphorus, deterministic techniques such as CRS and IM-Q were the most accurate at 0–5 cm and >10 cm soil depth. These results are in agreement with those obtained by Wollenhaupt et al. [31]. However, coinciding with Shen et al. [12] and Duan et al. [76], OK was the best method for predicting P at 5–10 cm. Furthermore, in our case, OK and IDW showed the same behaviour at 5–10 cm depth, as also found by Schloeder et al. [71].

In the case of potassium models, good results were obtained at 0–5 cm depth. However, ability to ascertain the predictive capacity of the models at 5–10 cm and >10 cm was poor. For the first depth, the deterministic IDW method was the most accurate. In this sense, the results are in agreement with the findings of Bogunovic et al. [77] and Lei et al. [78] in which radial basis functions were observed as more accurate for the shallowest soil layers. These findings agree with our results in the sense that the deterministic CRS was also better to interpolate potassium at 5–10 cm. Conversely, EBK was the best method for predicting values >10 cm. This was also observed by Lingling et al. [79] and Karwariya et al. [5], who found geostatistical methods as more accurate than deterministic ones.

The models developed for the prediction of soil organic matter were good in the case of the first two soil layers. However, at >10 cm, model results were relatively worse, although still keeping acceptable errors. IDW was the most reliable method for predicting SOM at 0–5 cm. Nevertheless, geostatistical methods were the most accurate in the case of Long et al. [3] or Bouasria et al. [80]. At 5–10 and >10 cm, EBK and OK were better. These results could partially agree with Durdevic et al. [7], who found EBK as the most accurate method to interpolate SOM at 0–30 cm, followed by OK and IDW.

In all the case studies analysed in this work, the model’s performance varies according to the different properties. This highlights the spatial dependence of the data on intrinsic and soil formation factors. One of the main parameters determining model performance is soil depth. This, in turn, limits the number of samples in many cases due to the shallow soils in this study area. However, the sampling point’s density does not imply that the model’s performance is reduced but depends on other issues such as the variability of the data at depth, so much so that models with a lower number of samples provide better results than others with more samples, as is the case for silt. In the surface soil layers, the properties show a high variability. However, this spatial variability is considerably reduced at depth.

Another important issue in modelling soil properties is the date of the data used. In some environments (e.g., tropical climates) the use of soil samples exceeding 10–15 years may lead to unrealistic results due to the faster pattern rates of change in soil properties. However, in our environment (Mediterranean climate), soil properties do not usually undergo significant changes. Properties remain stable for 10–15 years, unless there are changes in land use that are very different from the previous ones, as pointed out by Pulido Fernández [81], who compared data from more than 30 years in similar environments. Nevertheless, it is important to add that soil organic matter content changes faster than nutrients and cations, as found by Llorente et al. [82], which shows how in this type of environment only organic matter increases, especially in farms without excessive stocking rates. It is also true that, logically, with proper management, levels increase, but slowly.

When the performance of all the studied interpolation techniques were jointly assessed by means of the analysis described in Section 3.3, it was clearly ascertained that three of the deterministic methods (IDW, CRS and SWT) provided better results than the geostatistical ones. Although the difference is minor in some cases, our results differed from the general consideration by which the geostatistical methods are more commonly used to spatially predict soil properties values.

Working on the search for the most accurate mapping technique is one of the main tasks of this group. However, the main idea is to clarify which parameters have the greatest influence on the model’s performance. To this end, the use of deep learning techniques is intended, in which a multitude of environmental covariates can be incorporated. Moreover, new trends in soil mapping are along these lines, as is the use of hybrid techniques for soil mapping.

5. Conclusions

In this study, nine interpolation methods were used to predict 12 soil variables that were measured at three different soil depth intervals. Statistics such as mean error, coefficient of determination and mean square error were used to evaluate the accuracy of the methods. Although a general preference to use geostatistical methods is observed in general, we conclude that deterministic methods provide better results than geostatistical ones. Our results show that geostatistical methods were more accurate in 19 of the 36 case studies. However, the observed difference between the interpolation techniques is negligible in some cases, allowing different ones to be used interchangeably. In this regard, our results indicate that the accuracy of the methods varies depending on the case study. Results also varied, in general, when the different depths are considered, identifying deterministic methods as more accurate for the topsoil and geostatistical ones for the deeper layer. Therefore, we also conclude the necessity to use a variety of soil mapping methods and techniques to achieve the best results.