Adjohoun is a commune in Benin located in the center of the Ouémé department, 32 km from Porto-Novo and 62 km from Cotonou, with a total area of 308 km². It is bordered to the South by Dangbo, to the North by Bonou, to the East by Sakété and Akpro-Missérété, and to the West by Abomey-Calavi and Zè. It is home to more than 90,000 inhabitants distributed across eight arrondissements: Adjohoun, Awonou, Azowlissè, Dèmè, Gangban, Kodé, and Togbota [16]. The study was conducted on a private six-hectare farm in the village of Hlankpa, Kodé arrondissement, owned by Mr. Behi OWA, Director of Solution Plus (Figure 1). The study area is characterized by alluvial sediments with relative pedological homogeneity.

Figure 1. Geographical location of the study area.

Field survey allowed for the in-situ collection of morphological and physical data. A pedological reconnaissance carried out on the study perimeter confirmed the characteristic homogeneity of this alluvial sediment area. Using a GPS projected in linear metric units (WGS84; UTM Zone 31 N), the coordinates of each point were recorded. The study began with a systematic grid of the study area with equidistant sampling points spaced 25 m apart. Each point was subjected to a soil survey using a Dutch auger down to one meter depth. In total, 93 soil surveys were conducted (Figure 2). These surveys allowed for the assessment of the hydraulic characteristics of the soils in the field. Soil samples were taken at each sampling point, packaged in labeled polyethylene bags (sample point number, sample depth), and analyzed in the laboratory.

Figure 2.Grid of the perimeter with pedological sampling points.

Hydrogen potential (pH) was measured using a pH meter in an aqueous solution (soil/water ratio 1:2.5). Total nitrogen (N) content was determined by the Kjeldahl method, involving mineralization with sulfuric acid followed by distillation and titration. Available phosphorus (P) was analyzed by the Olsen method using extraction with 0.5 M sodium bicarbonate at pH 8.5, while exchangeable potassium (K) was measured by atomic absorption spectroscopy after extraction with 1 N ammonium acetate at pH 7. Organic matter (OM) content was determined by the Walkley and Black method, based on the oxidation of organic carbon by potassium dichromate in a sulfuric medium. Finally, the cation exchange capacity (CEC) was assessed by the 1 N ammonium acetate method at pH 7, allowing for the saturation of exchange sites and their subsequent displacement by ammonium ions.

Data analysis was based on the geostatistical approach. As geostatistical methods are sensitive to data normality, a normality test was performed on all variables. In case of a significant deviation from normality, a logarithmic transformation was applied. The error metrics (Root Mean Square Error (RMSE) and Mean Absolute Error (MAE)) were calculated using the log-transformed data to ensure consistency with the fitted variogram models. However, for agronomic interpretation, the predicted values were back-transformed to original units. The very low MAE values (e.g., 0.00001 for Organic Matter) result from the logarithmic transformation and indicate a very close fit between observed and predicted values on the transformed scale; when back-transformed, these errors correspond to small relative errors in the original units (e.g., for OM with mean 2.49%, an MAE of 0.00001 on the log scale corresponds to a relative error of about 0.004%). ArcGIS version 10.1 and R software were used to generate continuous maps representative of the geostatistical variability of soil fertility. Several studies have compared geostatistical spatial interpolation methods [14][17]. In this study, four models were fitted for each parameter: spherical Equation (1), exponential Equation (2), Gaussian Equation (3), and circular Equation (4). Spatial dependence was modeled using semivariograms. An empirical semivariogram was calculated and plotted to assess the spatial variability between neighboring observations. The appropriate model among the available theoretical models was chosen according to the criteria of [17] and [18]. The parameters of the variogram model (nugget effect, range, and sill) were determined to characterize the spatial dependencies of the different soil fertility-related variables. For each parameter, the single variogram model that showed the best performance according to the cross-validation criteria (lowest MAE, RMSE closest to 1) was selected and then applied consistently across all kriging methods (Simple, Ordinary, Universal, and Indicator Kriging) for that parameter. This ensured a fair comparison of the kriging methods while using the optimal spatial structure model for each soil property. The mathematical expressions of the variogram models used are:

Spherical:

Exponential:

Gaussian:

Circular:

with h: lag distance, C₀: nugget effect, C: sill, a: range.

For indicator kriging (IK), critical threshold values (cutoffs) were defined for each parameter based on agronomic standards or data percentiles to transform continuous data into binary indicators (1 if above the threshold, 0 otherwise). The thresholds used were: water table depth ≤ 20 cm (shallow), phosphorus ≤ 15 mg/kg (deficient), potassium ≤ 0.35% (deficient), and CEC ≤ 12 cmol/kg (low). These thresholds were chosen to identify areas requiring specific management interventions.

The variogram models were compared using cross-validation criteria: the Root Mean Square Error (RMSE, Equation (5)) and the Mean Absolute Error (MAE, Equation (6)). The best model is the one with MAE values closest to 0 and RMSE values closest to 1 [18]. The formulas used are as follows:

where Z ( x i ) is the observed value, Z * ( x i ) is the predicted value and n is the number of observations.

Descriptive statistical analysis (Table 1) revealed the variability of the physico-chemical properties of the farm’s soils. The pH is 7.51 ± 0.39, indicating slightly alkaline soils. Soil depth is 101.29 ± 13.29 cm, while the water table depth is 19.62 ± 14.24 cm. The contents are 0.29 ± 0.05% for nitrogen, 0.40 ± 0.11% for potassium, 19.26 ± 4.45 mg/kg for phosphorus, 2.49 ± 0.04% for organic matter, and 15.89 ± 3.27 cmol/kg for the cation exchange capacity. The standard deviations indicate that all parameters show low dispersion around the mean, except for the water table depth. None of the parameters followed a normal distribution (p < 0.05), which required a logarithmic transformation of the data prior to geostatistical analysis.

Table 1. Descriptive statistics of the studied parameters.

N: Nitrogen; P: Phosphorus; K: Potassium; MO: Organic Matter; CEC: Cation Exchange Capacity; pH: Hydrogen Potential.

The comparative analysis of the four variogram models (Gaussian, exponential, circular, and spherical) reveals distinct performances depending on the parameters studied (Table 2). The exponential model best fits the spatial variability of pH (MAE = 0.003; RMSE = 0.979), soil depth (MAE = 0.019; RMSE = 0.887), and water table depth (MAE = 0.001; RMSE = 1.033), consistently presenting the lowest MAE values and RMSE values closest to 1 compared to the other models. The Gaussian model better explains the spatial variability of nitrogen (MAE = 0.006; RMSE = 1.077), phosphorus (MAE = 0.008; RMSE = 1.067), and cation exchange capacity (MAE = 0.006; RMSE = 1.078), demonstrating its superiority for these chemical parameters with optimal evaluation criteria. The circular and spherical models best fit potassium (MAE = 0.009; RMSE = 1.058) and organic matter (MAE = 0.00001; RMSE = 1.025), respectively, the latter showing exceptional performance with a quasi-null mean absolute error for organic matter.

Table 2.Comparison of variogram models.

MAE: Mean Absolute Error; RMSE: Root Mean Square Error.

Table 3 compares the performances of the different kriging methods based on cross-validation criteria. Simple kriging (SK) proves to be the most effective for soil depth (MAE = −0.003; RMSE = 0.979), pH (MAE = −0.003; RMSE = 0.979), nitrogen (MAE = −0.006; RMSE = 1.078), and organic matter (MAE = 0.00003; RMSE = 1.025), consistently presenting MAE values closest to zero and RMSE values closest to 1 compared to the other methods. Indicator kriging (IK) excels for water table depth (MAE = 0.003; RMSE = 0.948), phosphorus (MAE = 0.012; RMSE = 1.001), potassium (MAE = 0.011; RMSE = 1.005), and cation exchange capacity (MAE = 0.013; RMSE = 1.002), demonstrating optimal performance with very satisfactory evaluation criteria. In contrast, universal kriging (UK) shows poor performance with aberrant values for several parameters, notably pH (RMSE = 7.819), phosphorus (RMSE = 20.669), and CEC (RMSE = 17.39), confirming its inadequacy for this study.

Table 3. Comparison of kriging methods.

SK: Simple Kriging; OK: Ordinary Kriging; UK: Universal Kriging; IK: Indicator Kriging.

Figure 3. Spatial variability of soil parameters in Hlankpa village. (a) pH prediction by simple kriging; (b) Soil depth prediction by simple kriging; (c) Organic matter prediction by simple kriging; (d) Nitrogen prediction by simple kriging; (e) Water table depth prediction by indicator kriging; (f) Phosphorus prediction by indicator kriging; (g) Potassium prediction by indicator kriging; (h) Cation exchange capacity prediction by indicator kriging.

Figure 3 presents the spatial variability of eight soil parameters, offering a detailed visualization of their distribution within the Hlankpa farm. The spatial prediction maps reveal distinct patterns for each parameter. The pH map reveals strong spatial heterogeneity (Figure 3(a)). It is observed that the soil exhibits slightly alkaline zones in the North and South (pH > 7), contrasting with neutral zones in the West, Center, and East (pH between 6.5 and 7). The soil depth map indicates the presence of pockets of deep soils (>1 m) mainly in the North-East and from the North-West to the South of the farm. In contrast, shallower soils (<1 m) dominate in the North, Central-East, and South-East (Figure 3(b)). The organic matter map shows a generally high concentration across the entire plot. Areas of high concentration are noted in the center, which could be explained by the accumulation of crop residues or compost application (Figure 3(c)). Nitrogen exhibits strong spatial variability (Figure 3(d)). A high concentration is observed in the center of the farm, with values exceeding 0.25%, while the North-East and South areas show very low concentrations (<0.05%). The water table depth map indicates that the water is almost at the surface (<1 m) in the North-West, South-West, and East of the farm (Figure 3(e)). Conversely, it is deeper (>1 m) in the North-East, Center, and South-East.

The spatial distribution of phosphorus reveals a higher concentration in the center of the farm, reaching values > 100 mg/kg, with lower amounts in the South and North (Figure 3(f)). The predominance of areas with low phosphorus content is notable, suggesting that phosphorus fertilizer inputs are necessary to improve soil fertility over the majority of the plot. Similar to phosphorus, potassium is predominantly present in high amounts in the center of the plot, with high values (>120 mg/kg), and in low amounts in the South and North (Figure 3(g)). Targeted potassic fertilization in deficient areas is essential for crop development. The cation exchange capacity map shows a low chance of observing high CEC in the center of the farm, with even lower values in the South and North (Figure 3(h)). A low CEC indicates a low soil capacity to retain nutrients, which can lead to leaching and nutrient loss.