# The Effect of Soil Sampling Density and Spatial Autocorrelation on Interpolation Accuracy of Chemical Soil Properties in Arable Cropland

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}O

_{5}) and potassium oxide (K

_{2}O) values. The original set was split into eight subsets using a geographically stratified random split method, interpolated using the ordinary kriging (OK) and inverse distance weighted (IDW) methods. OK and IDW achieved similar interpolation accuracy regardless of the soil chemical property and sampling density, contrary to the majority of previous studies which observed the superiority of kriging as a deterministic interpolation method. The primary dependence of interpolation accuracy to soil sampling density was observed, having R

^{2}in the range of 56.5–83.4% for the interpolation accuracy assessment. While this study enables farmers to perform efficient soil sampling according to the desired level of detail, it could also prove useful to professions dependent on field sampling, such as biology, geology, and mining.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Soil Sampling Data

_{2}O

_{5}) and potassium oxide (K

_{2}O) contents, expressed in mg 100 g

^{−1}. The reliable spatial representation of P

_{2}O

_{5}and K

_{2}O, as the macro-nutrients in the soil, are traditionally important in sustainable agriculture, which is further intensified by the emergence of the concept of precise fertilization [6]. Monitoring the dynamics of P

_{2}O

_{5}and K

_{2}O at the micro-level enables quality management of agricultural land and environmental protection, enabling the optimal application of mineral fertilizer [23,24]. At the macro-level, it enables monitoring and remediation of soil degradation [25].

_{2}O

_{5}and K

_{2}O values, while $\overline{y}$ represents the arithmetic mean of all input values per subset. Distance weights for Moran’s I were determined using the K-nearest neighbors method, based on the four neighbors of each soil sample. The optimal spatial resolution of the interpolation results relates to the number of samples per subset and was determined for each of the eight subsets using the Inspection Density method according to Formula (2) by Hengl [28]:

#### 2.3. Spatial Interpolation Methods and Interpolation Parameters

_{2}O

_{5}and K

_{2}O values at the unknown locations was performed based on the variogram according to the Formula (4):

_{2}O

_{5}and K

_{2}O values in the soil was examined using the Shapiro–Wilk test, using R software v4.0.3. In the absence of normal distribution cases, the logarithmic transformation of the input values was performed as a preprocess for OK interpolation. Spatial autocorrelation in variogram modeling was evaluated at a distance of 1200 m from at least 15 known points, including 12 lags, each of which covered a distance of 100 m. The tested mathematical models for variogram fitting were linear, square root, power, Gaussian, and spherical models, explained in detail in [32]. The selection of the optimal mathematical model was performed according to the highest level of fitting the mathematical model to the variogram, expressed by the coefficient of determination (R

^{2}

_{v}). For each set of input data, the basic parameters of the selected mathematical model were examined, including the nugget (n), sill (s), and range (r).

_{2}O

_{5}and K

_{2}O values at an unknown location was performed using weighted inverse distances and sampled soil values according to Formula (5):

#### 2.4. Interpolation Accuracy Assessment and Relationship with Sampling Density and Spatial Autocorrelation

^{2}), root mean square error (RMSE), and normalized root mean square error (NRMSE) were metrics used for the accuracy assessment. R

^{2}and RMSE allow a comprehensive analysis of the interpolation accuracy due to their complementarity [33]. NRMSE resulted in a relative interpolation error value and allowed a parallel interpolation accuracy assessment of both soil parameters with different value intervals [7]. These values were calculated according to Formulas (6)–(8):

_{2}O

_{5}and K

_{2}O values. Sampling density and Moran’s I values for both interpolation methods were compared with the interpolation accuracy results represented by R

^{2}and RMSE. The relationship of the spatial autocorrelation and soil sampling density to interpolation accuracy was modeled using linear regression separately for P

_{2}O

_{5}and K

_{2}O. The strength of their dependence was quantified proportionally by the coefficient of determination.

## 3. Results

_{2}O

_{5}values in the soil in the study area was observed, while K

_{2}O values showed low variability (Table 2). For both soil chemical properties, CV values retained a close value range, which began to increase for sampling densities of less than 37.5% of the original soil samples. The p values of the Shapiro–Wilk test resulted in values below 0.05 for five subsets with the highest percentages of soil samples for P

_{2}O

_{5}, as well as the top seven subsets for K

_{2}O. The null hypothesis of normal data distribution for these subsets was rejected, and logarithmic transformation as a preprocess for OK was performed. The spatial resolution determined by the Inspection Density method showed a relatively low difference of between 100% and 50% of soil samples, dropping off more intensively for sparser subsets.

_{2}O resulted in a slightly higher spatial autocorrelation than P

_{2}O

_{5}values. The distance of the spatial autocorrelation per subset was analyzed by correlograms, showing stable value and a noticeable increase for the 25% and 12.5% subsets (Appendix A, Figure A1).

^{2}

_{v}values were observed for denser soil subsets, especially for 62.5% and higher percentages of the original soil samples. Both OK and IDW achieved high spatial interpolation accuracy for subsets containing 37.5% or more of the original samples (Table 3). The P

_{2}O

_{5}was more accurately predicted by IDW in six cases, per RMSE and NRMSE values. IDW achieved maximum interpolation accuracy for the 87.5% subset, followed by the full soil subset using the OK. Considering the R

^{2}values for P

_{2}O

_{5}, the top two subsets produced a large gap in the results for 75%, 62.5%, 50%, and 37.5% values, while the bottom two subsets further showed a considerable decline in interpolation accuracy. OK was a more accurate interpolation method in seven of eight cases for the K

_{2}O samples, with higher spatial autocorrelation than the P

_{2}O

_{5}values. Similar to the previous case, the most accurate interpolation variant was achieved using the 100% soil samples, with accuracy significantly dropping for the two sparsest subsets.

_{2}O

_{5}and K

_{2}O values are shown in Figure 5. All interpolation results predicted the highest state of soil P

_{2}O

_{5}in the northern and western parts of the study area, with variable levels of local heterogeneity. The highest concentration of K

_{2}O was observed in the central and northern part of the study area, declining along the borders of the study area to low intensity. The wide value range of both P

_{2}O

_{5}and K

_{2}O was retained from the input values of soil samples in the interpolation results, primarily in the case of IDW. IDW retained a nearly constant level of local soil P

_{2}O

_{5}heterogeneity, dropping off only in a sample density below 50%. For OK, the level of heterogeneity of the interpolation results is more uniform, due to the same applied mathematical model and similar n and s values.

^{2}and RMSE representing the interpolation accuracy of the combined OK and IDW results indicated a strong correlation to the sampling density (Figure 6). Sampling density resulted as a prime indicator of the interpolation accuracy, having a superior correlation with R

^{2}and RMSE for both soil chemical properties. The spatial autocorrelation represented by Moran’s I showed a lower impact on the interpolation accuracy, with a slightly higher impact on lower spatial autocorrelation P

_{2}O

_{5}values.

## 4. Discussion

^{2}for both P

_{2}O

_{5}and K

_{2}O values. This aligns with the observations of previous studies with a similar average area per sample, where interpolation accuracy achieved a high correlation with sampling density [7,10]. The exception to this statement related to previous studies at the micro-level occurred in cases of an extremely high sampling density of 0.02–0.04 ha per sample for precision agriculture [11,12]. Therefore, there is a strong indication that soil sampling was overly detailed in these cases, whereas the accurate spatial representation of soil properties could be accomplished with sparser soil sampling and higher time- and cost-efficiency. The spatial autocorrelation had a secondary impact on interpolation accuracy, although a higher R

^{2}with the accuracy metrics for the P

_{2}O

_{5}might indicate its suitability for the study of soil samples with lower spatial autocorrelation and higher variability. A similar approach to the application of Moran’s I for the assessment of interpolation accuracy was implemented in the process of spatial prediction of the distribution of heavy metals [34]. This reinforces the assumption of its potential in cases of different soil properties, value ranges, and autocorrelation in comparison to this study, but also requires further research for specific conclusions.

_{2}O values, while IDW achieved higher accuracy for the interpolation of P

_{2}O

_{5}values and retained its local variability. This observation indicates the suitability of IDW for heterogeneous agricultural parcels with the presence of extreme values and lower spatial autocorrelation.

## 5. Conclusions

- Interpolation accuracy primarily increases with the sampling density, having R
^{2}produced by linear regression in the range of 56.5–83.4%. Spatial autocorrelation indicated a lower impact on the interpolation accuracy but has potentially higher applicability in cases of lower spatial autocorrelation; - Both soil sampling density and spatial autocorrelation limit the interpolation accuracy if the number of input values is not large enough to accurately fit the mathematical model with a variogram for OK. In this study, sampling density below 37.5% on input data of 160 samples caused a rapid decrease in interpolation accuracy;
- OK and IDW resulted in a similar interpolation accuracy for both soil P
_{2}O_{5}and K_{2}O interpolation, while OK was more accurate in cases of lower CV and higher spatial autocorrelation. While deterministic interpolation methods, such as IDW, were inferior to OK in previous studies, they should be evaluated alongside geostatistical interpolation methods in similar studies.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Correlograms of soil subsets, with the grey line indicating an autocorrelation value of zero.

**Table A1.**OK interpolation parameters for mathematical models with the highest coefficient of determination with variogram per input data set.

Soil Property | Percentage of Soil Samples | n | s | r (m) | R^{2}_{v} |
---|---|---|---|---|---|

P_{2}O_{5} | 100% | 0.020 | 0.326 | 976 | 0.974 |

87.5% | 0.024 | 0.326 | 1020 | 0.981 | |

75% | 0.055 | 0.536 | 937 | 0.964 | |

62.5% | 0.089 | 0.475 | 1151 | 0.869 | |

50% | 0.032 | 0.488 | 985 | 0.943 | |

37.5% | 0.012 | 0.349 | 1068 | 0.862 | |

25% | 0.011 | 0.358 | 1501 | 0.908 | |

12.5% | 0.016 | 0.104 | 1630 | 0.761 | |

K_{2}O | 100% | 0.159 | 0.397 | 1490 | 0.993 |

87.5% | 0.017 | 0.242 | 1428 | 0.987 | |

75% | 0.020 | 0.238 | 1430 | 0.987 | |

62.5% | 0.006 | 0.235 | 1151 | 0.998 | |

50% | 0.058 | 0.461 | 985 | 0.951 | |

37.5% | 0.017 | 0.197 | 1068 | 0.747 | |

25% | 0.013 | 0.297 | 1651 | 0.745 | |

12.5% | 0.001 | 0.413 | 1585 | 0.759 |

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**Figure 1.**The number of scientific articles indexed in WoSCC from 2010–2020, based on the combination of terms “soil”, “interpolation”, or “prediction”, with specific terms listed.

**Figure 5.**Interpolation results for the combination of eight soil subsets with P

_{2}O

_{5}and K

_{2}O values.

**Figure 6.**The relationship of the spatial autocorrelation and sampling density with interpolation accuracy.

**Table 1.**Literature review of the effect soil sampling density in agricultural land has on spatial interpolation accuracy.

Reference | Study Area | Total Sample Count | Average Area per Sample (ha) | Correlation of Interpolation Accuracy and Sampling Density |
---|---|---|---|---|

Rodrigues et al. [12] | 72 ha | 4306 | 0.02 | low |

Kravchenko [11] | 20 ha | 529 | 0.04 | low |

Zhang et al. [14] | 72 km^{2} | 2755 | 2.61 | moderate |

Zhang et al. [10] | 40 km^{2} | 997 | 4.01 | high |

Long et al. [7] | 10,636 km^{2} | 188,247 | 5.65 | high |

Zhang et al. [15] | 40 km^{2} | 214 | 18.7 | high |

Shen et al. [1] | 173 km^{2} | 700 | 24.7 | high |

Li [3] | 400 km^{2} | 335 | 119 | low |

Sun et al. [16] | 683 km^{2} | 394 | 173 | high |

Zhao et al. [17] | 1450 km^{2} | 745 | 195 | moderate |

Ye et al. [18] | 16,400 km^{2} | 1458 | 1125 | high |

Liu et al. [9] | 620,000 km^{2} | 382 | 162,304 | low |

Soil Property | Percentage of Soil Samples | Mean | CV | Min | Max | Shapiro–Wilk | Target Spatial Resolution (m) | |
---|---|---|---|---|---|---|---|---|

W | p | |||||||

P_{2}O_{5} | 100% | 21.59 | 0.32 | 8.3 | 36.5 | 0.971 | 0.002 | 18 |

87.5% | 21.59 | 0.31 | 8.3 | 36.5 | 0.973 | 0.007 | 19 | |

75% | 21.44 | 0.32 | 10.3 | 36.5 | 0.968 | 0.006 | 21 | |

62.5% | 21.55 | 0.32 | 10.5 | 36.5 | 0.967 | 0.012 | 23 | |

50% | 20.75 | 0.31 | 10.5 | 35.0 | 0.963 | 0.022 | 25 | |

37.5% | 21.65 | 0.33 | 8.3 | 36.5 | 0.972 | 0.180 | 29 | |

25% | 22.01 | 0.33 | 8.3 | 36.5 | 0.965 | 0.236 | 36 | |

12.5% | 21.55 | 0.39 | 10.5 | 36.5 | 0.936 | 0.198 | 51 | |

K_{2}O | 100% | 24.43 | 0.15 | 16.7 | 34.4 | 0.944 | >0.001 | 18 |

87.5% | 24.49 | 0.15 | 16.7 | 34.2 | 0.942 | >0.001 | 19 | |

75% | 24.36 | 0.15 | 16.7 | 34.4 | 0.952 | >0.001 | 21 | |

62.5% | 24.28 | 0.15 | 16.7 | 33.6 | 0.945 | >0.001 | 23 | |

50% | 24.82 | 0.15 | 19.5 | 34.4 | 0.938 | 0.001 | 25 | |

37.5% | 24.67 | 0.16 | 17.2 | 34.4 | 0.937 | 0.004 | 29 | |

25% | 24.62 | 0.18 | 17.2 | 34.2 | 0.923 | 0.008 | 36 | |

12.5% | 24.02 | 0.18 | 17.2 | 34.4 | 0.935 | 0.192 | 51 |

Soil Property | Percentage of Soil Samples | OK | IDW | ||||
---|---|---|---|---|---|---|---|

R^{2} | RMSE | NRMSE | R^{2} | RMSE | NRMSE | ||

P_{2}O_{5} | 100% | 0.743 | 4.157 | 0.193 | 0.713 | 4.249 | 0.197 |

87.5% | 0.729 | 4.272 | 0.198 | 0.751 | 4.211 | 0.195 | |

75% | 0.628 | 4.468 | 0.208 | 0.653 | 4.308 | 0.201 | |

62.5% | 0.630 | 4.696 | 0.218 | 0.623 | 4.466 | 0.207 | |

50% | 0.618 | 4.702 | 0.227 | 0.614 | 4.526 | 0.218 | |

37.5% | 0.581 | 4.394 | 0.203 | 0.687 | 4.323 | 0.202 | |

25% | 0.445 | 5.135 | 0.233 | 0.449 | 5.182 | 0.235 | |

12.5% | 0.487 | 5.190 | 0.241 | 0.492 | 5.044 | 0.234 | |

K_{2}O | 100% | 0.794 | 2.080 | 0.085 | 0.759 | 2.172 | 0.089 |

87.5% | 0.774 | 2.127 | 0.087 | 0.704 | 2.473 | 0.101 | |

75% | 0.760 | 2.127 | 0.087 | 0.716 | 2.325 | 0.095 | |

62.5% | 0.727 | 2.324 | 0.096 | 0.668 | 2.438 | 0.100 | |

50% | 0.688 | 2.884 | 0.116 | 0.634 | 2.457 | 0.099 | |

37.5% | 0.637 | 2.275 | 0.173 | 0.629 | 2.327 | 0.094 | |

25% | 0.455 | 2.678 | 0.109 | 0.469 | 2.702 | 0.110 | |

12.5% | 0.518 | 2.751 | 0.115 | 0.508 | 2.703 | 0.113 |

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**MDPI and ACS Style**

Radočaj, D.; Jug, I.; Vukadinović, V.; Jurišić, M.; Gašparović, M. The Effect of Soil Sampling Density and Spatial Autocorrelation on Interpolation Accuracy of Chemical Soil Properties in Arable Cropland. *Agronomy* **2021**, *11*, 2430.
https://doi.org/10.3390/agronomy11122430

**AMA Style**

Radočaj D, Jug I, Vukadinović V, Jurišić M, Gašparović M. The Effect of Soil Sampling Density and Spatial Autocorrelation on Interpolation Accuracy of Chemical Soil Properties in Arable Cropland. *Agronomy*. 2021; 11(12):2430.
https://doi.org/10.3390/agronomy11122430

**Chicago/Turabian Style**

Radočaj, Dorijan, Irena Jug, Vesna Vukadinović, Mladen Jurišić, and Mateo Gašparović. 2021. "The Effect of Soil Sampling Density and Spatial Autocorrelation on Interpolation Accuracy of Chemical Soil Properties in Arable Cropland" *Agronomy* 11, no. 12: 2430.
https://doi.org/10.3390/agronomy11122430