# Application of Ordinary Kriging and Regression Kriging Method for Soil Properties Mapping in Hilly Region of Central Vietnam

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Area

#### 2.2. Remote Sensing Data

#### 2.3. Field Survey and Soil Quality Analysis

#### 2.4. Environmental Variables Data

#### 2.4.1. Transformed Soil Adjusted Vegetation Index (TSAVI)

#### 2.4.2. Topographic Wetness Index (TWI)

#### 2.5. Spatial Interpolation

#### 2.5.1. Ordinary Kriging

_{o}is given by predicting the value ${\mathrm{Z}}^{\ast}({\mathrm{x}}_{\mathrm{o}})$, which equals the line sum of the known measured values (i.e., observed values). Isaaks and Srivastava [59], Cressie [60] and many other researchers provide an elegant and simple description of OK as the following formula:

_{o}, $\mathrm{Z}({\mathrm{x}}_{\mathrm{i}})$ is the measured value at position x

_{i}, λ

_{i}is the weighting coefficient from the measured position to x

_{o}and n is the number of positions within the neighborhood searching [61]. A fitted model based on the input data distribution is needed to describe the spatial continuity of the data and show the spatial relationship between the pairs of points. In this study, the OK method was calculated using R software with a framework introduced by Hengl [61] and Omuto and Vargas [62].

#### 2.5.2. Regression Kriging

_{i}are the kriging weights determined by the spatial dependence structure of the residual and e(x

_{i}) is the residual at position x

_{i}. Thus, the first part of the right-hand side of Equation (5) represents the regression and the second part represents the kriging of the residual. Hengl et al. [14] introduced the process of using the RK method for spatial prediction of soil variables. In this study, RK was conducted using the R software [64,65,66] with a framework introduced by Hengl [61] and Omuto and Vargas [62].

#### 2.6. Validation

_{I}to compare the OK and RK methods and to improve the prediction accuracy index. If R

_{I}is positive, the accuracy prediction of RK is higher than that of OK and vice-versa [16].

_{oi}is the observed value at the ith position, and Z

_{pi}is the predicted value at the ith position.

## 3. Results

#### 3.1. Soil Samples Data Descriptions

#### 3.2. Regression Model for Soil Characteristics Mapping

#### 3.2.1. Environmental Variables Calculation

#### 3.2.2. Model for Regression Kriging

#### 3.3. Spatial Interpolation

_{I}show that OK is more accurate than RK (for SOC and TN mapping) by 3.33% and 10.00%, respectively.

## 4. Discussion

#### 4.1. The Impact of Environmental Variables on SOC, TN, and Soil pH

#### 4.2. Comparison between OK and RK

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Semivariogram of soil organic carbon (SOC), total nitrogen (TN), pH (

**left**) and their residuals (

**right**).

Soil Indicator | Mean | Median | Min | Max | Std. Deviation | Skewness |
---|---|---|---|---|---|---|

SOC | 1.31 | 1.29 | 0.42 | 3.02 | 0.48 | 0.90 |

TN | 0.11 | 0.10 | 0.05 | 0.21 | 0.03 | 0.82 |

pH | 4.10 | 4.11 | 3.60 | 4.68 | 0.19 | 0.02 |

Predictive Model | Variance Explanation (%) | ||
---|---|---|---|

SOC | TN | pH | |

y = f(TSAVI) | 2.08 | 0.01 | 4.03 |

y = f(TWI) | 7.19 | 0.01 | 4.59 |

y = f(LUT) | 14.52 | 7.00 | 18.40 |

y = f(TSAVI, TWI, LUT) | 14.51 | 5.60 | 17.15 |

y = f(TWI, LUT) | 14.98 | 6.30 | 17.77 |

y = f(TSAVI, LUT) | 13.91 | 6.25 | 17.71 |

y = f(TSAVI, TWI) | 7.00 | 0.01 | 5.90 |

Soil Property | Model | Initial Semivariogram | Residual Semivariogram | Nugget/Sill (Initial Data) | ||||
---|---|---|---|---|---|---|---|---|

Range (m) | Sill | Nugget | Range (m) | Sill | Nugget | |||

SOC | Spherical | 6500 | 0.23 | 0.13 | 3800 | 0.19 | 0.09 | 0.56 |

TN | Spherical | 5000 | 7.5 × 10^{−4} | 10^{−4} | 4000 | 7.5 × 10^{−4} | 10^{−4} | 0.13 |

pH | Spherical | 6500 | 0.029 | 0.025 | 2800 | 0.026 | 0.016 | 0.86 |

**Table 4.**Accuracy assessment of ordinary kriging (OK) and regression kriging (RK) method for SOC, TN, and pH mapping.

SOC | TN | pH | ||||
---|---|---|---|---|---|---|

OK | RK | OK | RK | OK | RK | |

ME | −0.034 | −0.041 | −0.008 | −0.008 | 0.001 | −0.019 |

RMSE | 0.327 | 0.337 | 0.018 | 0.020 | 0.202 | 0.198 |

R_{I} | −3.33% | −10.00% | 1.81% |

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**MDPI and ACS Style**

Gia Pham, T.; Kappas, M.; Van Huynh, C.; Hoang Khanh Nguyen, L. Application of Ordinary Kriging and Regression Kriging Method for Soil Properties Mapping in Hilly Region of Central Vietnam. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 147.
https://doi.org/10.3390/ijgi8030147

**AMA Style**

Gia Pham T, Kappas M, Van Huynh C, Hoang Khanh Nguyen L. Application of Ordinary Kriging and Regression Kriging Method for Soil Properties Mapping in Hilly Region of Central Vietnam. *ISPRS International Journal of Geo-Information*. 2019; 8(3):147.
https://doi.org/10.3390/ijgi8030147

**Chicago/Turabian Style**

Gia Pham, Tung, Martin Kappas, Chuong Van Huynh, and Linh Hoang Khanh Nguyen. 2019. "Application of Ordinary Kriging and Regression Kriging Method for Soil Properties Mapping in Hilly Region of Central Vietnam" *ISPRS International Journal of Geo-Information* 8, no. 3: 147.
https://doi.org/10.3390/ijgi8030147