# Spatio-Temporal Heterogeneity of Soil Moisture on Shrub–Grass Hillslope in Karst Region

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Sampling Point Layout

#### 2.3. Data Analysis

_{i}and x

_{j}are the values of the variable x at the adjacent pairing space points i and j, respectively. W

_{ij}is the adjacent weight, and n is the total number of spatial units.

_{i}) is the value of the regionalized variable Z at x

_{i}, and Z(x

_{i}+ h) is the value of the variable at a given lagged distance interval of x

_{i}+ h.

^{2}are optimal models for omnidirectional experimental semivariograms. We tried to fit with the same model, but it is difficult to achieve the desired results with the same model for different sampling dates. Therefore, we chose the optimal model for each of the sampling dates, and there are three models: an exponential model (Equation (3)), a spherical model (Equation (4)) and a Gaussian model (Equation (5)) in this work [35,36,37]. The formulas are as follows:

_{0}is the nugget variance, C

_{0}+ C is the total sill, C is the partial sill, h is the lagged distance, and a is the range (correlation length). For the spherical and Gaussian models, the range and effective range coincide; this is not the case for the exponential model, where the range is 1/3 of the effective range. For the spherical and Gaussian models, the effective range is the distance at which the sill is approached, but for the exponential variogram the effective range is the distance at which the exponential variogram approaches 95% of the sill.

## 3. Results

#### 3.1. Statistical Characteristics of Soil Moisture

#### 3.2. Spatial Autocorrelation Analysis of Soil Moisture

#### 3.3. Spatial Variability of Soil Moisture

^{2}) and RMSE were between 0.69–0.99 and 2.04–55.9, respectively. This indicates that the fitting models can reflect the spatial structure characteristics of soil moisture realistically. During the sampling period, the nugget and sill fluctuated between 0.1–19.6 and 13.16–65.5, respectively, and the largest nugget value appeared on 9 May. The range was between 12.96 m and 25.5 m and the maximum was approximately twice the minimum. It can be seen from Figure 4 that the omnidirectional experimental semivariogram on 21 April and 20 May performed a downward trend after reaching the sill, and the remaining omnidirectional experimental semivariogram of each sample tended to be stable after reaching the sill.

#### 3.4. Changes of Soil Moisture Omnidirectional Experimental Semivariogram Parameters

_{0}/(C

_{0}+ C).

#### 3.5. Spatial Distribution Pattern of Soil Moisture

## 4. Discussion

#### 4.1. Spatial Autocorrelation of Soil Moisture

#### 4.2. Spatial Distribution of Soil Moisture

#### 4.3. Comparative Analysis of Soil Moisture

## 5. Conclusions

_{0}/C

_{0}+ C. The distribution pattern of soil moisture on the slope looked like plaque or strip. The lower the soil moisture was distributed, the higher the degree of plaque fragmentation and the poorer the spatial continuity. Generally, soil moisture was higher in the lower and middle parts of the plot, and the areas with gentle slopes and higher vegetation coverage contributed to reserve soil moisture.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 5.**The variation trend of omnidirectional experimental semivariogram parameters during sampling period.

Sampling Date | Rainfall during 3 Days (mm) | Max (%) | Min (%) | Mean (%) | SD(%) | CV(%) | Skew | Kurtosis | Distribution Type |
---|---|---|---|---|---|---|---|---|---|

1 April | 34.54 | 56.80 | 22 | 42.60 | 8.23 | 19.32 | −0.42 | −0.29 | N |

14 April | 0.25 | 47.07 | 20.87 | 29.87 | 5.88 | 19.69 | 0.81 | 0.40 | S |

21 April | 0 | 38.17 | 11.63 | 25.67 | 5.37 | 20.91 | −0.33 | −0.02 | N |

28 April | 6.10 | 52.2 | 17.50 | 35.15 | 6.72 | 17.35 | −0.07 | 0.57 | N |

9 May | 29.72 | 58.37 | 24.80 | 41.03 | 7.24 | 17.65 | 0.15 | −0.36 | N |

16 May | 0.51 | 48.37 | 20.27 | 32.82 | 5 | 15.23 | −0.01 | 0.23 | N |

20 May | 19.8 | 49.07 | 21.83 | 35.81 | 4.93 | 13.77 | −0.16 | 0.27 | N |

27 May | 8.38 | 47.40 | 20.70 | 35.98 | 3.71 | 10.31 | −0.26 | 2.57 | N |

17 June | 0 | 53.07 | 11.50 | 35.63 | 7.41 | 20.78 | −0.41 | 0.72 | N |

**Table 2.**Characteristic parameters of omnidirectional experimental semivariogram function of soil moisture.

Sampling Date | Nugget C_{0} | Total Sill C_{0} + C | C_{0}/(C_{0} + C) | Range (m) | R^{2} | Residual | Models |
---|---|---|---|---|---|---|---|

1 April | 0.1 | 65.5 | 0.01 | 25.5 | 0.94 | 55.9 | Exponential |

14 April | 4 | 36.43 | 0.11 | 16.89 | 0.91 | 8.41 | Exponential |

21 April | 5.23 | 29.13 | 0.18 | 16.42 | 0.87 | 16.6 | Spherical |

28 April | 0.5 | 43.24 | 0.01 | 20.07 | 0.89 | 26.6 | Exponential |

9 May | 19.6 | 52.31 | 0.38 | 16.87 | 0.99 | 3.77 | Gaussian |

16 May | 5.28 | 26.21 | 0.20 | 16.22 | 0.98 | 2.04 | Spherical |

20 May | 1.1 | 25.6 | 0.04 | 15.65 | 0.80 | 25 | Spherical |

27 May | 1 | 13.16 | 0.08 | 12.96 | 0.69 | 2.95 | Exponential |

17 June | 3.6 | 54.04 | 0.07 | 15.76 | 0.97 | 15.8 | Spherical |

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**MDPI and ACS Style**

Li, J.; Meng, X.; Li, H.; Gu, X.; Cai, X.; Li, Y.; Zhou, Q.
Spatio-Temporal Heterogeneity of Soil Moisture on Shrub–Grass Hillslope in Karst Region. *Water* **2023**, *15*, 1868.
https://doi.org/10.3390/w15101868

**AMA Style**

Li J, Meng X, Li H, Gu X, Cai X, Li Y, Zhou Q.
Spatio-Temporal Heterogeneity of Soil Moisture on Shrub–Grass Hillslope in Karst Region. *Water*. 2023; 15(10):1868.
https://doi.org/10.3390/w15101868

**Chicago/Turabian Style**

Li, Juncai, Xiaorong Meng, Hua Li, Xiaoxiao Gu, Xiaojun Cai, Yuanlong Li, and Qiuwen Zhou.
2023. "Spatio-Temporal Heterogeneity of Soil Moisture on Shrub–Grass Hillslope in Karst Region" *Water* 15, no. 10: 1868.
https://doi.org/10.3390/w15101868