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Soil moisture is a crucial factor limiting the growth and survival of plants on the Loess Plateau. Its level has a severe impact on plants’ growth and development and the type and distribution characteristics of communities. This study area is the Jihe Basin in the Loess Plateau, China. Multiple linear regression models with different environmental variables (land use, topographic and meteorological factors, etc.) were developed to simulate soil moisture’s spatial and temporal changes by integrating field experiments, indoor analysis, and GIS spatial analysis. The model performances were evaluated in the Jihe Basin, with soil moisture content measurements. The result shows that soil moisture content is positively correlated with soil bulk density, monthly rainfall, topographic wetness index, land use coefficient, and slope aspect coefficient but negatively correlated with the monthly-averaged temperature and the relative elevation coefficient. The selected variables are all related to the soil moisture content and can account for 75% of the variations of soil moisture content, and the remaining 25% of the variations are related to other factors. Comparing the simulated and measured values at all sampling points shows that the average error of all the simulated values is 0.09, indicating that the simulation has high accuracy. The spatial distribution of soil moisture content is significantly affected by land use and topographic factors, and seasonal variation is remarkable in the year. Seasonal variation of soil moisture content is determined by the seasonal variation of rainfall and the air temperature (determining evaporation) and vegetation growth cycle. Therefore, the proposed model can simulate the spatial and temporal variation of soil moisture content and support developing the soil and water loss model on a basin scale.

The Loess Plateau of China, situated in the upper and middle reaches of the Yellow River, covers about 630,000 km^{2}, has an elevation of 1200–1600 m above sea level and is predominantly covered by loess deposits. This region has been prone to severe soil erosion that is a consequence of both natural factors (e.g., the unique geology and landforms, climate conditions, and vegetation coverage due to water resource constraints) and anthropic factors (e.g., poor land use management) [

The study area is the Xihe Basin located in the region of 34°20^{2}, with an average annual rainfall of 558.9 mm. Rainfall varies greatly annually and is unevenly distributed during a year, mainly from July to September. The terrain is fragmented, and ravines crisscross. It is high in the northwest and low in the southeast, at altitudes between 1069 and 2717 m. Soil and water loss occurs in a wide range and large areas; the erosion types are complex and varied; the erosion process is concentrated with large intensity. Water resources are still the main restricting factors of soil and water conservation and ecological environment construction in the basin.

The location and Digital Elevation Model (DEM) of the Xihe River Basin.

The original data used was a 1 : 50,000 topographic map (1954 Beijing coordinate system, 1956 Yellow Sea elevation system, contour interval 20 m, reference ellipsoid Krasovsky). The topographic map was scanned, and Geoway was used for vectorization to generate the required layers of contour lines, elevation points, and slopes, and then, E00 was derived after splicing, which was transformed into coverage format in ArcInfo, and topological relations are constructed. Finally, the professional ANUDEM interpolation software is used to set parameters according to existing studies to generate HC-DEM with 10 m resolution (Figure

The daily rainfall and temperature data were provided by the China Meteorological Data Network (

Based on DEM and by using multiple flow algorithm, topographic wetness index was calculated as shown in Figure

Topographic wetness index of the Xihe River Basin.

The land use map of the Xihe Basin is obtained by interpreting the TM remote sensing images acquired in 2005. According to current research results [

Land use coefficient of Xihe River Basin in 2005.

The result of a representative study on small watershed [

Slop aspect coefficient of Xihe River Basin.

Owing to the ravines crisscross in the Loess Hilly-gully region, the landform is complex, and the upper, middle, and lower parts of ridge, hills, and gully cannot be quantitatively represented accurately. Therefore, each sampling point’s relative elevation coefficients in a small watershed are selected to represent the slope position quantitatively. The calculation formula is shown in equation (

where

Relative elevation coefficient of the Xihe River Basin.

The layout of sampling points: sampling points are collected according to the combination of land use and landform type, the sampling points cover the primary land use types, prominent small- and medium-sized landforms, different slope aspects, different gradient grades, and slope positions, and a total of 70 points are selected. Because the study area was large, data were collected at 43 sampling points in November 2007 and 27 sampling points in May 2008. At each sampling point, handheld GPS is used to record the longitude, latitude, and altitude. The soil properties, including the moisture content and dry bulk density, and the topography near the site, soil erosion, and land use type are recorded. Measurement of soil moisture content: considering that near-surface soil is the central origin of the erosion-induced sediment yield, only the soil at a depth of 0-50 cm is taken as the research subject. When sampling, a ring knife is used to collect soil at a depth of 0-50 cm, and the interval between samples is 10 cm. The samples are sealed and then taken back to the laboratory, and the moisture contents of the samples are determined with the drying method (105°C, 10 h). The average soil moisture content in the depth of 0-50 cm at each sampling site is taken as the mean of soil moisture content in each soil layer

The mass content of moisture was converted into the thickness of soil water.
^{3}), respectively.

Regression analysis is the most basic quantitative analysis method. According to the data statistics principle, the regression analysis method can help process a large number of statistical data mathematically, determine the correlation between dependent variables and some independent variables, and establish a regression equation (function expression) with good correlation. Besides, it can also help find a good regression coefficient and then carry out a correlation test to determine the correlation coefficient, which can predict the change of dependent variables after meeting the correlation requirements.

In this study, the multivariate regression analysis method in Excel is used to analyze the relationship between the soil moisture content (mm) (the dependent variable) and the soil bulk density, monthly-averaged rainfall, monthly-averaged temperature, topographic wetness index, land use coefficient, slope aspect coefficient, and relative elevation coefficient (7 independent variables).

Multivariate regression analysis gives the following evaluation indexes: multiple correlation coefficient

The ratio of the absolute error caused by measurement over the measured true value (in agreement) is the relative error, which can better reflect the credibility of measurement.

where

In order to reflect the overall reliability of measurement, the average relative errors at all points are obtained by the following formula:

The soil moisture content (mm) is taken as the dependent variable, and the soil bulk density, monthly-averaged rainfall, monthly-averaged temperature, land use coefficient, topographic wetness index, slope aspect coefficient, and relative elevation coefficient are the independent variables. Use the regression function in the data analysis tool of Excel to carry out multivariate regression analysis. Some data required for regression analysis and simulated results are shown in Table

The model equation obtained through multivariate linear regression analysis is

Parameter attribute value of the samples.

Sampling point number (1) | Soil moisture content (2) | Volume density (3) | Rainfall (4) | Average air temperature °C (5) | Topographic humidity index (6) | Land use coefficient (7) | Slope aspect coefficient (8) | Relative elevation coefficient (9) | Simulated result (10) | Relative error (11) |
---|---|---|---|---|---|---|---|---|---|---|

1 | 129.68 | 1.25 | 84.50 | 10.44 | 6.27 | 1.06 | 0.89 | 0.25 | 129.97 | 0.0022 |

2 | 138.07 | 1.38 | 84.51 | 10.44 | 9.35 | 1.00 | 0.89 | 0.24 | 138.34 | 0.0020 |

3 | 134.90 | 1.40 | 84.52 | 10.44 | 7.21 | 1.06 | 0.81 | 0.24 | 136.13 | 0.0091 |

4 | 148.72 | 1.27 | 84.51 | 10.44 | 5.98 | 1.00 | 0.79 | 0.26 | 125.40 | 0.1568 |

5 | 76.60 | 1.24 | 84.50 | 10.44 | 8.12 | 1.06 | 0.79 | 0.26 | 124.08 | 0.6198 |

6 | 135.61 | 1.16 | 84.90 | 10.33 | 8.04 | 1.00 | 0.90 | 0.23 | 124.34 | 0.0831 |

7 | 154.36 | 1.30 | 84.93 | 10.32 | 6.77 | 0.65 | 0.87 | 0.20 | 129.87 | 0.1587 |

8 | 134.10 | 1.26 | 84.94 | 10.32 | 5.75 | 0.65 | 0.90 | 0.20 | 128.30 | 0.0433 |

9 | 150.96 | 1.38 | 84.25 | 10.52 | 7.21 | 1.00 | 1.00 | 0.08 | 146.22 | 0.0314 |

10 | 141.29 | 1.33 | 84.25 | 10.52 | 19.62 | 0.00 | 0.77 | 0.07 | 124.25 | 0.1206 |

11 | 112.93 | 1.14 | 84.65 | 10.40 | 8.22 | 0.65 | 0.90 | 0.26 | 119.29 | 0.0563 |

12 | 111.27 | 1.25 | 84.64 | 10.40 | 8.20 | 1.06 | 1.00 | 0.28 | 134.73 | 0.2108 |

13 | 93.63 | 1.25 | 84.61 | 10.39 | 5.44 | 1.06 | 0.79 | 0.17 | 126.73 | 0.3535 |

14 | 118.21 | 1.19 | 84.62 | 10.39 | 8.78 | 1.06 | 0.75 | 0.14 | 121.71 | 0.0296 |

15 | 111.83 | 1.19 | 84.26 | 10.51 | 8.14 | 1.00 | 0.81 | 0.22 | 122.09 | 0.0917 |

16 | 123.72 | 1.22 | 84.26 | 10.51 | 5.80 | 1.06 | 0.79 | 0.23 | 122.72 | 0.0081 |

17 | 138.85 | 1.50 | 84.48 | 10.39 | 6.72 | 0.65 | 0.81 | 0.22 | 139.00 | 0.0011 |

18 | 145.66 | 1.48 | 84.48 | 10.39 | 8.53 | 1.00 | 0.89 | 0.24 | 144.60 | 0.0073 |

19 | 144.87 | 1.34 | 84.43 | 10.40 | 6.85 | 1.00 | 0.79 | 0.16 | 132.38 | 0.0862 |

20 | 144.22 | 1.47 | 84.43 | 10.39 | 14.63 | 1.00 | 1.00 | 0.16 | 151.94 | 0.0535 |

21 | 148.92 | 1.43 | 84.44 | 10.33 | 6.47 | 1.00 | 0.90 | 0.23 | 142.18 | 0.0453 |

22 | 139.84 | 1.40 | 84.50 | 9.86 | 6.92 | 1.00 | 0.77 | 0.18 | 136.67 | 0.0227 |

23 | 122.13 | 1.25 | 84.42 | 10.38 | 8.02 | 1.06 | 0.89 | 0.27 | 129.43 | 0.0598 |

… | … | … | … | … | … | … | … | … | … | … |

70 | 85.81 | 1.24 | 34.57 | 18.59 | 19.69 | 1.06 | 0.77 | 0.41 | 92.79 | 0.0813 |

where ^{3});

The main statistical parameters of the model equation are shown in Table

The result of regression analysis shows that the multiple correlation coefficient

The

The

Analysis of the errors in simulation results

The parameters associated with regression analysis.

0.84 | 0.75 | 0.00038 | 0.9 | 0.71 | 0.79 | 0.54 | 0.064 | 0.41 |

If we substitute the data at each measuring point in Table

Considering that the seasonal variation of soil moisture content is mainly affected by rainfall and air temperature (evaporation), land use, soil factor, and topographic factors are relatively stable, the rainfall and temperature of each month in the year are inserted in equation (

The soil moisture content in from Apr. to Oct. in 2005.

The soil moisture content in Apr. 2005

The soil moisture content in May 2005

The soil moisture content in Jun. 2005

The soil moisture content in Jul. 2005

The soil moisture content in Aug. 2005

The soil moisture content in Sep. 2005

The soil moisture content in Oct. 2005

According to the simulated results shown in Figure

The average temperature and rain from Apr. to Oct. in 2005.

Based on the measured data, multiple linear regression analysis was carried out to obtain the simulated equation of soil water content, and the equation was applied in the study area.

The specific conclusions are given below: (1) The simulation method of antecedent soil moisture content in watershed scale was explored. The multiple regression equation of soil moisture content was established, which could simulate soil moisture content’s spatial and temporal distribution. (2) The proposed method produces reasonable estimates of soil moisture content. The average error of all the simulated values is 0.09, indicating that the simulation has high accuracy. (3) The map of soil moisture content in April-October 2005 obtained by the proposed method to the study area shows that the spatial distribution of soil moisture content is significantly affected by land use and the topographic index; seasonal variations in the year are significantly affected by the temperature (evaporation). The result can reflect the spatial and temporal variation of regional soil moisture content. This study provides methodological support for estimating regional soil moisture content and can be used to study regional soil erosion models.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare no conflict of interest.

This study was supported by the National Key Research and Development Project of China (No. 2019YFC0409202), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 51721006), High-level talent support program of North China University of water resources and electric power, and Special support for an innovative scientific and technological team of water ecological security in the water source area of the middle route of South to North Water Diversion in Henan Province.