1. Introduction

2. Materials and Methods

2.1. Study area description

The Shiyang River Basin lies between 101°41'-104°16'E and 36°29'-39°27'N, in the east of the Hexi Corridor in Gansu Province, west of Wushaoling and North of the Qilian Mountains, covering a total area of 41,600 square kilometers [62]. High mountains in the South characterize its topography with altitudes ranging from 2000 to 5000 meters; the central plain corridor area covering the east of Longshou Mountain extends to the remnants of the Hanmu Mountain, Hongya Mountain, and Aragua Mountain with the altitude ranging from 1400-2000 m [63]. The North Basin includes the Minqin Basin, Jinchuan, and Changning Basin, ranging from 1300 to 1400 m altitude [64]. In addition, the basin can be divided into four geomorphological units: the Qilian Mountains in the South, the Central Corridor Plain Area, the Northern Low Mountain and Hilly Area, and the Desert Area [65]. The Shiyang River Basin is deep in the continent's hinterland and belongs to the continental temperate arid climate, distinct by extreme sun radiation, sufficient sunshine, significant temperature difference, little precipitation, intense evaporation, and dry air [66].

Figure 1. The geographic location of the study area: The Shiyang River basin.

Figure 1. The geographic location of the study area: The Shiyang River basin.

The watershed runs from the South to the North, roughly divided into three climatic zones: Alpine, semi-arid, and semi-humid zone of the southern Qilian Mountains at the altitude of 2000 and 5000 m, with annual precipitation of 300 to 600 mm, with annual evaporation of 700 to 1200 mm, and drought index ranging between 1 and 4. The central corridor plain with altitude ranging between1500 to 2000 meters, annual precipitation of 150 to 300 mm, annual evaporation of 1300 and 2000 mm, and drought index between 4 and 15. The warm and dry Northern part comprises all of Minqin, North of Gulang, Northeast of Wuwei, and North of Longshou Mountain in Jinchang City. The altitude is between 1300 and 1500 m, the annual precipitation is less than 150 mm, and the North of Minqin is close to the edge of the Tengger Desert. The annual rainfall in the marginal zone is around 50 mm, yearly evaporation ranges between 2000 and 2600 mm, and the drought index ranges between 15 to 25 [67]. The Shiyang River basin comprises the Dajing River, Gulang River, Huangyang River, Zamu River, and Jinta River from east to West [68].

The administrative division of the basin includes Gulang County, Liangzhou District, Minqin County, Tianzhu County of Wuwei City, part of Yongchang County, Jinchuan District of Jinchang City, Sunan Yugur Autonomous County, and Shandan of Zhangye City[68]. The study area is one of the fast-growing industrial and agricultural activities among other regions in the Hexi corridor [69], with a total population of 2.2689 million according to The 2003 Census, where the urban population is 733,900 people, the rural population is 1.535 million people, and the urbanization rate is 32.35% [70,71].

Figure 2. Technological roadmap for the study.

Figure 2. Technological roadmap for the study.

2.3. Geographic detector model

The geographical detector model or GeoDetector is a tool that measures stratified spatial heterogeneity (SSH), generating a spatial differentiation between intra-strata and inter-strata phenomena while elucidating the validity of their spatial partition and driving factors [59]. GeoDetector measures and detects the SHH among data, then test the coupling between two variables, X and Y, based on their respective SSH without assuming their linearity, and finally explores the interaction between the two explanatory variables Xi and Xj in response to variable Y without any predefined form of interaction[80]. Stratified spatial heterogeneity gained a broad application, particularly in public health, environment, ecology, and forestry studies[81,82,83].

This universal tool has various applications and provides objective and accurate evaluation as it is insensitive to the results interference due to human errors [84]. In recent years, more researchers have investigated the adverse impacts of anthropogenic and natural-induced processes on desertification, suggesting a more comprehensive approach to thoroughly understand desertification's fundamental drivers [6,85].

The proposed method can numerically and quantitatively differentiate between independent variables and outline the interaction between two dependent variables. In addition, it can perform a spatial heterogeneity analysis for negatively distributed variables when independent variables are quantifiable [86]. Therefore, variables convert into discrete intervals, also known as discretization, based on the quantile and equal spacing classification by minimizing the variance within the interval and maximizing the variance between intervals [87]. The GeoDetector model comprises a Risk, Factor, Ecological, and Interaction detector [88]. Details about the conceptual basics of Geographic Detectors are illustrated in Table 2, while more information can be found in the R package, along with its manual and study case, at CRAN - Package GD (r-project.org).

2.3.1. Factor detector

The interoperation of different factors' impact on regional heterogeneity is based on spatial variance analysis on geographical strata following the model proposed by[89]. The association between spatial variance and a geographical detector model can be expressed using equation (2).

$$\mathbf{P}\mathbf{D}=1-\frac{{\sum }_{\mathbf{h}=1}^{\mathbf{L}}{\sum }_{\mathbf{i}=1}^{{\mathbf{N}}_{\mathbf{h}}}{\left({\mathbf{y}}_{\mathbf{h}1}-{\overline{\mathbf{y}}}_{\mathbf{h}}\right)}_{-}^2}{{\sum }_{\mathbf{i}=1}^{\mathbf{N}}{\left({\mathbf{y}}_{\mathbf{i}}-\overline{\mathbf{x}}\right)}^2}=1-\frac{\sum _{\mathbf{h}=1}^{\mathbf{L}}{\mathbf{N}}_{\mathbf{h}}{\mathsf{\sigma }}_{\mathbf{h}}^2}{\mathbf{N}{\mathsf{\sigma }}^2}$$

(2)

PD is the power determinant based on the spatial heterogeneity of the study object. L is the strata subdivisions of the study denoted by h=1,…, L. σ² and σ²_h are the units variances [90]. N and N_h are the study area units, and h is the strata. The PD interval varies between 0 and 1, i.e. [0,1], meaning that PD=0 if the determinant is utterly unrelated to the risk, whereas PD=1 when the determinant controls the risk.

The spatial discretization optimization aims to identify the optimum spatial scale for the spatial stratified heterogeneity analysis over different scales indicating that the obtained PD of all explanatory variables with their respective spatial discretization parameters at various scales must be compared with corresponding spatial scales to investigate their relationships. Optimizing the spatial discretization and scale requires a delicate selection of discretization methods and break numbers for each continuous geographical variable. The best parameter combination is determined by the PD value specified with the factor detector. During the PD values computation, a set of discretization methods and break numbers are provided for each variable[87,91]. Even though the combination is optional, spatial discretization covers almost all available choices where break numbers can be integer sequences depending on observations and practical requirements. A parameter combination with the highest PD is the best choice of a continuous variable for spatial discretization as it presents the variable's highest importance in stratified spatial heterogeneity[92,93].

2.3.2. Risk detector

The risk detector can be applied to test the significant difference among mean values of subregions classified following categorical or stratified variables [86,87]. The expression for Risk Detector is given by equation (3).

(3)

Ῡᶯ and Ῡ_k are the mean values of observations within sub-regions ᶯ and k. s²_ᶯ and s_k² represent sample variance, while N_ᶯ and N_k stand for observations number. The statistics for this factor follow the Student's distribution table; hence the degree of freedom can be expressed using equation (4).

$$\mathit{d}\mathit{f}=\frac{\left(\frac{{\mathit{s}}_{\mathit{ᶯ}}^2}{{\mathit{N}}_{\mathit{ᶯ}}}+\frac{{\mathit{s}}_{\mathit{k}}^2}{{\mathit{N}}_{\mathit{k}}}\right)}{\left[\frac{1}{{\mathit{N}}_{\mathit{ᶯ}}-1}{\left(\frac{{\mathit{s}}_{\mathit{ᶯ}}^2}{{\mathit{N}}_{\mathit{ᶯ}}}\right)}^2+\frac{1}{\left({\mathit{N}}_{\mathit{k}}-1\right)}{\left(\frac{{\mathit{s}}_{\mathit{k}}^2}{{\mathit{N}}_{\mathit{k}}}\right)}^2\right]}$$

(4)

The Student-t distribution table can test the null hypothesis H0, presented by equation (5), at a 0.05 significant level.

$${\mathit{H}}_0:\overline{{\mathit{Y}}_{\mathit{ᶯ}}}=\overline{{\mathit{Y}}_{\mathit{k}}}$$

(5)

2.3.3. Ecological detector

An ecological detector is a robust tool employed to test explanatory variables' efficiency by confirming whether one factor, X₁ has a higher impact over another X₂ [87], as expressed in equation (6).

$$\mathbf{F}=\frac{{\mathbf{N}}_{\mathbf{u}}\left({\mathbf{N}}_{\mathbf{v}}-1\right){\sum }_{\mathbf{j}=1}^{{\mathbf{M}}_{\mathbf{u}}}{\mathbf{N}}_{\mathbf{u}}{\mathsf{\sigma }}_{\mathbf{u},\mathbf{j}}^2}{{\mathbf{N}}_{\mathbf{v}}\left({\mathbf{N}}_{\mathbf{u}}-1\right){\sum }_{\mathbf{j}=1}^{{\mathbf{M}}_{\mathbf{v}}}{\mathbf{N}}_{\mathbf{v}}{\mathsf{\sigma }}_{\mathbf{v},\mathbf{j}}^2}$$

(6)

N_u and Nv stand for observations number. M_u and M_v are the sub-regions numbers, ${\sum }_{\mathit{j}=1}^{{\mathit{M}}_{\mathit{u}}}{\mathit{N}}_{\mathit{u}}{\mathit{\sigma }}_{\mathit{u},\mathit{j}}^2$ and ${\sum }_{\mathit{j}=1}^{{\mathit{M}}_{\mathit{v}}}{\mathit{N}}_{\mathit{v}}{\mathit{\sigma }}_{\mathit{v},\mathit{j}}^2$ are variance sums within sub-regions of variables u and v. As a result, with a given significance level, the null hypothesis.

${\mathbf{H}}_0={\sum }_{\mathit{j}=1}^{{\mathit{M}}_{\mathit{u}}}{\mathit{N}}_{\mathit{u}}{\mathit{\sigma }}_{\mathit{u},\mathit{j}}^2$= ${\sum }_{\mathit{j}=1}^{{\mathit{M}}_{\mathit{v}}}{\mathit{N}}_{\mathit{v}}{\mathit{\sigma }}_{\mathit{v},\mathit{j}}^2$ can be tested with the F-distribution table.

The systematic computation and visualization of the optimal geographical detector model can be executed in R using the GD software package. An extended presentation of the package can be found in R Documentation.

2.3.4. Interactive factor

Many factors influence the spatial heterogeneity of Y. The interaction between every two factors may enhance, weaken, or stay intact based on the spatial heterogeneity of Y [59]. For instance, the power of the determinant of factors X_i and X_j toward Y were calculated, then X_i and X_j overlaid to form a new stratum. Figure 4 and Figure 5 show that the newly formed stratum allows the determination of PD of interaction between X_i and X_j. The assessment of the interactive influence between the two factors is illustrated in Table 1. A thorough description of GeoDetector software and its operating mode can be found in [94].

Table 1. Interaction relationship between two variables and their impact categories. Min(PD(Xi), PD(Xj)) is the minimum of PD(Xi) and PD(Xj), while Max(PD(Xi), PD (Xj)) is the maximum of PD(Xi) and PD(Xj) [95].

Table 1. Interaction relationship between two variables and their impact categories. Min(PD(Xi), PD(Xj)) is the minimum of PD(Xi) and PD(Xj), while Max(PD(Xi), PD (Xj)) is the maximum of PD(Xi) and PD(Xj) [95].

Demonstration of interaction relationship	Factor interaction type
PD (Xi ∩ Xj) < Min (PD (Xi), PD (Xj))	The factors weakened & non-linear
Min (PD (Xi), PD (Xj)) < PD (Xi ∩ Xj) < Max (PD (Xi)), PD (Xj))	The factors weakened & univariate
PD (Xi ∩ Xj) > Max (PD(Xi), PD (Xj))	The factors enhanced & bivariate
PD (Xi ∩ Xj) = PD (Xi) + PD (Xj)	The factors are independent
PD (XiXj) > PD (Xi) + PD (Xj)	The factors are enhanced & non-linear

Table 2. Summary for conceptual basis of Geographic Detectors [92].

Table 2. Summary for conceptual basis of Geographic Detectors [92].

Type of Detector	Conceptual explanation
Factor detector	This method used the Power Determinant (PD) to evaluate the Impact of Land-cover, DEM, Soil salinization, Land surface temperature, water buffer, and road buffer on the spatial distribution of FVC. In addition, F-test was performed to determine whether each subregion's accumulated variance differed significantly from the variance of the whole region.
Risk detector	It compares the difference in average FVC between subregions strata.The t-tests were used to identify whether the FVC among different sub-regions is significantly different.
Ecological detector	It evaluates whether the impact of environmental and human factors on FVC is significantly different. The F-test was applied to compare the variance calculated in the subregion attributed to one triggering factor with the variance attributed to another.
Interaction detector	It evaluates the combined impact of two factors on desertification and their respective independent contribution. In addition, it assesses whether the combined factors weaken or enhance each other or independently influence desertification magnitude.The process comprises seven parts: Enhance, Enhance-bi, Enhance-nonlinear, Weaken, Weaken-uni, Weaken-nonlinear, and Independent.

3. Results

4. Discussion: Understanding factors' interaction effect on desertification in the Shiyang River Basin

5. Conclusions and Prospects

Authors contribution

Data availability

Conflicts of Interests

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