where \(r_{xy\bullet z}\) means that when variable \(z\) is fixed, the correlation coefficient is between \(x\) and \(y\); and\(r_{\text{xy}}\), \(r_{\text{xz}}\), and \(r_{\text{yz}}\) represent the correlation coefficients between variables \(x\) and \(y\), \(x\)and \(z\), and \(y\) and \(z\), respectively. A t-test was used to test the partial correlation coefficient.

3. Results

3.1 Wind erosion distribution

The spatial distribution of soil wind erosion in southern Africa is shown in Fig. 2. The average wind erosion modulus was 0–169.87 t/ha/a from 1991 to 2015 and the spatial distribution was heterogeneous. The soil wind erosion in most parts of South Africa is relatively light, with a modulus of less than 10 t/ha/a. However, the areas with severe soil erosion are in the Namib desert, which is a narrow strip along the western coastal area, and the Kahalari Basin, which is the border area between Namibia, southern Botswana, and South Africa, has an average wind erosion modulus of more than 90 t/ha/a. The strong wind, erodible soil texture, and sparse vegetation mean that soil erosion in these areas is very serious. The soil wind erosion had roughly the same spatial distribution at certain times (Figs. 2b–2f). The proportion of the area with a wind erosion modulus greater than 60 t/ha/a (very high erosion hazard) gradually decreased from 20.36% in 1991–1995 to 15.92% in 2001–2005 and 8.78% in 2011–2015. The wind erosion modulus in the western and central regions was always higher than that in the other regions, but severe soil erosion greatly improved after 2000 in the eastern coastal area, that is, the northeastern part of South Africa and Eswatini.