Relationship between slope spectrum's information entropy and terrain factors in water erosion areas of purple soil in southwest China

Abstract: In conventional soil erosion evaluation, the calculation of slope length and steepness (LS) factor requires the relatively complicated extraction of slope grade and slope length, and there are certain thresholds due to the determination of slope length to the location. Slope Spectrum's Information Entropy (SSIE) can comprehensively represent the characteristics of topographic relief, but it is not clear that how to apply for the prediction of soil erosion. This paper aims to explore the relationship between the SSIE and topographic factors, while the research area is taking the water erosion area of purple soil in southwest China, including the Qinba mountains region, Wuling mountain hilly area, and Sichuan and Chongqing mountainous region. The slope gradient, slope length, and hydrographic net were extracted using ArcGIS based on ASTER GDEM (30 m resolution). After the calculation, two relationships were established between the SSIE and LS factor, as well the SSIE and gully density based on 63 basins. The results showed that: 1) The whole region displayed the curves of slope spectrum in the shape of "L", "S" and approximate bell, while the different curves of slope spectrum were successively distributed in Sichuan and Chongqing mountainous region, Wuling mountain hilly area and Qinba mountains region. Meanwhile, the main peaks of slope spectrum curves were concentrated in 0°-3°,15°-18° and 24°-27°. 2) The mean of LS factor was 11.03, and the distribution range of LS factors was 0-5, 10-15 and greater than 20 in Qinba mountainous region and Wuling mountain hilly area. However, that in Sichuan and Chongqing mountainous region was mainly concentrated in 0-15, showing obvious north-south difference. 3) The gully density was 0.66km/km2 at the regional scale, particularly 0.72 km/km2 in Qinba mountains region, and 0.75 km/km2 in Wuling mountain hilly area. In Sichuan and Chongqing mountainous region, the gully density reached the minimum, 0.57 km/km2, lower than 17.39% mean value of the regional scale. The gully density ranged from 0.33 to 0.88 km/km2 at the watershed scale. 4) The SSIE showed a logarithmic relationship with LS factor in the different scales, expressed as y=0.589 7lnx+1.201 (R2=0.949 4, P<0.01) in first zone, y=0.577 7lnx+1.200 3 (R2=0.960 3, P<0.01), y=0.749lnx+0.907 3 (R2=0.983 8，P<0.01), and y=1.3165x0.302 (R2=0.989 1，P<0.01) in Qinba mountains region, Wuling mountain hilly area, and Sichuan and Chongqing mountainous region, respectively. However, there were significant differences in the relationships between the SSIE and gully density in the various scales. The relationship between the SSIE and gully density was a polynomial function with low degree of correlation in first and other secondary zone, except for the highly correlated exponential function (y=1.3045e1.0452x(R2=0.7475，P<0.05)) in Sichuan and Chongqing mountainous region. The method can reduce the tedious calculation of LS factor and gully density, while the calculation of SSIE can make the evaluation of soil erosion easier and simpler than before. The findings can be expected to provide a scientific basis for the evaluation and prediction of soil erosion in purple soil and water erosion areas.