Effect of scale spatial on gully distribution in northeastern China

Gully erosion is one of the world’s major environmental problems, and it is also an important cause of land degradation. To reveal how gully distribution changes with spatial scale and the optimal scale for their evaluation, gullies in northeastern China were visually interpreted via high-resolution imagery, and the methods of geo-spatial statistics and kernel density estimation were used to quantitatively evaluate the distribution of gully clusters in 27 sampling areas. The results show that changes in scale always led to changes in the average value and standard deviation of the kernel density, whose trend was the same for average kernel density and standard deviation. The spatial distribution of gullies was characterized by heterogeneity; the average kernel density undergoes complex change with the scale, which varied drastically in the low-value portion of the scale range but was relatively stable in its high-value portion. For 70% of the sample areas, scale was significantly correlated with average kernel density and its standard deviation with high or medium correlation, for which the correlation coefficient of over 2/3 of the sample areas is positive. The average kernel density of each sample area varied with the scale used. These relationships were simulated with the linear, logarithmic, power, S, and exponential function models. According to the relationship between kernel density and scale, the maximum value or inflection point was then used to evaluate the optimal scale (i.e., proposed area) of the gully distribution. The optimal scale of different regions also differed among them, being closely related to the statistical characteristics of gully kernel density (correlation coefficients with standard deviation, average, and coefficient of variation were 0.60, 0.47, and 0.38, respectively).