基于归一化植被指数的流域植被覆盖分形维数研究

量化和表征植被覆盖空间分布的复杂性是研究植被与地表物质迁移关系的重要问题。为研究植被覆盖分形维数的表征特点及其在不同尺度上的变化特征,该文基于地理信息系统平台,利用分形布朗运动理论,结合像元归一化植被指数(normalized difference vegetation index,NDVI)的空间分布,提出并计算了植被覆盖分形布朗运动(fractional brownian motion,FBM)分形维数。结果显示,流域植被覆盖的空间分布具有统计自相似性,可用分形维数表征,其值在2.5~3之间,越接近2.5,表示植被覆盖空间分布越复杂。植被覆盖FBM分形维数与流域内均值化NDVI值和NDVI值的变异系数无直接关系,与单位面积不同NDVI值的像元数呈极显著负相关(R=0.66,P0.01)。植被覆盖FBM分形维数具有尺度效应,随流域面积增大而增大,到一定尺度后趋于平稳。流域植被覆盖FBM分形维数能够克服NDVI像元点奇异值等对植被空间分布量化表征计算的干扰,相对传统表征植被覆盖的指数,其在水文、土壤侵蚀等模型中具有更广泛的应用意义。

Research on fractal dimension of vegetation cover based on normalized difference vegetation index in watershed scale

Abstract: It is a critical issue to quantify and characterize the complexity of the spatial distribution of vegetation cover when studying the effects of vegetation cover on material migration processes of the earth's surface at the watershed scale. Fractal theory, known as "geometry of nature", is the frequently-used tool for quantitative research on the distribution and complexity of vegetation at different scales. But fewer researches of the spatial distribution of vegetation with fractal theory at the pixel scale are reported. The objective of this work was to establish the method of using NDVI values and fractional Brownian motion (FBM) theory to describe the complexity of the spatial distribution of vegetation cover. Firstly, the spatial distribution pattern of pixel NDVI, which had the similar data structure with digital elevation model, was produced by using geographic information system (GIS) and the pixel NDVI values in this paper. Secondly, moving window method was developed with GIS software, and then it was used to measure the increments of each pixel NDVI in the watershed. Last, fractal dimension of vegetation cover based on the spatial distribution pattern of NDVI values at the pixel scale was calculated with FBM theory. Taking Dali River Basin as an example, it was divided into four orders according to the watershed area. The watershed area declined five times per order. FBM fractal dimension of watershed vegetation cover based on pixel NDVI values was calculated under different watershed scales. The results showed that spatial distribution of watershed vegetation cover on the watershed had the significantly (P<0.01) statistical self-similarity, which can be characterized with FBM theory. FBM fractal dimension for watershed vegetation cover was between 2.5 to 3.0, and the value closer to 2.5 demonstrated the more complex the spatial distribution of vegetation cover. FBM fractal dimension of vegetation cover ranged from 2.695 to 2.817 within the Dali River Basin at different area scales. It increased with power function as the watershed area increased, and the increase was smaller after a certain size with the drainage area increasing. FBM fractal dimension of vegetation cover tended to be stable and was infinitely closer to FBM fractal dimension of the entire watershed. These results indicated that FBM fractal dimension of vegetation cover was affected by the watershed scale. FBM fractal dimension of vegetation cover had no direct relationship with the mean NDVI of watershed and coefficient variation of pixel NDVI, but it was significantly (P<0.01) negatively correlated to the numbers of different NDVI per square kilometer at different watershed. FBM fractal dimension of watershed vegetation cover overcame the effect of the singular value of NDVI on quantifying and characterizing the complexity of the spatial distribution of vegetation cover and remedied the defect of NDVI diversity (such as information entropy) and other indices characterizing the complexity of vegetation coverage. Compared with the traditional indices of quantifying and characterizing the complexity of vegetation cover, it had a wider application in hydrology, soil erosion model when studying on the relationship between vegetation and material migration at the watershed scale.