Multi-scale spatial analysis on NDVI and topographical factors using wavelet transform
基于小波变换的NDVI与地形因子多尺度空间相关分析

It is now widely recognized that ecological analysis results are sensitive to the resolution of the source data. Wavelet transform is a fashionable tool of solving scale transform in geosciences and ecology due to their advantages of multi-resolution. In this study, the wavelet transform was applied to analyze the correlations between NDVI (Normalized Difference Vegetation Index) and topographic factors on different scales in the Tibet Plateau. By discrete wavelet transform for spatial sampling data along longitude 87°E and 90°E, latitude 30°N and 33°N, multi-scale patterns of NDVI and DEM were examined. Daubechies wavelet, a compactly supported wavelet with extremal phase and highest number of vanishing moments, was chosen as a mother function to decompose the NDVI and the geographical factors into multi-scale wavelet coefficients respectively according to the source data pattern. The results of wavelet coefficient variograms show that NDVI spatial patterns exist two dominant scales of 4 km and 25 km, and a co-dominant scale of 12 km in longitude and latitude directions. Topographical indicator DEM exhibits a dominant spatial scale of 12 km in latitude direction, and a dominant spatial scale of 25 km in longitude direction. The fact of synchronous variance peak of 25 km in 93°E suggests that tightly-coupled relationship exists between NDVI and DEM. Multi-scale correlation relationships among NDVI and geographical factors were also examined by using sampling data of spatial resolution 0.1°. Results suggest that the correlation is scale-dependent, i.e. different scales have different coefficients among the factors. Ihe coefficient values between NDVI and topographical factors such as elevation, CTI (Compound Topographic Index), aspect and slope are larger in coarser scales than those in finer scales, which suggest that topographical factors have important roles on controlling NDVI patterns in a larger scale.