Spatial statistical properties and scale transform analyses on the topographic index derived from DEMs in China

The topographic index (TI), frequently used in approximately characterizing the spatial distribution of variable source areas within a watershed, has been widely applied in topography-based land-surface process schemes coupled in regional or global climatic models. The TI concept, however, was originally developed for studying hill-slope scale hydrological processes and was most commonly used in simulations from small- to medium-sized watersheds. It is still questionable whether the TI computed from coarse-resolution digital elevation models (DEMs) for large-scale hydrology and climate studies can effectively reflect the spatial distribution of soil moisture, surface saturation, and runoff generation processes in most areas. In this study, we first proposed an improved multiple flow direction algorithm (IMFD) for accurately computing the TI distribution. We then evaluated the IMFD algorithm quantitatively by using four types of artificial mathematical surfaces. Subsequently, we conducted statistical analyses on the TI distributions computed with IMFD from 90×90 m² and 1000×1000 m² resolution DEM blocks sampled from across the whole of China. We found there are linear relationships between the mean TI values computed from the two different resolution DEMs in three sampled blocks of different sizes, i.e., 0.1°×0.1°, 0.5°×0.5° and 1°×1°. Systematic analyses further suggested that the forms of these linear relationships are evidently affected by the algorithm used for the TI computation, while the size, location, and number of the selected TI samples have minor effects on them. Finally, we investigated the influence of DEM resolution on the spatial statistical properties of TI. From the viewpoint of terrain discretization and smoothing effects, we also discussed the mechanism and the reasons causing the similarity on TI at different spatial resolutions.