| Because of Diversity and Spatial Combination Complexity of watershed geomorphology, the scientific and accurate quantification of watershed geomorphology has been one of key issues to be solved in building a watershed soil and water loss prediction model with broad applicability so far. According to the related theories such as multi-fractal theory and Geographic information system(i.e. GIS) and indoor simulated experiments, the DEM-based qualification model and its GIS-based realization method of watershed 3-D geomorphology multi-fractal characteristics were established in the paper. In addition, the dynamic variation and spatial distribution characteristics of the parameters of watershed 3-D geomorphology multi-fractal spectrums of indoor small geomorphology generalized watershed model, Dali River Watershed and Xingzi River Watershed were analyzed. And the difference of the distribution range of singularity exponents of watershed 3-D geomorphology multi-fractal spectrums of different spatial-scale sub-watershed of Dali River Watershed in the paper. And a coupled model based on the relationship between watershed geomorphology multi-fractal information entropy, which could be used to reflect the integrated characteristics of watershed geomorphology, and sediment yield of water erosion in single rainfall event was established too. The obtainded main study results in the paper are as follows:Firstly, the DEM-based qualification model and its GIS-based realization method of watershed 3-D geomorphology multi-fractal characteristics were established. The established qualification model, which was composed of probability measures submodel of watershed 3-D geomorphology characteristics, estimation submodel of step distance and the measurement submodel of watershed 3-D geomorphology multi-fractal spectrums, could provide reliable support for the realization of direct quantification of watershed geomorphology multi-fractal characteristics.Secondly, the dynamic variation characteristics of watershed 3-D geomorphology multi-fractal spectrum and its parameters of indoor small geomorphology generalized watershed model were analyzed. Based on the calculated geomorphology information entropies of indoor small geomorphology generalized watershed model during 25 simulated rainfalls, the geomorphology development of the small watershed model could be divided into two different stages,i.e. youthful stage and mature stage. The curves of watershed 3-D geomorphology multi-fractal spectrums of the small watershed model in different development stages had similar right-hooked bend shape. Along with the development of watershed geomorphology of the small watershed model, the distribution range of singularity exponents of watershed 3-D geomorphology multi-fractal spectrums tended to become bigger and bigger, while the height gap of the multi-fractal spectrum curves tended to become smaller and smaller, in addition, the variation scopes of the distribution range of singularity exponents and the height gap of the multi-fractal spectrum curves in geomorphology development youthful stage were smaller than those in geomorphology development mature stage. And the distribution range of singularity exponents of the small watershed model was highly correlated with six different traditional geomorphology quantitative parameters such as gully density, average gradient, etc.Thirdly, the spatial distribution rules of the parameters of watershed 3-D geomorphology multi-fractal spectrums of Dali River Watershed and Xingzi River Watershed were analyzed. The watershed 3-D geomorphology multi-fractal spectrum values firstly increased and then reduced with the increase of the singularity exponents of watershed 3-D geomorphology multi-fractal spectrum among the different sub-watersheds in both of Dali River and Xingzi River Watersheds, while the extreme values, variation scopes of watershed 3-D geomorphology multi-fractal spectrum value and singularity exponent were different in different sub-watersheds. The average values of the distribution range of singularity exponents of watershed 3-D geomorphology of the upstream, middle and downstream reaches of Dali River watershed was 0.1304,0.1544 and 0.1584 respectively, and that of right and left banks of Dali River watershed was 0.1431 and 0.1572 respectively, which indicated that the watershed geomorphology became more and more complex from upstream reach to downstream reach, and the complex degree of sub-watershed geomorphology on right bank is relatively bigger than that on left bank in Dali River Watershed. The average values of the distribution range of singularity exponents of watershed 3-D geomorphology of the upstream, middle and downstream reaches of Xingzi River watershed was 0.1712,0.1617 and 0.1461 respectively, and that of right and left banks of Dali River watershed was 0.1614 and 0.1557 respectively, which indicated that the watershed geomorphology became more and more complex from downstream reach to upstream reach, and the complex degree of sub-watershed geomorphology on left bank is relatively bigger than that on right bank in XIngzi River Watershed.Fourthly, the spatial-scale effect of watershed 3-D geomorphology multi-fractal characteristics of Dali River watershed was studied. The results indicated that watershed 3-D geomorphology of all the studied different spatial-scale sub-watershed of Dali River watershed had multi-fractal characteristics, the distribution ranges of singularity exponents of watershed 3-D geomorphology of Qingyangcha, Lijiahe and Xizhuang subwatersheds significantly increased with the increasing watershed controlled coverage area, with a average increase extent of 10.57%,5.26%and 11.79% individually. And the distribution ranges of singularity exponents of watershed 3-D geomorphology of Qingyangcha, Lijiahe and Xizhuang subwatersheds were highly logarithmically or linearly correlated with watershed controlled coverage area. As a result, the complexity and unhomogeneity of watershed geomorphology became more and more significant with the increasing watershed controlled coverage area.Finally, a coupled relationship between watershed geomorphology multi-fractal information entropy and sediment yield of water erosion in single rainfall event was established. The results showed that the grey correlation coefficient between the watershed geomorphology multi-fractal information entropy and the corresponding relative sediment transportation modulus in a single rainfall event was 0.8129 and 0.9050 respectively, which was significantly bigger than the traditional watershed geomorphology quantitative parameters. The quantitative coupled relationship between watershed geomorphology multi-fractal information entropy and the corresponding relative sediment transportation modulus indicated that there existed certain critical value of watershed geomorphology multi-fractal information entropy, i.e. when the watershed geomorphology multi-fractal information entropy of the indoor small watershed model and Chabagou watershed was 2.6162 and 4.077 respectively, the water erosion and sediment yield of the indoor small watershed model and Chabagou watershed in single rainfall events could be up to peak value.
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