基于GIS的流域地貌多重分形特征与侵蚀产沙关系研究
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摘要
由于流域地貌形态的多样性及空间组合的复杂性,其科学准确量化成为建立具有广泛适用性的流域水土流失预报模型所亟待解决的关键问题之一。本文依据多重分形等相关理论、结合GIS技术和室内模拟试验,提出了基于数字高程模型DEM的流域三维地貌多重分形特征量化模型及实现方法,揭示了小流域模型、大理河及杏子河流域三维地貌多重分形谱参数的动态变化及空间分布特征,探讨了大理河流域不同空间尺度子流域地貌奇异指数变化范围的差异性,建立了基于地貌多重分形信息熵的流域地貌多重分形特征与次降雨侵蚀产沙耦合关系模型,取得了如下主要研究成果：
(1)基于数字高程模型DEM的流域三维地貌多重分形特征量化模型和实现方法该量化模型包括三个子模型,即流域三维地貌特征概率测度子模型、阶距q估算子模型和多重分形谱测算子模型,此模型为实现流域地貌多重分形特征的直接量化提供了可靠保证。
(2)小流域模型地貌多重分形谱及各参数动态变化特征依据地貌信息熵可将历经25模拟降雨的小流域模型地貌发育划分为幼年期和壮年期两个阶段,不同阶段小流域模型地貌地貌多重分形谱曲线形状基本相似,均呈向右的钩状；随着小流域模型地貌的不断发育,地貌多重分形谱奇异指数分布范围Δα均呈现增长趋势,多重分形谱曲线高差Δf则表现出递减趋势,其中壮年期二者的变化幅度明显比幼年期小；同时,小流域模型地貌奇异指数分布范围Δα与沟谷密度、平均坡度等6个传统地貌量化参数呈极显著相关。
(3)大理河及杏子河流域地貌多重分形特征空间分异规律大理河、杏子河各子流域地貌的多重分形谱f(α)随地貌奇异指数α增大呈先增加后减小的变化趋势,但多重分形谱f(α)和地貌奇异指数α的极值、变化范围在各子流域均有所不同。大理河流域地貌奇异指数分布范围Δα平均值从上游到下游依次为：0.1304、0.1544和0.1584；左右岸分别为0.1431和0.1572；表明大理河流域地貌形态变化自上游向下游趋于复杂,右岸地貌复杂程度相对较大。杏子河流域地貌奇异指数分布范围Δα平均值从上游到下游依次为：0.1712、0.1617和0.1461；左右岸分别为0.1614和0.1557,表明杏子河流域地貌形态变化自上游向下游复杂性逐步减弱,左岸地貌复杂程度相对较大。
(4)大理河流域地貌多重分形特征空间尺度效应大理河流域不同空间尺度的子流域三维地貌均具有多重分形特征,清阳岔、李家河和西庄子流域地貌奇异指数Δα随流域面积增大呈明显增长趋势,平均增幅分别为10.57%、5.26%和11.79%,其变化曲线可分别用极显著的对数和线性函数来定量表达,表明随着空间尺度增加改变,流域地貌的复杂性和不均匀性更为明显。
(5)流域地貌多重分形信息熵与侵蚀产沙关系小流域模型地貌多重分形信息熵与次降雨相对输沙模数和径流模数关联度分别为0.8129和0.9050,明显高于其它传统地貌量化参数。地貌多重分形信息熵与次降雨输沙模数定量耦合关系表明,地貌对降雨侵蚀产沙的影响存在明显临界值,当地貌多重分形信息熵分别为2.6162和4.077时,小流域模型及野外典型流域岔巴沟次降雨侵蚀产沙出现峰值,成为其降雨侵蚀产沙的地貌临界点。
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.
(1)基于数字高程模型DEM的流域三维地貌多重分形特征量化模型和实现方法该量化模型包括三个子模型,即流域三维地貌特征概率测度子模型、阶距q估算子模型和多重分形谱测算子模型,此模型为实现流域地貌多重分形特征的直接量化提供了可靠保证。
(2)小流域模型地貌多重分形谱及各参数动态变化特征依据地貌信息熵可将历经25模拟降雨的小流域模型地貌发育划分为幼年期和壮年期两个阶段,不同阶段小流域模型地貌地貌多重分形谱曲线形状基本相似,均呈向右的钩状；随着小流域模型地貌的不断发育,地貌多重分形谱奇异指数分布范围Δα均呈现增长趋势,多重分形谱曲线高差Δf则表现出递减趋势,其中壮年期二者的变化幅度明显比幼年期小；同时,小流域模型地貌奇异指数分布范围Δα与沟谷密度、平均坡度等6个传统地貌量化参数呈极显著相关。
(3)大理河及杏子河流域地貌多重分形特征空间分异规律大理河、杏子河各子流域地貌的多重分形谱f(α)随地貌奇异指数α增大呈先增加后减小的变化趋势,但多重分形谱f(α)和地貌奇异指数α的极值、变化范围在各子流域均有所不同。大理河流域地貌奇异指数分布范围Δα平均值从上游到下游依次为：0.1304、0.1544和0.1584；左右岸分别为0.1431和0.1572；表明大理河流域地貌形态变化自上游向下游趋于复杂,右岸地貌复杂程度相对较大。杏子河流域地貌奇异指数分布范围Δα平均值从上游到下游依次为：0.1712、0.1617和0.1461；左右岸分别为0.1614和0.1557,表明杏子河流域地貌形态变化自上游向下游复杂性逐步减弱,左岸地貌复杂程度相对较大。
(4)大理河流域地貌多重分形特征空间尺度效应大理河流域不同空间尺度的子流域三维地貌均具有多重分形特征,清阳岔、李家河和西庄子流域地貌奇异指数Δα随流域面积增大呈明显增长趋势,平均增幅分别为10.57%、5.26%和11.79%,其变化曲线可分别用极显著的对数和线性函数来定量表达,表明随着空间尺度增加改变,流域地貌的复杂性和不均匀性更为明显。
(5)流域地貌多重分形信息熵与侵蚀产沙关系小流域模型地貌多重分形信息熵与次降雨相对输沙模数和径流模数关联度分别为0.8129和0.9050,明显高于其它传统地貌量化参数。地貌多重分形信息熵与次降雨输沙模数定量耦合关系表明,地貌对降雨侵蚀产沙的影响存在明显临界值,当地貌多重分形信息熵分别为2.6162和4.077时,小流域模型及野外典型流域岔巴沟次降雨侵蚀产沙出现峰值,成为其降雨侵蚀产沙的地貌临界点。
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.
引文
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