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首页> 外文期刊>Journal of Geophysical Research. Biogeosciences >Self-similarity and multifractality of topographic surfaces at basin and subbasin scales
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Self-similarity and multifractality of topographic surfaces at basin and subbasin scales

机译：盆地和亚盆地尺度地形表面的自相似性和多重分形

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摘要

Self-similarity of fluvial erosion topography manifests itself through statistical renormalization properties of drainage networks and river profiles. Results based on these renormalization properties are often inconsistent with those from spectral or variogram analysis of linear transects. We show that the inconsistency is due to two factors: (1) Network and transect analyses are based on different self-similarity conditions, and (2) elevation along transects depends on the hillslopes, where self-similarity either does not apply or applies with different parameters. As a result, transect methods produce misleading results when the topography has finite hillslopes. We also consider whether self-similarity is sufficient to describe the scaling invariance of natural river basin topography or more sophisticated multifractal conditions should be used. The conclusion of multifractality reached in recent studies was based on the use of gradient amplitudes rather than elevation increments. The gradient amplitude method is found to produce spurious multifractality also in cases when the surface is known to self-similar. When more appropriate methods are used, topography shows little evidence of multifractality. We support our conclusions through numerical analysis of synthetic and natural river basins.
机译：河流侵蚀地形的自相似​​性通过排水网络和河流剖面的统计归一化特性来体现。基于这些重归一化属性的结果通常与线性样条的光谱或变异函数分析的结果不一致。我们表明不一致之处是由于两个因素造成的：（1）网络和样面分析基于不同的自相似性条件，（2）沿样条的高程取决于山坡，其中自相似性要么不适用，要么适用于不同的参数。结果，当地形具有有限的坡度时，横断面方法会产生误导性的结果。我们还考虑自相似是否足以描述自然流域地形的尺度不变性，还是应使用更复杂的多重分形条件。在最近的研究中得出的多重分形结论是基于使用梯度幅度而不是仰角增量。发现在已知表面自相似的情况下，梯度幅度方法也会产生虚假多重分形。当使用更合适的方法时，地形几乎没有多重分形的迹象。我们通过对合成流域和天然流域进行数值分析来支持我们的结论。

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