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水系分形维数(Fractal dimension of gully network,D_g)反映了河网分布和水系发育的复杂程度。以位于黄河上游内蒙古段十大孔兑上游丘陵沟壑区为研究对象,利用计盒维数的方法,研究其水系分形特征,同时利用水系分维数D判断流域地貌所处的侵蚀发育阶段。结果表明,(1)以毛不拉孔兑为例,利用人工判定法,相关系数检验法和拟合误差相结合的方法确定无标度区为20~370 m。且各孔兑的地貌形态在该无标度区间内均表现出很好的分形特征,计盒维数可作为流域地貌形态分形特性的量化指标。求得十大孔兑上游丘陵沟壑区的水系分维数D_g为1.08~1.14。(2)十大孔兑水系分维值在不同的汇流面积阈值下变化不大;径流模数与河网分维存在正相关关系。产沙模数与河网分维的线性正相关关系反映了地貌发育幼壮年期地形条件对产沙的影响。(3)按水系分维数与流域起伏程度、坡度及等高线分维值的关系,就十大孔兑而言,当D_g≤1.06时,流域处于幼年期;当D_g>1.06时,流域进入壮年期。水系分维数、高程积分值指示十大孔兑上游流域地貌均处于壮年期。
Fractal dimension of gully network (D_g) reflects the complexity of river network distribution and water system development. Taking the upper reaches of the upper reaches of Yellow River in the upper reaches of hilly and gully regions as the research object, the method of box counting was used to study the fractal characteristics of water system. At the same time, the fractal dimension D of water system was used to judge the erosion development stage. The results showed that: (1) The example of Mao-Lao-kong was used to determine the scale-free zone from 20 to 370 m using the method of artificial judgment, correlation coefficient test and fitting error. The topography of each hole shows good fractal characteristics in this scale-free interval, and the box-counting dimension can be used as a quantitative index of the fractal characteristics of the topography of the basin. The fractal dimension D_g of the water system obtained from the top ten holes against the upstream hilly and gully area was 1.08 ~ 1.14. (2) The fractal dimension values of the ten major boreholes did not change much under different confluence area thresholds. There was a positive correlation between the runoff modulus and the fractal dimension of the river network. The linear positive correlation between sediment yield and river network fractal dimension reflects the influence of terrain conditions on the sediment yield during the young age. (3) According to the relationship between the fractal dimension of water system and the degree of undulation of the river basin, the slope and the fractal dimension of the contour line, when D_g≤1.06, the basin is in its infancy; when D_g> 1.06, Into the prime of life. The fractal dimension of water system and the elevation integral value indicate that the ten major holes are all in the prime of life when compared with the topography of upstream watershed.