水系分形维数(Fractal dimension of gully network,Dg)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Dg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Dg≤1.06时,流域处于幼年期;当Dg>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.%The fractal characteristics of drainage in the ten kongduis of the upper Yellow River were obtained using the box counting dimension, and the evolution stages of the watershed topography were defined by different ranges of the fractal dimensions of river networks (Dg). The results show that the fractal scaleless range of the Maobula River is 20-370 m based on a combination of artificial judgment, correlation coefficient test and fitting error. Other kongduis show good fractal characteristics in this fractal scaleless range as well. The box counting dimension can be used as a quantitative index of watershed topography fractal characteristics. The fractal dimension of stream networks is independent of the threshold contributing area used for extracting the drainage networks from the DEM.The values of Dg in the upper ten kongduis are in the range of 1.08-1.14. Both the runoff yield and the sediment yield are positively and linearly related with Dg. The positive relation between the sediment yield and Dg reflects the effect of landform features on sediment yield in the young and/or mature stages of landform evolution of the study area. By revising the critical value of Dg, the value of Dg of the basin in the young evolution stage is less than 1.06, while it is more than 1.06 for the basin in mature or old evolution stage. The upper ten kongduis are in the mature stage of landform evolution.
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