以赤水河干流选取的 86 组弯曲河段为研究对象, 应用网格覆盖法测算水边线长度信息维数和河床水上地貌面积信息维数, 通过归纳分维“粗算值” 的变化规律得出一种无标度区间的识别方法, 并对所选弯曲河段平面形态地貌特征进行分析。结果表明: 以粗算值 “失稳” 现象作为判别条件可有效识别分形体无标度区间, 且[ 10, 40] 为此次 信息维数测算的无标度区; 所测弯曲河段水边线信息维数区间范围为[ 0.915 7, 1.042 1] 、平均值为 0.997 9, 地貌面积信息维数区间范围为[ 1.301 3, 1.923 0] 、平均值为 1.676 0, 弯曲率值区间范围为[ 1.025 9, 2.651 2] 、平均值为 1.271 2; 赤水河中游、下游河段, 水边线信息维数与弯曲率的相关系数依次为 0.469 和 0.644, 均为显著性相关, 且相关程度逐渐加强, 在整个干流地貌面积信息维数与水边线信息维数、弯曲率相关性皆较弱, 且与水边线信息维数呈负相关。

Taking 86 groups of curved river sections selected from the mainstream of the Chishui River as the research object, the information dimension of the length of the waterline and the information dimension of the riverbed water landform area are calculated based on the g rid covering method. By summarizing the variation law of fractal dimension " rough calculation value" , a met hod of scale-free interv al identification is obtained, and the plane morphological and geomorphic characteristics of the selected curved river section are analyzed. The results show that: The " instability " phenomenon of the rough calculation value can be used as the criterion to ef fectively identify the scale-free interval of the fractal body, and [ 10, 40] is the scale-free area of the information dimension calculation; the information dimension range of the water edge line of the measured curved river section is [ 0.915 7, 1.042 1] with an averag evalue of 0. 997 9, the landform area information dimension range is [ 1.301 3, 1.923 0] with an averag evalue of 1.676 0, and the tortuosity value range is [ 1.025 9, 2.651 2] , the averag evalue is 1.271 2, respectively ; in the middle and lower reaches of the Chishui River, the correlation coefficients of the waterfront information dimension and the to rtuosity are 0.469 and 0.644 respectively , both of which are significantly correlated, and the degree of correlation is gradually strengthened. The correlation between the info rmation dimension of the landform area and the information dimension of the waterfront line and the curvature rate is weak and has a neg ative correlation with the information dimension of the water frontline.

国家自然科学基金( 51509271) ; 国家水专项( 2018ZX07105-002)