小流域地貌不同发育阶段的多重分形特征模拟研究

Simulation on Multi-fractal Features at Different Developmental Periods for Small Watershed Model

流域地貌形态的科学量化是研究地貌学复杂问题和流域土壤侵蚀模型研究的热点问题之一。以定雨强模拟降雨作为主要驱动力,以小流域模型不同发育时段的DEM数据为基础,利用多重分形模型计算分析了小流域不同发育阶段地貌多重分形及其参数,探讨了小流域地貌不同发育阶段的多重分形特征及其表征的流域地貌意义。结果表明:在小流域地貌发育的幼年阶段,随着地貌的不断发育,地貌奇异指数分布范围△α从第2期的0.5085增至第4期的0.6716,呈增长变化趋势,平均增长幅度为16.04%,多重分形参数△f则呈现出递减趋势,降幅为29.96%,这表明在该阶段地貌发育比较活跃,沟谷发育迅速。在小流域模型地貌发育的壮年阶段,随着小流域地貌大坡度的地貌单元不断增加,地貌表面形态复杂性和差异性增大,地貌奇异指数分布范围△α和多重分形参数△f的变化趋势与地貌发育幼年阶段基本一致,△α呈增长趋势,平均增幅度5.94%,△f呈递减趋势,平均降幅为21.34%,但二者的变化幅度明显地减小,这表明壮年阶段流域地貌发育相对趋于稳定,地貌变化趋于缓和。表明多重分形参数可以科学定量表达小流域模型不同发育阶段地貌动态演化特征及地表形态的不均匀性和复杂性,对流域地貌形态的复杂体系进行定量化研究具有重要的意义。

Scientifically quantifying geomorphology feature of watershed is one of the keys in the fields of geomorphology and watershed soil erosion prediction model.With regular rain as main drive to simulate rainfall and with the DEM data of different developmental periods of small watershed model as basis,the multi-fractal model was used to calculate the geomorphology multi-fractal parameters of different developmental periods of small watershed and analyze its geomorphic significance of characterization and geomorphologic meanings of multi-fractal spectrums and thire main parameters.The results showed that during the infantile developmental period of small watershed,with the continual development of geomorphology,the distribution range of geomorphology singularity exponentΔαwas from0.5085in the second phase to0.6716in the fourth phase,showing an increasing trend,with an average increase of16.04%,while the multi-fractal parameterΔf decreased by29.96%.Such results showed that in this period,the geomorphology development was active and the gully developed fast.During the meridian developmental period of small watershed geomorphology,with the increase of geomorphic units of large geomorphic gradients in small watershed,the complexity and diversity of geomorphic surface increased,and the variation trend of geomorphology singularity exponentΔαand multi-fractal parameterΔf were basically the same as those of the early stage of geomorphic development.Δαshowed an increasing trend,with an average increase of5.94%,andΔf showed a decreasing trend,with an average decrease of21.34%.The range of variation between the two was obviously narrow.This showed that the meridian developmental period was more stable and the surface configuration change became smooth.This research manifested that the multi-fractal parameters can express the inner heterogeneity of small watershed and geomorphology,complexity,structural difference and characteristics of dynamic change at different developmental periods quantitatively and scientifically.There is great scientific significance of the quantification research on the complex system of watershed geomorphology.