【作者】 常福宣；

【导师】 丁晶；

【作者基本信息】 四川大学 ， 水文学及水资源， 2001， 博士

【摘要】 本文着眼于水文尺度与水文现象的自相似性，运用分形理论研究了水文变量的时空分布特性，不同时空尺度下水文变量的变化规律以及水文变量与尺度之间的相互关系。 首先用盒子数法来计算日降雨过程和日径流过程的分形维数，研究了无标度区间的范围，并计算了日降雨过程和日径流过程的多重分形谱。 在洪水区域分析中一般采用洪水指标法，但该法的基本假定与实际情况存在矛盾，因此本文采用一种新的分析方法——标度分析法(或称为分形分析法)来研究洪峰的区域变化，将标度不变性引入年最大洪峰流量——汇流面积关系中，并将其用于嘉陵江流域的洪水，另外，本文在Smith提出的具有标度性质的二参数对数正态分布模型基础上创造性地提出了三参数对数正态分布模型来表征年最大洪峰流量分布中汇流面积的尺度影响。 暴雨公式是基于暴雨资料而建立起来的经验性公式，尚无合理的理论解释。本文将标度不变性引入暴雨强度——历时关系中。由年最大平均暴雨强度随历时变化的标度性质推导出暴雨公式的形式，找到了暴雨公式的理论根基——暴雨在时间上分配具有自相似性的结果。另外，本文提出了暴雨强度的对数正态分布模型来表征年最大暴雨强度分布中历时的尺度影响。 最后，本文将标度不变性引入洪水洪量——历时关系中，对大流域年最大洪量随历时变化的标度性质行了尝试性的研究。依照暴雨公式的思路，根据洪量随历时变化的标度性质建立了洪水强度历时公式。并提出了洪水洪量的对数正态分布模型来表征年最大洪量分布中历时的尺度影响。 总之，本文针对水文现象中广泛存在的自相似性，将分形理论引入水文水资源的研究中，研究了时空尺度对于水文变量变化规律的影响，加深了对水文运动规律的认识，并为水文水资源的研究提供了新的思路。更多还原

【Abstract】 In this paper, the self-similarity and scaling problem in hydrology are investigated by using the fractal theory. Emphases are given on the variation of hydrology variables on different scale and relationship of hydrology variables and scale.Firstly, the fractal dimensions of daily rainfall and daily runoff are calculated by using the box-counting method. The result demonstrated that daily rainfall and daily runoff has multifractal property in a range of temporal scale. So the multifractal spectra are calculated.Index flood method used in flood regional analysis has a shortcoming that one of its base assumption is not in accord with empirical observation. So a new method?scale analysis method(or called fractal analysis method) is applied to study the flood of Jialing River basin. The scaling hypotheses is applied to the relationship of annual maximum flood and drainage area. And basing on the scaling lognormal model with two parameters introduced by Smith, a lognormal model with three parameters of flood is introduced to represent the scale effect of drainage area in annual flood peak distributions.The rainfall Intensity-Duration-Frequency form is an experimental form based on a large number of rainfall data, but the theory base is unclear. The scaling hypothesesis applied to the relationship of annual maximum rainfall intensity and duration. The rainfall Intensity-Duration-Frequency form is proved based on the temporal scaling property of rainfall. And a scaling lognomial model of rainfall intensity is introduced to represent the affection of temporal scale of duration in annual maximum rainfall intensity distributions.Lastly, the scaling hypotheses is applied to the relationship of flood volume and duration in this paper. The flood Intensity-Duration-Frequency form is proved based on the temporal scaling property of flood. And a scaling lognormal model of flood volume is introduced to represent the affection of temporal scale of duration in annual maximum flood volume distributions.Above all, base on the self-similarity in hydrology, the fractal theory is applied to the hydrology and water resource research to study the affection of scale in the distribution of hydrology variables. It makes the hydrology law clearer and suggests a new idea for hydrology and water resource research.更多还原