分形理论在洪水分期研究中的应用

分析水文现象的非线性、随机性和确定性、相似性,以一定尺度范围内(如年内季节间)洪水表现出的自相似性和分形特性,作为应用分形理论的论据.探讨用分形理论进行洪水分期的方法,给出了按时间尺度容量维和空间尺度相似维计算相应分维数的具体算法.以漳河水库历年汛期日最大流量为系列样本进行研究,结果表明,无论是用容量维数算法还是用相似维数算法,划分的洪水分期一致,且与经验统计方法划分的洪水分期一致,但分形方法比经验统计方法进行洪水分期具有定量和客观、计算简便的明显优点,有利于在生产实际中推广应用.

Application of fractal theory to stage research of flood events

The nonlinearity,randomness,determinability,and similarity of hydrological phenomena were analyzed.The self-similarity and fractal characteristic of floods events for a certain duration(e.g.a season of a year) provide a theoretic basis for adoption of fractal theory.In the study,the method for dividing flood in stages with fractal theory was discussed,and certain methods for calculating the fractal dimension according to the capacity dimension in temporal scale and the resemble dimension in spatial scale were put forward.The calculation methods were used to divide the flood stage for the Zhanghe Reservoir in terms of the maximal daily discharge in flood season of each year,and the results of the two methods agree with each other and are in accordance with that from empirical statistics.Compared with empirical statistics,the fractal method is of quantitative and objective characteristics and convenient in calculation,and it is of wide scope of application in practice.