The Applications Of Fractal Theory In The Study Of Hydrology And Water Resources

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.