降雨随历时变化标度性质的探讨

降雨公式是水文计算的基本依据之一，也是工程师和水文学家十分关心的问题。长期以来水文中采用的降雨公式是基于大量降雨资料而建立起来的经验公式，多年的实践表明该公式能客观地反映降雨特性，计算结果符合实际，但是对该公式的理论基础却不太清楚。着眼于降雨在时间上的自相似性，将标度理论应用于降雨时间尺度问题，对降雨强度随历时变化的标度性质进行了研究，探讨了降雨公式的理论基础。由标度理论阐述了降雨标度性质（标度不变性）在时间尺度上的意义，并用此理论研究了成都望江楼站的降雨资料，计算了该站不同历时下降雨强度的各阶矩和变差系数，研究的结果表明，在一定的时间尺度范围内，降雨强度随历时变化确实具有多标度性质。最后由降雨强度随历时变化的标度性质推导出降雨公式，说明了降雨公式是降雨在时间尺度上标度特性的表示。

SCALING PROPERTY OF THE RAINFALL VARIATION IN RELATION WITH DURATION

The rainfall Intensity Duration Frequency formula is one of the bases in hydrology calculation,and has been of considerable interest to engineers and hydrologists.Over a long period of time,the form used in hydrology is experimental,based on a large number of rainfall data.It has been shown that this form could reflect the rainfall property in practice over decades,but the theory base of this form is unclear.On the basis of the temporal self similarity of rainfall,the scaling theory is applied to study the problem of scaling property of the variation in rainfall intensity in relation with duration in this paper.By using 37 years (from 1951 to 1987) daily rainfall data in Chengdu Wangjianglou station,we calculated the moments and \$Cv\$ (coefficient of variation) of rainfall intensity with different durations.The result demonstrated that the annual maximum mean rainfall intensity with duration has multiscaling property in the range from 1 to 7 days.Lastly,the rainfall Intensity Duration Frequency form is proved based on the temporal scaling property of rainfall.