基于分形理论的新安江模型参数空间尺度效应分析

Spatial scale effect analysis of Xin’anjiangmodel parameters based on fractal theory

水文尺度效应一直是当今水文科学研究的前沿问题。基于分形理论建立模型空间敏感参数在不同尺度之间的定量转换方程,进而提出了一种水文模型参数空间尺度效应分析方法。以三水源新安江模型为例,分析模型参数在嘉陵江小河坝站以上流域的空间尺度效应。结果表明:新安江模型空间敏感参数(SM、KG、KI、CG、CI、CS)具有随空间尺度变化的标度不变性,与流域集水面积之间定量关系可用幂函数关系进行描述,并可建立相应的定量转换方程。通过在研究流域不同空间尺度上的应用检验,发现基于分形理论标度不变性建立的新安江模型参数空间尺度转换方程具有较高的适用性,能实现有资料地区模型参数向无资料地区的移用,为无资料地区水文模型参数的确定提供参考。

Hydrological scale effect has always been the frontier research in hydrology.In this paper,aquantitative conversion equation between different spatial scales of a model′s sensitive parameters is established based on the fractal theory,and a method for analyzing the spatial scale effects of hydrological model parameters is proposed.Taking the three-source Xin′anjiang model as an example,the spatial scale effect of model parameters is analyzed above the Xiaoheba station of Jialing River Basin.The results showed that the spatial sensitive parameters(SM,KG,KI,CG,CI,and CS)of the Xin′anjiang model are scale-invariant with the change of spatial scale,and the quantitative relationship between them and catchment area can be described by power function relationship.Therefore,the corresponding quantitative conversion equation can be established by this relationship.Through the application and validation on different spatial scales in the basin,it is found that this spatial scale conversion equation of the Xin′anjiang model based on the scale-invariance using fractal theory has high applicability.It can realize that the migration of model parameters can be done from the data-rich region to the no data region and can provide references for the determination of model parameters in no data regions.