On fractal description of ponds distribution in irrigation system

The current interest in ponds stems mainly from their utilization for irrigation,domestic use,livestock watering, fishing and so on.The ponds,whose distribution results from geomorphological erosion and development as well as human activities,are important components for hydrologicl cycle in irrigation system. Here we report the analyses of the ponds distribution from Zhanghe irrigation system to determine their frcatal structure based on the geographic information system(GIS).The ponds areas,both in the whole region and the sub regions,are close to the hyperbolic distribution and exhibit power law properties of the fractal structure for the scale invariance in probability spaces.The covering cell method is used to obtain the box dimension and information dimension of ponds distribution in the whole region and 14 sub-regions,and the results show that the ponds are fratal structures lying on the two dimensional space Lastly,the linear relations between the two-fratal dimentions and the topographic factors are analyzed.