Study On Fractal Characteristics Of Canal System Distribution In Loess Irrigation Area

The irrigation canal systems of irrigated area are defined as the engineering systems which include water intaking from the water source, agriculture water supply with channel and its annexes and farm irrigation through field-project construction. In the system of irrigation canal of irrigated area, the lateral canal belongs to the main canal and is superior to the head ditch, which is superior to the field ditch. Different degrees of canal and ditch have similar hydraulic characteristic and canal system profile compared with the whole irrigation canal system, which together make up a fractal with self-similar characteristic. Although the irrigation system is artificial water system, it has the similar characteristics of natural water system such as the flow regularity of mass and energy and so on. In certain scale region, the canal systems have the statistical self-similarity in different spatial scale, which means that the canal system is of fractal characteristic.Based on the studies of the canal systems in Baojixia irrigation area and Jinghui irrigated area of loess area in Shanxi province, this paper has analyzed the relationship between morphological characteristics of canal system’s distribution and its service function(the sufficiency of irrigated area) as well as their mechanism of action with the fractal dimension of loess gulley and irrigated area as the standard and the Horton Law as the analytical method.The study results of this paper could provide a reference for optimizing the rational distribution and increase improving water use efficiency of irrigation canal systems in irrigated area.The main conclusions are as follows:(1) The fractal dimension of Baojixia irrigation area is situated between 0.56 and 1.02,most of them change between 0.6 and 1.0. Average fractal dimension is 0.89. The fractal dimension of first grade canal system is 0.99 and the fractal dimension of its subordinate canal system is situated between 0.92 and 1.02; The fractal dimension of second grade canal system is 0.89 and the fractal dimension of its subordinate canal system is situated between0.19 and 1.03; The fractal dimension of third grade canal system is 0.8 and the fractal dimension of its subordinate canal system is situated between 0.56 and 0.96, which is concentrated between 0.6 and 0.9; In addition, the branching ratios,bR, of first grade canalsystem to second grade canal system and second grade canal system to third grade canal system of Baojixia irrigation area are 8.25 and 0.70, respectively; The length ratios,lR, of first grade canal system to second grade canal system and second grade canal system to third grade canal system of Baojixia irrigation area are 1.78 and 0.36, respectively.(2) The fractal dimension of Jinghui irrigation area is situated between 0.67 and 1.04,most of them change between 0.8 and 1.0. The global fractal dimension is 0.92. The fractal dimension of first grade canal system is 0.89 and those of its general main canal and north trunk canal are 0.92 and 0.78, respectively; The fractal dimension of second grade canal system is 0.94 and the fractal dimension of its subordinate canal system is situated between0.86 and 0.98; The fractal dimension of third grade canal system is 0.92 and the fractal dimension of its subordinate canal system is situated between 0.67 and 0.99; The fractal dimension of fourth grade canal system is 0.91 and the fractal dimension of its subordinate canal system is situated between 0.80 and 1.03. In addition, the branching ratios,bR, of first grade canal system to second grade canal system, second grade canal system to third grade canal system and third grade canal system to fourth grade canal system of Jinghui irrigation area are 2, 1.5 and 0.70, respectively; The length ratios,lR, of first grade canal system to second grade canal system, second grade canal system to third grade canal system and third grade canal system to fourth grade canal system of Jinghui irrigation area are 4.5, 1.1 and 0.98,respectively.(3) Through studying of fractal theory and Horton law in the loess gully system and irrigation canal system in summary. The ditch divosion rate change in value from 3 to 5, river length ratio change in value from 1.5 to 3.5. The fractal dimension of the loess gully system value generally varys between 1.15 and 1.52. The fractal dimension of the irrigation canal system value in general changes between 1.1 and 1.3.(4) Suggestion for optimizing the canal systems of Baojixia irrigation area are as follows: we should properly reduce the redundishly second grade canal system, increase the third grade canal system and increase the number of the canal system levels within possible limits for the overmuch second grade canal system and too little third grade canal system of the irrigated area; the third grade canal system should be increased properly and its length should also be extended according the fact that the length ratio,lR, of second grade canal system to third grade canal system is undersize when comparing with the standard values.(5) Suggestion for optimizing the canal systems of Jinghuiqu irrigation area are as follows: long canal should be shortened and the third and fourth grade canal systems should be properly developed to optimize the distribution of canal systems for the reason that the number of canal systems is too few and some of those canal system are too long. On in thisway, the canal systems could be distributed evenly in the irrigated area to allocate the water resource more effectively under gravity with higher water-use efficiency.