基于Horton分形的灌区灌溉水有效利用系数影响因素分析

根据黑龙江省20个典型灌区的渠系资料，采用Horton定律计算各灌区分维值并与河流水系理论分维值进行对比，结果表明三级灌区分维值均在Horton水系定律理论范围内，四级灌区中只有梧桐河灌区的分维值为3.037，超过一般理论范围上限约1.23%. 利用灰色关联度分析得出:三级灌区有效灌溉面积、节水灌溉面积比例、渠系结构复杂度、渠道密度与灌溉水有效利用系数的关联度分别为0.695、0.556、0.606、0.700，与分维值的关联度分别为0.575、0.585、0.711、0.613；四级灌区各因素与灌溉水有效利用系数的关联度分别为0.700、0.730、0.605、0.675，与分维值的关联度分别为0.763、0.602、0.583、0.546. 分别利用上述因素对灌溉水有效利用系数及分维值进行回归分析，得出提高灌溉水有效利用系数的渠系结构改造方案，对黑龙江省典型灌区的渠系结构优化具有一定的参考价值. 

Factors influencing effective utilization coefficient of irrigation water as determined with Horton fractal

Canal system data from 20 typical irrigation districts in Heilongjiang Province were analyzed by Horton's law to calculate fractal dimension values of each irrigation district and comparison made with theoretical fractal dimension values. The fractal dimension values of three-level irrigation district were found to be within theoretical ranges from Horton's law. But the fractal dimension value of Wutonghe Irrigation District in four-level irrigation district was 3.037, about 1.23% higher than the upper limit of the theoretical range. Grey correlation degree analysis showed that correlation degree of effective irrigation area, water-saving irrigation area proportion, canal system structure complexity, canal density and effective utilization coefficient of irrigation water were 0.695, 0.556, 0.606, 0.700 respectively, with correlation degree of fractal dimension values of 0.575, 0.585, 0.711, 0.613 respectively. The correlation degree of each factor of four level irrigation area and effective utilization coefficient of irrigation water were 0.700, 0.730, 0.605, 0.675, correlation degree with fractal dimension values were 0.763, 0.602, 0.583, 0.546 respectively. The above factors were used to make regression analysis of effective utilization coefficient and fractal dimension value of irrigation water respectively. Transformation scheme of canal system structure to improve effective utilization coefficient of irrigation water was obtained, with certain reference value for optimization of canal system structure of typical irrigation areas in Heilongjiang Province.