基于分形理论的灌溉水有效利用系数空间尺度变异

基于2010年度广东省75处样点灌区的实测资料和遥感图像,应用分形理论,采用网格盒维数法计算了各样点灌区盒维数,结果表明:广东省灌区具有明显的分形特征,盒维数介于1.0004～1.675之间,分维数均值为1.308,形状指数均值为0.335,都随灌区规模呈同步减小趋势.不同规模灌区盒维数大型灌区(1.442)＞中型灌区(1.287)＞小型灌区(1.195).灌溉水有效利用系数与空间分形特征诸因子中以非空网格对数值最高,相关性达到0.941.基于此,建立了不同网格尺度下的灌区面积与灌溉水有效利用系数和盒维数空间尺度变异函数.同时,从影响灌溉水有效利用系数的众多因素中,选取了工程评价值、盒子维数、灌区形状指数、参考作物蒸发蒸腾量ET0和当年降水量5项指标进行了空间格局影响因素分析,结合灰关联计算结果表明:空间各影响因素中以工程评价因子的关联度最高,达到0.8478,其次为形态特征因子,自然气象因子影响最小.尝试利用分形理论为不同面积尺度灌区灌溉水有效利用系数的空间变异规律分析和尺度转换提供一种新的思路,该结果对于指导灌区投资改造和规划建设,具有较强的理论和应用价值.

Fractal-based Effective Utilization Coefficient of Irrigation Water Space Scale Variability

Based on the measured data and remote sensing images of 75 sample irrigation areas of Guangdong province in 2010,grid box dimension method was used to analyze the box dimension of sample irrigation area.The results show that irrigation area of the province is subjected to fractal characteristics with the box dimension ranging from 1.0004 to 1.675,the mean of fractal dimension of 1.308 and mean shape index of 0.335,and shows a decreasing trend with the irrigation area scale.The box dimension of irrigation area at different scales is listed in the order of large-scale irrigation area(1.442) > medium-sized irrigation area(1.287) > small-scale irrigation area(1.195).The most significant factor is logarithm of non-empty grid with the correlation coefficient of 0.941.In this case,a variation function of spatial scale between irrigation district area,the effective utilization coefficient of irrigation water and the box dimension under different grid scales is achieved.Meanwhile,five indicators related to many influencing factors,the value of the project evaluation,box dimension,irrigation area shape index,the reference crop evapotranspiration ET0 and precipitation are analyzed in this study.And the factors influencing the spatial pattern are also thoroughly investigated.The above-mentioned analysis and also those by the gray relational calculation show that the highest correlation of spatial influence factors is the engineering evaluation of 0.8478,followed by topographical features and meteorological factors.