农地细碎化度测度指数计算的改进

Simpson Index Calculation of Land Fragmentation

为了使得农地细碎化度的测度指数更加符合实际,论文采用概括和理论分析的手段,改进了测度指数的计算方法。首先,从农地细碎化的概念出发,从农地完整性视角,研究了农地完整度与细碎化之间的关系,认为完整度可以描述农地细碎化程度。其次,在不考虑地块空间邻近相互作用的情况下,用泰勒公式展开了农地细碎化度的测度指数函数,利用边界条件,给出了测度指数的计算公式。之后,在考虑地块在空间邻近相互作用的情况下,引入空间邻近矩阵,建立基于地块间空间相互作用的测度指数计算公式,分析该测度指数的相关特征。最后,用改进的农地细碎化度的测度指数计算方法,计算了江苏省仪征市新集镇的农地细碎化指数,对方法进行了验证。

Farmland fragmentation is one of the main problems facing China＇s agricultural production. With the implementation of the household contract responsibility system in China in the late 1970s, average farmland allocation resulted in serious farmland fragmentation and may hinder the development of agricultural production, slow down agricultural modernization, and lead to a decline in the efficiency of agricultural production and rural labor force. The Simpson index is one of the most important indexes to measure farmland fragmentation, but the spatial interaction among farmlands is often ignored. In order to comprehensively and more accurately measure farmland fragmentation we build on the Simpson index. First, the relationship between farmland integrity and fragmentation was analyzed. Second, without considering the spatial interaction among farmlands, the farmland integrity index function was expanded using the Taylor formula. The farmland integrity index was equivalent to 1-Simpson index. Later, under a hypothesis of farmland spatial interaction, a spatial contiguity matrix was introduced to construct the farmland integrity index formula. The farmland integrity index was the Eigenvalue of the farmland integrity matrix. The improved index formula was applied to calculate farmland integrity indexes for Huayuan and Miaoshan village, Yizheng City, Jiangsu province. Data sources were acquired from land-use surveys in 2010 and images in 2000. When the spatial interaction among farmlands was neglected, farmland integrity indexes in plain terrain were higher than that in hilly areas. However, when spatial interaction was considered, the spatial clustering coefficient in hilly areas was higher than that in plain terrain. This conclusion is consistent with previous findings. Farmland integrity indexes were contrasted in different periods, the farmland integrity index of Huayuan village in 2010 was lower than that in 2000.