基于组合模型的城镇化演进对耕地影响极限测算

以安徽省为例，选取城镇常住人口占总人口比例等18项指标，从人口、空间、经济、社会生活四维度构建了城镇化综合水平评价体系，采用熵值赋权法对其综合指数进行了测算；运用对数平均迪氏分解模型（Logarithmic Mean Divisia Index，LMDI），对城镇化进程引致的耕地减少份额进行了计算；基于经济学边际理论，采用最小二乘回归分析方法，构建了城镇化边际耕地变化率测度模型；借助EXCEL软件，通过作散点图并添加趋势线，采用最佳拟合优度获取曲线及高数极值求导判别方法，测算了城镇化演进对耕地影响最小的极限时刻，结果表明：安徽省城镇化综合指数由1996年的0.0319上升至2012年的0.9945；城镇化进程引致耕地面积减少量2002年后呈降幅态势，契合经济学边际效应递减规律；城镇化边际耕地变化率指数由2002－2003年的1292517.63下降至2011－2012年的7430.35，整体呈下降态势；边际耕地变化率拟合曲线为开口向上U形抛物线，当城镇化综合指数为7.325时，即2022－2023年间，城镇化对耕地影响处极小状态，2023年前，安徽省推进城镇化与耕地保护矛盾较突出。基于研究结果，从依靠产业结构优化升级促进城镇土地集约利用等方面提出了政策建议。该研究成果可为安徽省科学编制土地利用规划及制定协调城镇化演进与耕地保护政策提供参考，也可为同类研究提供借鉴。

Calculating effect extreme of urbanization evolution on cropland based on combination-model

Abstract: The process of urbanization is closely related to land use. When the level of urbanization evolves from primary level to senior level, land-intensive use of small towns will be continuously upgraded along with the increase of adjustment and optimization of industrial structure, urban high-rise buildings, and strengthening of national protection policy cultivated land, which is when the demand of cultivated land exhibits a decreasing trend in the process of transition of urbanization from the primary stage to the advanced stage, similar to the law of diminishing marginal returns of economics. Therefore, there is the effect of minimum ultimate moment of urbanization on cultivated land in theory. Exploring the ultimate moment has an important guiding significance for the policies of cultivated land under the evolutionary background of compilation of land-use planning and formulation of urbanization development. Taking Anhui Province as an example, a total of 18 indices, such as the proportion of urban permanent population in total population, are selected to establish the evaluation system of urbanization comprehensive level from four dimensions of population, space, economy, and social life, of which the composite index is calculated by the entropy weighting method. The Logarithmic Mean Divisia Index (LMDI) decomposition model is used to calculate the reduced cropland share due to urbanization. Based on economic marginal theory, the least-squares regression analysis method is adopted to construct the measurement model of marginal cropland change rate due to urbanization. With the aid of EXCEL software through scatter diagrams with trend lines, the optimal goodness of fit is applied to obtain the curves and the derivative method of advanced mathematic extremum, so as to estimate the extreme moment of urbanization evolution with the least impact on cropland. The results show that: the urbanization composite index of Anhui Province rose from 0.0319 in 1996 to 0.9945 in 2012, of which the increase range is faster than that of population urbanization level. Urbanization leads to cropland reduction declining after 2002, in line with the diminishing law of marginal effect in economics. The marginal cropland change rate due to urbanization in Anhui Province was reduced from 1 292 517.63 in 2002- 2003 to 7 430.35 in 2011-2012, presenting an overall downward trend; the fitting curve of marginal cropland change rate is a U-shaped parabola with an upward opening. When the urbanization comprehensive index is 7.325, i.e. in 2022-2023, the urbanization will have the least effect on cropland, while before 2023, the contradiction between urbanization and cropland protection will be more prominent in Anhui Province. Based on the results of the study, it is reasonable to arrange scale, structure, layout, and timing from the scientific establishment of the urbanization development of land use planning of urban construction land. Optimization and upgrading of industrial structure are used to promote intensive use of urban land. Various policies, laws, and regulations are strictly implemented in the state protection of cultivated land. Policy suggestions are put forward in strictly maintaining land gate, strengthening land inspection, and other aspects. The research results not only provide references for Anhui Province to scientifically formulate land use planning and coordinate the urbanization evolution and cropland protection policy, but also for other similar research.