不同样本尺度和分区方案的粮食产量空间化及误差修正

粮食产量数据空间化有助于粮食产量数据与其他自然、人文数据进行综合分析,但空间化过程中必然会产生误差。该文按照3种分区方案(全国不分区、全国分为7个区以及按省分区),选择3种尺度上(县级、地市级和公里网格)的总产及平均产量数据(即4种样本:县级粮食总产、县级平均粮食产量、地市级粮食总产、地市级平均粮食产量)分别为因变量,以对应的3种农田类型(水田、水浇地、旱地)面积数据为自变量,利用多元线性回归分析方法,得到15种空间化模型。采用两阶段误差分析方法,选取2个模型误差评价因子和5个空间化结果误差评价因子,对模型和空间化结果进行误差分析。结果表明:1)空间化过程中,模型精度与空间化结果的精度存在不一致性;2)对于采用同一样本的模型(常数项为0)而言,空间化结果精度随着分区方案的细化先提高再降低,而对于采用同一样本的模型(常数项非0)而言,空间化结果精度随着分区方案的细化而降低;3)在全国不分区和分为7个区2种情况下,空间化结果精度随着分析样本尺度的细化(从地市级到县级再到公里网格)先提高后降低。根据上述分析结果,最终以县级粮食总产为样本、常数项为0、全国分7个区建模的方案实现全国粮食产量数据空间化,并通过修正,得到2005年中国粮食产量公里网格分布图。该研究弥补了粮食产量空间化误差分析的不足,探寻了不同样本尺度和分区方案与空间化误差的关系,提高了空间化精度,同时对其他类型的社会经济统计数据空间化研究具有一定的参考价值。

Spatial distribution of grain yield based on different sample scales and partitioning schemes and its error correction

Abstract: Spatialization of grain yield can contribute to comprehensive analysis of grain yield with other natural and cultural data. Grain production has a close relationship with the distribution of farmland. Therefore, information on spatial distribution of farmland is an important parameter for spatialization of grain yield, and the statistical analysis and modeling are the basic means to realize spatialization of grain yield. Spatialization of nationwide grain yield relates to sample scales and partitioning schemes. Different sample scales and partitioning schemes will inevitably lead to different errors of spatialization. In this paper, models considering farmland distribution and sample scales and partition schemes were proposed to estimate grain yield and its spatial distribution. The grain yield data were collected from 2005 Yellow Book of China. Data of paddy field, irrigated land, and dry land areas in each county or district were calculated. Four datasets of 3 scales were selected including total grain yields of counties, total grain yields of prefectures and their average grain yields. A total of 2321 county data and 349 prefecture-level data were obtained. 3 partitioning schemes (no partition of China, 7 regions of China, partitions of China by province) were considered. A total of 15 kinds of multiple variable linear models were constructed with area of different types of farmland as independent variables, grain yields as dependent variables. The results showed that: 1) Based on model fitness of grain yield and its spatialization results, optimal models could be selected since the model fitness suggested that the model without constant term based on prefecture-level data and 7 regions was best but the spatialization results indicated that the model without constant term based on county-level data and 7 regions was best; 2) For models without constant term, precision of spatialization results increased first and then decreased with scaling down of partitioning scheme; For models with constant term, precision of spatialization results decreased with scaling down of partitioning scheme; 3) In the 2 partitioning schemes (no partition of China and 7 regions of China), the precision of spatialization results increased first and then decreased with scaling down of samples from prefecture level to county level and 1 km by 1 km level; and 4) Compared with other models, in the case of county grain yields as samples, the model without constant term and 7 regions of China had the highest precison with coefficient of determination of 0.655. The spatialization results were modified with error by a proportional coefficient method, and the precision was improved to coefficient of determination of 0.968. This research made up for the deficiency of spatial error analysis of grain yield, explored the relationship between different sample scales and partitioning schemes and spatial error. Meanwhile, it also provided valuable information for other types of social and economic statistical data.