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.