基于GWR模型的渭北黄土旱塬粮食单产空间分异 及其影响因子分析——以陕西彬县为例

doi:10.3864/j.issn.0578-1752.2019.02.007

摘要/Abstract

摘要：

【目的】通过探究渭北黄土旱塬区粮食单产在县域尺度上的空间分异特征及其影响因子,为小尺度粮食单产及其影响因子的空间分异研究、区域粮食单产提高提供科学依据。【方法】应用空间自相关、最小二乘法和地理加权回归模型（GWR）,研究渭北黄土旱塬区典型粮食主产县陕西彬县粮食单产的空间分布特征及其影响因子的空间分异。【结果】彬县粮食单产的Moran’s I指数为0.328,显著性检验的Z值为5.51,呈北高南低的局部空间集聚特征。坡度、耕层厚度、土壤有机质、道路密度和施肥成本对彬县粮食单产具有正向影响,土壤类型、侵蚀程度和地下水埋深对彬县粮食单产具有负向影响,各解释变量回归系数的相对极差范围为0.55—14.11。空间上,耕层厚度、土壤类型、侵蚀程度、土壤有机质和道路密度对彬县南部、东南部梁峁丘陵沟壑区粮食单产的影响强于北部黄土旱塬区,而坡度、地下水埋深和施肥成本则表现出相反的空间非平稳性特征。OLS模型回归系数的显著性与GWR模型回归系数的相对极差呈负相关关系。GWR模型的R ²比OLS模型提高了0.04,AIC值减少了11.04。【结论】彬县粮食单产之间存在显著的空间正相关关系;土壤有机质、施肥成本和地下水埋深是渭北黄土旱塬区县域粮食单产的最主要影响因子;同一影响因子在县域内的不同空间位置对粮食单产的影响程度存在较大差异,且各影响因子对粮食单产影响程度的空间非平稳性是导致OLS模型回归系数显著性水平较低的主要原因。GWR模型在空间非平稳性数据建模方面的解释能力与估计精度都优于OLS模型,且能够实现模型估计参数的空间可视化。

关键词: 粮食单产, 空间分异, 地理加权回归模型（GWR）, 影响因子, 县域尺度

Abstract:

【Objective】 This research was conducted to reveal the spatial differentiation characteristics and influencing factors of grain yield per hectare on the county scale in the Loess Plateau of Weibei, and to provide scientific references for similar researches on small scale and improvement of regional grain output. 【Method】 The spatial distribution characteristics of grain yield per hectare and spatial heterogeneity of its influencing factors were analyzed by using spatial autocorrelation, least square method and geographically weighted regression model in Binxian county of Shannxi province -a main grain producing county in Weibei Plateau. 【Result】 The Moran's I index of grain yield per hectare in Binxian County was 0.328, and the Z value of significance test was 5.51, and the characteristics of local spatial agglomeration were north high and south low. Slope, plough layer thickness, soil organic matter, road density and cost of fertilization had a positive effect on the grain yield in Binxian County. Soil type, erosion degree and groundwater depth had a negative influence on the grain yield in Binxian County. The relative range of regression coefficients for explanatory variables was between 0.55-14.11. In space, plough layer thickness, soil type, erosion degree, soil organic matter and road density had a stronger influence on the grain yield of the hilly and gully areas in the South and southeast in Binxian County than that in the northern Loess Plateau; while slope, groundwater depth and cost of fertilization showed opposite spatial non-stationary characteristics. The significance of regression coefficient of OLS model was negatively correlated with the relative range of regression coefficient of GWR model. The R ² of the GWR model was 0.04 higher than that of the OLS model, and the AIC value was reduced by 11.04. 【Conclusion】 There was a significant positive spatial correlation in grain yields per hectare of Binxian County. Soil organic matter, cost of fertilization and groundwater depth were the most important factors influencing grain yield per hectare in the county of Weibei Plateau. The influence degree of influencing factor on grain yield per hectare was of great difference in different spatial location, and the spatial non-stationarity of the influencing factors was the main reason for the lower significance level of regression coefficient of OLS model. The GWR model had better explanatory power and accuracy in modeling spatial non-stationary data than OLS model. And the spatial visualization of model estimation parameters could be realized by GWR model.

Key words: grain yield per hectare, spatial heterogeneity, GWR model, impact factors, county scale

邱孟龙,曹小曙,周建,冯小龙,高兴川. 基于GWR模型的渭北黄土旱塬粮食单产空间分异及其影响因子分析——以陕西彬县为例[J]. 中国农业科学, 2019, 52(2): 273-284.

QIU MengLong,CAO XiaoShu,ZHOU Jian,FENG XiaoLong,GAO XingChuan. Spatial Differentiation and Impact Factors of Grain Yield Per Hectare in Weibei Plateau Based on GWR Model: A Case Study of Binxian County, Shannxi[J]. Scientia Agricultura Sinica, 2019, 52(2): 273-284.

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变量 Variable	非标准化系数 Unstandardized coefficients	标准误差 Standard error	标准化系数 Standardization coefficient	t值 t value	P值 P value
常数项 Intercept	288.55	31.11	---	9.28	0.00
坡度 Slope	16.81	26.87	0.04	0.63	0.53
耕层厚度 Plough layer thickness	45.95	32.57	0.10	1.41	0.16
土壤类型 Soil type	-37.13	23.88	-0.08	-1.95	0.09
侵蚀程度 Erosion degree	-26.84	22.74	-0.07	-1.18	0.24
土壤有机质 Soil organic matter	218.80	32.83	0.45	6.66	0.00
地下水埋深 Groundwater depth	-87.97	17.81	-0.28	-4.94	0.00
道路密度 Road density	35.05	22.57	0.09	1.95	0.09
施肥成本 Cost of fertilization	178.33	22.61	0.42	7.89	0.00

参数 Parameters	平均值 Mean	最小值 Minimum	最大值 Maximum	上四分位值 Upper quartile	下四分位值 Lower quartile	中位数 Median	相对极差 Relative ranges
常数项 Intercept	297.57	246.90	329.88	286.52	314.55	299.85	0.28
坡度 Slope	5.18	-45.30	27.81	-9.53	22.16	11.83	14.11
耕层厚度 Plough layer thickness	42.30	33.35	66.25	37.63	45.30	42.05	0.78
土壤类型 Soil type	-35.94	-100.74	6.57	-51.11	-20.31	-33.44	2.99
侵蚀程度 Erosion degree	-24.85	-46.13	7.77	-38.97	-13.68	-25.11	2.17
土壤有机质 Soil organic matter	225.50	172.00	311.23	189.92	254.17	220.21	0.62
地下水埋深 Groundwater depth	-82.94	-116.71	-60.55	-98.08	-69.51	-79.40	0.68
道路密度 Road density	28.28	-18.36	70.14	11.46	48.93	25.63	3.13
施肥成本 Cost of fertilization	168.07	93.21	185.42	162.60	178.68	175.91	0.55
粮食单产实测值 Crop yield per unit (kg·hm^-2)	3257.88	1775.00	4950.00	2653.12	3893.75	3198.75	0.97
粮食单产预测值 Estimating crop yield per unit (kg·hm^-2)	3254.35	1888.21	5139.93	2773.27	3680.76	3246.47	1.00
条件数 Cond	22.10	19.64	29.73	20.74	23.02	21.78	0.46
Local R²	0.81	0.73	0.89	0.78	0.83	0.81	0.20
残差 Residual	3.53	-769.77	576.19	-172.61	160.68	19.67	381.29

模型 Model	信息准则 AIC	R²	调整后的R² Adjust R²	残差平方和 RRS	残差估计标准差 Sigma
OLS模型 OLS model	1080.07	0.80	0.78	198694.52	46.22
GWR模型 GWR model	1069.03	0.86	0.82	140028.34	41.53
GWR模型对模拟精度指标的提高 Improvement of simulation accuracy by GWR model	11.04	0.06	0.04	58666.18	4.69