基于不同插值方法的三江平原白浆土磷素空间分布预测及其适用性分析

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张迪^1,,,
姜柏志¹,
刘国辉²,
张慧³,
聂凡¹,
孙琦¹,
纪明元¹
1.东北农业大学资源与环境学院哈尔滨 150030
2.黑龙江省农业环境与耕地保护站哈尔滨 150000
3.东北农业大学公共管理与法学院哈尔滨 150030
基金项目: 国家重点研发计划项目2017YFD0300500

详细信息

通讯作者:张迪, 主要从事土壤地球化学调查与评价研究。E-mail: zhangdi6283@neau.edu.cn

中图分类号:S159.2

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出版历程

收稿日期:2020-12-02
录用日期:2021-03-05
刊出日期:2021-08-01

Applicability of spatial interpolation methods to predict total phosphorus in the typical irrigated areas of the Sanjiang Plain

ZHANG Di^1,,,
JIANG Baizhi¹,
LIU Guohui²,
ZHANG Hui³,
NIE Fan¹,
SUN Qi¹,
JI Mingyuan¹
1. College of Resources and Environment, Northeast Agricultural University, Harbin 150030, China
2. Heilongjiang Agricultural Environment and Cultivated Land Protection Station, Harbin 150000, China
3. College of Public Administration and Law, Northeast Agricultural University, Harbin 150030, China
Funds: the National Key Research and Development Project of China2017YFD0300500

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Corresponding author:ZHANG Di, E-mail: zhangdi6283@neau.edu.cn

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摘要
摘要:土壤磷素含量是反映农业生态系统土壤肥力的重要指标。准确预测磷素空间异质性是评价土壤生产力和质量的关键。本研究采用反距离加权法（IDW）、径向基函数法（RBF）、普通克里金法（OK）、全局多项式法（GPI）、局部多项式法（LPI）、地理加权回归（GWR）和地理加权回归克里金法（GWRK）等插值方法，分别预测了三江平原白浆土典型灌区八五三、七里沁以及大兴灌区土壤磷素分布，并运用交叉验证法，通过平均误差（ME）、均方根误差（RMSE）和改进效果（RI）对各种方法精度进行比较，以期确定同一土壤类型不同采样密度土壤中磷素空间异质性最佳插值方法。对比7种插值方法，在空间插值平滑性方面，LPI、GPI、GWR、GWRK表现较好，在插值速度方面，IDW、RBF、LPI、GPI、OK较快，GWR和GWRK方法运算复杂、速度较慢。IDW、RBF等6种方法与OK相比，根据RI判定，GWRK方法提高了磷素空间分布模拟精度，IDW、GPI和LPI方法降低了磷素空间分布模拟精度，RBF方法在提高磷素空间分布模拟精度上表现不一致。采样密度会影响预测结果，对于本文而言，不论采样密度如何，GWRK方法均方根误差（RMSE）均最低，为最佳插值方法，而RBF方法是在采样密度较低时一种可选方法。GWRK法在本文是最佳的插值方法，但其结果会受到辅助变量多少和各变量之间是否存在共线性的影响。
关键词:白浆土/
磷素/
插值方法/
交叉验证/
空间自相关性/
适用性
Abstract:In the late 1990s, the "Dryland to Paddy" project was implemented in the Sanjiang Plain. After planting rice in the Albic soil, the barrier soil layer turns into a favorable soil layer, the low-yield soil becomes high-yield soil, and the Albic soil phosphorus pool increases. After flooding, the availability of phosphorus (closed storage phosphorus[O-P] and iron-bound phosphorus[Fe-P]) increases with the decrease in soil redox potential (Eh) and the increase in pH, which substantially affects soil phosphorus heterogeneity. Therefore, we urgently need an optimal interpolation method to improve the prediction accuracy of total phosphorus in the Albic soil of typical irrigation areas of the Sanjiang Plain. This will help evaluate the impact of climate change and land use on the soil phosphorus pools and provide a reference for estimating future soil phosphorus pools. This study used the inverse distance weighting (IDW) method, radial basis function (RBF), ordinary Kriging (OK), global polynomial method (GPI), local polynomial method (LPI), geographic weighted regression (GWR), and geographic weighting regression to Kriging (GWRK) to predict the distribution of soil phosphorus in the Bawusan, Qiliqin, and Daxing irrigation areas of the Sanjiang Plain. The cross-validation method was used to obtain the mean error (ME), root mean square error (RMSE), and relative improvement (RI) to compare the accuracies of the various methods to determine the best interpolation method for assessing the spatial heterogeneity of phosphorus in the same soil type with different sampling densities. Based on the assumptions of regression analysis, this study incorporated 24 environmental variables for exploratory regression analysis, including elevation, pH, organic matter, exchangeable sodium, total nitrogen, available phosphorus, available copper, cultivated layer bulk density, and rice yield. According to the regression results, the auxiliary variables that were significantly correlated with phosphorus were selected for least square analysis. Finally, exchangeable sodium, cation exchange capacity, and available phosphorus were selected as auxiliary variables for the Bawusan irrigation area; organic matter, available zinc, and available boron were selected as auxiliary variables for the Qiliqin irrigation area; and cation exchange capacity, available zinc and copper were selected as auxiliary variables for the Daxing irrigation area. Compared to OK, RI indicated that the GWRK method with environmental auxiliary variables significantly improved the simulation accuracy of the spatial distribution of phosphorus. The IDW, GPI, and LPI methods reduced the accuracy of phosphorus spatial distribution simulation, whereas the RBF method was inconsistent. When comparing the mapping effect and interpolation speed of the seven interpolation methods, LPI, GPI, GWR, and GWRK had better mapping effects, whereas IDW, RBF, LPI, GPI, and OK were faster. The GWRK method had a better mapping effect, but it should be combined with environmental auxiliary variables, and the operation was complicated and slow. Sampling evenness also affected the prediction results. Nonetheless, GWRK had the lowest ME and RMSE, indicating that it is the best interpolation method. RBF is an optional method when the sampling evenness is lower. GWRK is the best interpolation method, but the results are affected by the number of auxiliary variables and collinearity between the variables.
Key words:Albic soil/
Phosphorus/
Interpolation method/
Cross validation/
Spatial autocorrelation/
Applicability

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图1三江平原典型灌区的白浆土样点分布
Figure1.General situation and distribution of sample points in Albic soil area in the typical irrigation area of the Sanjiang Plain

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图2三江平原典型灌区白浆土磷素正态性分布检验
Figure2.Inspection of normal distribution of phosphorus in Albic soil in the typical irrigation areas of the Sanjiang Plain

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图3八五三灌区不同插值方法磷素(TP)空间分布预测
IDW: 反距离加权; RBF: 径向基函数; OK: 普通克里金; GPI: 全局多项式法; LPI: 局部多项式法; GWR: 地理加权回归; GWRK: 地理加权回归克里金法。
Figure3.Prediction of spatial distribution of phosphorus (TP) by different interpolation methods in Bawusan Irrigation Area
IDW: inverse distance weighting method; RBF: radial basis function; OK: ordinary Kriging; GPI: global polynomial method; LPI: local polynomial method; GWR: geographic weighted regression; GWRK: geographic weighting regression to Kriging.

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图4大兴灌区不同插值方法磷素(TP)空间分布预测
IDW: 反距离加权; RBF: 径向基函数; OK: 普通克里金; GPI: 全局多项式法; LPI: 局部多项式法; GWR: 地理加权回归; GWRK: 地理加权回归克里金法。
Figure4.Prediction of spatial distribution of phosphorus (TP) by different interpolation methods in Daxing Irrigation Area
IDW: inverse distance weighting method; RBF: radial basis function; OK: ordinary Kriging; GPI: global polynomial method; LPI: local polynomial method; GWR: geographic weighted regression; GWRK: geographic weighting regression to Kriging.

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图5七里沁灌区不同插值方法磷素空间分布预测
IDW: 反距离加权; RBF: 径向基函数; OK: 普通克里金; GPI: 全局多项式法; LPI: 局部多项式法; GWR: 地理加权回归; GWRK: 地理加权回归克里金法。
Figure5.Prediction of spatial distribution of phosphorus by different interpolation methods in Qiliqin Irrigation Area
IDW: inverse distance weighting method; RBF: radial basis function; OK: ordinary Kriging; GPI: global polynomial method; LPI: local polynomial method; GWR: geographic weighted regression; GWRK: geographic weighting regression to Kriging.

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表1研究区土壤概况
Table1.Soil profile in the typical irrigation area of the Sanjiang Plain

研究区 Research area	面积 Area (km²)	土类 Soil	亚类 Subcategory	成土母质 Parent material	≥10 ℃积温 ≥10 ℃ accumulated temperature (℃)	年降水量 Annual precipitation (mm)	土壤侵蚀类 Soil erosion	障碍层类型 Type of barrier
八五三灌区 Bawusan Irrigation Area	829.0639	白浆土 Albic soil	典型白浆土 Typical Albic soil	黄土状黏质土 Loess-like clay soil	2487	565.0	混合侵蚀 Mixed erosion	白浆层 Albic layer
大兴灌区 Daxing Irrigation Area	387.9494	白浆土 Albic soil	潜育白浆土、草甸白浆土 Gleed Albic soil, meadow Albic soil	残积物 Residue	2761	561.0	无侵蚀 No erosion	无 Null
七里沁灌区 Qiliqin Irrigation Area	121.4848	白浆土 Albic soil	潜育白浆土 Gleed Albic soil	冲积物 Alluvial deposit	2330	586.3	混合侵蚀 Mixed erosion	无 Null

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表2典型灌区白浆土采样点磷素含量分析
Table2.Phosphorus contents in sampling points of Albic soil in the typical irrigation areas

灌区 Irrigation area	采样点数 Sampling points	最小值 Min (g?kg^–1)	最大值 Max (g?kg^–1)	平均值 Average (g?kg^–1)	方差 Variance	标准偏差 Standard deviation (g?kg^–1)	变异系数 Coefficient of variation	峰度 Kurtosis	偏度 Skewness	采样密度 Sampling density (points?km^–2)
七里沁 Qiliqin	7	0.83	1.21	1.00	0.0219	0.1480	0.1482	–1.8930	0.4090	0.06
八五三 Bawusan	27	0.97	1.58	1.19	0.0194	0.1392	0.1169	0.8357	0.6007	0.03
大兴 Daxing	39	0.65	1.22	0.92	0.0194	0.1394	0.1514	–0.8081	–0.0064	0.10

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表3典型灌区白浆土辅助变量与磷素相关显著性分析
Table3.Significance analysis of the correlation between auxiliary variables and phosphorus of Albic soil in the typicalirrigation areas %

辅助变量 Auxiliary variable	八五三灌区 Bawusan Irrigation Area	七里沁灌区 Qiliqin Irrigation Area	大兴灌区 Daxing Irrigation Area	辅助变量 Auxiliary variable	八五三灌区 Bawusan Irrigation Area	七里沁灌区 Qiliqin Irrigation Area	大兴灌区 Daxing Irrigation Area
土壤pH Soil pH	50.67^*	—	—	土壤有效铜 Soil available cuprum	2.26	3.15	82.61^*
土壤交换性钠 Soil exchangeable sodium	44.95^*	1.18	13.58^*	土壤速效钾 Soil available potassium	1.88	0.79	0.14
土壤全氮 Soil total nitrogen	41.15^*	3.15	1.08	土壤锌 Soil zinc	0.31	0.39	0.48
土壤有效磷 Soil available phosphorus	31.66^*	0.39	0.18	水稻产量 Rice yield	0.25	—	—
海拔 Altitude	29.63^*	—	—	耕层容重 Cultivated layer bulk density	0.14	—	2.04
土壤有效硅 Soil available silicon	24.23	0.39	72.41^*	土壤有效硼 Soil available boron	0.14	1.18	0.05
土壤镉 Soil cadmium	22.51	—	—	土壤铜 Soil cuprum	0.14	2.76	—
土壤CEC Soil CEC	20.20	2.36	—	土壤有效锌 Soil available zinc	0.07	10.24^*	100.00^*
土壤铬 Soil chromium	7.96	26.38^*	0.07	土壤缓效钾 Soil slow potassium	0.02	—	4.37
土壤有效锰 Soil available manganese	3.44	12.20^*	—	土壤全钾 Soil total potassium	0.01	1.57	55.24
土壤镍 Soil nickel	2.75	1.18	2.45	土壤有效铁 Soil available iron	0.01	—	1.07
土壤铅 Soil plumbum	2.30	7.87	28.74	土壤有机质 Soil organic matter	—	3.15	—
表中数据大小表示该变量作为预测因子的强度, 数值越大表明其作为预测因子趋势越大, 代表该辅助变量与磷元素具有显著相关性。Data in the table indicates the strength of the variable used as a predictor parameter, and the larger the data, the greater the trend as a predictor. “” means that the auxiliary variable is significantly correlated with soil phosphorus content.

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表4典型灌区白浆土辅助变量与磷素多元线性逐步回归分析
Table4.Multiple linear stepwise regression analysis between auxiliary variables and phosphorus of Albic soil in the typical irrigation areas

灌区 Irrigation area	变量 Variable	系数 Coefficient	标准差 Standard deviation	T统计量 T statistics	概率 Probability	VIF值 VIF value
八五三 Bawusan	土壤交换性钠Soil exchangeable sodium	–1.8121	0.3927	–4.6149	0.0001	1.4022
	耕层容重Cultivated layer bulk density	–0.6753	0.2895	–2.3329	0.0297	2.0655
	土壤CEC Soil CEC	0.0141	0.0050	2.8038	0.0106	2.1943
	土壤有效磷Soil available phosphorus	0.0033	0.0016	2.0901	0.0490	1.4460
	土壤有效锰Soil available manganese	0.0054	0.0015	3.5205	0.0020	2.3576
大兴 Daxing	土壤交换性钠Soil exchangeable sodium	–0.3065	0.1185	–2.5870	0.0141	1.1004
	土壤有效锌Soil available zinc	–0.0961	0.0346	–2.7776	0.0089	1.1790
	土壤有效铜Soil available cuprum	0.1311	0.0476	2.7533	0.0094	1.300
	土壤镉Soil cadmium	0.9035	0.8165	1.1065	0.2763	1.0242
七里沁 Qiliqin	土壤有机质Soil organic matter	0.0141	0.0038	3.7262	0.0223	1.7061
	土壤有效锌Soil available zinc	–0.6213	0.1789	–3.4733	0.0331	1.6344
	土壤有效硼Soil available boron	1.7556	0.5317	3.3019	0.0411	2.3092

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表5三江平原白浆土磷素空间分布的7种插值方法评价
Table5.Evaluation of seven interpolation methods for spatial distribution of phosphorus of Albic soil in the typical irrigation areas of the Sanjiang Plain

灌区 Irrigation area	指标 Index	OK	RBF	IDW	LPI	GPI	GWR	GWRK
七里沁 Qiliqin	ME	0.0008	0.0017	0.0049	0.0215	0.0105	—	0.0004
	RMSE	0.1494	0.1530	0.1579	0.2201	0.1733	—	0.0084
	RI (%)	—	–2.41	–5.79	–47.32	–16.00	—	94.38
八五三 Bawusan	ME	0.0088	0.0024	0.0073	0.0075	0.0048	—	0.0003
	RMSE	0.1366	0.1130	0.1374	0.1348	0.1393	—	0.1426
	RI (%)	—	17.28	–0.59	1.32	–1.98	—	–4.39
大兴 Daxing	ME	0.0088	0.0014	0.0053	0.0137	0.0004	—	0.0022
	RMSE	0.1198	0.1231	0.1235	0.1292	0.1335	—	0.0511
	RI (%)	—	–2.75	–3.09	–7.85	–11.44	—	57.35
ME: 平均误差; RMSE: 均方根误差; RI: 相对改进程度。IDW: 用反距离加权; RBF: 径向基函数; OK: 普通克里金; GPI: 全局多项式法; LPI: 局部多项式法; GWR: 地理加权回归; GWRK: 地理加权回归克里金法。ME: mean error; RMSE: root-mean-square error; RI: relative improvement. IDW: inverse distance weighting method; RBF: radial basis function; OK: ordinary Kriging; GPI: global polynomial method; LPI: local polynomial method; GWR: geographic weighted regression; GWRK: geographic weighting regression to Kriging.

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