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摘要: 土壤环境变量具有较强空间异质性, 为空间插值精度的提升带来了困难, 仅基于空间相关性和空间异质性的空间插值方法难以获得较高的插值精度。机器学习方法能够融合多维辅助变量的信息, 提高土壤属性的插值精度, 但是不能有效融合空间位置关系信息进一步改善插值精度。本文基于随机森林空间预测框架, 将空间半变异函数与随机森林算法融合, 提出了融合半变异函数的空间随机森林插值方法。应用所提出的方法对湖南省湘潭县土壤重金属数据进行空间插值, 并与随机森林方法、基于距离的随机森林空间预测方法、普通克里金方法和回归克里金方法进行对比, 检验了所提出方法的插值精度。结果表明, 融合半变异函数的空间随机森林插值方法相较于传统克里金方法精度提升10%以上, 相较于新型机器学习空间插值方法精度提升5%以上, 同时基于半变异函数的空间随机森林插值方法的插值制图结果具有更加合理的空间分布和丰富的细节信息。因此, 融合半变异函数的空间随机森林插值方法能够有效结合辅助变量信息与空间位置关系信息, 有效提高土壤环境变量插值精度。Abstract: The strong spatial heterogeneity of soil environmental variables causes difficulties in improving spatial interpolation accuracy. It is difficult to obtain a high interpolation accuracy by leveraging spatial correlation and spatial heterogeneity. Machine learning methods can fuse the information of multi-dimensional auxiliary variables to improve the interpolation accuracy of soil attributes, but they cannot effectively utilize the spatial position relationship information to further improve the interpolation accuracy. Based on the random forest spatial prediction framework, this study combined the spatial semi-variogram with the random forest algorithm and proposed a spatial random forest interpolation method with a semi-variogram. Taking soil heavy metal data from the Xiangtan County of Hunan Province as an example, the proposed method was used to implement spatial interpolation of soil Cr. The interpolation accuracy was compared with the random forest method, distance-based random forest spatial prediction method, ordinary Kriging method, and regression Kriging method. The results showed that the accuracy was improved by more than 10% compared with the traditional Kriging method. Compared with the new machine learning spatial interpolation method, the accuracy was improved by more than 5%. Furthermore, the mapping of the proposed results had a more reasonable spatial distribution and detailed information. Thus, we concluded that the proposed method could effectively combine auxiliary variable information and spatial location information and improve the interpolation accuracy of soil environmental variables.
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Key words:
- Spatial interpolation /
- Random Forest /
- Semi-variogram /
- Machine Learning /
- Regression Kriging
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图 2 研究区辅助变量土壤类型(a)、土地利用类型(b)、海拔(c)和坡度(d)的映射
Figure 2. Mapping of auxiliary variables in the study area. a: soil type; b: land use type; c: altitude; d: slope.
图 4 不同插值方法交叉验证结果的平均绝对误差(MAE)和均方根误差(RMSE)
RF: 随机森林法; RFsp: 随机森林空间预测框架; SRFsei: 融合半变异函数的空间随机森林插值法; UK: 泛克里金; OK: 普通克里金。
Figure 4. Mean absolute error (MAE) and root mean square error (RMSE) of cross-validation results of different interpolation methods
RF: random forest; RFsp: random forest for spatial predictions framework; SRFsei: spatial random forest with semi-variogram interpolation; UK: universal Kriging; OK: ordinary Kriging.
图 5 融合半变异函数的空间随机森林插值法的插值结果图(a)与误差标准差图(b)
Figure 5. Interpolation results (a) and standard deviation variance of error (b) of spatial random forest with semi-variogram interpolation
图 6 不同插值方法的插值结果图(a)及误差标准差图(b)
RF: 随机森林法; RFsp: 随机森林空间预测框架; OK: 普通克里金; UK: 泛克里金。
Figure 6. Interpolation results (a) and standard deviation variance of error (b) of different interpolation methods
RF: random forest; RFsp: random forest for spatial predictions framework; OK: ordinary Kriging; UK: universal Kriging.
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