局部加权线性回归模型的PM2.5空间插值方法

PM2.5 spatial interpolation method based on local weighted linear regression model

针对传统空间插值方法对影响PM2.5的插值因素考虑不全面和局部加权线性回归模型中近邻个数选择困难等问题,该文基于局部加权线性回归模型提出了一种引入正则化项的空间插值方法。以北京市3个月的PM2.5数据为例,选取SO_2、NO_2、O_3、CO作为观测指标,通过正则化进行权重系数修正、L曲线法确定正则化系数,提高了该插值模型的稳定性与自适应性。交叉验证结果显示,本方法相对于普通克里金法,3个月的平均绝对误差(MAE)与均方根误差(RMSE)分别降低28.44%、26.25%;相对于反距离加权插值法的MAE、RMSE分别降低18.07%、17.02%。研究结果表明,基于局部加权线性回归模型的PM2.5空间插值相对于传统方法有一定提升。

In this paper,a spatial interpolation method for regularization based on locally weighted linear regression model is proposed in order to solve the problem that the traditional interpolation method for influencing PM2.5 interpolation factor was considered incompletely and it was difficult to select the number of neighbors in local weighted linear regression model.Taking the PM2.5 data of Beijing for 3 months as an example,the SO2,NO2,O3 and CO were selected as observation indexes,the regularization coefficient was corrected by regularization,and was determined by L curve method,and the stability and self-adaptability of the interpolation model was improved.The results of cross validation showed that the average mean absolute error（MAE）and root mean square error（RMSE）of the three-month had been reducedby 28.44%,26.25% respectively compared with the ordinary Kriging method,and 18.07%,17.02%,respectively,compared with MAE and RMSE of inverse distance-weighted interpolation method.The results indicate that there was a certain improvement of the PM2.5 spatial interpolation based on local weighted linear regression model compared with the traditional method.