基于线性混合效应模型的河北省PM2.5浓度时空变化模型研究

京津冀地区大气PM_2.5污染严重.为揭示区域PM_2.5时空分布规律，使用2013-2014年河北省地面站点PM_2.5监测数据、MODIS AOD（气溶胶光学厚度）遥感数据、地面气象站点数据和土地利用调查数据，基于线性混合效应模型（LME），建立了ρ（PM_2.5）时空变化与AOD因子、气象因子、土地利用因子之间的关系模型.采用十折交叉验证法对模型精度进行检验，并利用计算得到的校正因子全部实测的ρ（PM_2.5）年均值除以参与建模的所有实测ρ（PM_2.5）年均值]纠正因AOD非随机性缺值导致的抽样偏差.结果表明:①河北省区域模拟精度R2（决定系数）为0.85，经交叉验证后R2为0.77，RMSE（均方根误差）和RPE（相对预测误差）分别为18.28 μg/m3和28.68%.②ρ（PM_2.5）年均值模拟结果的校正因子范围为1.24~2.05，校正后的研究区ρ（PM_2.5）年均值为89.84 μg/m3，与实际监测数据相近.③ρ（PM_2.5）空间分布呈平原高、山区低，平原地区西南高、东北低的趋势.④ρ（PM_2.5）与AOD、温度、相对湿度呈正相关，与风速、大气能见度呈负相关.研究显示，线性混合效应模型能有效对ρ（PM_2.5）进行时空变化模拟，并实现对非地面监测地区ρ（PM_2.5）时空变化的预测，恰当的预测因子组合和模型校正有助于模型预测精度的提升. 

Spatial-Temporal Simulation of PM2.5 Concentration in Hebei Province based on Linear Mixed Effects Model

The atmospheric particulate pollution is serious in the Beijing-Tianjin-Hebei Region. To explore the spatial-temporal distribution of ρ(PM_2.5), based on the measured ρ(PM_2.5), MODIS aerosol optical depth (AOD), meteorological and land use data from 2013 to 2014, we developed a linear mixed effect model to make regress ρ(PM_2.5) measurements with AOD, meteorological and land use factors in Hebei Province. Then ten-fold cross validation was used to validate the accuracy of the predictions. Finally, the correction factors, which were calculated from the measured annual average ρ(PM_2.5) divided those in the models, were employed to correct biases in the predicted ρ(PM_2.5) caused by nonrandom missing of AOD. The results showed that:(1) The R2 of the mixed effects model for Hebei Province was 0.85. The cross-validation R2 was 0.77, the Root Mean Square Error (RMSE) and Relative Prediction Error (RPE) were 18.28 μg/m3 and 28.68%, respectively. (2) The correction factors of 2013-2014 ranged from 1.24 to 2.05. The corrected annual ρ(PM_2.5) of Hebei Province was 89.84 μg/m3, which was close to the monitoring data. (3) For the spatial pattern, the PM_2.5 concentrations in the plains were higher than those in the mountainous areas, the ρ(PM_2.5) in the southwestern plain were higher than those in the northeastern part. (4) The ρ(PM_2.5) had positive correlation with the AOD, temperature, relative humidity and negative correlation with the wind speed and atmospheric visibility. All these results suggested that the mixed effect model allows one to assess the spatial-temporal distribution of the ρ(PM_2.5) reliably; it can also predict the spatial-temporal pattern of the ρ(PM_2.5) in non-measured regions. Proper combination of forecasting factors and model correction factor are able to help improve the prediction accuracy of the model.