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地球信息科学学报 >

2017 , Vol. 19 >Issue 3: 382 - 389

DOI: https://doi.org/10.3724/SP.J.1047.2017.00382

遥感科学与应用技术

顾及风向和风速的空气污染物浓度插值方法

  • 李佳霖 , 1 ,
  • 樊子德 1, 2 ,
  • 邓敏 , 1, *
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  • 1. 中南大学地理信息系,长沙 410083
  • 2. 中国科学院地理科学与资源研究所 资源与环境信息系统国家重点实验室,北京 100101
*通讯作者：邓 敏（1974-）,男,江西临川人,博士,教授,主要从事时空数据挖掘分析。E-mail:

作者简介：李佳霖（1992-）,男,山东滨州人,硕士生,主要从事时空插值方法的研究工作。E-mail:

收稿日期: 2016-05-09

  要求修回日期: 2016-09-22

  网络出版日期: 2017-03-20

基金资助

国家“863”计划（2013AA122301）

高等学校博士点专项科研基金（20110162110056）

湖南省博士生优秀学位论文资助项目（CX2014B050）

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A Method of Spatial Interpolation of Air Pollution Concentration Considering WindDirection and Speed

  • LI Jialin , 1 ,
  • FAN Zide 1, 2 ,
  • DENG Min , 1, *
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  • 1. Department of Geo-informatics, Central South University, Changsha 410083, China
  • 2. State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, CAS, Beijing 100101, China
*Corresponding author: DENG Min, E-mail:

Received date: 2016-05-09

  Request revised date: 2016-09-22

  Online published: 2017-03-20

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《地球信息科学学报》编辑部 所有
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摘要

随着经济的快速发展,中国大部分地区空气污染状况日趋严重。空气污染物浓度插值对于进一步分析污染物时空分布情况,估计不同地区人群的暴露风险,制定防范措施具有重要作用。然而,现有空间插值方法由于没有充分考虑风向和风速因素对于污染物扩散的影响,故直接应用于空气污染物浓度插值,会对插值结果造成不利的影响。因此,本文提出一种顾及风向和风速的空气污染物浓度插值方法（Direction-Velocity IDW,DVIDW）。该方法首先根据离散气象站点处的风向和风速数据建立风场表面,然后利用风场数据计算空气污染物的扩散距离,根据扩散距离计算风场中待求点与采样点间的最短路径距离,最后由最短路径距离替代欧式距离进行反距离加权插值。本文分别采用2组实际空气污染物浓度数据,对DVIDW方法和其他常用的空间插值方法进行实验对比分析,验证了本文方法的可行性和优越性。

关键词： 空间插值; 风向风速; 空气污染物浓度; 风场; 最短路径距离

本文引用格式

李佳霖 , 樊子德 , 邓敏 . 顾及风向和风速的空气污染物浓度插值方法[J]. 地球信息科学学报, 2017 , 19(3) : 382 -389 . DOI: 10.3724/SP.J.1047.2017.00382

Abstract

With the rapid development of economy, air pollution becomes more and more serious in China. The quality of the interpolation results of air pollutant concentration is very significant for analyzing the spatial-temporal distribution of the air pollutant, estimating the exposure risk of people in different areas, and making precaution. However, there are some problems when applying the existing spatial interpolation methods directly to the interpolation of air pollutant concentration. One of the most important problems is that the existing spatial interpolation methods cannot fully consider the influence of wind direction and speed on the air pollutant diffusion. We proposed a method (Direction-Velocity IDW) of spatial interpolation of air pollutant concentration taking wind direction and speed into account. First, we constructed a wind-field surface based on the discrete wind direction and speed data and the diffusion distance is computed in the wind-field. Then, we used Dijkstra algorithm to obtain the shortest path in wind-field. Finally, we interpolated the attribute value using IDW by the shortest path distance instead of the Euclidean distance. In the experiment, we verified the effectiveness of the method we proposed by comparing DVIDW and the commonly used spatial interpolation methods. We concluded that the proposed method (DVIDW) can produce interpolation results with higher precision.

Key words： spatial interpolation; wind direction and speed; air pollutant concentration; wind field; shortest path distance

1 引言

近年来,由于受到PM2.5等空气污染物的影响,中国大部分地区空气污染状况日趋严重[1]。PM2.5等空气污染物的危害广泛,不仅对人体的心肺功能、呼吸系统、神经系统和免疫系统等造成损害[2],而且会对太阳辐射产生一定影响,造成局部地区天气恶劣,能见度低,引发其他危害[3]。
空间插值一方面可以利用已有观测数据修补缺失的观测数据,另一方面可以根据离散数据构建连续表面数据[4]。利用准确的空间插值可以进一步分析空气污染物浓度的空间分布情况,对于估计不同地区人群的暴露风险[5],制定防范措施具有至关重要的作用。近几年,国内外学者对空间插值方法进行大量研究,不仅从理论上对经典空间插值方法进行了一系列优化改进,还针对各种应用需求发展了一些空间插值方法[6-12],但是对空气污染物浓度的空间插值方法研究较少。Nalder等[13]考虑经纬度和高程对气象数据插值的影响,将多元线性回归方法和IDW方法结合提出一种梯度下降反比法（GIDW）,通过对月均气温和降水量的实验对比,发现GIDW方法的插值结果精度高于其他空间插值方法。Luis O等[14]通过4种插值方法对墨西哥城的多种空气污染物浓度进行空间插值,发现IDW方法和普通克里金方法的插值结果较好,精度明显高于CWA（CityWide Average）方法和NM（Nearest Monitor）方法。Reyes等[15]将LUR（Land Use Regression）模型和BME（Bayesian Maximum Entropy）结合,同时考虑多种因素和多源空气污染物浓度数据进行建模,实验结果优于普通克里金方法,但是这种框架中要用到实际难以同时获得的多种气象环境等数据和多源污染物浓度观测数据。Li等[16]通过一种风场最短路径距离替代IDW方法中的欧式距离对空气中细颗粒物浓度进行空间插值,结果优于传统的IDW方法,但是这种方法没有充分考虑风速对插值结果的影响。
通过对上述关于空间插值研究的深入分析可以发现,现有的空间插值方法应用于空气污染物浓度插值中存在一个问题：通常空气污染物的传播会显著受到风向和风速因素的影响,但是现有的空间插值方法并没有充分考虑风向和风速因素对插值结果产生的影响。风向和风速对空气污染物的扩散分别有以下影响：① 风向对于污染物的扩散有非常显著的影响[17-18],风向在很大程度上决定了空气污染物的传播方向,不同的风向导致污染物向不同方向传播。空气中的污染物随风在空气中传播,扩散到上风向的难度比扩散到下风向的难度大。例如,冬季中国北方燃煤和秸秆燃烧产生的空气污染物通常会随西北风传播到东南地区,并对当地空气状况产生不良影响,但却难以传播到处于上风向的蒙古等地区。因此,空气污染物到下风向位置的扩散距离较近,到上风向位置的扩散距离较远。② 不同风速对于污染物的扩散也有不同的影响,风速的大小决定了空气污染物的扩散距离。风场中的某一点处的风速越大,空气污染物传播的距离越远,这一点处的污染物扩散到下风向区域越容易,扩散到上风向区域越困难。例如,工厂排出的空气污染物会随风传播,如果风速较大,污染物传播的距离比较远,会影响较大范围内的空气质量;如果风速较小,由于沉降作用和地表物体的阻挡,污染物的传播距离比较近,只会对小范围内的空气质量产生影响。
由于现有空间插值方法没有充分考虑风向和风速因素对空气污染物扩散的影响,故将会把风向风速因素产生的偏差引入到空间插值结果中,从而对插值结果造成影响。因此,针对现有空间插值方法应用于空气污染物浓度插值问题所存在的局限性,本文充分顾及风向和风速因素的影响,提出一种顾及风向和风速因素的空气污染物浓度空间插值方法（DVIDW）。为了验证本文提出算法的优越性和可行性,分别以2组实际空气污染物浓度数据进行实验,并采用本文方法与其他常用方法进行插值分析和对比验证。

2 顾及风向和风速的空气污染物浓度插值方法

为了充分顾及风向和风速因素对于空间插值结果的影响,DVIDW方法首先利用已知气象监测站点处的风向和风速数据建立覆盖研究区域的风场;然后,计算风场中相邻单元的扩散距离,由此得到扩散距离表面;接着根据风场扩散距离计算加权邻接矩阵,进而计算待求点和采样点之间的最短路径距离;最后,根据待求点和邻域内采样点之间的最短路径距离,进行反距离加权插值。算法流程如图1所示。
Fig. 1 Flow chart of the DVIDW algorithm

图1 DVIDW算法流程图

2.1 矢量插值生成风场

为了顾及风向和风速因素对空间插值结果的影响,DVIDW方法利用气象观测站点处风向和风速的采样数据生成覆盖整个研究区域的风场。首先将研究区域划分成网格单元,计算每个网格单元中心点的坐标,然后根据风向风速采样点处的矢量数据采用反距离加权法进行空间插值,计算每个网格单元的风向风速属性值。
矢量数据的空间插值首先将代表风向风速的矢量分解到东西方向和南北方向（图2）,然后分别根据这2个方向上分量的模进行插值计算,最后将待求点处东西向和南北向上插值计算的分量利用三角形法则合成为该点处的风向风速矢量数据,得到风向和风速的属性值。
Fig. 2 Decomposition of vector data

图2 矢量数据的分解

2.2 计算风场中相邻网格单元间的扩散距离

由于PM2.5等空气污染物在风场中不是自由扩散,而会受到风向和风速的显著影响。扩散距离可以用来描述风场相邻网格单元间空气污染物扩散的难度。因此,DVIDW方法充分考虑风向和风速因素对空气污染物扩散的影响,计算风场中每个网格单元扩散到其相邻网格单元的扩散距离。
扩散距离根据空气污染物在风场中扩散问题中的标准模型——高斯扩散模型[19]来计算,其模型的基本公式如下：
C 0 ( x , y , z , u ) = Q πu σ y σ z exp - y 2 2 σ y 2 - z 2 2 σ z 2 （1）
式中： C 0 ( x , y , z , u ) 表示空气污染物浓度; x 和 y 分别表示下风向距离和待求点与风向中心线的水平距离; z 是空气污染物释放点的高度; u 是水平风速, σ y 和 σ z 分别代表水平方向和垂直方向的扩散标 准差。
然而,由于现阶段本文方法只考虑水平方向的空气污染物扩散,式（1）又过于复杂,难以直接应用于风场中相邻单元扩散距离的计算,因此要对其进行简化[16]。另外,简化公式没有考虑风速的影响,因此顾及风速影响的简化公式可表示为：
Cost = [ F ( D A , D M ) × W A + F ( D B , D M ) × W B ] × L AB （2）
F ( D A , D M ) = D A - D M （3）
F ( D B , D M ) = D B - D M （4）
式中： D A 和 D B 分别代表A和B网格单元处风向所表示的方位角; D M 代表AB方向的方位角。F函数考虑风向因素对于相邻网格单元间扩散的影响,下风向的扩散距离小,上风向的扩散距离大;通过 式（5）、（6）权重 W A 和 W B 充分顾及风速因素对于扩散的影响,对于下风向,风速越大扩散距离越小,对于上风向,风速越大扩散距离越大; L AB 代表AB之间的相邻关系类型,如果是边邻接,则 L AB = 1 ,如果是点邻接,则 L AB = 2 。
W A = cos ( D A - D M ) × V A - sgn [ cos ( D A - D M ) ] （5）
W B = cos ( D B - D M ) × V B - sgn cos ( D B - D M ) （6）
式中： cos ( D A - D M ) 为风速为单位大小时网格单元A处的风力矢量在AB方向上的分量,代表其对空气污染物从A到B扩散距离的影响; V A 和 V B 分别代表网格单元A处和B处的风速,风速越大,对于扩散距离的影响越大,反之亦然。式中的指数 - sgn [ cos ( D A - D M ) ] 表示,当 cos ( D A - D M ) ≥ 0 时,网格单元A处的风速在AB方向上的分量为正值,对污染物的扩散过程有正向的影响,权重 W A 的次数为-1,对其赋予较小的扩散距离;同理,当 cos ( D A - D M ) < 0 时,对其赋予较大的扩散距离。

2.3 计算风场中的最短路径距离

根据风场中相邻网格单元间的扩散距离,建立所有网格单元的有向加权邻接矩阵,用于计算风场中待求点和采样点之间的风场最短路径距离。
计算风场中的网格单元有向加权邻接矩阵时,认为每个网格单元仅与其相邻的网格单元邻接,对应的权重即为该网格单元扩散到相邻网格单元的扩散距离。
然后,根据有向加权邻接矩阵,利用Dijkstra最短路径算法[20]计算在风场中所对应网格单元不相邻的待求点和采样点之间的风场最短路径距离。如图3所示,结点表示风场中的网格单元,箭头代表扩散方向,线段上标注的数字是该方向的扩散距离,从A网格结点到B网格结点的风场最短路径即为加粗箭头线段所表示的路径。
Fig. 3 The calculation of the shortest path in the wind field

图3 风场最短路径计算

2.4 反距离加权插值

反距离加权法（IDW）[21]是以待求点与采样点之间的距离为权重的插值方法,距离待求点越近的采样点赋予的权重越大,即其权重贡献与距离成反比。
对于待求点,分别计算每个采样点与其之间的风场最短路径距离,将距该待求点风场最短路径距离最近的n个点作为该采样点的邻域。以邻域内采样点距离待求点的风场最短距离代替反距离加权法中的欧式距离,计算公式如下：
Z R = ∑ i = 1 m Z i d pat h _ i α ∑ i = 1 m 1 d pat h _ i α （7）
式中： Z R 为待求点处的属性值; Z i 为采样点的属性值; d pat h _ i 为待求点和采样点间的风场最短路径 距离。

3 实验算例及结果分析

本文实验采用目前北京市的主要空气污染物PM2.5的浓度数据进行验证,其中实验1和实验2分别采用2014年9月15日和16日北京市35个空气污染物浓度观测站的PM2.5浓度数据进行实验,实验中采用的风向和风速数据为北京市15个气象观测站点在对应时间的数据,空气污染物浓度观测站和气象观测站点的分布如图4所示。气象数据来源于中国气象数据网,数据经过质量控制,实有率和正确率均接近100%。本文中暂时只考虑水平方向的空气污染物扩散,不考虑观测站点的高程问题。
Fig. 4 The distribution map of air pollutant observation stations and meteorological observation stations

图4 空气污染物观测站点和气象观测站点分布图

通过实验对比经典IDW方法,顾及风向因素的反距离加权法(DIDW)[16],普通克里金方法（OK）以及本文提出的DVIDW方法。其中,DIDW方法顾及风向因素对于空气污染物传播的影响,但是未充分考虑风速大小的影响。由于距离衰减参数对于插值结果的影响较大,所以为了保证实验的准确性,在用对比方法进行插值时,距离衰减参数分别采用最常用的1、2、3进行实验。实验采用留一法进行交叉验证,通过平均绝对误差（MAE）和均方根误差（RMSE）来表达空间插值结果的精度。
MAE = ∑ i = 1 m ABS ( Z o , i - Z e , i ) m （8）
RMSE = ∑ i = 1 m ( Z o , i - Z e , i ) 2 m （9）
式中： Z o , i 和 Z e , i 分别为观测值和估计值;m为采样点的数量。

3.1 实验1

采用4种空间插值方法进行实验并得出结果,进行交叉验证得到各项误差指标,如表1所示。
Tab. 1 Results of experiments by the four different spatial interpolation methods (Test 1)

表1 4种空间插值方法实验结果（实验1）

MAE/(μg/m3) RMS/(μg/m3)
IDW_1 7.2732 15.2666
IDW_2 7.4573 16.0977
IDW_3 7.6951 17.0742
DIDW_1 6.6000 14.5153
DIDW_2 6.8691 14.8112
DIDW_3 7.0291 15.0007
Kriging 7.1302 15.0958
DVIDW_1 6.2557 14.5614
DVIDW_2 6.4666 14.6923
DVIDW_3 6.5208 14.7595
为直观体现各种空间插值方法的实验结果误差,将4种插值方法的平均绝对误差（MAE）绘制柱状图（图5）。由图5可以发现,Kriging方法的插值结果精度明显高于IDW方法,DIDW方法的插值结果精度相比Kriging方法有较大的提高,而本文提出的DVIDW方法又明显优于其他的空间插值方法。4种空间插值方法均选取效果较好的情况,其插值结果误差的空间分布情况如图6所示。
Fig. 5 Results of experiments by the four differentspatial interpolation methods (Test 1)

图5 4种空间插值方法实验结果柱状图（实验1）

Fig. 6 The spatial distribution of results of four interpolation methods (Test 1)

图6 4种方法插值结果误差空间分布（实验1）

根据2014年9月15日空气污染物观测站的PM2.5浓度观测数据利用本文方法进行空间插值的结果如图7所示。
Fig. 7 The map of PM2.5 concentration interpolationresults

图7 PM2.5浓度插值结果图

3.2 实验2

本文采用4种空间插值方法进行实验,并对结果进行交叉验证得到各项误差指标,如表2所示。
Tab. 2 Results of experiments by the four different spatial interpolation methods

表2 4种空间插值方法的实验结果（实验2）

MAE/(μg/m3) RMS/(μg/m3)
IDW_1 15.6575 20.2964
IDW_2 14.5205 19.5501
IDW_3 13.8425 19.1654
DIDW_1 10.4757 14.5905
DIDW_2 10.6549 14.6874
DIDW_3 10.8367 14.8179
Kriging 15.1735 19.8676
DVIDW_1 10.1501 14.6334
DVIDW_2 10.2418 14.6044
DVIDW_3 10.2829 14.5789
为了直观地体现各种空间插值方法的实验结果误差,将4种插值方法的平均绝对误差（MAE）绘制柱状图（图8）。由图8可发现,Kriging方法与IDW方法的插值结果精度相近,DIDW方法的插值结果精度明显高于Kriging方法和IDW方法,而本文提出的DVIDW方法的插值精度相比DIDW方法又有所提高。4种空间插值方法均选取效果较好的情况,其插值结果误差的空间分布情况如图9所示。
Fig. 8 Results of experiments by the six differentspatial interpolation methods (Test 2)

图8 4种空间插值方法的实验结果柱状图（实验2）

Fig. 9 The spatial distribution of results of four interpolation methods (Test 2)

图9 4种方法插值结果误差的空间分布（实验2）

根据2014年9月16日空气污染物观测站的PM2.5浓度观测数据利用本文方法进行空间插值的结果如图10所示。
Fig. 10 The map of PM2.5 concentration interpolation results

图10 PM2.5浓度插值结果图

4 结论与展望

本文针对现有空间插值方法应用于空气污染物浓度插值问题没有充分考虑风向和风速因素影响的局限性,提出一种顾及风向和风速因素的空气污染物浓度插值方法（DVIDW）。该方法充分顾及了风向和风速因素对于空气污染物扩散的影响,利用研究区的风力数据建立风场,考虑风向和风速因素对空气污染物扩散的影响,以气象学中的扩散模型为基础计算空气污染物在风场中传播的扩散距离,根据风场最短路径距离进行反距离加权插值,得到待求点处插值结果。最后,通过2组实际空气污染物浓度数据进行实验分析,验证了本文方法的可行性和优越性。
本文提出的顾及风向和风速因素的空气污染物浓度插值方法（DVIDW）与现有常用方法相比插值结果精度明显提高,今后将在以下2方面进行更加深入的研究：① DVIDW方法中风场的建立过程,考虑到风场建立需要较大的计算量,因此根据采样点处风向风速的矢量数据采用IDW方法进行空间插值。今后计划将气象学领域中较为成熟的风场建立方法引入到空气污染物浓度的空间插值中,进一步提高其空间插值结果的精度。② 将顾及风向风速因素的空气污染物浓度插值方法应用于路网约束内,提高路网空间插值结果的精度,从而方便居民出行对路径的选取。

The authors have declared that no competing interests exist.

参考文献

原文顺序 | 文献年度倒序 | 文中引用次数倒序
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