Advanced Materials Research Online: 2014-06-18 ISSN: 1662-8985, Vols. 955-959, pp 2505-2512 doi:10.4028/www.scientific.net/amr.955-959.2505 2014 Trans Tech Publications, Switzerland Analysis of Density of PM2.5 under Diffusion and Attenuation Based on Non-Stationary Two-Dimensional Multi-Box Model Caoyuan Hu, Haiyan Li, Xiaoming Huang, Zhi Li School of Science, Huazhong Agricultural University, Wuhan 430070, China Keywords: Two-Dimensional Multi-Box model, PM2.5, Diffusion, Attenuation. Abstract High density of PM2.5 that has an insignificant contribution to the increasing dusty weather threats the physical and mental health of approximate six hundred millions Chinese recently. In this paper, we investigate the diffusion and attenuation of PM2.5 and give a prediction of its density in Xi an city, which is based on non-stationary two-dimensional multi-box model, while considering the effect of seasons and wind direction. A simulation is conducted with data from thirteen random selected stations. Furthermore, by comparing the real measured value and numeric value, we evaluate the validity of our proposed model as well as giving the relative error. Introduction Air quality is an extreme important index to measure the standard of citizens living. In recent years, with the accelerating development of economic, the quantity of particles in air is increasing in an alarming rapid with the number of vehicles, burning fossil fuel and arbitrary emission of industrial dust result in more and more dusty days and higher density of PM2.5. Taking the continuous dusty weather that cover a quart of china for example, it leads to severe suffering for approximately six hundred millions residents [1]. Thus, dusty weather mainly caused by PM2.5 turns into an urgent problem which threw a hot discussion among government, environmentprotecting organisation and residents. The reason for dusty weather is that the dust in air is over-contained. In order to monitor, forecast and control air quality, central and local government re-enact the Environment and Air Quality Standard (GB3095), which categories the environment and air quality in a new way. The standard replaced the original Air Pollution Index (API) by Air Quality Index (AQI) and added three indexes of PM2.5, O 3 and CO into the already-included indexes of SO 2, NO2, PM10. At the same time, a threshold to density of PM2.5 and the average density of O 3 in eight hours is also given as well as adjusting the threshold of PM10, NO2, Pb and C6H6 in this new standard [2].PM2.5 is the dust in air whose diameter is equal or big than 2.5um. As creating health and environmental hazards, PM2.5 has already been included into regular monitor system in some countries such as America, Canada, Japan, and India. While this index is also firstly taken into new air quality monitor standard by china. But in china, there are few researches about PM2.5 for short time monitor and lacking awareness. Related work focus on the follow three aspects. (1) Analysing distribution of PM2.5; early-warning and evaluating the degree of contamination [3-6]. (2) Addressing the evolutional rule of diffusion of PM2.5 by combining GIS technologies with numeric simulation and considering natural factor such as wind-force, temperature and humidity [7-10]. (3) Predicting the sudden increase of PM2.5 in emergency [11-14]. However, lacking of monitor station between cities leads to insufficient, further far from wellrounded data resulting in scarcity of academic research about features of diffusion and attenuation of PM2.5 based on real cases, which restricts further study under domestic situation. In this paper, taking Xi an as instance, we try to find out the rule of diffusion and attenuation of PM2.5 from the data which collected from thirteen monitor stations, while considering the effect of wind-force, humidity, seasons and so on. A non-stationary two-dimensional multi-box model is All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, www.ttp.net. (#69814899, Pennsylvania State University, University Park, USA-18/09/16,15:26:17)
2506 Advances in Environmental Technologies III established to give an effective and efficient prediction of the diffusion and attenuation of PM2.5. Simulation results show our proposed methods can work out the distribution of PM2.5 with low time complexity, which can facilitate quick reaction for prevention or compensation. Station Distribution Figure 1 give information of thirteen monitor stations in Xi an. Comparing with the transportation map, we can see that four stations locate within second circle road in which residents live intensively, and five stations scatter over the area between the second circle road and third circle road, which accommodate major factories. The other four stations are distributed the district out of the third circle road. We collected data from thirteen monitor stations [15] from 1 th January 2013 to 9 th September 2013. The missing value is replaced by Lagrange interpolation. Meanwhile, we found abnormal index value of PM2.5 by statistical methods. So, to ensure integrity and validity of collected data, we apply wavelet transformation to de-noising, which can keep continuity of data on time line at the same time. The data related to density of PM2.5 is measured in. As shown in Table 1, we can see site 1 comes the highest value and site 8 own the minimum. Although limited by data, we still observe that the density of PM2.5 within second circle road is highest for intensive residents and the density Figure.1 Geographical Position of thirteen monitor stations in Xi an city of PM2.5 out of third circle road is lowest. On the whole the density of PM2.5 declines from core city to outskirts. Table 1: Density of PM2.5 in thirteen monitor stations in Xi an city Within second circle road Between second and third circle road Out of third circle road Site 1 Site 2 Site 3 Site 4 Yearly average 142 125 146 118 133 Site 5 Site 6 Site 7 Site 8 Site 9 Yearly average 139 132 125 115 136 129 Site 10 Site 11 Site 12 Site 13 Yearly average 120 125 125 141 128 Diffusion and Attenuation Model Many methods [16-17] are proposed to predict density of PM2.5 with different conditions and three of them are typical: Gaussian diffusion model, photochemical oxidation model (such as UAM model,
Advanced Materials Research Vols. 955-959 2507 etc.), and atmospheric system models---the box model. Gaussian model is widely used to predict diffusion of point source pollution. However, Gaussian model has some limitations. When a case where enormous pollution sources with low height is considered, Gaussian model is so difficult to obtain the probable calculation matrix about weather in some areas, which significantly degraded its effort. So, in city circumstance with such loads of low pollution source, a reasonable method should be formulated to achieve more accurate prediction of pollutant. Box model is a candidate to meet such requires with low complexity and providing high accuracy. Those edge features enables box model to adapt itself to application in copying with point gas pollution source. 1.1 Single Box Model Box-style model features in simplicity and easy operating, including single-box model and multi-box model. Single-box model assume that every site is an independent box whose density is equal to the density of the contained site. Single-box model has been widely used to forecast the urban air qualify [18-21]. The major assumptions of the single-box model are as follow: (1) The density of PM2.5 is uniformly distributed in each single-box; (2) PM2.5 emissions varies with time to time cased by not only the cleaning process in vertical direction(rainout, flushing), but also the horizontal transportation either. (3) The emission rate is fixed, and the vertical directional diffusion rate of PM2.5 is limited by the thickness of inversion layer above the single-box. According to the relationship between input and output, the quality balance equation can be written as: (3.1.1) where d is the distance between pollution source and one site in km;c is density inside of a box in mg/m 3 ;l is the length of box in m;h is the height of box in m;b is the width of box in m;u is average wind speed, mg/s;c 0 is density of the currency flowing into a box, mg/m 3 ;Q is the strength of pollution sources;as shown in figure 2 [18] : The equilibrium of density can be shown as follows: Fig 2 Single-box model (3.1.2) As can be seen, C increases proportionally with the strength of pollution sources Q and the length of the box l, and it decreases proportionally with average wind speed u and mixed inversion layer thickness (Eq.3.1.2). It shows that density of PM2.5 also rely on the total emissions and air conditions. (3.1.3) (3.1.4) We assume site1 is the pollution source, and thus site 4 was influenced by site1. Since any site could probably own the highest density of PM2.5 in daily life, without loss of generality, we
2508 Advances in Environmental Technologies III randomly take two site for example to find the strongest pollution source. Inputting real PM2.5 data of xi an into single-box model, we can solve the pollution sources of strength Q=68.96mg/s, equilibrium density C is shown as: The density of a single box at different time t can be calculated by (3.1.5). 1.2 Non-Stationary Two-Dimensional Multi-Box Model. (3.1.5) Multi-box model is a model improved from the single-box model [22-23]. It ultimately fulfil the box model potential to tackle prediction of air quality with more pollutant sources in urban areas. Each contaminated area can be seen as a box which is shown as figure3. By calculating the density of outflow and inflow of pollutants, we can find out the density of each box. Fig.3. Two-Dimensional Multi-Box Model The main assumptions about Two-dimensional multi-box model [23-27] : (1) PM2.5 is uniformly distributed in each box; (2) Ignore chemical reaction and deposition of PM2.5 in each box; Xi an is divided into m boxes in south-north direction and each of their length is L. The east-west direction of xi an city is divided into n boxes and each of their width is W. h is the height of a box owing p boxes in gravity-direction. So xi an city is totally divided into m n p sub-boxes. is direction of wind and north direction is defined as zeros in. Thus, we can easily transform coordinate of wind to X-Y coordinate system. (3.2.1) Depending on the law of conservation of mass, we can get the equation as shown as follow: (3.2.2) is the density of PM2.5 in sub-box is PM2.5 diffusional coefficient in the horizontal direction; h is height of sub-box; l is length of sub-box ; W is width of sub-box ; is the strength of pollution sources of sub-box ; is average speed of wind in the X-axis direction; is average wind speed in the X-axis direction; Analysis of Density of PM2.5 under Diffusion and Attenuation Since Factors, such as distance, the direction and force of wind, weather conditions, are considered, non-stationary two-dimensional multi-box model can accurately forecast the density of PM2.5 in Xi an. It treats Xi an city as a whole non-stationary two-dimensional multi-box system concentrating on exchanges of PM2.5 between sub-boxes. So such a dynamic system is built which show not only the exchange of PM2.5 but also the diffusion and attenuation within the whole system. Initial average density curve of PM2.5 in Xi an is shown in Figure.4.
Advanced Materials Research Vols. 955-959 2509 Figure.4. The level curve of average density of PM2.5 in xi'an Fig.5. Two-dimensional multi-boxes in Xi'an city Xi an city is dived into multi-box as Figure 5. Each sub-box s length and width were 7.7km 4.75km(Fig.5), and the height is defined as a fixed value. 1.3 Prediction of Density of PM2.5 under Diffusion and Attenuation Substituting original data into non-stationary two-dimension multi-box model, we can derive the diffusion and attenuation of PM2.5. But, for simplicity of calculation, we randomly selected one day (10 February 2013) to predict the density of PM2.5, while verifying the validity of this model. For instance, Table 2 shows initial density of PM2.5 on February 10, 2013. Figure 6 shows the spatial distribution of density of PM2.5. February 10 Monitoring data Table 2 PM2.5 initial density on February 10, 2013 in Xi'an city Within circle Site 1 Site 2 Site 3 Site 4 second road 361 94 499 101 Between second Site 5 Site 6 Site 7 Site 8 Site 9 and third circle road 500 500 446 500 373 Out of third Site 10 Site 11 Site 12 Site 13 circle road 500 494 500 458 And we can get the density of PM2.5 which is depleted by diffusion and attenuation in the whole day. It is shown as figure 7.
2510 Advances in Environmental Technologies III Fig.6 The initial spatial distribution of PM2.5 density Fig.7 The forecastle spatial distribution of PM2.5 density From Figure 7, we can see that PM2.5 density is much lower than the day before. 1.4 Validation Test of Proposed Method In order to verify the prediction accuracy of non-stationary two-dimensional multi-box model, we compare the relative error between monitoring data and predicted data at February 11 (tab.3). Table 3 Monitoring data and prediction data of PM2.5 in Xi an at February 11 Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 Site 7 February 11 258 242 262 100.6 255 257 249 Monitoring Site 8 Site 9 Site 10 Site 11 Site 12 Site 13 data 253 187 257 226 225 244 February 11 prediction data Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 Site 7 215 198 242 220 251 257 246 Site 8 Site 9 Site 10 Site 11 Site 12 Site 13 256 221 217 225 213 211 Table 4 The relative error between monitoring data and prediction data of PM2.5 Site 1 Site 2 Site 3 Site 4 Site 5 Site 6 Site 7 0.166 0.182 0.076-1.186 0.016 0.000 0.012 Relative Error Site 8 Site 9 Site 10 Site 11 Site 12 Site 13-0.012-0.182 0.156 0.004 0.053 0.135 The results of relative error in Table 4 show that the relative error value are within 20%. In short, non-stationary two-dimensional multi-box model has a high accuracy to predict the PM2.5 density under diffusion and attenuation distribution in Xi'an city. This model can effectively predict the diffusion attenuation of air pollution, and can be extended to other corresponding application widely. Conclusions In this paper, we study a case, where Xi an is taken as an example, and build non-stationary twodimensional multi-box model to analyze diffusion and attenuation of PM2.5 and further to predict its density. A simulation is constructed to demonstrate our proposed method by comparing forecastle value and corresponding real value. Simulation results show that our formulated model can provides accurate prediction in effective and efficient way with relative error within 0.2. Moreover, this method can be extended to application of predicting density of pollutant, such as SO2, N02, PM10. Government and environmental institution can make decision according the accurate prediction in emergency circumstance.
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