Receptor Modelling

Fugitive dust emission rate estimates by reverse-dispersion modelling


1 Introduction
2 Reverse-dispersion modelling
3 Required input variables
4 Experimental set up for long-term monitoring
5 Requirements of the measuring devices
6 Statistical evaluation of long-term mean emission rates

1 Introduction

For open dust sources, measurements at the source are usually difficult. Instead, indirect measurements are applied. Particularly, reverse-dispersion modelling may be applicated for fugitive dust emission rate estimates. This method requires assessment of all relevant input parameters for the dispersion model and sufficient measurements at various locations and during various weather conditions. In this paper, this method is described in more detail.
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2 Reverse-dispersion modelling

2.1 Short-term monitoring

The dispersion of emitted matter is influenced by the location and geometry of the source, weather conditions and terrain roughness. The dispersion factor a is the contribution of a local source i with emission rate e = 1 g/s to the concentration c at a receptor site r downwind of the source. For dust particles, the dispersion factor also depends on the aerodynamic particle size d.

c_ird = a_ird e_id

2.2 Long-term monitoring

In many cases, different sources contribute to the concentration at the measuring site. To distinguish the contributions of these sources, a network of receptor sites is needed.

Furthermore, accuracy will increase by using time-series of measurements.
The emission rates are calculated by multiple regression.
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3 Required input variables

The necessary input variables for calculating the dispersion factors are:
- wind speed, wind direction, stability of the atmosphere, mixing height, temperature
- roughness length of the area under investigation
- location, height and geometry of the local sources
- location and height of the receptor sites
- aerodynamic particle size distribution
For coarse fugitive dust, mixing height and temperature are of minor importance, due to the very local character of the dispersion. Aerodynamic particle size distribution, however, is essential.
For accurate calculations of dispersion factors the meteorological data must be available on a hourly basis. For accurate emission calculations, concentration measurements and particle size distribution also must be available on an hourly basis.
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4 Experimental set up for long-term monitoring

Scale

In order to use reverse-dispersion modelling, the emitted component must disperse over some distance, at least 30 m or more. Therefore, it is not applicable for leak detection which takes place at a much smaller distance from the source. To distinguish local sources, the measurements should be performed within several kilometers of the source. At larger distances, the contribution of the local source may be mixed up with the background concentration and the meteorological conditions may require a trajectory analysis instead of a dispersion model.

Distinguishing different sources

Contributions of different sources can be distinguished when their sets of dispersion factors are not correlated. For instance, when a receptor site is located in between two sources one sources is located downwind (a =0) and the other one upwind (a > 0). With the wind blowing from the opposite direction, it is the reversed. Then, the dispersion factors are not correlated.
This way of distinguishing sources is based on the spatial distribution of the sources. Meteorological conditions and time-dependent fluctuations act as a tracer for these sources.
The use of other tracers may improve the interpretation of the results. Some sources have a characteristic temporal tracer such as traffic (rush hours) or industrial activities (working hours). By using these temporal tracers, contributions of different sources within the same area may be distinguished.
Some sources can be traced back due to the chemical or elemental composition. Using a chemical or elemental tracer mostly implies a loss of time resolution.
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5 Requirements of the measuring devices

Time resolution

Reverse-dispersion modelling requires a time resolution of at least one hour. The main reason is the constantly changing weather conditions. To calculate dispersion factors accurately, they must be calculated for every hour. Another reason is the ability to analyse the temporal characteristics of sources.

Fine and coarse dust

When measuring dust, fine and coarse dust must be distinguished because of their different dispersion chracteristics, their different effects and (partly) their different origin.

Particle size resolution

When measuring coarse dust, the particle size distribution must be assessed while particle size is very important in calculating the dispersion factor. For fine dust, particle size is of minor importance.

Available measuring devices

For long-term fine dust measurements, several samplers are commercially available. The most well-known samplers are the TEOM and the Beta-dust sampler. A slight disadvantage of the Beta dust sampler is the lower time resolution which is three hours or more. Samplers based on light scattering need a calibration for the dust source under investigation. On the other hand, these samplers can simultaneously assess both PM2.5 and PM10, like the Osiris sampler.
For short-term measurements, the battery-driven Osiris is useful due to its mobility.

For short-term measurements of coarse dust, a rotary impactor is used: the dust is sampled on a rotating strip by inertial impaction. There are several rotary impactors commercially avail-able. Commonly used are the R--otorod sampler and the Dustviewer. The advantage of the Dustviewer is the practical use at field locations without any facilities.
A strip of 5 mm width and 210 mm length is mounted in a holder and rotated radially by a battery-driven drill. The strip is coated with a silicone oil to stick the dust particles. Image analysis of the strip results in the dust concentration and the particle size distribution

For long-term measurements of coarse dust, the Coarse Dust Recorder is used. The Coarse Dust Recorder consists of a tube, a fan, and a cassette containing a long sticky strip. The fan draws air through the tube at a rate of 8.8 m.s-1. The tube is 0.3 m wide and is continuously aligned towards the wind by means of a weather vane. Inside the tube, a small part of a long strip is exposed to the airflow. Fugitive dust is collected on the sticky strip by inertial impaction. The lower cut-off diameter is 14 µm. The strip is moved little by little, so that success-ively new parts are exposed. After a period of one week, the cassette containing the strip is removed and analysed by means of image analysis. The result is the hourly course of the dust concentration and the particle size distribution.
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6 Statistical evaluation of long-term mean emission rates

6.1 Standard error and coefficient of multiple determination

The standard error of the emission rate is a measure of the accuracy of the emission rate estimate, assuming that the errors are normally and independently distributed.

The coefficient of multiple determination R² is the fraction of the variations in concentration that is explained by the model. As with linear regression, the value of R² lies between 0 and 1. Fluctuating emission rates cause a low value of R². Still, the mean emission rate might be calculated accurately.
R² is split in partial R²s, which denote the contribution of sources to the value of R².

6.2 Variable fugitive emissions

The method described above calculates mean fugitive emissions of the local dust sources. In many cases, however, the emission will vary, due to weather conditions and industrial activities. These variations are investigated by creating subsets based on relevant parameters. The emission rate is calculated for every subset.
For fugitive dust sources such as open storage sites of coal and iron ore, relevant parameters for creating subsets are wind speed and rainfall and industrial activities such as unloading ships and traffic hours. Of course, the created subsets contain less data than the total set. The number of receptor sites and the duration of the measuring campaign must be tuned to the required number of subsets, in order to have sufficient data for statistical analysis.

6.3 Residual analysis

The residuals from the multiple regression model being the difference between measured and predicted concentration play an important role in evaluating model adequacy, just as they do in simple linear regression. Residual plots are used for investigating normality, the possible neglect of regressors, autocorrelation and outliers.
One way to deal with non-normality is to create subsets on the basis of the residuals. The subset with small negative and small positive residuals describes the regular emission. Recalculating the emission rates for this set, usually provides normally distributed residuals. The large negative values mark the moments with very low concentration and the large positive values the events with extremely high dust concentrations. These subsets can be checked too on normality. If this is not the case the accuracy of the mean emission rate of these sets is low. Evaluation of the individual events might be more informing.
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