Monte carlo simulation of regional aerosol: transport and kinetics

Source Receptor Relationship

The source receptor relationship defines the attribution of a receptor’s concentration to specific sources and/or source types. The Monte Carlo model was designed to be used as a diagnostic tool for the investigation and quantification of the source receptor relationship. This tool is based upon the fact, that in the Monte Carlo approach physical/chemical processes are simulated as discrete events. Thus, the influence of each process on the source receptor relationship can be analyzed separately.

It can be shown, that from the Lagrangian formulation of the dispersion equation (42, 43) the source receptor relationship can be defined as:

= (11)

where i identifies the receptor volume

j identifies the source volume
k identifies the receptor time
l identifies the source release time (k - l= pollutant age)
the mass within the receptor volume i at time k due to emissions from source j released at time l
the mass released from source j at time l
the transfer matrix, the relative fraction of mass released from the source volume j at time l that impacts the receptor volume i at time k
the transit probability
the kinetic probability

This equation states that the pollutant mass at a receptor i and time k, due to emissions from source j released at time l, is proportional to the mass released at the source j at time l, where the proportionality constant is the element of the transfer matrix T_ijkl. The physical interpretation of a transfer matrix element is that it represents the fraction of matter emitted from a source that reaches the receptor in the chemical form of interest. The total mass contribution to a receptor volume from a source can be found by simply summing over the source release time l.

Each element of the transfer matrix can be decomposed into a transit probability, P_t and a kinetic probability P_k. P_t defines the transport of the emissions, and can be thought of as the probability of a conservative species being transported from the source to the receptor. P_k defines the kinetic processes of the emitted pollutant mass. P_k for a primary species, such as SO₂, is the probability that the pollutant mass will not be transformed or removed before being transported to the receptor, while for a secondary species, P_k is the probability that the pollutant mass will be transformed and not removed before being transported to the receptor. For example, P_k for SO₄^2- is the probability that a quantum's initial SO₂ mass is transformed to SO₄^2- and the resulting SO₄^2- mass is not removed before being transported to the receptor. For a conservative species, P_k is unity.

The source receptor relationship is presented graphically in Figure 13. The maps in this figure represent the three components of the source receptor relationship, m_E, P_t, and P_k, and the resulting average source contributions to the and column concentrations at a receptor located in Massachusetts during quarter 3, 1992. The source grid is overlaid each map. The emission rate map shows that the highest values are over the Ohio River Valley where they can exceed 10⁶ tons/yr. In the transit probability map, there is a decreasing probability of source impact with distance from the receptor. For example, sources in Michigan are about 7 times less likely to impact the Massachusetts receptor then the source located in Vermont. There is also a higher likelihood of emissions impacting the Massachusetts receptor from sources to the west and south than from the north. The kinetic probability map also displays an inverse relationship with distance. Sources in the vicinity of the receptor have P_k higher than 50% while in the Ohio River Valley the P_k is approximately 20%. The inverse relation with distance is expected since is a reactive primary species, and the residence time is roughly proportional to transport distance. The source attribution map shows that the concentration is dominated by contributions from nearby sources. The Massachusetts and Connecticut source grids supply over 35% of the mass. The large contributions from these sources are the result of their relatively high transit and kinetic probabilities. However, the high emissions in the Ohio River Valley lead to this area contributing almost 25% of the mass.

The kinetic probability map for presents a very different picture then seen for the . is a secondary species, and it takes time before a significant fraction of the in an airmass can be transformed to . This leads to kinetic probabilities that at first increase and then decrease with distance from the receptor. As shown, the P_k is about 2 to 5% for sources close to the receptor. This increases to almost 10% in western Pennsylvania and Northern Virginia, and again decreases to 2-5% in Illinois and Missouri. The source attribution map shows that the nearby sources contribute less than 10% of the mass to the receptor while the Ohio River Valley contributes nearly 30%.