Bret A. Schichtel
Center for Air Pollution and Trend Analysis
Washington University, St. Louis, MO, 63130

Presented at the A&WMA/AGU Specialty Conference on
Visual Air Quality, Aerosol and Global Radiation Balance
Bartlett New Hampshire, September 9-12, 1997,
Paper 120-S9.123

Valid emission fields are an essential component for air quality modeling and management. However, there are a number of important species, such as dust, NO_x and NH₃, that have large uncertainties.^1,2,3 This is partly due to these emission fields having large fugitive and biogenic contributions which are not easily quantified by traditional source oriented techniques, such as source measurement⁴, modeling ⁵ and material balances ⁶.

An alternative approach attempts to back out the emission fields from receptor data using a-priori information on the transport, transformation and removal processes.^7-13 These methods invert the source receptor relationship, essentially running an air quality model in reverse tracing the pollutant pathway backward from the receptor to their source of origin and reversing the removal and transformation processes.

In this work a receptor oriented approach for the retrieval of emission fields is presented. The approach is demonstrated on the retrieval of known seasonal SO₂ emission fields using fine particle data from the IMPROVE ¹⁴ and NESCAUM networks ¹⁵ and wet deposition data from the NADP/NTN network.¹⁶ The approach is then used to retrieve seasonal NO_X and NH₃ emission fields from wet deposition data. All emission fields are compared to estimates from the 1985 NAPAP emission inventory. ¹⁷

The emission retrieval approach is based on the inversion of the source receptor relationship (SRR). The SRR in its simplest form for an ambient concentration can be defined as^18,19,20,13:

The transfer coefficient can be viewed as the probability per unit volume that the emitted mass will be transmitted from the source to the receptor. The SRR is not limited to ambient concentrations but can also be defined for deposition rates. A universal SRR can be defined which combines the ambient concentration and deposition rates into one relationship.¹³ This relationship linearly relates the receptor concentrations to source emissions via the transfer matrix. Therefore, provided the transfer matrix is known, the emissions can be retrieved by inverting Equation 1, i.e. e = (T)^-1 c.

In this work the transfer matrices were computed from a regional Monte Carlo particle dispersion model whose kinetics were calibrated for the simulation of SO2 and SO42- over the Eastern US.²¹ In the calibration procedure, the ambient and wet deposited sulfur were simulated using the 1985 NAPAP SO2 emission field (Figure 2). The kinetics processes were then adjusted to obtain the best match between the simulator and measured fine particle sulfur concentrations from the IMPROVE and NESCAUM networks and wet deposited sulfur from the NADP/NTN network.

The emission retrieval approach was tested by retrieving the seasonal SO₂ emissions using the tuned transfer matrices and ambient data. The retrieval method inverts Equation 1 using a robust singular value decomposition ²² technique. Singular value decomposition is a least square inversion technique that employs a dampening function to reduce the instabilities inherent in the inversion of ill-conditioned problems²², such as the retrieval of emission fields.^8,9 The inversion procedure was made robust by implementing a W-estimator²³ into the singular value decomposition. This convert the least square estimate into a maximum likelihood estimator, basically reducing the weights of the largest residuals in the least square procedure¹³.

Figure 1 presents the reconstructed and 1985 NAPAP emission fields for quarters 1 and 3. As shown, the third quarter reconstructed emissions identify the major source regions and their strengths, such as in the Ohio River Valley and Alabama. However, they are spread out over a larger area than seen in the NAPAP emission field. The spreading results from the dampening function in the retrieval approach. The quarter 1 results identify the central Eastern US as the highest emission region, but the emission densities are more uniform over the Eastern US compared to quarter 3 reconstructed and NAPAP emission fields. The retrieved emissions were, on average, about 7% larger than the NAPAP emissions (Table 1).

The inversion procedure was used to retrieve the North American seasonal NH3 and NO_X from NH4+ and NO3- wet deposition data respectively. The SO₂ – SO₄^2- wet deposition transfer matrices were used for both retrieval process. The NO_X emission fields compared favorably with 1985 NAPAP estimates, identifying the large source regions in the Industrial Midwest and along the Gulf Coast (Figure 2). However, there was considerable spreading of the high emission areas to neighboring regions, and the reconstruction shows high emissions in Michigan and Wisconsin that are not seen in NAPAP. The reconstructed NO_X emissions also have nearly two times the emission rate of NAPAP (Table 2).

The NH3 retrieved emissions showed poor correspondence with the 1985 NAPAP inventory, estimating the highest emissions over the Industrial Midwest while NAPAP estimates them to be over Iowa (Figure 3). The reconstructed emissions are also about 2.5 times larger than those estimated in NAPAP, but they are more in line with the emissions estimated by combining the US anthropogentic estimates of Harris and Michael ²⁴ and natural emission estimates of the EPA²⁵(Table 3). The poor correspondence may be the result of the SO₂ – SO₄^2- wet deposition transfer matrices being inadequate to simulate ammonium wet deposition. The solubility of the SO₂ is inversely related to the precipitation acidity while the solubility of NH₃ is directly related to acidity. Also, at the acidity typically found in the atmosphere, the solubility of NH₃ is about an order of magnitude greater than SO₂.²⁶ Therefore, the transfer matrices used in the retrieval may have systematically underestimated the NH₃ wet deposition rates and may have been spatially biased.

Table 1. The total reconstructed and 1985 NAPAP SO₂ emission rates Figure 1.

Table 2. The total reconstructed and 1985 NAPAP NO₂ emission rates in Figure 2.

Table 3. The total reconstructed and 1985 NAPAP NH₃ emission rates in Figure 3. Also the sum of the estimated US NH₃ anthropogenic emission by Harris and Michaels ²¹ and natural estimate by the USEPA.²²

Figure 1. A) Reconstructed Q1 and Q3 SO₂ emission fields (n ) IMPROVE/NESCAUM sulfur and (t ) NADP SO₄^2- wet deposition monitoring sites. B) NAPAP Q1 and Q3 SO₂ emission fields.

Figure 2 A) Reconstructed Q1 and Q3 NO₂ emission fields. B) NAPAP Q1 and Q3 NO₂ emission fields.

Figure 3. A) Reconstructed Q2 and Q4 NH₃ emission fields (t ) NADP SO₄^2- wet deposition monitoring sites. B) NAPAP Q2 and Q4 NH₃ emission fields.