The inversion technique developed in the previous sections was applied to the retrieval of US seasonal emission fields for SO₂, NH₄⁺, and NO_x during 1992. This section presents the results from these emission retrievals. A comparison of the NAPAP SO₂ emission fields with the retrieved SO₂ is also given. The NAPAP emission inventory contains reliable North American SO₂ emission fields, and the 1985 NAPAP annual emission inventory was used to tune the Monte Carlo model (Section 3.4). Consequently, it is expected that the retrieval of the SO₂ emission field should be comparable to the 1985 NAPAP SO₂ emission inventory. The comparison will allow for the testing of the capabilities and limitations of the inversion technique.

The retrieved emission fields were calculated using the transfer matrices created using the Monte Carlo Model for the SO₂ - SO₄^2- system in Section 3.5. The justification of using SO₂ - SO₄^2- kinetics for the retrieval of NH₃ and NO_X is presented below. The same polar stereographic grid as the NGM meteorological data (Figure 3-11) covering the continental US including southern Canada and northern Mexico was used as the spatial domain for the retrieval of all of the emission fields. Over this domain, 504 emission grid cells were modeled. The observation data came from the IMPROVE/NESCAUM aerosol monitoring network, and the NADP wet deposition network (see Section 3.4.1). In some locations, multiple receptor sites from the IMPROVE/NESCAUM or the NADP database resided in the same receptor volume of the transfer matrices. In these cases, the observation values from the same network were averaged together. The transfer matrices generated from the Monte Carlo model had a two hour receptor time and age resolution. Subsequently, they were averaged over a 24 hour and a week time period for use with the IMPROVE/NESCAUM and NADP data, respectively. Since seasonal emissions were retrieved, the age dimension of the transfer matrix was integrated out. The averaging and integration was performed as described in Section 2.3.

The inversion of the SRR was conducted using the robust singular value decomposition technique developed in Sections 4.1 & 4.2. The range of suitable eigenvalues that could be used in each retrieval was determined from the metrics of inversion. The metrics of inversion were calculated by inverting the system multiple times, incrementing the number of eigenvalues used by 25 for each successive inversion, to a maximum of 500. The metrics and approach for determining the eigenvalue range was described in the Section 4.4.1 Metrics of the Inversion performance.

The available monitoring data for the retrieval of SO₂ emission fields are the sulfate data in the IMPROVE/NESCAUM network and the wet deposited sulfate from the NADP precipitation chemistry network. These are two independent networks that monitor different variables, and have different spatial and temporal resolutions. The NADP network measured wet deposited SO₄^-2, which contains contributions from primary SO₂ and secondary SO₄^2-. The IMPROVE/NESCAUM network measured ambient sulfur concentrations from secondary sulfate aerosols. The NADP network has higher spatial resolution, with three times the number of monitoring sites as the IMPROVE /NESCAUM network that are well distributed over the US. The IMPROVE /NESCAUM network has a higher temporal resolution (see Section 3.4.1).

emissions that are negative continually increase with increasing eigenvalues, and is greater than 100% of the total emission rate when 400/504 eigenvalues are used. The upper bound of the eigenvalue range is approximately 200/504. At this point, the fraction of emission grids and total emissions that are negative are 25% and 20%, respectively, and the sum of the standard error is approximately equal to the sum of the emission rates over the emission field, ~87 kTons/day.

The reconstructed emissions and their standard errors using the lower and upper bounds of 75 and 200/504 eigenvalues are presented in Figure 4-22. The high emissions in the central part of the East are similar to the NAPAP emission field (Figure 4-23), but the highest emission rate in a grid cell is 1.5 kTons/day compared to 3 kTons/day for NAPAP. The high emissions of the NAPAP inventory in the Ohio River Valley appears to be spread out over the eastern US in the reconstructed emission field. This spreading of the emissions is a result of the low resolution of a reconstructed emission field caused by using only 15% of the available eigenvalues. The standard error is also low, generally less than 0.18 kTons/day. Using 200/504 eigenvalues, the emission pattern is much less uniform, indicating better resolved emissions. However, there is now a distinct checker board pattern over much of the spatial domain resulting from instabilities in the solution. The areas of high emissions are in the central eastern US and northern GA and AL. The standard error has also increased substantially to over 0.3 kTons/day over much of the eastern US.

Figure 4-24 presents the reconstructed emissions using the middle number of eigenvalues, 125/504, and the emission field with the negatives adjusted. The reconstructed emission field is stable with only about 10% of the total emission rates and emission grid cells being negative. The high emissions in the Ohio River Valley have been spread out over a domain from the Great Lakes to Alabama and Georgia. The highest retrieved emissions are located in three grid cells in Northern Virginia and Maryland. These high emissions are not seen in the NAPAP inventory. Also, many of the emission grid cells with high emission rates in Canada are not identified. In the West,

Figure 4-22. Reconstructed Q3 SO₂ emission fields and standard errors using the IMPROVE/NESCAUM sulfur data and A) 75/504 eigenvalues in the inversion B) 200/504 eigenvalues in the inversion. n identifies the IMPROVE/NESCAUM monitoring sites.

Figure 4-24. Reconstructed Q3 SO₂ emission fields and standard error using IMPROVE/NESCAUM sulfur data and A) 125/504 eigenvalues in the inversion B) 125/504 eigenvalues in the inversion and the negative values adjusted. n identifies the monitoring sites

the reconstruction identifies emission grid cells in southern Arizona and central California with emission rates above the background. The standard error map shows that there is slightly higher uncertainty in the emissions in the East than in the West. However, with the exception of a few eastern emission grid cells, the standard error is less than 0.18 kTons/day, compared to the typical emission rate of 0.5 kTons/day. The total standard error is 4 kTons/day, about half the total emission rate.

The NAPAP inventory does not contain any estimates of emission rates in Mexico. Therefore, the reconstructed emission can provide insights into the areas of high emissions and the overall magnitude of the SO₂ emissions in Northern Mexico. In the reconstruction, there are no emissions throughout the northwestern part of Mexico. Along the Texas-Mexican border, the emission rates can exceed 0.5 kTons/day, and are about 0.35 kTons/day just south of the Big Bend National Park where a monitoring site exists. The standard errors are less than 0.12 kTons/day, well below the estimated emissions.

During the third quarter of 1992, 1485 weekly SO₄^2- observed wet deposition values were available from the NADP network. This resulted in an over determined system with approximately 3 known input data points per unknown emission grid cell. The metrics of inversion performance as a function of the number of eigenvalues used in the inversion are presented in Figure 4-25. The total reconstructed emission rates vary only between 70 and 75 kTons/day when between 75 and 375/504 eigenvalues are used (Figure 4-25C). From the total emission rate plot and the forward model fit metrics (Figure 4-25C & E), it is evident that the lowest number of eigenvalues that can be used is 75/504. The upper bound is approximately 225/504 eigenvalues. The solution using 225/504 eigenvalues appears to be a transition point where the total emissions increase from 70 to 75 kTons/day, and the fraction of emission grid cells with negative emissions is equal to the fraction of the total emissions that are negative, ~ 30% (Figure 4-25F).

From this point on, the fraction of total emissions that are negative increases rapidly. Within the eigenvalue range of 75 to 225/504, the reconstructed emissions have the highest correlation with the NAPAP, greater than 0.45, and have a total emission rate approximately equal to NAPAP's.

Figure 4-26 presents the reconstructed emission fields and standard errors when 75 and 225 eigenvalues are used. These emission fields are similar to those generated by the IMPROVE/NESCAUM data, but the high emission band in the Central East is more to the north, centered around Indiana and New York. Figure 4-27 presents the reconstructed emission using the middle number of eigenvalues, 150, and the same emission field with the negative values adjusted. As shown, the reconstruction identifies the high emissions in the Ohio River Basin, with the maximum emission of 1.6 kTons/day compared to 3 kTons /day for the NAPAP emissions (Figure 4-23). The high emissions in eastern Tennessee are not retrieved. Also, all sources of high SO₂ emission in Canada have not been retrieved. In the West, the southern Arizona source has not been identified. The high emission in Northern Virginia and Maryland seen in the reconstruction with IMPROVE/NESCAUM data were also not present.

Contrasting these results with those from the IMPROVE /NESCAUM networks, it is seen that each of the reconstructions have benefits. The reconstruction using the NADP data was superior in several aspects. First, it had a smaller fraction of the total emission rate being negative resulting in a slightly larger number of eigenvalues that could be used in the reconstruction. The upper bound of eigenvalues was 225 compared to 200/504 when using the IMPROVE/NESCAUM data. Second, the NADP data had a relatively constant total emission rate over most of the eigenvalue range, while in the reconstruction using the IMPROVE/NESCAUM sulfate data it continually increased as the number of eigenvalues increased. A constant total emission rate over the eigenvalue range is beneficial because it provides confidence that the stability added to the inversion process does not remove emitted mass from the domain. The greater stability in the

Figure 4-26. Reconstructed Q3 SO₂ emission fields and standard errors using NADP SO₄^2- wet deposition data and A) 75/504 eigenvalues in the inversion B) 225/504 eigenvalues in the inversion. t identifies the NADP monitoring sites.

Figure 4-27. Reconstructed Q3 SO₂ emission fields and standard error using NADP SO₄^2- wet deposition data and A) 150/504 eigenvalues in the inversion B) 150/504 eigenvalues in the inversion and the negative values adjusted. t identifies the monitoring sites.

NADP reconstructed emission is most likely the result of receptor sites being more evenly distributed throughout the US.

The IMPROVE/NESCAUM reconstructed emission field was superior to the NADP reconstruction in that it compared slightly better to the NAPAP emission field with a correlation coefficient of r = 0.53 compared to r = 0.48. The region of high emissions in the East for the IMPROVE/NESCAUM reconstruction was closer to the region of high emissions indicated by the NAPAP emissions. In addition, the NADP reconstruction did not resolve any emissions in Canada or Mexico where there were no monitoring sites, even when the upper bound of eigenvalues, 225/504, was used (Figure 4-26). However, the reconstructed emission field using the IMPROVE /NESCAUM data do show indications of high emissions in both regions.

The ability of the ambient sulfate data to be able to identify Canadian sources, and the lack of ability of the SO₄^2- wet deposition data to do so, can be seen from examining their respective transfer matrices. As shown in Figures 3-28 - 3-31, in Section 3.5, sources primarily from the south and southwest of the receptor site contributed to the receptor's wet deposited mass. However, sources both north and south of the receptors contributed to the ambient SO₄^2- concentrations. The lack of wet deposition receptor sites in Canada, combined with the fact that Canadian sources contribute little to the US wet deposition rates, is responsible for the inability of the wet deposition data to retrieve the Canadian sources.

In this section, the two observation data sets are combined to retrieve the SO₂ emissions. This allows for the testing of whether or not the combination of the data can produce a superior emission field than retrievals using either data set alone. The combined data sets create 2801 input observation values, producing an overdetermined system of approximately 5.5 input observations for every one emission grid cell. The

metrics of inversion performance for the system is presented in Figure 4-28. The total reconstructed emission rates display a relatively constant pattern between 75 and 300/504 eigenvalues, varying between 70 and 77 kTons/day (Figure 4-28C). However, when more than 400/504 eigenvalues are used it varies considerably. The lower eigenvalue bound is approximately 75/504, where the correlation between reconstructed observations and input observations, and the ratio of their averages is 0.8. Using fewer than 75/504 eigenvalues, the forward model fit metrics (Figure 4-28E) deteriorate rapidly and the total reconstructed emission rate decreases. The upper bound is approximately 275/504 eigenvalues where the fraction of negative emissions and sources are ~25%. Above this point, the fraction of negative emissions increase rapidly. Within the eigenvalue range of 75 to 275/504, the reconstructed emissions have the highest correlation with the NAPAP (>0.55), and have a total retrieved emission rate between 0-10% higher than NAPAP's.

Figures 4-29 and 4-30 present the reconstructed emission fields and standard errors when 75 and 275/504 eigenvalues are used, and the reconstructed emissions using the middle number of eigenvalues, 175/504, with and without the negative emission rates adjusted. This retrieved emission field displays the high emission rates in the central eastern US extending from southern Illinois to Maryland. The highest emission rates are found in emission grid cells in northern Virginia where they exceed 2 kTons/day. This is similar to the reconstructed emission field using the IMPROVE/NESCAUM data. In the West, the reconstructed emission field indicates high emissions in southern Arizona, ~ 0.4 kTons/day, central California, ~0.5 kTons/day, and around Seattle, WA, > 0.25 kTons/day. These regions also contain many negative emission grid cells. In Canada, there are two source cells with emission rates ~0.3 kTons/day; one in Manitoba and the other one in Saskatchewan. These two emission grid cells are located in the vicinity of emission grid cells in the NAPAP inventory with high emission rates, >0.8 kTons/day. The high emission rates around Toronto indicated in NAPAP have not been retrieved.

Figure 4-29. Reconstructed Q3 SO₂ emission fields and standard errors using (n ) IMPROVE/NESCAUM sulfur data and (t ) NADP SO₄^2- wet deposition data and A) 75/504 eigenvalues in the inversion B) 275/504 eigenvalues in the inversion.

Figure 4-30. Reconstructed Q3 SO₂ emission fields and standard error using (n ) IMPROVE/NESCAUM sulfur data and (t ) NADP SO₄^2- wet deposition data and A) 175/504 eigenvalues B) 175/504 eigenvalues in the inversion and the negative values adjusted.

Throughout the northwestern part of Mexico, the reconstruction has low emission rates of <0.25 kTons/day. Along the Texas-Mexican border, the emission rates are approximately 0.4 kTons/day, and fall to less than 0.25 kTons/day in the northwestern Mexico. The standard errors throughout this region are all <0.12 kTons/day.

Comparing these results to those generated using the IMPROVE/NESCAUM sulfate aerosol or NADP SO₄^2- wet deposition data alone, it is seen that the reconstructed emissions share some characteristics with each of the other retrievals. The retrieval using the combined data produces a relatively constant total emission rate curve (Figure 4-28C) similar to the reconstruction using the NADP data. This indicates a dependence of the total emission rate on the number of eigenvalues that was not seen using the IMPROVE/NESCAUM data alone. The influence of the IMPROVE/NESCAUM sulfate aerosol data is seen from the comparison of the retrieved emission fields. The combined reconstruction produces a SO₂ emission field that is more similar to the IMPROVE/NESCAUM reconstruction than it is to the NADP reconstruction. The region of high emissions in the central region of the East, for the combined reconstruction, is located in the same area as in the IMPROVE/NESCAUM reconstruction, and southwest of the high emission rate region in the NADP reconstruction. Also, grid cells with emission rates above the background are seen in Canada and Mexico that were not present in the NADP reconstruction, but exist in the IMPROVE/NESCAUM reconstruction. This shows the ability of the combined data to resolve sources that do not have any receptors in proximity.

The reconstruction using the combined data sets produced a better emission field as compared to the reconstructions using either data set alone. When fewer than 400/504 eigenvalues are used in the solution, the total standard error of the combined data reconstruction is ~15% lower than the other reconstructions. At low numbers of eigenvalues, the fraction of the total emission rate and emission grid cells that are negative are low for all three reconstructions (< 5%), with the reconstructions using the NADP data being slightly lower. However, above 200 eigenvalues, the combined data have a lower fraction of emission and emission grid cells that are negative. Consequently, the retrieval using the combined data is more stable when larger numbers of eigenvalues are used in the solution than reconstructions using either data set alone. This resulted in the retrieved emission field with the highest resolution where the upper eigenvalue bound for the reconstruction using the combined data was 275/504 compared to 200/504 and 225/504 for the retrievals using the IMPROVE/NESCAUM and NADP data, respectively. Also, the reconstruction using the combined data compared better with the NAPAP SO₂ emission field over the range of suitable eigenvalues.

These results indicate that combining the data produced an emission field with higher resolution, lower standard error, and better comparison with the NAPAP SO₂ emissions than the reconstructions using either the IMPROVE/NESCAUM or NADP data alone produced. The reconstructed emissions demonstrated the higher stability resulting from the large number of receptor sites in the NADP network that covers the entire US. In addition, the combined data allowed for the retrieval of emissions from distant sources that could not be resolved by the NADP data alone.

Comparison of Input Observations to Simulated Observations. One measure of the success of the inversion process is the comparison of the input observations to simulated observation data. The simulated data were generated using the reconstructed emissions and the transfer matrix. This is the forward solution of the SRR presented in Section 2.4, Equation 2-31.

Statistics comparing the simulated to input observations are presented in the Forward Model Fit section of the metrics of the inversion performance (Figure 4-25). These statistics are the correlation coefficient and the ratio of the average values of all input and simulated observation data. However, lost in these statistics is the spatial aspect of the comparison and the differences between the sulfate concentrations and wet deposition rates. In order to investigate these aspects, correlations between the simulated and observed ambient sulfate concentrations and wet deposition rates over the New

Figure 4-33. A) Simulated SO₄^2- wet deposition data, during Q3 1992. Created from the Q3 reconstructed emission field. B) NADP SO₄^2- wet deposition data during Q3 1992.  represent the location of the NADP monitoring sites and the data value.

England and the Central East regions were made (Figure 4-31 & 4-32). Also, a comparison was made between the average simulated and observed Q3 wet deposition rates over the US (Figure 4-33). These figures are identical to those present in Section 3.4.4, Figure 3-21 - 3-22, for the tuning the Monte Carlo model, except the annual 1985 NAPAP SO₂ emission fields were used to generate the simulated data. Consequently, the comparison of these two sets of figures provide an opportunity to test the validity of the reconstructed emissions against the NAPAP emission field.

As shown in Figure 4-31 & 4-32, the Q3 simulated observations match the input data well in the New England and Central East regions. The wet deposition data have slightly higher correlation coefficients than the sulfate concentrations, r = ~0.7 compared to r = ~0.6. Comparing these plots to Figure 3-21 & 3-23, it is evident that there is little to no improvement of the simulated observations using the reconstructed emissions over those generated from the NAPAP emission field.

The spatial comparison of the average Q3 simulated total SO₄^2- wet deposition rates to the NADP data is presented in Figure 4-33. The prominent feature of the average NADP data is the high deposition rates, > 3.5 g/m²/yr over eastern Ohio, Pennsylvania and western New York. The simulated observations also display this region of high deposition, however, it is centered over western Ohio. The simulated observations also have depositions that can exceed 4.5 g/m²/yr throughout northern Virginia and Maryland. The NADP data shows this region to have depositions less than 3 g/m²/yr. Over the rest of the eastern US, the simulated wet depositions match the observed data well with values that vary between 1-2 g/m²/yr. In the West, both the observed and simulated data show that the depositions are generally < 0.5 g/m²/yr.

The discrepancy between the simulated and observed wet deposition data over northern Virginia is not present when the NAPAP emissions are used to simulate the wet deposition rates (Figure 3-22). The overestimation of the wet deposition rates when the reconstructed emissions are used in the simulation results from the high emissions over northern Virginia. These high emissions are due to the IMPROVE data. There are three IMPROVE monitoring sites in this region. As shown in Figures 3-14 & 3-20, using the NAPAP emission field, the average simulated sulfate concentrations underestimated the observed values by a factor of 2 over northern Virginia. The inversion process increased the emissions around northern Virginia, relative to NAPAP, to reduce these residuals. While there are four NADP monitoring sites in this region, the inversion process sacrificed the residuals between the simulated and observed wet deposition data for the reduction in residuals of the sulfate concentrations.

The bias toward fitting the IMPROVE data in northern Virginia can be seen in the three reconstructed SO₂ emission fields. The reconstructed emission field using the combined data in northern Virginia was more similar to the reconstruction using the IMPROVE/NESCAUM data than the NADP data. This implies that the IMPROVE/NESCAUM data had a larger influence upon the reconstruction using the combined data than the NADP data. The reasons for this are not known, however, there were 72 IMPROVE observations compared to 48 NADP observations in this region.

Comparison of the Retrieved SO₂ Emission Field to 1985 NAPAP Emission Field. In order to better understand the similarities and differences between the reconstructed emissions and 1985 NAPAP emission fields, three spatial statistical measures comparing these two emission fields were developed: 1) the absolute difference between the emission grid cells, 2) the percent difference between 25 grid cells in a 5 by 5 grid cell "window" centered over each grid cell, and 3) the correlation between 49 grid cells in a 7 by 7 grid cell "window" (Figure 4-34). The percent difference statistic was calculated for each emission grid cell, by summing all of the reconstructed emission rates and NAPAP emission rates within a 5 by 5 window centered over the grid then subtracting these two values and dividing by the summed NAPAP emissions. The window was then moved to the adjacent grid cell and the procedure was repeated.

The difference map (Figure 4-34A) shows that in the Ohio River Valley, most of the sources with high emission, i.e. greater than 1 kTons/day, in the NAPAP inventory were underestimated, while the emission rates in many of the neighboring grid cells with lower emissions were overestimated. This is a result of the spreading out of the emissions over a larger domain in the retrieval. Also, many of the high emission grid cells in the retrieved emissions inventory are located in source cells next to the high source emission rates in the NAPAP inventory. The percent difference map (Figure 4-34B) shows that in the East, the reconstructed emissions underestimate the NAPAP emissions by about 20% from a region extending from the Great Lakes to Alabama and Mississippi. The largest underestimations are at the Great Lakes and around Toronto where the retrieval did not reproduce the high Toronto emissions in the NAPAP inventory. In the West, the reconstruction generally overestimated the NAPAP emissions by up to a factor of four (Oregon). However, in Colorado and New Mexico, the reconstructed emission severely underestimated the NAPAP emissions by up to a factor of two. In this region, many of sources in the reconstruction had negative emissions.

The spatial correlation map (Figure 4-34C) shows that the best correlations between the reconstructed and NAPAP SO₂ emissions are in the Midwest, with r ~ 0.9 in parts of Iowa and Missouri. Correlations as high as r=0.5 are in the Southeast. The lowest correlations are seen in the West and Canada where r is generally < 0.2. The low correlations in Canada can be attributed to the lack of any receptor sites. As noted previously, the wet deposition data in the US have difficulty resolving sources located north of the receptor sites. Therefore, only the IMPROVE/NESCAUM data could identify the Canadian sources, and this monitoring network has only about 8 receptor sites located near the Canadian-US border. The low and even negative correlations found in the West can be attributed to the low SO₂ emissions in that region. According to the NAPAP inventory, only southern Arizona had emission grid cells with emission rates above 0.25 kTons/day. Consequently, the retrieved western emissions are near the noise level. This can be seen by the standard errors being greater than many of the grid cells emission rates.

In previous sections, it was shown that the best retrieved emission field occurred when the IMPROVE/NESCAUM sulfate and NADP total SO₄^2- wet deposition data were combined together. Consequently, the SO₂ emissions for the other three calendar quarters were retrieved using the combined data. The inversion metrics for Q1, Q2, and Q4 are presented and discussed in Appendix A, where it is shown that the approximate range of suitable eigenvalues is between 75 and 250/504 for all three quarters. The reconstructed emissions at the upper and lower bounds exhibit the same patterns as those for Q3. That is, the lower bound produces a smooth spatial pattern with poorly resolved sources, while at the upper bound instabilities mask many of the features of the emission inventories. Therefore, only the reconstructed SO₂ emissions for the middle number of eigenvalues, 175/504, will be presented.

Reconstructed SO₂ Emissions, Q1. The first quarter reconstructed emission field using 175/504 eigenvalues is presented in Figure 4-35. Using this eigenvalue, the total emission rate over the emission field is 72 kTons/day. This is about 7% lower than the total emission from Q3. The emission pattern shows a rather uniformly distributed emission field over the East with most sources having an emission rate > 0.25 kTons/day. The single highest emission field is in Kentucky with an emission rate of 1.4 kTons/day. Over all, Pennsylvania and New England have the highest average emission rates at greater than 0.9 kTons/day. Over large areas of the West, there are no significant emissions. The highest emission are in southern Arizona and California, ~0.5 kTons/day. No significant emissions are identified in Mexico.

The comparison of the simulated sulfate concentrations and wet deposition rates, using the Q1 reconstructed SO₂ emission field, to the input observation data is presented in the scatter plots in Figures 4-31 & 4-32. In the New England region, the simulated sulfate reproduces the observed data well with r² = 0.8. In the Central East, it is lower with, r² = 0.4. The simulated wet deposition data reproduced the results in the Central East better than in New England, r² = 0.84 compared to r² = 0.5. Both the simulated SO₄^2- wet deposition and ambient concentrations tend to underestimate the observations, as indicated by the slopes of the correlation lines.

Figure 4-35. Reconstructed Q1 SO₂ emission field and standard error using
(n ) IMPROVE/NESCAUM sulfur and (t ) NADP SO₄^2- wet deposition data and 175/504 eigenvalues in the inversion. The negative values have been adjusted.

The simulated sulfate, using the reconstructed emissions, compares more favorably with the IMPROVE/NESCAUM sulfate data than the simulated observations do based upon the NAPAP emission field (Figure 3-21). In New England, the correlations are the same, but the slope of the correlation line decreased from 1.6 to 0.9, while in the Central East domain, the correlations increased from r² = 0.35 to r² = 0.5 when the reconstructed emission were used to create the simulated sulfate. The scatter plots for the wet deposition data have approximately equal correlations and correlation line equations when the simulated SO₄^2- wet deposition data are created using either the reconstructed or NAPAP emissions.

Comparing the average Q1 simulated wet deposition rates to the observed data, Figure 4-36, the simulation reproduces the general pattern of the observed data. However, the simulated data underestimate the observed values in the Ohio River Valley, ~0.6 g/m²/yr compared to ~1.3 g/m²/yr. The simulated wet deposition data using the NAPAP emissions perform better in reproducing the average values, having deposition rates ~1.6 in the Ohio River Valley (Figure 3-22).

The comparison of the retrieved emissions to the NAPAP is presented in Figure 4-37. The difference map shows that all of the emission grid cells with high emissions were underestimated. This was compensated for in the retrieved emission by overestimating the sources with low emissions. The exception to this is in New England where nearly all of the sources had emission rates greater than the corresponding NAPAP. This is displayed in the percent difference map (Figure4-37B) where in New England the reconstruction overestimated the NAPAP emission by more than 60%, but underestimates the NAPAP emissions throughout the Central East by 40 to 60%. In the West, the comparison of NAPAP and reconstructed emissions is more varied.

The spatial correlation plot (Figure 4-37C) shows very poor correlation with the NAPAP emissions, where the correlations are actually negative over much of the East, Canada, and in the West over Wyoming and Montana. The best correlations are seen in the Midwest with a maximum of r = 0.4 over parts of Kansas and Nebraska. The negative correlations over the East are due to the underestimation of the NAPAP emission rates in the Ohio River Valley, and the overestimation in New England, while the low correlations in Canada and the western US occur for the same reasons discussed for the retrieval of Q3 SO₂ emission field.

Figure 4-36. A) Simulated SO₄^2- wet deposition data, during Q1 1992. Created from the Q1 reconstructed emission field. B) NADP SO₄^2- wet deposition data during Q1 1992.  represent the location of the NADP monitoring sites and the data value.

The striking features of the Q1 reconstructed emissions are the uniformity of the emission rates in the Eastern US, and the fact that New England has higher emission rates than the Ohio River Valley does. This emission field differs substantially from the retrieved Q3 and NAPAP SO₂ emission fields.

The two sets of simulated ambient SO₄^2- concentrations and SO₄^2- wet deposition generated from the reconstructed emission field and the NAPAP emission field compare about equally well with the input observations. The only difference being that the reconstruction using the retrieved emissions tends to underestimate the observed data. Consequently, there are two significantly different emission fields that, when combined with the transfer matrices, fit the input observations about equally well. It is highly unlikely that the variations in SO₂ emissions from Q1 and Q3 vary as much as is indicated by the reconstructed emission fields. In fact, the variation between Q1 and Q3 NAPAP emissions is minimal (Figure 4-23). The source of the observed deviations is not known.

Reconstructed SO₂ Emissions, Q2. The Q2 reconstructed emissions using 175/504 eigenvalues are presented in Figure 4-38. Using 175 eigenvalues, the total emission rate over the emission field is 77 kTons/day, which is about equal to the Q3 total emission rate. As shown, the highest density of emission rates occur in the Central East covering Illinois, Kentucky and Ohio where they vary between 0.5 and 1 kTons/day. The highest emissions are located over Maryland at 1.4 kTons/day. Over much of the Great Lakes and Southeast, the emissions vary between 0.3 and 0.6 kTons/day. New England generally displays low emissions, < 0.15 kTons/day, except for a few emission grid cells located along the coast. The only source in Canada with an emission rate greater than the background is located near Toronto. The West shows low emission rates except along the Pacific coast and western Washington, where they can exceed 0.25 kTons/day. In Mexico, an emission grid cell has an emission rate above the background south of Big Bend National Park.

The scatter plots in Figure 4-31 & 4-32 show that the simulated sulfate and SO₄^2- wet deposition observations compare well with the input data. The correlation for the wet deposition rates are r² = 0.88 and r² = 0.83 in the New England and Central East regions, respectively. The correlations are slightly lower for the sulfate data where r² = 0.78 in New England and r² = 0.6 in the Central East. However, like Q1 and Q3, the simulated observations tend to underestimate both the wet deposition data and the ambient sulfate concentrations. The simulated observations using the NAPAP emission fields (Figure 3-21 & 3-23) compared about equally well with the input observations as the simulated

Figure 4-38. Reconstructed Q2 SO₂ emission field and standard error using (n ) IMPROVE/NESCAUM sulfur and (t ) NADP SO₄^2- wet deposition data and 175/504 eigenvalues in the inversion. The negative values have been adjusted.

Figure 4-39. A) Simulated SO₄^2- wet deposition data, during Q2 1992. Created from the Q2 reconstructed emission field. B) NADP SO₄^2- wet deposition data during Q2 1992.  represent the location of the NADP monitoring sites and the data value.

observations using the reconstructed emission field, with some correlations increasing and others decreasing.

The comparison of the Q2 average simulated and NADP wet deposition rates is presented in Figure 4-39. As shown, the largest observed depositions occurs over northern New Jersey, >3.5 g/m²/yr. Wet deposition rates as high as 2.8 g/m²/yr are also in the Ohio River Valley and eastern Tennessee. In the deep south it decreases to ~1 g/m²/yr. The simulated observations do not reproduce the high deposition rates in New Jersey or the Ohio River Valley. However, the simulated observations reproduce the depositions over most of New England well with wet deposition rates ~ 1.5 g/m²/yr, and they do reproduce the high wet deposition rates in Tennessee. Also, the simulated observations show deposition rates greater than 3 g/m²/yr in parts of Virginia and Arkansas that are not seen in the observation wet deposition map. The seasonal pattern for both the simulated and observed wet deposition data shows uniformly low deposition rates in the West, <0.5 g/m²/yr. This simulation using the reconstructed emissions is similar to the simulation using the 1985 NAPAP SO₂ emission field (Figure 3-22).

To better understand the causes of the deviations between the simulated and observed wet deposition rates, comparisons of simulated with observed data from individual sites in northern New Jersey were made where the simulated wet deposition severely underestimated the observed data. The Ringwood, NJ site in the NESCAUM network is located in this region, while the NADP network has the monitoring site Milford, PA located just to the west of Ringwood, NJ. Both receptor sites are located in the same transfer matrix receptor grid cell. Scatter plots that compare the simulated observations, generated by the reconstructed and NAPAP emission inventories, are presented in Figure 4-40. As shown, the simulated sulfate concentrations, using the reconstructed emission field, compare well with the observed sulfate, and have a higher correlation with the observations than the simulated sulfate generated from the NAPAP emission field, r² = 0.59 compared to r² = 0.48. Both simulations reproduce the average observed values. The simulated wet deposition data using the reconstructed and NAPAP emission fields do not compare as well, r² = 0.45, and underestimate the observed wet depositions by nearly a factor of two.

These results show that the wet deposition data had little influence on the retrieved emissions. In fact, the retrieval process optimized the emissions to improve the fit between the simulated and observed sulfate concentrations at the expense of the wet deposition rates. The reason for this is that the simulations using either the reconstructed or NAPAP emission fields reproduce the sulfate concentrations well throughout New England, and except for a narrow band from Lake Erie to New Jersey, the wet deposition rates were well simulated, as seen in Figures 4-39. Consequently, many of the observations in the high wet deposition band were identified as outliers in the robust inversion process and given low weights to reduce their influence upon the reconstruction. This is a demonstration of how the robust procedure "sacrificed" the residuals of the observations at several sites for the reduction of the residuals at many sites.

The comparison of the Q2 reconstructed emissions to the NAPAP inventory is similar to Q3 (Figure 4-41). All of the NAPAP emission grid cells with high emission rates are underestimated by as much as 3 kTons/day. The NAPAP emission grid cells neighboring those with high emission rates were overestimated by the retrieved emissions. In New England and along the Atlantic Coast, the reconstructed emissions are more than 60% greater than NAPAP's (Figure 4-41B). In the central part of the East, the reconstruction has emission rates between 15 and 40% smaller than NAPAP's. In the West, the reconstructed emission rates can be greater than 5 times NAPAP's in the Dakotas and California, while in southern Arizona, northern Utah and Canada, the reconstructed emissions are between 20 and 100% less than the NAPAP emission rates. The spatial correlation map shows that the highest correlations occur over Iowa, with correlations up to r = 0.7, but generally < 0.2 in the rest of the domain.

The reconstructed emissions using the Q2 input produced a less uniform emission field than the Q1 reconstruction, however, the emission grid cells with high emission rates are not as well resolved as those in the Q3 reconstruction. Also, the Q2 reconstruction compares better to the NAPAP emission field than Q1, but not as well as Q3.

Reconstructed SO₂ Emissions, Q4. The Q4 reconstructed emissions using 175/504 eigenvalues are presented in Figure 4-42. Using 175 eigenvalues, the total emission rate over the emission field is 72 kTons/day which is about equal to the Q1 total emission rate, and 7% lower than the total emission from Q2 and Q3. As shown, the emission field has a rather uniform pattern over the eastern US, similar to the Q1 reconstructed emission field. The source with the largest emission rate at ~1 kTons/day is located in Massachusetts. The highest emission region is in Illinois and Indiana where the emission rates are ~0.6 kTons/day. In Canada, north of the Great Lakes there are several sources with emission rates above the background of 0.25 kTons/day. The emissions in the West are similar to the other three quarters, uniformly low emission except in southern Arizona where the emission rate is ~300 kTons/day. Other emission grid cells with emission rates above the background, are at Portland, OR, and Seattle, WA and along the Texas-Mexican border.

Figure 4-42. Reconstructed Q4 SO₂ emission field and standard error using
(n ) IMPROVE/NESCAUM sulfur and (t ) NADP SO₄^2- wet deposition data and 175/504 eigenvalues in the inversion. The negative values have been adjusted.

Figures 4-31 & 4-32 present the comparison of the simulated sulfate concentrations and wet deposition rates to the input observation data. The simulated data were generated from the Q4 reconstructed SO₂ emission field. In both the New England and Central East regions, the simulated sulfate reproduces the observed data well with r² = 0.74 and r² = 0.68, respectively, but on average they underestimate the observed concentrations, with correlation line slopes of ~0.75. The simulated wet deposition data have higher correlations with the observation data with r² ~ 0.8 in both regions. Comparing these scatter plots to those produced using the NAPAP emission field, Figure 3-21 & 3-23, the simulated sulfate using the reconstructed emissions significantly reduces the scatter in the

Figure 4-43. A) Simulated SO₄^2- wet deposition data, during Q4 1992. Created from the Q4 reconstructed emission field. B) NADP SO₄^2- wet deposition data during Q4 1992.  represent the location of the NADP monitoring sites and the data value.

Central East, r² = 0.68 compared to r² = 0.4. In New England, the correlations are about the same, but the slope of the correlation line decreased from 1.2 to 0.73. The correlation plots for the wet deposition data show a slight increase in the scatter using the reconstructed emissions.

The average Q4 simulated wet deposition rates compare well with the observations (Figure 4-43). In the East, both observed and simulated wet deposition rates are approximately 1.5 g/m²/yr. The simulation reproduces the highest deposition rates over Illinois at ~2 g/m²/yr, and the lowest eastern deposition rates over the Smoky Mountains, ~ 0.8 g/m²/yr. The simulation also reproduces the low wet deposition rates throughout the West, less than 0.5 g/m²/yr, and the higher deposition rates along the Northwest coast ~0.8 g/m²/yr.

The comparison of the retrieved emissions to NAPAP is presented in Figure 4-44. The difference map shows that all of the sources with high emission rates were underestimated. This was compensated for in the retrieved emissions by overestimating the sources with low emission rates. In New England, the emission rates were all greater than the corresponding NAPAP rates. The largest overestimation occurred along the Atlantic Coast, where the reconstructed emission rates were about three times NAPAP's. As shown by the percent difference map in Figure 4-44B, the reconstruction overestimated the NAPAP emissions by more than 60% along the entire Atlantic Coast. However, from the Great Lakes to northern Alabama, the reconstruction had emission rates on average 50% smaller than NAPAP's. Along the Pacific Coast and Great Plains the reconstructed emissions were greater than NAPAP's by as much as a factor of 10. But from western Montana to northern Texas, the reconstructed emissions were less than the NAPAP emissions from 10 to 100%. This is expected because many of the sources in this region had negative reconstructed emission rates.

As with the other quarters, the spatial correlation plots have the highest correlation with the NAPAP emission field in the Midwest where the correlation is

generally above 0.4, with a maximum correlation of r = 0.7 over parts of Iowa. In the West and Canada, the correlations are generally less than 0.2 and some are even negative.

The Q4 reconstruction is most like Q1, having the same relatively uniform emission rates over the East. However, the Q4 reconstruction has a higher emission density over the Ohio River Valley and compares better with the NAPAP emission field.

Two independent observation data sets, IMPROVE/NESCAUM sulfate aerosol and NADP SO₄^2- wet deposition rates, were available for the retrieval of SO₂ emission fields. Combining these data produced a retrieved emission field with higher resolution and lower standard error that compared better to the 1985 NAPAP emission inventory than retrievals using either data set alone. Demonstrating the benefits of increasing the amount of data used in the retrieval process.

Using the combined data, the total emission rates during the summer, Q2 and Q3, were about 7% greater than during the winter, Q1 and Q4 (Table 4-3). The total reconstructed emission rates were about 10% greater than the NAPAP emission fields except for Q1 where they were equal. The reconstructed emissions during the summer reproduced the high emission rates in the Ohio Valley and northern Alabama and Georgia seen in the NAPAP inventory. However, in these regions, the retrieved emissions underestimated the emission grid cells with high emission rates and overestimated the neighboring grid cells with low emission rates. The retrieved emissions in the West had uniformly low emission rates, with the largest occurring in southern Arizona and

California, ~ 0.4 kTons/day. The largest Mexican emissions were along the Texas-Mexico border, ~0.4 kTons/day. During the winter, the reconstructed emissions were uniformly spread out over the eastern US. This uniform pattern was not seen in the NAPAP inventory. The cause of this discrepancy is not known. Using the reconstructed SO₂ emission fields and transfer matrices, the input observation data were simulated. It was found that for all quarters, the simulated data reproduced the general spatial and temporal patterns of the input data, but tended to underestimated them by about 10 - 20%. The simulated observations using the reconstructed emissions compared to the input data about as well as the simulated data using the NAPAP emissions.

In the atmosphere, ammonia exists as either ammonia gas, NH₃, or as ammonium, NH₄⁺ in an aerosol. In the following discussion, the term "ammonia" refers to both NH₃ and NH₄⁺. Atmospheric concentrations of ammonia is the result of direct emissions of ammonia and ammonium containing species into the atmosphere. The significant sources of are animal waste, ammonification of humus followed by emission from soils, emissions from ammonia based fertilizers applied to soils, and industrial emissions. Other ammonia sources result from anthropogenic activities, with animal waste being the chief contributor. Stedman and Shetter (1983) estimate that in the northern hemisphere the anthropogenic NH₃ emissions are ~100 kTons/day, with natural emissions of 170 kTons/day. Over the contiguous US, Harris and Michaels (1982) estimate that the anthropogenic emissions are ~10 kTons/day, while EPA (1984) estimate the natural emissions to be ~3.5 kTons/day, for a total NH₃ emission rate of 13.5 kTons/day.

The 1985 NAPAP emission inventory contains an estimate of the NH₃ emission rate. Figure 4-45, presents the seasonal NAPAP emission fields, and Table 4-4 list the total emission rates over the entire emission field. The total annual NAPAP emissions are more than a factor of 2 less than those estimated by Harris and Michaels (1982), and EPA (1984). The cause of this discrepancy is not known, but it does provide an illustration of the overall uncertainty associated with the NH₃ emission fields.

The largest NH₃ emission density occurs from Iowa to Indiana, with Q2 and Q4 having higher emissions than Q1 and Q3. The Detroit, MI - Toledo, OH and Washington, DC emission grid cells have emission rates ~1 kTons/day. This is an order of magnitude larger than that of any of the other emission grid cells. For example, the Q2 emissions in all of Iowa are ~0.5 kTons/day, half of the Detroit, MI-Toledo, OH emission grid cell value.

The ammonia emissions in North America result in surface concentrations ranging from 0.5 to 25 ppb (McClenny and Bennett, 1980; Levine et al., 1980), with average sea level estimates in the Northern Hemisphere of ~1 ppb of NH₃ and 1.5 mg/m³ of NH₄⁺ (Seinfeld, 1986). NH₃ is readily absorbed by surfaces such as water, soil, and vegetation. Consequently, dry and wet deposition causes the ammonia to have atmospheric residence times on the order of several days. NH₃ can be oxidized to NO_X, but the gas-phase chemistry of NH₃ is not well understood, and a quantitative loss rate of NH₃ due to the reaction is not available (Seinfeld, 1986).

Surface concentration data of NH₃ and NH₄⁺ over North America were not available for the retrieval of ammonia emission fields. However, the NADP monitoring network measured the NH₄⁺ wet deposition rates consisting of the removal of the NH₃ and NH₄⁺ by precipitation. The kinetic probabilities, P_k, characterizing the ammonia wet deposition rates in the transfer coefficient was estimated from the same P_k characterizing the wet deposition of SO₂ and SO₄^2-. The use of the SO₂ - SO₄^2- wet deposition transfer matrices is justified on the following grounds. First, atmospheric SO₄^2- is usually neutralized by ammonia. Therefore, a fraction of the emitted ammonia will have the same removal rates as the SO₄^2- aerosol. Second, it is believed that the dry deposition rates of NH₃, are similar to the SO₂ dry deposition rates. Dry deposition is dependent upon the ability of the molecules of a gas to be transported to a surface and subsequently transferred onto the surface. The transport of a gas to the surface is the result of atmospheric turbulence, wind speed, molecular diffusion, and etc. These processes are equal for all gases. The uptake of a molecule at the surface is dependent upon how well the surface can "capture" the molecule and is also dependent upon the solubility or absorptivity of the species. Both NH₃ and SO₂ are highly soluble and readily deposited on surfaces. The dry deposition mechanisms are complex leading to high uncertainty in the deposition rates. These uncertainties will mask any differences between the NH₃ and SO₂ dry deposition rates, and the SO₂ rates should be applicable to NH₃. In fact, the EMEP Lagrangian acid deposition model used to study the long range transmission of air pollutants in Europe assumes equal dry deposition rates for NH₃ and SO₂ (Tuovinen et al., 1994)

The wet deposition rates are dependent upon the species’ solubility and precipitation rate. The solubility of the SO₂ is inversely dependent upon the acidity of the solution. This dependence was taken into account in the SO₂ wet deposition rates by using the SO₂ column concentrations as a measure of the acidity (Section 3.4.3). The solubility of NH₃ is directly dependent on the acidity of the solution. At the acidity typically found in the atmosphere, 3-6 pH, the solubility of NH₃ can be an order of magnitude greater than the solubility of SO₂ (Hegg and Hobbs, 1984). The difference in the SO₂ and NH₄⁺ solubility rates and their inverse relationship to the solution acidity will certainly be a source of error in the retrieval. However, wet deposition rates are highly dependent upon the precipitation frequency and rates. In regions of high precipitation frequency and/or rates, the high solubility of SO₂ causes it to be quickly washed out of the airmass, thus differences between the SO₂ and NH₃ wet deposition rates will be reduced.

It is expected that, on average, the SO₂ wet removal rate will underestimate the NH₃ wet removal rates causing NH₄⁺ deposition rates to be also underestimated. In the retrieval process, the low deposition rates will be compensated for by overestimating the NH₃ emissions.

The seasonal NH₃ emission fields were retrieved by inverting the SRR using the 1992 NADP NH₄⁺ wet deposition data. Appendix B presents the metrics of the inversion performance, and the determination of the suitable eigenvalue range for each season. Table 4-5 presents the middle number of eigenvalues used in each season and the correlation between the input observations and simulated observations from the forward model fit metrics. As shown, the correlations range between r = 0.55 and 0.7. The correlations between the simulated and observed SO₄^2- concentration and wet deposition rates were between r = 0.8 and 0.9. The poorer comparison between the simulated and observed NH₄⁺ data is an indication that the SO₂-SO₄^2- transfer matrices are not completely adequate for the simulation of NH₄⁺ wet deposition. If this is so, then the retrieved emissions could be in error because they are compensating for the inadequate transfer matrices.

The "best" reconstructed NH₃ seasonal emission fields and standard error, using the number of eigenvalues in Table 4-5 are presented in Figures 4-46 - 4-49. These figures show a seasonal pattern with the largest emissions occurring during Q2. The total Q2 emission rate is 22 kTons/day, compared to 14-17 kTons/day for the other three quarters (Table 4-6). The highest emission densities are in and around the Great Lakes. Many emission grid cells from North Dakota to New York have emission rates greater than 0.15 kTons/day, and can exceed 0.3 kTons/day from Illinois to Ohio during Q1 and Q2. The emission rates are lower during Q3 and Q4 and display a more uniform pattern over this region. In the Southeast, high emissions are found in northern Alabama and Georgia for all four quarters where they range between 0.1 and 0.2 kTons/day. Also, high emission rates are seen in southern Louisiana. During Q1, one emission grid cell has an emission rate of 3 kTons/day, but for the other quarters the emission rates are all less than 0.5 kTons/day.

Figure 4-46. Reconstructed Q1 NH₃ emission field and standard error calculated from NADP NH₄⁺ wet deposition data and SO₂ - SO₄^2- transfer matrices. 125/504 eigenvalues were used in the inversion. The negative values have been adjusted. t represent the locations of the NADP monitoring sites

Figure 4-47. Reconstructed Q2 NH₃ emission field and standard error calculated from NADP NH₄⁺ wet deposition data and SO₂ - SO₄^2- transfer matrices. 100/504 eigenvalues were used in the inversion. The negative values have been adjusted. t represent the locations of the NADP monitoring sites

Figure 4-48. Reconstructed Q3 NH₃ emission field and standard error calculated from NADP NH₄⁺ wet deposition data and SO₂ - SO₄^2- transfer matrices. 125/504 eigenvalues were used in the inversion. The negative values have been adjusted. t represent the locations of the NADP monitoring sites

Figure 4-49. Reconstructed Q4 NH₃ emission field and standard error calculated from NADP NH₄⁺ wet deposition data and SO₂ - SO₄^2- transfer matrices. 125/504 eigenvalues were used in the inversion. The negative values have been adjusted. t represent the locations of the NADP monitoring sites

The NH₃ emissions in the West are significantly less than those in the East. The largest emissions are in California during Q1 and Q4 where several emission grid cells have emission rates around 0.3 kTons/day. The emission grid cells from Oregon to Texas have emission rates ranging from 0.05 to 0.13 kTons/day. For most of the rest of the West they are below 0.05 kTons/day. Mexico has several emission grid cells above the background emission rate of 0.05 kTons/day along the Texas-Mexican border, as well as south of Arizona during Q1, Q2 and Q4.

There are no significant emissions in Canada. This is a pattern seen in all four quarters of the reconstructed NH₃ emission fields. As discussed in the subsection of 4.5.1 "Emissions Retrieved Using NADP Wet Deposition Data", this is most likely the result of not having any Canadian wet deposition monitoring sites, as opposed to uniformly low Canadian emissions.

Comparing the reconstructed emissions to the NAPAP NH₃ emission fields, Figure 4-45 and Table 4-4, the total reconstructed emissions are about 2.5 times larger than NAPAP's. However, they are only about 25% larger than those estimated by combining the anthropogenic emission of Harris and Michaels (1982) and the natural emissions of EPA (1984). Also, the Q4 NAPAP total emissions are about equal to Q2, but for the reconstructed emissions the Q4 total emission rate is the lowest, 14 kTons/day. The overestimation of the total reconstructed emission rate over the other two estimates is evidence that the SO₂ washout ratios used for NH₃ were, on average, too low.

Comparing the reconstructed to NAPAP NH₃ emission fields, Figure 4-45, the high reconstructed emission rates in and around the Great Lakes are shifted west and centered over Iowa in the NAPAP inventory. The high NAPAP emissions over Washington, DC are also not seen in the reconstructed emissions. However, both emission fields indicate high emission rates in southern Louisiana. In the West, both the reconstruction and NAPAP have the largest emission rates in California and high emissions in eastern Texas. The NAPAP emission fields show uniformly low emission rates throughout the rest of the West, while the reconstructed emissions have emission grid cells with rates from 0.05 to 0.25 kTons/day in Colorado, Utah, and Oregon.

The largest difference between the reconstructed and NAPAP emission fields is the shift of the high emission rate grid cells from the Industrial Midwest to Iowa during Q2. One possible cause for this discrepancy is that the high NAPAP emissions at the Detroit - Toledo Ohio grid cell have been spread out over the Industrial Midwest. The reconstruction used only one fifth of the possible number of eigenvalues in the solution. This will cause the emission rates to be spread out over neighboring cells as was seen in the SO₂ reconstructions.

Another possible cause of the discrepancy has to do with using the SO₂ washout ratios to simulate NH₃ wet removal. The SO₂ washout ratio is defined as being inversely dependent upon the SO₂ concentration (Section 3.4.3) simulating its dependence on the solution acidity. The true washout ratio of NH₃ is directly dependent on the solution acidity. The largest SO₂ concentrations occur over the Industrial Midwest causing the SO₂ washout ratios in this region to be about two times larger than those occurring over Iowa. The simulated NH₃ deposition rates will be underestimated relative to those in Iowa and surrounding regions. The retrieval process most likely compensated for this by increasing the emission rates of those sources with the largest impact on the receptors in the Industrial Midwest. These sources are also located in the Industrial Midwest (see Section 3.5).

As shown in Figures 4-50 - 4-53, the simulated wet deposition rates do reproduce the spatial pattern of the NADP data, but they tend to underestimate the input data by about 20%. During Q1, high deposition rates, ~0.3 g/m²/yr, in Iowa, southern Louisiana, and along the California coast are evident in both the simulated and observed data. The Q2 simulated data reproduces the high deposition rates in southern Minnesota, Ohio, and Oklahoma, and the low rates in the Southeast and the West. The underestimation of the observed wet deposition rates is particularly noticeable in southern Minnesota where the observed NH₄⁺ deposition rate is about 0.7 g/m²/yr compared to ~0.55 g/m²/yr, for the simulation. During Q3, both the simulated and observed data have the highest deposition rates occurring around the Great Lakes, between 0.3 - 0.4 g/m²/yr, which decreases moving away from this region. The simulation matches the highest deposition rates found in Iowa, > 0.5 g/m²/yr, but does not reproduce the high deposition rate in central California. During Q4, both the simulated and observed wet deposition rates are the largest, >0.2 g/m²/yr, stretching from Missouri to Michigan, and the lowest in Florida, Maine, and the Smoky Mountains.

Comparing the Q2 wet deposition map to the emission field, it is seen that there is a displacement between the region of highest deposition rates in southern Minnesota, and the highest emission rates in a region from Illinois to Ohio. Two possible causes of this displacement are that precipitating airmasses tend to travel to the northwest from the high NH₃ emission region where they contribute to the large deposition rates in southern Minnesota, and that the frequency and rate of precipitation in Minnesota were higher than in surrounding areas. Examination of transfer matrices and precipitation fields revealed that both the transport and precipitation frequency contributed to this displacement. In Section 3.5, receptor oriented Q2 transfer matrices for the Minnesota (Figure 3-28) and other receptors are displayed. As can be seen, sources with high emission rates from Iowa and western Illinois contribute to the deposited mass. Also, the total relative source contribution at the Minnesota receptor is 0.0054, while at the nearby Illinois receptor it is 0.0027. This is due to the higher precipitation rates at Minnesota, ~ 1 m/yr compared to 0.4 m/yr in Illinois.

Figure 4-50. A) Simulated NH₄⁺ wet deposition rates, during Q1 1992. Created from the Q1 reconstructed NH₃ emission field. B) NADP SO₄^2- wet deposition rates during Q1 1992. t represent the location of the NADP monitoring sites and the data value.

Figure 4-51. A) Simulated NH₄⁺ wet deposition rates, during Q2 1992. Created from the Q2 reconstructed NH₃ emission field. B) NADP SO₄^2- wet deposition rates during Q2 1992. t represent the location of the NADP monitoring sites and the data value.

Figure 4-52. A) Simulated NH₄⁺ wet deposition rates, during Q3 1992. Created from the Q3 reconstructed NH₃ emission field. B) NADP SO₄^2- wet deposition rates during Q3 1992. t represent the location of the NADP monitoring sites and the data value.

Figure 4-53. A) Simulated NH₄⁺ wet deposition rates, during Q4 1992. Created from the Q4 reconstructed NH₃ emission field. B) NADP SO₄^2- wet deposition rates during Q4 1992. t represent the location of the NADP monitoring sites and the data value.

The seasonal NH₃ emission fields were reconstructed using the 1992 NADP NH₄⁺ wet deposition rates, and SO₂ - SO₄^2- wet removal kinetics. The reconstructed emissions peaked during Q2 with a total emission rate of 22 kTons/day, and were the lowest during Q4 at 14 kTons/day. These total emission rates are about 2.5 times larger than those in the NAPAP emission inventory, but only 25% larger than those estimated by combining the anthropogenic emissions of Harris and Michaels (1982) with the natural emissions of EPA (1984). It is believed that the reconstructed emission rates are overestimated due to the SO₂ washout ratio underestimating the actual NH₃ wet removal rates. During all quarters, the largest reconstructed emission rates were in and around the Great Lake states from North Dakota to New York. During Q2, the NAPAP emission fields showed many of the emission grid cells with high emission rates centered over Iowa. However, in the reconstructed emission field they were in the Industrial Midwest states. A possible cause of this is that the SO₂ washout ratios were inadequate for the simulation of the NH₃ wet deposition in this region.

Two important oxides of nitrogen encountered in the atmosphere are nitrogen oxide, NO, and nitrogen dioxide, NO₂, and are collectively referred to as NO_X. These oxides are important species in air pollution participating in smog formation, acid rain, visibility degradation, among other air pollution issues. Natural sources of NO_X include emission from biological processes, forest fires, and lighting. Practically all anthropogenic NO_X is the result of combustion of fossil fuels in stationary and mobile sources (Seinfeld 1986; Manahan, 1994). Natural sources are globally distributed, and emit several times as much NO_X as anthropogenic sources (National Research Council 1976; Manahan, 1994). However, anthropogenic sources tend to be consolidated in small areas. The consolidation of the anthropogenic sources causes high NO_X concentrations, which leads to air pollution problems. Concentrations in the clean troposphere range from 0.01-0.05 mg/m³ for NO and 0.2 - 1 mg/m³ for NO₂. The concentrations in urban centers range from 50 - 1000 mg/m₃ for NO and 100 - 500 mg/m³ for NO₂ (Seinfeld, 1986; EPA 1984). Most anthropogenic NO_X enters the atmosphere as NO, but the conversion to NO₂ is relatively rapid. It is customary to report NO_X emissions as NO₂.

The 1985 NAPAP emission inventory contains an estimate of the NO₂ emission rates. Figure 4-54, presents the seasonal NAPAP emission fields, and Table 4-7 has the total emission rate over the entire emission field. As shown, there is almost no seasonal variation. The highest emission rates occur in the Ohio River Valley ranging between 0.4 - 1 kTons/day. Other areas with emission greater than 0.5 kTons/day are Illinois, around Lake Erie, from Washington, DC to New York City, and from east Texas to southern Louisiana. In the West, the emission rates around Los Angeles and San Francisco are between 0.1 and 0.3 kTons/day. Also, at the four corners the emission rate is ~0.3 kTons/day.

Nitrogen oxides are highly insoluble and have very low wet and dry deposition rates. Their primary means of removal is the oxidation of NO_X to nitric acid, HNO₃, which is readily removed by dry and wet deposition. The oxidation of NO_X to HNO₃ is a fast reaction. In an urban environment, during the midday under sunny summer skies, the transformation rate can be as high as 20 - 30 %/hr with a daily average rate of 16.4 %/day (Calvert and Mohnen, 1983; Stockwell and Calvert 1983). HNO₃ is a highly soluble material, and has higher wet and dry deposition rates than SO₂ (National Research Council, 1983; Seinfeld, 1986; Tuovinen et al., 1994). An alternative oxidation pathway for NO_X is to PAN which occurs in the formation of smog. PAN can then decay back to NO₂ extending the atmospheric residence of the NO_X nitrogen.

The available data for the retrieval of NO₂ emission fields were the NO₃^- wet deposition data from the NADP monitoring network. The SO₂ - SO₄^2- wet deposition transfer matrices were used in the retrieval process. NO_X nitrogen has a very different kinetic history than SO₂ sulfur, and the SO₂ - SO₄^2- wet deposition transfer matrices will most likely produce over and underestimations of the NO_X source contributions to receptors. The insolubility of NO_X will cause the transfer matrices to overestimate the nearby source contributions to receptors. In addition, the high transformation rate of NO₂ to HNO₃ and the high dry deposition rate of HNO₃ relative to SO₂ can conceivably result in the transfer matrices overestimating the source contributions from distant sources. It is not known whether or not the differences in the NO_X kinetics from the SO₂ - SO₄^2- kinetics will balance out in the retrieval, and how it will affect the resulting emission fields.

The seasonal NO₂ emission fields were retrieved by inverting the SRR using the 1992 NADP NO₃^- wet deposition data. Appendix C presents the metrics of the inversion performance, and the determination of the suitable eigenvalue range for each season. Table 4-8 presents the middle number of eigenvalues used in each season and the correlation between the input and simulated observations from the forward model fit metrics. As shown, the correlation for all four quarters is about r = 0.75. This is not as high as was found for the SO₂ reconstructions where r = 0.8 - 0.9, but it is higher than that of the NH₃ reconstructions where r = 0.55 - 0.7. The high correlations for the NO₂ is evidence that the SO₂ - SO₄^2- wet deposition transfer matrices are not inadequate for the simulation of NO₃^- wet deposition. However, this provides no information as to whether the emission retrieved emission fields are correct. Given a different set of transfer matrices, different emission fields would be reconstructed that could conceivably have correlations between the input and simulated observations greater than or equal to r = 0.75.

Using the middle number of eigenvalues, 125/504, the reconstructed NO₂ emission fields and their accompanying standard errors are presented in Figures 4-55 - 4-58, and the total emission rates in Table 4-9. There is some seasonality in the total emission rates with the largest emissions during Q1, 69 kTons/day and the lowest emission rates during Q3, 54 kTons/day, but the emission pattern does not change significantly with season.

In the East, the largest emissions occur around the Ohio River Valley and in the Industrial Midwest where they exceed 0.8 kTons/day. Emission rates ranging from 0.4 - 0.9 kTons/day are also found in and around Lake Michigan, New York state and along the East coast from Massachusetts to Washington, DC. During Q3 the East Coast emissions are lower, < 0.6 kTons/day. In the Southeast, the emission rates are the largest in Alabama and Georgia where they are greater than 0.6 kTons/day during Q1. Southern Louisiana also has high emission rates exceeding 0.4 kTons/day in every quarter with the emission rate from one emission grid cell > 1 kTon/day during Q2.

In central and southern California during Q1 and Q4 there are several emission grid cells with emission rates above 0.6 kTons/day, and one with a Q4 emission rate of 1.2 kTons/day. Except during Q4, Colorado has several emission grid cells with emission rates between 0.3 and 0.5 kTons/day. Mexico does not have any emissions above the background, except around Big Bend National Park, TX during Q2 and Q4. Canada does not have any emission grid cells with emission rates above the background. This further displays the inability of the system to retrieve Canadian sources without any wet deposition monitoring sites in this region.

Comparing the reconstructed emissions to the NAPAP NO₂ emission fields, Figure 4-54 and Table 4-7, the total reconstructed emissions are about 60% larger than NAPAP's. Also, the reconstruction has a more defined seasonality in the emission rates compared to NAPAP. Comparing the reconstructed emission patterns to NAPAP’s, it is seen that both show high emissions in Illinois, Ohio River Valley, and around Lake Erie. The reconstructed emissions tend to be spread out over a larger domain. As discussed in Section 4.3, this is an inevitable result of the inversion process used to retrieve the emissions. The NAPAP emission fields also show emission rates >0.2 kTons/day in Georgia, Florida, and southern Louisiana. In and around all of these areas, the reconstructed emissions have emission rates in excess of 0.2 kTons/day. In the West, NAPAP has significant emissions in east Texas that are not present in the reconstruction. Also, the reconstruction show emission rates greater than 0.8 kTons/day in California during Q1 and Q4. In NAPAP, only the Los Angeles and San Francisco emission grid cells have rates above 0.2 kTons/day.

The simulated seasonal NO₃^- wet deposition field and the accompanying observed wet deposition field are presented in Figures 4-59 - 4-61. The simulated data reproduced the general observed wet deposition patterns for all four quarters, but underestimated the observed values by about 15% on average. In the West, the uniformly low NO₃^- wet deposition rates are reproduced along with the depositions greater than 0.5 g/m²/yr in California and Colorado during Q1 and Q4. In the East, both the simulation and observed data show that the highest deposition rates are in the Great Lake States and New York. The observed data show deposition rates below 1 g/m²/yr from Mississippi to Georgia in all four quarters. The simulated depositions reproduce this except during Q3 where the deposition rates are above 1 g/m²/yr in Alabama and Georgia.

The Q2 observed wet deposition rates show a high deposition band, >1 g/m²/yr, from Minnesota to the Gulf of Mexico, with a maximum deposition of 1.8 g/m²/yr in Oklahoma. The simulated wet deposition field generally reproduced this high deposition band, but underestimates the deposition rates, with a deposition rate of 1.5 g/m²/yr in Oklahoma. In the reconstructed emission field, Figure 4-56, most of the emission grid cells surrounding Oklahoma have low emission rates, between 0 and 0.1 kTons/day. This raises the question of where the NO₃ mass that is deposited in Oklahoma came from, and why the Oklahoma deposition rates are higher than those in nearby locations, such as in Missouri and Illinois, which are surrounded by higher emission rates, but have wet deposition rates less than half of Oklahoma's. This question can be answered by examining the Q2 receptor oriented transfer matrices for the Oklahoma and an Illinois receptor grid cell (Figure 3-28 and 3-30 in Section 3.5).

As shown, both the non weighted and the weighted receptor oriented transfer matrices show that a larger source domain impacts the Oklahoma receptor compared to the Illinois receptor. Also, the relative source contributions are much greater for the Oklahoma than the Illinois receptor. Integration over the spatial domain of the transfer matrices shows a total relative source contribution of 0.009 for Oklahoma and 0.0027 for the Illinois receptor. Although, sources with higher emission rates impact Illinois as opposed to the Oklahoma receptor, more sources impact the Oklahoma receptor, and on average contribute more than three times the relative source emissions. As discussed in Section 3.5, the primary cause of the different relative source contributions to these receptors is the higher precipitation rates and frequencies at Oklahoma. These results show that areas of high wet deposition can exist in regions of low emission rates due to the spatial variability of precipitation rates and frequencies. In the emission retrieval process, the low emission rates in high deposition regions, and vice versa, are retrieved because the information of the varying precipitation rates and frequencies are part of the wet deposition transfer matrices.

Figure 4-59. A) Simulated NO₃^- wet deposition rates, during Q1 1992. Created from the Q1 reconstructed NO₂ emission field. B) NADP NO₃^- wet deposition rates during Q1 1992. Ž represents the location of the NADP monitoring sites and the data value.

Figure 4-60. A) Simulated NO₃^- wet deposition rates, during Q2 1992. Created from the Q2 reconstructed NO₂ emission field. B) NADP NO₃^- wet deposition rates during Q2 1992. Ž represents the location of the NADP monitoring sites and the data value.

Figure 4-61. A) Simulated NO₃^- wet deposition rates, during Q3 1992. Created from the Q3 reconstructed NO₂ emission field. B) NADP NO₃^- wet deposition rates during Q3 1992. Ž represents the location of the NADP monitoring sites and the data value.

Figure 4-62. A) Simulated NO₃^- wet deposition rates, during Q4 1992. Created from the Q4 reconstructed NO₂ emission field. B) NADP NO₃^- wet deposition rates during Q4 1992. Ž represents the location of the NADP monitoring sites and the data value.

The seasonal NO₂ emission fields were reconstructed using the 1992 NADP NO₃^- wet deposition rates, and the SO₂ - SO₄^2- wet removal kinetics. The reconstructed emissions show some seasonality in the total emission rates, with the highest emissions occurring during Q1 (69 kTons/day), and the lowest during Q3 (54 kTons/day). The emission patterns had little seasonality. The largest reconstructed emission rates were in the Ohio River Valley and the Industrial Midwest (0.4 - 1 kTons/day). Emission grid cells around Lake Michigan, and from Massachusetts to Washington, DC had emission rates that could exceed 0.8 kTons/day. The spatial pattern of the reconstructed emission fields were similar to the NAPAP inventory, indicating high emissions in the same regions as NAPAP shows. However, the reconstructed emission were spread out over a larger domain, and were approximately 60% greater than NAPAP's. Using the reconstructed emission fields, the input observation data were simulated. The results were able to reproduce the general spatial and temporal trends of the observed data. The simulation also compared well with the observed data on a point by point basis with correlations of r = 0.75.