Appendix A
Metrics of the Inversion Performance for the Retrieval of Q1, Q2, and Q4 SO2 Emission Fields
The retrieval of the Q1, Q2, and Q4 SO2 emissions was accomplished by combining the IMPROVE/NESCAUM sulfate aerosol and NADP SO42- wet deposition data. The number of input observations for all three quarters was approximately 2900, resulting in an overdetermined system of over 5.5 observations per unknown emission grid cell. The inversion metrics for Q1, Q2, and Q4 are presented in Figures A-1 - A-3. The metrics have been calculated for a maximum of 300 out of 504 eigenvalues. This is because, after examining the reconstructions during Q3 (see Section 4.5.1) it was found that it was not meaningful to examine reconstructions using more than 300 eigenvalues.
Examining the metrics of inversion for Q1, the obvious lower bound is 75/504 eigenvalues, where the total reconstructed emission and forward model fit metrics begin to level off (Figure A-1C & E). An appropriate upper bound is approximately 250/504, where the total standard error equals the total reconstructed emissions, 25% of sources have negative emission rates, and about 20% of the total emission rate is negative. For both Q2 and Q4, the total reconstructed emission rate and forward model fit metrics (Figure A-2C & E & A-3 C & E) changed little as the number of eigenvalues increase. For example, the correlation coefficient between the input and simulated observations varies between 0.8 and 0.86 as the number of eigenvalues used in the solution increases from 25 to 300/504. However, the greatest changes occur when less than 75/504 eigenvalues are used, leading to 75/504 eigenvalues as the lower bound. The upper bounds for Q2 and Q4 can be set at 250/504 eigenvalues where the total standard error is approximately equal to the total reconstructed emission, and the fraction of negative emissions and source are all above 20%.
Figure A-1. Metrics of the inversion performance for the reconstructed Q1 SO2 emission field using IMPROVE/NESCAUM sulfur and NADP SO42- wet deposition data. The metrics are: A) The value of the eigenvalues. B) Trade-off curve between chi-square and norm of reconstructed emissions. C) Total reconstructed emission rate. D) Total standard error. E) Ratio of the average simulated and input observations and their correlation F) Ratio of the negative reconstructed emission rates to the total, and the fraction of the emission grid cells with negative emission rates. G) Correlation coefficient between the reconstructed and NAPAP emission rates. H) Ratio of the total reconstructed to NAPAP emission rates, and norm of the emission fields.
Figure A-2. Metrics of the inversion performance for the reconstructed Q2 SO2 emission field using IMPROVE/NESCAUM sulfur and NADP SO42- wet deposition data. The metrics are: A) The value of the eigenvalues. B) Trade-off curve between chi-square and norm of reconstructed emissions. C) Total reconstructed emission rate. D) Total standard error. E) Ratio of the average simulated and input observations and their correlation F) Ratio of the negative reconstructed emission rates to the total, and the fraction of the emission grid cells with negative emission rates. G) Correlation coefficient between the reconstructed and NAPAP emission rates. H) Ratio of the total reconstructed to NAPAP emission rates, and norm of the emission fields.
Figure A-3. Metrics of the inversion performance for the reconstructed Q4 SO2 emission field using IMPROVE/NESCAUM sulfur and NADP SO42- wet deposition data. The metrics are: A) The value of the eigenvalues. B) Trade-off curve between chi-square and norm of reconstructed emissions. C) Total reconstructed emission rate. D) Total standard error. E) Ratio of the average simulated and input observations and their correlation F) Ratio of the negative reconstructed emission rates to the total, and the fraction of the emission grid cells with negative emission rates. G) Correlation coefficient between the reconstructed and NAPAP emission rates. H) Ratio of the total reconstructed to NAPAP emission rates, and norm of the emission fields.
Appendix B
Metrics of the Inversion Performance for the Retrieval of Seasonal NH3 Emission Fields
The Q1 NH3 emission field was retrieved by inverting the source receptor relationship using the NADP NH4+ wet deposition data during Q1 1992. There were 1352 observations available creating and overdetermined system by a factor of ~2.7. The metrics of inversion are presented in Figure B-1. As shown, the total reconstructed emission rate increases slightly from 16.7 to 19 kTons/day as the number of eigenvalues used in the solution increases from 50 and 200/504. Based on these metrics, an appropriate lower bound is 50/504 eigenvalues where the correlation between the input and simulated observation values is r = 0.56, and the ratio of their averages is 0.68, about 20% and 15% less respectively then using 300/504 eigenvalues in the solution (Figure B-1E). The upper bound of eigenvalues is 175/504, where approximately 25% of the total emission rate and emission grid cells are negative (Figure B-1F), and the total standard error is about 33% greater than the total emission rate. Above 175/504 eigenvalues, the percent of the total emissions that are negative increases substantially. The range of suitable eigenvalues for Q1 is 50 - 175/504, and the middle number of eigenvalues to use in the solution is 125/504.
The retrieval of the Q2 NH3 emissions was conducted using 1322 NH4+ wet deposition rate observations, creating an over determined system by a factor of ~2.6. The metrics of inversion are presented in Figure B-2. The lower bound of eigenvalues is ~75/504 where the correlation between the simulated and input observations is r = 0.7 and ratio of the simulated to observed average value is 0.75 (Figure B-2E). Below this point, the forward model fit metrics deteriorate rapidly. The upper bound is between 125 and 150/504 eigenvalues where the reconstructed emission field stability metrics (Figure B-2F) show that between 20 and 30% of the total emission rate and emission grid cells are negative. Also, when more than 150/504 eigenvalues are used, the total emission rate of the reconstructed emissions increases with increasing number of eigenvalues used in the solution. In the eigenvalue range of 75 - 150/504, the total emission rate is ~23 kTons/day, approximately 45% larger than the other three quarters. The range of suitable eigenvalues for Q2 is 75 - 150/504, and the middle number of eigenvalues to use in the solution is 100/504.
The retrieval of the Q3 NH3 emissions was conducted using 1358 NH4+ wet deposition rate observations, creating an over determined system by a factor of ~2.7. The metrics of inversion are presented in Figure B-3. These metrics are similar to Q1, and the suitable eigenvalue range is approximately 50 - 175/504. In this eigenvalue range, the total emission rate is relatively constant at ~15.5 kTons/day, which is lower than both Q1 and Q2 total emission rates. This quarter also has the lowest correlations between the simulated and input observations, r ~ 0.55.
The retrieval of the Q4 NH3 emissions was conducted using 1367 NH4+ wet deposition rate observations, creating an over determined system by a factor of ~2.7. The metrics of inversion are presented in Figure B-4. These metrics are similar to Q1 and Q3, and the suitable eigenvalue range is approximately 75 - 150/504. In this narrow eigenvalue range, the total emission rate varies between 14.3 and 15.7 kTons/day, which is approximately equal to the total emission rate for Q3. The correlations between the simulated and input observations ranges between r = 0.68 and 0.75.
Figure B-1. Metrics of the inversion performance for the reconstructed Q1 NH3 emission field using NADP NH4+ wet deposition data. The metrics are: A) The value of the eigenvalues. B) Trade-off curve between chi-square and norm of reconstructed emissions. C) Total reconstructed emission rate. D) Total standard error. E) Ratio of the average simulated and input observations and their correlation. F) Ratio of the negative reconstructed emission rates to the total, and the fraction of the emission grid cells with negative emission rates. G) Correlation coefficient between the reconstructed and NAPAP emission rates. H) Ratio of the total reconstructed to NAPAP emission rates, and norm of the emission fields.
Figure B-2. Metrics of the inversion performance for the reconstructed Q2 NH3 emission field using NADP NH4+ wet deposition data. The metrics are: A) The value of the eigenvalues. B) Trade-off curve between chi-square and norm of reconstructed emissions. C) Total reconstructed emission rate. D) Total standard error. E) Ratio of the average simulated and input observations and their correlation. F) Ratio of the negative reconstructed emission rates to the total, and the fraction of the emission grid cells with negative emission rates. G) Correlation coefficient between the reconstructed and NAPAP emission rates. H) Ratio of the total reconstructed to NAPAP emission rates, and norm of the emission fields.
Figure B-3. Metrics of the inversion performance for the reconstructed Q3 NH3 emission field using NADP NH4+ wet deposition data. The metrics are: A) The value of the eigenvalues. B) Trade-off curve between chi-square and norm of reconstructed emissions. C) Total reconstructed emission rate. D) Total standard error. E) Ratio of the average simulated and input observations and their correlation. F) Ratio of the negative reconstructed emission rates to the total, and the fraction of the emission grid cells with negative emission rates. G) Correlation coefficient between the reconstructed and NAPAP emission rates. H) Ratio of the total reconstructed to NAPAP emission rates, and norm of the emission fields.
Figure B-4. Metrics of the inversion performance for the reconstructed Q4 NH3 emission field using NADP NH4+ wet deposition data. The metrics are: A) The value of the eigenvalues. B) Trade-off curve between chi-square and norm of reconstructed emissions. C) Total reconstructed emission rate. D) Total standard error. E) Ratio of the average simulated and input observations and their correlation. F) Ratio of the negative reconstructed emission rates to the total, and the fraction of the emission grid cells with negative emission rates. G) Correlation coefficient between the reconstructed and NAPAP emission rates. H) Ratio of the total reconstructed to NAPAP emission rates, and norm of the emission fields.
Appendix C
Metrics of the Inversion Performance for the Retrieval of Seasonal NO2 Emission Fields
The retrieval of the NO2 emission fields was conducted using approximately 1340 NO3- wet deposition rate observations, creating an over determined system by a factor of less than 2.7 for each quarter. The metrics of inversion for the retrieval of all four quarters are presented in Figures C-1 - C-4. As shown, there is little difference between the metrics from one quarter to another. The total reconstructed emission rate shows a slight increase when increasing numbers of eigenvalues are used in the solution, increasing about 20% over the eigenvalue range of 50 to 300/504. The total emission rate is greatest during Q1, ~ 70 kTons/day, lowest during Q3, 54 kTons/day and approximately 62 kTons/day for both Q2 and Q4. The lower bound of eigenvalues for all four quarter is 50/504. Above 50 eigenvalues, the forward model fit metrics show little to no improvement, with the correlation between the simulated and input observations approximately r = 0.7 and the ratio of the simulated to input observation values at ~0.8, Figures C-1E - C-4E. The upper bound of eigenvalues is between 175 and 200/504, where the percentage of the total emission rate and emission grid cells that are negative vary between 20 and 28%, Figures C-1F - C-4F. When more than 200/504 eigenvalues are used, the percentage of total emissions that are negative, the total standard error, and the emission field norm increase rapidly, indicating a highly unstable retrieved emission field. The range of suitable eigenvalues for all four quarters is 50 - 200/504, and the middle number of eigenvalues to use in the solution is 125/504.
Figure C-1. Metrics of the inversion performance for the reconstructed Q1 NO2 emission field using NADP NO3- wet deposition data. The metrics are: A) The value of the eigenvalues. B) Trade-off curve between chi-square and norm of reconstructed emissions. C) Total reconstructed emission rate. D) Total standard error. E) Ratio of the average simulated and input observations and their correlation. F) Ratio of the negative reconstructed emission rates to the total, and the fraction of the emission grid cells with negative emission rates. G) Correlation coefficient between the reconstructed and NAPAP emission rates. H) Ratio of the total reconstructed to NAPAP emission rates, and norm of the emission fields.
Figure C-2. Metrics of the inversion performance for the reconstructed Q2 NO2 emission field using NADP NO3- wet deposition data. The metrics are: A) The value of the eigenvalues. B) Trade-off curve between chi-square and norm of reconstructed emissions. C) Total reconstructed emission rate. D) Total standard error. E) Ratio of the average simulated and input observations and their correlation. F) Ratio of the negative reconstructed emission rates to the total, and the fraction of the emission grid cells with negative emission rates. G) Correlation coefficient between the reconstructed and NAPAP emission rates. H) Ratio of the total reconstructed to NAPAP emission rates, and norm of the emission fields.
Figure C-3. Metrics of the inversion performance for the reconstructed Q3 NO2 emission field using NADP NO3- wet deposition data. The metrics are: A) The value of the eigenvalues. B) Trade-off curve between chi-square and norm of reconstructed emissions. C) Total reconstructed emission rate. D) Total standard error. E) Ratio of the average simulated and input observations and their correlation. F) Ratio of the negative reconstructed emission rates to the total, and the fraction of the emission grid cells with negative emission rates. G) Correlation coefficient between the reconstructed and NAPAP emission rates. H) Ratio of the total reconstructed to NAPAP emission rates, and norm of the emission fields.
Figure C-4. Metrics of the inversion performance for the reconstructed Q4 NO2 emission field using NADP NO3- wet deposition data. The metrics are: A) The value of the eigenvalues. B) Trade-off curve between chi-square and norm of reconstructed emissions. C) Total reconstructed emission rate. D) Total standard error. E) Ratio of the average simulated and input observations and their correlation. F) Ratio of the negative reconstructed emission rates to the total, and the fraction of the emission grid cells with negative emission rates. G) Correlation coefficient between the reconstructed and NAPAP emission rates. H) Ratio of the total reconstructed to NAPAP emission rates, and norm of the emission fields.
Bret A. Schichtel May 1996
Date of Birth: 5/24/67
Place of Birth: Wheatridge, Colorado
Undergraduate Study: Received a B.S. in Mechanical Engineering from Virginia Polytechnic Institute & State University, Blacksburg VA, May 1989
Graduate Study: Received a M.S. in Mechanical Engineering from Washington University, St. Louis MO,
May 1991
Experience: Employed as a research assistant with the Center for Air Pollution Impact and Trend Analysis from September 1991 to date.
Publications:
Schichtel, B.A., R.B. Husar, and J.D. Husar. 1991. Visibility data filters for Europe. Presented at the A&WMA conference in Vancouver, British Columbia. Paper 91-116.3.
Schichtel, B.A., R.B. Husar, W. Wilson, R. Poirot, and W.C. Malm. 1992. Reconciliation of visibility and aerosol composition data over the U.S. Presented at the A&WMA conference in Kansas City, MO. Paper 92-59.08.
Schichtel, B.A. and Husar, R.B. 1992. Aerosol types over the continental U.S.: spatial and seasonal patterns. Presented at the A&WMA conference in Kansas City, MO. Paper 92-60.07.
Schichtel, B.A. and Husar, R.B. 1994. The CAPITA Monte Carlo Model: PC-Implementation. Presented at the A&WMA/AGU International Specialty Conference, Snowbird, Utah.
Schichtel, B.A. and Husar, R.B. 1995. Regional simulation of atmospheric pollutants with the CAPITA Monte Carlo model. J. Air & Waste Manage. Assoc. Accepted for publication.