3.2.1. Manual Fitting
 We estimated the relative contribution from each source area during the experimental period from the tagged tracer simulation results. Figure 4 shows the time series of observed HCFC-22 and calculated tracer concentrations at Hateruma for January–March 2005 with the tagged simulation results shown by source region. For each sharp observed peak, except for several minor peaks, the tagged simulation results show one or more corresponding peaks at the same time. In February, more plumes arrived at Hateruma from Japan and Korea, whereas in March more plumes originated in China. However, when we compared intensities between observed and calculated peaks, the sum of the simulated regional peaks did not agree with the observed peak intensity. In particular, the calculated peaks for plumes originating in China tended to be significantly smaller than the observed peaks, suggesting a large discrepancy between the actual source distribution and the emission inventory employed for this calculation.
Figure 4. Observed and simulated time series of chlorodifluoromethane (HCFC-22) concentrations at Hateruma for January to March 2005. The tagged tracer simulation results show the concentration contributed by each source region. The simulation results have been multiplied by a factor of 5, and 12 pptv has been added to the original mixing ratios. The factor (5) and the offset (12 pptv) were chosen arbitrarily to make the comparison of the simulation results with the observation data easier to visualize.
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 We also compared the sum of the simulated values from all regions with the observation peaks (Figure 5), with the observed time series smoothed by 6-hourly adjacent averaging. Only emissions from China, multiplied by a normalization factor of 15, were enhanced in January and March (Figure 5, dotted line), whereas emissions from all sources, multiplied by a normalization factor of 5, were enhanced in February (Figure 5, dashed line). The time evolution of the plumes as determined by examining the 3-D concentration field resulting from the RAMS tagged tracer simulation showed that more plumes arriving at Hateruma originated in China in January and March and that in February, more of the arriving plumes originated in Japan, Korea, or Taiwan. By comparing the areas of calculated peaks originating exclusively in China, judged from the tagged simulation results (peaks 1–4 in Figure 5) with those of the observed peaks, we estimated the difference between the emissions values used in the simulation and the actual emissions. On average, the areas of the calculated and observed peaks differed by a factor of 14.8 (±4.6) in 2005. For the winters of 2006 and 2007 (Figure 6), we similarly estimated the observed and simulated emissions from China to differ by a factor of ∼10.
Figure 5. (upper) Observed and (lower) simulated time series of HCFC-22 concentrations at Hateruma for January to March 2005. The summed results for the 12 source regions by the tagged tracer simulation are shown by the solid line (factor = 1; the original emission values are used). The dashed line is the result of the simulation using the input emissions all factored by 5. The dotted line is the result of the simulation using the input emissions, of which only the emission from China was factored by 15, but emissions from other regions remained as original magnitudes.
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Figure 6. Observed and simulated time series of HCFC-22 concentrations at Hateruma for the winters of (a) 2006 and (b) 2007. The dotted line shows the simulated results when sources in China only were multiplied by a factor of 10.
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3.2.2. Inversion (Optimal Estimation)
 As described in section 3.2.1, manual fitting yielded a rough factor for Chinese sources from a limited number of events (n = 3–4) per year. An optimal inverse calculation was conducted by the Bayesian least squares technique to extract additional information from events that were not used in the manual fitting because of their more complicated source-receptor relationship. For the a priori data set, we used the forward simulation results for the Chinese sources multiplied by a factor of 10 in accordance with the manual fitting results. We prepared a covariance matrix for both the observation error and the a priori parameter error as the prior information required as input for the Bayesian estimation. The observation error consisted of the HCFC-22 measurement error, the forward model transport error, the peak-fitting error, and representativeness error. The representativeness error was estimated from the difference in the simulation result between a horizontal resolution of 40 km and one of 80 km. The measurement error was negligibly small (<1%) compared with the transport error and the peak fitting error. However, the transport error and the peak fitting error are not easy to estimate. In this study, we estimated the transport error as the RMSE between the calculated and observed peak areas after a preliminary inverse calculation with a single initial transport error value, under the assumption that any mismatch of the model and the observation after the source is improved by inversion is due to transport error. We estimated the peak fitting error as the difference between the smallest and largest peak areas obtained by different fitting procedures (∼30%). The overall observation error for each event ranged from 1% to 80% during the experimental period. The peaks with large transport error tended to have a large peak fitting error and vice versa, resulting in the wide range of observation error. In the inverse calculation, peaks with a large assigned error received much less weight than those with a small assigned error, with the result that the inversion solution was mainly constrained by the better modeled peaks. We set the a priori flux error to 5% for fluxes from Japan, Korea, and Taiwan, to 50% for fluxes from China, and to 10% for the northeast and west regions in the calculation domain (Figure 2). The a priori flux error for China was set to 10 times that for Japan, Korea, and Taiwan because the a priori flux itself was set to 10 times the initial inventory value for China on the basis of the manual fitting results (see section 3.2.1). We consider the larger error resulting from the large scaling factor (10) obtained by the manual fitting to be reasonable, given the assumed much faster change in the emission rate in China, owing to the recent rapid development compared with developed countries and regions, which have been emitting considerable amounts of HCFCs since the 1990s [Nakicenovic et al., 2000].
 Figure 7 and Table 2 show the inversion results for the winters of 2005–2007, with the combined data of all three winters inverted at once. In these results, the relative standard deviation (r.s.d.; Table 2) for the different Chinese regions ranged from 28% to 56%, reflecting the differences in their contributions to the concentration events at Hateruma among the 3 years. The results for 2005–2007 did not show a clear increasing or decreasing trend over these 3 years. Since HCFC-22 is predominantly used for refrigeration and air conditioning, it should be released mainly from urban or industrialized areas. However, the timing of the release may be irregular because it is released primarily when refrigeration and air conditioning equipment is produced, installed or uninstalled, or decommissioned. If the production of HCFC-22 has been monotonically increasing during the past decade, as suggested by McCulloch et al. , then the large annual variation (indicated by the r.s.d. values in Table 2) also suggests that the inversion results depend greatly on the selection of the events used for the calculation. As the proportion of emissions picked up from different source regions and contributing to high-concentration events observed at Hateruma vary each year, we presume that the error due to the variation in transport between years is large. Therefore, to increase the sample size (number of events) and reduce the standard error, we present the inversion results for the events of all 3 years together (Figure 7 and Table 2).
Figure 7. Results of the inverse calculation. The inventory data are the emission data for each region from Global Emissions Inventory Activity (GEIA), the a priori values are those with Chinese emissions multiplied by a factor of 10, and the a posteriori values are those after the inversion calculation. Error bars on the a priori and the a posteriori values indicate the covariance before and after the inversion.
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Table 2. Inversion Results for Data From the Winter of 2005–2007a
| ||HCFC-22 (Mg)||post./pri.||SD||unc. red. (%)||2005–2007 r.s.d.(%)|
|a priori||a posteriori||a pri.||a post.|
 We examined how the RMSE (used to estimate the transport error) was changed by the inversion by comparing the fitted peak areas of 39 selected events from the winters of 2005–2007 (Figure 8). Prior values and posterior values are from the forward model results and the inverse model results, respectively, and the error bars of the prior values represent the observation errors. As described above in this section, a large observation error was assigned to peaks whose RMSE was not reduced by the preliminary inversion, which resulted in a large RMSE remaining between the observation and posterior values of those peaks.
Figure 8. Fitted values of peak areas for 39 events selected from the HCFC-22 time series for winter 2005 (events 1–11), 2006 (events 12–25), and 2007 (events 26–39). Prior and posterior values are from the forward model and the inverse model results, respectively, and the error bars represent the data uncertainty assigned to each event.
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 Among the 12 source regions, only the uncertainties of the fluxes from China were significantly reduced by the inverse calculation. This result was expected, owing to the experimental design of this study, which uses the winter data. Most of the high-concentration events observed at Hateruma originated in China in winter, so the information extracted from those events mostly reflects the source fluxes from China (Table 3). The uncertainty reduction was largest for southern and central China, where most of the plumes observed at Hateruma during winter originated. The much higher a priori uncertainty level used for the Chinese source regions (a priori errors were set to 10 times those of other regions) also contributed to the larger uncertainty reduction. The total uncertainty for Chinese emissions was reduced from 50% (a priori) to 15% (a posteriori) by the inverse calculation. To examine the influence of different a priori values, we examined the sensitivity of the inversion results to different a priori emission values and assumed uncertainties. We examined a priori emission values for China between 10 and 160 Gg, with an a priori uncertainty range from 50% to 300%. The resulting a posteriori values ranged from 30–36 Gg, indicating that the inversion results for China were not constrained very much by the a priori values. In contrast, the a posteriori values for other source regions (Japan, Korea, and Taiwan) varied greatly when the a priori values were changed; they tended to stay close to the a priori values, but they exhibited more variation as the uncertainty level increased (Table 2, shaded parts). A possible cause of this result is that the plumes from these three regions during the calculation period often became mixed before their arrival at Hateruma, resulting in relatively large transport errors that prevented the inversion from constraining the individual source regions.
Table 3. The Estimated Relative Contributions (%) of the Source Regions to the High-HCFC-22 Concentration Events Observed in the Winters of 2005–2007 at Hateruma Station
 The estimated annual emission of HCFC-22 from all four source regions within China ranged from 3 to 16 Gg, and the estimated total annual emission was 32 Gg. This result is consistent with the annual emission from China of 52 (±34) Gg estimated from the observed concentrations of HCFC-22 and CO at Hateruma in 2005 by the tracer-ratio technique based on an independent CO emission inventory [Yokouchi et al., 2006]. Stohl et al.  recently estimated annual HCFC-22 emissions from China to be 59 and 71 Gg for 2005 and 2006, respectively, by an inversion procedure based on the Lagrangian particle dispersion model. They used an a priori value of 166 Gg for the inversion, which they obtained from the United Nations Environment Programme (UNEP; http://ozone.unep.org) inventory. This value is about six times the a priori value used in our study. After the inversion, a posteriori values decreased by ∼60% from their a priori value for China [Stohl et al., 2009] but were still approximately twice as high as the a posteriori value in our study. The difference between these two estimates is likely due to the different models and approaches used for each study, since our sensitivity study indicated little dependency on the a priori values used. In addition, the two studies selected and processed the observational data differently, which may account for the different results: Stohl et al.  used a 3-hourly time series for 2005 and 2006, whereas we used only the winter peak areas for 2005–2007. The significant discrepancy between the HCFC-22 emissions from China estimated by this study and the available inventories indicates that emissions of this compound have been increasing so rapidly that they are difficult to estimate by a conventional bottom-up approach. A top-down approach is very efficient at detecting signals of a rapid emission change when reliable observation data are available, although it is critically important to use a well-validated model because the transport error can significantly affect the results. It is important that we continue our efforts to increase the quality of observation data and to reduce the transport error to improve the results obtained by top-down approaches.
 Among the four defined source regions in China, the absolute emissions derived for central China were largest. This area includes the Yangtze River delta area, one of the most densely populated areas in the world and an economic center of China. The a posteriori emissions from this area accounted for half of the total emissions from China. The North China region showed the largest increase after the inversion (a posteriori/a priori ratio = 2.2; Table 2), indicating that HCFC-22 emissions are more concentrated in this region in relation to the population size. The North China region includes the Beijing-Tianjing area, where industrial and economic activities, along with the population, have been growing very rapidly, especially in recent years in preparation for the Olympic Games in 2008. This growth led to a great demand for resources and energy, which may explain the significant emission increase. In contrast, the a posteriori/a priori ratio was lowest for South China among the source regions in China. South China includes the Pearl River delta area, which has been a leading economic region and a major Chinese manufacturing center since the late 1970s. Nevertheless, the annual variability of the inversion results for 2005–2007 was particularly large for both North China and South China (r.s.d. values; Table 2). To evaluate their recent emission trends quantitatively, observations are required for several more years. Higher resolution bottom-up inventory data will also help to reduce the uncertainty in this type of top-down estimation approach, because halocarbon emissions tend to be more point-source-like than the distribution of population. In addition, introducing more constraints for other parts of East Asia (e.g., Japan, Korea, Taiwan) would also allow more precise estimation of regional flux distributions. For this purpose, the use of additional observation points, which would compensate for the transport error at Hateruma station, might be most effective.