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 The Numerical Atmospheric Dispersion Modeling Environment (NAME) dispersion model driven by three-dimensional (3-D) synoptic meteorology from the Unified Model has been used to determine the fraction of air arriving at Mace Head, Ireland, from different European regions over a 6-year period. These data, along with observations of pollutants at Mace Head and a best fit algorithm, have been used to derive emission estimates over Western Europe. The algorithm starts from randomly generated emission maps and iterates toward the best solution. Using an idealized case study, it has been shown to be effective at distinguishing between distinct source regions. The technique has been applied to two ozone-depleting gases, CFC-11 and CFC-12, and two greenhouse gases, methane and nitrous oxide. The emissions derived compare favorably with existing inventories. The technique is able to provide information regarding the emission distribution across Europe and to estimate area and country contributions; information that for some species is not readily available by other means. It is a different methodology to those currently used and so is a useful tool in verifying existing inventories.
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 Knowledge of the emission patterns of different pollutants and how they vary from year to year assists regulators in formulating new and monitoring existing policies. The common approach taken to derive emission maps is through a detailed understanding of the distribution of the processes required to release each pollutant. For example, McCulloch and Midgley  estimated European emissions of CFC-11 and CFC-12 using EU production and sales figures.
 The generic problems and uncertainties of generating emission inventories using these bottom-up techniques are discussed by Lindley et al.  and Winiwarter and Rypdal . The techniques require individual information on each of the pollutants assessed. They require for each pollutant; sales and production figures, a comprehensive understanding of the commercial, domestic and natural processes involved; and information on how the processes identified vary from region to region and in time. The information required for such an undertaking is extensive, maybe commercially restricted, out of date, poorly resolved spatially or even unavailable. The complete set of data is rarely complete and varies from species to species. The uncertainties in calculating global emissions from production figures and the release patterns of different activities are discussed by Fisher and Midgley . The uncertainty figures will change each year as the production, use and “banked” (used but not yet released) quantities change [McCulloch et al., 2001].
 The European emission maps derived using this type of method can now be compared against those derived using an entirely different approach. This is the technique of measurement and back attribution and has previously been reported by Ryall et al. [2001a]. This current study moves this concept forward by introducing a new method of attributing pollution back to its source called simulated annealing replacing the more simplistic approach taken in the previous work. The strengths and limitations of this new approach are investigated and the results are compared with existing estimates for four species; CFC-11, CFC-12, methane and nitrous oxide.
 Inverse methods have been used in previous studies [Brown, 1993; Mahowald et al., 1997; Mulquiney and Norton, 1998; Mulquiney et al., 1998; Hartley and Prinn, 1993; Houweling et al., 1999; Hein et al., 1997] to estimate global emission distributions and lifetimes of trace gases. Two- or three-dimensional chemical transport models are used to simulate the average movement and dispersion of air from source to receptor. As the modeling is on a global scale the atmospheric loss of the pollutants owing to chemistry are simulated and the resolutions of the models are coarse (2°–22° horizontally, 7+ vertical levels). The geographical size of the source regions estimated for are large; for example, Hartley and Prinn  use 5 (North America, Western Europe, eastern Europe, Asia and the Southern Hemisphere). The inversion methods used vary but most, with the exception of Mulquiney et al. , use an initial emission estimate for each source region and a total global budget to assist the inversion procedure. Measurements from around the world are used to constrain the problem. In the majority of these studies the nature of the meteorology used (climatological or averaged analysis fields) means that there is no attempt to capture the day-to-day synoptic air movements only the characteristic nature of the flow. Hence in these studies only the observed baseline concentrations are simulated, individual regional pollution events are averaged out of the observation time series prior to use. One exception to this is the study by Mahowald et al.  who used analysis winds from two forecast centers and compared the data on a monthly mean timescale at nine sites spread around the global.
 The current study uses the deviations from observed baseline trends at one observation site and highly resolved synoptic motions in both time and space to best fit estimates of fine-scale emissions across Europe. No a priori emission estimates or totals are used by the inversion technique. As the problem is overdetermined the use of a priori information in the minimization would, if good, simply reduce the speed of convergence. As speed is not an issue and current high-resolution estimates are not well know it was thought unnecessary to include such information. This assumption has been tested for CFC-11.
2. Measurements at the Mace Head Site
 Since 1994, high-frequency (40 min interval) real-time gas chromatographic measurements of the principal halocarbons and radiatively active trace gases have been made as part of the Global Atmospheric Gases Experiment (GAGE/AdvancedGAGE) at Mace Head, County Galway, Ireland [Prinn et al., 2000]. The species measured include CFC-11, 12, and 113, methyl chloroform, carbon tetrachloride, carbon monoxide, methane, nitrous oxide and chloroform.
 The station is situated on the west coast of Ireland where the prevailing winds are westerly, bringing clean well-mixed air from the Atlantic. Only between 7% (in 2000) and 21% (in 1996) of the time did the wind not have a westerly component and so bring “polluted” air from Ireland, UK and the rest of Europe to Mace Head. The observed concentrations during these “polluted” times can be well above baseline levels (maximum deviations from baseline: 18.1 ppt for CFC-11 on 5 May 1999 and 358 ppb for methane on 22 March 1996).
3. NAME Model
 NAME is a Lagrangian particle model [Ryall and Maryon, 1998; Ryall et al., 1998]. It uses three- hourly three-dimensional meteorology fields from the complex numerical weather prediction model, the Unified Model (UM) [Cullen, 1993], to move the abstract particles around the model domain. The 3-D model flow is interpolated to each particle location at each 15 min time step. Using a random walk technique [Thomson, 1987] each particle moves under the influence of the mean flow, wind meander and sub grid-scale turbulence. The random walk scheme uses velocity variance and Lagrangian timescale profiles determined from empirical fits to observational data to simulate the turbulent motion. Gaussian velocity distributions are assumed and the components of the turbulent motions are assumed uncorrelated. The model simulates the enhanced mixing owing to convection by randomly mixing particles within convective cloud. The effects of wind meander, motions with timescales less than the resolution of the Unified Model but longer than each time step, are represented. The low-magnitude free-tropospheric turbulence quantities are considered uniform. Entrainment, the movement of particles between the boundary layer and the free troposphere, is modeled separately. At each time step a 2D field of boundary layer height is diagnosed using a combination of the parcel method [Verver and Holtslag, 1992] and the conventional gradient Richardson number technique. NAME has been used for a range of applications including air quality forecasts [Manning et al., 2001], episode studies [Ryall et al., 2001b], regional atmospheric chemistry modeling [Malcolm et al., 2000; Malcolm and Manning, 2001] and international dispersion experiments [Ryall and Maryon, 1998].
4. Baseline Concentrations for Each Species
 For each pollutant there is a residual amount of material present in the global atmosphere, this background level is referred to as the baseline concentration and is unaffected by local and regional sources. Baseline levels can vary on timescales of the order of weeks and, depending on the pollutant, may have seasonal or annual trends. As this technique requires the deviation of the observation from baseline, it is necessary to calculate a time series of baseline concentrations over the 6 years for each pollutant. A baseline is derived for each pollutant using the NAME model and then subtracted from the measurement data. The inversion technique searches for the emission solution which best fits this observed deviation from the baseline time series.
 Using a large model domain (−30° to 25° west-east and 30° to 70° south-north), a coarse grid (1.11° latitude by 1.67° longitude) and limited numbers of particles emitted per grid (4 per hour), the NAME model was used to simulate the period 1995–2000 inclusive. Using a similar technique as described by Ryall et al. [2001a], a time series of baseline information for each species was estimated. The method ignores times when the air was modeled to have come from east of Mace Head (i.e., Ireland, UK and the rest of Europe) or southern latitudes (latitudes less than 35°N), or when the air was not well mixed (i.e., in stable atmospheric conditions; modeled as boundary layers less than 300 m). Figure 1 shows the raw data (gray), the values chosen as baseline (black crosses) and the derived continuous baseline time series (solid black line) for CFC-11 between January and March 1995. The standard deviation (STD) of the observations used for the baseline calculation has a contribution from the noise in the measurements and from inaccuracies in defining the baseline. For CFC-11 over the 6-year period this was calculated to be 0.367 ppt, for methane it was 10.14 ppb.
 By removing the time-varying baseline concentration from the raw measurement data, a time series of excursions from the general background value was generated. The observed deviations from baseline are averaged over 6 hours with all negative values considered to be zero. This resultant series will be referred to as the observation time series, o(t), with each species, in principle, having a unique trace.
5. Modeling the Air Concentration at Mace Head
 The model grid was defined to cover 19°W to 25°E and 35°N to 65°N. The grid was set equal to the horizontal resolution of the modeled meteorology namely 0.555° latitude by 0.833° longitude and with 11 (1995–1998) or 18 (1999–2000) vertical levels. Thirty particles each hour were randomly released in time and space within 80 m of the ground from each grid. The number released was chosen to fully utilize the computational resources available. Each grid square was simulated to emit 1 g m−2s−1 of passive material spread uniformly between the released particles. At each time step (15 min) information about all of the particles within the boundary layer in the target square, a grid square 0.555° latitude by 0.833° longitude centered on the Mace Head measurement site were recorded. The location and time of the particle's creation, the current time and the particle's contribution to the boundary layer air concentration at Mace Head were stored. In this study the model simulated the movement of particles between 1995 and 2000 inclusive. The particles were defined as passive tracers meaning that the dry and wet deposition and atmospheric chemistry schemes in the model were not utilized. Owing to the long lifetimes of the four trace gases and the regional scale of the domain studied in this paper, this simplification was considered to have negligible impact.
 Using the stored information it is possible to determine the total contribution to the modeled concentration at the Mace Head grid box from each grid in the model domain at each time step. These data were accumulated into 6-hourly attribution maps (see Figure 2 for a typical example) and so provided 4 (maps a day) × 365 (days a year) × 6 (years) maps.
 For some of the 6-hour periods the modeled meteorology or dispersion processes transporting material to Mace Head may have been poorly represented. To improve the accuracy of the back-attribution technique it is beneficial to identify situations where the transport errors are likely to be high and remove them from the analysis.
 If the number of grids contributing to the modeled concentration at Mace Head is large, indicating slack winds and long transit times, there are potentially significant errors in the modeled transportation. To reduce the impact of such situations, all 6-hour periods during which at least 20% of the total modeled contribution at Mace Head is made up of “active” grids each adding less than 0.1% to the total have been removed. Other problem periods are thought to occur when the trajectories material took to reach Mace Head leave the model domain. In these situations the model will fail to correctly attribute the source of the concentrations measured at Mace Head. To minimize the problems of large horizontal recirculations any 6-hour period that has widely spaced noncontiguous active grids on the edge of the domain have been removed. In total approximately 9% of the possible time periods were excluded from the analysis.
6. Attributing the Observations to Areas of Emission
 The modeled attribution data are an array of data A (n × m), where m is the number of grid points in the model domain (36 × 37) and n is the number of 6-hour time intervals accepted in the 6-year period. The object of the study is to determine the n-element vector of scaling factors, s, to transform the modeled 1 g m−2s−1 grid emissions to the observed values for each species. So,
Each species has its own s and o vectors but uses the same A matrix.
 Owing to the potential errors in both the modeled and measured data and nonuniform (in time and space) emissions this equation is not precise and could be written with explicit error components:
Rearranging this implies
where e is the n-dimensional error vector. The causes and effects of errors are discussed further in section 10. In addition to (2) the problem is further constrained by
(A ≥ 0 and o ≥ 0 by definition.) Since n is much greater than m, equation (2) is overdetermined, i.e., has either zero or an infinite solution set. Since e is potentially significant and unknown, equation (2) cannot be solved exactly. Exact matrix inversion techniques like simplex [Press et al., 1992] are thus inappropriate. In order to derive a vector s per species that best fits (minimizes e) equations (2) and (3) a version of the method of simulated annealing is used [Press et al., 1992] as discussed in section 7.
 The back-attribution technique is sensitive to the number of times a grid cell contributes to Mace Head and to the magnitude of that contribution. Emissions from grids close to Mace Head affect it frequently and with a significant signal, therefore their average impact on Mace Head can be resolved with a high degree of accuracy. Emissions from distant grids are more difficult to clarify as they contribute infrequently and with proportionally smaller signals. Since distant grids from the same geographical area are likely to contribute to Mace Head during the same time periods it is possible to compensate for the disparity between local and distant grids by amalgamating distant grids and only solving for the combined grid.
 Owing to the distance from Mace Head and overriding climatological effects, each grid contributes a widely varying number of times to the modeled concentrations. For example the grid containing Dublin in Ireland contributes on 1873 (21.4%) 6-hour periods and provides 0.35% of the total modeled concentration over the 6 years, whereas the grid containing Rome in Italy contributes on just 124 (1.4%) occasions and provides just 0.002% of the total. This disparity is compounded by the magnified errors in modeled meteorology with travel time, on average air from Italy takes more than 4 days to reach Mace Head, whereas air from Dublin will arrive within the day. It is therefore more difficult to distinguish between adjacent distant emissions than those closer to Mace Head. Given the limited number of particles released within each grid box, combining adjacent grid cells reduces the noise in the modeled trace (noise ∼1/√number of particles).
 Grid cells were either individually represented or combined into 4 × 4 or 2 × 2 blocks depending on the frequency of times each cell contributed to the modeled total or on their distance from Mace Head. The domain is gridded separately for each species because for each there are periods of missing observations that have been excluded from the data set. Figure 3a shows the distribution of 1 × 1, 2 × 2 and 4 × 4 grid cells and Figure 3b shows the number of times each cell contributed to the Mace Head trace for CFC-11 for the 6-year period. The limits set on amalgamating the grid cells were chosen to ensure that each solved-for grid contributed on more than 224 6-hour occasions (8 weeks) over the 6-year period.
7. Simulated Annealing Technique
 From m + 1 randomly generated possible solutions (the solution set), and a measure of the best fit (the skill score), the solution set is iterated toward the best solution. At each step the solution set spans a section of the whole solution space. At each step a new solution is added to the solution set and the worst solution is discarded. This sequence is repeated many times and the solution set gradually contracts around the best score within the spanned solution space. The difference between the current worst solution and the new possibility is slowly reduced between iterations. Initially the change can be large enabling the new possible solutions to investigate a wide area of the solution space.
 After a set number of iterations (120,000) this process is halted and only the current best solution is taken forward to the next stage. This best solution is iterated to a potentially even better skill score by randomly choosing one grid box, perturbing its value (randomly between ±60% of the grid's current value) and discarded or retained on the basis of the skill score of the new solution. This process is continued until the total change in skill score after each 2000 iterations is less than 1 × 10−4. The choice of the number of iterations, the fraction of perturbation and when to stop were made after a variety of sensitivity tests to optimize the speed of convergence. The solution that emerges from this process is considered to be one possible (local minima) solution to the equation set (equations (2) and (3)). The value for each grid box is the scaling factor needed to scale the modeled 1 g m−2s−1 release rate to the actual emission rate of that area.
 The whole process of simulated annealing should be repeated, each time starting with a different set of randomly generated solutions, a sufficient number of times per species to minimize the likelihood of missing the “best” solution. In this study, 52 times per species was considered suitable. The result is 52 possible solutions (maps of scaling factors) to the equation set, i.e., an ensemble of different possible solutions from which the mean scaling values for each grid box can be derived.
8. Skill Score Attributed to Each Solution Possibility
 The choice of the measure of a solution's skill is critical to the success of the technique. In this study the following was used:
where r = Pearson correlation coefficient, nmse = normalized mean square error , and fac2 = fraction of model values within a factor of 2 of the observations. If an observed value is less than the STD of the derived baseline value then the corresponding model value is considered to be within a factor of two if it lies between zero and twice this STD value.
 The skill score was devised using the standard statistics used for validating dispersion models, Hanna et al. , it is always positive and a perfect map, assuming no errors, would have a skill score of zero. The use of all three statistics in the skill score was found, with reference to the idealized case study, to be necessary as each contributes differently to the characterization of the observed trace. The weights given to each component (r, nmse, fac2) were chosen to attempt to equally balance each quantity. However, in completing a sensitivity study of the skill score, it was found that the solution set is not sensitive to the actual weights used, for example doubling each individual weight in turn gave consistent results when applied to CFC-11.
 The use of a priori information to assist convergence was investigated using CFC-11 and a high-resolution emission map (private communication A. McCulloch). The a priori map had a score of 5.80 (r = 0.834, nmse = 3.34, fac2 = 0.81) and after the inversion the mean of 52 ensembles had a score of 2.94 (r = 0.859, nmse = 1.05, fac2 = 0.88) which is no better than that achieved starting from totally random maps, see section 11. The use of a priori information was therefore considered unnecessary.
9. Idealized Case Study
 In order to test the technique an idealized case study has been devised, a similar approach was taken by Hartley and Prinn . This involves generating an “observation” time series from the model data. In this example, each grid square (0.55° × 0.83°) containing a Western European capital (Belfast, Dublin, Cardiff, Edinburgh, London, Paris, Copenhagen, Oslo, Brussels, The Hague, Berlin, Rome, Luxembourg) was assumed to emit 1 g m−2s−1 of material uniformly in time and space with no other emissions. The modeled amount of material arriving at Mace Head from each grid square is used to generate an idealized “observation” time series with a baseline concentration of zero. As this time series is derived directly from the model data it has no errors owing to modeled meteorology or dispersion or measurement inaccuracies and is purely a test of the back-attribution technique. The mean emission map using 52 ensemble solutions is shown in Figure 4a, it has a score of 0.11 (r = 0.997, nmse = 0.04, fac2 = 0.99, std = 0.24). The total amount emitted into the domain was 1432 Gton year−1, the modeled result was 1496 Gton year−1.
 As can be seen from Figure 4a the emission squares which are grouped together into larger blocks are less well resolved than the 1 × 1 blocks. In a 2 × 2 (4 × 4) block the mean emission should be 0.25 g m−2s−1 (0.0625 g m−2s−1). In this idealized case there are no errors in the data and so the grouping actually prevents the true solution from being found. If the cells are not grouped together then the true solution in this idealized case can be more accurately attained (score = 0.001, r = 1.000, nmse = 0.001, fac2 = 1.00, std = 0.03, map total = 1473 Gton year−1). For a nonidealized case, the errors in the modeled meteorology and dispersion and the measurements are significant and prevent accurate fine resolution solutions of distant sources from being found (see section 5). Adding random noise (with a std equal to the CFC-11 baseline noise of 0.718) to the idealized observational time series prior to applying the inversion routine reduces the mean skill score of 52 ensembles to 0.93 (r = 0.977, nmse = 0.198, fac2 = 0.874, std = 0.645, map total = 1732 Gton year−1). The resulting mean emission map solution is shown in Figure 4b.
 In using this back-attribution technique there are three main assumptions made, the validity of each varies from species to species. The idealized case completely satisfies all three of them.
 1. The baseline levels calculated are accurate and correctly reflect the pollutant concentrations of air entering the model domain from any direction.
 2. The emissions from each grid box are uniform in both time and space over the duration of the study.
 3. The pollutants are well mixed within the boundary layer by the time they arrive at the Mace Head receptor.
 Assumption 1 implies that the air entering the domain from any direction is clean and well mixed. Obviously this is not always accurate, especially for air entering the eastern domain where Russian emissions will be influential. The effect of this import of pollution from outside will lead to edge effects, where the emissions from cells at the edge of the domain are artificially increased as they not only reflect the releases from those cells but also the average import of pollution to them. As the number of distinct trajectory paths through a cell to Mace Head increases the errors due to imported pollution reduce.
 The four gases investigated here have long atmospheric lifetimes (e.g., 45 years for CFC-11), i.e., their baselines are unaffected by rapid chemical or deposition processes.
 The validity of assumption 2 will vary strongly from species to species. The main factors, which could influence this assumption, are as follows:-
 1. A pollutant has a natural (biogenic) component, e.g., methane release from wetlands (estimated to be 22% (115 Tg CH4) of the annual global emission [Nilsson et al., 2001]). Usually natural emissions are strongly dependent on a range of meteorological factors such as temperature and diurnal/annual and growth/decay cycles.
 2. The anthropogenic activities leading to the release of a pollutant have a definite cycle. An example of a strong dependence to a diurnal cycle is the release of carbon monoxide where emissions are dominated by traffic sources.
 3. The anthropogenic practices leading to the release of a pollutant may change over the time span covered by the back-attribution technique. For example, the opening or closing of an industrial complex may add or remove a significant source at some point during the time period under review.
 For all three of these problems the back-attribution method will smooth the changes out. If for example a factory operated at full capacity from 1995 to 1998 and then closed. The calculated solutions will oscillate between the source being active and inactive with the mean solution falling somewhere in between. The balance point of the mean solution will depend on how often and how many trajectories reach Mace Head when the emissions are active and inactive.
 Species emitted near to the receptor site (within approximately 50 km) may not be well mixed and so the measurements will be strongly influenced by local features such as terrain and shore breezes resulting in a high degree of intermittency in the concentrations. Averaging the measurements over 6 hours significantly reduces this error, also the remoteness of the site means that few anthropogenic sources fall into this category.
11. Estimated Emission Maps
 The mean and best emission maps generated from the 52 calculated solutions for methane using this back-attribution technique are shown in Figures 5a and 5b. The mean skill score was 2.33 (r = 0.878, nmse = 0.57, fac2 = 0.87, STD = 18.6 ppb) and the best score was 2.26. From each map an estimate of country totals can be derived. The range, mean and standard deviations of the country totals have been tabulated (Table 1). The boundaries of the countries used to derive these totals must conform to the map grid as defined in section 5. Figure 6 illustrates the grid boxes used for each country.
Table 1. Range, Mean, and Standard Deviation (STD) of the NAME-Derived Estimated Emissions of Methane for Different Countriesa
Values are in millions of tons per year. Boldface indicates the most significant values.
 The emissions estimated for methane by the back-attribution technique (NAME estimates) can be compared directly with those published by the European Monitoring and Evaluation Programme (EMEP; see www.emep.int). Table 2 shows the average emissions of methane over five years (1995 to 1999 inclusive) from EMEP.
Table 2. Average and Annual Range of EMEP Estimated Methane Emissions for 1995–1999 Inclusivea
EMEP Estimated Methane Emissions for 1995–1999 Inclusive
Values are in millions of tons per year.
 The estimates in Table 2 compare very favorably with the NAME estimates. The annual variability given in the EMEP estimates all fall in the range given in Table 1 with the exception of Germany. The NAME estimates for Germany may have been affected by the import of pollution from east of the domain leading to an overestimate, as discussed in section 10. The countries close to Mace Head and the ones which should give the most robust NAME estimates (UK and Ireland) both have mean estimates within 10% of the average figures in Table 2. It should also be noted that the totals given in Table 2 do not represent absolute truth and each has an associated error bar. The uncertainty in the EMEP emissions is not known but they will be affected by the problems discussed in section 1.
 The methane emission map generated by the back-attribution technique compares favorably with the EMEP emission estimates indicating that the technique is able to distinguished between different source areas when there are errors in the input data (owing to inaccuracies in the meteorology, dispersion and measurements).
11.2. CFC-11 (CFCl3)
 The emission maps generated for CFC-11 using the back-attribution technique are shown in Figure 7 and Table 3. The mean skill score was 2.91 (r = 0.859, nmse = 1.03, fac2 = 0.88, STD = 0.72 ppt) and the best score was 2.88.
Table 3. Range, Mean, and Standard Deviation (STD) of the NAME-Derived Estimated Country Emissions of CFC-11a
Values are in millions of tons per year. Boldface indicates the most significant values.
 The release of CFC-11 from 1995 onward has been dominated by emissions from “banked” quantities, mainly from discarded closed cell plastic foams. As the release of “banked” gases is generally from landfill sites there should be a strong correlation with population density and should show only small variation year to year. The release is also unlikely to have a significant diurnal or seasonal cycle and therefore more fully satisfies the assumptions made by the back-attribution technique (section 10) than for methane with its large biogenic component.
 The mean emission map (Figure 7) shows significant emissions from all the large conurbations in Western Europe (central and southern England, the Benelux countries, the Ruhr and northern France) and minimal emission over the sea sectors.
McCulloch and Midgley  reported emission estimates from the EU for a range of CFCs for each year 1986–1996. The average of the 1995 and 1996 values are shown in Table 4. Using the revised emission function put forward by McCulloch et al. , these values have been recalculated for the years 1995–1999 (A. McCulloch, private communication, 2002) and are also tabulated. The 1995–1998 emission estimates derived using the original NAME back-attribution technique [Ryall et al., 2001a] and those presented in this paper are given for comparison.
Values are in thousands of tons per year. McCulloch estimates EU totals, whereas the two NAME techniques estimate map totals. The range for McCulloch and Ryall is the annual variability, whereas for the new technique it is the range over the 52 ensemble solutions.
 The values calculated by McCulloch [1998, 2001] are estimates for the whole European Union (EU) and therefore cover a different geographical area from those derived using NAME, however the majority of the large population areas and therefore emissions are covered by both estimates. It is encouraging to note that the estimates are all within a factor of three with the exception of the now superseded original figures by McCulloch. The difference between the original and modified McCulloch estimates illustrate the sensitivity of the calculations to subtle changes in the temporal release function used in bottom-down emission estimations. This study supports the suggestion made by Derwent et al. [1998, p. 3701] that “the industrial production and use data for CFC-11 may have led to an underestimation of CFC-11 emissions at their peak” and “an overstating of the tail of emissions long after use.”
11.3. CFC-12 (CCl2F2)
 From 1995 onward the release of CFC-12 has been dominated by “banked” quantities, for example leakage from old refrigeration units. Therefore, like CFC-11, its release should correlate with population density and have little diurnal or seasonal variability.
 The mean and best emission maps generated for CFC-12 using the back attribution technique are shown in Figure 8 and tabulated in Table 5. The mean skill score was 3.66 (r = 0.806, nmse = 1.19, fac2 = 0.87, STD = 1.36 ppt) and the best score was 3.63. The maps show low emission from sea sectors and high emission from most populated areas. An exception to this is the low emission from the Marseille (southern France) and Po Valley (northern Italy) regions and the large emission from the Tyrrhenian Sea (Mediterranean Sea). This demonstrates the difficulty the method has in geographically distinguishing between distant sources when the amount of transport from that region is limited.
Table 5. Range, Mean, and Standard Deviation (STD) of the NAME-Derived Estimated Country Emissions of CFC-12a
Values are in thousands of tons per year. Boldface indicates the most significant values.
 The estimated emissions using this new technique have again been compared (Table 6) with those previously published [McCulloch and Midgley, 1998; McCulloch et al., 2000; Ryall et al., 2001a; A. McCulloch, private communication, 2002]. Given that the estimated totals cover different areas (map totals versus EU totals) and time periods they are encouragingly similar, with both NAME estimates falling between the original and modified McCulloch estimates. The modified McCulloch figures show significant decline over the period (in 1995 25.0 thousand ton year−1 was estimated whereas in 1999 it was 9.6 thousand tons year−1). If it is assumed that the 2000 estimate is the same as the 1999 value, the 6-year average modified McCulloch figure would fall to 15.6 thousand tons year−1.
Values are in thousands of tons per year. McCulloch estimates EU totals whereas the two NAME techniques estimate map totals. The range for McCulloch and Ryall is the annual variability whereas for the new technique it is the range over the 52 ensemble solutions.
11.4. Nitrous Oxide (N2O)
 Nitrous oxide is a strong greenhouse gas, 310 times more potent than CO2 on a mass emitted basis. The main activities in Europe resulting in its release are; agricultural soils (∼60%), chemical industry (∼20%) and combustion (∼15%) (United Nations Framework Convention on Climate Change (UNFCCC); see www.unfccc.int, 1998 figures). The amount emitted from soil is driven by the availability of nitrogen, the temperature and the soil moisture content, hence has a diurnal and seasonal release cycle. There is still significant uncertainty in the emission of nitrous oxide, especially from soils, where an uncertainty within a factor of two might be an improvement on the existing inventories [Winiwarter and Rypdal, 2001].
 The emission maps estimated using the NAME back attribution technique are shown in Figure 9. The mean skill score was 3.06 (r = 0.833, nmse = 0.80, fac2 = 0.85, STD = 0.42 ppb) and the best score was 2.91. The country and regional emission estimates are compared with those in the literature (Table 7). All agree within a factor of 1.5, with four of the regions (Ireland, France, Benelux countries and the total) showing agreement within 10%.
Table 7. Mean and Range of the Estimated Emission of Nitrous Oxidea
New Technique 1995–2000
Values are in thousands of tons per year of nitrous oxide for different countries using different techniques. United Nations Framework Convention on Climate Change (UNFCCC) estimates EU total whereas the two NAME techniques estimate map totals. The totals given for UNFCCC and Ryall et al. [2001a] cover 1995–1998 and the range represents the annual variability, whereas the new technique covers 1995–2000 and the range is over the 52 ensemble solutions. Boldface indicates the most significant values.
EU or map total
 At the end of 1997, the BASF adipic acid plant in Ludwigshafen (central western Germany) has been estimated to have cut its emission by 90% from 54 thousand tons year−1 [Schmidt et al., 2001]. If the UNFCCC figure for Germany is extended to 2000 using the 1998 value for 1999 and 2000, the German 6-year mean would reduce to 186 thousand tons year−1. Similarly, late in 1998, DuPont introduced technology at its adipic acid plant in Wilton (northeast England) that has been estimated to have cut its emissions of N2O by 90% from 46 thousand tons year−1 [Department of the Environment, Food and Rural Affairs (DEFRA), 2000]. Assuming all other UK emissions remained fixed, the UNFCCC's UK emissions for 1999 and 2000 would be 139 thousand tons year−1 bringing their 6-year mean down to 168 thousand tons year−1. Using these adjusted totals the NAME UK value would be 47 thousand tons year−1 lower and the NAME German value 61 thousand tons year−1 higher than those estimated by the UNFCCC. These significant changes in release profile during the 6-year period violates the technique's uniform release assumption and will have increased the uncertainty of the emission estimates made for these two countries.
 The NAME Lagrangian model is able to estimate the fraction of air arriving at Mace Head from different European regions at different times over a 6-year period. Using this matrix of data along with observations of a range of pollutants at Mace Head it is possible, using the best fit algorithm called simulated annealing, to derive estimates of emissions over Western Europe. The algorithm starts from a randomly generated emission map and iterates toward the best solution, the process is repeated many times to build up an ensemble of different solution possibilities, all local minima to the equations. The simulated annealing technique has been shown, using an idealized case study, to be effective at distinguishing between distinct source regions when there are no errors in the input data.
 The NAME back attribution technique makes three assumptions, namely an accurate baseline can be derived, the release is uniform and that there are no significant local sources. The validity of each assumption varies for each pollutant considered. The technique has been applied to two ozone-depleting gases, CFC-11 and CFC-12, and two greenhouse gases, methane and nitrous oxide.
 The study using methane showed that the emission estimates for Ireland, UK and France using the back attribution technique were within 10% of those in the literature. Only the German total was substantially different with the NAME estimates being 1.53 times larger. The possible influx of significantly above baseline air into the eastern edge of the domain maybe a factor in the larger value attributed to the German total. The comparison using methane demonstrated that even though the pollutant has significant biogenic sources, and hence a nonuniform release pattern, the technique is able to generate an emission map which is in good agreement with the published figures.
 The degree of conformity with the assumptions for CFC-11 and CFC-12 are similar, therefore the technique should perform to the same level of robustness for both species. The CFC-12 comparison with the literature is much closer than the corresponding comparison for CFC-11. The conclusion is that the accuracy of the existing inventories significantly varies between the two species.
 The uncertainty in the emission figures published in the literature for nitrous oxide are potentially high owing to the problems of describing the dominant release from agricultural soils. The comparison between the NAME back-attribution technique and the literature is therefore surprisingly good with all area and country totals agreeing within a factor of 1.5.
 It is interesting to note that in Figures 5, 7, 8, and 9 the emissions in the lower right-hand corner are poorly resolved and invariably low. The Po Valley encompassing the heavily populated areas of Milan and Turin would be thought to emit increased levels of all four of the pollutants considered, the technique fails to indicate any such sources. The frequency of transport from this region to Mace Head is low, although through amalgamation of grid cells this effect has been to some extent mitigated. Previous work [Gangoiti et al., 2001] has indicated that emissions from around the Mediterranean basin usually pool over several days with complex vertical structure and large circulations throughout the whole region. On the limited occasions when such phenomena are followed by a northerly flow, the Mediterranean air is forced through the Carcasonne/Toulouse Gap between the Pyrenees and the Alps into France. One conclusion is that the UM and resulting dispersion fail to adequately capture the complex orographic flows associated with the northwestern Mediterranean area and consequently the transport from there to Mace Head. All four emission maps support this idea, all show high emissions in the Toulouse/Barcelona area and low emissions in the rest of the Mediterranean area.
 It has been demonstrated that when real data are used the errors due to inaccuracies in the modeled meteorology and dispersion and the observations, although significant, do not prevent the NAME back attribution technique from extracting real information. The technique is able to provide information regarding the emission distribution across Europe and to estimate area and country contributions, information that for some species is not currently available. The technique employs a very different methodology in deriving emission estimates than those currently used and so is a useful tool in verifying existing emission estimates.
 The work has been supported by DEFRA as part of the Global Atmospheric division contracts EPG 1/1/103, EPG 1/1/37, and PECD 7/10/154, and by the Government Meteorological Research Programme of the Met Office. We specifically acknowledge the cooperation of all members of the AGAGE team in collecting and calibrating the Mace Head observations. The authors would like to thank Archie McCulloch for allowing the use of his emission figures and the referees for helping to improve the paper.