Global three-dimensional (3-D) model calculations have been used to inversely determine OH concentrations from 1,1,1-trichloroethane (methyl chloroform or CH3CCl3) measurements at the Atmospheric Lifetime Experiment (ALE)/Global Atmospheric Gases Experiment (GAGE)/Advanced GAGE (AGAGE) measurement stations. Annual global and biannual hemispheric estimates of OH show large fluctuations. With the aid of “pseudo data,” it is shown that these estimates are sensitive to simplifying assumptions in the model that is used for the inversion. The use of climatological transport and errors in the emissions cause spurious fluctuations in the retrieved OH levels. If only the slow OH variations are considered, an OH increase of about 12% is calculated in the 1978–1990 period, which is followed by a slightly larger decline in the 1991–2000 period. The N/S interhemispheric ratio is optimized to a value of about 0.98. Model calculations indicate that because of a rapidly decreasing CH3CCl3 burden in the 1990s, the stratospheric sink has become less important. Moreover, owing to the changed CH3CCl3 distribution, interhemispheric transport of CH3CCl3 has ceased in recent years. These effects lead to systematic differences with results obtained with highly parameterized models with very low resolution. The large OH anomaly that is inferred around 1990 vanishes if CH3CCl3 emissions of about 65 Gg were delayed from the early to the late 1990s.
 The hydroxyl radical (OH) plays an important role in the oxidation power of the troposphere. This short-lived species with a lifetime of about 1 s initiates the breakdown of hydrocarbons (CH4 and nonmethane hydrocarbons (NMHCs)) and carbon monoxide (CO). OH production is initiated by photolysis of ozone at ultraviolet (UV) wavelengths (λ < 320 nm). The highly reactive oxygen atom that is formed, O(1D), can react with water vapor to generate two OH radicals. Consequently, the highest OH concentrations are expected in the humid tropics where both water vapor and the UV light intensity maximize. Owing to the variability in tropospheric UV radiation, water vapor, and ozone, the OH concentration in the troposphere is highly variable. In-situ measurements have confirmed this variability [e.g., Mauldin et al., 2001], as well as the order of magnitude of the tropospheric concentration as estimated by chemistry transport models (≈1 × 106 molecules cm−3 [World Meteeorological Organization (WMO), 1999]).
 Since the sources and sinks of OH vary considerably in space and time, in situ measurements are generally not representative of large-scale average OH concentrations. A global average can be obtained in an indirect way by monitoring species that are destroyed by OH. Spivakovsky et al.  explored many of these species and indicated that 1,1,1 trichloroethane (methyl chloroform or CH3CCl3) is arguably the best to constrain calculations of global tropospheric OH concentrations. The global average OH concentration determined in this way is then weighted with the reaction rate between CH3CCl3 and OH [Lawrence et al., 2001].
 Since 1978 CH3CCl3 has been measured at several stations that are evenly distributed over the globe. The Atmospheric Lifetime Experiment (ALE) was followed by the Global Atmospheric Gases Experiment (GAGE) and the Advanced Global Atmospheric Gases Experiment (AGAGE) [Prinn et al., 2000]. Independently, Montzka et al.  analyzed CH3CCl3 flask samples that were collected at 7 to 10 remote locations.
 The measurements show first of all that the atmospheric CH3CCl3 concentrations have been declining since about 1992 as a consequence of the Montreal Protocol and its amendments. As a result, the atmospheric concentrations are currently lower than in 1978. The CH3CCl3 increase up to 1992 and its subsequent decline has also been recorded in the accumulated firn of Greenland and the South Pole [Butler et al., 1999].
 Second, the measurements reveal that the lowest mixing ratios are currently observed in the tropics. Since the emissions are now small compared to the atmospheric burden [Prinn et al., 2001] this observation can only be explained by a relatively strong destruction by OH in the tropics. Thus, in addition to the global OH concentration, important information about the global OH distribution can be obtained from the CH3CCl3 measurements [Spivakovsky et al., 2000].
 From the CH3CCl3 decline in 1998 and 1999, Montzka et al.  inferred a global CH3CCl3 lifetime of about 5.2 years, which is somewhat longer than the estimate by Prinn et al.  (4.9 years, estimated as burden divided by total loss) using the ALE/GAGE/AGAGE data. This latter estimate, however, represents an average over the entire 1978–2000 period. Prinn et al.  furthermore inferred a global OH increase during the 1980s followed by an even stronger decrease in the 1990s. As a result, the inferred OH levels in 1998 and 1999 are lower than the 1978–2000 average.
 In our earlier work [Krol et al., 1998] we derived a positive 1978–1992 OH trend of about 0.5% year−1 using the ALE/GAGE measurements. This work was criticized by Prinn and Huang  who obtained essentially a zero trend using a slightly longer time series (1978–1993) [Prinn et al., 1995]. In a lengthy discussion it became clear that the difference was primarily caused by differences in the 1970–1978 emissions [Prinn and Huang, 2001; Krol et al., 2001]. Whereas we optimized our initial condition, Prinn et al.  used one specific emissions scenario. The fact that their recent analysis also reveals a positive OH trend in the 1980s reflects the different emissions that were used in previous work [Prinn et al., 1995] compared to later work [Prinn et al., 2001]. A small modification in the absolute calibration of the measurements also slightly increased the inferred OH trend over this period.
 The recent analysis of the entire 1978–2000 ALE/GAGE/AGAGE CH3CCl3 record [Prinn et al., 2001] revealed rapidly dropping OH levels in the 1990s. The estimated OH concentration in 2000 appeared to be 10 ± 22% lower than the 1979 values. Moreover, Prinn et al.  inferred that OH concentrations in the Southern Hemisphere (SH) were on average 15 ± 35% higher than those in the Northern Hemisphere (NH). These latter values are in good agreement with the independent estimate of Montzka et al. . Although the error margins are large, Prinn et al.  conclude that there are “important and unexpected gaps in our understanding of the capability of the atmosphere to cleanse itself.”
 Chemistry transport models can alternatively be used to simulate the OH distribution and the associated change in time. When preindustrial model calculations are compared to simulations of the modern atmosphere, most models predict a small reduction in tropospheric OH. For instance, Wang and Jacob  calculated an OH reduction of only 9%, despite the fact that methane and CO concentrations increased by much higher percentages. Model studies that have focused on the changing emissions during the recent decades inferred a small positive trend [Karlsdöttir and Isaksen, 2000; Dentener et al., 2002]. From the model simulations it appears that the tropospheric OH abundance is quite efficiently buffered, i.e., stable to large perturbations [Lelieveld et al., 2002]. To validate the modeled OH changes, independent estimates of the OH trend using CH3CCl3 inversions are extremely valuable [Singh, 1977; Prinn et al., 1995, 2001; Krol et al., 1998]. In this work, the 1978–2000 ALE/GAGE/AGAGE CH3CCl3 measurements are used to infer tropospheric OH concentrations with a three-dimensional (3-D) atmospheric model. We emphasize the quality of the inverse approach to obtain spatial and temporal variations in OH and the role of model errors, giving rise to caution for overinterpretation of CH3CCl3 analyses.
2.1. Inverse Method
 The inverse problem that is considered here can be written as:
Here, χs,t and σs,t (pmol/mol) denote time series of the measured monthly mean CH3CCl3 concentrations and corresponding standard deviations at the five ALE/GAGE/AGAGE stations; F(P, b) denotes the model simulated CH3CCl3 at the stations. These values depend on the state vector P and on other parameters that are collected in vector b. To optimize the OH temporal or spatial variations, parameters that are linked to these variations are included in the state vector. The other parameters, for example, those linked to transport, emissions, and CH3CCl3 destruction in the stratosphere and oceans, are included in b.
 The optimization of the parameters in the state vector is based on minimization of the cost function, which is defined as:
where ϵ is the absolute measurement calibration; vector P refers to np free model parameters; Λ scales the prior information given by ϵap and Pap with standard deviations σϵ and σP. Note that the absolute measurement calibration is always optimized along with the parameters in the state vector P.
 The first term of equation (2) sums the squared differences between model and measurements, weighted with the measured standard deviation during a month. Owing to declining emissions in the 1990s, these standard deviations have substantially reduced since the 1980s. The current approach does not use polynomial fitting like in the work of Krol et al. . These polynomials filter out seasonal and interannual variability. One reason to use polynomial fitting was the inability of our climatological model to simulate interannual variability. However, the extension of the ALE/GAGE measurements with the AGAGE data hamper the use of low order polynomials. Moreover, when polynomials are used, the weighting at the beginning and the end of the time series might be slightly different compared to the original data [Prinn and Huang, 2001]. Although we showed that the derived OH trend and concentration are not influenced by the use of polynomials [Krol et al., 2001], we decided to use the monthly averages and standard deviations directly in the optimization. Since the model uses monthly averaged winds, pollution events are excluded from the measurements [Prinn et al., 2000].
 Differences between model and measurements are caused by inaccuracies in the model transport, the applied CH3CCl3 emissions, the OH distribution and its temporal variation, other CH3CCl3 sinks (stratosphere, oceanic sink), the CH3CCl3 measurement calibration and chemical rate constants. Moreover, representation errors occur because point measurements are compared to large grid boxes in the model. It is assumed that the variations in the mixing ratios during a month (σs,t, pollution events excluded) provide an estimate for these representation errors [Prinn et al., 2001]. It is not likely, however, that σs,t provides a reliable estimate of modeling errors caused by the parameters (e.g., transport, emissions, collected in b) that are not optimized. One option would be to increase the observational uncertainty σs,t to account for these modeling errors. Another, which is employed here, is to introduce a weight in front of the prior information in the cost function (see below).
 In the period 1978–2000 1248 (N) monthly averaged CH3CCl3 concentrations at the ALE/GAGE/AGAGE stations are publicly available (http://cdiac.ornl.gov/ftp/ale_gage_Agage/). The resulting correspondence between measurements and model will be reported as the value of the cost function divided by the number of measurements (J/N). J/N ≈ 1 thus corresponds to an average deviation of about 1.4σ between model and measurements.
 The second term in equation (2) represents the costs related to deviations from the prior information. The use of prior information has two well-known advantages [see, e.g., Tarantola, 1987]: (1) The optimized parameters are constrained to values that are physically realistic, and (2) the solution is stabilized. An unstable solution may occur if a parameter in the state vector is strongly correlated to other parameters. In that case, a range of parameter values corresponds to the same minimum of the cost function. The use of prior information resolves this ambiguity, since the optimized parameters should remain consistent with their prior information. Correlations between the determined parameters can be inferred from the posterior covariance matrix.
 The model relation F(P, b) is not exact and the resulting model errors will be highly correlated. This would require the evaluation of the full prior covariance matrix σs,t in the first term of equation (2). Moreover, the number of observations is much larger than the number of unknowns in the current inversion, which would put a relatively large weight on this first term. To resolve these problems, a factor Λ is introduced to scale the prior information in the cost function. Without this factor, estimated parameters can deviate a few standard deviations from the prior information without contributing significantly to the cost function, which would make the solution unrealistic. Introduction of Λ = 100 guarantees that, in this inverse problem, the free parameters are optimized well within their σap values. Parameters that are not constrained by prior information are given large σap values. On the other hand, small σap values can be used to constrain a parameter to a predefined value. No prior constraints are placed on parameters that are related to OH. The absolute calibration uncertainty σϵ is set to 5% [Prinn et al., 2001] and whenever emissions are estimated, the associated 1σ uncertainty is used as a prior constraint.
 The effect of the use of Λ instead of a more realistic prior covariance in equation (2) is that the posterior errors in the optimized parameters will only reflect the errors that are associated with the inverse procedure, that is, assuming a perfect model. Moreover, the average deviation between the measurements and the optimized model will generally be larger than 1σ since the σs,t values in equation (2) only partly reflect the true modeling errors.
 The cost function is minimized by varying the state vector P until a minimum is obtained. Practically, the model is linearized around a solution P0:
After minimization of the cost function (equation (2)) P0 is replaced by the new solution and the procedure is repeated until convergence is reached. Owing to the linear nature of the perturbations, convergence is usually obtained in one iteration. The error covariance matrix of the estimated state vector is obtained from the linearized model, the measurement errors, and the prior errors in the state vector [Tarantola, 1987]. It is assumed that the measurement errors are uncorrelated and Gaussian. The same assumptions apply to the prior errors.
 The procedure outlined here leads to results that are identical to our earlier approach which employed an ensemble smoother [Krol et al., 1998], but is computationally more efficient. Additionally, the absolute calibration ϵ of the measurements is now optimized along with the other parameters in the state vector.
2.2. Model Description
 Two models have been used to perform the CH3CCl3 simulations. The TM3 model [Dentener et al., 1999; Lelieveld and Dentener, 2000; Peters et al., 2001] is employed to perform simulations using 6-hourly analyzed wind fields from the European Centre for Medium range Weather Forecasts (ECMWF). The TM3 model is operated with a relatively coarse horizontal resolution of 7.5° latitude and 10° longitude and with 19 layers in the vertical. The upper five layers represent the stratosphere in which, apart from OH oxidation, photolysis of CH3CCl3 is important. Photolysis rates in the stratosphere are calculated using a look-up table approach. The DISORT model [Stamnes et al., 1988] has been used to construct the look-up table. Cross-sections and quantum yield are taken from DeMore et al. . Monthly averaged OH fields as calculated for the year 1986 are used to oxidize CH3CCl3 [Lelieveld and Dentener, 2000]. The 1986 meteorological fields are used in all years of the 1951–2000 simulation period.
 The calculated lifetime for stratospheric loss (total atmospheric burden over stratospheric loss) calculated by TM3 amounts to about 45 years, in excellent agreement with other work [WMO, 1999]. The corresponding stratospheric loss rate (0–100 hPa burden over 0–100 hPa loss) amounts to about 2.5 year. Two reasons hamper the use of the TM3 model for CH3CCl3 inversions: (1) The TM3 model is computationally too expensive, and (2) owing to the more detailed meteorology in TM3, pollution events will be partly resolved. A full simulation of all the pollution events, for example, at the Ireland station [Ryall et al., 2001] would require the use of all years of meteorological data and a higher resolution of the model. Therefore, the TM3 simulations are used to tune the stratospheric loss in the MOGUNTIA model and to check the CH3CCl3 budget (see Appendix A).
 Similar to Krol et al.  the MOGUNTIA model is used in the inversion of the CH3CCl3 observations. The replacement of the Oregon station (45°N) by the California station (41°N) does not change the sampled grid box in the MOGUNTIA model. In MOGUNTIA, monthly averaged wind fields of the year 1986 are used to transport CH3CCl3. Emissions have been adapted from McCulloch and Midgley  and the spatial distribution is similar to Krol et al. . For the recent years the emissions are distributed similar to that given by Prinn et al. .
 In previous work [Krol et al., 1998] we accounted for the stratospheric sink by applying hemispheric mean and monthly varying loss rates at 100 hPa (the top of the model). Before 1990, CH3CCl3 emissions increased continuously and caused a large concentration difference between the troposphere and the stratosphere. However, the emissions declined strongly in the 1990s and it is therefore expected that during this period the stratosphere becomes a less important sink for troposphere CH3CCl3. For this reason, we modified the stratospheric loss parameterization. Two reservoirs which represent the stratosphere (0–100 hPa) in the NH and the SH are added on top of the MOGUNTIA model. Exchange between the stratospheric reservoir and the upper model layer is calculated from the concentration difference multiplied by an exchange rate. The SH exchange rate is taken 33% slower than the NH value. The exchange rate and the stratospheric CH3CCl3 lifetime are obtained from a simulation with the TM3 model as described previously. A more detailed discussion of the stratospheric parameterization is given in Appendix A.
 Uptake and subsequent hydrolysis of CH3CCl3 in ocean water is modeled by a first order loss process [Krol et al., 1998; Kanakidou et al., 1995; Kindler et al., 1995]. The loss rate is based on measurements reported by Butler et al. , who observed negative saturation anomalies in the tropical pacific ocean in 1990. Hydrolysis of CH3CCl3 is most efficient in warm ocean waters but CH3CCl3 is much more soluble in the colder oceans at higher latitudes. Hydrolysis in these waters proceeds much slower owing to the lower temperatures. Hydrolysis in cold oceans [Gerkens and Franklin, 1989] is expected to be even slower than the observed atmospheric decay time since 1992. Cold oceans may therefore have acted as a buffer for the atmosphere since dissolved CH3CCl3 may have returned to the atmosphere. This idea is highly speculative and not tested while biological degradation in the productive waters at high latitudes cannot be ruled out [Butler et al., 1991]. Possible consequences for the CH3CCl3 inversion, which appear to be small, are discussed in Appendix B.
3. Annual and Hemispheric OH Optimization
 Following Prinn et al. , we optimized 23 yearly and global OH scaling factors (1978–2000). These scaling factors are multiplied to our reference OH field [Krol et al., 1998]. Simulations are performed from 1951 to 2000 and the 1978 scaling factor applies to all years before 1978 as well. Krol et al.  optimized the initial condition. In the inversion of annual OH levels, however, optimization of the initial condition is no longer necessary because an increase in the pre-1978 emissions has the same effect on the cost function (equation (2)) as a decrease in the pre-1978 OH level. As a consequence, the optimization of both pre-1978 OH and pre-1978 emissions simply returns the prior information for the emissions.
 In addition to the optimization of global OH scaling factors, we also determined hemispheric OH scaling factors. These scaling factors are optimized in 2-yearly periods, which leads to a state vector length of 24. In our reference OH distribution, the OH concentration (weighted with the CH3CCl3 + OH reaction rate) in the NH exceeds the SH value by about 20%.
 The results of the optimizations are shown in Figure 1. The values for ϵ are 0.989 ± 0.003 and 0.996 ± 0.005 for the global and hemispheric OH optimizations, respectively (reported errors from inversion only). The optimized J/N values are 0.77 and 0.60, respectively. With an average deviation close to the 1σ level, the optimized model results are in excellent agreement with the ALE/GAGE/AGAGE measurements. Hemispheric OH optimization gives an even better fit to the measurements than the global OH optimization.
 Similar to the results of Prinn et al. , the optimized OH levels show large fluctuations. Year to year jumps of more than 10% in hemispheric and global OH concentrations are not uncommon. Are these temporal and spatial variations real, or are they associated with the estimation method? In the following, we will show that these variations are most likely an artifact of the method.
4. Analysis of the OH Fluctuations
 An important aspect to consider in the inversion is the atmospheric lifetime of CH3CCl3 (about 5 years). It exceeds the mixing time in the troposphere and is also large compared to the temporal variations in the retrieved OH. By fixing all parameters b in equation (1) it is implicitly assumed that all discrepancies between model and measurement are explained by variations in OH. This means that errors in b (transport, other sinks, etc.) are potentially translated in OH variations during the inversion process. As an example, the derived reductions in global OH during El Niño Southern Oscillation (ENSO) events might be real, but might also be caused by the fact that the model does not account for interannual transport variability [Prinn et al., 2001].
 Another possible cause for the retrieved OH fluctuations might be the ill-posed nature of the inversion itself. This situation occurs when parameters become redundant and do not longer reduce the value of the cost function. Ill-posed inversions can be stabilized by applying some kind of regularization, such as providing prior information or, alternatively, a smoothness constraint [e.g., Hasekamp and Landgraf, 2001].
 The possibility of an ill-posed inversion is investigated by replacing the ALE/GAGE/AGAGE measurements with “pseudo data” that are calculated by the model itself. We prescribed a linear OH trend to the model (−6% in 1978 to +5% in 2000, relative to the reference field). The 1σ errors in the calculated pseudo data are taken identical to errors of the true ALE/GAGE/AGAGE measurements. The pseudo data are perturbed with small random noise. If the inversion procedure is applied to these data, we indeed retrieve the prescribed trend in OH (see Figure 2a). Therefore, the inversion itself is not ill-posed.
 This leaves the possibility that the retrieved OH fluctuations are caused by model errors. Therefore, the inversion of the model generated pseudo data is repeated, but now with slightly modified model formulations. To account for uncertainties in the model transport we performed two simulations with the more advanced transport model TM3. In one simulation, the 1986 meteorological data are used for all years in the 1951–2000 period. In the second simulation, the meteorology of the years 1979–1997 is used for the corresponding years. As an example, Figure 3 shows the ratio of the monthly mean concentrations in these two simulations as sampled in the Barbados grid box.
 Obviously, transport alone generates interannual variability of the order of a few percent in the simulated monthly averaged concentrations. The calculated ratio of the two simulations is used to estimate the magnitude of the interannual transport variability at the stations. To test the influence on the OH inversion, we multiplied this ratio evaluated at the five ALE/GAGE/AGAGE stations to the pseudo measurements, and repeated the inversion. The result is included in Figure 2a (dotted line). Also included are the inversion results of simulations in which (1) the emissions were randomly varied within their 1σ uncertainties (dash-dotted), and (2) the convective fluxes in the model were multiplied by a factor 0.5 (dashed).
 Clearly, the calculated yearly OH concentrations are very sensitive to errors in meteorology and CH3CCl3 emissions. Global deviations from the true solution may be as large as 7%, for example in 1994 and 1998. Moreover, changing the convective fluxes results in systematic deviations. However, the linear trend in the true solution can still be inferred from all results. It can thus be concluded that the inversion of OH scaling factors for single years is very sensitive to modeling errors and that only variations on the longer timescales can be inferred from CH3CCl3 inversions.
 The fact that OH concentrations can only be retrieved as long-term means implies that the retrieval of hemispheric OH values will also be sensitive to model errors, since interhemispheric transport times are of the order of 1 year. To show this sensitivity, we repeated the inversion of pseudo data, prescribing a positive OH trend in the NH and a negative trend in the SH. We inverted 2-year OH averages in the NH and the SH, using the different model versions described earlier. The results are summarized in Figures 2b and 2c. Again, some skill in inverting the prescribed OH trend in the hemispheres seems to be present. However, the deviations become particularly large in the inversion with modified transport. For instance, the large negative OH deviations in the NH are partly compensated by positive deviations in the SH. These correlations are quantified in the covariance matrix. Correlation coefficients between the biannual OH estimates of the hemispheres range from −0.68 to −0.98.
 From these experiments with pseudo data it can be concluded that the large OH fluctuations that are retrieved from the global annual and hemispheric biannual OH inversions are probably caused by modeling errors. A similar observation was made by Houweling et al.  who optimized methane emissions from a surface measurement network. Our results indicate that some information about OH variations on the slower timescale can be retrieved as long as model errors are not too large. Therefore, the inversion of the ALE/GAGE/AGAGE data is only meaningful by focusing on these slower OH variations.
5. OH Changes on a Long Timescale
 The OH levels are now estimated in 3- and 5-year periods. These periods are sufficiently long to smooth the effects of the errors in emissions and meteorology, at least the random part of these errors. In addition, the OH change in time has been expressed as a second-order polynomial [Prinn et al., 2001]:
in which N amounts to 11 years and t runs from 0 (1978) to 2N (2000) and P1 and P2 are Legendre polynomials. a (%), b (% yr−1), and c (% yr−2) are included in the state vector. Alternatively, coefficient a is determined for the NH and SH separately, to estimate the time-averaged N/S interhemispheric ratio. In the inversions, the 1970–1978 emissions are also optimized by determining a single factor that is multiplied to the yearly emissions in this period. The prior error for this factor is assumed to be 2%.
 The results are summarized in Figures 4 and 5and Tables 1–4. Figure 5 shows the modeled and observed e-fold decay times calculated from monthly means at the end of each yearly period as e.g., τ2000.5 = (ln χ2000.5 − ln χ1999.5)−1 [Montzka et al., 2000]. The results have been obtained with the OH variation optimized according to equation (4). The average e-fold decay time calculated from the AGAGE data and from our model (about 5.7 years) is slightly slower than the decay time deduced by Montzka et al. . Note that the remaining discrepancies between model and measurements may be explained by OH variations on both hemispheres. However, we have shown above that model errors or uncertainties in the CH3CCl3 emissions are a more plausible explanation. The resulting correspondence between the model and the measurements is very good, especially considering possible model errors and emission uncertainties.
 With regard to the deduced variations in OH, our results confirm those obtained by [Prinn et al., 2001] with a few important exceptions. Their optimized polynomial yields 15% lower OH levels in 2000 compared to the levels in 1978. This lower OH level has been interpreted as a possible collapse of the oxidizing capacity of the troposphere. In contrast, our optimization leads to OH levels in 2000, which are only slightly lower than the pre-1980 levels. The N/S hemispheric OH ratio optimized in our model (see Table 4) amounts to 0.98, which also differs from the ratio of 0.88 presented by Prinn et al.  (14 ± 35% more OH in the SH). Nevertheless, these results appear to confirm that the CH3CCl3 measurements point to a significant increase in OH levels during the 1980s and a subsequent decline in the 1990s.
 Although the results presented here fall well within the wide error margins given by Prinn et al.  the N/S hemispheric ratio and the OH decline in the late 1990s differ systematically. These differences can be understood from model differences. A very low-resolution model has limited ability to simulate the effects of the changing CH3CCl3 distribution on interhemispheric CH3CCl3 transport and on CH3CCl3 exchange between the troposphere and stratosphere. For instance, the transport in the model used by Prinn et al.  has been tuned to observations of F11 and F12. However, these tracers behave distinctly different from CH3CCl3, which has an important tropospheric sink. The N/S interhemispheric OH ratio of 0.88 as calculated by Montzka et al.  is based on a two-box budget approach. This approach assumes that interhemispheric transport is proportional to the interhemispheric concentration difference.
 Our model results indicate that the interhemispheric exchange in the late 1990s becomes negligible with equal amounts of OH in both hemispheres. Since the major CH3CCl3 sink is located in the tropics, transport of CH3CCl3 in recent years occurs mainly between the high and low latitudes within both hemispheres. To model small interhemispheric transport of CH3CCl3 in the presence of a large OH gradient requires a higher resolution than is provided by two or four boxes. The same argument applies to stratosphere-troposphere exchange. Although the stratosphere in the MOGUNTIA model is also very simple, it has been tuned to a model that explicitly resolves the stratosphere (see Appendix A).
 The fact that we estimate more OH on the SH (in apparent conflict with our model calculations) might well be due to model or emission errors as discussed above. For instance, additional NH CH3CCl3 emissions of 30 Gg yr−1 in the period 1998–2000 requires 12% higher 1998–2000 global OH levels to remain consistent with the measurements. Moreover, such an additional source would change the optimized N/S interhemispheric ratio from 0.98 into 1.06.
 Another factor is that the mean location of the Intertropical Convergence Zone (ITCZ) is at 6°N [Waliser and Gautier, 1993], so that the average SH air mass, for which the CH3CCl3 burden is calculated from SH measurements [Montzka et al., 2000], is approximately 12% larger than the NH, for which the NH stations are assumed to be representative. The “division” between the two hemispheres strongly influences the interhemispheric OH ratio calculations from CH3CCl3 distributions, notably for the period when CH3CCl3 concentrations were substantially higher in the NH. The apparent discrepancy between the CH3CCl3 derived OH asymmetry and that calculated by chemistry-transport models may therefore be an artifact from the assumption that the well-mixed “meteorological” hemispheres are symmetrical around the equator. Improved estimates of interhemispheric OH differences from CH3CCl3 analyses therefore await inversion models that properly resolve the ITCZ. The fact that our inversion model (10°resolution) calculates a significantly higher N/S interhemispheric ratio than models with an even lower resolution, points to a high sensitivity of this ratio to the model resolution.
 To show which emissions correspond to a time-invariant OH burden, the global CH3CCl3 source can be optimized assuming constant OH levels [Prinn et al., 2001]. Thus we scaled our reference OH field by −7.4% (according to Table 3 and equation (4)), and estimated the emissions in 3-year periods. As for OH, emission scaling factors have been determined without taking any prior information into account. Note that this approach does not maintain constant total emissions (a quantity that can be estimated relatively accurately).
 The results, summarized in Table 5, indicate that a shift in emissions of in total 100–150 Gg from the 1983–1991 period to the pre-1983 and post-1991 periods would be required to arrive at a constant OH level. Such a shift represents a small fraction of the emissions that occurred in the early 1990s, but is large compared to the emission estimates for the recent years. For the recent years, the optimized emissions are not consistent with the error estimate given by McCulloch and Midley . We note, however, that additional banking of CH3CCl3 or an underestimate of “slow-use” CH3CCl3 applications during the early 1990s would explain the AGAGE measurements in the recent years without a significant drop in OH. Note also that the optimization of the emissions results in a slightly better fit to the observations (J/N ≈ 0.9) than the optimization of OH (J/N ≈ 1.0, see Table 1).
Table 5. Optimization of the Emissions in 3-Year Periods
 Based on calculations using chemistry-transport models, large interdecadal swings in global tropospheric OH concentrations are not expected. Furthermore, the methane growth rate varied from about 20 ppbv yr−1 in the 1970s and 12 ppbv yr−1 in the 1980s, to almost zero in 1992–1993 [Lelieveld et al., 1998; Dlugokencky et al., 1998]. It is moreover unlikely that OH level changes are the sole cause of the decline in the methane growth rate in the early 1990s. More likely, the natural wetland emissions temporarily declined after the Mt. Pinatubo eruption [Hogan and Harriss, 1994; Walter et al., 2001; Dentener et al., 2002] and the changing methane emissions from the former Soviet Union may have influenced the methane budget [Dlugokencky et al., 1995]. Positive methane growth rates were restored after 1993, whereby variability has been attributed to the variability in emissions [Dlugokencky et al., 2001].
 Model calculations that focused on the 1979–1993 period point to a small increase in OH of about 0.25% yr−1 during this period [Dentener et al., 2002]. This increase can partly be attributed to changes in stratospheric ozone, OH precursor emission changes, and meteorological variability. Meteorological variability alone causes year-to-year changes in the global tropospheric OH burden of a few percent. This variability might become somewhat larger if also the full variability in emissions (e.g., from biomass burning) would have been taken into account. From these model calculations it nevertheless appears that interdecadal variability of more than 10% is in contradiction with observed methane growth rates.
 In fact, the remarkable covariation of the global CH3CCl3 burden and the optimized OH variations (with maximum OH levels around 1990), both in our results and even more strongly in those by Prinn et al. , might signal a systematic modeling error. A common cause of these variations is unlikely, since the OH budget is hardly affected by the CH3CCl3 concentrations in the atmosphere. If the CH3CCl3 emissions shifted from the early 1990s to the recent years, understandable in the light of enhanced stockpiling associated with the phase-out of CH3CCl3 production under the Montreal Protocol, this would leave the total source (which can be estimated relatively accurately) unaffected. It would also lead to much smaller interdecadal OH variations, which in turn is more consistent with observed methane growth rates and atmospheric chemistry modeling [Dentener et al., 2002; Lelieveld et al., 2002].
 Using a 3-D global transport model, variations in tropospheric OH have been determined from CH3CCl3 measurements at the ALE/GAGE/AGAGE stations. The main conclusions are:
Interannual global and hemispheric OH inversions are very sensitive to modeling errors, in particular of the CH3CCl3 emission estimates.
Inverse OH retrieval techniques based on CH3CCl3 observations are not suited to accurately infer short-term OH variability (<3 years), unless highly accurate models are used that resolve actual meteorology. Provided that CH3CCl3 emissions are known accurately, these techniques are, however, adequate to study long-term OH changes.
Estimates of the slow and large-scale OH variations indicate a substantial increase (≈12%) in the 1978–1990 period, followed by a slightly larger decrease in the decade 1991–2000. Hence the overall trend over the entire period is close to zero.
The calculated CH3CCl3 decline depends relatively strongly on changes of the stratospheric CH3CCl3 sink. Owing to the fast decline of tropospheric CH3CCl3 and a “buffering” effect, this sink has become substantially less important in the recent years.
Large swings of OH on interdecadal timescales are in conflict with observed methane growth rates and with model calculations. A shift in CH3CCl3 emission estimates from the early 1990s to the recent years offers a plausible explanation to the observed decline in atmospheric CH3CCl3.
The question of interhemispheric OH (a)symmetry will remain unresolved until CH3CCl3 emissions are quantified with higher accuracy, and until CH3CCl3 transport models are used that resolve the ITCZ and accurately describe interhemispheric exchange. Our results indicate a small interhemispheric OH difference.
 Definite conclusions about the trend in tropospheric OH cannot be drawn before the quantitative understanding of the CH3CCl3 emissions is improved. Measurements that aim at the localization of possible ongoing CH3CCl3 emissions are therefore urgently required.
Appendix A:: Stratospheric Loss
 Timescales associated with stratospheric CH3CCl3 loss are larger than the mixing time in the troposphere. Loss predominantly occurs by photolysis in the upper stratosphere and therefore the turnover time (burden/loss) in the stratosphere is not only determined by chemistry, but also by transport. During the 1980s CH3CCl3 emissions increased strongly and the stratospheric concentrations were relatively low compared to tropospheric concentrations. This situation changed in the late 1990s. Emissions dropped and, due to the time delay associated with stratospheric transport, the relative concentration difference between the stratosphere and troposphere decreased [Prather, 1997].
 The TM3 model explicitly takes the stratospheric removal of CH3CCl3 into account. Although one might argue that the vertical resolution in the upper stratosphere (levels at 10, 30, and 50 hPa) is not sufficient to model the CH3CCl3 photolysis correctly, the estimated lifetime with respect to stratospheric loss agrees well with other estimates [WMO, 1999]. Table A1 lists the lifetimes as calculated in the TM3 and MOGUNTIA models, both operated with unscaled and constant OH fields. The MOGUNTIA stratosphere has been parameterized as described in section 2.2. The lifetimes are defined as tropospheric burden over process loss [Prather, 1997]. The processes considered are (1) OH oxidation, (2) removal by ocean uptake, and (3) loss to the stratosphere. Note that the lifetimes are calculated for the tropospheric burden (1000–100 hPa), which results in smaller values compared to calculations that also include the stratospheric burden.
Table A1. Tropospheric Lifetimes of CH3CCl3 in TM3 and MOGUNTIA
Tropospheric CH3CCl3 burden divided by OH oxidation in the troposphere.
Tropospheric CH3CCl3 burden divided by loss to the stratosphere.
Tropospheric CH3CCl3 burden divided by ocean uptake.
Tropospheric CH3CCl3 burden divided by the total loss.
 Although the results of the two models differ slightly, the tendencies are the same. The lifetime of the tropospheric burden with respect to stratospheric loss increases significantly from about 34 years to 58 years. As a result, the total tropospheric lifetime increases in both models by about 6%. Given the substantial differences between the TM3 and MOGUNTIA models it can be concluded that the simple parameterization outlined in section 2.2 performs well.
Appendix B:: Oceanic Removal
 The timescale that is associated with hydrolysis of CH3CCl3 in cold ocean water is longer than the atmospheric decay observed in the 1990s [Gerkens and Franklin, 1989; Butler et al., 1991]. For this reason, the cold ocean water may have become supersaturated relative to the atmosphere during the period of fast atmospheric decline. To estimate the effect of such a buffering effect on the OH inversion, the ocean sink parameterization was modified. Thus, the ocean mixed layer was treated as a well-mixed reservoir that is in equilibrium with the lower atmosphere. The CH3CCl3 budget in the mixed layer is calculated by uptake or release to the atmosphere and a temperature dependent hydrolysis reaction [Gerkens and Franklin, 1989]. Other terms, like horizontal transport and transport to the deep ocean have been neglected. Similar to Krol et al. , monthly mean climatologies of the mixed layer temperature and thermocline depth were used.
 By using this simple parameterization in the inversion, the 2000 OH level is calculated to be about 4% higher than with the first-order oceanic loss, which implies that the effect on the OH trend calculations is only small. At present, however, not enough measurements are available to validate the buffering effect of the cold oceans. Moreover, the effects of horizontal and vertical transport within the ocean has been neglected. For these reasons, and because the effect is calculated to be relatively small, oceanic removal was still treated as a first order loss process, as described by Krol et al. .
 This research was supported by Space Research Organization Netherlands. M.K. is grateful for support from many colleagues. Otto Hasekamp and Jochen Landgraf are acknowledged for their insight in inverse problems, Sander Houweling and Frank Dentener for their stimulating discussions, and C. Brühl for assistance with the stratospheric methyl chloroform removal calculations. R. Prinn and colleagues are acknowledged for the ALE/GAGE/AGAGE measurements.