5.1. Factors of Variability
 We now examine the variability in tropospheric ozone budgets for the ensemble of models reported in the literature. Values of P(Ox) vary from 2300 to 4300 Tg yr−1 in the 1996–2000 literature reviewed by IPCC TAR and from 3300 to 5300 Tg yr−1 in the post-2000 literature compiled in Table 1. Compared to the older generation of models compiled in IPCC TAR, the ensemble of post-2000 models shows significant mean differences in global ozone budgets, including a 35% increase of ozone production, a 34% decrease of STE ozone flux, and a 10% increase of ozone burden (Table 2). The recent intercomparison of 21 current-generation models (including different versions of the same models) by Stevenson et al.  shows a 10% further increase in mean P(Ox) relative to the post-2000 literature (Table 2). All models in that intercomparison were constrained to use the same ozone precursor emissions from anthropogenic sources and biomass burning, while natural emissions were allowed to vary from model to model.
 The definitions for the tropopause and for the odd oxygen family (Ox) used to compute tropospheric ozone budgets may vary from one model to another, and this is a factor of variability in the budgets in Table 2. Most model studies use the thermal tropopause as determined by the temperature lapse rate, while some use a chemical tropopause ([O3] = 150 ppb) [e.g., Prather et al., 2001; Stevenson et al., 2004, 2006]. Logan  showed from ozonesonde data that the mixing ratio of ozone is usually less than 150 ppbv at the thermal tropopause, except in summer at middle and high latitudes. We find in GEOS-Chem that the tropospheric ozone burden is 10% higher if we use the chemical versus thermal tropopause definition. Stevenson et al.  previously found that P(Ox) is relatively insensitive to the definition of the tropopause but that the ozone burden and lifetime are more affected. Some model budgets include peroxyacetylnitrates (PANs) and HNO3 in their definition of the Ox family, while others do not, but this has little importance since peroxy radicals + NO reactions are the main contributors to P(Ox) and are included in all models [Stevenson et al., 1997; Wauben et al., 1998; Wang et al., 1998a; Crutzen et al., 1999]. We find in our model that excluding PANs and HNO3 from the Ox family causes a 10% increase in P(Ox). These effects are relatively small, and there is no trend in their use that could explain the mean difference in budgets between the IPCC TAR and post-2000 models.
 The STE ozone fluxes in the older IPCC TAR models ranged from 390 to 1440 with a mean of 770 ± 400 Tg yr−1. It is now recognized that many of these fluxes were too high, driven by artifacts in the vertical winds at the tropopause, particularly when using assimilated meteorological fields [Tan et al., 2004; van Noije et al., 2004]. Robust constraints from observed NOy-N2O-O3 correlations in the lower stratosphere impose an STE ozone flux of 540 ± 140 Tg yr−1 [Murphy and Fahey, 1994; Olsen et al., 2001]. The STE ozone flux in the current generation of global models in Table 2 (510 ± 90 Tg yr−1) reflects that constraint, often through the use of a flux boundary condition (as in GEOS-Chem) or by relaxation to observed ozone concentrations above the tropopause region [Horowitz et al., 2003].
 The lower STE ozone flux in the newer models leads to stronger tropospheric ozone production by reducing the NO2/NO concentration ratio in the upper troposphere. We conducted a sensitivity study using our GISS-driven GEOS-Chem simulation with the STE ozone flux increased by 25% to 625 Tg yr−1 (Table 4). The 25% increase resulted in a 5% increase of O3 burden, a 3% increase of O3 lifetime, and a 1% decrease of P(Ox). The increase in P(Ox) between the IPCC TAR models and more recent ones is much larger, and the trend in O3 burden is positive, so this cannot be a dominant effect.
Table 4. GEOS-Chem Model Sensitivities of Global Tropospheric Ozone and OH Budgetsa
| ||Chemical Production Rate of Ozone, Tg yr−1||Chemical Loss Rate of Ozone, Tg yr−1||Ozone Burden, Tg||Ozone Lifetime, days||OH, 1 × 106 molecules cm−3||Methane Lifetime, years|
|Fossil fuel NOx emission +25%||4649||4113||325||23.0||1.11||10.3|
|Lightning NOx emission +25%||4672||4158||328||23.2||1.14||10.1|
|Isoprene emission −25%||4486||3991||319||23.4||1.13||10.1|
|No isoprene emission||4394||3900||315||23.5||1.28||8.8|
|No NMVOCs emissions||3986||3566||298||24.3||1.31||8.7|
 Tropospheric ozone production is highly sensitive to the supply of NOx. Stevenson et al.  pointed out that the higher NOx and isoprene emissions used in their model intercomparison study were two important factors for their much higher ozone production rates compared to IPCC TAR values, with each factor accounting for about half of the increase of P(Ox) in one specific model (FRSGC/UCI). Comparison of the older global models compiled by IPCC TAR [Prather et al., 2001] versus the post-2000 literature of Table 1 shows a mean increase across models in global surface NOx emission (excluding lightning and aircraft) from 34.9 to 38.8 Tg N yr−1, and an increase in lightning NOx emission from 4.0 to 4.9 Tg N yr−1 (Table 5). The former reflects an actual rise in Asian NOx anthropogenic emissions between the ca. 1985 inventories used by the IPCC TAR models versus the early 1990s inventories used in the more recent models [Fusco and Logan, 2003]. There is large uncertainty associated with lightning NOx emissions. State-of-science estimates range from 1 to 20 Tg N yr−1 [Price et al., 1997; Boersma et al., 2005], though global models use values in the range 2–7 Tg N yr−1 to reproduce observed ozone and NOy concentrations in the tropics [e.g., Levy et al., 1996; Martin et al., 2002; Tie et al., 2002; Li et al., 2005].
 Another significant difference between the newer and older generation of global models is the treatment of NMVOCs. Only about half of the models compiled in IPCC TAR included NMVOC chemistry while almost all models in the post-2000 literature do. Isoprene from vegetation generally accounts for most of total NMVOC emissions (Table 3). Houweling et al.  found in their model that P(Ox) would decrease by 27% in the absence of NMVOCs. Subsequent model studies [Roelofs and Lelieveld, 2000; Poisson et al., 2000; von Kuhlmann et al., 2004] found a somewhat weaker effect, ranging from 16% to 24%. Changing methane would also have a major effect on global tropospheric ozone budgets [Wang and Jacob, 1998; Fiore et al., 2002], but models simulating present-day conditions all use sensibly the same methane levels constrained by observations.
5.2. Regression Analysis for Global Ozone Production in Models
 To explore these issues further, we conducted a multivariate regression analysis of present-day P(Ox) versus model parameters for the ensemble of 32 models compiled in Table 2 for which sufficient information was available. This included 18 models from the literature plus the 14 models from the Stevenson et al.  intercomparison that reported a model STE (Table 5). We find that 74% of the variance of P(Ox) across models can be explained by the global total NOx emissions (ENOx), STE, and NMVOC emissions (ENMVOC) through the following regression (R2 = 0.74, n = 32):
where P(Ox) and STE are in Tg yr−1, ENOx is in Tg N yr−1, and ENMVOC is in Tg C yr−1. The 85% confidence intervals for the coefficients of ENOx, ENMVOC and STE are [73, 136], [0.48, 1.45] and [−0.93, −0.01] respectively.
 We also find that an alternative regression model with on/off dependence on NMVOC emissions can equally explain (R2 = 0.74) the variation of P(Ox) across models:
where δ(NMVOC) is 1 if NMVOCs are included in the model and 0 otherwise. The step dependence on NMVOCs will be discussed below. The success of equations (1a) and (1b) in reproducing the P(Ox) for each of the 32 models included in the regression analysis is shown in Figures 6a and 6b. Differences are less than 500 Tg yr−1 for most of the models. Higher-order terms in the regression, including the product ENOxENMVOC, did not improve the regression results.
Figure 6a. Global ozone production rates from the 32 models in Table 5 as derived from the regression equation (1a) versus the actual values reported in the literature. Results from the three GEOS-Chem simulations presented in this work (driven by GEOS-3, GEOS-4, and GISS) are also plotted.
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 Applying equation (1a) to the values of ENOx, ENMVOC, and STE in the individual models yields a mean P(Ox) increase of 870 Tg yr−1 from the IPCC TAR models to the post-2000 literature, which is 72% of the actual increase shown in Table 2 (1200 Tg yr−1). Additive increases of 520, 230 and 120 Tg yr−1 result respectively from the increases of NOx and NMVOC emissions and from the decrease of STE. The other 28% of the P(Ox) increase may be due to other changes in models over the past decade including better parameterizations of convection [Chatfield and Delany, 1990; Pickering et al., 1992; Horowitz et al., 2003], cloud radiative effects [Wild et al., 2000], and aerosol extinction [Martin et al., 2002; Bian et al., 2003; Tie et al., 2005], as well as equatorward shift of anthropogenic emissions [Gupta et al., 1998; Stevenson et al., 2006]. Similarly, 1510 Tg yr−1 or 89% of the actual increase (1690 Tg yr−1, Table 2) of P(Ox) in the work by Stevenson et al.  relative to IPCC TAR models can be explained with equation (1a). Equation (1b) yields similar results. The higher P(Ox) in the Stevenson et al.  intercomparison relative to the ensemble mean of post-2000 models can be largely explained by higher NOx emissions.
5.3. Interpretation of the Regression Analysis
 We now offer a physical interpretation for the individual terms in the regression equation (1) that successfully describe global tropospheric ozone production in models. The coefficient of ENOx represents the ozone production efficiency (OPE = ∂P(Ox)/∂ENOx), and is 30 mol mol−1 in (1a) and 31 mol mol−1 in (1b). Fossil fuel combustion accounts for about half of total NOx emission in the models (Table 3). We conducted a sensitivity analysis in GEOS-Chem increasing the global NOx emission from fossil fuel combustion by 25%, which raises ENOx by 13% or 5.9 Tg N yr−1 (Table 4). We found that the global ozone production increased by 162 Tg yr−1. The OPE derived from this perturbation (8 mol mol−1) is much smaller than the OPE derived from equation (1). In a separate sensitivity test, we increased the global lightning NOx emission by 25% (1.2 Tg N yr−1, representing a 2.7% increase of ENOx) and found that P(Ox) increased by 185 Tg yr−1 (Table 4). The OPE derived from this perturbation (45 mol mol−1) is much larger than the OPE derived from equation (1). Thus lightning NOx is about 6 times more efficient in driving ozone production than anthropogenic NOx. Separating lightning from other sources of NOx in the linear regression (1) does not however produce a significantly higher correlation.
 The dependence of P(Ox) on STE is expressed in equation (1) by a linear sensitivity coefficient ∂P(Ox)/∂STE, which is −0.47 mol mol−1 in (1a) and −0.40 mol mol−1 in (1b). We find in GEOS-Chem that P(Ox) decreases by 45 Tg yr−1when we increase STE by 25% (Table 4), yielding a sensitivity coefficient of −0.36 mol mol−1 which is consistent with the result from the linear regression.
 Equations (1a) and (1b) can explain the differences of P(Ox) across global models equally well but imply different sensitivities to ENMVOC. Equation (1a) implies a linear dependence while (1b) implies a step dependence where P(Ox) increases by 670 Tg yr−1 when NMVOC emissions are included but does not increase further within the typical range of 500–900 Tg C yr−1 used in models (isoprene being the dominant contributor).
 We conducted further analysis to reconcile the discrepancy between equations (1a) and (1b). Figure 7 shows the sensitivity of P(Ox) to NMVOC emissions for the ensemble of models used in the regression analysis, after standardizing to the same values of STE (510 Tg yr−1) and ENOx (45 Tg N yr−1) using equation (1a). We see that the models results can be classified into two groups, with versus without NMVOCs. Models with NMVOCs tend to have higher ozone production, with the exception of two outliers [Hauglustaine et al., 1998; Lelieveld and Dentener, 2000]. Among the models including NMVOC chemistry, however, there is no clear dependence of P(Ox) on NMVOC emission. Although it is well known from regional ozone models that ozone production is often NMVOC-saturated, this refers to the local ozone production rate [e.g., Sillman et al., 1990], not to the ultimate ozone production as computed in a global model. Increasing NMVOCs would be expected to increase the OPE both by decreasing OH levels (and hence increasing the lifetime of NOx) and by promoting the sequestration of NOx as PAN and its eventual release in regions of high OPE [Lin et al., 1988; Houweling et al., 1998; Wang et al., 1998c; Poisson et al., 2000; Roelofs and Lelieveld, 2000; Hudman et al., 2007; von Kuhlmann et al., 2004].
Figure 7. Sensitivity of global ozone production rate P(Ox) to NMVOC emissions for the ensemble of models compiled in Table 5, and also including results from this study. The values of P(Ox) from the original publications have been standardized to the same STE (510 Tg yr−1) and ENOx (45 Tg N yr−1) using equation (1a). The dashed line shows results from GEOS-Chem sensitivity simulations (see text for details).
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 We conducted three GEOS-Chem sensitivity simulations with NMVOC emissions modified from the standard values in Table 3: one with isoprene emission reduced by 25%, one with isoprene emission set to zero, and one with all NMVOC emissions set to zero (Table 4). The sensitivity simulations show saturation (Figure 7) for NMVOC emissions greater than 200 Tg C yr−1. We find that the saturation is due to the formation of organic nitrates, especially isoprene nitrates, providing a significant sink for NOx as discussed in section 4. The importance of this sink for NOx has been discussed in previous model studies [Horowitz et al., 1998; Liang et al., 1998; von Kuhlmann et al., 2004; Fiore et al., 2005]. As shown in Figure 8, increasing isoprene emissions in GEOS-Chem saturates PAN as well as ozone, while causing sharp decreases in NOx and OH.
Figure 8. Sensitivity to NMVOC emissions of tropospheric ozone production P(Ox), mass-weighted tropospheric OH concentration, and tropospheric PAN and NOx burdens. Values are global annual means from GEOS-Chem sensitivity simulations.
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 Although it is most likely (as assumed in GEOS-Chem) that isoprene nitrate formation is a terminal sink for NOx [Giacopelli et al., 2005], some models recycle isoprene nitrate to NOx through reaction with OH [Grossenbacher et al., 2001] or do not include isoprene nitrate formation. Those models would have greater positive response of P(Ox) to the magnitude of isoprene emissions [Fiore et al., 2005]. We find in GEOS-Chem that P(Ox) decreases by 11% in the absence of NMVOCs. This sensitivity is at the low end of values reported in the literature, e.g., 16% [Roelofs and Lelieveld, 2000], 22% [von Kuhlmann et al., 2004], 22% [Poisson et al., 2000], 27% [Houweling et al., 1998]. Roelofs and Lelieveld  viewed isoprene nitrate as a terminal NOx sink, as we do here, while the other studies allowed it to recycle to NOx.
 We find that the annual mean, mass-weighted tropospheric OH concentration in GEOS-Chem increases by 21% and the methane lifetime against oxidation by tropospheric OH decreases by 18% in the absence of NMVOCs. This sensitivity is at the high end of model results reported in literature: Houweling et al.  found that including NMVOCs hardly affected the tropospheric OH burden; Roelofs and Lelieveld  reported that tropospheric OH decreases by about 8% when NMVOCs are accounted for; Poisson et al.  and von Kuhlmann et al.  found that in the absence of NMVOCs the methane lifetime would decrease by 12% and 2%, respectively. Our higher sensitivity of OH to NMVOCs again appears to reflect the treatment of isoprene nitrate as a terminal sink for NOx; NMVOCs not only provide a sink for OH but also for NOx, further reducing OH levels.