Excitation of the primary tropospheric chemical mode in a global three-dimensional model

. Coupling of local chemical processes over the globe by atmospheric transport leads to the existence of chemical modes that are a fundamental characterization of global atmospheric chemistry and provide a true description of the atmospheric response to small changes in trace-gas emissions. Such coupled chemistry-transport modes in global tropospheric chemistry are an inherent feature of three-dimensional chemical transport models (CTMs). In CTMs these modes cannot be solved for explicitly, as they have been for the case of low-order, fully linearized systems, but they are investigated here through a series of perturbation experiments. When using meteorological fields that recycle every year, the long-lived modes are readily seen as seasonal decay patterns that e-fold each year. An important application of chemical modes is the study of how emissions of CO and NO excite perturbations to the CH4-1ike mode, the longest-lived (primary) mode found in tropospheric chemistry (i.e., with fixed stratospheric composition). Perturbation experiments are conducted with the University of California, Irvine, three-dimensional tropospheric CTM to identify this primary tropospheric mode and to determine its five-dimensional structure. The previous demonstrations of a long-lived chemical mode with 1.5 times the lifetime of CH4 are corroborated. The ability of emissions of CO and NO to excite this mode is then demonstrated, and a quantitative evaluation of the indirect effect of CO emissions on the greenhouse gases CH4 and tropospheric O(cid:127) is made, showing that 100 kg of CO is equivalent to 5-6 kg of CH4 emissions.

Knowledge of these natural modes can help in prediction of the atmosphere's response to changing anthropogenic emissions. Most human perturbations to the chemical composition of the atmosphere over the past several decades may be described by excitation of a linear combination of the chemical modes, each of which decays with its characteristic e-folding time. The lifetime of the longest-lived, excited mode provides a better measure of the duration of the chemical perturbation than the steady state lifetimes of individual compo-levels from the surface to 10 hPa, with six to eight levels in the troposphere. Advection is calculated using the Prather scheme conserving second-order moments [Prather, 1986]. Entraining and nonentraining convective mass fluxes are supplied as 3-hour averages from the meteorological fields. The height of the boundary layer is diagnosed from the fields, and a bulk-mixing scheme is applied, mixing the full depth of the layer every CTM time step.
A detailed tropospheric chemical scheme has been included in the model using the ASAD modular chemistry package [Carver et al., 1997], with a fast implicit solver for the chemical equations. The scheme includes an explicit treatment of inorganic HOx/Ox/NOx chemistry and methane oxidation and a lumped "family" treatment of hydrocarbon oxidation for the representative species butane, propene, xylene, and isoprene. A total of 32 species are considered, with 25  Photolysis rates are calculated using the Fast-J photolysis scheme , which has an on-line treatment of molecular and aerosol absorption and scattering. Ozone, temperature, surface albedo, and cloud optical depth are supplied from the CTM or meteorological fields every 3 hours; the optical depth is apportioned between different water droplet sizes and phas-

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es depending on the cloud type. This allows the full variability of photolysis rates to be captured on short timescales, as cloud and aerosol fields vary. Fast-J is a significant step forward coupling ozone, aerosols, and clouds in global CTMs, although it still does not address the problems of partial cloud cover in a grid cell.
Emissions of trace species are taken from the Global Emissions Inventory Activity inventories at 1 ø x 1 ø resolution, (see Table 1 Calculation of the tropospheric chemical tendencies under stratospheric conditions is unnecessary here and can produce so,ne undesired numerical artifacts, especially in stratosphere-troposphere exchange fluxes. Thus the U CI CTM carries a synthetic O3-1ike tracer which is used to distinguish instantaneously between stratospheric and tropospheric "air" for each 3-D grid cell. This approach allows for separate chemical treatments and works particularly well in the case of tropopause folds for which no clear tropopause height can be defined. The additional tracer, "Synoz", is forced with a stratospheric source in the uppermost CTM level and is removed in the lowest 2 km of the model by resetting it to 30 ppbv. This technique is described in detail by McLinden et al. [2000]. The 120-ppbv isopleth of the annually repeating distribution of the tracer is used to define the tropopause. Below this isopleth, tropospheric chemistry is applied; above, the effects of stratospheric chemistry are simulated by imposing a first-order decay on many species to ensure that they are not returned to the troposphere. A source of ozone is supplied in the highest layer, 475 Tg yr -1 (as for Synoz), based on our assessment of tracer correlations in the midlatitude stratosphere [Murphy and Fahey, 1994;McLinden et al., 2000], and a source for the NO v species, 0.45 Tg N yr -1, is likewise injected with an HONO2:NOx ratio of 4:1. Since there is no chemistry applied when the $ynoz tracer exceeds 120 ppbv, this technique ensures control of the global, annual mean net stratospheric influx of NOx, HONO2, and 03.
This numerical study of tropospheric chemical modes requires some computationally necessary compromises along with strict control of the degrees of freedom. With multiyear integrations required, we chose to increase the grid size of the CTM to 8 ø x 10 ø by combining variables at 4 ø x 5 ø, a large saving in computational time without significant loss of accuracy. The single year of GCM meteorological fields has been repeated for multiyear runs, thus providing a clear e-folding of the primary mode and avoiding the noise caused by interannual variability. A fixed, parameterized stratospheric chemistry is used to ensure that the primary mode reflects only the chemistry of the troposphere; with full stratospheric chemistry the primary mode would be dominated by N20, which has a century-long timescale, much greater than any of the species important in tropospheric chemistry [Prather, 1998]. This mode study requires that all tropospheric species be driven with flux boundary conditions, as use of fixed mixing ratio conditions would prevent derivation of the correct modes. Monthly-mean surface mixing ratios of ozone are shown in Figure 1; the solid lines represent modeled values, and the dots are mean mixing ratios over a number of years for selected measurement stations collated by Logan [1999]. The distribution and seasonality of ozone are reproduced well in tropical and equatorial regions, but the agreement is less good at higher latitudes in each hemisphere, where there is a tendency to overpredict the surface concentrations, particularly in spring when the cross-tropopause flux is at a maximum. Although use of the Synoz tracer allows the total flux of ozone into the troposphere to be well constrained, the * .. The high-latitude discrepancies seen in the ozone distribution are less pronounced here due to the negligible contribution of stratospheric air to CO abundance. The measurements at Mace Head, Ireland, are sensitive to meteorological differences between the GISS fields and the real climate because of the position of the site immediately to the west of major European sources. Cuiba, in the Amazon rain forest, sees extremely high CO mixing ratios in the spring due to biomass burning, and though the CO concentrations modeled at the peak of the burning season are rather low, as would be expected at the coarse resolution used in these studies, the seasonality of burning is well reproduced. Figure 3 shows the time series of monthly mean concentrations for a variety of species at Mauna Loa, com-  spheric lifetime against tropospheric OH in this CTM simulation is 10.2 years, and no effort to adjust the OH fields has been made to bring it into closer agreement with the recommended value of 9.6 yeaxs. Including stratospheric loss, the global mean lifetime in this model is 9.7 years (see Table 2). The soil sink for CH4 was

The Primary Mode
Among the species in the tropospheric chemical system studied here, CH4 has the longest global-mean atmospheric lifetime, and hence the longest-lived (primary) mode is dominated by methane perturbations. This mode has been found in simplified one-box CH4-CO-OH systems [Prather, 1994;Prather, 1996;Daniel and Solomon, 1998]  number of degrees of freedom present in the tropospheric chemical system, nor do they include the wide range of photochemical environments over which a global CT-M integrates. Unfortunately, the chemical modes in a CTM are not as easily determined as in low-order systems, and we turn to numerical experiments to find the primary mode.
The primary mode can be found readily (but with extensive computation) by following the decay of a perturbation introduced, for example, by a pulse of CH4. /'1-• 1 .11 zne primary mode wm become apparent as shorterlived modes decay more quickly. For chemical transport models the modes vary from short-term modes involving radical chemistry (e.g., OH) or nearest-neighbor transport, up to longer-lived modes that integrate globalscale chemistry with transport. All modes identified thus far, in low-order models and 3-D global models  decadal timescale in the tropospheric chemical system here. It is often mistakenly believed that this perturbation must be applied to a system that is at steady state, whereas the only pragmatic requirement is that the background system (or control run) should be slowly evolving so that the modes themselves, as functions of the background chemistry, are not significantly changing during the integration.
In the present studies a control run has been performed for 10 years, beginning with the near steady state simulation discussed above, forcing CH4 with an-

nual mean emissions of 490 Tg yr -•, and repeating the year of GISS IY meteorological fields for subsequent years. A parallel perturbation run is initialized identically to the control run, being forced with a 20% increase in CH4 emissions for the first year, and then returning to the near steady state emissions for all subsequent years. The perturbation-minus-control differences in the concentrations of methane and other
species are followed for the remainder of the 10-year period. Beginning in year 2, this difference in atmospheric species decays to zero over a range of successively longer timescales, approaching the e-folding and characteristic pattern of the primary mode. For this global tropospheric chemical system the primary mode becomes apparent and dominates the decay of the perturbations by year 3 (see Figure 5).
The primary tropospheric chemical mode in this case involves all of the chemical species and is seen as an annually repeating pattern that varies throughout the atmosphere. Figure 5 shows timeseries for this difference in terms of the total burden (in teragrams), while  Ireland (53øN, 10øW), to a 20% perturbation in global CH4 emissions, expressed as the difference (in ppbv) between perturbation and control runs with the U CI CTM.

Relating Mode Time to Perturbation
Lifetime From this perturbation-minus-control series of all species, the e-folding time of the primary mode is found by fitting the long-term decline in the CH4 perturbation to an exponential decay, discarding the first few years of the series where short-lived modes influence the decay. These short-term modes can be chemistrytransport or just transport modes [e.g., Prather, 1997].
The same, long-term exponential decay rate applies to all species, at all locations and at all times of year, provided one looks at the 12-month decay, calculating ratios at comparable times of year. This time is calculated as 14.2 years, a factor of 1.46 greater than the steady state, global atmospheric lifetime (LT) of methane, 9.7 years. For a methane perturbation in this tropospheric chemical system, the primary mode accounts for 99.3% of the removal; i.e., for I Tg CH4 emitted from the surface, 0.993 Tg appear in the primary mode and e-fold in 14.2 years, whereas 0.007 Tg appear in more rapidly decaying modes. The integrated CH4 burden following a 1-Tg addition can be calculated by explicitly integrating over the first few years and then implicitly integrating the e-folding decay of the primary mode, thus saving the substantial computational effort required to follow the primary mode until it becomes sufficiently small. Note that this computational effort is also required in steady state calculations using a methane flux since the steady state is approached at the same rate as the perturbation decays. In this case, only the primary mode contributes substantially to the integrated burden, and we can calculate it from the product of the emission and the e-folding time, 14.2 Tg yr.
On the basis of analytic expansion of linear perturbations into their different chemical modes [Prather, 1996]

Mode Structure
The latitudinal and seasonal variations in the primary mode are revealed in Figure 9, which shows a repeating 3-year cycle of zonal-mean midtropospheric mixing ratios, detrended to remove the e-folding decay. The mode pattern itself is dimensionless, and we have chosen to use a single scale factor here to give a +100 ppbv global, annual mean perturbation in methane. The CH4 perturbation is not uniform, but ranges from 98 to 102 ppbv, with a minimum in the tropics and a distinct seasonality at middle and high latitudes. This distribu-tion, reminiscent of the chemical loss signature of Fung at al. [1991], reflects the tropospheric distribution of the OH radical, with low values where loss to OH is quickest in the tropics and summer hemisphere and a maximum at high latitudes in the cleaner Southern Hemisphere. The range in size of the perturbation is small, reflecting the long chemical lifetime of CH4 relative to tropospheric mixing. The CO perturbation ranges from +1.5 to +2.5 ppbv and shows a reversed pattern compared with CH4, reflecting formation of CO when OH is high. The larger relative amplitude reflects the shorter chemical lifetime of CO.
The 03 perturbation, ranging from +0.2 to +0.5 ppby, has a still different pattern, with elevated concentrations generally at midlatitudes and particularly in the high-latitude Northern Hemisphere in summer. The Northern Hemisphere shows much greater seasonality, reflecting the higher N Ox concentrations and greater importance of photochemical formation of 03 from the added CH4 in the region. The N Ox mode pattern is principally negative, ranging from -2.0 to +0.5 pptv on a zonal monthly average throughout the midtroposphere. The largest negative perturbation is in northern winter.
There is little vertical variation of the primary mode in the troposphere for CH4 and CO, as the chemical lifetimes are long compared with the convective turnover time. Dynamical considerations and the shorter lifetime of 03 and its precursors become important, and the 03 perturbation has slightly greater vertical structure than that of CH4 or CO.
The average relative perturbation to each species that occurs with the primary mode is summarized in Figure 10. The percent perturbations refer to changes in the global, annual mean values, integrated over the troposphere, and normalized to the global mean CH4 perturbation. For example, a 1.0% increase in CH4 in the mode is coupled with a 0.26% decrease in OH and a 0.45% increase in CO. The net increase in CH4 oxidation (+0.74%) leads to greater formation of peroxy and methylperoxy radicals, and therefore to a higher efficiency of 03 production from the NO• cycle, and an increase in 03. The ratio of NO to NO2 falls slightly, and the greater proportion of NO2 leads to more efficient removal of NOz to form NO u. Although formation of nitric acid HONO2 is reduced due to lower OH levels, formation of pernitric acid HNO4 and methyl nitrate CH3ONO2 is greater due to the greater concentrations of peroxy radicals. This pattern of perturbation to key chemical species will be the only long-term pattern following almost all types of perturbations to this tropospheric chemical system.

Uncertainties and Sensitivity
The primary mode accounts for about 99.3% of the methane perturbation. The remaining 0.7% can be attributed to shorter-lived modes that are exceedingly d- The calculated e-folding time of the primary, CH4like mode is sensitive to the chemical system considered. Future changes to the atmosphere affecting OH will alter the e-folding time for the mode and hence the tropospheric recovery time for chemical perturbations.
As noted by Prather [1996], this includes future increases in CH4 emissions, as a positive feedback: Increased abundances of CH4 will lead to increased lifetimes and hence ultimately to the possibility of CH4 emissions exceeding the oxidizing capacity of the troposphere and causing runaway growth.
The mode time depends on the treatment of other losses that are not coupled to the CH4 abundance. For example, the atmospheric lifetime against stratospheric loss is projected here to be constant and reduces the ra-tio of mode timescale to atmospheric lifetime. The soil sink for CH4 is another possible loss without feedbacks and would likewise reduce this ratio. However, inclusion of a fully interactive stratospheric chemistry would allow coupling of the CH4-1ike tropospheric mode with the N20-NOy-03 mode in the stratosphere [Prather, 1998], and thus the N20 mode, with a timescale of about 110 years, would be the primary mode in response to a CH4 perturbation. The key question in this fully coupled system is what proportion of the CH4 addition would be manifest in this century-long mode.

Excitation of the Primary Mode
Any perturbation to the tropospheric chemical system generally affects OH, directly or indirectly, and excites the primary mode to some degree. As the mode is global in extent, this provides a mechanism for regional perturbations to exhibit global effects and for short-lived species to create long-lived perturbations. While the majority of perturbations to such species are removed rapidly close to the emissions (represented by short-lived, regional modes), the much smaller fraction 24,657 In both cases 1 and 2, the initial decay of CO happens very rapidly, within 2-3 months, reflecting removal of the excess CO by OH radicals (see Figure 11). However, the short-term suppression of OH leads to a buildup of CH4. After about 12 months, both cases resemble a CH4 perturbation, with all species decaying in the pattern of the primary mode and with a 14.2-year e-folding, similar to the situation shown in Figure 5. Thus, in addition to any short-term perturbations to the troposphere, additions of CO are equivalent in all ways to additions of CH4, with a long-term tail of global CO perturbations that are part of the primary mode.
Over industrial Europe, the 25-Tg CO perturbation is equivalent to a CH4 perturbation of 1.28 Tg, indicating that the primary mode contributes to 0.16% of the CO loss. Over equatorial Africa the CO perturbation is equivalent to a 1.44-Tg CH4 perturbation, and the primary mode contributes to 0.18% of CO loss. The slightly increased importance of the primary mode in the latter case is due to the greater importance of tropical CO in the global CH4 budget. The CO-CH4 equivalency can be assessed to some degree from the CO amplitudes of the primary mode shown in Figure 9, with greatest excitation of the mode associated with tropical and northern summer additions and the least associated with northern winter and most southern midlatitude emissions.
Although the excitation of the primary mode by CO may appear small compared with the initial perturbation, the much greater duration means that it will likely dominate any global environmental impact. For CO the excitation of the primary mode, with its concurrent perturbations to the greenhouse gases CH4 and tropospheric 03, makes CO a very important indirect greenhouse gas [Prather, 1996;Daniel and Solomon, 1998]. For CO emissions from major anthropogenic source regions, we estimate that 100 Tg of CO emissions is equivalent to 5-6 Tg of CH4, including the indirect effects of CH4 on tropospheric 03 and stratospheric H20 [IPC-C, 1996] (see Table 3). What is not included in this equivalence is the additional impact that CO may have on tropospheric 03 via the short-lived modes. Integration of Figure 11 shows that for case 2 these short-term increases in tropospheric 03 account for 55% of the increase in the integrated tropospheric 03 burden, with the long-lived primary mode accounting for the remaining 45%. However, this short-term 03 response will depend greatly on the regional N Ox abundances and thus is likely to vary substantially from region to region and season to season.   Experiments with short-lived NOx emissions parallel to CO indicate that these also excite the long-lived primary mode with its consequent changes in CH4 and tropospheric 03, but in the opposite sense, with a negative amplitude. In a sample numerical experiment with aviation NO• (not shown), we find a negative amplitude of the primary mode that would build up in steady state to give suppressed CH4 levels similar to those reported in the IPCC model study [Penner et al., 1999]. The excitation of the primary mode by NO• emissions depends greatly, more than a factor of 5, on the location and timing of the emissions and requires further study.

Conclusions
In this paper we describe a new tropospheric chemical 3-D model and use it to identify and characterize the primary mode in the tropospheric chemistry-transport system. As anticipated from earlier box-model studies [Prather, 1994;Prather, 1996;Daniel and Solomon, 1998], the key component of this mode involves the CHa-CO-OH chemical coupling, and the e-folding of the mode (14.2 years) is about 50% longer than the global mean atmospheric lifetime of CH4 (9.7 years).
Further, it is shown that almost the entire amount of any CH4 additions to the current atmosphere go into this mode, as has been adopted in recent assessments [IPCC, 1995]. Along with contemporaneous work (R. G. Derwent et al., submitted manuscript, 2000), this new work now quantifies the ability of CO to excite this long-lived mode. It also provides a credible calculation of the increase in global tropospheric ozone that accompanies this CH4 and helps us understand the complex response of both these greenhouse gases to NO•