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Trace gas mixing ratio variability versus lifetime in the troposphere and stratosphere: Observations

. Several archived data sets have been reviewed to examine the relationship between mixing ratio variability and lifetime for hydrocarbon and halocarbon species in the troposphere and stratosphere. The dependence on lifetime was described by the power law relationship SlnX = A'c-b, where SlnX is the standard deviation of the In of the mixing ratios, A is a proportionality coefficient, and b is an exponent that relates to the dominance of sink terms in the regional variability budget. At the Harvard forest ground site, winter and summer data displayed the same lifetime dependence, x-o.18, which was significantly weaker than the x-0.5 dependence of remote tropospheric data, indicating that source terms dominated regional variability at Harvard. In addition, the ratio of summer to winter SlnX values was found to be similar for all species except ethane, averaging 1.54 + 0.04. This ratio is consistent with a factor of 11 seasonal change in the species lifetimes, given a x-o. 18 lifetime dependence. Stratospheric data displayed a stronger lifetime dependence than tropospheric trends, indicating a more dominant role for sink terms in describing spatial variability in this region of the atmosphere. We show that a unique power law relationship between SlnX ratios for two species Xi and Xj and the kinetic slope of ln(Xi) versus ln(Xj) correlation plots is found to hold in both observations and theory. Thus knowledge of the coefficient b allows for a clearer understanding of the relationship between observed slopes of ln(Xi) versus ln(Xj) correlation plots and the ratio of the species lifetimes. latitudes. Gases with lifetimes


Introduction
The relationship between trace gas mixing ratio variability in the atmosphere and atmospheric lifetime has not been widely studied either from observations or from a theoretical standpoint. The most widely cited reference is Junge [1974], who found an empirical relationship between the global spatial variability of several trace gases in the troposphere and their steady state lifetimes. Junge's empirical relationship is 0.14 RSD - where RSD is the relative standard deviation (the standard deviation divided by the mean concentration) and x is the residence time in years. This relationship is often cited in the literature as it substantiates our intuitive notion that the more reactive trace gases are the more variable. The global spatial variability-lifetime relationship for the troposphere has been reexamined by Jaenicke [1982] and Hamrud [1983],  [1998]. They examined a relationship similar to (1) and found the dependence on 'r to vary with geographic location. Within their model, continental source regions displayed a weaker x dependence than remote ocean environments, and importantly, on a regional basis the lifetime dependence was much weaker than Junge's [1974] inverse relationship. The purpose of this paper is to extend the scope of Jobson et al. [1998] by including halocarbons and thus examine the robustness of the regional variability-lifetime relationship over a much broader lifetime range. In addition, stratospheric data will be examined with respect to (2) and compared to tropospheric trends. To our knowledge, tracer variabilitylifetime relationships have not been examined in the stratosphere. The goal is to evaluate the exponent b and thereby gain a better sense of the range of values it takes within the atmosphere. This exponent would appear to be a unique and important indicator for describing the dominance of sink terms on regional-scale tracer variability budgets [Ehhalt et al., 1998]. We will show that knowledge of the value of b allows for a straightforward relationship between the observed slopes of tracer correlation plots and the ratio of the species lifetimes. This paper is a retrospective analysis of previously published data. In section 2.1, data from three of NASA's Global Troposphere Experiments (GTE) will be examined: the Arctic Boundary Layer Expedition 3B (ABLE 3B), the Transport and Atmospheric Chemistry Near the Equator -

Atlantic (TRACE-A), and the Pacific Exploratory Mission in the Western Pacific Ocean Phase B (PEM-West B). The wide
range of species and species lifetimes measured in these campaigns provides a good starting point for evaluating the robustness of the regional scale variability-lifetime relationship. In section 2.2, variability-lifetime relationships in the stratosphere from the Airborne Southern Hemisphere Ozone Experiment (ASHOE), the Airborne Arctic Stratospheric Expedition II (AASE II), and the Stratospheric Photochemistry Aerosols and Dynamics Expedition (SPADE) field campaigns will be examined. In section 2.3, seasonal differences in the trend will be discussed using hydrocarbon data from the Harvard forest experimental site [ Goldstein et al., 1995].
These data provide some unique additional insights into how the relationship in (2) can be used to infer seasonal changes in regional HO concentrations from tracer variability. In section 2.4 some data from the 1992 Polar Sunrise Experiment [Jobson et al., 1994a] will be reexamined with respect to using variability-lifetime relationships to infer relative oxidant abundances. The global atmospheric lifetime or residence time of a trace gas is defined as x = atmospheric burden atmospheric loss rate Most of the gases considered here are removed in the troposphere through their reaction with the hydroxyl radical. The loss rate depends on the concentration of HO, which has pronounced temporal and spatial variability, the spatial distribution of the trace gas, and the respective HO rate coefficient that may have a significant temperature dependence. Lifetimes are thus determined by a convolution of the spatial-temporal distribution of these three terms [Prather and Spivakovsky, 1990]. The loss rate and concentration of the trace gas X at a particular location and time define the local lifetime [X] 1

Xloca• = k[HO][X] -k[HO] (4)
where k is the HO rate coefficient and the square brackets indicate the concentration of the species of interest. Our previous analysis [Jobson et al., 1998] examined the relative variability for hydrocarbons that were oxidized by HO exclusively. In that case the absolute value assumed for HO is unimportant in determining the coefficient b in (2). However, in this study the variability of species lost by HO are compared with those lost by photolysis and the absolute value of lifetimes with respect to HO relative to those lost by photolysis must be considered. The tropospheric data analyzed here, with the exception of the Harvard forest data, were collected during field campaigns spanning no more than a month so that changes in mean concentrations of HO due to seasonal changes in insolation were negligible. In the analysis of the winter and summer hydrocarbon data from Harvard forest, estimates of the appropriate HO concentrations were obtained from chemical-transport models [Goldstein et al., 1995].
For the GTE campaigns the range of HO reactivity for the gases considered is large, about a factor of 100, and we must consider whether local lifetimes or global mean lifetimes should be used in the analysis of regional variability-lifetime relationships. These studies used an aircraft as the sampling platform and sampled from a wide range of altitudes (from the near surface to 11 km) and latitudes. Gases with lifetimes greater than a year, such as CH3CC13, are fairly evenly distributed through the troposphere. However, species with lifetimes of the order of days, such as acetylene and propane in summer, are oxidized rapidly in the boundary layer close to their emission sources. Boundary layer concentrations of H O are thus more important in determining the lifetimes of these hydrocarbons compared to longer lived gases. Accurately calculating the relative lifetimes of the gases considered here will be difficult, and we must accept a degree of uncertainty in our analysis. As discussed later, results are fairly insensitive to assumed HO levels for the more reactive hydrocarbons. For species with lifetimes more than 100 days their mean global lifetimes were used. Estimates of the CH3CC13 atmospheric lifetime inferred from measurements of the Atmospheric Lifetime Experiment (ALE) and Global Atmospheric Gas Experiment (GAGE) monitoring network [Prinn et al., 1995] provide a reference lifetime to which other similarly long lived gases can be scaled [Prather and Spivakovsky, 1990]. Atmospheric lifetimes for the gases CH3C1 and CH3Br were scaled to the 4.9 year global mean lifetime of CH3CC13 due to removal by HO according to Prather and Spivakovsky [1990]. The CH3Br lifetime also includes losses due to ocean uptake (x = 3.7 years) and loss in the stratosphere (  coefficients used to calculate lifetimes are given in Table 1, and the resulting lifetimes are given in Table 2.

Tropospheric Data
In this section the regional trends from the ABLE 3B, TRACE-A, and PEM-West B field experiments will be discussed. All three experiments were aircraft-based field campaigns sponsored by NASA, pertinent details of which are given in Table 3. More detailed information can be found in the overview papers of the specific experiments: ABLE 3B [Harriss et al., 1994], TRACE-A [Fishman et al., 1996], and PEM-West B [Hoell et al., 1997]. Each experiment had specific objectives, so aircraft flight plans were not designed for a random sampling of the atmosphere. The trace gas distributions therefore reflect the sampling bias inherent to the mission objectives. The data from these experiments were obtained by the same research group so there is internal consistency amongst the various experiments. In general, the samples were collected from aircraft over relatively remote regions of the Northern and Southern Hemispheres with some sampling of air that had been recently influenced by urban and biomass burning sources. Overall, the trace gas distributions should be representative of reasonably well processed anthropogenic and natural emissions. the plane descended through the urban plume of Yokota, Japan, to the airport. Typically, 0 3 was very depleted when these samples were taken, reflecting the large NO concentration that was likely present (the NO instrument did not sample during these approaches to prevent inlet contamination). These few "airport" samples, from this flight and others, strongly influenced the variability of the longlived gases such as CH3CC13 and the CFCs because of their extremely elevated mixing ratios relative to regional levels.
For example, CH3CC13 mixing ratios in this plume were up to 3 times higher than the campaign average. Such samples were not included in the analysis of the GTE data since they are unrepresentative of processed tropospheric air. Also not included were samples collected during the transit flights to and from the study region for the ABLE 3B and TRACE-A experiments. process in shaping mixing ratio distributions in the troposphere by injecting photochemically processed air and hence low mixing ratios of these trace gases, particularly for ß CFCs.

Statistical distributions.
The statistical distributions of the trace gases measured in the GTE experiments tended to become more skewed or approximately lognormal as the reactivity of the species increased. To illustrate this point, Figure 3 shows the cumulative distribution of several species measured in ABLE 3B. These gases span a lifetime range from ~ 10 days for acetylene to -40,000 days for CFC-12. There is a clear tendency for the dynamic range to increase with increasing reactivity. In these logarithmic cumulative distribution plots, lognormal distributions define straight lines. Taking the natural log of the mixing ratios transforms the distributions into a more symmetric form so that the character of the distributions are more comparable across the large lifetime range of these gases. Figure 4 compares histograms of the In of the mixing ratios for several trace gases. For most species these distributions can be approximated by a Gaussian probability density function, but some species distributions are more complex. For example, In(acetylene) is not well described by a Gaussian distribution; the Pem-West B data is bimodal, while the ABLE 3B and TRACE-A data display distinct shoulders. Thus Sinx may not be the perfect statistic for comparing relative variability amongst these gases, but as the following figures attest, it is sufficient for capturing the general trends in the data. 2.1.2. Variability versus lifetime. Figure 5 displays the relationship between Sing versus lifetime for the ABLE 3B, TRACE-A, and PEM-West B data. Individual flights displayed the same trends to a greater or lesser degree. In general, though, there was much more scatter in the trends of individual flights.
The Sinx value was calculated from all the samples collected from the flights indicated in Table 3. Some species did not have 100% data coverage because of being below detection limits or other analytical problems. For the C4 and higher alkanes, no data were reported for a large fraction of the collected samples in all three field campaigns. The variability statistics for these species would be biased low relative to species with complete quantithtion of their spatial distribution. Species with a significant fraction of unreported data (>11%) were not included in the analysis. Table 4 lists the SlnX values and the percentage of missing data for each of the field missions. In general, the data from these field missions define a relatively coherent relation between Sinx and lifetime of the form Sln x --A x -b, with the exponent b approximately equal to 0.5. Some species were clearly outliers to the general trend and were not included in the regression fit. These outliers will be discussed below in terms of differences in trace gas source distributions and emissions history. Table 5 lists the fit parameters and the associated 1(5 uncertainties. The parameter values were found from a linear regression of ln(SlnX) versus In(lifetime). As compared to an exponential fit, the linear regression of the In transformed data yielded more reliable estimates of the uncertainties for A and b, particularly for the GTE data where the lifetimes spanned 4 orders of magnitude. In Figure 5a two other fits are shown by dashed lines to illustrate the uncertainty associated with the estimated local lifetimes. Using an HO concentration of 1 x 106 molecules cm-3 resulted in a w 0-44 dependence, while an HO concentration of 2 x 106 yielded a x-0.48 dependence. This range of lifetime dependencies is within the 1(5 uncertainty in the lifetime dependence in Table 5 In(mixing ratio in pptv)

Fisure 4. Histograms of the In of the mixi•[ ratios of selected trace •ases measured in ABEE 3B, Transport and Atmospheric. Chemistr• Near the Equator -Atl•fic (•ACE-A), •d PEM-West B.
2.1.3.1. CH3CI: It is evident that CH3C1 is a significant outlier in the PEM-West B data set. This is likely due to its much different source distribution. Blake et al. [1997] have noted that the spatial distribution of its mixing ratio was significantly different from that of the other species, likely a result of the large distributed emission source from the Pacific Ocean. A large distributed emission source would result in a smaller spatial variability than gases of urban or industrial origin that are transported in regional plumes originating from Asia. In the TRACE-A data set, CH3C1 also displays a lower variability than the general trend but to a smaller extent. The better fit is likely due to the larger contribution of biomass burning as a CH3C1 source, which made its emission distribution more like the other trace gases plotted. Because CH3CI's source distribution can be significantly different than the other gases, it was not used in the regression fits shown in

CFC-114, H-1211, and H-1301: These species
displayed significantly higher variability than the general trend. The measured spatial variability is greater than the estimated measurement precision (although the measurement variances do contribute to the observed variability). These species are anthropogenic in origin, and there is no reason to believe that their source distribution is significantly different than that of the other CFCs. The high spatial variability of these species with respect to the other similarly long lived CFCs is likely a consequence of their much lower regional mixing ratios. Their lower mixing ratios are a result of their historical emission rates being a factor of 10 or more lower than those of CFC-11, CFC-12, CFC-113, and HCFC-22 [Kaye et al., 1994]. We can imagine this effect arising as follows. Assume that the variability of species Xi in some region is driven by pollution plumes from an anthropogenic source. With steady emissions the ratio between plume concentrations and the average regional background will decrease as Xi accumulates in the atmosphere. Therefore the spatial and temporal variability, as described by dX i/Xi,avg will decrease with time until Xi is in steady state with respect to loss and production. One might anticipate that with continued emissions and increasing global concentrations of these species that their spatial variability will decrease and become a better fit to the regional trend. If the regional variability of these species is dominated by source terms, then they will exhibit a weaker x dependence than the general trend.

ASHOE, Tuck et al. [1997]; AASE II, Anderson and Toon [1993]; SPADE, Wofsy et al. [1994b]. Data from the ASHOE experiment have been discussed by Volk et al. [1997] and have stated the lo measurement precision to be-
.... : The ASHOE data display a bimodal statistical distribution, with both modes being reasonably symmetric. A narrow peak is evident in the distribution at high mixing ratios for all species. This mode corresponds to data collected in the tropics. The other mode is much broader and corresponds to samples collected in the extratropics. The SPADE data are also reasonably symmetric, but a minor mode or tail is evident at low mixing ratios. The AASE I! data have a significant tail at low mixing ratios and the In-transformed data are much less symmetric than the ASHOE or SPADE data. Plate 1 illustrates several points. First, stratospheric trends from individual flights were typically much more coherent and more similar to the overall trend in the respective field campaigns than the tropospheric data. Second, there is significant uncertainty in estimated lifetimes of individual species and in their relative lifetimes, as reflected in the wide spread of recommended lifetimes for individual species. Third, the relative stratospheric lifetimes are much different than their atmospheric lifetimes shown in Figure 5. For example, CH3CC13 and CC14 are considered to have similar stratospheric lifetimes but have very different atmospheric lifetimes because CH3CC13 is consumed relatively rapidly in the troposphere by reaction with the HO radical. In the troposphere, CH3CC13 is much more variable than CC14, but in the stratosphere they displayed similar variability. Another example is methane, which has a shorter atmospheric lifetime than N20, again because of its relatively rapid consumption in the troposphere by the HO radical, but is considered to have a comparable stratospheric lifetime. In the data we have examined, methane always displayed a lower variability than N20 in the stratosphere, suggesting that its stratospheric lifetime should be longer. The Availone and Prather [1997] lifetimes for CH 4 and N20 are consistent with this observation. The other lifetime estimates have the CH 4 lifetime being equal to or less than that of N20.
The lifetimes that are probably the most uncertain are those of CH 3CC13, CH 4, and CH3C1. These lifetimes are difficult to define in terms of stratospheric loss because of differences in the stratosphere-troposphere division between models. This leads to differences in the calculated lifetimes because these particular species have a significant HO removal rate (which is sensitive to H20 concentrations) whereas the other species are removed primarily by photolysis higher up in the atmosphere. For this reason we will exclude these species from the regression fits of the Sln X versus x trends. In Plate 1 the regression fits for three lifetime recommendations are shown as the solid lines, the dashed lines being an extrapolation over the x axis lifetime range. Of the five recommendations, the Availone and Prather [1997]   The Availone and Prather [1997] chemical transport model based lifetimes yielded the most coherent relationship between variability and lifetime in the stratospheric data sets we examined, and in all cases with b values <1.0. In particular, the difference in the N20 and CH 4 lifetimes given by Availone and Prather [1997] is consistent with observed differences in the variability of these species, though as stated before, we will not use CH 4 in the analysis that is to follow. Given the better overall fit to the data, we will use the Avallone and Prather stratospheric lifetimes for evaluating the variability-lifetime relationship. Our intent is to contrast the b value of the stratospheric data trends with those of the troposphere; thus any of the recommendations could have been used in the analysis and would not have changed the general conclusions drawn.
The timescale for photochemical removal in the stratosphere is defined in terms of the stratospheric burden x = stratospheric burden strat stratospheric sink This is the timescale of interest for investigating variabilitylifetime relationships in the stratosphere. The stratospheric burden is -10% of the atmospheric burden for a well-mixed long-lived gas such as SF 6, so the stratospheric lifetime defined by (6) is -10% of the value defined by (5). For shorter-lived species with mixing ratio profiles that fall off rapidly with height in the stratosphere their burden will be less than the 10% mass fraction factor. This fraction could be calculated  I  I  I  I  I  I I  I  I  I  I  I  with chemical transport models, but to simplify our analysis, we will apply the 10% fraction to all species so that the lifetimes shown in Plate 1 will be divided by 10 in Figures 7,  8, and 9. Applying the same factor to all species will bias our lifetime distribution somewhat, resulting in b values biased high. However there is some practical advantage to using the same factor because the b values determined from plots using the lifetime definition in (5) will be the same as those using the definition in (6), and gaining a general understanding of how b varies between atmospheric regions is our primary goal. Of course, the choice of lifetime definitions will dramatically influence the value obtained for the proportionality coefficient A. The meaning of this coefficient will be briefly discussed for stratospheric data in section 3 where it will become more obvious why SlnX should be plotted against the lifetime definition given in (6). It is apparent in the histograms of the ASHOE data that the tropical and extratropical data defined different statistical distributions, and it is informative to plot these data separately. Figure 7a shows the relationship between Sln x and lifetime for the tropical data divided into two periods on the basis of the large difference in the variability of the measurements. The late October flights displayed less variability than flights flown early in the year. Despite the large differences in variability the two periods displayed a similar lifetime dependence given the uncertainty in the exponent b. This dependence is stronger than that observed in the troposphere, and the data contain a clear stratospheric processing signature since CC14 and CH3CC13 displayed similar variability. The ASHOE extratropical data in Figure  7b displayed a stronger lifetime dependence than the tropical data; b is not significantly different than unity. Figures 8 and 9 show the relationship between S•n x and stratospheric lifetime for the AASE II and SPADE data sets.

So far, we have been looking at different data sets with the aim to understand better the physical significance of the lifetime dependence. For short-lived species such as hydrocarbons, seasonal changes in insolation drive a significant change in local lifetimes and hence large seasonal changes in mixing ratios
In Figure 1 l a the winter to summer ratio of medians are plotted against HO rate coefficients. The seasonal change in the median mixing ratios (seasonal amplitude) shows a similar relationship to reactivity as that shown by Goldstein et al. [1995] for "background" mixing ratios, except that the amplitudes are smaller. Seasonal amplitudes for light alkanes typically increase with increasing hydrocarbon reactivity [Jobson et al., 1994a simple relationships between seasonal concentration changes and reactivity. In addition, mixing ratios of reactive species in summer will be more strongly influenced by local emission sources than longer-lived species. The small seasonal amplitudes for i-pentane, n-pentane, and hexane might reflect the greater influence of local sources on these species than on the longer-lived hydrocarbons. The relationship between the summer to winter ratios of Sln X and lifetime in Figure 1 lb shows different behavior. The more reactive a species, the greater its variability; therefore summer to winter ratios of Sin X should be >1. With the exception of ethane and /-butane the SlnX seasonal ratio was found to be surprisingly similar, averaging 1.54 + 0.04. For ethane the Sln X value was only 7% larger in summer, while for/-butane it was 74% larger. Ethane, however, displayed a distinctly different seasonal cycle of monthly Sln X values than the other hydrocarbons. Monthly SlnX values for ethane maximized in November (0.40) and minimized in April (0.15), and thus its cycle was -3 months out of phase with the other hydrocarbons. Interestingly, using a 3 month averaging period over the minimum and maximum $1nX periods for ethane yields a seasonal S•nX amplitude of 1.57, similar to the other hydrocarbons. Figure 1 l c shows S•nx versus lifetime for the summer and winter data. Lifetimes were calculated using the HO concentrations from Goldstein et al. [1995], which are a factor of 10 larger in summer than in winter, and the rate coefficients in Table 1. The summer and winter data appear to define a similar. trend, except that the summer ethane data display a low variability. A fit through the winter data alone yields a x -0-]7 + 0.02 dependence. A fit through the summer data, excluding the ethane point, yields a similar x-0.20 + 0.04 dependence, although the correlation is poorer. The choice of lifetimes does not influence the x dependence, and thus there appears to be no significant seasonal change in the regional x can contribute a significant fraction of ethane mass to the site, and its source footprint is continental in scale. The short lifetimes of the other species qualitatively imply a regionalscale footprint. Therefore ethane variability may be influenced to a greater degree by nonregional sources, which result in a different variability-lifetime relationship than the other hydrocarbons. In winter the lifetimes of all species are >20 days, and it would appear that the species are influenced by the same source distribution. Interestingly, this larger source footprint in winter yields the same x dependence as the summer footprint for reactive species. Moody et al. [1998] have analyzed 48 hour back trajectories arriving at Harvard forest to assess the degree to which regional-scale transport influences trace gas concentrations measured at the site. Transport patterns were found to be similar between winter and summer. Highest hydrocarbon mixing ratios were associated with air parcels arriving from the southwest (a densely urbanized and industrialized area of the United States) and from more local origins. Lowest mixing ratios were associated with northern flow from Canada. They found that differences in regional wind flow explained a large amount of the hydrocarbon (specifically, acetylene and ethane) variability at the site. The weak x dependence observed in the data is consistent with their conclusion.

kHo[HO] + kc•[C1] + km[Br] (7)
Halogen atom rate coefficients were taken from Hooshiyar and Niki [1995] and Atkinson and Aschmann [1985]. Structure reactivity relationships [Atkinson, 1987] were used to calculate the HO + hydrocarbon rate coefficients for hexane and i-pentane. By assuming an arbitrary C1 atom concentration of 6 x 103 atoms cm-3 [Ariya et al., 1998] and by appropriate adjustment of the relative amounts of HO and Br atom concentrations a highly correlated trend between and lifetime develops. The best fit is given by a relative HO:CI:Br radical abundance of -17:1:3300. The resulting 0.92 dependence in the 1992 data is surprisingly strong and approaches the b=l dependence expected for variability dominated by chemical loss [Job'on et al., 1998]. This ratio of Br to C1 is higher than the 400-1200 range calculated from hydrocarbon trends at Alert during this time using a different approach [Jobson et al., 1994b] but is similar to those calculated by Ariya et al. [1998] for the 1994 Polar Sunrise Experiment.

The Exponent b
To this point we have demonstrated that coherent variability-lifetime relationships exist on the regional scale, both within the troposphere and the stratosphere over a wide range of lifetimes. The dependence on lifetime for the remote tropospheric data displays an approximate 'r -0.5 dependence, much weaker than the Junge [1974] relationship and the stratospheric trends. The ,r-0.5 dependence in remote areas is similar to that found by Ehhalt et al. [1998] in a 3-D CTM simulation of tracer relationships. The model results from Ehhalt et al. [1998] show a geographic distribution in the x dependence, the farther away from sources, the larger the exponent b. The observations presented here follow the same general trend with the Harvard forest data displaying a weaker dependence than those found in the more remote NARE locations [Jobson et al., 1998] and in the GTE data. Following Ehhalt's analysis, the exponent b can be qualitatively viewed as an index that relates to source-receptor distances. The lower limit of b=0, which has been observed in urban data [Jobson et al., 1998] and over source regions [Ehhalt et al., 1998], indicates that the variability is driven by differences in the strengths of local sources that are in close proximity to the measurement location. The limit of b=l was discussed in Jobson et al., [1998] and can be considered the chemical kinetic limit where the variability is dominated by chemical loss alone. The Arctic data discussed in section 2.4 and the extratropical stratospheric data from ASHOE and AASE II approached this b=l limit and suggest a remoteness or isolation from sources at these locations and therefore a variability that is driven largely by differences in the degree of photochemical processing of the sampled air masses. Interestingly the extratropical SPADE data displayed a significantly weaker 'r dependence than the ASHOE or AASE II data. Waugh et al. [1997] noted that the tracer-tracer correlations for the SPADE mission were different than those of either the ASHOE or AASE II data and attributed this difference to the mixing of vortex air with midlatitude air. Evidence of this mixing was the appearance of a linear relationship between CFC-11 and N20 in a normally curved region of the correlation diagram. This mixing has evidently resulted in a weaker 'r dependence in the SPADE data, though it should be noted that a much smaller latitude range was sampled in SPADE compared to ASHOE or AASE II. It has been our general working hypothesis that mixing amongst air parcels with different processing times would weaken the 'r dependence. At this stage we have cradled the meaning of b in terms of an index relating to source-receptor distances, although it may be more physically meaningful to view b as an index that relates to mixing influences. Locations where widely different air mass ages are mixed will display smaller values of b. In the troposphere this will happen close to source regions where fresh emissions are dispersed into the more photochemically processed background air. The influence of mixing through concentration gradients gives rise to an overall distribution of b that reflects distances from sources.
The stronger lifetime dependence, greater spatial variability, and generally lower mixing ratios in the extratropics compared to the tropical data are consistent with the notion of extratropical air being older and having passed through the higher altitude regions of the stratosphere where photochemical destruction of these gases occurs. The tropical air is more recently arrived to the stratosphere and, at the altitudes sampled by the ER2, has not had a chance to be thoroughly photochemically processed. The tropical region might be characterized as tropospheric air diluted with air that has been photochemically processed in the stratosphere, hence the weaker lifetime dependence but clear stratospheric processing signature.  [Rosenlof, 1995;Hall and Waugh, 1997]. This is in contrast to the extratropics where a wide range of ages can be encountered over a relatively small latitude range. For example, Rosenlof [1995] estimates Southern Hemisphere ages at 50 mbar ranging from -3.5 to -2 years, and a nearly uniform tropical age of-0.75 years. Such stratospheric age estimates are considered to be averages of a probability density function of air parcel ages (or age spectrum) at a given altitude and latitude [Rosenlof, 1995;Hall and Waugh, 1997]. Again, it should be noted that the choice of lifetime definitions used in plotting the data does not affect the determination of the exponent b but does influence •F. We have focused on evaluating b, but realizing that •F may be physically meaningful for the stratosphere and therefore constrained by a physically plausible range of values imposes constraints on the estimated lifetimes. This may be useful for evaluating tracer lifetime estimates in the stratosphere. A more rigorous understanding of the physical meaning of the coefficients in (8) will require an examination of tracer relationships in a 3-D CrM.

The Meaning of In(X/) Versus ln(Xj) Correlations
As a final application of S]nx analysis, we relate the relationships between S]nx and lifetime to the more conventional analysis of ln(Xi) versus ln(Xj) tracer scatter plots between species i and j.
It has been noted within the troposphere that plots of ln(n:butane/ethane) versus In(propane/ethane) yield very similar slopes (-1.40)or-50% less than the kinetic slope (given by the ratio of the HO rate coefficient differences: kn_butane-kethane / kpropane-kethane). Such slopes have been observed for latitudinal gradients [Rudolph and Johnen, 1990], seasonal changes at background midlatitude and high-latitude sites [Jobson et al., 1994a[Jobson et al., , 1994b and over a wide range of regional scales in the summertime [Parrish et al., 1992]. Using the PEM-West A data set, McKeen et al. [1996] argue that this deviation from pure kinetics is a result of dilution with background air at a rate comparable to the lifetime of n-butane. Through the analysis of 3-D model tracer studies, Ehhalt et al. [1998] came to the same conclusion, and further illustrated how this deviation depends on the proximity of the sampling area to emission sources. Ehhalt et al. [1998] also suggested a power law relationship between the slopes of ln(X i) versus ln(Xj) correlations and the ratio of species lifetimes. We show below that such a power law relationship follows naturally whenever SlnX is related to x as in Equation (2 Figure 13 tests the relationship between (10) and (11) by comparing variability ratios and the slope of ln(Xi)versus ln(Xj) correlations from the various tropospheric data sets incorporated in this study. Shown are only those data from scatter plots where the correlation coefficient r > 0.8. The slopes through the data were determined by a linear regression that assumed uncertainty in both variables. Some field campaigns exhibited poor correlations between species although yielded an overall coherent SlnX versus lifetime trend (i.e., TRACE-A). Figure 13 shows that (11) relates the variability in the observations to the slopes of In correlation plots remarkably well, especially for those species that have variability ratios <2. Those correlations that do not adhere to (11) are species with large differences in photochemical lifetimes (i.e., hexane and ethane), which generally display lower correlations, as discussed above.
By combining (2) and (11), one derives the relationship between rn and x: where b is determined from the slope of S]nx versus x correlations (e.g., (2)). Equation (12) is very similar to that proposed by Ehhalt et al. [1998, equation (22)], and the b term in (12) is equivalent to the at.'/term within their paper.
The difference between the two approaches is that the b term is a constant, independent of the value of xi and xj, whereas their aij is a variable that depends on the particular species pair plotted. This difference is a consequence of using RSD as a measure of variability.
For very skewed statistical distributions the RSD statistic tends to asymptotically approach a constant value for short lived species [cf. Jaenicke, 1982;Slinn, 1988].
In Figure 14a the observed slope of ln(Xi) versus ln(Xj) scatter plots is shown as a function of the kinetic slope (given by the ratio of the lifetimes' xj/xi). Clearly the observed slopes are not linear functions of the kinetic slope and fall well off the y=x line when species lifetimes become significantly different. The largest difference between observed and kinetic slopes are for the Harvard forest winter data. Figure 14b tests the relationship in (12). The linear relationship between the observed slope and the power transformed kinetic slope (given by (xj/xi) b ) fall about the y=x line. Returning to the nature of the In(n-butane/ethane) versus In(propane/ethane) slopes, we conclude that the similarity in slopes from different locations results from the similarity in the regional S•nx versus lifetime dependence. Knowing the power law relationship allows a straightforward analytical interpretation of the observed slopes of ln(Xi) versus ln(Xj) plots that is independent of assumptions about the regional background. This highlights an important point as correlation plots are a key tool for organizing data and relating relative changes in concentration to photochemical processes. In particular, within the troposphere the study of the photochemical transformation of constituents such as NO x, NOy, CO and 0 3 in urban and power plant plumes often relies on the use of correlations between these species as a means of understanding the underlying photochemistry and their relative rates of production and loss.

Summary and Conclusion
In this paper we have examined previously published data sets of hydrocarbons, halocarbons, and CFCs to investigate the relationship between variability and lifetime on a regional scale. The data examined were collected in the troposphere and stratosphere. The standard deviation of the In-transformed data (Sin x) was used as a comparative measure of trace gas variability. Variability was found to follow a power law relationship with lifetime given by (2). The lifetime dependence given by the exponent b differed considerably between the data sets and relates the relative importance of sources and sinks in describing regional variability of trace gases. In the GTE data sets the correlation between Sln X and lifetime spanned a lifetime range of 4 orders of magnitude. The dependence on lifetime for these remote tropospheric data was--,r-0.s0, with the proportionality factor A varying between the different field campaigns. Some species, such as CH3C1 and the halons, did not fall along the trends. The low variability of CH3C1 relative to the trend may illustrate the importance of its oceanic source in determining its spatial variability.
The Harvard forest hydrocarbon data displayed no seasonal dependence in the variability-lifetime relationship. The summer to winter Sln X ratios may therefore provide a means of estimating the relative change in HO concentrations on a regional scale. The average ratio of summer to winter Slnx values of 1.54 is consistent with the Goldstein et al. [1995] estimated factor of 10 seasonal change in lifetime given the observed ,r-0.1g dependence.
The stratospheric data displayed a strongly correlated trend between Sln X and stratospheric lifetime. There is still much uncertainty regarding stratospheric lifetimes. On the basis of the good correlation obtained we used the CTM-derived lifetimes from Availone and Prather [1997].
Both the ASHOE and AASE II extratropical data displayed a very strong lifetime dependence, ,r-0.97 and ,r-0.90, respectively, much stronger than the tropospheric data. Tropical data from the stratosphere generally displayed a significantly weaker 'r dependence than the extratropical data. The proportionality coefficient ß was also much smaller for the tropical data. The value of ß compared well to published estimates of chronological age ranges of stratospheric air for the tropical and extratropical regions sampled by the ER2 and supports the idea that ß is likely some measure of the source-receptor transit time range implicit in the tracer measurements.
We also examined a small data set collected on the sea ice of the Lincoln Sea during the spring of 1992 where hydrocarbon distributions suggest the occurrence of C1 and Br atom oxidation in the Arctic. The time series data were used to illustrate the point that regional variability-lifetime relationships for hydrocarbons might be profitably used to estimate the relative abundance of radicals. The approach assumes that such a relationship exists (but makes no assumptions regarding the lifetime dependence) and that the relevant rate coefficients are well known. The estimated Br:C1 ratio found from the variability-lifetime approach was similar to those estimated at Alert during the same period using a different approach.

Finally, we have shown how the variability-lifetime relationships can help in the interpretation of In versus In correlation plots of tracers such as In[n-butane] versus
In[propane] commonly considered in the troposphere. Plots of ln(Xi) versus ln(Xj) are often highly correlated linear trends for which a slope can be determined with confidence, particularly in the stratosphere. The coefficient b in (2) gives the appropriate power trav, sformation in order to relate linearly the observed slope of ln(Xi) versus ln(Xj) plots to their kinetic slope. Equation (2) promises to be a powerful analytical tool for understanding the relative influence of sources and sinks on the variability of reactive trace gases and for understanding the relationships amongst these gases in the atmosphere.