Seasonal evolutions of N20, and CO2: Three-dimensional simulations of stratospheric correlations

. Fluctuations in the concentrations of stratospheric trace gases are often correlated over a large range of space and time scales, an observation frequently used to infer the existence of various chemical processes. Three-dimensional models provide a tool to examine the causes and variations of trace gas relationships, because they can reahstically simulate the interplay between stratospheric photochemistry and meteorology. Thus such models can aid the interpretation of observed trace gas relationships. We use the general circulation model of the Goddard Institute for Space Studies to simulate the evolution and distribution of NaO, COa, and 03 over a year. In the modeled lower stratosphere the constituents NaO and COa have well-correlated spatial variations, but the slope of the regression line depends on both the season and the direction of sampling. This departure from a universal form is due both to the annual cycle in tropospheric COa and to transport of air from the upper stratosphere photochemically depleted in NaO. Due to the short photochemical lifetime of tropical 03, its relationship with N(cid:127)O is still more varied. In particular, the slope of the 03-N;(cid:127)O regression hne changes significantly from middle to high latitudes, behavior relevant to the use of NaO for estimating the rate of polar winter 03 depletion. In general, a tight correlation between two trace gases such as NaO and 03 is often observed, but this datum cannot be used to infer a similar universal relationship because a different direction of sampling may change the slope and the scatter about it. In this modeling study, the three trace gases N20, CO(cid:127), and O3 have no interactions. We are thus free to simulate each separately, and consider interrelationships after-wards. Details of the CO(cid:127), N(cid:127)O, and O3 simulations are described below.


Introduction
Trace gases in the stratosphere are observed to vary rapidly in space and time. Only photochemical reactions can create or destroy a given species. Dynamical motions are responsible for the mixing of air parcels with different chemical histories. Thus observed variations in trace gases involve an interplay between chemical creation of gradients and dynamical relaxation of these structures. A major challenge to the interpretation of measurements and to their comparison with models is to separate and evaluate the roles of each process.
Observations of mixing ratios for the long-lived trace gases, such as CH4 and N20, show on average large-fall [Prather and Rodriguez, 1988], dilution of the ozone hole [Prather et al., 1990a], the space shuttle [Prather et al., 1990b], and CO2 [Hall and Prather, 1993]. In this modeling study, the three trace gases N20, CO•, and O3 have no interactions. We are thus free to simulate each separately, and consider interrelationships afterwards. Details of the CO•, N•O, and O3 simulations are described below.

Carbon Dioxide
Emission and uptake of atmospheric CO2 are not in balance today. Atmospheric concentrations have been increasing throughout the industrial era at a rate of about 1.5 ppm/yr in the 1980s [Keeling et al., 1989], but much more slowly (0.5 ppm/yr) during the apparently anomalous years 1991-1993 [Conway et al., 1994].
On top of this trend, there are large seasonal variations driven by the annual cycle of biospheric uptake and release of carbon. This cycle, having typical peakto-peak amplitude at the surface as large as 14 ppm, is neither sinusoidal nor symmetric between hemispheres, but repeats regularly with some interannual variability [Keeling et al., 1989]. We model CO2 without chemistry in the stratosphere, and therefore neglect the small source (up to 1.5 ppm) due to CH4 oxidation. The CO• simulation employed here is identical to that of Hall and Prather [1993]. Briefly, a time-dependent surface boundary condition on the mixing ratio has two components: (1) a steady 1.5 ppm/yr increase, and (2) a latitude-dependent, but zonally averaged, annual cycle based on obvservations. In this case the model itself, through advection by winds and monthly mean patterns of cumulus convection, determines the amplitude and phase of the CO• cycle in the troposphere. Although clearly not adequate for accurate modeling of CO• throughout the troposphere (see, e.g., Fung et al. [1987]), the scheme used here is sufficient for our goal of simulating the the CO2 distribution in the upper troposphere and stratosphere. The influence of the steady trend reach 40 km in about 3.5 years. The annual cycle propagates into the stratosphere with a phase delay extending outward from the tropical tropopause. In the lower stratosphere this cycle has an amplitude of about 2.0 ppm peak-to-peak in the tropics attenuating to 1.0 ppm at high latitudes, with the two hemispheres in phase.

Nitrous Oxide
A major source of N20 involves microbial activity in the soils and oceans but is clearly influenced by human activity [Houghton et al., 1992]. N20 loss occurs via stratospheric dissociation and reaction with O( x D).
Although atmospheric concentrations are observed to be increasing about 0.25% per year and the interhemispheric gradient is about i ppb, we adopted a fixed boundary condition of 300 ppb. (For the current best value of 310 ppb, the results presented here could be scaled linearly.) A table of loss frequencies is calculated with the off-line photochemical model and used to derive N20 losses at each CTM time step as a function of latitude, altitude, and month. Local loss frequencies vary from (10 yr) -• at 29 km to (1 yr) -• and greater above 37 kin. We derive a global-mean lifetime (defined as total burden divided by loss) for N•O of 131 years.
Because of the exponential fall•off in NaO loss frequency with increasing pressure, the variation in NaO losses from the top to the bottom of a 5-krn-thick level can be large. Thus we take advantage of the additional information in the vertical moments of the NaO distribution to calculate the losses (i.e., change in $0) and redistributions of the moments (i.e., changes in $z and $zz). There is a unique solution for coupling the mo- This is the first presentation of N20 modeling for the CTM. In Figure I the zonal-mean mixing ratio contours for January, April, July, and October display the basic observed climatic distributions from satellite data (Nimbus 7 Stratospheric and Mesospheric Sounder (SAMS)) [Jones and Pyle, 1984], with upwelling of N•O rich air in the tropics and descent of N20 poor air at high latitudes. We adopt the model-measurement test described by Remsberg and Grose [1993] to analyze the seasonal patterns of N•O, recognizing the problems with SAMS N20 observations at low altitudes. Figure 5øN, 35øN, and 65øN) for each of four months (January, April, July, and October). Basic agreement is good, although our simplified lower boundary condition and lack of tropospheric ozone chemistry makes these comparisons less useful in the upper troposphere. The most important fact is that the sharp vertical gradient of 03 through the lower stratosphere and across the tropopause is well represented in these simulations.

Tracer Correlations-CO2-N20
In this section we analyze the simulated CO2-N20 relationships which are summarized graphically by plotting one trace gas concentration against the other. These "scatterplots" often display compact, smoothly varying features called "correlation curves." In the CO2 plots shown here we have compensated for the regular increase in CO2 concentrations (1.5 ppm/yr in the troposphere in these simulations) by linearly shifting values to a common reference time, preserving seasonal variations. The first subsection describes our realistic sire-ulations of CO2 and N20 and demonstrates the large seasonal and spatial variations in both shape and compactness of the correlation curves. In order to understand the mechanisms responsible for these departures from a single universal curve, the second subsection analyzes results from simulations of several hypothetical tracers: (1) a tracer like CO2, but driven only by a smooth linear increase in time, and (2) three tracers like N20, but each with a different, highly simplified form of stratospheric loss. This section concludes with discussion of selected CO2-N20 observations.   Figure 4. Modeled CO2 versus N20 instantaneously every 5 days (for a full year), every 10 ø longitude, every 2 km pressure altitude from 6 to 44 kin, at 44øN (points). Also shown (triangles) are data from A trace gas is in the "slope-equilibrium" limit in the lower stratosphere when all its chemical processes and time variations are negligibly slow compared to waveinduced quasi-isentropic mixing. Such tracers have isopleths conforming to a common shape, with a downward slope from low to high latitudes determined by the balance between the rapid quasi-horizontal mixing along isentropes and the slower Brewer-Dobson mass circulation [Holton, 1986]. When two trace gases have parallel isopleths, the concentration of one uniquely determines that of the other, their fluctuations are correlated, and the scatterplots form compact, universal curves. The relationship between N20 and CO2 does not fit this approximation perfectly. In the lower stratosphere (N20 > 275 ppb in Figure 4) a major reason is the annual cycle in CO2, which we shall show produces significant seasonal variations in the shape of the N20-CO2 correlation curve and, in particular, the scatter about the curve. The presence of scatter indicates that CO2 seasonal variations, which enter the stratosphere in the tropics, are too rapid to be homogenized on mixing surfaces (isentropes); thus the relative slope of CO2 and N20 surfaces changes seasonally. Similarly, on mixing surfaces in the upper stratosphere, the photochemical loss of N20 is too rapid in the tropics for its effects to be evenly distributed. In the upper stratosphere CO2 and N20 surfaces are also not parallel, producing the scatter about the curve at N20 concentrations below  I  I  I  I  I  I  I  I  I  I   I  I  I  I  I  I  I  I  I Figure 14 on top of the N20 contours. Another question might be how losses in the middle stratosphere impact the isopleths of N20 in the lower stratosphere. Therefore we define a tracer N20 B with no photochemical loss below 48 km (1 mbar) and a uniform loss frequency of (2 weeks) -1 above. The zonally and annually averaged isopleths of N20 B are shown in Figure 15, also on top of the N20 contours. As a third example, consider what would happen if the N20 chemistry were uniform throughout the stratosphere. We define the tracer N20 C to have a uniform loss frequency, (20 yr) -•, at all altitudes above the 200 mbar (approximately 11 km) level in the CTM. The zonally and annually averaged isopleths of N20 C are shown in Figure 16 on top of the CO• T contours.

Realistic CO•-N20 Simulations
In the upper stratosphere N20 isopleths slope less steeply toward the poles than those of COa T (Figure 13).  On a bulging CO• T surface, the photochemical destruction of N20 is more rapid in the tropics than at high latitudes (which is also at a lower altitude), and losses are too rapid to be homogenized by quasi-horizontal mixing. This effect is seen also for N20 A, which only has vertical, not latitudinal gradients in chemistry. There is no variation in loss frequency along C02 T surfaces for N20 s and N20 C, and these tracers show no tropical suppression relative to CO• T. Apparently, it is the vertical gradient in photochemistry, rather than latitu-  dinal, that is primarily responsible for the N20-CO2 difference in the upper stratosphere. Even for the case of spatially uniform loss, a tracer will have isopleth shapes more shallow than CO2 T if its chemical loss is rapid enough. For lifetimes less than about 7 years the tracer mixing ratio is no longer a simple measure of age because the exponential decay cannot be approximated as linear over the spread of ages present in the air parcel (the age spectral width [see Hall and Plumb, 1994]). On surfaces of constant age (co2T), the width of the age spectrum increases slightly from low to high latitudes [Hall and Plumb, 1994]. The additional younger air components present in high-latitude parcels are weighted preferentially by the exponential decay of the tracer, producing isopleth slopes more shallow than those of CO2 •. This effect is negligible for N20 c because the loss is too slow. However, it may play some role in flattening N20 contours relative to COa T in the middle and upper stratosphere.
In the lower stratosphere, Figures 13, 14, and 15 show that isoplcths of N20 A and N20 B, like those of N20, slope downward at midlatitudes more steeply than those of CO2 T. The cause of this difference must be found in transport from the upper stratosphere because N20 $ has no loss in the lower stratosphere. It must also be due to the increase in chemical loss frequency with altitude because isopleths of N20 c (uniform chemistry) line up with those of CO2 T (Figure 16).
In the midlatitude lower stratosphere, a tracer with a remote source establishes a family of isopleths that

90S
,  slope downward to the poles relative to pressure surfaces. Holton [1986] explained the basic shape of these contours. To a first approximation, the isopleths fall along surfaces of rapid adiabatic mixing (i.e., surfaces of constant potential temperature). A tracer on these mixing surfaces, however, can never be homogenized because it is continuously perturbed by a small residual mass flux across these surfaces. On average, air pushes up through the equatorward side of this surface and downward through the poleward side. Thus for a tracer with a vertical gradient at midlatitudes, the isopleths must slope downward to the pole more steeply than the mixing surfaces. This criterion applies to long-lived chemical tracers such as N20, N20 A, N2 B, and N2 c and those in the slope-equilibrium limit discussed by Plumb and Ko [1992]. It also applies to linearly changing, chronological tracers such as CO•.
We have also seen that in the midlatitude lower stratosphere of the model N20-like tracers (N20, N20 A, and N20 is) have isopleths that slope downward to the poles more steeply than chronological tracers (CO• and N2OC). Each stratospheric air parcel has a mix of irreducible fluid elements with a range of transit times whose average is defined as the age of the parcel [Hall and Plumb, 1994  the trace gas.) The mean CO• concentration of a parcel does not depend on the paths of the fluid elements comprising the parcel; however, the concentration of N20 does. The average photochemical history of parcels along the constant-age surface varies with latitude. For the same transit time since leaving the troposphere, the stratosphcric circulation has caused a fluid element on the poleward side of the age surface to traverse higher altitudes on average, and thus have less remaining N20, than an element on the equatorward side. The integrated photochemical activity along fluid element paths, which can be thought of as a "photochemical age" since elements entered the stratosphere, increases poleward on an age surface for all gases with increasing chemical loss aloft. Thus N•O (also N•O A and N•O s) isopleths must slope downward to the pole more steeply than those of CO• T (also N•oC). At midlatitudes in the lower stratosphere all such tracers slope more steeply than isentropes, and N20 tracers slope more steeply than chronological tracers. Thus chronological tracer isopleths are the closest to isentropes.

COa-NaO Observations
Along with the modeled COa-NaO scatterplot at midlatitudes, Figure 4 also displays simultaneous measuremen• s of CO2 and NaO from a decade of balloon soundings in Europe [Schmidt e! al., 1991]. To obtain this composite we removed linear trends from CO•, for two different periods, before and after 1987, because of an abrupt, large jump in the COa measurements after 1987. In fact, one flight from 1987 was discarded due to excessive scatter, as were three outlier points in the subsequent NaO-COa scatterplot. Note that the modeled and observed data have been scaled to a common surface CO2 value. The resulting observations show the same basic structure as the modeled correlation curve: a clear decline in CO2 along with N aO, including some evidence for curvature in this relationship. The observations show large scatter which, in addition to noise, may include effects from interannual variability in both transport and sources, not part of the simulation here. Meaningful model-measurement comparison will require greater precision and more frequent measurements, emphasizing the need for high-resolution aircraft measurements of CO2 in the lower stratosphere [e.g., Boering e! al., 1994].

Tracer Simulations: O3-NaO
Ozone has in general the most rapid photochemistry of the tracers simulated here. In the middle and upper stratosphere, O3 is nearly in local photochemical steady state and has a maximum mixing ratio near 35 km altitude. Because transport plays no direct role in its distribution here, its relationship with long-lived tracers is not compact. In the lower stratosphere, the photochemical timescale for O3 change, defined by either production or loss terms, ranges from a month or two in the tropics to a few years at high latitudes. Thus its global distribution is controlled neither by photochemistry nor by dynamics alone [Ko et al., 1989  In addition to increasing scatter with altitude, the curves fitted through the Oa-N20 correlations for different altitudes are not continuous but form a "banded" structure similar to, but more pronounced than, that of N20-CO2 t. Note that these bands are a consequence of the particular sampling scheme (i.e., quasi-horizontal at distinct altitudes), and other sampling strategies as described by (7)   for O3, and thus so is the chemical loss. However, when the evolution of the O3.-N20 relationship is followed through the winter, beginning at high altitude as noted above, this approach should be robust.
In Figure 21  nearly as large as the observations; however, the curve is continuous. The observed discontinuity clearly indicates some dynamical barrier to mixing between tropics and subtropics at the time of the observations. The simulation accurately portrays the different chemistries of the two regimes but fails to achieve this dynamical separation. It is not clear what type of circulation would be needed to create the observed pattern.

Conclusions and Discussion
Simulations of different chemical species in a threedimensional model provide a means to understand more thoroughly observed trace gas correlations in terms of Regarding Arctic ozone loss, it is difficult to separate the influence of background structure (i.e., the relative slopes of the isopleths as a function of latitude and altitude) from that of enhanced chemistry when using a long-lived tracer such as N20 as a coordinate. Defining this background structure, for example using the full set of altitudes covered by the ER 2 and DC 8, should help. (3) The lack of compactness in the observed trace gas correlations contains important information on the chemical and mixing times in the lower stratosphere. Unfortunately, testing the model predictions for N20-CO2 requires N20 precision better than 5 ppb, and thus the measurements from the Stratospheric Photochemistry, Aerosols, and Dynamics Expidition (SPADE) [Boering e! at.. 1994], the most precise to date, may not be suitable. The third conclusion points to a fundamental measurement of the stratospheric circulation. The relative orientation of the isopleths of two tracers can be obtained directly from the change in the tracer-tracer correlation slope with sampling direction, or equivalently, the spread about the regression line. For species having negligible chemical loss in the lower stratosphere and slowly varying tropospheric sources, the nonuniversality of tracer relationships is a consequence of the finite rate of quasi-horizontal mixing compared to highlatitude descent of "photochemically aged" air, as discussed for N20--CO•. Thus the relative rate of residual advection to horizontal mixing can be obtained from analysis of such correlations. This approach is far more feasible than intensive measurements of individual tracers to determine the mean slope of the isopleths on pressure surfaces, which would require many years of observations to reduce meteorological noise. It is not yet clear which tracers would be optimal for this type of correlation study. Consistent calibration and high precision are vital, although not necessarily high accuracy. Apparently, because of the large influence of the annual cycle in the lower stratosphere, CO2 is not a good choice for illuminating these long term processes below 20 km altitude. However, it likely provides unique information about transport on seasonal time scales and less.
In addition to these general conclusions, there arc some specific lessons from the N20-CO2-Oa studies: (1) The model's maintenance of a reversed vertical gradient in CO2 throughout the autumn in northern midlatitudes agrees with observations [Boering ½! at., 1994] and demonstrates that only small amounts of tropospheric air enter the stratosphere directly a• midlatitudes. (2) The realistic N20-Oa slopes at low latitudes indicate that the CTM simulates tropical photochemistry well, and in particular, accurately reproduces the relative rates of Oa production to N20 loss. How-ever, the observed discontinuity between the tropics and subtropics seen in the O3-N20 observations of Murphy et at. [1993] cannot be readily understood with the present model. (3) From both the CO2 and N20 simulations it appears that the GCM used here mixes air too rapidly into the stratosphere below 20 to 25 km. If both aircraft and SAMS observations of N20 are consistent, then steeper vertical gradients are required below 20 km with more rapid mixing somewhere above. Clearly, the present model, with 5-km vertical resolution, must be viewed primarily as a didactic tool.