nitrous oxide ( n2o ) is the thirdmostimportant , longlived greenhouse gas , after carbon dioxide and methane [ myhre et al . ,
these topthree greenhouse gases have a mixture of natural and anthropogenic sources , and the challenge has always been to quantify the human perturbation to their budgets [ prather et al . , 2012 ; ciais et al . ,
surface emissions of n2o have an average atmospheric residence time of a century or more [ ko et al . ,
1991 ; world meteorological organization ( wmo ) , 2014 ] , and thus , the current imbalance between emissions and atmospheric loss , as quantified by the observed growth rate of 3.8  tg  n / yr ( 0.8  ppb / yr ) , is expected to lead to further increases in n2o abundances over this century , even if anthropogenic emissions are stabilized .
anthropogenic emissions of n2o are driven primarily by fertilizer use and the handling of animal wastes , sources difficult both to control and to quantify [ galloway et al . , 2008 ;
estimates of n2o emissions from summing individual sources have greater than factor of 2 uncertainties [ prather et al . , 2009 ; ciais et al . ,
2013 ] , and atmospheric inversions rely on the accuracy of stratospheric losses and emission patterns [ thompson et al . ,
scenarios for future n2o levels make assumptions about both presentday and preindustrial n2o lifetimes to determine the anthropogenicnatural balance in emissions levels [ meinshausen et al . , 2011 ; kirtman et al . ,
thus , the uncertainties in the current budget and 21st century projections of n2o are its lifetime and the feedback that an n2o perturbation has on its lifetime [ prather , 1998 ] .
assessment of the lifetime and feedback has been notably absent from climate and ozone assessments [ intergovernmental panel on climate change ( ipcc ) , 2007 ; wmo , 2011 ; ipcc , 2013a ] but has received more attention in the past couple years [ stratospheric processes and their role in climate ( sparc ) , 2013 ; chipperfield et al . , 2014 ; wmo , 2014 ] . in this paper
we combine satellite measurements of n2o , o3 , and temperature ( t ) from the aura microwave limb sounder ( mls ) instrument [ lambert et al . , 2007 ;
2008 ] with global chemistry models to derive a semiempirical ( measured ) lifetime for n2o .
previous studies have been done with less extensive satellite data [ ko et al . , 1991 ; minschwaner et al . , 1998 , 2013 ] .
this lifetime is constrained by the observation of all quantities controlling n2o loss , is independent of transport uncertainties , and includes seasonal and yeartoyear variability .
the only chemical modeling involves photolysis rates for n2o and o3 and the kinetics of the o(d ) reactions .
uncertainties in this semiempirical lifetime are due only to possible errors in these chemical rates and in the measured profiles of n2o , o3 , and t in the critical region ( 330  hpa in the tropics ) .
four chemistrytransport models ( ctms ) using meteorological data for the aura period are compared with monthly mls observations of stratospheric n2o and o3 , the n2o losses derived therefrom , and stratospheric noy from the environmental satellite michelson interferometer for passive atmospheric sounding ( mipas ) [ funke et al . ,
2014 ] in order to understand the cause of model errors in n2o lifetime . in addition , two chemistryclimate models ( ccms , one 3d and one 2d ) with climatedriven circulations are also evaluated against the average mlsderived lifetime . the models evaluated here overestimate the semiempirical lifetime , 116    9  years , by a wide range , but agree on the negative sensitivity of lifetime to burden of 0.065    0.010 ( not constrained by observations ) that results in a lower residence time for n2o perturbations of 109  years . a best estimate for preindustrial conditions gives a longer lifetime of 123  years due primarily to reduced photochemical rates for n2o loss because of increased midstratospheric and upper stratospheric o3 caused by reduced levels of chlorine and n2o .
results from the mls data and the constrained photochemical models are described in section 2 .
the ctms , their calculation of n2o lifetimes , and their comparison with stratospheric constituents and the constrained n2o loss are presented in section 3 . in section 4 , four models are used to estimate the reduction in lifetime when n2o increases and the change in lifetime since the preindustrial era . an overview of issues related to n2o lifetime is discussed in section 5 .
the mls instrument on the nasa aura satellite provides highly accurate , wellresolved latitudebyaltitude colocated profiles of n2o , o3 , and t throughout the stratosphere [ lambert et al .
we use monthly mean mls data sets from august 2004 to december 2010 ( version 2.2 for o3 and version 3.3 for n2o and t ) .
profiles are averaged longitudinally and within 5 latitude bins from 85s80s to 80n85n ( 34 in total ; mls observations are limited to 82s82n ) . for global budgets ,
the 8085 latitude bins were extended to 90. there are six standard pressure levels per decade in pressure ( i.e. , 100 , 68 , 46 , 32 , 22 , 15 , 10 , up to 0.10  hpa ) .
these data sets are very similar to the monthly mean data records produced for the global ozone chemistry and related trace gas data records for the stratosphere project [ froidevaux et al . ,
the vertical profiles of o3 and t define all the conditions needed to calculate the profiles of n2o loss and noy production from the following reactions ( ( r1)(r5 ) ) .
the rates of these reactions respond primarily to overhead o3 column and t. 
 o3+hv=>o1d+o2 
 o1d+n2,o2=>o+n2,o2 
 n2o+hv=>n2+o1d 
 n2o+o1d=>n2+o2 
 n2o+o1d=>no+no 
  we use two independent photochemical submodels , one from nasa goddard space flight center ( gsfc , embedded in the g2d model ) and one from university of california , irvine ( embedded in the uci ctm ; see table 1 ) .
these submodels solve the 1d radiative transfer problem to calculate jn2o ( reaction ( r3 ) ) and o(d ) densities ( reactions ( ( r1 ) and ( r2 ) ) and are documented in photolysis studies [ olson et al . , 1997 ; photocomp , 2010 ] .
while the methodologies and numerical approaches for both are independent , they ( and all the chemistrytransport models here ) adopt standard values for the cross sections ( o2 , o3 , and n2o ) and rate coefficients controlling these reactions [ sander et al .
the uci version ( mlsu ) uses the standard mls levels ( 2.7  km ) and integrates monthly , latituderesolved losses from 0.10  hpa to 100  hpa . the gsfc version ( mlsg ) interpolates and fills the mls data and integrates at 1  km resolution through the atmosphere .
given the linear n2o profile in the dominant loss region ( figures 1a and 2a ) , the integrated loss should not be sensitive to interpolation methods .
from mlsg we find that about 2% of n2o loss occurs at altitudes below 100  hpa . from previous studies with the uci ctm [ prather and hsu , 2010 ] we found
thus , n2o losses from mlsu are corrected upward by 2% , and those from the uci ctm ( running here without tropospheric chemistry ) are corrected upward by 1% .
measurements and models multiyear annual average loss of n2o plotted against ( a ) pressure altitude ( z * km , units tg  n / yr / km ) and ( b ) latitude ( degrees , units tg 
results are shown for mlsg ( black solid line ) and mlsu ( black vertical bars or diamonds ) .
mlsu primary production of noy ( times 20 ) is also shown in figure 1a ( red dashed vertical bars ) .
n2o loss from the uci ctm is shown for ifs cycles 29 ( blue ) and 36 ( green ) .
tropical ( 30s30n ) profiles of ( a ) n2o ( ppb ) and ( b ) o3 ( ppm ) as a function of pressure altitude ( z * km ) average over 20052010 where available .
mlsg ( solid black ) is interpolated to 1  km resolution , and mlsu ( black dots ) shows the original mls resolution .
also shown are the modeled profiles for gmi ( orange ) , g2dm ( red ) , ucic29 ( blue ) , ucic36 ( green ) , and g2d ( gray ) .
the critical region for n2o loss is the tropical middle stratosphere as shown in figures 1a and 1b .
photochemical loss ( dominated by r3 ) peaks at the equator near 32  km pressure altitude .
both models mlsg and mlsu agree on the integrated loss averaged over years 20052010 , although coarse vertical layering for mlsu ( vertical black bars ) obscures the peak loss . in terms of total loss , 81% occurs between 24 and 40  km including all latitudes , while 76% occurs between 30s and 30n including all heights .
polar regions produce only 4% of the loss , and that occurs at high altitudes , so that ozone depletion below 24  km has minimal direct photochemical impact on the n2o lifetime .
ozone depletion from the clo catalytic cycle ( 4050  km altitudes ) does impact the n2o lifetime : see discussion of preindustrial lifetime ( section 4 ) .
figure 2a shows the vertical profile of mls n2o from 16 to 48  km in pressure altitude averaged over 30s to 30n for years 20052010 , and figure 2b , that of mls o3 .
note that the peak loss ( figure 1a ) centers on the 50% ( ~160 
ppb ) level of n2o at about 10  hpa ( 32  km ) .
the critical region for modeling the n2o lifetime thus centers on the region 30s30n and 24  km to 40  km .
the mls observations show that monthly zonalmean n2o abundances at 10  hpa have large seasonal and interannual variations ( figure 3a ) .
the upwelling region with highest n2o levels , and hence greatest loss , occurs in the tropics ( 20s20n ; white lines in figures 3a3e ) , where the mls monthly average at 10  hpa ranges from 147 to 206  ppb .
contours of n2o at 10  hpa plotted as function of latitude and month from january 2004 to december 2011 .
results are shown for ( a ) mls , ( b ) ucic29 , ( c ) ucic36 , ( d ) g2dm , and ( e ) gmi . with this variability in the critical loss region
the 5  year averaged monthly mean loss rates are shown in figure 4 for mlsg ( black solid  +  dots ) and mlsu ( black dashed ) .
not unexpectedly , both chemical submodels give nearly identical results with a mean loss rate of 13.2  tg  n / yr and peaktopeak amplitude of 25% . the peak losses occur with the peak upwelling ( januaryfebruarymarch ) seen in figure 3 . the interannual variation in n2o lifetime is calculated as 12  month running averages of the burden ( tg  n  =  4.79 times lower tropospheric mean abundance in ppb ) divided by the 12  month accumulated loss ( tg  n / yr ) and is plotted for mlsg and mlsu from 1 february 2005 to 1 july 2010 in figure 5 .
the calendar mean ( january  december ) lifetimes for mlsg are shown as dots . the mean burden over the mls period is calculated as 1539  tg  n , and the mean loss is 13.2  tg  n / yr , giving a lifetime of ~116.5  years for both photochemical submodels ( see table 1 ) .
a quasibiennial signal is clear over the 5  years of mls data , and the minimumtomaximum amplitude is about 10%
. monthly n2o loss rate ( units of tg  n / yr ) for the mls period of 20052010 or best equivalent period from mlsg ( black solid  +  dots ) , mlsu ( black dashed ) , gmi ( orange ) , g2dm ( red ) , g2d ( gray ) , ucic29 ( dark blue ) , osloc29 ( light blue ) , ucic36 ( dark green ) , and osloc36 ( light green ) .
values are derived from 12  month average burden ( tg  n ) and loss rate ( tg  n / yr ) centered on each month
the n2o lifetime varies with solar activity , and mlsg and mlsu evaluated this by changing the solar spectrum and thus the photolysis rates , which are summarized in table 2 .
mlsg has the more accurate treatment , and its 20052010 lifetime value uses the actual solar activity of the time period ( mostly solar minimum ) .
mlsg then repeated the calculation using constant minimum and maximum solar activities , giving a span of 7% ( 109  years at solar maximum to 117  years at solar minimum ) .
this range uses the fixed mls observations of o3 and t , which are more suitable to solar minimum conditions , and thus , background atmospheric changes expected at solar maximum ( including the n2o ) are not included .
mlsu uses a solar spectrum that averages minimum and high ( but not maximum ) solar activity .
thus , the standard 20052010 mlsu lifetime represents higher solar activity than occurred for the period , and the agreement with mlsg is fortuitous since the solarminimum calculation gives a slightly longer lifetime of 119  years .
both models show a similar response to changes in the solar spectrum when the difference in minimummaximum ranges is considered .
the 20052010 period covers an extended solar minimum period ; the solar activity of the current cycle 24 is weaker than average and expected to reach maximum in 2015 [ pesnell , 2014 ] .
presentday n2o lifetime and other model comparisonsa 
  note that stratospheric n2o is multiyear average at 10  hpa , 20s20n .
ln(lifetime)/ln(burden ) is related to the feedback factor as ff  =  1/(1    s ) [ prather , 2007 ] .
lifetimes are calculated as the annual average burden ( tg  n ) divided by the accumulated annual loss ( tg  n / yr ) , and all are based on a transient n2o burden increasing at 0.25%/yr .
oslo and uci models ran with fixed n2o burden and , based on a ucic29 test case , have their lifetimes increase by 0.4% .
because models have different atmospheric dryair masses , all burdens are calculated from the lower tropospheric mean n2o abundance ( ppb ) using the relationship 4.79  tg  n / ppb [ prather et al . ,
mlsg standard simulation used transient solar activity for the period of mls observations , while mlsu used the average of two solar conditions ( solar ultraviolet spectral irradiance monitor 11 november 1994(low ) and 29 march 1992(high ) ) .
mlsg solar maximum conditions are representative , while the mlsu  solar maximum  simulation is high , but not maximum . the mlsu lifetime has been corrected for missing 2% of loss below 100  hpa ( the lower limit of mls data ) .
ucic29/36 model is a stratosphereonly chemistry model , and its lifetimes are corrected by 1% to account for lack of tropospheric o(d ) loss .
both c29 results stop in year 2007 , but correction is made because the mlsu lifetime derived for 20052007 is almost identical to that over the full period of 20052010 .
likewise , comparisons of the period 2004/2007 versus period 2004/2010 using cycle 36 and merra fields show little difference ( 0.9  years ) . g2d has reduced variability using yearly repeating steady state transport . combining interannual variability and other uncertainties , we derive the n2o lifetime of 116    9  years for the period of 20052010 .
comparison with modeled values follows , and the 1 sigma uncertainty of 8% is derived in section 4 .
four ctms used meteorological data for the mls period and before , calculating n2o lifetimes to compare with the mlsg / u results . see table 1 .
two of these ( nasa global modeling initiative ctm ( gmi ) and gsfc 2d model ( g2dm ) ) used the modernera retrospective analysis for research and applications ( merra ) goddard earth observing system version 5(geos5 ) assimilation met data ( designated gmi and g2dm , respectively ) .
the gsfc 2d model with interactive transport ( g2d ) also ran a standard simulation and sensitivity studies for steady state , yearly repeating 2010 conditions .
the gsfc goddard earth observing system chemistry climate model ( geosccm ) is a freerunning atmospheric climate model driven by prescribed sea surface temperatures .
uc irvine and university of oslo ctms used the european centre for mediumrange weather forecasts ' ( ecmwf ) integrated forecast system ( ifs ) to generate pieced forecasts , and two different cycles of the ifs generated met data that partially overlap ( designated ucic29 , ucic36 , osloc29 , and osloc36 according to which ifs cycle was used ) .
the oslo and uci models used identical met data and tracertransport models , but oslo has full stratospheretroposphere chemistry ( like gmi ) , whereas uci uses a linearized stratospheric chemistry model ( o3 , n2o , noy , ch4 , and h2o [ see hsu and prather , 2010 ] ) .
globally integrated n2o loss versus altitude from ucic29 and ucic36 are compared with mlsg / u in figure 1a .
both uci models match the mls shape but calculate losses that are smaller by 10% ( c29 ) and 20% ( c36 ) with largest differences near the peak loss at 10  hpa .
these results are explained for the most part by the lower average tropical abundances of the modeled n2o between 24 and 40  km , see figure 2a .
the difference between two ifs versions are clear in figure 2 : ucic29 has more rapid upwelling and higher n2o below 30  km , whereas ucic36 has slower upwelling ( or more rapid horizontal dispersion ) from 20 to 40  km .
the best matches to the mls n2o profiles are from gmi , ucic29 and osloc29 ( not shown ) .
g2dm ( using 2d monthly mean residual circulation fields derived from the same merra fields used directly in gmi ) and g2d ( using a steady state yearly repeating transport ) are similar to ucic36 , and all have consistently lower n2o abundances than mls .
a more quantitative comparison of the 10  hpa n2o abundances is given in table 2 , where the mean and standard deviation of the monthly mean 20s20n abundances are given under 
 this statistic emphasizes the core tropics more than in figure 2 , and the spread across models widens .
three models ( gmi , ucic29 , and osloc29 ) are about 10% below mls values , and the other models ( g2dm , g2d , ucic36 , and osloc36 ) are about 20% below .
mls observations of n2o show largescale , quasibiennial variability within the tropical upwelling region ( 20s20n ) at the critical altitude of 10  hpa on a monthly zonalmean basis .
as noted before , ucic29 ( and osloc29 , nearly identical and not shown ) as well as gmi are similar in magnitude to mls data but down one contour level ( 20  ppb ) , while ucic36 ( osloc36 ) and g2dm are reduced by two or more contour levels .
the ucic36 n2o variability is less well correlated with observations than is that of ucic29 .
overall , both the ecmwf and merra meteorology produce a modeled 10  hpa n2o surface that is biased but highly correlated with the mls observations , indicating that transport variations in the tropical midstratosphere on a monthbylatitude basis are well represented . the other major controlling factor for n2o lifetimes is the profile of overhead o3 .
differences in the o3 profiles ( figure 2b ) can help explain why the lifetimes listed in table 2 are not inversely related to the 10  hpa n2o abundances .
ucic29 matches the mls tropical o3 profiles with gmi being slightly smaller and ucic36 being larger .
the greater o3 in ucic36 absorbs more solar ultraviolet , thus reducing the n2o loss even more than expected from the smaller n2o abundances .
both gsfc 2d models ( g2dm and g2d ) have nearly identical o3 profiles that in the 3040  km region are almost 10% less than mls .
these g2d offsets cancel in terms of total n2o loss with more solar ultraviolet enhancing the loss of the reduced levels of n2o .
thus , both g2d lifetimes are smaller than the gmi lifetime , even though their n2o abundances are 1020% smaller .
all models match the monthly seasonality of n2o loss in mlsg / u as shown in figure 4 .
the oslo / ucic29 results are not so smooth since there are only three overlapping years .
other models show different levels of flattening ( or reduction ) of the octobernovemberdecember month period , but the overall cycles with the februarymarch peak and junejuly trough are in agreement .
the greatest difference in figure 4 is the overall magnitude of the loss , and this large range in modeled n2o lifetime is summarized in table 2 . for models using met data back to 1997 , we find that the 19972010 average lifetime was about 2  years shorter than the 20052010 mls period lifetime , indicating more rapid loss of n2o in the earlier period .
the pre2005 period thus has a systematically different circulation in the tropical middle stratosphere leading to more rapid upwelling of n2o , which might be a response to the last solar maximum that occurred during this preaura period or to a change in the observing system used to generate the met data .
it can not be due to photochemical changes driven by the solar cycle since several models did not include this .
the models using ifs forecast or merraassimilated met data show realistic variations when compared with the mlsg / u results .
the steady state g2d results are shown as a gray bar for the year 2010 . in terms of correlations , mlsg and mlsu
are nearly identical ( r  =  0.98 ) . in terms of model correlations with mlsg , the g2dm , osloc29 , and ucic29 models are excellent ( 0.850.90 ) , but gmi , osloc36 , and ucic36 models do not match as well ( ~0.78 ) .
it is not clear why the gmi and g2dm should not be more closely correlated with each other .
this may be due to small differences caused in converting the merra met fields to 2d transport ( via the heating rates and eddy fluxes ) for g2dm as opposed to using the direct merra 3d wind field in gmi .
a critical part of the stratospheric nitrogen chemistry involves production via reaction ( r5 ) of odd nitrogen ( noy  =  no  +  no2  +  hno3  +  others ) , which in turn drives catalytic o3 loss centered about 35  km [ crutzen , 1970 ; johnston , 1971 ] . for mlsu
, 5.7% of the n2o loss produces noy , and this primary production ( figure 1a ) has a lower center of mass than the total n2o loss because o(d ) reactions become relatively more important than photolysis in the lower stratosphere .
consequently , the n2onoy tracer relationship [ murphy and fahey , 1994 ] is curved in the lower stratosphere . about 30% of primary noy produced is lost following photolysis of no ( jno ) in the upper stratosphere and mesosphere [ olsen et al . ,
while this photochemical process is included in the ctms , it can not be derived simply from the mls data , and modeling of jno remains highly uncertain ( 30% or more [ see photocomp , 2010 ] ) .
stratospheric noy , however , is the key link between n2o and o3 chemistries that causes an n2o perturbation to decay more rapidly than indicated by the atmospheric lifetime [ prather , 1998 ] , and thus , we seek an observational test of the modeled noy to understand differences in the modeled lifetime sensitivity to burden , s    ln(lifetime)/ln(burden ) , and the resulting lifetime feedback factor , ff  =  1/(1    s ) ( see table 4.5 of prather et al . ) .
we focus on the tropics where most n2o is lost : values of noy derived from satellite observations show a broad peak of about 16  ppb near 40  km that varies with season and year and that falls off rapidly at lower altitudes [ brohede et al . , 2008 ; jones et al . , 2011 ] .
as a robust measure of the total amount of stratospheric noy , we integrate the 30s30n column of noy above 100  hpa ( expressed in dobson unit ( du ) , 2.687    10  molecules / cm ) and compare with mipas observations ( figure 6 ) .
the observations have a mean column of 0.39 du with a march minimum and july maximum and with a minimumtomaximum amplitude of ~12% .
the g2d model is an exception with a very weak seasonal cycle in noy columns .
stratospheric tropical noy columns ( du , p  <  100  hpa , 30s30n ) by month showing ( a ) absolute columns and ( b ) monthly standard deviations over the mls period .
the n2o lifetimes from the mls data and the ctms are summarized in table 2 .
all the models in this study have too little n2o loss and hence longer lifetimes .
numerous small , percentlevel corrections to the lifetimes have been made due to the different chemistries and methods of calculation . many are noted above and summarized in the table notes .
for example , the results here consist of both transient ( mlsg / u , gmi , and g2dm ) and steady state calculations ( uci and oslo ) , and the difference between these two approaches has been discussed [ sparc , 2013 ; wmo , 2014 ] . in the transient calculations , the n2o lower tropospheric abundance increases at the observed rate of about 0.8  ppb / yr ( 0.25%/yr ) .
given that the lag for the mixed tropospheric abundance to reach the tropical midstratosphere is a couple of years , the troposphere accumulates an additional burden . in transient versus steady state simulations with ucic29
, we find that transient lifetimes are about 0.4% larger than steady state ones , and we have so corrected the oslo and uci lifetimes in table 2 .
our semiempirical estimate of the current lifetime , 116    9  years , is based on the mlsg / u calculations and has a 1 sigma uncertainty of 8% .
the only sources of uncertainty here are those in the mlsmeasured profiles ( n2o , o3 , and t ) and those in the photochemical submodels ( jn2o and o(d ) ) .
we assume that uncertainties in the o3 and t profiles ( affecting the photochemical model uncertainty ) are negligible since these measurements have a longer history of satellite measurement and calibration .
we identify the primary measurement uncertainty with the n2o profile in the 303  hpa altitude range ( n2o~40240  ppb ) .
the possible bias in the mls n2o measurements near 10  hpa has been assessed as being less than 10% [ lambert et al .
, 2007 ] , and taking this as a 90% confidence level , we place a generous 1 sigma uncertainty of 7% on the n2o abundances which translates directly to the n2o loss .
uncertainty in the photochemical data leads to a 1 sigma uncertainty of 3% in the photochemically modeled lifetime ( see chapter 3 of sparc ) .
the uncertainty in the n2o burden is negligible because the mass of the atmosphere is well known and the falloff of n2o in the stratosphere is well characterized [ prather et al . ,
2012 ] . combining the two major uncertainties , we get 7.6% and adopt 8% as a symmetric 1 sigma uncertainty in the lifetime .
note that the dominant factor is the n2o abundance and that adding another 3% uncertainty ( e.g. , from o3 and t ) would not change this value .
geosccm is the only model here whose lifetime fits within this uncertainty ; osloc29 , ucic29 , and both g2d models lie just above the upper range ; and osloc36 , ucic36 , and gmi models have lifetimes more than 2 sigma above . some but not all of the model range in lifetimes can be attributed to the low n2o abundances near 10  hpa in the tropics .
our uncertainty is notably less than previous semiempirical estimates based on the premls satellite data [ ko et al . , 1991 ; minschwaner et al . , 1998 ] , in part because of the much denser , more accurate set of mls colocated observations of n2o , o3 , and t that resolve the quasibiennial cycle .
the separately modeled and satellitederived n2o lifetimes updated in sparc   are based on premls data and have essentially the same lifetime as our best estimate , especially when one considers the large interannual variability ( 6 years ) not resolved in the premls data ( see figure 5 ) . the stratospheric processes and
their role in climate ( sparc ) overall best estimate , based on models , satellite data , and tracertracer lifetimes , is slightly higher with greater uncertainty , 123 years ( range of 104152 years ) , because of the inclusion of a 144 year lifetime determined from tracertracer correlations .
tracertracer correlations in the lower stratosphere are used to derive relative lifetimes [ volk et al . , 1997 ;
2013 ] , but this approach is not useful here because the uncertainties are much larger ( e.g. , they propagate from the reference gas lifetime , and even modeled two gas tracer correlations like n2ocfcl3 are difficult to interpret as a single slope [ avallone and prather , 1997 ] ) . our estimate of the lifetime sensitivity of n2o to its burden is s  =  0.065    0.010 , where the 0.010 is a 1 sigma uncertainty as it includes almost the entire range of models except for g2d .
thus , the feedback factor is ff  =  0.94    0.01 , and the effective residence time of an n2o perturbation is 109    10  years [ e.g. , prather , 2007 ; prather and holmes , 2013 ] .
unfortunately , there is no semiempirical method to derive this sensitivity using mls observations , but given the limited range for this value since first reported in 1998 , we feel that 15% 1 sigma uncertainty is a conservative choice .
all chemistrytransport models here are consistent with this range , except for g2d , whose sensitivity is nearly twice as large ( table 2 ) .
both g2d and g2dm have identical chemistries and similar n2o lifetimes and tropical noy columns but very different sensitivities .
analysis shows that with a greater burden of n2o , g2d 's interactive circulation is responding as slightly reduced o3 ( 2% ) , heating rates , and temperatures ( 0.3  k ) ; enhanced upwelling with age of air changed by 0.05  years ; and consequently more n2o loss . while the freerunning geosccm shows similar reductions in o3 and temperature , it does not simulate a circulation enhancement . at this time
we do not include the 0.11 feedback factor in g2d in our uncertainty range but must recognize it as presenting an open question .
there is also no simple relationship found in table 2 between the lifetime sensitivity and the noy column , in contrast to what was expected .
an interesting finding from the 14  year ucic36 calculation was that the lifetime sensitivity took more than 7  years to stabilize following a sudden 10% increase at the lower boundary , even though the lifetime appeared to stabilize more rapidly .
surprisingly , our best estimates of lifetime and feedback factor have not changed much since the first multimodel estimates were made in 2001 ( see table 4.5 of prather et al . ) .
analysis of the preindustrial ( pi ) lifetime of n2o was made with g2d , osloc29 , and ucic29 , with results shown in table 3 .
the pi simulations assumed n2o tropospheric abundance of 270  ppb ( versus 321  ppb ) , ch4 abundance of 722  ppb ( versus 1785  ppb ) , co2 abundance of 278  ppm ( versus 384  ppm , used in g2d only ) , and zero anthropogenic ozonedepleting substances ( odss ) [ ipcc , 2013b ] .
changes in lifetime , calculated as the natural log of pi lifetime divided by presentday lifetime , are estimated at + 1 to + 2% due to the lower levels of n2o alone .
the other major change , a + 3 to + 5% increase due to the lack of anthropogenic ods , is caused by the higher levels of pi 4050  km tropical o3 , leading to reduced penetration of solar radiation to 32  km , and hence reduced losses of n2o .
the full pi lifetime is estimated from these three models to be + 4% to + 8% larger than present day , with the upper range including co2 dynamical effects ( g2d only ) .
as long as the uncertainty in this change ( 2% ) is independent of other errors , then the 1 sigma range remains at about 8% .
preindustrial ( pi ) n2o lifetime changes ( approximately % ) separated by key factors , shown as ln [ lifetime(pi)/lifetime(present day)]a 
  note that pi changes include n2o dropping from 321  ppb ( 20042010 ) to 270  ppb , anthropogenic ozonedepleting substances ( ods ) dropping to zero , ch4 dropping from 1785  ppb to 722  ppb , and climate change driven by co2 dropping from 384  ppm to 278  ppm .
individual models chose slightly , but insignificantly different ranges for the pi , and the values from ipcc [ 2013b ] are quoted here .
g2d has a stratospheric circulation that responds dynamically to heating changes from o3 and co2 ( in full pi ) ; see fleming et al . .
this study has rigorously tested four global chemistrytransport models ' ability to simulate the observed distribution and loss patterns of n2o based on 5  years of mls observations .
these tests address seasonal and interannual variability showing that the models have high fidelity in reproducing the measurements on a monthbymonth basis in spite of having lifetimes that are biased high by 9% to 26% , outside of the 8% uncertainty range .
most biases can be understood in terms of lower model n2o abundances in the middle stratosphere or ( in some cases ) o3 profiles that are notably different from mls data .
the geosccm , a freerunning climate model not expected to reproduce the observed variations in n2o lifetime ( e.g. , figure 5 ) , was added to check if the n2o lifetime sensitivity was significantly perturbed by induced circulation changes .
geosccm has the most accurate simulation of multiyear average n2o abundances in the middle tropical stratosphere among all the models here , and it has a lifetime within the uncertainty range of the mlsderived value .
overall , this points to the importance of circulation and net tracer transport in the middle tropical stratosphere in determining n2o lifetime . what is the best estimate for the current n2o lifetime , one that includes the steady slow increase ( 0.25%/yr ) in burden ?
the sparc assessment 's recommendation ( see table 6.1 of sparc ) is 123  years with a 1 sigma range of 113 to 148  years based on a range of models , observations , and tracer correlations .
our 1 sigma range of 109 to 125  years overlaps with but is limited to the lower half of the sparc range .
; also chapter 5 from sparc ] averaged the results from six chemistryclimate models to estimate a steady state lifetime of 115  years with a model variance of 8% . to correct this to current observations ( the transient as recorded in mls data ) would add about 0.5  years , and thus , this result is essentially identical to the semiempirical mls lifetime derived here .
what is unusual is that the models in this study ( ccm and ctms ) calculate much longer lifetimes , 120 to 146  years , almost outside the range of the sparc models , 105 to 127  years .
geosccm participated in both studies ( 120  years in this study versus 117  years in sparc ) as did g2d ( 130  years versus 125  years ) .
the differences are not greatly significant and may depend on the scaling of tropospheric abundance ( ppb ) to burden ( tg  n ) , but both models are at the high end of the sparc models and the low end of the models here .
geosccm used here and in sparc is closely related in terms of chemistry to gmi but has very different lifetimes , 120 versus 137  years .
the merra fields are known to have excessive subtropical mixing in the lower stratosphere , which reduces n2o in the tropics , thus reducing its flux to the tropical midstratosphere .
similarly , the ifs fields for cycle 36 appear to have more stagnant vertical transport in the midstratosphere than cycle 29 .
the n2o lifetime is a good diagnostic of the circulation and mixing below the middle stratosphere [ strahan et al . ,
how does this new lifetime change our estimates of n2o emissions , both preindustrial and presentday anthropogenic ?
the evaluation of emissions based on observed abundances and lifetime ( both pi and present ) gave pi emissions of 9.1    1.0  tg  n / yr and present anthropogenic emissions of 6.5    1.3  tg 
n / yr ( assuming that pi emissions , but not lifetime , remain constant ) [ prather et al . ,
those values were based on the thenmostrecent model study with a lifetime of 131  years [ fleming et al . , 2011 ] .
correcting to our current lifetime recommendation increases the pi natural sources to 10.5  tg 
n / yr but hardly changes the anthropogenic source , 6.6  tg  n / yr . uncertainties do not significantly change . how will the n2o lifetime change in the future ?
the sparc model 's year 2100 simulations showed a wide range of changes in lifetime from 6  years to + 6  years [ chipperfield et al . ,
if a 5% uncertainty in the future lifetime was a true bound , then the climate and ozone impacts of future n2o emissions can be evaluated with some confidence .
however , the seemingly random shifts in future lifetime need to be evaluated in terms of the key factors driving them , as was attempted for the pi lifetime in table 3 here .
were able to identify the primary factors causing the wide range of future ozone projections in ccms by separating their responses to increasing greenhouse gases from their temperature and chemistry responses to decreasing odss .
if the goal is to understand future changes in the lifetimes of gases controlled by stratospheric chemistry , then a more rigorous protocol of model studies is needed to assess separately , e.g. , the decline in ods , future stratospheric temperatures , and the role of changes in transport .
 abstractthe lifetime of nitrous oxide , the thirdmostimportant humanemitted greenhouse gas , is based to date primarily on model studies or scaling to other gases . 
 this work calculates a semiempirical lifetime based on microwave limb sounder satellite measurements of stratospheric profiles of nitrous oxide , ozone , and temperature ; laboratory crosssection data for ozone and molecular oxygen plus kinetics for o(1d ) ; the observed solar spectrum ; and a simple radiative transfer model . 
 the result is 116    9  years . 
 the observed monthlytobiennial variations in lifetime and tropical abundance are well matched by four independent chemistrytransport models driven by reanalysis meteorological fields for the period of observation ( 20052010 ) , but all these models overestimate the lifetime due to lower abundances in the critical loss region near 32  km in the tropics . 
 these models plus a chemistryclimate model agree on the nitrous oxide feedback factor on its own lifetime of 0.94    0.01 , giving n2o perturbations an effective residence time of 109  years . combining this new empirical lifetime with model estimates of residence time and preindustrial lifetime ( 123  years ) 
 adjusts our best estimates of the humannatural balance of emissions today and improves the accuracy of projected nitrous oxide increases over this century . 
Introduction
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ModelMeasurement Comparisons
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An Overview of Lifetimes, Budgets, and Uncertainties