Top-down estimate of methane emissions in California using a mesoscale inverse modeling

14 Pages·2015·2.97 MB·English

PUBLICATIONS
Journal of Geophysical Research: Atmospheres
RESEARCH ARTICLE Top-down estimate of methane emissions in California
10.1002/2014JD023002 using a mesoscale inverse modeling technique:
The South Coast Air Basin
KeyPoints:
• Amesoscaleinversionensembleis
usedtoestimateCH4emissionsin YuYanCui1,2,JeromeBrioude1,2,3,StuartA.McKeen1,2,WayneM.Angevine1,2,Si-WanKim1,2,
theLAbasin GregoryJ.Frost1,2,RavanAhmadov1,2,JeffPeischl1,2,NicolasBousserez4,ZhenLiu5,6,ThomasB.Ryerson1,
• Emissionestimatesareconsistentwith
publishedobservation-basedestimates SteveC.Wofsy7,GregoryW.Santoni7,EricA.Kort8,MarcL.Fischer9,andMichaelTrainer1
• Oilandgasindustriesexplainthe
differencesbetweenposterior 1ChemicalSciencesDivision,EarthSystemResearchLaboratory,NOAA,Boulder,Colorado,USA,2CooperativeInstitutefor
andpriorinventories ResearchinEnvironmentalSciences,UniversityofColoradoBoulder,Boulder,Colorado,USA,3Laboratoiredel’Atmosphere
etdesCyclones,UMR8105,CNRS-MeteoFrance-UniversiteLaReunion,LaReunion,France,4DepartmentofMechanical
SupportingInformation: Engineering,UniversityofColoradoBoulder,Boulder,Colorado,USA,5SandiaNationalLaboratories,Livermore,California,
• DataSetS1 USA,6NowatRambollEnvironUSCorporation,Novato,California,USA,7DepartmentofEarthandPlanetarySciences,
• FiguresS1andS2andTableS1 HarvardUniversity,Cambridge,Massachusetts,USA,8DepartmentofAtmospheric,Oceanic,andSpaceSciences,University
ofMichigan,AnnArbor,Michigan,USA,9EnvironmentalEnergyTechnologiesDivision,LawrenceBerkeleyNational
Correspondenceto: Laboratory,Berkeley,California,USA
J.Brioude,
[email protected]
Abstract Methane (CH ) is the primary component of natural gas and has a larger global warming
4
Citation: potentialthanCO2.Recenttop-downstudiesbasedonobservationsshowedCH4emissionsinCalifornia’s
Cui,Y.Y.,etal.(2015),Top-downestimate SouthCoastAirBasin(SoCAB)weregreaterthanthoseexpectedfrompopulation-apportionedbottom-up
ofmethaneemissionsinCalifornia
stateinventories.Inthisstudy,wequantifyCH emissionswithanadvancedmesoscaleinversemodeling
usingamesoscaleinversemodeling 4
technique:TheSouthCoastAirBasin, systemataresolutionof8km×8km,usingaircraftmeasurementsintheSoCABduringthe2010NexusofAir
J.Geophys.Res.Atmos.,120,6698–6711, QualityandClimateChangecampaigntoconstraintheinversion.Tosimulateatmospherictransport,weuse
doi:10.1002/2014JD023002.
theFLEXiblePARTicle-WeatherResearchandForecasting(FLEXPART-WRF)Lagrangianparticledispersion
modeldrivenbythreeconfigurationsoftheWeatherResearchandForecasting(WRF)mesoscalemodel.We
Received18DEC2014
Accepted8JUN2015 determinesurfacefluxesofCH4usingaBayesianleastsquaresmethodinafour-dimensionalinversion.
Acceptedarticleonline10JUN2015 SimulatedCH concentrationswiththeposterioremissioninventoryachievemuchbettercorrelationswith
4
Publishedonline14JUL2015 themeasurements(R2=0.7)thanusingthepriorinventory(U.S.EnvironmentalProtectionAgency’sNational
EmissionInventory2005,R2=0.5).TheemissionestimatesforCH intheposterior,46.3±9.2MgCH /h,
4 4
areconsistentwithpublishedobservation-basedestimates.ChangesinthespatialdistributionofCH
4
emissionsintheSoCABbetweenthepriorandposteriorinventoriesarediscussed.Missingorunderestimated
emissionsfromdairies,theoil/gassystem,andlandfillsintheSoCABseemtoexplainthedifferencesbetween
thepriorandposteriorinventories.Weestimatethatdairiescontributed5.9±1.7MgCH /handthetwo
4
sectorsofoilandgasindustries(productionanddownstream)andlandfillstogethercontributed39.6±8.1
MgCH /hintheSoCAB.
4
1. Introduction
Theaverageatmosphericmixingratioofthegreenhousegasmethane(CH )hasincreasedbyatleastafactor
4
of2.5sincepreindustrialtimes[Myhreetal.,2013].Atcurrentglobalconcentrations,CH isthesecondmost
4
importantgreenhousegasbehindCO foranthropogenicradiativeforcing.TheatmosphericlifetimeofCH
2 4
of~12.4yearsismuchshorterthanthatofCO ,butCH hasasignificantlyhigherglobalwarmingpotential
2 4
thanCO (~86timeshigherover20yearsand~34timeshigherover100years)[Myhreetal.,2013,Table8.7].
2
IthasbeenarguedthatreducingemissionsofCH maybeanimportantcomponentofaninitialstrategyfor
4
avoidingthemostsevereimpactsofglobalwarming[Alvarezetal.,2012;Brandtetal.,2014].
Recently, many studies [Pétron et al., 2012; Brandt et al., 2014] found discrepancies in CH inventories
4
derivedfrombottom-upmethods,basedonanaccountingofprocess-levelactivityandemissionfactors,
andtop-downapproaches,whichrelyonatmosphericobservationstoinferemissionsfromageographic
region and often from a particular type of emissions source. Differences between bottom-up and
top-downestimatessuggestthattheunderstandingofCH sourcesisincomplete,leadingtouncertainty
©2015.AmericanGeophysicalUnion. 4
AllRightsReserved. intheapplicationofregulationstomitigateCH4emissions.
CUIETAL. INVERSEESTIMATEOFMETHANEEMISSIONS 6698
Journal of Geophysical Research: Atmospheres 10.1002/2014JD023002
Recenttop-downapproacheshaveshownthatCH emissionsintheU.S.wereunderestimatedinexisting
4
surface inventories [Kort et al., 2008; Miller et al., 2013; Brandt et al., 2014], especially in the south-central
U.S. and California. Greenhouse gas emissions in California have been regulated by the state legislature,
which required that statewide greenhouse gas emissions be reduced to 1990 levels or lower by the year
2020. Recent studies have estimated CH emissions both across California [Jeong et al., 2012, 2013, 2014]
4
andwithintheSouthCoastAirBasin(SoCAB)[Wunchetal.,2009;Wennbergetal.,2012;Peischletal.,2013]
using either bottom-up inventory or top-down atmospheric approaches. The SoCAB region is particularly
interestingbecauseofthelargepopulationandknownCH sourcesfromadenselypopulatedurbanarea
4
(Los Angeles) containing a large oil and natural gas production and distribution network, large landfills,
anddairylivestockagriculture.
Bottom-upestimatesofCH emissionintheSoCABrangefrom26.2MgCH /hforNEI2005to34.3MgCH /h
4 4 4
forCaliforniaAir ResourcesBoard(CARB) 2009(availableathttp://www.arb.ca.gov/cc/inventory/data/data.
htm)and61.6MgCH /hforEmissionDatabaseforGlobalAtmosphericResearchversion4.2(EDGARv4.2)
4
(available at http://edgar.jrc.ec.europa.eu [Rogelj et al., 2014]). One top-down technique to estimate CH
4
emissionsusesobservationsofmixingratiosofcoemittedorwell-mixedspecies(COandCO )andexisting
2
inventories of those species to infer CH emissions. Wunch et al. [2009] estimated CH emissions in the
4 4
SoCABusingobservedratiosofCH mixingratiowiththoseofCOandCO2fromaground-basedFourier
4
transform spectrometer and found that CH emissions in this area were 45.6 to 68.4±11.4 Mg CH /h.
4 4
Wennberg et al. [2012] and Peischl et al. [2013] used measurements on board the NOAA P-3 aircraft from
theCaliforniaNexus,ResearchattheNexusofAirQualityandClimateChange(CalNex)campaignin2010
[Ryersonetal.,2013]toinferSoCABCH emissions,takingadvantageofP-3flightplansdesignedforgood
4
spatialcoverageoverthebasin.TheyusedobservedratiosbetweenCH andCO orCOmixingratiosand
4 2
theiremissionestimatesfromCaliforniaAirResourcesBoard(CARB)toderivetotalCH emissionsfromthe
4
SoCAB of 50.2±11.4 and 46.7±4.6 Mg CH /yr, respectively. The accuracy of this method is limited by (i)
4
theaccuracyofthesurfaceemissionestimatesofthecoemittedorwell-mixedspecies(CO andCO),and
2
(ii) differences between the spatiotemporal emission patterns of CH and the reference species. Peischl
4
etal.[2013]alsocharacterizedthesourceattributionofCH usingCH andlightalkanemeasurementsin
4 4
theSoCABandfoundthatnaturalgaspipelines,geologicseeps,andtheoilandgasindustriesaccounted
formostoftheunderestimationincurrentbottom-upCH inventories.
4
Recently,aninversionmethodwasappliedtoSoCABCH emissionsbyWechtetal.[2014],usingtheadjointof
4
the Goddard Earth Observing System-Chemical (GEOS-Chem) model at 2/3°×1/3° resolution and prior
emissionsestimatesfromtheEDGARinventory.Wechtetal.[2014]estimatedCH emissionsof35.3±9.1and
4
47.9±9.1 Mg CH /h using either GOSAT satellite or aircraft observations during the CalNex campaign,
4
respectively.WhiletheWechtetal.[2014]CH emissionestimatesagreewiththoseofWennbergetal.[2012]
4
andPeischletal.[2013],largeuncertaintiesmayarisefromthecoarseresolutionoftheGEOS-Chemmodel.
The SoCAB region is associated with atmospheric mesoscale transport, such as land-sea breezes, and
complex terrain, leading to impacts on the planetary boundary layer (PBL) and upslope transport, which
influence pollution transport [Angevine et al., 2013]. Hence, an inverse model at mesoscale should enable
moreconfidentestimatesofthestrengthandspatialdistributionsofCH emissionsintheSoCABregion.
4
Totacklethisproblem,weusetheoff-lineLagrangianparticledispersionmodelFLEXiblePARTicle-Weather
Research and Forecasting (FLEXPART-WRF) coupled to three different Weather Research and Forecasting
(WRF) model configurations to estimate source-receptor relationships and apply an inverse model at
mesoscale. The mesoscale inverse system uses a Bayesian least squares method assuming lognormal
distributionsfortheobservationsandthesurfacefluxes.Inversemodelsminimizethemismatchbetween
measured and simulated observations of CH concentrations by modifying surface flux densities from
4
individualgrid cells. The U.S. Environmental Protection Agency’s (EPA’s) NationalEmission Inventory (NEI)
2005isusedasapriorestimateoftheCH surfaceflux.MajorsourcesofCH inNEI2005includelandfills
4 4
andlivestockbutdonotincludeoilandgasemissions.Thisinversesystemhasbeenusedsuccessfullyto
estimateCO,NO ,andCO intheSoCAB[Brioudeetal.,2013a].Hereweusethesameinversionmethodto
y 2
optimizesurfaceemissionfluxesofCH withobservationsfromsixP-3flightsinMayandJune2010during
4
the CalNex intensive field campaign. Section 2 presents the details of the methods used. The results are
presentedanddiscussedinsection3,followedbytheconclusionsofthiswork.
CUIETAL. INVERSEESTIMATEOFMETHANEEMISSIONS 6699
Journal of Geophysical Research: Atmospheres 10.1002/2014JD023002
2. Methods
2.1. Observations
The NOAA P-3 aircraft measured
CH mixing ratios over the SoCAB
4
duringCalNex2010[Ryersonetal.,
2013]. In our inverse modeling
analysis of the CalNex campaign,
we use six flights (4 May, 8 May,
14 May, 16 May, 19 May, and 20
June)toestimateCH emissionsin
4
theSoCAB(Figure1).Theseflights
were dedicated to characterizing
daytime emissions and chemistry
in the area, focusing on late
morning and afternoon periods
Figure 1.The prior inventory of CH4 emissions from the U.S. EPA NEI 2005 after a well-mixed boundary layer
(unit:μgs(cid:1)1m(cid:1)2)averagedat8km×8kmspatialresolution.Coloredlinesare wasestablished.Verticalmixingat
flighttracksofsixaircraftflights.TheblacklinedenotestheSoCABdomain.
night is very uncertain in models
andmeasurements,andtherefore,
nighttimedataarenotusedinthisstudy.Moreover,onlyobservationsintheboundarylayerareusedinthe
inversion, and we exclude the overwater segmentations of the 16 May flight because the models did not
handle the boundary layer over the water properly [Angevine et al., 2012]. No precipitation events were
associatedwiththesesixflights.
On the research aircraft, CH was measured once per second using wavelength-scanned cavity ring-down
4
spectroscopy (WS-CRDS) by a Picarro 1301m instrument [Peischl et al., 2012, 2013]. The detailed information
aboutWS_CRDScalibrationsisdescribedinsection2.1ofPeischletal.,2012.Theyestimatedatotalinaccuracyof
CH measurementsof±1.2ppbvandreporteda1sprecisionof±1.4ppbvduringsmoothflightand±2.0ppbv
4
during turbulent flight. For 8 May, we use quantum cascade laser direct absorption spectroscopy (QCLS)
measurements[Kortetal.,2011],withanuncertaintyof±1ppbv,asthePicarroinstrumentwasnotoperatingon
thisflight.Themediandifferencebetween1saveragedQCLSandWS-CRDSwas4.5(±5.1)ppbshowninFigure
13ofSantonietal.[2014],whichcorrespondtoanerrorof0.25%formeasuredCH using1800ppbbackground.
4
Theaverageflightspeedwas100m/s,andweuse30saveragedvalues,equivalenttoahorizontalresolution
of ~3km. The P-3 measurements in the SoCAB were collected close to the surface sources, and hence,
chemical loss and soil sinks of CH can be neglected. The uncertainty on simulated concentrations
4
introduced by assuming CH to behave as a passive tracer is lower than other sources of uncertainty
4
pertainingtothesimulationofatmospherictransport,suchasthoserelatedtotheerrorsinmodeledwind
field, PBL height, linear interpolations of the data, and turbulent mixing, estimated to be 20 to 30% in
Angevineetal.[2014].Therefore,wetreatCH asapassivetracerthroughoutthepaper,regardlessofthe
4
positionofthemeasurementsrelativetothesources.
2.2. ThePriorEmissionInventory
The4km×4kmEPANEI2005v4[U.S.EnvironmentalProtectionAgency(EPA),2015]isusedtoprovidethe
prior emission inventory in the inverse system. CH surface emissions from mobile on-road and off-road
4
sources, nonpoint area sources, and point sources (negligibly small) are processed following EPA
recommendations in the EPA SPECIATE 4.1 database [Simon et al., 2010]. The 4km×4km NEI data are
averagedontothe8km×8kmspatialresolutiongrid(Figure1)usedfortheinversemodelingtorelatively
reducetheuncertaintywithalossofresolution.Wedonotincludewetlandandfireemissionsbecausewe
considerthemtobenegligiblecontributorsoverthetimeperiodofourstudy.Emissionsfromoilandgas
industriesareverysmallintheNEI2005.
ItisexpectedthatthelimitationsoftheNEI2005inventory(underestimationofemissionsfromoilandgas
industries and spatial distribution of sectors) will be compensated by the inversion method. Changes in
spatialdistributionintheposteriorarediscussedinsection3.2.
CUIETAL. INVERSEESTIMATEOFMETHANEEMISSIONS 6700
Journal of Geophysical Research: Atmospheres 10.1002/2014JD023002
Dairies Landfills µg m-2 s-1
35 35 1
34 34
33 33
-120 -118 -116 -120 -118 -116
OG Production OG Downstream 0.5
35 35
34 34
33 33
-120 -118 -116 -120 -118 -116 0
Figure2.Methaneemissions(unit:μgm(cid:1)2s(cid:1)1)intheSoCABarea(redbox)fromfoursectorsat8km×8kmspatial
resolution:dairy,landfill,oil/gasproduction,andoil/gasdownstream(storage,transmission,anddistributions),withunit
μgm(cid:1)2s(cid:1)1.
2.3. SpatialDistributionsofDairy,Landfills,andtheOil/GasIndustries
Dairy farms, landfills, and the oil and gas industries (production and distribution system) are known to be
important sources in the SoCAB area [e.g., Peischl et al., 2013]. Figure 2 shows their spatial distributions at
8km×8kmresolution.DairiesandlandfillsaremappedusingthesamedataasthoseshowninFigure1cof
Peischl et al. [2013]. The oil/gas production and downstream (including storage, transmission, and
distribution)sectorsaremappedusingahybridinventoryfromLiuetal.(Mappingmethaneemissionsfrom
oil and natural gas systems in the contiguous United States, submitted to Environmental Science and
Technology, 2015). Specifically, the spatially resolved emissions from oil and gas production are generated
based on the 12km gridded inventory of nonmethane hydrocarbons (NMHCs) for nonpoint oil and gas
production sources from NEI-2011 and state-specific CH -to-NMHCs emissions ratios from Eastern Research
4
Group,Inc.[2013].Downstreamoilandgasemissionsfromprocessing,storage,transmission,anddistribution
were from a spatial allocation of the national total emission from the EPA Greenhouse Gas Inventory [EPA,
2014] based on geospatial data of natural gas processing facilities, interstate and intrastate pipelines,
compressorstations,andpopulationdensity.ThespatialdistributionofthosesectorsinFigure2willbeused
to test independently the spatial distribution in the posterior and discuss CH emissions per sectors. More
4
discussionaboutthesesectorsisfoundinsection3.2.2.
2.4. Modeling
2.4.1. TrajectoryandMeteorology
Athree-dimensionalLagrangiandispersionmodel(FLEXPART)[Stohletal.,2005]wasusedtosimulatehourly
back trajectories along the flight tracks. High-resolution meteorological simulations were performed using
the Weather Research and Forecasting (WRF) model [Skamarock et al., 2005] to drive FLEXPART [Brioude
etal.,2013b].Inthisstudy,FLEXPART-WRFversion3.1servedasourmesoscaleatmospherictransportmodel
to simulate contributions to airborne CH4 mixing ratios from surface CH4 fluxes, which has been used to
constrainspeciessuchasCO,NO ,andCO2inairbornemeasurement-basedinversions[Brioudeetal.,2013a].
x
Following Brioude et al. [2013a], we also consider three transport models. Uncertainties introduced by the
transport models are, in part, taken into account in the inversion method and estimated in our results.
ThethreetransportmodelsweredesignedusingthreedifferentWRFmeteorologyconfigurations(Table1).
The first WRF configuration [Angevine et al., 2012, 2013] (hereafter referred to as “WRF1”) and the second
WRF-Chem3.1configuration[Kimetal.,2011;Leeetal.,2011](hereaftercalled“WRF2”)havebeenpreviously
evaluated and showed reasonable performance for scientific studies in the SoCAB [Angevine et al., 2013].
WRF1 and WRF2 were used in Brioude et al. [2013a]. The third WRF configuration (“WRF3”) is based on
WRF-Chemversion3.4,withanestedhorizontalgridat4kmoverCaliforniaand60verticallevels.Global
Forecast System/National Centers for Environmental Prediction (GFS/NCEP) data are used for the initial
and boundary conditions to the WRF3 model. The Noah land surface model with the U.S. Geological
CUIETAL. INVERSEESTIMATEOFMETHANEEMISSIONS 6701
Journal of Geophysical Research: Atmospheres 10.1002/2014JD023002
Table1. NamesandConfigurationsoftheThreeWRFRunsUsedinThisStudy
Name Version Initialization PBLScheme GridSpacing(km) VerticalLevels LSM,Data WindField
WRF1a WRF3.3 ERA-Interim MYJ 4 60 Noah,UCM,MODIS Time-averagedwinds
WRF2a WRF-Chem3.1 ERA-Interim YSU 4 60 Noah,UCM,USGS Sigmadotðσ˙ÞWinds
WRF3b WRF-Chem3.4 NCEP-GFS YSU 4 60 Noah,USGS Time-averagedwinds
aThetwoconfigurationswereusedinBrioudeetal.[2013a].
bThedetaileddescriptionofWRF3.4parameterizationscanbefoundinhttp://www.mmm.ucar.edu/wrf/users/docs/userguideV3/contents.html.
Survey(USGS)landcover-landuseandtheYonseiUniversity(YSU)boundarylayerschemeareused.WRF2
onlyprovidesthesigmadot(thederivativeofWRFverticalcoordinatewithrespecttotime)instantaneous
windfieldwhiletheothertwoprovidetime-averagedwindfields.Weestimatecorrelationsbetweenthe
threeWRFconfigurationsandobservations(TableS1in thesupportinginformation)oftheentireCH time
4
series for the six flights analyzed during CalNex. The correlation coefficients between the three FLEXPART-
WRFCH timeseriesarenotmuchlargerthanthecorrelationcoefficientsbetweenthemeasuredCH time
4 4
seriesandsimulatedtimeseriesofeachFLEXPART-WRFmodel.Therefore,eachmodelcanbeconsideredas
independentoftheothersinthesensethatthereisnocorrelationbias.
TheHannascheme[Stohletal.,2005]isusedinFLEXPART-WRFtoprescribeaturbulentprofileincludingboth
horizontalandverticalturbulencesinthePBL.Time-averagedwindsgeneratedbytheWRFmodelareused
instead of instantaneous wind to reduce uncertainties in the Lagrangian trajectories in complex terrain
[Brioude et al., 2012]. PBL height, surface sensible heat flux, and friction velocity were taken directly from
the WRF simulation. A total of 10,000 computational particles are released either every 30s along the
aircraft flight tracks or every 100m during vertical profiles. No convection, chemical transformation, and
deposition were simulated. FLEXPART simulates the trajectories over 24h to focus on the local transport
within the study area (i.e., the SoCAB). The trajectories are also limited to 24h for computational
feasibilities. Hence, the influence of previous-day transport and emissions is ignored, which will increase
theuncertaintyinthefluxestimates.Brioudeetal.[2013a]estimatedthatrestrictingthetrajectoriesto24h
addedanuncertaintyof~7%tothesurfaceemissionestimates.
The FLEXPART-WRF output has a horizontal resolution of 8km×8km, with 1h output time interval. The
output, also referred to footprint (in sm3kg(cid:1)1), consists of a residence time within a surface layer (in
meter) weighted by the atmospheric density, which represents the sensitivity of the airborne
measurements to surface emissions. When combined with a surface emission inventory (in kgm(cid:1)2s(cid:1)1),
one can calculate a mixing ratio for each set of trajectories along the aircraft flight track. In this way,
FLEXPART-WRF linearizes the transport processes between the surface and the aircraft. This approach
alleviates the need for an adjoint model of WRF-Chem (not currently available) in the application of the
inversiontechnique[Brioudeetal.,2013a;deFoyetal.,2015].
2.4.2. InverseModeling
WeapplytheinversemodelingapproachdescribedinBrioudeetal.[2011,2013a]totheCH datacollectedin
4
the SoCAB during CalNex. The observations used in the inverse modeling are the CH mixing ratio
4
enhancements above background. We define the background CH for each flight as the lowest mixing
4
ratiofoundintheatmosphericboundarylayerbelow2kmupwindoftheSoCAB,whichisalsoclosetothe
valueofthemodeinthedistributionofallmixingratiosmeasuredbelow2kmduringthecampaign.The
enhancementsinCH are~10%ofbackgroundconcentrationsonaverage.Thebackgroundconcentration
4
estimates were associated with an uncertainty of 10ppb due to the variability in the low concentrations
found in the PBL for each flight. This uncertainty was added to the measurement uncertainties in the
inversion. Negative deviations from the background are removed from the observation data set and a
smallvalueof10^-5ppbwasusedinstead.
To calculate the best estimates of CH surface flux emissions, we use an iterative method to minimize a
4
lognormalBayesianleastsquarescostfunctionwithsolutionsinamedianofthedistribution,similartothe
oneusedinBrioudeetal.[2011]:
1 1
J¼ ðlnðy Þ(cid:1)lnðHxÞÞTR(cid:1)1ðlnðy Þ(cid:1)lnðHxÞÞþ αðlnðxÞ(cid:1)lnðx ÞÞTB(cid:1)1ðlnðxÞ(cid:1)lnðx ÞÞ (1)
2 0 0 2 b b
CUIETAL. INVERSEESTIMATEOFMETHANEEMISSIONS 6702
Journal of Geophysical Research: Atmospheres 10.1002/2014JD023002
wherey istheobservationenhancementabovethebackgroundvalueowingtosurfaceemissionswiththe
0
p×1dimensionandpisthenumberofobservations.Parameterxisam×1vectoroftheposteriorsolutions
andmisthenumberofgriddedfluxesinspaceandtime.HaretheFLEXPART-WRFoutputs,whichconstructa
linear linkagebetween surfaceemissions andmixing ratios atgiven receptors, and thedimensionofH is
p×m.Parameterx isam×1vectorofpriorfluxes,andR(dimension:p×p)andB(dimension:m×m)are
b
errorcovariancematricesofobservationsandpriorfluxesinthelognormaldistributionspace.Parameterα
as a regularization parameter that comes from the L-shape criterion [Henze et al., 2009], which is used to
balance theerrors in both covariance matrices to obtain thesmallest sensitivity to the error in either the
observationsortheprior.
Theadvantageofusingalognormaltransformationinthecostfunctionisthatnonegativefluxesarefoundinthe
posteriorsothatweobtainaminimumvariancesolution(equivalenttothemeanofthedistribution)andnota
likelihood,andthelognormaldistributionfollowsmorecloselytheobservedCH mixingratios(aftersubtracting
4
thebackgroundvalue).Thisapproachavoidsthedrawbacksofothertechniquesusedtopreventnegativefluxes,
suchasmodifyingcovariancematricesorboundedinversemethods[e.g.,Stohletal.,2009;Milleretal.,2014].
The observation errors, which include uncertainties from the measurements and from the background
definitionforeachflight,typically,areassumedtobeuncorrelated.Likewise,weassumethaterrorsinthe
priorsurfaceinventoryareuncorrelated.Hence, theerrorcovariancematrices oftheobservations (R)and
prior(B)aremodeledasdiagonalmatrices.
We use four time intervals to construct a four-dimensional (three spatial dimensions plus time) inversion
following Brioude et al. [2013a]: (i) morning rush hours between 13:00 UTC and 16:00 UTC (06:00–09:00
localtime),(ii)middayhoursbetween17:00UTCand21:00UTC(10:00–14:00localtime),(iii)eveningrush
hours between 22:00 UTC and 01:00 UTC (15:00–18:00 local time), and (iv) nighttime hours between
02:00 UTC and 12:00 UTC (19:00–5:00 local time). The four time intervals are applied to both trajectories
andprioremissions.Thevaluesreportedinsection3aretheaveragesforthetwotimeintervalsbetween
17:00UTCand01:00UTC(10:00–18:00localtime)whenwehavethestrongestconfidenceinthetransport
modelsandthereforeintheinversion.
Over the SoCAB domain, the Jacobian matrix H, representing the transport model in the inversion, has a
dimensionof 768 to 1109 rows (the total numberof 30s averaged observations in each individualflight)
by 23280 columns (the total number of surface grid cells with four time intervals). To reduce the
dimensionof thematrix in order to obtain inversion solutions efficiently and to reduce cross correlations
between surface fluxes in the posterior, we cluster surface grid cells in the domain using an optimality
criterionbasedontheFisherinformationmatrix,whichisdifferentthanBrioudeetal.[2013a]thatlimited
theinversionongridcellswithsignificantemissionintheprior.HereweuseasimilarcriterionasBocquet
etal.[2011]toconstructadaptivegridsinthecontrolspace:
(cid:1) (cid:3)
J ¼Tr BWTR(cid:1)1W (2)
whereJ isthecriterionandWisthederivativeoftheJacobianmatrixHassumingalognormaldistribution.
Weclassifythesurfacegridcellsintoclustersaccordingtotheneighbormethod:namely,neighboringgrid
cellshavingsimilarvaluesareaggregatedasacluster.Inaddition,gridcellswithhighvalues(e.g.,equalto
andabove(cid:1)5)ofJ arenotaggregated.Afterapplyingthiscriterion,thedomaininFigure3,showingthe
controlspaceoftheinversion,uses1201clustersforeachtimeinterval,reducingthetotalgridcellsinthe
inversionbyafactorof~5(from23,280)whilemitigatinginformationlossonsurfacefluxes.
Foreachflightandtransportmodel,weused100iterationsoftheinversionswitharandomterm(equivalent
toastandarddeviationof5%ofalognormaldistributionofpriorfluxestimates)tominimizecrosscorrelation
inthepriorandhenceintheposterior.Theuncertaintyintheposterioremissionestimatefromtheensemble
ofsingle-flight-basedinversionsisthenestimatedbyusingtheposteriorcovariancematrixtoestimatethe
posterioruncertaintyforeachrealizationandasthestandarddeviationofthedistributionrepresentedby
the1800realizationsfromtheensembleofsixflightsandthreetransportmodels.
TheuncertaintyfromtheFLEXPARTLagrangianmodelcannotbeassessedfullywiththisapproach,butwe
assume that this uncertainty is small compared to the uncertainties in the meteorological fields [Hegarty
etal.,2013].Angevineetal.[2014]evaluatedtheuncertaintyinatmospherictransporttobe20to40%ina
CUIETAL. INVERSEESTIMATEOFMETHANEEMISSIONS 6703
Journal of Geophysical Research: Atmospheres 10.1002/2014JD023002
36 5
FLEXPART-WRF ensemble of six WRF
configurations due to uncertainties in
0
35 meteorological fields. It is still unclear
5 how this uncertainty propagates in the
inversion system. However, our ensemble
34 10 of only three WRF configurations might
underestimate the uncertainty introduced
15
by the FLEXPART-WRF simulated transport
33
20 intheposteriorestimates.
32 25
121 120 119 118 117 116 115
3. Results andDiscussion
Figure3.Amap(logscale)oftheFisherinformationmatrixcriterion 3.1. Posterior-PriorDifferencesin
intheSoCABbasedontheWRF1transportmodelataspatialresolution
EmissionStrengths
of8km×8km.Seethetextinsection2.4.2forthedetails.Gridcellsare
3.1.1. TotalEmissionsofCH
aggregatedintoclusterswhenvaluesofthecriterioninadjacentcells 4
arebelow(cid:1)5.Cellswithvaluesequaltoandabove(cid:1)5arenotaggre- Back-trajectory footprints of the six flights
gated.Afteraggregating,theoriginal5820gridcellsareaggregated fromthethreetransportmodelsareshown
into1201,1199,and1200clustersfortheWRF1,WRF2,andWRF3 in Figure 4. The footprints provide a sense
transportmodels,respectively.
of theabilityof theaircraft observations to
constrainsurfacesourcesacrosstheSoCAB.
The spatial distributions of footprints have similar patterns and emphasize the impact of northerly and
northwesterly background airflow on the SoCAB domain. The six flights sampled predominantly
downwindofthesurfaceemissionsintheSoCABarea.
ThetotalposterioremissionsfortheSoCABdomainarecalculatedforeachflightandforeachtransportmodel
overtheSoCABarea(Table2andFigureS1inthesupportinginformation).Accordingtoarecentreport[United
StatesEnergyInformationAdministration,2015],theseasonalityofnaturalgasconsumptioninCaliforniahadan
amplitudeof15%in2010.Asseasonalvariationinnaturalgasdistributionleakissmall[McKainetal.,2015],one
canassumeaseasonalityof15%fromNGleaksinLosAngeles.Peischletal.[2013]foundthat47%oftotalCH
4
emissioninSoCABwasduetoNGleaks.AstheseasonalityfromLandfillsandDairiesintheLosAngelesbasin
shouldbesmall,onecanexpectaseasonalityof~10%intheCH4emission.
Diurnalanddaytodayvariationsinmethaneemissionhavebeenobservedfromfeedlots[Gaoetal.,2011]
and landfills. One can expect smaller emission variation from oil and gas facilities as their industrial
activities have no particular diurnal variation. Finally, mobile sources, which have a strong diurnal
profile, contribute only 1% of the total methane emission and should have a small impact. The six
flights used in this study are not enough to fully cover the diurnal and day to day emission variations
from landfills and feedlots, sources that contribute 44% to the total methane emissions in Los Angeles
(LA) basin [Peischl et al., 2013]. Hence, our posterior emission uncertainty estimates should be
considered as a lower limit.
WRF1 WRF2 WRF3 log (s m3/kg)
10
35 35 35
1
34 34 34 0
-1
33 33 33
-120 -118 -116 -120 -118 -116 -120 -118 -116
Figure4.Averaged1daybackwardtrajectoryfootprintswithlogscaleforthesixaircraftflights,basedoneachofthethree
WRFconfigurations,respectively.TheyellowlineshowstheSoCABdomain.Footprintsrelatedtotheoverwatersegments
ofthe16Mayflightareexcludedhere.
CUIETAL. INVERSEESTIMATEOFMETHANEEMISSIONS 6704
Journal of Geophysical Research: Atmospheres 10.1002/2014JD023002
Table2. TotalEmissionsofCH4(Mg/h)OverSoCABDerivedFromEachoftheP-3FlightsWiththeEnsembleofThreeDifferentTransportModelsandanAveraged
EstimateofCH4EmissionsBasedonSixFlightsandThreeTransportModels
Fight 4May 8May 14May 16May 19May 20June Mean
Totalemissions(MgCH4/h) 46.6±10.6 46.9±5.5 47.9±10.1 47.8±6.4 48.6±11.2 39.9±7.1 46.3±9.2
Theposteriorvaluesforthethreetransportmodelsrangefrom45.1to48.2MgCH /h.Themeanvaluesover
4
thesixflightsforeachtransportmodelarealsoshowninFigureS1.Thethreetransportmodels’posterior
estimates have a mean value 46.3 Mg CH /h with uncertainties of 21%, 19%, and 19%, respectively.
4
Combining the three transport models, we estimate an optimized value of 46.3±9.2 Mg CH /h for the
4
SoCAB area (Figure 5 and Table 2). The uncertainty here includes the posteriors’ uncertainty and the
transportmodels’uncertainty.
Ourestimateishigherbyfactorof~1.8thanNEI2005(26.2MgCH /h).Ourestimateisinagreementwith
4
previous estimates derived from observations taken over the same time period (Figure 5; 50.2±11.4 Mg
CH /h[Wennbergetal.,2012],46.7±4.6MgCH /h[Peischletal.,2013],31.9–44.5MgCH /h(Santonietal.,
4 4 4
California’s methane budget derived from CalNex P-3 Aircraft Observations and a Lagrangian transport
model,submittedtoJournalofGeophysicalResearch,2014),and47.9±9.1MgCH /h[Wechtetal.,2014]).
4
Theprecisionandtheaccuracyofthesurfacefluxestimatesbasedonasingleflightcanalsobeevaluated.
Thetotalposterioremissionestimatesvaryby~6%betweenthesixflightsshowninTable2.However,as
mentioned above, the variation in posterior emission across the meteorological models is closer to
20% [Angevine et al., 2014]. Hence, a given day surface emission estimates in the SoCAB can likely
be estimated to within ~20% from a single flight’s data and a single meteorological model for this
summerperiod.
3.1.2. TimeSeriesofCH MixingRatio
4
Figure 6 presents the comparisons between observed and simulated time series of CH mixing ratio
4
enhancements over background using the prior and posterior estimates for each flight. The simulated
time series using the posterior estimates optimized by the inversion shows better agreement with
observations than the simulated time series using the NEI 2005 prior inventory. We calculate the mean
bias between observations with the simulations using prior estimates and those using the posterior
inventory resulting from the inversion. Mean biases with the posterior estimates distinctly decrease in
thesestudiesby50%to85%comparedwithpriorestimates.Weexcludetheoverwatersegmentsofthe
16 May flight because models did not handle the boundary layer over the water properly [Angevine
et al., 2012]. The correlations and the correlation coefficients, R2, between the observations and the
simulated time series are shown in Figure 7 for each flight and each transport model. The slope of
the correlations is closer to 1, and R2 is higher using the posterior estimates compared with the prior
estimatesforallflights.
3.2. SpatialDistributionof
Posterior-PriorDifferences
3.2.1. CH andCORatios
4
We use the inversion system and
the same six flights as for CH to
4
calculate the posterior inventory
of CO for the SoCAB using the
updated FLEXPART-WRF version.
Ourresults(~65kg/sintheSoCAB)
are consistent with the CO emis-
sions estimates in Brioude et al.
[2013a] (68kg/s). This negligible
Figure5.PreviousestimatesoftotalemissionsofCH4intheSoCABduringthe difference comes from the fact
CalNexcampaign(blue)comparedwiththeestimatesfromthisstudy.The
that(i)weclusteredgridcellsthat
Tehrreorpbriaorrse(s1tismigamteao)fptroetsaelnetmthisesiuonncseorftaCiHnt4ieinsothfeCSHo4CaAnBnfuraolmemNEisIs2io0n05esistismhaotwesn. havesmallinfluenceontheinver-
aswell(orange). sion, and hence, all the grid cells
CUIETAL. INVERSEESTIMATEOFMETHANEEMISSIONS 6705
Journal of Geophysical Research: Atmospheres 10.1002/2014JD023002
Figure6.ThecomparisonofobservationsandmodelsforthetimeseriesoftheCH4mixingratioforNOAAP-3flightson4,
8,14,16,and19Mayand20June2010.Theplotincludestheobservations(blackline),estimatesfromFLEXPARTbased
onthepriorinventory(blueline),andinversionestimatesbasedontheposteriorinventory(redline).Theshadedareas
indicate1σvariabilityforthethreeWRFconfigurations.Meanbiaseswerecalculatedbetweenobservationsandsimulations
usingthepriorinventory(bluetext)andbetweentheobservationsandsimulationsusingtheposterior(redtext).For
16Mayflight,weexcludetheflightoverwatersegmentsbecausethemodelsdidnothandletheboundarylayerover
thewaterproperly.
Figure7.CorrelationsofthesimulatedandobservedabovebackgroundCH4mixingratioforeachflightusingthethreetransportmodels.Thelinesindicatetheleast
squaresfitstothecorrelationsbetweenobservationsandsimulationswitheithertheposteriorinventory(red)orpriorinventory(blue).Allcorrelationsinthecolumn
aresignificantwithP<0.05.
CUIETAL. INVERSEESTIMATEOFMETHANEEMISSIONS 6706
Journal of Geophysical Research: Atmospheres 10.1002/2014JD023002
Figure8.ScatterplotofCH4versusCOmixingratiosformeasurements(black)andsimulations,usingprior(blue)andposterior
(red)emissionsfortheflightson4,8,14,16,and19Mayand20June.Simulationsincluderesultsfromalldatainthree
WRFconfigurations.TheblackdotsrepresentobservationsofCH4andCOmixingratios,thebluedotsshowestimatesfrom
FLEXPART-WRFbasedontheNEI2005priorinventoriesofCOandCH4,andthereddotsshowFLEXPART-WRFdatabased
ontheposteriorsfromtheinversioninthisstudy.Thesolidlinesrepresenttheleastsquaresfittoeachsetofdata,andthedash
linesrepresent1standarddeviationdifferencesintheslopeofthefits.
withinthedomainareused,whileBrioudeetal.[2013a]limitedtheinversionongridcellswithsignificant
emissionintheprior,(ii)FLEXPART-WRFversionhaschangedwithnotablyabugfixonthesensibleheat
flux.TheratiobetweenCH4andCO,equivalenttotheslopeofthecorrelationbetweentheatmospheric
mixing ratios of thesespecies, is used to evaluatechanges in the spatialdistributions ofCH4 relativeto
those of CO between the prior and posterior. Figure 8 presents CH4 and CO correlations and their least
CUIETAL. INVERSEESTIMATEOFMETHANEEMISSIONS 6707