Empirical STORM-E model: I. Theoretical and observational basis

21 Pages·2013·1.18 MB·English

by  Christopher J. Mertens

https://ntrs.nasa.gov/search.jsp?R=20140002434 2018-11-29T10:27:56+00:00Z
Availableonlineat www.sciencedirect.com
AdvancesinSpaceResearch51(2013)554–574
www.elsevier.com/locate/asr
Empirical STORM-E model: I. Theoretical and observational basis
Christopher J. Mertensa,⇑, Xiaojing Xub,1, Dieter Bilitzac,2, Martin G. Mlynczakd,3,
James M. Russell IIIe,4
aNASALangleyResearchCenter,ScienceDirectorate,MailStop401B,Hampton,VA23681-2199,USA
bScienceSystems&ApplicationsInc.,OneEnterpriseParkway,Suite200,Hampton,VA2366,USA
cSchoolofPhysics,Astronomy,andComputationalSciences,GeorgeMasonUniversity,4400UniversityDrive,MS3F3,Fairfax,VA22030-4444,USA
dNASALangleyResearchCenter,ScienceDirectorate,MailStop457,Hampton,VA23681-2199,USA
eCenterforAtmosphericSciences,HamptonUniversity,Hampton,VA23688,USA
Availableonline19September2012
Abstract
AuroralnighttimeinfraredemissionobservedbytheSoundingoftheAtmosphereusingBroadbandEmissionRadiometry(SABER)
instrument onboard the Thermosphere–Ionosphere–Mesosphere Energetics and Dynamics (TIMED) satellite is used to develop an
empirical model of geomagnetic storm enhancements to E-region peak electron densities. The empirical model is called STORM-E
andwillbeincorporatedintothe2012releaseoftheInternationalReferenceIonosphere(IRI).TheproxyforcharacterizingtheE-region
responsetogeomagneticforcingisNO+(v)volumeemissionrates(VER)derivedfromtheTIMED/SABER4.3lmchannellimbradi-
ancemeasurements.Thestorm-timeresponseoftheNO+(v)4.3lmVERissensitivetoauroralparticleprecipitation.Astatisticaldata-
baseofstorm-timetoclimatologicalquiet-timeratiosofSABER-observedNO+(v)4.3lmVERarefittowidelyavailablegeomagnetic
indicesusingthetheoreticalframeworkoflinearimpulse-responsetheory.TheSTORM-Emodelprovidesadynamicstorm-timecorrec-
tionfactortoadjustaknownquiescentE-regionelectrondensitypeakconcentrationforgeomagneticenhancementsduetoauroralpar-
ticleprecipitation.PartIIofthisseriesdescribestheexplicitdevelopmentoftheempiricalstorm-timecorrectionfactorforE-regionpeak
electron densities, and shows comparisons of E-region electron densities between STORM-E predictions and incoherent scatter radar
measurements.Inthispaper,PartIoftheseries,theefficacyofusingSABER-derivedNO+(v)VERasaproxyfortheE-regionresponse
tosolar-geomagneticdisturbancesispresented.Furthermore,adetaileddescriptionofthealgorithmsandmethodologiesusedtoderive
NO+(v)VERfromSABER4.3lmlimbemissionmeasurementsisgiven.Finally,anassessmentofkeyuncertaintiesinretrievingNO+(v)
VER ispresented.
PublishedbyElsevier Ltd.on behalfofCOSPAR.
Keywords: Auroralparticleprecipitation;Ionosphere;E-region;Magneticstorm;Infraredremotesensing;SABER
1. Introduction
STORM-Eisanempiricalmodelforadjustingaknown
quiescentionosphericE-regionelectrondensityforgeomag-
neticactivity(Mertensetal.,2007a,b,2009b).TheSTORM-
⇑ Correspondingauthor.Tel.:[phone];fax:[phone]. EmodelprimarilyaccountsforenhancementintheE-region
E-mail addresses: [email protected] (C.J. Mertens), peakelectrondensityduetoparticleprecipitationandisbest
[email protected](X.Xu),[email protected](D.Bilitza),Martin.G.
suitedforapplicationintheauroralovalregion.Theproxy
[email protected] (M.G. Mlynczak), [email protected]
used to derive an empirical storm-time correction to
(J.M.RussellIII).
1 Tel.:[phone];fax:[phone]. E-regionelectrondensitiesisNO+(v)volumeemissionrates
2 Tel.:[phone];fax:[phone]. (VER), which are derived from 4.3lm limb radiation
3 Tel.:[phone];fax:[phone]. measurements observed from the Sounding of the
4 Tel.:[phone];fax:[phone].
0273-1177/$36.00PublishedbyElsevierLtd.onbehalfofCOSPAR.
http://dx.doi.org/10.1016/j.asr.2012.09.009
C.J.Mertensetal./AdvancesinSpaceResearch51(2013)554–574 555
Atmosphere using Broadband Emission Radiometry thatNO+(v)4.3lmemissioncanprovideanexcellentproxy
(SABER) instrument onboard the Thermosphere– forcharacterizingtheresponseoftheE-regionelectronden-
Ionosphere–Mesosphere Energetics and Dynamics sity to solar-geomagnetic disturbances. This conjecture is
(TIMED) satellite (Russell et al., 1999). SABER-derived foundational to the development of STORM-E, and its
NO+(v) VER is the fundamental observation-based quan- validity is addressed throughout this two-part series of
tity used in STORM-E. The theoretical formulation used papers.
to develop the empirical STORM-E model, given the The remainder of the paper is organized as follows.
NO+(v) VER as input data, is presented in Part II of this Section2providesobservationalsupportfortheplausibility
series (Mertens et al., submitted for publication). In this ofusingNO+(v)4.3lmemissionasaproxyforcharacteriz-
paper,PartIoftheseries,thetheoreticalandnumericaltech- ingtheE-regionresponsetogeomagneticforcing.Explicitly,
niques used to retrieve NO+(v) VER from the SABER vertical profiles of NO+(v) VER are used as the E-region
4.3lmlimbemissionmeasurementsaredescribedindetail. proxy. Section 2 also presents the method of deriving
AspecificapplicationofSTORM-Eistoprovideastorm- NO+(v)VERfromSABER4.3lmlimbradiancemeasure-
time correction to the International Reference Ionosphere ments. Results from the NO+(v) VER retrieval algorithm
(IRI) E-region peak electron densities. Integration of and an uncertainty assessment are given in Section 3. The
STORM-E into IRI-2012 is currently underway. The IRI summaryandconclusionsarepresentedinSection4.
isawidelyuseddata-basedmodelforspecificationofiono-
spheric parameters and is recommended for international 2. SABER-derived E-region proxy
use by the Committee on Space Research (COSPAR) and
the International Union of Radio Science (URSI) (Bilitza Themeasurementquantityusedtodeveloptheempirical
and Reinisch, 2008). An important capability of the IRI STORM-E model is SABER-derived nighttime NO+(v)
requiredforspace-weather-relatedapplicationsistheaccu- 4.3lm VER. During the daytime, radiative emission at
rate characterization of ionospheric parameters during 4.3lm in the mesosphere, lower thermosphere and iono-
solar-geomagnetic storms. The goal of developing algo- sphere (MLTI) is dominated by CO due to solar pumping
2
rithmsforupdatingIRIparametersduringstorm-timecon- oftheCO (m ;m ;m )vibration–rotationbands(Lopez-Puer-
2 1 2 3
ditionsremainsahighpriorityoftheIRIteam.However,the tas et al., 1986a,b, 1998; Sharma and Wintersteiner, 1985;
specification of the ionospheric response to geomagnetic Nebeletal.,1994).Thus,anydaytimeauroralemissionisa
activity in IRI has been mainly focused on the F-region. comparatively small enhancement above the nominal CO
2
Thefirstattempttoincorporategeomagneticinfluencesinto contribution. During nighttime, on the other hand, MLTI
IRIwasbyFuller-Rowelletal.(2000)andAraujo-Pradereet CO 4.3lmemissionisordersofmagnitudelessthanitsday-
2
al. (2002, 2003, 2004) in the development of the STORM timevalue.Consequently,analysisofthenighttimeSABER
model. The STORM model provides a storm-time correc- 4.3lmchannelmeasurementsenablestheNO+(v)contribu-
tion to F-region electron density peak concentrations, and tion to be separated reliably from the background CO (m )
2 3
demonstrates that the underlying ionospheric F-region contribution over a broad dynamic range of geomagnetic
responsetosolar-geomagneticactivitycanbecapturedina storm conditions, a feature necessary for developing an
relatively simple empirical model. The success of the empiricalstorm-timeresponsetogeomagneticactivity(Mer-
STORM model in accounting for geomagnetic variations tensetal.,2007a,b).Therefore,thenighttimeSABER4.3lm
in F-region electron densities prompted the adoption of a limbradiancemeasurementsareusedtoderiveNO+(v)VER,
similartechniqueinthedevelopmentofSTORM-E. which provides an observation-based proxy to characterize
Themeasurementdatasourceusedinthedevelopmentof the E-region response to solar-geomagnetic disturbances.
STORM-E is SABER 4.3lm broadband limb radiance Additionalobservationalsupportfortheplausibilityofusing
measurements. SABER has obtained continuous, global NO+(v)4.3lmVERasanE-regionproxyispresentedinSec-
measurements since the launch of the TIMED satellite in tion2.1.ThemethodofderivingverticalprofilesofNO+(v)
December,2001.Observationsfromthegeomagneticstorms 4.3lm VER from SABER limb radiance measurements is
ofsolarcycle23haveshownthatnighttimeSABER4.3lm discussedinSections2.2and2.3.
limb radiance measurements can be enhanced by several
orders of magnitude above the nominal CO (m ) contribu- 2.1. Particle precipitation and auroral 4.3lm emission
2 3
tion.Analysisofthesemeasurementsrevealedthatnighttime
4.3lmradianceisdominatedbyNO+(v)vibration–rotation AuroralNO+(v)4.3lmemissionisapromptindicatorof
bandemissionduringgeomagneticallydisturbedconditions theionosphere–thermosphereresponsetoparticleprecipita-
(Mertens et al., 2009a,b, 2008, 2007a,b). During magnetic tion. This is observed by comparing outgoing ionosphere–
storms, auroral particle precipitation ionizes the neutral thermosphere NO+(v) 4.3lm radiative flux with incoming
atmosphere, producing vibrationally excited NO+ (i.e., auroralelectronenergyflux,asshowninFig.1for4daysdur-
NO+(v))throughfastexothermicion-neutralchemicalreac- inglargegeomagneticstormperiods.Theparticleandradia-
tions, which promptly emit in the 4.3lm region (Mertens tivefluxquantitiesselectedforcomparisonwerebasedona
et al., 2007a, 2008). Since NO+ is the terminal E-region spatial-temporal coincidence criteria of being within 2deg
ion,andbychargeneutrality,theabovediscoveriessuggest in magnetic latitude and within 1.5h in UT-time. The flux
556 C.J.Mertensetal./AdvancesinSpaceResearch51(2013)554–574
SABER NO+ (v) 4.3um Flux
2003-10-29 2003-11-20 2004-11-08 2005-01-18
180 180 180 180
270 90 270 90 270 90 270 90
60N 60N 60N 60N
0 30N 0 30N 0 30N 0 30N
0 2 4 6 8 10 12 14 16 18 20 22 24 x10-2ergs/cm2/s
POES Electron Flux
2003-10-29 2003-11-20 2004-11-08 2005-01-18
180 180 180 180
270 90 270 90 270 90 270 90
60N 60N 60N 60N
0 30N 0 30N 0 30N 0 30N
0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.3 3.6 ergs/cm2/s
Fig. 1. The top row is total outgoing ionosphere–thermosphere SABER-derived NO+(v) 4.3lm radiative flux. The bottom row is NOAA/POES
precipitating electron total energy flux. The flux data are averaged SABER-POES nighttime coincidence measurements during representative solar-
geomagneticstormperiodsofsolarcycle23.The60-degreemagneticlatitudecircleisidentified.Magneticlongitudesat0,90,180,and270-degreesarealso
labeled.SeeSection2.1fordetailsoncoincidencecriteriaandradiativefluxcomputations.
quantitieswerefurthersortedinto5(cid:2)18degmagneticlati- bands in this case) to the in-band volume emission rate
tude and magnetic longitude bins, respectively, for plotting measured by the SABER 4.3lm radiometer channel
purposes,andaveragedoverthenighttimedataonthedate (2290–2405cm). Using model simulations of NO+(v)
indicated in the title of each panel in Fig. 1. The bottom 4.3lm emission, as described by Mertens et al. (2007a,
row shows total precipitating electron energy flux (ergs 2008, 2009a), the unfilter factor was determined to be 3.5,
cm(cid:3)2s(cid:3)1)derivedfrommeasurementstakenbytheNational roughly independent of altitude. As mentioned previously,
Oceanic and Atmospheric Administration (NOAA) Polar the method of deriving the NO+(v) 4.3lm VER is de-
Orbiting Environment Satellites (POES). The POES low scribed in Sections 2.2 and 2.3.
energy Total Energy Detector (TED) and Medium Energy Thelimitsofintegrationin(1)aretakenasz =100km
B
Proton and Electron Detector (MEPED) instruments were andz =200km,whichcontainsmostoftheoutgoingion-
T
used to derive the total electron energy flux. The top row osphere–thermosphere radiative emission from NO+(v).
shows the SABER-derived total outgoing ionosphere– Recall from the introduction that the NO+(v) vibrational
thermosphereNO+(v)4.3lmradiativeflux.Priortocomput- states are excited by exothermic ion-neutral chemical reac-
ing averages of the SABER radiative flux data, individual tions. During geomagnetic storms, the magnitude and
profiles of NO+(v) 4.3lm radiative flux F (ergs cm(cid:3)2s(cid:3)1) shape of the atmospheric ion density profiles are governed
werecomputedbyverticallyintegratingeachSABER-derived bytheprecipitatingparticle totalenergyfluxandthechar-
NO+(v)VERV(z)(ergscm(cid:3)3s(cid:3)1),suchthat acteristic energy, respectively. Moreover, the steady-state
Z NO+(v) concentrations are a balance between production
zT
F¼ VðzÞdz: ð1Þ from exothermic ion-neutral chemistry and loss by radia-
zB tive emission and collisional quenching. The combination
of these processes yield a NO+(v) 4.3lm VER profile that
The radiative flux includes thecontributionfrom allofthe generally peaks in altitude between 105 and 110km, with
NO+(v) 4.3lm vibration–rotation bands, which requires most of the outgoing radiative emission confined to alti-
the SABER-derived NO+(v) 4.3lm VER to be multiplied tudes between 100 and 200km (Mertens et al., 2007a,
by an unfilter factor (Mlynczak et al., 2002). The unfilter 2008; Fernandez et al., 2010). This is evident from Fig. 2,
factor is defined as the ratio of the total volumetric emis- which shows representative NO+(v) 4.3lm VER during
sion rate of radiative energy (all 4.3lm vibration–rotation the Halloween 2003 storm period.
C.J.Mertensetal./AdvancesinSpaceResearch51(2013)554–574 557
Nighttime NO+(v) 4.3um Volume Emission Rate(VER), Halloween Storm 2003
Zonal-Averaged VER profile
180 180 180 180
2003-10-24 2003-10-25 2003-10-26 2003-10-27
160 160 160 160
m)
k 140 140 140 140
Alt(
120 120 120 120
100 100 100 100
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0
180 180 180 180
2003-10-28 2003-10-29 2003-10-30 2003-10-31
160 160 160 160
m)
k 140 140 140 140
Alt(
120 120 120 120
100 100 100 100
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0
180 180 180 180
2003-11-01 2003-11-02 2003-11-03 2003-11-04
160 160 160 160
m)
k 140 140 140 140
Alt(
120 120 120 120
100 100 100 100
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0
VER(ergs/cm3/s)x10-8 VER(ergs/cm3/s)x10-8 VER(ergs/cm3/s)x10-8 VER(ergs/cm3/s)x10-8
50N 60N 65N 70N 75N 80N
Fig. 2. Nighttime-averaged, zonal-mean NO+(v) 4.3lm VER profiles during the Halloween 2003 storm period. The width of the indicated magnetic
latitudebandsis±2.5deg.
From the geomagnetic storm days shown in Fig. 1, it is gradients in Fig. 3 fall within the gradient error envelope,
clearthatNO+(v)4.3lmemissionrespondstoauroraldos- asdeterminedfromthefittingalgorithm.Nodoubt,analysis
ing. The morphology of the outgoing ionosphere–thermo- ofmorestormperiodswouldreducegradienterrorenvelope.
sphere NO+(v) 4.3lm radiative flux bears a striking Fig.4combinesthedatafromallthestormperiodsshownin
resemblance to the patterns of auroral electron precipita- thepreviousplot.Bycombiningthesedata,thecorrelation
tion. There is one notable exception. The radiative flux on coefficientbetweenauroralelectronprecipitatingenergyflux
October29,2003isenhancedatmuchlowerlatitudesthan and outgoing ionosphere–thermosphere NO+(v) 4.3lm
theparticlefluxbetween90and180degmagneticlongitude. radiativefluxis0.88.
ThePOESmeasurementsshowlowlatitudeprotonfluxnear ThePOESandSABERobservationspresentedinthissec-
180deg magnetic longitude (not shown). Although proton tion strongly support the conjecture that nighttime NO+(v)
flux may contribute somewhat, cross correlation analysis 4.3lm emission is a suitable proxy for characterizing the
oftheSABERauroralradiativeemissionsstronglysupport auroralzoneE-regionresponsetosolar-geomagneticdistur-
chemical–dynamical processes as the cause of the low lati- bances. In particular, the explicit observation-based proxy
tudestorm-time enhancement intheNO+(v) 4.3lm radia- used to develop the STORM-E model is the nighttime
tive flux (Mertens et al., 2007b, 2009b; Fernandez et al., NO+(v)4.3lmVER.Thefollowingtwosubsectionsdescribe
2010).Thatis,NOistransportedouttheauroralregionto thealgorithmsandmethodologiesusedtoderivethisquantity
lowerlatitudesandtheNO+(v)4.3lmemissionisenhanced fromSABER4.3lmlimbemissionmeasurements.
by the OþþNO charge transfer reaction (Mertens et al.,
2008). 2 2.2. Removal of CO2(m3)contribution from SABER 4.3lm
Therelationshipbetweentheradiativeandparticlefluxis measurements
quantified by plotting nightly-averaged, zonal-mean
NOAA/POES total electron energy flux versus SABER- NO+(v)VERisderivedfromSABER4.3lmlimbemis-
derivedNO+(v)4.3lmradiative flux formagneticlatitude sionmeasurementsby(1)removingthebackgroundcontri-
bands that overlap the auroral oval region and for seven butions of CO2(m3) emissions from the measured 4.3lm
solar-geomagnetic storm periods. These results are shown limb radiance, and (2) performing an Abel inversion on
in Fig. 3. The correlation coefficient between the particle the subsequent residual limb radiance (i.e., measured –
and radiative flux data during each storm period varies CO2(m3) contributions) to obtain vertical profiles of
between 0.83 and 0.94. Note that both northern and NO+(v) VER. In this section, the method of obtaining
southern hemispheric storm data are shown in Fig. 3. The the residual limb radiance is described.
558 C.J.Mertensetal./AdvancesinSpaceResearch51(2013)554–574
2m/s) 4 2005 day14-24 2m/s) 4 2004 day312-319 2m/s) 4 2003 day298-305
s/c 3 corr=0.90 s/c 3 corr=0.94 s/c 3 corr=0.94
g g g
x(er 2 52.5N x(er 2 52.5N x(er 2 52.5N
u u u
S efl 1 5672..55NN S efl 1 5672..55NN S efl 1 5672..55NN
OE 0 67.5N OE 0 67.5N OE 0 67.5N
P 0.00 0.05 0.10 0.15 0.20 0.25 P 0.00 0.05 0.10 0.15 0.20 0.25 P 0.00 0.05 0.10 0.15 0.20 0.25
NO+ flux (ergs/cm2/s) NO+ flux (ergs/cm2/s) NO+ flux (ergs/cm2/s)
2m/s) 4 2003 day319-326 2m/s) 4 2002 day107-114 2m/s) 4 2004 day203-210
s/c 3 corr=0.83 s/c 3 corr=0.89 s/c 3 corr=0.94
g g g
x(er 2 52.5N x(er 2 52.5S x(er 2 52.5S
u u u
S efl 1 5672..55NN S efl 1 5672..55SS S efl 1 5672..55SS
OE 0 67.5N OE 0 67.5S OE 0 67.5S
P 0.00 0.05 0.10 0.15 0.20 0.25 P 0.00 0.05 0.10 0.15 0.20 0.25 P 0.00 0.05 0.10 0.15 0.20 0.25
NO+ flux (ergs/cm2/s) NO+ flux (ergs/cm2/s) NO+ flux (ergs/cm2/s)
2m/s) 4 2005 day251-258 2m/s) 4 All NH storms 2m/s) 4 All SH storms
s/c 3 corr=0.90 s/c 3 corr=0.87 s/c 3 corr=0.89
g g g
x(er 2 52.5S x(er 2 52.5S x(er 2 52.5N
u u u
S efl 1 5672..55SS S efl 1 5672..55SS S efl 1 5672..55NN
OE 0 67.5S OE 0 67.5S OE 0 67.5N
P 0.00 0.05 0.10 0.15 0.20 0.25 P 0.00 0.05 0.10 0.15 0.20 0.25 P 0.00 0.05 0.10 0.15 0.20 0.25
NO+ flux (ergs/cm2/s) NO+ flux (ergs/cm2/s) NO+ flux (ergs/cm2/s)
Fig. 3. Scatter plots of nighttime-averaged, zonal-mean NOAA/POES precipitating total electron energy flux versus SABER-derived NO+(v) 4.3lm
radiativefluxforhigh-latitudemagneticlatitudebands.Thesescatterplotsareshownforsevensolar-geomagneticstormperiodsandthelinearcorrelation
coefficientbetweentheparticleandradiativefluxdataareindicatedinthelegends.Scatterplotsforthesevenstormperiodsarecombinedandseparated
intonorthernandsouthernhemispheredatainthelasttwocolumnsofthebottomrow.
The atmospheric radiance observed by the SABER
4
4.3lmbroadbandradiometercanbemodeledbythespec-
trally-integrated solution of the infrared radiation transfer All storms
corr=0.88
equation for limb-viewing geometry (Goody and Yung,
3
1989), such that s)
XZ xobs Z @sðm;x;z Þ 2cm/
RDmðzTÞ¼ i xs DmJiðm;x;zTÞ i @x T UðmÞdmdx; ð2Þ x(ergs/ 2
u
where x is the position along the limb line-of-sight (LOS) efl
S 52.5N/S
between the satellite observation point (xobs) and a point OE 57.5N/S
atthefurthestextendofthelimb(xs).Thetangentaltitude P 1 6627..55NN//SS
and wavenumber variables are denoted z (km) and m
T
(cm(cid:3)1), respectively. The normalized spectral response
function of the SABER 4.3lm channel is represented by 0
UðmÞ (unitless), and the integration over wavenumber is 0.00 0.05 0.10 0.15 0.20 0.25
NO+ flux (ergs/cm2/s)
performed over the spectral width of the radiometer chan-
nel (2290–2405cm). The radiative source function and Fig. 4. Scatter plot of nighttime-averaged, zonal-mean NOAA/POES
transmittance are denoted J ðm;x;z Þ (W/(m2srcm(cid:3)1)) precipitating total electron energy flux versus SABER-derived NO+(v)
and sðm;x;z Þ (unitless), respecitively,Tand the summation 4.3lmradiativefluxforhigh-latitudemagneticlatitudebands.Thisfigure
i T combinesdatafromallthestormperiodsinthepreviousplot,independent
is over each ith vibration–rotation band that emits within
ofwhetherthedataarefromthenorthernorsouthernhemisphere.
the 4.3lm channel spectral bandpass. The monochromatic
transmittancealongtheLOSfortheithvibration–rotation absorbing molecules, which is taken to be CO2 in this sec-
band is given by tion. The absorption coefficient can be written in terms of
(cid:2) Z (cid:3) the spectral line strength S ðx;z Þ (cm2/(molecules
sðm;x;z Þ¼exp (cid:3) xobskðm;s;z ÞNðs;z Þds : ð3Þ (cm(cid:3)1)(cid:3)1))andthe normalized spteictraTlline shape function
i T x i T T gðm;mtiÞ ((cm(cid:3)1)(cid:3)1). Thus,
Here kðm;s;z Þ (cm2/molecules) is the molecular absorp- X
i T
tion coefficient for the ith vibration–rotation band and kðm;x;z Þ¼ S ðx;z Þgðm;v ;x;z Þ; ð4Þ
i T ti T ti T
Nðs;zTÞ (molecules/cm3) is the total number density of ti
C.J.Mertensetal./AdvancesinSpaceResearch51(2013)554–574 559
wherethesumin(4)isoverallradiativevibration–rotation SABER non-LTE CO model, which is described in more
2
transitions that emit within the ith vibration–rotation detail below.
band. The main source of atmospheric input data below
ThemethodologyofcalculatingtheCO (m )contribution 120kmisSABERroutinev1.06dataproducts.Theseinput
2 3
to the SABER 4.3lm limb radiance measurements is to dataareneededinthecalculationofradiativesourcefunc-
numerically solve (2) using the 4.3lm forward radiance tions and the transmittances, and for the computation of
modelcomponentoftheSABERoperationalnon-localther- the broadband LOS radiance in (2). The Tk and pressure
modynamic equilibrium (non-LTE) kinetic temperature data used are retrieved data products from the SABER
(Tk) and CO volume mixing ratio (vmr) retrieval measurementsandareavailableintheSABERLevel2data
2
algorithm, with atmospheric input data obtained from the file. The source of CO vmr data is a climatological data-
2
routine SABER data products (Mertens et al., 2001, 2002, base developed from the daytime simultaneous Tk/CO
2
2004, 2009a,c). The nighttime CO (m ) contributions that retrieval data products (Mertens et al., 2009c). Daytime
2 3
emit within the SABER 4.3lm channel spectral bandpass SABER-retrieved CO vmr profiles are interpolated onto
2
arisefromeightvibrationalemissionbands:themajorisoto- afixedpressuregridandsortedandaveragedasafunction
pic(16O12C16O)fundamentalband,firsthotband,andthree of latitude and season. Since diurnal variations in CO are
2
second hot bands; and three minor isotopic (16O13C16O, expected to be small, this CO vmr database is used in the
2
16O12C18O, and 16O12C17O) fundamental bands. Thus, the nighttimeCO (m )LOSradiancecalculations. Otheratmo-
2 3
summation in (2) includes these eight vibration–rotation sphericinputdatarequiredbythenon-LTECO modelare
2
bands. However, the radiative source functions and the themainMLTIneutralspeciesconcentrations:N ,O ,and
2 2
transmittances for each emission band, which embody the O(3P). These data are also included in the SABER Level 2
microphysical properties of atmospheric emission and data file, which originate from the NRLMSIS-00 model
absorption, respectively, must be known prior to solving (Picone et al., 2002).
the spectrally-integrated LOS infrared radiation transfer TheSABERatmosphericinputdatadescribedinthepre-
equationin(2). vious paragraph are extended above 120km using the
MLTI CO (m ) emissions are in vibrational non-LTE NRLMSIS-00 model. The thermospheric temperature
2 3
(Lopez-Puertas et al., 1986a,b; Nebel et al., 1994). Thus, above 120km in the NRLMSIS-00 model is based on the
the radiative source functions and the transmittances for Bates–Walker representation (Picone et al., 2002). The
eachoftheithvibration–rotationbandsin(2)arefunctions Bates–Walker representation is an analytical solution for
oftheupper-levelandlower-levelvibrationalstatedensities thermospherictemperatureasafunctionofaltitude,which
fortheradiativetransitionsthatemitinthe4.3lmspectral isparameterizedbytheexospherictemperatureattheupper
region. For these non-LTE emissions, the vibrational state boundaryandbytheglobalmeantemperatureatthe120km
densitiesdependexplicitlyonthechemical,collisional,and lowerboundary.Theexospherictemperatureisexpressedas
radiative processes that excite and de-excite each vibra- a function of geographical parameters and solar/magnetic
tional state. The so-called non-LTE CO model obtains indices(F10.7,81-dayaverageofF10.7,andAp).Thetem-
2
the CO vibrational state densities by simultaneously solv- peratureatthe120kmlowerboundaryisrepresentedby
2
ing the coupled steady-state statistical equilibrium equa- T ¼T(cid:2) ½1þG ðLÞ(cid:4); ð5Þ
tions for the relevant vibrational states, and the infrared 120 120 120
radiative transfer equations that radiatively couple the where the overbar represents a global and temporal mean.
vibrational states to the ground-state or to each other. The function GðLÞ includes time-dependent terms, spheri-
These coupled sets of equations are solved using the Mod- cal harmonic terms, time-dependent lower-order harmonic
ified Curtis Matrix approach (Lopez-Puertas et al., terms, and polynomial terms in solar/magnetic activity.
1986a,b, 1998). The calculation of the broadband LOS The approach used to extend the SABER temperature
radiance in (2) and the vibrational band radiation transfer profileusingtheNRLMSIS-00modelistoreplacethelow-
calculationswithinthenon-LTECO2modelareperformed er-boundary temperature in the Bates–Walker thermo-
usingBANDPAKroutines(Marshalletal.,1994).BAND- spheric temperature representation, i.e., T in (5), with
120
PAK solves the spectrally-integrated infrared radiation the retrieved SABER Tk at 120km for each SABER mea-
transfer equation along a specified viewing path by com- surement scan used in the analysis. To improve stability,
bining path-integrated composite emissivities, utilizing a since the uncertainty in the retrieved SABER Tk at
database ofpre-computedemissivity tables. The emissivity 120km is quite high (see Mertens et al., 2001, 2004 for a
tabledatabasesarecomputedline-by-lineusingLINEPAK discussion of the sources of uncertainty), the SABER tem-
routines (Gordley et al., 1994). The non-LTE CO2 model peratureprofileisaveraged5kmaboveandbelowthealti-
used in this analysis is largely based on the non-LTE tude closest to 120km. The averaged-120km SABER
CO2modelusedintheoperationalSABERTk/CO2retrie- kinetic temperature is then input into the NRLMSIS-00
val algorithm (Mertens et al., 2001, 2002, 2004, 2009c). model to supply the lower-boundary condition, and the
However, accurate modeling of nighttime CO2(m3) emis- Bates–WalkerrepresentationisusedtoextendtheSABER
sions required an important addition to the nominal temperature profile to 200km. The composition data
560 C.J.Mertensetal./AdvancesinSpaceResearch51(2013)554–574
(N , O , and O(3P)) is extended from 120 to 200km using from about 70km to over 120km (Lopez-Puertas et al.,
2 2
the NRLMSIS-00 model as well. The composition profiles 2004).TheOH(v69)statesarecomputedbycombiningan
generated from NRLMSIS-00 above 120km are scaled to OH(v) kinetics model with the total chemical production
match the profiles contained in the SABER Level 2 data rate of OH(v69) determined from the OH(v) VER data
at 120km. productderivedfromSABER2.0lmchannellimbradiance
Once the SABER temperature and composition data measurements,usingtheapproachofMlynczaketal.(1998).
havebeenextendedfrom120to200kmusingtheNRLM- The method of calculating the rate of production of N (1)
2
SIS-00 model, the pressure profile is rebuilt, starting from fromOH(v)wasadoptedfromLopez-Puertasetal.(2004).
the lowest altitude in the SABER Tk(p) profile IncorporatingthissourceofnighttimeCO (m )4.3lmemis-
2 3
((cid:5)12–15km), using the barometric law and including the sion represents a significant update to the nominal opera-
altitude dependence of the mean-molecular mass in a self- tional SABER non-LTE CO model (Mertens et al.,
2
consistent iterative scheme. The SABER-derived climato- 2009a,c).
logicalCO vmrprofilesareinterpolatedinlog-pressureto The above paragraphs presented an overview of the
2
the updated pressure profiles described above. This proce- algorithms and methodologies employed in simulating
dure for extending the SABER routine and climatological nighttime CO (m ) 4.3lm limb radiance. These techniques
2 3
data products to 200km is performed for each simulation can be assessed by comparing CO (m ) 4.3lm limb emis-
2 3
of the CO (m ) contributions to the nighttime SABER sion calculations with SABER 4.3lm channel measure-
2 3
4.3lmlimbradiancemeasurements. ments during quiescent conditions (kp 63). A large
A significant source of nighttime CO 4.3lm emission statistical ensemble of zonal-mean comparisons have been
2
originates from energy transfer from vibrationally excited carried out for all seasons and for pole-to-pole latitudinal
OH (i.e., OH(v69)) to N (1) by collisional quenching, coverage(Mertensetal.,2009c).Onaverage,thenighttime
2
which is subsequently transferred to the CO (m ) states by MLTI CO (m ) 4.3lm limb radiance calculations generally
2 3 2 3
a V–V exchange mechanism (Lopez-Puertas et al., 1986b; agree with the corresponding SABER measurements to
Lopez-Puertasetal.,2004).Theinfluenceofthisexcitation within20%(Mertensetal.,2007a),asshownforquiescent
process extends well above the OH layer due to the non- equinox conditions in Fig. 5.
LTE process of local excitation (OH(v69)!N (1)! Once thenighttimeCO (m )4.3lmlimb radianceiscal-
2 2 3
CO (m )) followed by radiative loss and re-absorption at culated, using the algorithms andmethodologies described
2 3
higher altitudes. This energy transfer mechanism accounts above, the SABER 4.3lm residual limb radiance is
for 20–40% of the nighttime CO (m ) 4.3lm limb radiance obtained by
2 3
Comparisons of monthly-median Limb Radiance Difference between SABER 4.3um Measurements and Simultions
March 2002
10-3 10-3
80 km 90 km
10-4 10-4
10-5 10-5
10-6 10-6
90S 60S 30S 0 30N 60N 90N 90S 60S 30S 0 30N 60N 90N
2m/sr) 10-3 100 km 10-3 110 km
W/ 10-4 10-4
e (
c
an 10-5 10-5
di
a
R
10-6 10-6
90S 60S 30S 0 30N 60N 90N 90S 60S 30S 0 30N 60N 90N
10-3 10-3
115 km 120 km
10-4 10-4
10-5 10-5
10-6 10-6
90S 60S 30S 0 30N 60N 90N 90S 60S 30S 0 30N 60N 90N
Latitude (degree) Latitude (degree)
Fig. 5. Monthly zonal-median 4.3lm limb radiance comparisons for quiescent conditions (kp63) during March 2002. The black solid lines are the
SABERmeasurements.Theredsolidlinesarethenon-LTECO(m)simulationsdescribedinSection2.2.(Forinterpretationofthereferencestocolorin
2 3
thisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)
C.J.Mertensetal./AdvancesinSpaceResearch51(2013)554–574 561
dRDmðzTÞ¼RMDmeasðzTÞ(cid:3)RCDmO2ðzTÞ: ð6Þ rotation transition in the MLTI region. As a result, (12)
canbeapproximatedby
During geomagnetic activity, the residual 4.3lm radiance XX
isduetoNO+(v)emission.Thisisaffirmedbythestatistical Vðx;z Þ(cid:6) hcm A n ðx;z ÞUðm Þ: ð13Þ
T ti ti uti T ti
correlations between the SABER-derived NO+(v) 4.3lm i ti
radiative flux and the precipitating particle flux (i.e., Figs. EvaluatingtheNO+(v)4.3lmVERfrom(13)requiresa
1, 3, and 4), and explicit physics-based simulations of
detailed understanding of the ion-neutral chemistry, and
NO+(v) 4.3lm emission (Mertens et al., 2007a, 2008,
the collisional and radiative processes that excite and de-
2009a).
excite each ith vibration–rotation band that emits within
The broadband LOS radiative transport equation in (2) the SABER 4.3lm channel spectral bandpass, along with
canbesimplifiedforNO+(v)emissionsinceNO+(v)4.3lm
the corresponding chemical, kinetic, and spectroscopic
radiation transfer is optically thin at all altitudes (Winick
parameters. The advantage of the SABER measurements
et al., 1987a,b). Under weak-line, or optically thin, condi- isthat the NO+(v) 4.3lmVER canbe obtainedby invert-
tions the transmittance in (3) is approximated by
ing the weak-line LOS integral radiation transfer equation
Z
xobs in(11),withoutknowledgeofthephysicsandchemistryof
siðm;x;zTÞ(cid:6)1(cid:3) kiðm;s;zTÞNðs;zTÞds ð7Þ NO+(v) energetics. The method of solving (11) for the
x NO+(v) VER, given the SABER 4.3lm residual limb
and radiance profile, is discussed in the next section.
@sðm;x;z Þ
i @x T (cid:6)kiðm;x;zTÞNðx;zTÞ: ð8Þ 2.3. Deriving NO+(v) 4.3lm volume emission rates
In this case, the sum over the i-index includes the four
Thissectiondescribesthesecondandfinalstepinderiv-
NO+(v) vibration–rotation bands that emit within the
ingNO+(v)VERfromSABER4.3lmlimbemissionmea-
SABER 4.3lm channel spectral bandpass (Mertens
surements. The first step is to obtain the 4.3lm residual
et al., 2009a), and Nðs;zTÞ is the total number density of limbradiancebyremovingtheCO (m )contributionsfrom
NO+.Substitute(2)into (6)using(8)and(4).The resultis the SABER 4.3lm limb emission m2 e3asurements using the
Z Z
dRDmðzTÞ(cid:6)X xobs Jiðm;x;zTÞkiðm;x;zTÞNðx;zTÞUðmÞdmdx ð9Þ aTlhgeorsiitghnmifiscaanndcemoefththoidsssdteispcuissstehdaitnththeeSpAreBvEioRu-sobsescetrivoend.
i Zxs ZDm
XX xobs 4.3lmresidualradianceisidentifiedwiththeLOSintegral
(cid:6) Jiðm;x;zTÞStiðx;zTÞgðm;vti;x;zTÞ of the NO+(v) VER, as expressed in (11). The final step is
i ti xs Dm toinverttheintegralequationin(11)inordertoobtainthe
(cid:2)Nðx;z ÞUðmÞdmdx: ð10Þ
T NO+(v) VER profile, given that the 4.3lm residual limb
By substituting the microphysical expressions for the radi- radiance is known a priori.
ative source functions and absorptioncoefficients into (10) The NO+(v) 4.3lm VER is assumed to be symmetric
(Lopez-Puertas et al., 1986a,b; Wintersteiner et al., 1992), about thetangentheight zT such that (11) isapproximated
the broadband limb radiance in the weak-line limit can by
Z
be written as a LOS integral over the VER, such that C xobs
dRDmðzTÞ(cid:6)41p Z xobsVðx;zTÞdx; ð11Þ dInRDtmhðezTaÞb(cid:6)ov2epequ0atioVnð,xa;zuTnÞditx:conversion factor C has bðe1e4nÞ
xs
introduced.TheSABER-observedresidual4.3lmlimbradi-
where the VER is given by Z ance (dRDmðzTÞ) is in units of W/(m2sr). Distance along the
XX LOS(x)isinunitsofkm.Thevolumeemissionrateischosen
Vðx;zTÞ¼ i ti hcmtiAtinutiðx;zTÞ Dmgðm;vti;x;zTÞUðmÞdm: toordbeergtoivceonvienrtu(nkimtseorfgsercgms/(cid:3)(3cms(cid:3)31s))t.oA(sWamre(cid:3)s2ulstr,(cid:3)C1).¼100 in
ð12Þ The integral over the LOS path (x) in (14) is converted
to an integral over radial distance RðzÞ, where RðzÞ is the
In the above equation, h and c are Planck’s constant and radial distance from the center of the earth at altitude z.
the speed of light, respectively. The Einstein A-coefficient Thus, (14) is equivalently expressed as
for the radiative transition t within the ith vibration– Z
ruoptpaetrionvibbraantdionisaldesntaotteednuAmti;baienrddneuntisðixty;zToÞfdNesOig+naftoers tthhee RDmðzTÞ¼2Cp RðRzðT1ÞÞKðRðzÞÞVðRðzÞÞdRðzÞ; ð15Þ
radiative transition labeled by t.
i where the kernel of the integral equation is given by
An additional approximation can be applied to the
expression for the VER in (12). Generally, the normalized RðzÞ
KðRðzÞÞ¼qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi: ð16Þ
instrument spectral response function (UðmÞ) varies slowly
R2ðzÞ(cid:3)R2ðz Þ
over the spectral width of a single radiative vibration– T
562 C.J.Mertensetal./AdvancesinSpaceResearch51(2013)554–574
An integral equation with the above form is known as V ¼a þbR ð28Þ
j j j j
an Abel integral equation (Arfken, 1985). The inversion Vjþ1 ¼ajþbjRjþ1: ð29Þ
of (15) and (16) is referred to as an Abel inversion. The
Abel integral equation can be inverted analytically. How- After deriving expression for the constants a and b from
j j
ever, the analytic solution requires computing derivatives (28) and (29), and substituting them into (27), and group-
of integral functions of the left-hand side of (14) (Arfken, ing all terms proportional to V , the integrals in (24) and
j
1985). This approach is numerically unstable in remote (25) can be expressed as a matrix–vector product. The re-
sensing applications since the left-hand side of (14) is sult is
obtained from (noisy) measurement data. An alternative
XN XN
approach is employed in this section, which is to develop I ¼ I ¼ A V ; ð30Þ
i ij ij j
a stable numerical inversion of the Abel integral equation.
j¼i j¼i
To obtain a numerical solution, the Abel integral equa-
tion in (15) is discretized. Let the i-index label the tangent where Vj is the volume emission rate at the jth radial dis-
altitude and let the j-index label the radial distance above tance and the matrix elements Aij are given by
Z
the radial distance at the tangent height, such that
A ¼(cid:3) Rj(cid:3)1 Rj K ðRÞdRþ Rjþ1
ðR2ðpzT=ÞC!ÞdRRDimðzTÞ(cid:7)yðzTÞ!yðziÞ!yi ðð1178ÞÞ ij RZj(cid:3)RjþR1 j(cid:3)1 Rj(cid:3)1 i 1 RjZþ1R(cid:3)j Rj
RRðð1zÞÞ!!RjR1: ðð2109ÞÞ (cid:2) Rj 1 KiðRZÞdRRjþ1þRj(cid:3)Rj(cid:3)1 Rj(cid:3)1KiðRÞRdR
(cid:3) K ðRÞRdR: ð31Þ
Incorporating the above definitions, (15) and (16) become Rjþ1(cid:3)Rj Rj i
Z
y ¼ R1K ðRÞVðRÞdR; ð21Þ The four integrals in (31) can be evaluated analytically, gi-
i i ven the expression for the kernel in (22). The final expres-
Ri
sion for the A matrix elements is
ij
where the kernel is now given by (cid:5)qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(cid:6)
KiðRÞ¼qffiRffiffi2ffiRffiffi(cid:3)ffiffiffiffiffiRffiffiffi2iffiffi: ð22Þ Aij ¼Rj(cid:3)1 (cid:5)qR2j(cid:3)ffiffi1Rffiffiffi(cid:3)jffiffiffi(cid:3)ffiffiRffiffiffiR2iffiffijffi(cid:3)ffi(cid:3)ffiffi1 qR2jffiffi(cid:3)ffiffiffiffiRffiffiffi2iffiffiffiffiffiffiffi(cid:6)
Define the integral on the right-hand side of (21) as þRjþ1 R2jþ1(cid:3)R2i (cid:3) R2j (cid:3)R2i
Z R1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiRffiffijþ1(cid:3)Rqj ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
I (cid:7) K ðRÞVðRÞdR: ð23Þ
i Ri i þRj R2j (cid:3)R2i (cid:3)Rj(cid:3)1 R2j(cid:3)1(cid:3)R2i
The integral in (23) can be divided into N sub-intervals qffiffiffiffiffiffiffiffiffiffi2ffiffiffiðffiRffiffi j(cid:3)Rj(cid:3)q1Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
sIui ¼chXtNhaItij; ð24Þ þRj R2j (cid:3)2Rð2iR(cid:3)jþ1R0(cid:3)jþ1RjÞRq2j(cid:3)1ffiffiffi(cid:3)ffiffiffiffiffiRffiffiffi2iffiffiffiffiffi1
j¼i þ R2i ln@Rjþ R2j (cid:3)R2iA
where 2ðRj(cid:3)Rj(cid:3)1Þ Ri
Z
Rjþ1 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
Iij ¼ Rj KiðRÞVðRÞdR ð25Þ (cid:3)2ðRj(cid:3)R2iRj(cid:3)1Þ ln@Rj(cid:3)1þ RRi2j(cid:3)1(cid:3)R2iA
and R designates the highest altitude in the model atmo-
N 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
saprlhyerteh.roAusgshumtheetshuabt-tinhteervvoalul:me emission rate varies line- þ R2i ln@Rjþ R2j (cid:3)R2iA
VðRÞ¼ajþbjR; ðRj 6R6Rjþ1Þ: ð26Þ 2ðRjþ1(cid:3)RjÞ 0 Rqi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1
SubstZituRtjþin1g (26) into (25) gives (cid:3)2ðRjþR12i(cid:3)RjÞ ln@Rjþ1þ RRi2jþ1(cid:3)R2iA: ð32Þ
I ¼ KðRÞða þbRÞdR: ð27Þ
ij i j j
Rj Combining(21),(23),(24),and(30),thediscretizedformof
The constants a and b can be determined by the require- the Abel integral equation for weak-line LOS radiation
j j
ment that transfer in (14) is expressed as
C.J.Mertensetal./AdvancesinSpaceResearch51(2013)554–574 563
XN Thissectioncompletes thedescriptionofthealgorithms
yi ¼ AijVj: ð33Þ and methodologies used to derive NO+(v) VER from
j¼i SABER 4.3lm limb emission measurements. The
In matrix–vector notation, (33) can be written as SABER-derived NO+(v) 4.3lm VER is the observation-
y¼A~V: ð34Þ based proxy used to characterize the response of the
E-region to solar-geomagnetic activity. The next section
TheAbelintegralequationin(14)isclassifiedasaFred- presents results from the NO+(v) VER retrieval algorithm
holmintegralequationofthefirstkind(commonlydenoted and discusses important uncertainties.
IFK). Eq. (34) is a discretized IFK (denoted DKF). A
unique, numerically stable solution to the DKF in (34) 3. Results and discussion
can be obtained using the Philips–Tikhonov–Twomey
(PTT) regularization method (Phillips, 1962; Tikhonov, The purpose of the results presented in this section is
1963; Twomey, 1963, 1977), which is the solution Vc that threefold: (1) illustrate the fidelity and robustness of the
minimizes the following expression numerical Abel inversion algorithm presented in Section
(cid:5) (cid:6)
min kAeV(cid:3)yk2þckLeðV(cid:3)V Þk2 ; ð35Þ 2.3, (2) quantify known sources of error in the NO+(v)
0 VER retrieval algorithm, and (3) assess the influence of
e spatially structured emission sources on the 1-D Abel
where L is the matrix representation of the regularization
(orsmoothing)operatorL,whichcanbetheidentityoper- inversion. The results presented in this section provide
ator, a first derivative, LV¼V0, a second derivative, important guidance in the development of the E-region
LV¼V00, or any higher order derivative operator, etc. peak electron density empirical storm-time correction fac-
tor presented in Part II of this series.
The vector V can be any specified mean-state, or zero.
0
Fig. 6 demonstrates that the Abel inversion algorithm
The solution to (35) is unique, and is formally given by
(cid:5) (cid:6) (cid:5) (cid:6) faithfully reproduces a known NO+(v) VER profile from
Vc ¼ AeTAe þcLeTLe (cid:3)1 AeTyþcLeTLeV0 : ð36Þ a simulation of the corresponding SABER 4.3lm channel
limb radiance. The input atmospheric state and auroral
TheLagrangemultipliercisaconstraintthatensuresaun- dosingparametersweretakenfromthegeomagneticstorm
ique, stable solution, and is closely related to the measure- event studied by Mertens et al. (2008). The event was dur-
ment errors (Twomey, 1977). An additional constraint ingtheHalloween2003storm:October30,2003,67N,12E,
imposedisthatthevectornormofthemeasurementerrors and 1.69 UT. The reference NO+(v) VER profile (not
inyisbounded.If(cid:2)representstheerrorsiny,thenthecon- shown) was computed by the NO+(v) chemical-kinetic
straint is model described in Mertens et al. (2007a, 2008, 2009a)
X
using the input specifications for the aforementioned
(cid:2)2 ¼d2: ð37Þ
i Halloween 2003 event. The non-LTE radiation transfer
i
algorithms discussed in Section 2.2 were used to simulate
Anoptimalsolutionisfoundbyadjustingcuntilthevector thetotal(CO (m )+NO+(v))limbradiancethat,inprinci-
2 3
norm of the solution residual satisfies ple, would be observed from the SABER 4.3lm channel,
rdðcÞ¼kAeVc(cid:3)ydk¼d(cid:8)De; ð38Þ which is shown in the left-hand column of Fig. 6. The fig-
ure also shows the separate contributions from CO (m )
whereDe isapre-defined tolerance(e.g.,1%, 5% etc.). The and NO+(v). The Abel inversion algorithm was app2lie3d
algorithm steps are as follows: to the NO+(v) component of the SABER 4.3lm channel
limbradiance.TheresultistheNO+(v)VERprofileshown
1. Set c¼d.
in the right-hand column of Fig. 6, which exactly repro-
2. Compute the solution from (36). duces the reference NO+(v) VER profile (see Fig. 4 from
3. Compute the solution residual from (38). Mertens et al., 2008). Recall that in practice, the NO+(v)
4. If d(cid:3)D(cid:2)6rdðcÞ6dþD(cid:2), then STOP. contribution is derived by first modeling the CO (m ) com-
5. If rdðcÞ<d(cid:3)D(cid:2), then increase c; goto 2. ponent, which is subsequently subtracted from2th3e mea-
6. If rdðcÞ>dþD(cid:2), the decrease c; goto 2. sured (total) SABER 4.3lm channel limb radiance, as
described in detail in Section 2.2.
In the inversion of SABER 4.3lm residual limb radiance
The above demonstration of the Abel inversion algo-
measurements in (14), the mean-state NO+(v) VER in
rithmwasatestunderidealconditionswherethelimbradi-
(36)isassumedtobezero(i.e.,V ¼0),andthesmoothing
0 ance was assumed to be known perfectly. Actual radiance
e
matrix operator L is set equal to the second-order deriva-
measurements are subject to both systematic and random
tive operator (Twomey, 1977). Error analysis studies
errors. The radiometric calibration error is less than 2%
demonstrated that this constrained producesthe minimum
(Mertens et al., 2001). The largest systematic error in
mean bias and statistical uncertainty in retrieved NO+(v) retrievingNO+(v)VERfromSABER4.3lmchannellimb
VER profiles.
radiance measurements arises from subtracting the