Which solar EUV indices are best for reconstructing the solar EUV irradiance?

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  • aV

    tzsu

    a LPCE, CNRS and University of Orleans, 3A avenue de la Recherche Scientique, 45071 Orleans, France

    Using multivariate statistical methods, we represent in a single graph the measure of relatedness between these indices and various

    Many studies have been devoted to the comparisonbetween solar EUV proxies and the solar EUV irradiance;Floyd et al. (2005) have recently reviewed three decades ofresults. The physical connection between these indices andthe irradiance, however, is at best indirect, and there arealso substantial dierences in the way these dierent quan-

    * Corresponding author.E-mail address: ddwit@cnrs-orleans.fr (T. Dudok de Wit).

    1 It is common practice in aeronomy to distinguish XUV (130 nm),EUV (30121 nm) and FUV (122420 nm). We shall use the generic termEUV for all of them.

    Available online at www.sciencedirect.com

    Advances in Space Research 4strong spectral lines. The ability of each index to reproduce the EUV irradiance is discussed; it is shown why so few lines can be eectivelyreconstructed from them. All indices exhibit comparable performance, apart from the sunspot number, which is the least appropriate. Nosingle index can satisfactorily describe both the level of variability on time scales beyond 27 days, and relative changes of irradiance onshorter time scales. 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

    Keywords: Solar EUV irradiance; Solar EUV proxies; Solar EUV indices; Multivariate statistics

    1. Introduction

    The solar irradiance in the EUV range1 is a key param-eter for aeronomy (Hinterregger, 1981) and for spaceweather (Lathuille`re et al., 2002). It is also one of the leastaccessible parameters, as EUV measurements must be car-ried out above the terrestrial atmosphere. Moreover, space-

    borne EUV detectors suer from instrument degradation.Not surprisingly, there have been very few continuousand spectrally resolved measurements in the spectral rangethat is of interest for aeronomy, typically between 20 and150 nm. This situation has led to the widespread use ofproxies as substitutes for the irradiance (Cebula et al.,1998; Tobiska et al., 2000; Lathuille`re et al., 2002).b SIDC, Royal Observatory of Belgium, Ringlaan 3, 1180 Brussel, Belgiumc LESIA, Paris Observatory, 5 Place Jules Janssen, 92195 Meudon, France

    d GIPSAlab, CNRS, 961 Rue de la Houille Blanche, BP 46, 38402 Saint-Martin dHe`res, Francee IAS, CNRS and University of Paris-Sud, Batiment 121, 91405 Orsay, France

    f LPG, CNRS and Joseph Fourier University, Batiment D de Physique, BP 53, 38041 Saint-Martin dHe`res, France

    Received 31 October 2006; received in revised form 31 January 2007; accepted 4 April 2007

    Abstract

    The solar EUV irradiance is of key importance for space weather. Most of the time, however, surrogate quantities such as EUV indi-ces have to be used by lack of continuous and spectrally resolved measurements of the irradiance. The ability of such proxies to repro-duce the irradiance from dierent solar atmospheric layers is usually investigated by comparing patterns of temporal correlations. Weconsider instead a statistical approach. The TIMED/SEE experiment, which has been continuously operating since February 2002,allows for the rst time to compare in a statistical manner the EUV spectral irradiance to ve EUV proxies: the sunspot number, thef10.7, Ca K, and Mg II indices, and the He I equivalent width.Which solar EUV indicesthe solar EU

    T. Dudok de Wit a,*, M. KreP.-O. Amblard d, F. A0273-1177/34.00 2007 COSPAR. Published by Elsevier Ltd. All rights reserdoi:10.1016/j.asr.2007.04.019re best for reconstructingirradiance?

    chmar b, J. Aboudarham c,che`re e, J. Lilensten f

    www.elsevier.com/locate/asr

    2 (2008) 903911ved.

  • The lack of continuous observations in the EUV is a

    in Slong-standing problem in solar irradiance studies. This sit-uation rst improved in 1991 with the continuous irradi-ance measurements from the SOLSTICE and SUSIMinstruments (Rottman, 2000). A second major improve-ment came from the EUV spectrometer onboard theTIMED satellite (Woods et al., 2005). With several yearsof continuous operation, this instrument for the rst timeallows the EUV spectral irradiance to be compared statis-tically against EUV indices. The EVE instruments onboardthe future Solar Dynamics Observatory will soon provideadditional spectral resolution and coverage.

    In this study, we make use of four years of daily TIMEDdata. Although four years is not sucient for properly val-idating the impact of the solar cycle, it already providesinteresting insight. Our time interval (February 2002 untilMay 2006) starts shortly after solar maximum, andincludes the full decay of the cycle down to solar minimum.

    The six quantities we consider here are:The spectral irradiance measured by the Solar Extreme

    Ultraviolet Experiment (SEE) (Woods et al., 2005)onboard TIMED. We consider daily-averaged solar spec-tral irradiance measurements made by EUV grating spec-trograph that is part of SEE. This spectrograph covers26194 nm with 0.4 nm spectral resolution; its measure-ments are corrected for atmospheric absorption and instru-tities are measured. In spite of this, most proxies reproducethe variability of the EUV irradiance remarkably well.Their strong temporal correlations emerge as a result ofclose connections between the irradiance mechanisms atdierent solar atmospheric layers, and yet signicant dis-crepancies persist. The accurate reconstruction of the solarEUV irradiance from surrogate quantities remains an openproblem.

    Most solar irradiance studies are based on detailed com-parisons of events. Dierences in the time evolution indeedprovide direct insight into the underlying physics. We con-sider here a dierent and novel approach that uses a globalrepresentation and shows how the EUV irradiance and theproxies are related to each other. This statistical approachwas recently introduced with the aim to determine how thesolar spectral irradiance could be reconstructed from thelinear combination of a few (typically 48) spectral lines(Dudok de Wit et al., 2005), following an earlier investiga-tion based on physical criteria (Kretzschmar et al., 2004).Here we use the same approach to compare several EUVindices with a selection of strong EUV lines. Using two dif-ferent normalisations, we investigate how well each indexreproduces emissions that originate from dierent layersof the solar atmosphere, and which combination of indiceswould be appropriate.

    2. Solar indices for the EUV spectral irradiance

    904 T. Dudok de Wit et al. / Advancesment degradation, and are normalised to 1 AU. TIMEDmakes several measurements per day and so the contribu-tion of solar ares is subtracted. Our analysis is based onversion 8 data.

    We focus here on daily intensities of 38 strong spectrallines, from February 8th, 2002 until May 14th, 2006.Although more recent SEE data exist, our time span is con-strained by the availability of the indices. The 38 spectrallines are shown in Fig. 1.

    The international sunspot number, as computed daily bythe Royal Observatory of Belgium. This oldest and bestknown gauge of solar activity is connected to the EUV irra-diance through the presence around sunspots of hot plagesand faculae, in which the EUV emission is enhanced.Short-term variations of the sunspot number, however,do not always correlate well with the EUV irradiance(Donnelly et al., 1986). This quantity cannot properly cap-ture features such as centre-to-limb variations and theemission of decaying sunspots.

    The decimetric f10.7 index which is a daily measurementof the radio ux at 10.7 cm made by the Penticton observa-tory. This radiometric index measures both thermal emis-sion and electron gyro-resonance emission, which issuefrom the high chromosphere and low corona. The f10.7index is today widely preferred to the sunspot number sinceit is easier to measure from ground and it is better corre-lated with the EUV irradiance (Donnelly et al., 1983; Floydet al., 2005).

    The Mg II index, which is the core-to-wing ratio of theMg II line at 280 nm and probes the high chromosphere.This index, which was rst developed by Heath and Schle-singer (1986) has been shown to be an excellent surrogatefor the UV irradiance; it also ts the EUV irradiance alsoquite well (Thuillier and Bruinsma, 2001; Viereck et al.,2001) in spite of dierences in the way the index is derivedfrom various experiments. We use the composite Mg IIdata set compiled by the Space Environment Center(NOAA).

    The Ca K index is the normalised intensity of the Ca IIK-line at 393 nm and has been recognised early on as ainteresting index for the UV domain (Lean et al., 1982).Ca K line images are routinely used to track the evolutionof plages and the network, whereas the Mg II line is bettersuited for faculae. The Mg II index is generally consideredto be better correlated with chromospheric emissions thanthe Ca K index (Hedin, 1984). Our Ca K data were com-piled by the NSO at Kitt Peak.

    The equivalent width of the He I 1083 nm infrared absorp-tion line has been computed from ground-based imagessince the 1980s (Harvey and Livingston, 1994). This quan-tity has been shown to probe the cold contribution of theEUV spectrum quite well (Donnelly et al., 1986). We usethe He I index compiled by the NSO at Kitt Peak.

    All quantities, apart from the Mg II index and the EUVirradiance, can be measured from ground. The He I and CaK indices, however, are susceptible to weather conditions.Several quantities suer from data gaps and the He I data

    pace Research 42 (2008) 903911are only available until September 21, 2003. Data gaps ofless than a month can easily be lled by a multivariate var-

  • 00

    C II

    IH

    IO

    VI

    theight

    in Siant of the interpolation scheme developed by Kondrashovand Ghil (2006), which performs here remarkably well,owing to the redundancy of the data. We made no attempt,however, to extrapolate the He I data. This restriction doesnot aect our analysis but it means that the resultsobtained with the He I index may be biased by lack of suf-cient temporal coverage.

    All EUV irradiances and indices are strongly correlatedfor yearly variations, but show signicant dierences intheir short-term variations. Direct visualisation of theirtime series has so far been the standard way of lookingat these dierences. To the best of our knowledge, Pear-sons correlation coecient is the only quantity that hasbeen used to quantify similarity. Such statistical measures,however, only reveals how quantities are related pairwise.We shall now show how all the information can be gath-ered in a single representation.20 40 60 80 1

    101

    102

    103

    104

    105

    106

    aver

    age

    flux

    [W/m

    2 /sec

    /nm

    ]

    Fe X

    VH

    e II

    Fe X

    VIFe

    XVI

    Mg

    IXFe

    XV Ne

    VII

    Si X

    IISi

    XII

    He

    IO

    IVH

    e I

    Mg

    X O V

    O II

    IN

    IV Ne

    VIII

    Ne

    VIII

    O IV

    O II

    H I H

    I

    Fig. 1. Time-averaged EUV spectrum from SEE. The shaded area expressesspectral lines of our set are shown. A lter blocks out the wings of the br

    T. Dudok de Wit et al. / Advances3. The method: multidimensional scaling

    The analysis method we advocate here is identical to theone we used for reconstructing the EUV spectrum from areduced set of spectral lines (Dudok de Wit et al., 2005).We rst quantify the connectivity between two observablesby means of their Euclidean distance

    dkl Z

    ykt ylt 2dts

    ; 1

    where yk(t) and yl(t) are the time series of any of the quan-tities listed in the preceding section, after some suitablenormalisation (to be discussed later). The smaller this dis-tance is, the more related the dynamics of the two quanti-ties is and the more likely their common physical origin is.

    We next represent each quantity by a single point in amultidimensional connectivity map, in which the distancebetween any pair of points equals the dissimilarity d. Thenumber of observables is 43 (38 spectral lines + 5 indices),which means that this map should formally have 42 dimen-sions. Since, however, most quantities are strongly corre-lated, the dimensionality can be strongly reduced withoutlosing pertinent information. This reduction considerablyeases the visualisation and the interpretation. The tech-nique for building such a connectivity map is called multi-dimensional scaling and is well known in the multivariatestatistics literature (Chateld and Collins, 1990). Inciden-tally, since we are using an Euclidean distance, the low-dimensional representation of the connectivity map isnothing but a projection onto the rst principal axes ofthe data. Using principal component analysis, we thenexpress the spectral variability as a linear combination ofseparable modes (Chateld and Collins, 1990)

    ykt XNi1

    Aifitgik; k 1; 2; . . . ; 43 2

    120 140 160 180 200 [nm]

    O V

    IN

    II

    H I

    O I

    C II

    Si IV

    Si IV

    C IV

    C I H

    e II C

    I

    Si II Si

    II

    variability of the irradiance between February 2002 and May 2006. The 38H I Lyman-a emission.

    pace Research 42 (2008) 903911 905with the orthonormality constraint

    hfitfjti hgikgjki 0 if i 6 j1 if i j

    ; 3

    where . means ensemble averaging. The weights are tradi-tionally sorted in decreasing order A1P A2P PANP 0. The number of modes N here equals the numberof observables. Large weights correspond to modes that de-scribe features shared by many observables. Since mostquantities exhibit very similar time evolutions, we can ex-pect very few modes to capture the salient features of thefull data set. The proportion of variance accounted forby the ith mode is

    V i A2iPN

    j1A2j

    : 4

    As will be shown below in Section 5, one or two modesonly are needed to describe over 90% of the variance. Thisremarkable result is a direct consequence of the strong con-

  • in Snections between solar emission processes at dierentaltitudes.

    As shown by Chateld and Collins (1990), the coordi-nates of our observables along the ith axis of the connectiv-ity map are simply given by Aigi(k). A two-dimensionalmap is needed if two modes describe the data. Three ormore dimensions are necessary if there are more outstand-ing modes with large weights. The time-prole fi(t) associ-ated with the ith axis expresses the type of dynamics that isshared by observables lying along that axis. An inspectionof these time-proles is needed to interpret the axes.

    4. Choice of the normalisation

    The main quantity of interest here is the relative positionof our observables on the low-dimensional connectivitymap. The multidimensional scaling technique is not scalinginvariant and so it is important to specify how the data arenormalised. There are essentially two choices:

    (1) The default choice in statistics is standardisation

    ykt !yk ykrk

    5

    in which each quantity is centered with respect to its timeaverage yk and then reduced by its standard deviation rk.By doing so, we put all quantities on equal footing irrespec-tive of their level of temporal variability. Such a normalisa-tion is appropriate for comparing UV indices with hotcoronal lines, since the two exhibit very dierent levels ofmodulation with solar rotation. If two standardised quan-tities yk and yl overlap on the connectivity map, then theyare connected by a linear relationship yk ayl + b, where aand b are two constants.(2) Another choice (hereafter called normalisation) con-

    sists in normalising each quantity with respect to itstime-average only

    ykt !yk yk

    yk6

    This choice preserves the information about the level ofvariability. Two normalised quantities yk and yl coincideon the connectivity map if they are linearly proportionalto each other: yk a yl, where a is a constant.

    In principal component analysis, the decomposition ofstandardised data involves the diagonalisation of the datacorrelation matrix, whereas for normalised data, the datacovariance matrix is diagonalised. The two normalisationsare illustrated in Figs. 2 and 3, in which we respectively plotstandardised and normalised quantities. Five typical spec-tral lines and the ve indices are shown. The most conspic-uous features are the decaying solar cycle and the solarrotation, which is responsible for a 27-day modulation. A13.5-day modulation, which is caused by centre-to-limb

    906 T. Dudok de Wit et al. / Advancesvariations (Crane et al., 2004), is sometimes apparent.The stronger variability of hot coronal lines, such as FeXVI, only comes out in normalised quantities, whereasstandardisation is better suited for comparing ne detailsin the time evolution.

    By representing each observable by a single point on theconnectivity map, we gain a global view that provides inter-esting insight into the connection between the dierentindices and the EUV irradiances. It must be stressed, how-ever, that dierences in long-term trends may be aected byinstrumental eects and in particular by sensor degradation(e.g. Deland and Cebula, 1998). Short-term dierences aremore likely to be associated with dierences in the emissionprocesses (Donnelly et al., 1986; Crane, 2001; Floyd et al.,2005). Unfortunately, all scales are mixed here. A moregeneral method for overcoming this is in preparation(Dudok de Wit et al., in preparation).

    Caution should also be exercised in extrapolating ourresults, since our statistical sample covers less than onesolar cycle. It has been shown before (e.g. Floyd et al.,2005) that some indices may not agree equally well duringdierent phases of the solar cycle. We checked this byrepeating our analysis for shorter sequences. No strikingdierences were found. Nevertheless, a statistical descrip-tion like ours formally is complete only once the samplecovers at least one full magnetic cycle (22 years).

    5. Comparison between indices and irradiances

    Figs. 4 and 6 show the connectivity maps obtainedrespectively with normalised and with standardised data.These two plots contain the main results of our study.We built the connectivity maps using 38 spectral lines fromTIMED/SEE and 5 indices. Although their true dimensionis 42, two dimensions are sucient to display the cloud ofpoints while preserving the distances as dened above. Thefraction of signal variance that is described by the rst fouraxes or dimensions is listed in Table 1.

    5.1. Comparison with normalised data

    The rst axis of the connectivity map (see Fig. 4) is byfar the most important one, as it describes over 93% ofthe variance. The corresponding time-prole is shown inFig. 5. Not surprisingly, the time-prole captures thedecaying solar cycle and the 27-day modulation, whichare common to all indices and to all spectral lines. The sec-ond axis captures a slow trend and the 13.5-day modula-tion that is typical for hot coronal lines. These resultshave already been discussed by Dudok de Wit et al.(2005). For standardised data, the second axis only cap-tures slow trends. The third and subsequent axes still con-tain some variance and so cannot be fully neglected. Theircontribution, however, is weak and in contrast to the rsttwo axes, depends on the time interval of the observations.Adding a third dimension would also considerably compli-cate the visualisation.

    pace Research 42 (2008) 903911The connectivity map obtained with normalised data isvery similar to the one published by Dudok de Wit et al.

  • T. Dudok de Wit et al. / Advances in S21012(2005), using half as many data.2 The rightmost lines orindices are those which are most strongly modulated bythe solar cycle and by solar rotation. Hot coronal linesare well known to be strongly modulated (Woods et al.,

    2 The main dierence is in the location of the f10.7 index, which tends tomove downward as the solar cycle progresses.

    2002 2003 2004 20

    2

    1

    0

    1

    2

    ye

    ampl

    itude

    of n

    orm

    alis

    ed q

    uant

    ities

    Fig. 3. Same plot as Fig. 2, but

    2002 2003 2004 200ye

    ampl

    itude

    of s

    tand

    ardi

    sed

    quan

    titie

    s

    Fig. 2. Time evolution of ve spectral lines andFe XVI @ 33.54 nm

    Mg X @ 60.98 nm

    pace Research 42 (2008) 903911 9072005). Some colder but optically thick lines such as He II(30.4 nm) and He I (53.7 nm) are also modulated, presum-ably because they are driven by coronal emissions. One ofthe most conspicuous features is a strong correlationbetween the horizontal position of the lines (i.e. theirdegree of modulation) and their emission temperature, withthe coldest ones on the left. The only exceptions are the

    05 2006 2007 2008ar

    Fe XVI @ 33.54 nm

    Mg X @ 60.98 nm

    He II @ 30.38 nm

    H I @ 121.57 nm

    Si II @ 181.69 nm

    Sunspot nr

    F10.7 index

    Ca K

    Mg II

    He I

    with normalised quantities.

    5 2006 2007 2008ar

    He II @ 30.38 nm

    H I @ 121.57 nm

    Si II @ 181.69 nm

    Sunspot nr

    F10.7 index

    Ca K

    Mg II

    He I

    ve indices. All quantities are standardised.

  • 3.5 4 4.5 5

    5

    F

    axi

    Si II

    180.

    8C

    I15

    6.1

    C I

    165.

    7Si

    II18

    1.7

    O I

    130.

    4H

    e II

    164

    Ne

    VII 4

    6.5

    C IV

    154.

    9O

    III

    70.4

    N IV

    76.5

    O IV

    78.8

    C II

    133.

    5Si

    IV14

    0.3

    O V

    63O

    IV55

    .4Si

    IV13

    9.4

    H I

    121.

    6O

    II83

    .4N

    e VI

    II 78

    l linlabispe

    908 T. Dudok de Wit et al. / Advances in Soptically thick H and He lines, whose dynamics is clearlydierent.

    The vertical axis in Fig. 4 mainly describes the level of13.5-day modulation, see Fig. 5. This axis may thereforebe associated with centre-to-limb variations that peak asexpected for hot coronal lines. Lines that are located ator below the transition region are clustered in the upper leftcorner, close to the thermal continuum.

    The main point of interest in Fig. 4 is the location ofthe indices. All of them are located in the vicinity of thecloud of spectral lines, which conrms their validity as

    5 0 5 10

    5

    0 MC H

    axis

    2

    Fig. 4. Two-dimensional connectivity map, showing 38 normalised spectrareects the degree of dissimilarity in their time evolution. The ve indices are(H), Ca K index (C) and Mg II index (M). Each wavelength of TIMED/SEEgrey level indicates the decimal logarithm of the characteristic emission temsurrogates for the EUV irradiance. A closer look, how-ever, reveals signicant dierences. No single line liesclose to the sunspot number, which means that theEUV irradiance cannot be proportional to it. This iso-lated location of the sunspot number can be explainedby its strong sensitivity to solar activity (making itappear on the far right) and its non-radiometric nature(making it insensitive to the geometric location of activeregions). The f10.7 index is better located between thecoronal lines and the colder ones, and is therefore bettersuited for EUV studies.

    The Mg II and Ca K indices in comparison appear muchcloser to the origin, where the chromospheric lines arelocated. The reason for this is their weak modulation by

    Table 1Fraction of the variance of the data that is described by the rst four axesof the connectivity map

    Axis i Normalised data [%] Vi Standardised data [%] Vi

    1 93.83 88.462 1.56 5.313 1.01 0.864 0.54 0.65

    The axes are conventionally sorted by decreasing variance.the solar cycle. These two indices are therefore appropriatefor describing the less energetic part of the EUV spectrum.Notice however that both are located slightly outside of thecluster of EUV irradiances, which means that they do notfully describe the latter.

    The He I index has been advocated for transition regionlines (Donnelly et al., 1986) and this is indeed clearly con-rmed by our plot. The third axis of the connectivity map(not shown), however, reveals a small but signicant sepa-ration that excludes an exact reproduction of any of theEUV lines. Let us also recall that this index should be inter-

    5.5 6 6.5

    15 20 25 30

    S

    s 1

    He

    II30

    .4N

    II10

    8.5

    Mg

    IX36

    .8N

    e VI

    II 77

    H I

    93.8

    He

    I53

    .7H

    I95

    O V

    I10

    3.8

    C II

    I97

    .7H

    I10

    2.6

    O V

    I10

    3.2

    He

    I58

    .4M

    g X

    61Fe

    XV

    28.4

    Fe X

    V41

    .7Si

    XII

    49.9

    Si X

    II52

    .1Fe

    XVI

    36.1

    Fe X

    VI33

    .5

    es and 5 normalised indices. The distance between each pair of quantitieselled by letters: f10.7 index (F), sunspot number (S), He I equivalent widthrepresented by a small dot, except for the 38 strongest spectral lines, whoserature. The coordinates along each axis are dened in Section 3.

    pace Research 42 (2008) 903911preted with care by lack of recent data.Some words of caution are needed regarding the inter-

    pretation of the lines. Because of the 0.4 nm spectral reso-lution of SEE, what we call a spectral line actually is ablend of emission originating from the centre of the line,its wings and often from unresolved nearby lines. This typ-ically happens with the strong He II emission at 30.38 nm,which is polluted in active regions by the weaker Si XI lineat 30.32 nm. Because of this, some lines may actually belocated slightly o their true position. This eect is hardto quantify without having access to higher resolution data.We nevertheless tested it by articially mixing some lines. Amaximum horizontal displacement of about one unit inFig. 4 is not excluded, especially for the hot coronal lines.

    A second problem is the degradation of the EUV detec-tors and the subsequent decrease in the signal-to-noiseratio. This problem is accentuated by the absence of recal-ibration since the last calibration rocket ight in October2004. We do indeed see an increase of the scatter of thepoints in the connectivity maps (especially with standar-dised data) when the analysis is restricted to more recentintervals. This increased scatter probably also has to dowith the lack of variability as compared to earlier years.An indication may be given by the number of modes that

  • 20ye

    ta (tted

    in Sare needed to properly reproduce a given spectral line.More modes are needed to describe features that exhibita more complex dynamics (Aubry et al., 1991). In our case,this additional complexity may be interpreted as a depar-ture from redundancy, i.e. an increased noise level.

    5.2. Comparison with standardised data

    The connectivity map we obtain with standardised data(Fig. 6) diers quite substantially from the one obtainedwith normalised data. The curved boundary of the cluster

    2002 2003 2004

    0.1

    0.05

    0

    0.05

    0.1

    f i(t)

    Fig. 5. Time-proles associated with the rst two axes of the normalised dadynamics is described by the dierent axes. The time series have been shif

    T. Dudok de Wit et al. / Advancesof irradiances is a consequence of the standardisation,which distributes the points on a hypersphere in 42 dimen-sions, from which we see a two-dimensional projection.The spectral lines are now packed more tightly together,except for some cold and intense chromospheric lines thatappear near the bottom. We believe this eect to be instru-mental. The lowermost lines are indeed also strong onesthat are more susceptible to degradation. Fig. 6 must there-fore be interpreted with care.

    Notice that the dierence between coronal and loweraltitude lines is now much less evident than in Fig. 4, eventhough a temperature ordering is still apparent with hotlines on the left, some transition region lines on the rightand chromospheric lines in between. Unfortunately, noneof the indices is located in the middle of any of these threeclusters. Surprisingly, the three indices that were supposedto describe low altitude regions are now found to be muchmore closely associated with coronal lines. This hadalready been noticed before (Donnelly et al., 1986; Vierecket al., 2001). The Mg II index, for example, reproduces theHe II line at 30.4 nm more eectively than the f10.7 index.All indices show about equal poor performance but thef10.7 index and the sunspot number are the leastappropriate.The representation we use in Figs. 4 and 6 has theadvantage of showing in a single glance what the relativecorrespondence between spectral lines and indices is. Thisrepresentation conrms older results but also reveals con-vincingly why and by how much some indices fail todescribe the EUV irradiance. Notice in particular that noneof the indices is located right within a cluster of spectrallines. We conclude that none of them can fully reproducethe irradiance either with a linear relationship or with adirect proportionality. The key result is that EUV indicessuch as Mg II, Ca K and He I are appropriate for describ-

    05 2006 2007 2008ar

    f1(t) normalised

    f2(t) normalised

    f1(t) standardised

    f2(t) standardised

    op) and the standardised data (bottom). These proles reveal what kind ofvertically.

    pace Research 42 (2008) 903911 909ing photospheric and chromospheric lines as far as theirlevel of variability is concerned, but that their relative vari-ations are better for reproducing coronal lines when itcomes to short-term variations. This result is an incentivefor decomposing EUV indices into dierent temporal scalesbefore trying to reconstruct the EUV irradiance from them.

    Another interesting property of Figs. 4 and 6 is worthmentioning: the connectivity map preserves distances. Anylinear combination of two quantities will therefore beapproximately located on a straight line that connects thetwo. Fig. 4, for example, shows that several spectral linescan be reconstructed from a linear combination of thef10.7 andMg II (or CaK) indices. Some could also be recon-structible using either He I and f10.7, or He I and Mg II (orCa K). The Mg II and Ca K pair, however, or any combina-tion containing the sunspot number, would be worthless.

    Ideally, the indices should be located in dierent partsof the cluster of spectral lines (for both normalisations),in order for all spectral lines to be reconstructed eec-tively. This is in contradiction with the distributions weobserve, in which the indices are either grouped together(with standardised data) or tend to be aligned (with nor-malised data). Figs. 4 and 6 thus vividly illustrate theEUV reconstruction problem by showing that no signif-

  • 0ax

    C IV

    154.

    9ith standardised data. Axis 1 is now the vertical one.

    in Sicant improvement can be expected from a linear combi-nation of indices. As long as we do not nd indices thatcover (even partly) the dierent parts of the clusters ofspectral lines, any irradiance reconstruction procedurethat is based only on indices is deemed to miss signi-cant features of the EUV variability.

    6. Conclusion

    The rst objective of this study was to nd a simple wayof determining how well EUV spectral lines can be recon-structed from various EUV proxies. We introduced a novelrepresentation that expresses the measure of relatednessbetween any pair of spectral lines or proxies; 38 EUV linesbetween 26 and 194 nm and ve EUV/UV indices (the sun-

    3.5 4 4.5

    20 15 10 52830323436384042444648

    F

    S

    MCHaxis

    1

    Fe X

    VI33

    .5Fe

    XVI

    36.1

    Mg

    IX36

    .8Fe

    XV

    41.7

    Fe X

    V28

    .4H

    e II

    30.4

    Si X

    II52

    .1Si

    XII

    49.9

    Mg

    X61

    Ne

    VII

    46.5

    Si IV

    139.

    4H

    I12

    1.6

    He

    II16

    4Si

    IV14

    0.3

    C II

    133.

    5C

    I15

    6.1

    He

    I53

    .7Fig. 6. Same connectivity map as in Fig. 4, but w

    910 T. Dudok de Wit et al. / Advancesspot number, the f10.7, Ca K, and Mg II indices, and theHe I equivalent width) were compared. This representationreadily shows why some indices are more adequate forreconstructing spectral lines that originate from one givensolar altitude.

    The second objective was to determine which indiceswould be needed for empirical modelling of spectral lines.It is dicult to give clear preference to one particular index(excluding instrumental constraints), apart from the sun-spot number, which is the least appropriate by our stan-dards. No single index can successfully describe both thelevel of variability on dierent time scales. The Mg IIand the Ca K indices are appropriate for describing thelong-term (27 days) evolution of the least-energetic partof the EUV spectrum but less so for modelling the short-term evolution. Conversely, the Mg II, Ca K and He I indi-ces are found to be rather good proxies of the short-termevolution of coronal lines. No combination of indiceswas found to be appropriate for reconstructing dierentparts of the EUV spectrum.

    The next obvious step consists in doing a multiscaleanalysis and repeat this procedure after decomposing theCenter (NOAA, Boulder) for the f10.7 and Mg II indices,and the National Solar Observatory at Kitt Peak for theHe I and Ca K data. NSO/Kitt Peak data used here are pro-duced cooperatively by NSF/NOAO, NASA/GSFC andNOAA/SEC. This work was supported by COST actiondata beforehand into dierent time scales. Anotherimprovement, which is in progress, consists in using a moregeneral measure of correlation that also gauges nonlineardependencies.

    Acknowledgements

    We gratefully acknowledge the TIMED/SEE team forproviding the EUV irradiance data, the Royal Observatoryof Belgium for the sunspot data, the Space Environment5 5.5 6 6.5

    5 10 15 20is 2

    Si II

    180.

    8H

    e I

    58.4

    C I

    165.

    7H

    I93

    .8O

    I13

    0.4

    Si II

    181.

    7N

    II10

    8.5

    H I

    95N

    e VI

    II77

    O V

    63N

    e VI

    II78

    O IV

    55.4

    C III

    97.7

    O V

    I10

    3.8

    H I

    102.

    6O

    VI

    103.

    2O

    III

    70.4

    O II

    83.4

    N IV

    76.5

    O IV

    78.8

    pace Research 42 (2008) 903911724 and by the French solar-terrestrial physics programme.

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    Which solar EUV indices are best for reconstructing the solar EUV irradiance?IntroductionSolar indices for the EUV spectral irradianceThe method: multidimensional scalingChoice of the normalisationComparison between indices and irradiancesComparison with normalised dataComparison with standardised data

    ConclusionAcknowledgementsReferences