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

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<ul><li><p>aV</p><p>tzsu</p><p>a LPCE, CNRS and University of Orleans, 3A avenue de la Recherche Scientique, 45071 Orleans, France</p><p>Using multivariate statistical methods, we represent in a single graph the measure of relatedness between these indices and various</p><p>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-</p><p>* Corresponding author.E-mail address: ddwit@cnrs-orleans.fr (T. Dudok de Wit).</p><p>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.</p><p>Available online at www.sciencedirect.com</p><p>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.</p><p>Keywords: Solar EUV irradiance; Solar EUV proxies; Solar EUV indices; Multivariate statistics</p><p>1. Introduction</p><p>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-</p><p>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</p><p>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</p><p>f LPG, CNRS and Joseph Fourier University, Batiment D de Physique, BP 53, 38041 Saint-Martin dHe`res, France</p><p>Received 31 October 2006; received in revised form 31 January 2007; accepted 4 April 2007</p><p>Abstract</p><p>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</p><p>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?</p><p>chmar b, J. Aboudarham c,che`re e, J. Lilensten f</p><p>www.elsevier.com/locate/asr</p><p>2 (2008) 903911ved.</p></li><li><p>The lack of continuous observations in the EUV is a</p><p>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.</p><p>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.</p><p>The six quantities we consider here are:The spectral irradiance measured by the Solar Extreme</p><p>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.</p><p>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.</p><p>2. Solar indices for the EUV spectral irradiance</p><p>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.</p><p>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.</p><p>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.</p><p>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).</p><p>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).</p><p>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.</p><p>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.</p><p>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</p><p>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-</p></li><li><p>00</p><p>C II</p><p>IH</p><p> IO</p><p> VI</p><p>theight</p><p>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.</p><p>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</p><p>101</p><p>102</p><p>103</p><p>104</p><p>105</p><p>106</p><p>aver</p><p>age </p><p>flux </p><p>[W/m</p><p>2 /sec</p><p>/nm</p><p>]</p><p>Fe X</p><p>VH</p><p>e II</p><p>Fe X</p><p>VIFe</p><p> XVI</p><p>Mg </p><p>IXFe</p><p> XV Ne </p><p>VII</p><p>Si X</p><p>IISi</p><p> XII</p><p>He </p><p>IO</p><p> IVH</p><p>e I</p><p>Mg </p><p>X O V</p><p>O II</p><p>IN</p><p> IV Ne </p><p>VIII</p><p>Ne </p><p>VIII</p><p>O IV</p><p>O II</p><p>H I H</p><p> I</p><p>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</p><p>T. Dudok de Wit et al. / Advances3. The method: multidimensional scaling</p><p>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</p><p>dkl Z</p><p>ykt ylt 2dts</p><p>; 1</p><p>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.</p><p>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)</p><p>ykt XNi1</p><p>Aifitgik; k 1; 2; . . . ; 43 2</p><p>120 140 160 180 200 [nm]</p><p>O V</p><p>IN</p><p> II</p><p>H I</p><p>O I</p><p>C II</p><p>Si IV</p><p>Si IV</p><p>C IV</p><p>C I H</p><p>e II C</p><p> I</p><p>Si II Si</p><p> II</p><p>variability of the irradiance between February 2002 and May 2006. The 38H I Lyman-a emission.</p><p>pace Research 42 (2008) 903911 905with the orthonormality constraint</p><p>hfitfjti hgikgjki 0 if i 6 j1 if i j</p><p>; 3</p><p>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</p><p>V i A2iPN</p><p>j1A2j</p><p>: 4</p><p>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-</p></li><li><p>in Snections between solar emission processes at dierentaltitudes.</p><p>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.</p><p>4. Choice of the normalisation</p><p>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:</p><p>(1) The default choice in statistics is standardisation</p><p>ykt !yk ykrk</p><p>5</p><p>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...</p></li></ul>