Retrieving the solar EUV spectral irradiance from the observation of 6 lines
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osphere Mesosphere Energetics and Dynamics satellite to investigate the possibility to retrieve the whole solar EUV irradiance from
tainly amongst the most important parameters to mon-
sphere Explorer missions in July 1976 (the radio ux at
ods of solar activity. Torr et al. (1979) and Torr and
iska et al., 2000). Another model is EUVAC (Richards
et al., 1994). Its main dierence with previous modelsis the reference ux chosen from a rocket observation,
and denes a modied F10.7 proxy named P10.7 that
is the average of the daily F10.7 and the 81-day
* Corresponding author.
E-mail address: email@example.com (M. Kretzsch-
Advances in Space Research 370273-1177/$30 2005 COSPAR. Published by Elsevier Ltd. All rightsitor and forecast space weather. It constitutes the rst
and main source for the creation of the ionosphere
and also aects the thermosphere. The EUV emission
is strongly variable in all time scale, from minutes (erup-
tive phenomena) to years (solar cycle) and more.
In order to reach a better understanding of thesepoints, it is necessary to have real time solar EUV irra-
diance with the best possible radiometric accuracy. Sev-
eral solar EUV irradiance models have been developed
since the 1970s to compensate the lack of observations.
A rst reference irradiance spectrum SC#21REF was
assembled from measurements performed by the Atmo-
Torr (1985) proposed two reference irradiance spectra
for aeronomy called F79050N (F10.7 = 243) and
SC#REFW (F10.7 = 68). The UV spectrum was divided
in 37 bins. Tobiska and co-authors (Tobiska and Barth,
1990; Tobiska, 1991; Tobiska and Eparvier, 1998) devel-
oped a model called EUV97, which takes data fromother sources into account. This model takes into ac-
count the solar emission zone (i.e. chromosphere, coro-
na) of each line. A new version, SOLAR2000, has been
recently developed and uses F10.7, Lyman-a, and Mg IIcore-to-wing (C/W) index for the coronal, transition re-
gion, and chromospheric emissions, respectively (Tob-a minimum number of measurements. Computing a dierential emission measure for the whole Sun from the irradiances of 5 lines
and using a sixth line to model optically thick emission, we are able to reproduce with a good agreement the variability of the whole
solar EUV irradiance.
2005 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Solarterrestrial relationship; Solar EUV irradiance; Dierential emission measure
The extreme ultraviolet (EUV) solar irradiance is cer-
10.7 cm F10.7 was 70), and given in 1659 wavelengths.
An extrapolation model (SERF1, Hinteregger et al.,1981) allows estimating the irradiance during other peri-Retrieving the solar EUVobservatio
M. Kretzschmar a,*, J. L
a Istituto di Fisica dello Spazio Interplanetario, CNR,b LPG, Bat. D de physique, BP 53, 3
c LESIA, Observatoire de
Received 25 October 2004; received in revised
We use recent solar extreme ultraviolet (EUV) irradiance dadoi:10.1016/j.asr.2005.02.029ectral irradiance from theof 6 lines
sten b, J. Aboudarham c
l Fosso del Cavaliere, 100, BP 53, 00133 Roma, Italy
Saint Martin dHe`res cedex, FranceF-92190 Meudon, France
4 February 2005; accepted 14 February 2005
om the Solar EUV Experiment aboard the Thermosphere Ion-
in Spsmoothed F10.7. An important improvement to the EU-
VAC model was the increase of the solar irradiance, as
compared to earlier models, by a factor of 23 in the
020 nm range in order to match the photoelectron
observations. Warren and co-authors (Warren et al.,
1998, 2001) have undertaken a radically dierent ap-proach. They combined a spectral emission line data-
base, solar emission measure distributions, and
estimates from ground-based solar images of the frac-
tion of the Sun covered by the various types of activity
to synthesize the irradiance. One can thus distinguish
two class of model: the rst one is based on a reference
irradiance spectrum and its extrapolation using proxies,
while the second one is based on a combination of refer-ence radiance spectra for the dierent features of the so-
All of these solar irradiance models are very impor-
tant for aeronomic computation and as input for atmo-
spheric models. However, until 2002 there has been no
permanent monitoring of the solar EUV irradiance,
and the lack of data has prevented accurate enough
modeling of the solar EUV irradiance. Yet, thermo-sphere/ionosphere (T/I) models often make use of prox-
ies such as F10.7 or the Mg index (Mg II h and k
emission lines core to wing ratio). Their correlation with
the solar EUV/UV irradiance is not accurate enough for
the demanding space weather operation requirement to
know the solar EUV irradiance with a relative accuracy
of 10% or better. In December 2001, a new instrument
devoted to the observation of this part of the solar spec-trum has been launched to space, onboard the Thermo-
sphere Ionosphere Mesosphere Energetics and
Dynamics (TIMED) (NASA) spacecraft. The Solar
EUV Experiment (SEE) (Woods et al., 1998) is com-
prised of a spectrometer and a suite of photometers de-
signed to measure solar ultraviolet radiation. In this
paper, we use TIMED SEE data version 7 of the EUV
Grating Spectrograph (EGS) to investigate the possibil-ity to retrieve the solar EUV irradiance with spectral res-
olution from a minimum set of line irradiance
measurements; this approach is supported by a statisti-
cal analysis of the solar EUV spectrum, based on clus-
tering analysis and dendogram classication which
shows that at least 6 classes of equivalence could be
drawn in the solar spectrum (Dudok de Wit, personal
communication).In detail, we succeed in reproducing the solar EUV
irradiance and its variability from the measurements of
6 lines. The spectrum reconstruction makes use of a pre-
vious work aiming at building a quiet Sun reference
spectrum using dierential emission measure (DEM)
(Kretzschmar et al., 2004); the optically thin part of
the spectrum, i.e. the part which escapes freely from
the Solar atmosphere, is computed using a Full SunDEM, while the optically thick part is deduced from
342 M. Kretzschmar et al. / Advancesthe measurement of the H I Ly d line at 95 nm.2. EUV irradiance spectrum modeling
The TIMED SEE EGS consists of two instruments to
measure the solar vacuum ultraviolet (VUV) spectral
irradiance from 0.1 nm to 195 nm (Woods et al.,
1998). The EUV Grating Spectrograph (EGS) is a nor-mal incidence Rowland circle spectrograph that has a
spectral range of 26 to 195 nm. The SEE level 2 EGS
data product consists of a spectrum from 26 to 195
nm per day. The uxes are averaged over all the mea-
surements of the day (typically 1415 recording se-
quences of about 3 min) and corrected to one
astronomical unit. Flare contribution is removed. In this
work, we use the data from 8 February 2002 to 1 Febru-ary 2004.
To reproduce the whole EUV spectrum from a min-
imum number of emission lines, we distinguish between
optically thin and optically thick emission: the latter is
assumed to be composed of the continua of C I, H I,
He I, and He II, some lines emitted between 91 and
110 nm by low-ionized elements, and the blue wing
of the H I Ly a line. Contrary to the optically thinlines, optically thick lines cannot be deduced from a
DEM. We rst describe the procedure for optically
2.1. Optically thin emission
Assuming that a EUV line is optically thin, its inten-
sity may be computed from the following equation:
Ikij; h;/ Z
Gkij; T fT ; h;/ dT ; 1
where G(kij,T) is the contribution function of the line,which depends on atomic parameters, and
fT ; h;/ n2e dlh;/dT is the dierential emission measure(DEM) for which the dependance with the foot point
position of the line of sight has been made explicit.
The extension of Eq. (1) to the whole Sun is quietstraightforward. Dening the Full Sun DEM fx(T) byIx = G(T)fx(T) dT, with Ix the mean solar intensityat disk center deduced from the line irradiance measure-
ment, it can then be easily shown that the Full Sun
DEM is linked to the local DEMs by
d/fT ; h;/sin2h cos/: 2
Thus, the Full Sun DEM fx dened this way is simplythe sum over the half solar sphere of all the DEMs asso-ciated with each surface element, taking into account the
geometry and the change of emitting plasma state. Note
that one cannot retrieve information on the spatial dis-tribution of the emission measure from fx. Eq. (1) al-lows us to compute the DEM from a set of observed
lines. Once the DEM computed, one is able to compute
ace Research 37 (2006) 341346the intensity of all the others optically thin lines.
The inversion of Eq. (1) involves the computation of
the contribution functions of the lines, and an adapted
mathematical procedure. We compute the contribution
functions using the CHIANTI database (Dere et al.,
2001), solar abundances from Meyer (1985), and ioniza-
tion equilibria computed by Arnaud and Raymond(1992) and Arnaud and Rothenug (1985). The DEM
is represented by the exponential of a Chebyshev poly-
nomial, and we use a LevenbergMarquardt algorithm
to compute it.
The computation of the DEM is a very (and well-
known, see Craig and Brown, 1986) ill-posed mathemat-
ical problem, and our main criterion for the choice of
the lines is simply the success of the computation, as wellas its reproducibility; to this purpose, note that the more
recent ionization equilibria computed by Mazzotta et al.
(1998) lead to less stable computation of the DEM.
While the reason is unclear, this explains while we use
older computations. Starting with 30 intense lines and
using a try and test approach to select the subset,
we found that the lowest number of lines which leads
to a good agreement is 5. The contribution functionsof the 5 lines forming the best subset and the computed
DEM obtained for the rst day of observation are
shown in Fig. 1. Note that not all of the 5-lines subset
10-8C III 97.7
O IV 55.5 Fe XVI 33.5
M. Kretzschmar et al. / Advances in Sp1018
104 105 106 107
N II 108.5Ne VII 46.5
Fig. 1. (Top) Contribution functions for the 5 lines of the best set.
(Bottom) Full Sun DEM for the rst day of observation (full line)
compared with the DEM for the quiet Sun region of Kretzschmaret al. (2004) (dotted).allows to compute the DEM; in fact, only some lines
of the set of Fig. 1 may be changed (such that using an-
other Fe XVI line), and the results obtained in these case
were found to be less satisfying.
2.2. Optically thick emission
Optically thick emission can not be modeled using the
DEM approach. These continua and lines are empiri-
cally deduced from the measurement of one of them.
We chose the H I Ly d line at 95 nm as our observed in-dex, its value coming directly from the EGS data; this
choice is motivated by the relative isolated spectral posi-
tion of this line, which makes it easier to measure. Thespectral evolution of the continua and of the blue wing
of the Ly a line is modeled as Ik Ih expkkhk0 , withthe decay values kh assumed constant for each contin-uum. The optically thick lines intensities and the peak
intensity Ih of each continuum are assumed to be pro-
portional to the H I Ly d intensity. Ratio values are ta-ken from two averaged quiet Sun spectra previously
published; in detail, values for the emission of He I,He II, and Ly a are taken from Warren et al. (1998)while the others values, including several lines of low-
ionized elements between 91 nm and 120 nm, come from
Kretzschmar et al. (2004). However, neither of the two
published values for the Lyman continuum was in agree-
ment with the observation, and we then use the average
slope (k0 = 57.46) and ratio (Ih/ILy d = 7.3) over allthe samples at our disposition.
2.3. Discussion on the best subset of lines
The best subset of lines that we found in that study
should include the emission lines which are the most rep-
resentative of the dierent kinds of variation; however,
other factors might play a role in our method. In partic-
ular, the contribution function of the lines, whichstrongly inuence the inversion of Eq. (1), and the math-
ematical procedure used to eectively inverse this equa-
tion might restrict the capacity of this method to identify
unambiguously the most representative lines. To tackle
this problem, we have started a statistical analysis of
the solar EUV spectrum, based on clustering analysis
and dendogram classication, which allows to identify
rigorously other valuable set of lines; results from thisanalysis will be published elsewhere (Dudok de Wit, per-
sonal communication) and the method presented here
will then be adapted to the other relevant set of lines.
This will allow to address instrument issues on this mod-
eling approach and discuss in more detail its technical
feasibility. Possible instrument issues include spectral
resolution, higher grating order corrections, and degra-
dation with time. Spectral resolution is important in or-der to remove contributions from other lines. For the
ace Research 37 (2006) 341346 343subset here selected, the N II emission may have coronal
thick emission dominates (i.e. the Lyman continuum,and above 90 nm) are also reasonably reproduced. The
DEM, the optically thin and the optically thick parts
of the modeled spectrum. For each day, we can thus
reconstruct the spectrum as shown in Fig. 2 and compare
ux ( W
Fig. 2. For each panel, observed (dashed) and modeled (full line)
spectra vs wavelength for the rst day of observation. The small upper
plot of each panel shows the relative deviation (Fmodel Fobs)/Fobsbetween 1 and 1, with a zero dashed line. The 5 lines used to computethe optically thin part of the spectrum are highlighted with a rectangle,
while the line used to determinate the optically thick part is highlighted
with an oval.
in Space Research 37 (2006) 341346relative deviation for the integrated irradiance over the
whole spectral range is 17% while the mean relativedeviation is 15%. Local disagreements for the linesmay come from one or more failures of the hypothesis
and/or errors in the atomic parameters.
It is also interesting to check the capacity of our model
to reproduce the solar EUV variability time series. Weuse an automatic procedure which extracts the irradiancecontribution from higher order. Since the C III line at
97.7 nm is very intense, detector degradation in time
should also be taken into account. As optically thick
emission is computed using a constant ratio between
these lines, all optically thick line should give the same
results. However the H I ly d line is quite spectrally iso-lated and then should be easier to measure. An alterna-
tive solution could be the strong He I line at 58.4 nm.
The spectral range of the modeled spectra here pre-
sented is 26 nm 6 k 6 110 nm. The lower limit corre-sponds to the lower bound of the EGS spectrum while
the upper limit corresponds to the usual upper limit in
the EUV irradiance models. We plan to extend the
model output in the XUV range; a preliminary analysis
suggest that the model underestimates the irradiance at
short wavelength and that we must add other emission
lines and/or emission mechanisms. Fig. 2 shows the
TIMED-SEE spectrum measured on 8 February 2002,with the one deduced from the 6 lines; the lines of the
computed spectrum have been convoluted with a Gauss-
ian prole with a 3 A width. The background emission
in the computed spectrum is generally 60% lower below
70 nm; a part of this disagreement can be explained by
the dierence between observed and computed line pro-
les. As can be seen from the plots of the relative devi-
ation, the distribution of the photons in the core and thefar wings of the prole is badly reproduced while the
integrated irradiance is in better agreement (see for
example the line at 58 nm). However, this alone can-not explain the whole disagreement and it is yet not clear
if this lower computed irradiance is due to the lack of
numerous low intensity emission lines in our model, or
if other emission processes have to be included. Another
possibility is that the correction for grating scatteredlight might not be large enough in the EGS data at these
shorter wavelengths. Brekke et al. (2000) show higher
wing results for the rocket EGS data as compared
to the higher spectral resolution measurements by
All the observed intense EUV lines appear in our
model and the parts of the spectrum where optically
344 M. Kretzschmar et al. / Advancesof the 6 lines from the SEE spectrum, computes the our results with the original observed irradiance. Fig. 3
shows this comparison for 5 wavelength bins in the for-
mat generally used by T/I modelers (Torr et al., 1979).
The irradiance of the 3035 nm bin is dominated by coro-
nal lines near 1 MK (the contribution from the He II line
at 30.34 nm is subtracted and the emission is then dom-
inated by lines Mg VIII, Si VIII, Al VIII, Al X and theblue wing of a Fe XIV line), the He I line at 58.43 nm
and H I Ly b line at 102.5 nm are optically thick, theO IV line at 78.9 nm is emitted in the solar transition re-
gion, and the 8590 nm bin is dominated by the Lyman
continuum. These dierences are well represented by the
In this work, we have shown that the solar EUV irra-
diance and its variability may be reproduced with a
We gratefully acknowledge Tom Woods (LASP,
Boulder) team for providing the SEE/EGS data and
He I 58.43 nm
O IV 78.9 nm
H I 102.5 nm
M. Kretzschmar et al. / Advances in Sp1.2
Fig. 3. Observed (dotted) and computed (dashed) variations for
several EUV bins. irradiance have been normalized to the rst day.
Rms of the relative deviation (Icalc Iobs)/Iobs between computed andobserved ux are, respectively (from top to bottom) 0.015, 0.016,0.011, 0.003, and 0.011.Thierry Dudok de Wit (LPCE, Orleans) for useful dis-cussions. The TIMED spacecraft was developed by the
Johns Hopkins University Applied Physics Laboratory.
The TIMED mission, including the SEE instrument, is
sponsored by NASAs Oce of Space Science. CHI-ANTI is a collaborative project involving the NRL
(USA), RAL (UK), and the Universities of Florence
(Italy) and Cambridge (UK). MK acknowledges sup-
port by the European Communitys Human PotentialProgram under contract HPRN-CT-2001-00314 Tur-good precision from the observation of 6 lines. In partic-
ular, the mid-term variability has been recovered suc-
cessfully by this method which, in our opinion, may be
a good candidate to model the solar EUV irradiance
variability at shorter time scale, where eruptions take
place.In order to investigate furthermore the possibility to
retrieve the solar EUV irradiance from the observation
of a few lines, we refer to a statistical analysis in progress
of the solar EUV spectrum which aims at identifying
other relevant subset of lines (Dudok de Wit, personal
communication). The method to reconstruct the EUV
spectrum presented here will then be adapted to these
other subsets, with protable comparison of the results,and more instrument oriented discussion.
This method relies on the direct observation of 6 solar
EUV lines without spatial resolution and has good po-
tential to predict the solar irradiance at all EUV wave-
lengths at possibly a lower instrument cost than a
spectrograph that observes over the full EUV range.
However, the good results obtained here through the
Full Sun DEM computation can be of interests for otherexperiments, such as those for solar imaging.
Acknowledgmentsdierences in the amplitude of the irradiance variations
for these bins in Fig. 3. As seen from the closed vicinity
of the curves for each boxes, our model is able to repro-
duce with a good precision the long term (decrease due to
the descending phase of the solar cycle) and mid term
(solar rotation with period of 27 days) variations. More-over, the amplitude of the solar rotation eect and its
dependance on wavelengths are well reproduced, as visi-
ble for the strong irradiance enhancement at the end of
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346 M. Kretzschmar et al. / Advances in Space Research 37 (2006) 341346
Retrieving the solar EUV spectral irradiance from the observation of 6 linesIntroductionEUV irradiance spectrum modelingOptically thin emissionOptically thick emissionDiscussion on the best subset of lines