Author name code: yeo
ADS astronomy entries on 2022-09-14
author:Yeo, Kok Leng
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Title: Reconstructing solar irradiance from historical Ca II K
    observations. I. Method and its validation
Authors: Chatzistergos, Theodosios; Krivova, Natalie A.; Ermolli,
   Ilaria; Yeo, Kok Leng; Mandal, Sudip; Solanki, Sami K.; Kopp, Greg;
   Malherbe, Jean-Marie
Bibcode: 2021A&A...656A.104C
Altcode: 2021arXiv210905844C
  Context. Knowledge of solar irradiance variability is critical to
  Earth's climate models and understanding the solar influence on Earth's
  climate. Direct solar irradiance measurements have only been available
  since 1978. Reconstructions of past variability typically rely on
  sunspot data. However, sunspot records provide only indirect information
  on the facular and network regions, which are decisive contributors to
  irradiance variability on timescales of the solar cycle and longer. <BR
  /> Aims: Our ultimate goal is to reconstruct past solar irradiance
  variations using historical full-disc Ca II K observations to describe
  the facular contribution independently of sunspot observations. Here,
  we develop the method and test it extensively by using modern CCD-based
  (charge-coupled device) Ca II K observations. We also carry out initial
  tests on two photographic archives. <BR /> Methods: We employ carefully
  reduced and calibrated Ca II K images from 13 datasets, including some
  of the most prominent series, such as those from the Meudon, Mt Wilson,
  and Rome observatories. We convert them to unsigned magnetic field
  maps and then use them as input to the adapted Spectral and Total
  Irradiance Reconstruction (SATIRE) model to reconstruct total solar
  irradiance (TSI) variations over the period 1978-2019, for which
  direct irradiance measurements are available. <BR /> Results: The
  reconstructed irradiance from the analysed Ca II K archives agrees well
  with direct irradiance measurements and existing reconstructions. The
  model also returns good results on data taken with different bandpasses
  and images with low spatial resolution. Historical Ca II K archives
  suffer from numerous inconsistencies, but we show that these archives
  can still be used to reconstruct TSI with reasonable accuracy provided
  the observations are accurately processed and the effects of changes
  in instrumentation and instrumental parameters are identified and
  accounted for. The reconstructions are relatively insensitive to the
  TSI reference record used to fix the single free parameter of the
  model. Furthermore, even employment of a series, itself reconstructed
  from Ca II K data, as a reference for further reconstructions returns
  nearly equally accurate results. This will enable the Ca II K archives
  without an overlap with direct irradiance measurements to be used to
  reconstruct past irradiance. <BR /> Conclusions: By using the unsigned
  magnetic maps of the Sun reconstructed from modern high-quality Ca
  II K observations as input into the SATIRE model, we can reconstruct
  solar irradiance variations nearly as accurately as from directly
  recorded magnetograms. Historical Ca II K observations can also be
  used for past irradiance reconstructions but need additional care,
  for example identifying and accounting for discontinuities and changes
  in the quality of the data with time.

Title: The relationship between bipolar magnetic regions and their
    sunspots
Authors: Yeo, K. L.; Solanki, S. K.; Krivova, N. A.; Jiang, J.
Bibcode: 2021A&A...654A..28Y
Altcode: 2021arXiv210914313Y
  Context. The relationship between bipolar magnetic regions (BMRs)
  and their sunspots is an important property of the solar magnetic
  field, but it is not well constrained. One consequence is that it is a
  challenge for surface flux transport models (SFTMs) based on sunspot
  observations to determine the details of BMR emergence, which they
  require as input, from such data. <BR /> Aims: We aimed to establish
  the relationship between the amount of magnetic flux in newly emerged
  BMRs and the area of the enclosed sunspots, and examine the results
  of its application to an established SFTM. <BR /> Methods: Earlier
  attempts to constrain BMR magnetic flux were hindered by the fact that
  there is no extensive and reliable record of the magnetic and physical
  properties of newly emerged BMRs currently available. We made use of
  the empirical model of the relationship between the disc-integrated
  facular and network magnetic flux and the total surface coverage by
  sunspots reported in a recent study. The structure of the model is such
  that it enabled us to establish, from these disc-integrated quantities,
  an empirical relationship between the magnetic flux and sunspot area
  of individual newly emerged BMRs, circumventing the lack of any proper
  BMR database. <BR /> Results: Applying the constraint on BMR magnetic
  flux derived here to an established SFTM retained its key features,
  in particular its ability to replicate various independent datasets
  and the correlation between the model output polar field at the end
  of each cycle and the observed strength of the following cycle. The
  SFTM output indicates that facular and network magnetic flux rises
  with increasing sunspot magnetic flux at a slowing rate such that
  it appears to gradually saturate. This is analogous to what earlier
  studies comparing disc-integrated quantities sensitive to the amount
  of faculae and network present to sunspot indices had reported. The
  activity dependence of the ratio of facular and network flux to sunspot
  flux is consistent with the findings of recent studies: although the
  Sun is faculae-dominated (such that its brightness is mostly positively
  correlated with activity), it is only marginally so as facular and
  network brightening and sunspot darkening appear to be closely balanced.

Title: Modeling Stellar Ca II H and K Emission Variations. I. Effect
    of Inclination on the S-index
Authors: Sowmya, K.; Shapiro, A. I.; Witzke, V.; Nèmec, N. -E.;
   Chatzistergos, T.; Yeo, K. L.; Krivova, N. A.; Solanki, S. K.
Bibcode: 2021ApJ...914...21S
Altcode: 2021arXiv210313893S
  The emission in the near-ultraviolet Ca II H and K lines is modulated
  by stellar magnetic activity. Although this emission, quantified via
  the S-index, has been serving as a prime proxy of stellar magnetic
  activity for several decades, many aspects of the complex relation
  between stellar magnetism and Ca II H and K emission are still
  unclear. The amount of measured Ca II H and K emission is suspected
  to be affected not only by the stellar intrinsic properties but
  also by the inclination angle of the stellar rotation axis. Until
  now, such an inclination effect on the S-index has remained largely
  unexplored. To fill this gap, we develop a physics-based model to
  calculate S-index, focusing on the Sun. Using the distributions of
  solar magnetic features derived from observations together with Ca II
  H and K spectra synthesized in non-local thermodynamic equilibrium,
  we validate our model by successfully reconstructing the observed
  variations of the solar S-index over four activity cycles. Further,
  using the distribution of magnetic features over the visible solar
  disk obtained from surface flux transport simulations, we obtain
  S-index time series dating back to 1700 and investigate the effect
  of inclination on S-index variability on both the magnetic activity
  cycle and the rotational timescales. We find that when going from
  an equatorial to a pole-on view, the amplitude of S-index variations
  decreases weakly on the activity cycle timescale and strongly on the
  rotational timescale (by about 22% and 81%, respectively, for a cycle
  of intermediate strength). The absolute value of the S-index depends
  only weakly on the inclination. We provide analytical expressions that
  model such dependencies.

Title: Modelling Solar Ca II H&amp;K Emission Variations
Authors: Krishnamurthy, Sowmya; Shapiro, Alexander I.; Witzke,
   Veronika; Nèmec, Nina-E.; Chatzistergos, Theodosis; Yeo, Kok Leng;
   Krivova, Natalie A.; Solanki, Sami K.
Bibcode: 2021csss.confE.154K
Altcode:
  The emission in the near ultraviolet Ca II H&amp;K lines, often
  quantified via the S-index, has been serving as a prime proxy of solar
  and stellar magnetic activity. Despite the broad usage of the S-index,
  the link between the coverage of a stellar disk by magnetic features
  and Ca II H&amp;K emission is not fully understood. In order to fill
  this gap we developed a physics-based model to calculate the solar
  S-index. To this end, we made use of the distributions of the solar
  magnetic features derived from the simulations of magnetic flux
  emergence and surface transport, together with the Ca II H&amp;K
  spectra synthesized using a non-local thermodynamic equilibrium
  (non-LTE) radiative transfer code.We show that the value of the
  solar S-index is influenced by the inclination angle between the
  solar rotation axis and the observer's line-of-sight, i.e. the solar
  S-index values obtained by an out-of-ecliptic observer are different
  from those obtained by an ecliptic-bound observer. This is important
  for comparing the magnetic activity of the Sun to other stars. We
  computed time series of the S-index as they would be observed at
  various inclinations dating back to 1700. We find that depending on
  the inclination and period of observations, the activity cycle in solar
  S-index can appear weaker or stronger than in stars with a solar-like
  level of magnetic activity. We show that there is nothing unusual
  about the solar chromospheric emission variations in the context of
  stars with near-solar magnetic activity.

Title: Reconstructing solar irradiance from Ca II K observations
Authors: Chatzistergos, T.; Krivova, N.; Ermolli, I.; Yeo, K. L.;
   Solanki, S. K.; Puiu, C. C.; Giorgi, F.; Mandal, S.
Bibcode: 2020AGUFMA237...10C
Altcode:
  To understand the influence of the Sun on Earth's system, long and
  accurate measurements of solar irradiance are a prerequisite. The
  available direct measurements of solar irradiance since 1978 are
  clearly not sufficient for this purpose. This stimulated development
  of models used to reconstruct past solar irradiance variations from
  alternative observations. The main driver of the irradiance variations
  on time scales of days to millennia is the evolution of the solar
  surface magnetic field in form of dark sunspots and bright faculae
  and network. Therefore, models require input data describing the
  contributions of these various magnetic regions on the Sun at earlier
  times. Unfortunately, records that can be used to describe the facular
  and network contributions are barely longer than the direct irradiance
  measurements. Thus, irradiance reconstructions to earlier periods have
  to rely on sunspot data alone. Data that have hardly been used for solar
  irradiance reconstructions until now are full-disc solar observations in
  the Ca II K line. Such data exist since 1892 from various observatories
  and include all the needed information describing faculae and the
  network. However, they are plagued by a bunch of various problems and
  artefacts, and recovering the non-linear response of the photographic
  material to the radiation is non-trivial since the required information
  is usually missing, too. We have developed a method to process Ca II K
  observations from various sources and demonstrated the higher accuracy
  achieved by our method compared to other techniques presented in the
  literature. Here we use the carefully reduced Ca II K observations
  from multiple archives to reconstruct solar irradiance variations.

Title: How faculae and network relate to sunspots, and the
    implications for solar and stellar brightness variations(Corrigendum)
Authors: Yeo, K. L.; Solanki, S. K.; Krivova, N. A.
Bibcode: 2020A&A...642C...2Y
Altcode:
  No abstract at ADS

Title: The Dimmest State of the Sun
Authors: Yeo, K. L.; Solanki, S. K.; Krivova, N. A.; Rempel, M.;
   Anusha, L. S.; Shapiro, A. I.; Tagirov, R. V.; Witzke, V.
Bibcode: 2020GeoRL..4790243Y
Altcode: 2021arXiv210209487Y
  How the solar electromagnetic energy entering the Earth's atmosphere
  varied since preindustrial times is an important consideration in
  the climate change debate. Detrimental to this debate, estimates
  of the change in total solar irradiance (TSI) since the Maunder
  minimum, an extended period of weak solar activity preceding the
  industrial revolution, differ markedly, ranging from a drop of 0.75
  W m<SUP>-2</SUP> to a rise of 6.3 W m<SUP>-2</SUP>. Consequently, the
  exact contribution by solar forcing to the rise in global temperatures
  over the past centuries remains inconclusive. Adopting a novel approach
  based on state-of-the-art solar imagery and numerical simulations, we
  establish the TSI level of the Sun when it is in its least-active state
  to be 2.0 ± 0.7 W m<SUP>-2</SUP> below the 2019 level. This means TSI
  could not have risen since the Maunder minimum by more than this amount,
  thus restricting the possible role of solar forcing in global warming.

Title: How faculae and network relate to sunspots, and the
    implications for solar and stellar brightness variations
Authors: Yeo, K. L.; Solanki, S. K.; Krivova, N. A.
Bibcode: 2020A&A...639A.139Y
Altcode: 2020arXiv200614274Y
  Context. How global faculae and network coverage relates to that
  of sunspots is relevant to the brightness variations of the Sun and
  Sun-like stars. <BR /> Aims: We aim to extend and improve on earlier
  studies that established that the facular-to-sunspot-area ratio
  diminishes with total sunspot coverage. <BR /> Methods: Chromospheric
  indices and the total magnetic flux enclosed in network and faculae,
  referred to here as "facular indices", are modulated by the amount
  of facular and network present. We probed the relationship between
  various facular and sunspot indices through an empirical model, taking
  into account how active regions evolve and the possible non-linear
  relationship between plage emission, facular magnetic flux, and sunspot
  area. This model was incorporated into a model of total solar irradiance
  (TSI) to elucidate the implications for solar and stellar brightness
  variations. <BR /> Results: The reconstruction of the facular indices
  from the sunspot indices with the model presented here replicates
  most of the observed variability, and is better at doing so than
  earlier models. Contrary to recent studies, we found the relationship
  between the facular and sunspot indices to be stable over the past four
  decades. The model indicates that, like the facular-to-sunspot-area
  ratio, the ratio of the variation in chromospheric emission and
  total network and facular magnetic flux to sunspot area decreases
  with the latter. The TSI model indicates the ratio of the TSI excess
  from faculae and network to the deficit from sunspots also declines
  with sunspot area, with the consequence being that TSI rises with
  sunspot area more slowly than if the two quantities were linearly
  proportional to one another. This explains why even though solar cycle
  23 is significantly weaker than cycle 22, TSI rose to comparable levels
  over both cycles. The extrapolation of the TSI model to higher activity
  levels indicates that in the activity range where Sun-like stars are
  observed to switch from growing brighter with increasing activity to
  becoming dimmer instead, the activity-dependence of TSI exhibits a
  similar transition. This happens as sunspot darkening starts to rise
  more rapidly with activity than facular and network brightening. This
  bolsters the interpretation of this behaviour of Sun-like stars as
  the transition from a faculae-dominated to a spot-dominated regime.

Title: Readdressing the UV solar variability with SATIRE-S: non-LTE
    effects
Authors: Tagirov, R. V.; Shapiro, A. I.; Krivova, N. A.; Unruh, Y. C.;
   Yeo, K. L.; Solanki, S. K.
Bibcode: 2019A&A...631A.178T
Altcode: 2019arXiv190911736T
  Context. Solar spectral irradiance (SSI) variability is one of the key
  inputs to models of the Earth's climate. Understanding solar irradiance
  fluctuations also helps to place the Sun among other stars in terms of
  their brightness variability patterns and to set detectability limits
  for terrestrial exoplanets. <BR /> Aims: One of the most successful
  and widely used models of solar irradiance variability is Spectral
  And Total Irradiance REconstruction model (SATIRE-S). It uses spectra
  of the magnetic features and surrounding quiet Sun that are computed
  with the ATLAS9 spectral synthesis code under the assumption of local
  thermodynamic equilibrium (LTE). SATIRE-S has been at the forefront
  of solar variability modelling, but due to the limitations of the LTE
  approximation its output SSI has to be empirically corrected below
  300 nm, which reduces the physical consistency of its results. This
  shortcoming is addressed in the present paper. <BR /> Methods: We
  replaced the ATLAS9 spectra of all atmospheric components in SATIRE-S
  with spectra that were calculated using the Non-LTE Spectral SYnthesis
  (NESSY) code. To compute the spectrum of the quiet Sun and faculae,
  we used the temperature and density stratification models of the FAL
  set. <BR /> Results: We computed non-LTE contrasts of spots and faculae
  and combined them with the corresponding fractional disc coverages,
  or filling factors, to calculate the total and spectral irradiance
  variability during solar cycle 24. The filling factors have been derived
  from solar full-disc magnetograms and continuum images recorded by
  the Helioseismic and Magnetic Imager on Solar Dynamics Observatory
  (SDO/HMI). <BR /> Conclusions: The non-LTE contrasts yield total and
  spectral solar irradiance variations that are in good agreement with
  empirically corrected LTE irradiance calculations. This shows that
  the empirical correction applied to the SATIRE-S total and spectral
  solar irradiance is consistent with results from non-LTE computations.

Title: Recovering the unsigned photospheric magnetic field from Ca
    II K observations
Authors: Chatzistergos, Theodosios; Ermolli, Ilaria; Solanki, Sami K.;
   Krivova, Natalie A.; Giorgi, Fabrizio; Yeo, Kok Leng
Bibcode: 2019A&A...626A.114C
Altcode: 2019arXiv190503453C
  Context. A number of studies have aimed at defining the exact form
  of the relation between magnetic field strength and Ca II H and K
  core brightness. All previous studies have however been restricted
  to isolated regions on the solar disc or to a limited set of
  observations. <BR /> Aims: We reassess the relationship between the
  photospheric magnetic field strength and the Ca II K intensity for
  a variety of surface features as a function of the position on the
  disc and the solar activity level. This relationship can be used to
  recover the unsigned photospheric magnetic field from images recorded
  in the core of Ca II K line. <BR /> Methods: We have analysed 131
  pairs of high-quality, full-disc, near-co-temporal observations from
  the Helioseismic and Magnetic Imager (SDO/HMI) and Precision Solar
  Photometric Telescope (Rome/PSPT) spanning half a solar cycle. To
  analytically describe the observationally determined relation, we
  considered three different functions: a power law with an offset,
  a logarithmic function, and a power-law function of the logarithm
  of the magnetic flux density. We used the obtained relations to
  reconstruct maps of the line-of-sight component of the unsigned
  magnetic field (unsigned magnetograms) from Ca II K observations,
  which were then compared to the original magnetograms. <BR /> Results:
  We find that both power-law functions represent the data well, while
  the logarithmic function is good only for quiet periods. We see
  no significant variation over the solar cycle or over the disc in
  the derived fit parameters, independently of the function used. We
  find that errors in the independent variable, which are usually
  not accounted for, introduce attenuation bias. To address this, we
  binned the data with respect to the magnetic field strength and Ca II
  K contrast separately and derived the relation for the bisector of
  the two binned curves. The reconstructed unsigned magnetograms show
  good agreement with the original ones. Root mean square differences
  are less than 90 G. The results were unaffected by the stray-light
  correction of the SDO/HMI and Rome/PSPT data. <BR /> Conclusions:
  Our results imply that accurately processed and calibrated Ca II K
  observations can be used to reconstruct unsigned magnetograms by using
  the relations derived in our study.

Title: Intensity contrast of solar network and
    faculae. II. Implications for solar irradiance modelling
Authors: Yeo, K. L.; Krivova, N. A.
Bibcode: 2019A&A...624A.135Y
Altcode: 2021arXiv210209530Y
  <BR /> Aims: We aim to gain insight into the effect of network
  and faculae on solar irradiance from their apparent intensity. <BR
  /> Methods: Taking full-disc observations from the Solar Dynamics
  Observatory, we examined the intensity contrast of network and faculae
  in the continuum and core of the Fe I 6173 Å line and 1700 Å,
  including the variation with magnetic flux density, distance from
  disc centre, nearby magnetic fields, and time. <BR /> Results: The
  brightness of network and faculae is believed to be suppressed by nearby
  magnetic fields from its effect on convection. We note that the degree
  of magnetically crowding of an area also affects the magnetic flux tube
  sizes and the depth at which magnetic concentrations are embedded in
  intergranular lanes, such that intensity contrast can be enhanced in
  magnetically crowded areas at certain flux densities and distances
  from disc centre. The difference in intensity contrast between the
  quiet-Sun network and active region faculae, noted by various studies,
  arises because active regions are more magnetically crowded and is
  not due to any fundamental physical differences between network and
  faculae. These results highlight that solar irradiance models need to
  include the effect of nearby magnetic fields on network and faculae
  brightness. We found evidence that suggests that departures from
  local thermal equilibrium (LTE) might have limited effect on intensity
  contrast. This could explain why solar irradiance models that are based
  on the intensity contrast of solar surface magnetic features calculated
  assuming LTE reproduce the observed spectral variability even where
  the LTE assumption breaks down. Certain models of solar irradiance
  employ chromospheric indices as direct indications of the effect of
  network and faculae on solar irradiance. Based on past studies of the
  Ca II K line and on the intensity contrast measurements derived here,
  we show that the fluctuations in chromospheric emission from network
  and faculae are a reasonable estimate of the emission fluctuations in
  the middle photosphere, but not of those in the lower photosphere. This
  is due to the different physical mechanisms that underlie the magnetic
  intensity enhancement in the various atmospheric regimes, and represents
  a fundamental limitation of these solar irradiance models. Any time
  variation in the radiant properties of network and faculae is, of
  course, relevant to their effect on solar irradiance. The data set,
  which extends from 2010 to 2018, indicates that their intensity contrast
  was stable to about 3% in this period. <BR /> Conclusions: This study
  offers new insights into the radiant behaviour of network and faculae,
  with practical implications for solar irradiance modelling.

Title: Spectral variability of photospheric radiation due to
    faculae. I. The Sun and Sun-like stars
Authors: Norris, Charlotte M.; Beeck, Benjamin; Unruh, Yvonne C.;
   Solanki, Sami K.; Krivova, Natalie A.; Yeo, Kok Leng
Bibcode: 2017A&A...605A..45N
Altcode: 2017arXiv170504455N
  Context. Stellar spectral variability on timescales of a day and
  longer, arising from magnetic surface features such as dark spots
  and bright faculae, is an important noise source when characterising
  extra-solar planets. Current 1D models of faculae do not capture the
  geometric properties and fail to reproduce observed solar facular
  contrasts. Magnetoconvection simulations provide facular contrasts
  accounting for geometry. <BR /> Aims: We calculate facular contrast
  spectra from magnetoconvection models of the solar photosphere with
  a view to improve (a) future parameter determinations for planets
  with early G type host stars and (b) reconstructions of solar spectral
  variability. <BR /> Methods: Regions of a solar twin (G2, log g = 4.44)
  atmosphere with a range of initial average vertical magnetic fields
  (100 to 500 G) were simulated using a 3D radiation-magnetohydrodynamics
  code, MURaM, and synthetic intensity spectra were calculated from
  the ultraviolet (149.5 nm) to the far infrared (160 000 nm) with the
  ATLAS9 radiative transfer code. Nine viewing angles were investigated
  to account for facular positions across most of the stellar disc. <BR
  /> Results: Contrasts of the radiation from simulation boxes with
  different levels of magnetic flux relative to an atmosphere with no
  magnetic field are a complicated function of position, wavelength
  and magnetic field strength that is not reproduced by 1D facular
  models. Generally, contrasts increase towards the limb, but at UV
  wavelengths a saturation and decrease are observed close to the
  limb. Contrasts also increase strongly from the visible to the UV;
  there is a rich spectral dependence, with marked peaks in molecular
  bands and strong spectral lines. At disc centre, a complex relationship
  with magnetic field was found and areas of strong magnetic field
  can appear either dark or bright, depending on wavelength. Spectra
  calculated for a wide variety of magnetic fluxes will also serve to
  improve total and spectral solar irradiance reconstructions.

Title: Solar Irradiance Variability is Caused by the Magnetic Activity
    on the Solar Surface
Authors: Yeo, K. L.; Solanki, S. K.; Norris, C. M.; Beeck, B.; Unruh,
   Y. C.; Krivova, N. A.
Bibcode: 2017PhRvL.119i1102Y
Altcode: 2017arXiv170900920Y
  The variation in the radiative output of the Sun, described in terms
  of solar irradiance, is important to climatology. A common assumption
  is that solar irradiance variability is driven by its surface
  magnetism. Verifying this assumption has, however, been hampered by
  the fact that models of solar irradiance variability based on solar
  surface magnetism have to be calibrated to observed variability. Making
  use of realistic three-dimensional magnetohydrodynamic simulations
  of the solar atmosphere and state-of-the-art solar magnetograms from
  the Solar Dynamics Observatory, we present a model of total solar
  irradiance (TSI) that does not require any such calibration. In doing
  so, the modeled irradiance variability is entirely independent of the
  observational record. (The absolute level is calibrated to the TSI
  record from the Total Irradiance Monitor.) The model replicates 95%
  of the observed variability between April 2010 and July 2016, leaving
  little scope for alternative drivers of solar irradiance variability
  at least over the time scales examined (days to years).

Title: The nature of solar brightness variations
Authors: Shapiro, A. I.; Solanki, S. K.; Krivova, N. A.; Cameron,
   R. H.; Yeo, K. L.; Schmutz, W. K.
Bibcode: 2017NatAs...1..612S
Altcode: 2017arXiv171104156S
  Determining the sources of solar brightness variations<SUP>1,2</SUP>,
  often referred to as solar noise<SUP>3</SUP>, is important because
  solar noise limits the detection of solar oscillations<SUP>3</SUP>,
  is one of the drivers of the Earth's climate system<SUP>4,5</SUP> and
  is a prototype of stellar variability<SUP>6,7</SUP>—an important
  limiting factor for the detection of extrasolar planets. Here,
  we model the magnetic contribution to solar brightness variability
  using high-cadence<SUP>8,9</SUP> observations from the Solar Dynamics
  Observatory (SDO) and the Spectral And Total Irradiance REconstruction
  (SATIRE)<SUP>10,11</SUP> model. The brightness variations caused by
  the constantly evolving cellular granulation pattern on the solar
  surface were computed with the Max Planck Institute for Solar System
  Research (MPS)/University of Chicago Radiative Magnetohydrodynamics
  (MURaM)<SUP>12</SUP> code. We found that the surface magnetic field
  and granulation can together precisely explain solar noise (that
  is, solar variability excluding oscillations) on timescales from
  minutes to decades, accounting for all timescales that have so far
  been resolved or covered by irradiance measurements. We demonstrate
  that no other sources of variability are required to explain the
  data. Recent measurements of Sun-like stars by the COnvection ROtation
  and planetary Transits (CoRoT)<SUP>13</SUP> and Kepler<SUP>14</SUP>
  missions uncovered brightness variations similar to that of the Sun,
  but with a much wider variety of patterns<SUP>15</SUP>. Our finding
  that solar brightness variations can be replicated in detail with
  just two well-known sources will greatly simplify future modelling of
  existing CoRoT and Kepler as well as anticipated Transiting Exoplanet
  Survey Satellite<SUP>16</SUP> and PLAnetary Transits and Oscillations
  of stars (PLATO)<SUP>17</SUP> data.

Title: EMPIRE: A robust empirical reconstruction of solar irradiance
    variability
Authors: Yeo, K. L.; Krivova, N. A.; Solanki, S. K.
Bibcode: 2017JGRA..122.3888Y
Altcode: 2017arXiv170407652Y
  We present a new empirical model of total and spectral solar irradiance
  (TSI and SSI) variability entitled EMPirical Irradiance REconstruction
  (EMPIRE). As with existing empirical models, TSI and SSI variability
  is given by the linear combination of solar activity indices. In
  empirical models, UV SSI variability is usually determined by
  fitting the rotational variability in activity indices to that in
  measurements. Such models have to date relied on ordinary least
  squares regression, which ignores the uncertainty in the activity
  indices. In an advance from earlier efforts, the uncertainty in the
  activity indices is accounted for in EMPIRE by the application of
  an error-in-variables regression scheme, making the resultant UV SSI
  variability more robust. The result is consistent with observations and
  unprecedentedly, with that from other modeling approaches, resolving
  the long-standing controversy between existing empirical models and
  other types of models. We demonstrate that earlier empirical models,
  by neglecting the uncertainty in activity indices, underestimate UV
  SSI variability. The reconstruction of TSI and visible and IR SSI from
  EMPIRE is also shown to be consistent with observations. The EMPIRE
  reconstruction is of utility to climate studies as a more robust
  alternative to earlier empirical reconstructions.

Title: Modelling the Spectral Contrasts of Stellar Faculae.
Authors: Norris, Charlotte M.; Beeck, Benjamin; Unruh, Yvonne; Solanki,
   Sami; Yeo, Kok Leng; Krivova, Natalie
Bibcode: 2016csss.confE..63N
Altcode:
  Facular contrasts are an important parameter in modelling stellar
  variability and exoplanet transits. The ultimate goal of this work
  will be to model the contrasts of faculae for different spectral types
  and thus improve the modelling of solar and stellar photospheric
  variability. This is done by using a radiative transfer algorithm
  (ATLAS9) on magneto-convection simulations. Starting with solar twins,
  we derive facular contrasts as a function of limb angle and discuss
  their wavelength dependence.

Title: Reconstruction of spectral solar irradiance since 1700 from
    simulated magnetograms
Authors: Dasi-Espuig, M.; Jiang, J.; Krivova, N. A.; Solanki, S. K.;
   Unruh, Y. C.; Yeo, K. L.
Bibcode: 2016A&A...590A..63D
Altcode: 2016arXiv160502039D
  <BR /> Aims: We present a reconstruction of the spectral solar
  irradiance since 1700 using the SATIRE-T2 (Spectral And Total Irradiance
  REconstructions for the Telescope era version 2) model. This model
  uses as input magnetograms simulated with a surface flux transport
  model fed with semi-synthetic records of emerging sunspot groups. <BR
  /> Methods: The record of sunspot group areas and positions from the
  Royal Greenwich Observatory (RGO) is only available since 1874. We
  used statistical relationships between the properties of sunspot
  group emergence, such as the latitude, area, and tilt angle, and the
  sunspot cycle strength and phase to produce semi-synthetic sunspot
  group records starting in the year 1700. The semi-synthetic records
  are fed into a surface flux transport model to obtain daily simulated
  magnetograms that map the distribution of the magnetic flux in active
  regions (sunspots and faculae) and their decay products on the solar
  surface. The magnetic flux emerging in ephemeral regions is accounted
  for separately based on the concept of extended cycles whose length
  and amplitude are linked to those of the sunspot cycles through the
  sunspot number. The magnetic flux in each surface component (sunspots,
  faculae and network, and ephemeral regions) was used to compute the
  spectral and total solar irradiance (TSI) between the years 1700
  and 2009. This reconstruction is aimed at timescales of months or
  longer although the model returns daily values. <BR /> Results: We
  found that SATIRE-T2, besides reproducing other relevant observations
  such as the total magnetic flux, reconstructs the TSI on timescales
  of months or longer in good agreement with the PMOD composite of
  observations, as well as with the reconstruction starting in 1878
  based on the RGO-SOON data. The model predicts an increase in the TSI
  of 1.2<SUP>+0.2</SUP><SUB>-0.3</SUB> Wm<SUP>-2</SUP> between 1700
  and the present. The spectral irradiance reconstruction is in good
  agreement with the UARS/SUSIM measurements as well as the Lyman-α
  composite. <P />The complete total and spectral (115 nm-160 μm)
  irradiance reconstructions since 1700 will be available from <A
  href="http://www2.mps.mpg.de/projects/sun-climate/data.html">http://www2.mps.mpg.de/projects/sun-climate/data.html</A>

Title: Are solar brightness variations faculae- or spot-dominated?
Authors: Shapiro, A. I.; Solanki, S. K.; Krivova, N. A.; Yeo, K. L.;
   Schmutz, W. K.
Bibcode: 2016A&A...589A..46S
Altcode: 2016arXiv160204447S
  Context. Regular spaceborne measurements have revealed that
  solar brightness varies on multiple timescales, variations on
  timescales greater than a day being attributed to a surface magnetic
  field. Independently, ground-based and spaceborne measurements suggest
  that Sun-like stars show a similar, but significantly broader pattern
  of photometric variability. <BR /> Aims: To understand whether the
  broader pattern of stellar variations is consistent with the solar
  paradigm, we assess relative contributions of faculae and spots to
  solar magnetically-driven brightness variability. We investigate
  how the solar brightness variability and its facular and spot
  contributions depend on the wavelength, timescale of variability,
  and position of the observer relative to the ecliptic plane. <BR />
  Methods: We performed calculations with the SATIRE model, which
  returns solar brightness with daily cadence from solar disc area
  coverages of various magnetic features. We took coverages as seen by
  an Earth-based observer from full-disc SoHO/MDI and SDO/HMI data and
  projected them to mimic out-of-ecliptic viewing by an appropriate
  transformation. <BR /> Results: Moving the observer away from the
  ecliptic plane increases the amplitude of 11-year variability as it
  would be seen in Strömgren (b + y)/2 photometry, but decreases the
  amplitude of the rotational brightness variations as it would appear
  in Kepler and CoRoT passbands. The spot and facular contributions to
  the 11-year solar variability in the Strömgren (b + y)/2 photometry
  almost fully compensate each other so that the Sun appears anomalously
  quiet with respect to its stellar cohort. Such a compensation does not
  occur on the rotational timescale. <BR /> Conclusions: The rotational
  solar brightness variability as it would appear in the Kepler and
  CoRoT passbands from the ecliptic plane is spot-dominated, but the
  relative contribution of faculae increases for out-of-ecliptic viewing
  so that the apparent brightness variations are faculae-dominated for
  inclinations less than about I = 45°. Over the course of the 11-year
  activity cycle, the solar brightness variability is faculae-dominated
  shortwards of 1.2 μm independently of the inclination.

Title: Modelling Solar and Stellar Brightness Variabilities
Authors: Yeo, K. L.; Shapiro, A. I.; Krivova, N. A.; Solanki, S. K.
Bibcode: 2016ASPC..504..273Y
Altcode:
  Total and spectral solar irradiance, TSI and SSI, have been measured
  from space since 1978. This is accompanied by the development of
  models aimed at replicating the observed variability by relating
  it to solar surface magnetism. Despite significant progress,
  there remains persisting controversy over the secular change and the
  wavelength-dependence of the variation with impact on our understanding
  of the Sun's influence on the Earth's climate. We highlight the recent
  progress in TSI and SSI modelling with SATIRE. Brightness variations
  have also been observed for Sun-like stars. Their analysis can profit
  from knowledge of the solar case and provide additional constraints
  for solar modelling. We discuss the recent effort to extend SATIRE to
  Sun-like stars.

Title: UV solar irradiance in observations and the NRLSSI and
    SATIRE-S models
Authors: Yeo, K. L.; Ball, W. T.; Krivova, N. A.; Solanki, S. K.;
   Unruh, Y. C.; Morrill, J.
Bibcode: 2015JGRA..120.6055Y
Altcode: 2015arXiv150701224Y
  Total solar irradiance and UV spectral solar irradiance has been
  monitored since 1978 through a succession of space missions. This is
  accompanied by the development of models aimed at replicating solar
  irradiance by relating the variability to solar magnetic activity. The
  Naval Research Laboratory Solar Spectral Irradiance (NRLSSI) and
  Spectral And Total Irradiance REconstruction for the Satellite era
  (SATIRE-S) models provide the most comprehensive reconstructions of
  total and spectral solar irradiance over the period of satellite
  observation currently available. There is persistent controversy
  between the various measurements and models in terms of the wavelength
  dependence of the variation over the solar cycle, with repercussions on
  our understanding of the influence of UV solar irradiance variability
  on the stratosphere. We review the measurement and modeling of UV solar
  irradiance variability over the period of satellite observation. The
  SATIRE-S reconstruction is consistent with spectral solar irradiance
  observations where they are reliable. It is also supported by an
  independent, empirical reconstruction of UV spectral solar irradiance
  based on Upper Atmosphere Research Satellite/Solar Ultraviolet Spectral
  Irradiance Monitor measurements from an earlier study. The weaker
  solar cycle variability produced by NRLSSI between 300 and 400 nm is
  not evident in any available record. We show that although the method
  employed to construct NRLSSI is principally sound, reconstructed solar
  cycle variability is detrimentally affected by the uncertainty in the
  SSI observations it draws upon in the derivation. Based on our findings,
  we recommend, when choosing between the two models, the use of SATIRE-S
  for climate studies.

Title: Solar Cycle Variation in Solar Irradiance
Authors: Yeo, K. L.; Krivova, N. A.; Solanki, S. K.
Bibcode: 2015sac..book..137Y
Altcode:
  No abstract at ADS

Title: Solar Spectral Irradiance Variability in November/December
2012: Comparison of Observations by Instruments on the International
    Space Station and Models
Authors: Thuillier, G.; Schmidtke, G.; Erhardt, C.; Nikutowski, B.;
   Shapiro, A. I.; Bolduc, C.; Lean, J.; Krivova, N.; Charbonneau, P.;
   Cessateur, G.; Haberreiter, M.; Melo, S.; Delouille, V.; Mampaey,
   B.; Yeo, K. L.; Schmutz, W.
Bibcode: 2014SoPh..289.4433T
Altcode: 2014SoPh..tmp..120T
  Onboard the International Space Station (ISS), two instruments
  are observing the solar spectral irradiance (SSI) at wavelengths
  from 16 to 2900 nm. Although the ISS platform orientation generally
  precludes pointing at the Sun more than 10 - 14 days per month, in
  November/December 2012 a continuous period of measurements was obtained
  by implementing an ISS `bridging' maneuver. This enabled observations to
  be made of the solar spectral irradiance (SSI) during a complete solar
  rotation. We present these measurements, which quantify the impact
  of active regions on SSI, and compare them with data simultaneously
  gathered from other platforms, and with models of spectral irradiance
  variability. Our analysis demonstrates that the instruments onboard the
  ISS have the capability to measure SSI variations consistent with other
  instruments in space. A comparison among all available SSI measurements
  during November-December 2012 in absolute units with reconstructions
  using solar proxies and observed solar activity features is presented
  and discussed in terms of accuracy.

Title: Solar Cycle Variation in Solar Irradiance
Authors: Yeo, K. L.; Krivova, N. A.; Solanki, S. K.
Bibcode: 2014SSRv..186..137Y
Altcode: 2014arXiv1407.4249Y; 2014SSRv..tmp...25Y
  The correlation between solar irradiance and the 11-year solar activity
  cycle is evident in the body of measurements made from space, which
  extend over the past four decades. Models relating variation in solar
  irradiance to photospheric magnetism have made significant progress
  in explaining most of the apparent trends in these observations. There
  are, however, persistent discrepancies between different measurements
  and models in terms of the absolute radiometry, secular variation and
  the spectral dependence of the solar cycle variability. We present an
  overview of solar irradiance measurements and models, and discuss the
  key challenges in reconciling the divergence between the two.

Title: Analysis and modeling of solar irradiance variations
Authors: Yeo, K. L.
Bibcode: 2014arXiv1412.3935Y
Altcode:
  A prominent manifestation of the solar dynamo is the 11-year activity
  cycle, evident in indicators of solar activity, including solar
  irradiance. Although a relationship between solar activity and the
  brightness of the Sun had long been suspected, it was only directly
  observed after regular satellite measurements became available with the
  launch of Nimbus-7 in 1978. The measurement of solar irradiance from
  space is accompanied by the development of models aimed at describing
  the apparent variability by the intensity excess/deficit effected by
  magnetic structures in the photosphere. The more sophisticated models,
  termed semi-empirical, rely on the intensity spectra of photospheric
  magnetic structures generated with radiative transfer codes from
  semi-empirical model atmospheres. An established example of such
  models is SATIRE-S (Spectral And Total Irradiance REconstruction
  for the Satellite era). One key limitation of current semi-empirical
  models is the fact that the radiant properties of network and faculae
  are not adequately represented due to the use of plane-parallel model
  atmospheres (as opposed to three-dimensional model atmospheres). This
  thesis is the compilation of four publications, detailing the results
  of investigations aimed at setting the groundwork necessary for the
  eventual introduction of three-dimensional atmospheres into SATIRE-S
  and a review of the current state of the measurement and modelling of
  solar irradiance. Also presented is an update of the SATIRE-S model. We
  generated a daily reconstruction of total and spectral solar irradiance,
  covering 1974 to the present, that is more reliable and, in most cases,
  extended than similar reconstructions from contemporary models.

Title: Reconstruction of total and spectral solar irradiance from
    1974 to 2013 based on KPVT, SoHO/MDI, and SDO/HMI observations
Authors: Yeo, K. L.; Krivova, N. A.; Solanki, S. K.; Glassmeier, K. H.
Bibcode: 2014A&A...570A..85Y
Altcode: 2014arXiv1408.1229Y
  Context. Total and spectral solar irradiance are key parameters in the
  assessment of solar influence on changes in the Earth's climate. <BR />
  Aims: We present a reconstruction of daily solar irradiance obtained
  using the SATIRE-S model spanning 1974 to 2013 based on full-disc
  observations from the KPVT, SoHO/MDI, and SDO/HMI. <BR /> Methods:
  SATIRE-S ascribes variation in solar irradiance on timescales
  greater than a day to photospheric magnetism. The solar spectrum
  is reconstructed from the apparent surface coverage of bright
  magnetic features and sunspots in the daily data using the modelled
  intensity spectra of these magnetic structures. We cross-calibrated
  the various data sets, harmonizing the model input so as to yield a
  single consistent time series as the output. <BR /> Results: The model
  replicates 92% (R<SUP>2</SUP> = 0.916) of the variability in the PMOD
  TSI composite including the secular decline between the 1996 and 2008
  solar cycle minima. The model also reproduces most of the variability
  in observed Lyman-α irradiance and the Mg II index. The ultraviolet
  solar irradiance measurements from the UARS and SORCE missions are
  mutually consistent up to about 180 nm before they start to exhibit
  discrepant rotational and cyclical variability, indicative of unresolved
  instrumental effects. As a result, the agreement between model and
  measurement, while relatively good below 180 nm, starts to deteriorate
  above this wavelength. As with earlier similar investigations,
  the reconstruction cannot reproduce the overall trends in SORCE/SIM
  SSI. We argue, from the lack of clear solar cycle modulation in the
  SIM record and the inconsistency between the total flux recorded
  by the instrument and TSI, that unaccounted instrumental trends are
  present. <BR /> Conclusions: The daily solar irradiance time series
  is consistent with observations from multiple sources, demonstrating
  its validity and utility for climate models. It also provides further
  evidence that photospheric magnetism is the prime driver of variation
  in solar irradiance on timescales greater than a day.

Title: Analysis and modeling of solar irradiance variations
Authors: Yeo, Kok Leng
Bibcode: 2014PhDT........92Y
Altcode:
  No abstract at ADS

Title: Point spread function of SDO/HMI and the effects of stray
    light correction on the apparent properties of solar surface phenomena
Authors: Yeo, K. L.; Feller, A.; Solanki, S. K.; Couvidat, S.;
   Danilovic, S.; Krivova, N. A.
Bibcode: 2014A&A...561A..22Y
Altcode: 2013arXiv1310.4972Y
  <BR /> Aims: We present a point spread function (PSF) for the
  Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics
  Observatory (SDO) and discuss the effects of its removal on the
  apparent properties of solar surface phenomena in HMI data. <BR />
  Methods: The PSF was retrieved from observations of Venus in transit
  by matching it to the convolution of a model of the Venusian disc and
  solar background with a guess PSF. We described the PSF as the sum of
  five Gaussian functions, the amplitudes of which vary sinusoidally with
  azimuth. This relatively complex functional form was required by the
  data. Observations recorded near in time to the transit of Venus were
  corrected for instrumental scattered light by the deconvolution with the
  PSF. We also examined the variation in the shape of the solar aureole in
  daily data, as an indication of PSF changes over time. <BR /> Results:
  Granulation contrast in restored HMI data is greatly enhanced relative
  to the original data and exhibit reasonable agreement with numerical
  simulations. Image restoration enhanced the apparent intensity and
  pixel averaged magnetic field strength of photospheric magnetic features
  significantly. For small-scale magnetic features, restoration enhanced
  intensity contrast in the continuum and core of the Fe I 6173 Å line
  by a factor of 1.3, and the magnetogram signal by a factor of 1.7. For
  sunspots and pores, the enhancement varied strongly within and between
  features, being more acute for smaller features. Magnetic features are
  also rendered smaller, as signal smeared onto the surrounding quiet
  Sun is recovered. Image restoration increased the apparent amount of
  magnetic flux above the noise floor by a factor of about 1.2, most
  of the gain coming from the quiet Sun. Line-of-sight velocity due to
  granulation and supergranulation is enhanced by a factor of 1.4 to 2.1,
  depending on position on the solar disc. The shape of the solar aureole
  varied, with time and between the two CCDs. There are also indications
  that the PSF varies across the FOV. However, all these variations were
  found to be relatively small, such that a single PSF can be applied to
  HMI data from both CCDs, over the period examined without introducing
  significant error. <BR /> Conclusions: Restoring HMI observations
  with the PSF presented here returns a reasonable estimate of the stray
  light-free intensity contrast. Image restoration affects the measured
  radiant, magnetic and dynamic properties of solar surface phenomena
  sufficiently to significantly impact interpretation.

Title: What can we learn about the Sun with PREMOS/PICARD?
Authors: Cessateur, Gaël; Shapiro, Alexander; Schmutz, Werner;
   Krivova, Natalie; Solanki, Sami K.; Yeo, Kok Leng; Thuillier, Gérard
Bibcode: 2013EGUGA..1511720C
Altcode:
  Total and Spectral Solar Irradiance are key input parameters to
  atmospheric/oceanic and space weather models. We present here
  spectral solar irradiance data from the radiometer PREMOS onboard
  the PICARD satellite. This instrument convers the solar spectrum from
  the Ultraviolet to near-infrared, and provides valuable information
  and nourishes theoretical models. Based on redundancy strategies,
  instrumental degradation has been mostly corrected, revealing
  surprising behavior from the visible and near-infrared filters. We
  compare these data with those from the VIRGO/SOHO and SOLSTIC/SORCE
  experiments. Finally we use COSI to model the variability of the
  irradiance, assuming that the latter is determined by the evolution
  of the solar surface magnetic field as seen with SDO/HMI data. A
  direct comparison shows a very good correlation for most of channels
  from PREMOS.

Title: Intensity contrast of solar network and faculae
Authors: Yeo, K. L.; Solanki, S. K.; Krivova, N. A.
Bibcode: 2013A&A...550A..95Y
Altcode: 2013arXiv1302.1442Y
  <BR /> Aims: This study aims at setting observational constraints
  on the continuum and line core intensity contrast of network and
  faculae, specifically, their relationship with magnetic field and
  disc position. <BR /> Methods: Full-disc magnetograms and intensity
  images by the Helioseismic and Magnetic Imager (HMI) onboard the Solar
  Dynamics Observatory (SDO) were employed. Bright magnetic features,
  representing network and faculae, were identified and the relationship
  between their intensity contrast at continuum and line core with
  magnetogram signal and heliocentric angle examined. Care was taken
  to minimize the inclusion of the magnetic canopy and straylight from
  sunspots and pores as network and faculae. <BR /> Results: In line
  with earlier studies, network features, on a per unit magnetic flux
  basis, appeared brighter than facular features. Intensity contrasts
  in the continuum and line core differ considerably, most notably, they
  exhibit opposite centre-to-limb variations. We found this difference in
  behaviour to likely be due to the different mechanisms of the formation
  of the two spectral components. From a simple model based on bivariate
  polynomial fits to the measured contrasts we confirmed spectral line
  changes to be a significant driver of facular contribution to variation
  in solar irradiance. The discrepancy between the continuum contrast
  reported here and in the literature was shown to arise mainly from
  differences in spatial resolution and treatment of magnetic signals
  adjacent to sunspots and pores. <BR /> Conclusions: HMI is a source of
  accurate contrasts and low-noise magnetograms covering the full solar
  disc. For irradiance studies it is important to consider not just the
  contribution from the continuum but also from the spectral lines. In
  order not to underestimate long-term variations in solar irradiance,
  irradiance models should take the greater contrast per unit magnetic
  flux associated with magnetic features with low magnetic flux into
  account.

Title: Solar Spectral Irradiance as observed by LYRA/PROBA2 and
    PREMOS/PICARD
Authors: Cessateur, Gaël.; Kretzschmar, Matthieu; Krivova, Natalie;
   Schmutz, Werner; Solanki, Sami K.; Thuillier, Gerard; Shapiro,
   Alexander; Schoell, Micha; Shapiro, Anna; Dominique, Marie; Tagirov,
   Rinat; Wehrli, Christoph; Yeo, Kok Leng
Bibcode: 2012cosp...39..287C
Altcode: 2012cosp.meet..287C
  No abstract at ADS

Title: Solar Spectral Irradiance as observed by LYRA/PROBA2 and
    PREMOS/PICARD
Authors: Cessateur, G.; Shapiro, A. I.; Dominique, M.; Kretzschmar,
   M.; Krivova, N.; Shapiro, A. V.; Schmutz, W.; Schoell, M.; Solanki,
   S.; Tagirov, R.; Thuillier, G.; Wehrli, C.; Yeo, K. L.
Bibcode: 2012EGUGA..14.8254C
Altcode:
  Total and Spectral Solar Irradiance are key input parameters to
  atmospheric/oceanic and space weather models. Both vary on time-scales
  ranging from days to millennia, although a complete picture of the
  solar irradiance variability is still missing. The recent launch of
  two European missions PROBA-2 with LYRA radiometer onboard and PICARD
  with PREMOS package onboard provides therefore valuable information and
  nourishes theoretical models. Both instruments covers the solar spectrum
  from the EUV to near-infrared. Here we present spectral solar irradiance
  data from these two recent missions. After a proper correction of the
  degradation and non-solar signatures, we compare these data with those
  from the VIRGO/SOHO and SOLSTICE+SIM/SORCE experiments. Both LYRA and
  PREMOS have also observed several solar eclipses, which allows us to
  accurately retrieve the center-to-limb variations (CLVs) of the quiet
  Sun's brightness at the wavelengths of the corresponding channels. CLVs
  play indeed an important role in modelling of the solar irradiance
  variability. We show that calculations with the published COde for
  Solar Irradiance (COSI) yield CLVs that are in good agreement with
  measurements. Finally we use COSI to model the variability of the
  irradiance, assuming that the latter is determined by the evolution
  of the solar surface magnetic field as seen with SDO/HMI data. These
  theoretical results are compared to PREMOS and LYRA measurements.

