Models of Total Solar Irradiance
Based on Different Proxies
Are they compatible with each other
and with spacecraft composites?
Dora Preminger
(dora.preminger@csun.edu)
Angela Cookson
Gary Chapman
San Fernando Observatory
Cal State Northridge
May 2010
Acknowledgements: NSF grant ATM-0848518
NASA Living with a Star grant NNX07AT19G
Abstract
Total solar irradiance [TSI] has been measured by different spacecraft and the
records composited to form a continuous time-series. Since there is more than
one way to do this, several different composites exist, and it is difficult to
choose between them. One way is to compare them with proxy models of TSI.
We have shown that TSI variability can be reconstructed from ground-based solar
data with a FIR model. This approach assumes that there is a physical
relationship between the different manifestations of solar activity and that this
relationship is time-invariant. The FIR model is a single-parameter model; the
parameter chosen may be one of several ground-based measurements of solar
variability. This is useful because we can choose a parameter whose
measurement is easy and stable over the long term.
Here we consider 2 such models, one based on RGO sunspot area and one based
on F10.7 cm radio flux. We compare the models with each other and with the
TSI composite records to see how well they reconstruct long- and short-term
irradiance variability. We pay particular attention to the maximum of solar
cycle 23 and the level of the most recent solar minimum.
TSI composites
PMOD World
Radiation Center
www.pmodwrc.ch
Active Cavity
Radiometer
TSI version 12/09
www.acrim.com
Royal
Meteorological
Institute of Belgium
http://remotesensi
ng.oma.be/
FIR proxy model
• Assume a physical relationship exists between different
manifestations of solar activity
• Assume the relationship is time-invariant
• Changes in TSI are related to changes in solar activity
measurement X:
TSI= X  hX(t)
(Signal theory)
hX(t) is a Finite Impulse Response function (FIR)
 represents convolution
• Derive FIR from the data
– Is it a well-defined, finite function?
– Yes Use it to reconstruct TSI for all times when X is known
Advantages of FIR model
• Single parameter model
• Parameter may be any measurement of solar
activity
• Choose a ground-based measurement that is
easy and stable over the long-term
– Here, we choose Sunspot area and F10.7 cm radio flux
• Successsful at reconstructing TSI, Spectral irradiance and
magnetic flux from sunspot measurements
Preminger and Walton (GRL, 2005; Sol Phys, 2006)
Proxy A: RGO Sunspot area [As]
Proxy B: F10.7 cm solar radio flux [F10.7]
Reconstructing PMOD from As
R2 =0.76
rms residual = 0.286 W m-2
Reconstructing PMOD from F10.7
R2 =0.73
rms residual = 0.305 W m-2
Comparing two reconstructions of
TSI: PMOD
•
•
•
•
Similar goodness-of-fit parameters
Good fit to both long-term and short-term trends
Models match most recent solar minimum
Max. of Solar cycle 23 is reconstructed better by
the F10.7 model
– Indicates increased presence of small bright features
that are not the product of sunspot evolution
• Sunspot dips best matched by As model
Detail for Proxy model of PMOD
based on F10.7
Comparing FIRs for PMOD
Temporal signal shows how evolution of active region affects TSI
Reconstructing ACRIM from F10.7
R2 =0.45
rms residual = 0.513 W m-2
Reconstructing IRMB from F10.7
R2 =0.55
rms residual = 0.389 W m-2
Reconstructions of ACRIM and IRMB
• FIR model not successful
• Neither short-term nor long-term variations
are well-modeled
• FIR models based on F10.7 and As give similar
(poor) reconstructions
• Investigate FIR function to find out why
Comparing FIRs for different composites
• 14 day smoothing: Central portions - similar
FIRs derived from F10.7
Comparing FIRs for different composites
• 6-month smoothing: outer portions - different
FIRs derived from F10.7
Comparing FIRs for different composites
For FIRs derived from F10.7 :
• the central portions are similar for all
• 6-month smoothing brings out the differences
– FIRs for ACRIM and IRMB
•
•
•
•
Are similar to each other
Different from FIR for PMOD
Have strong low-frequency signal
Are too wide to be considered finite, well-defined
functions
Conclusions
• TSI: PMOD
– FIR model works well
– Active region evolution accounts for both short and
long-term trends in TSI
– F10.7 model best match for Solar Cycle 23 Maximum
– As model best match for sunspot dips
• TSI: ACRIM and IRMB
– FIR model unsuccessful
– There are long-term trends in these composites that
are not related to the evolution of solar active regions