introduction: tsi and solar activity a tsi model based on active region emergence and decay

Sofia/Turekian Forum, Yale 28/03/08 1

A semi-empirical model for TSI variationsPaul Charbonneau (+ Ashley Crouch),

Département de Physique, Université de Montréal

1. Introduction: TSI and solar activity2. A TSI model based on active region emergence and decay3. Evidence for a secular trend in TSI4. Evidence for additional cycle-related modulation5. Outlook


Ashley DanahéPaul Geneviève

Submitted to Astrophys. J., 17 March 2008

Astrophys. J., 677, in press [ 10 April 2008 ]


Observed TSI variations

Foukal, Fröhlich, Spruit & Wigley 2006, Nature, 443, 161-166


Cycle-related TSI variationsThe solar magnetic activity cycleshows strong amplitude fluctuationand/or intermittency

What does TSI do in times of secularrise in activity levels? In Maunder Minimum epoch of suppressed activity?


Origin of TSI variations

1. Solar irradiance variations reflect the changes in the photospheric coverage of various magnetic structures having different radiative emissivities;

2. On long timescales (> a few yr), TSI variations reflect a deep-seated magnetically-mediated modulation of convective energy transport.

Two classes of explanations (NOT mutually exclusive!):


A TSI model based on the emergence and decay of active regions

AIM: Produce a model for TSI reconstruction based on simplephysical mechanism, rather than statistical correlations;

WHY Oh WHY …?

WHY: Belief in the universality of physical laws suggests that such models can be extrapolated more safely outside of theparameter regime in which they were calibrated


A TSI model based on the emergence and decay of active regions

1. Observational underpinnings

2. Model design

3. Parameter fitting

4. Results for 1978-2007

6. Long-term trends in quiet-sun irradiance

5. Reconstruction from 1874


Evolutionary link 1: fragmentation


Evolutionary link 2: boundary erosion

QuickTime™ et undécompresseur codec YUV420

sont requis pour visionner cette image.


Emergence+fragmentation+erosion

A FRAGMENTATION MODEL:

1. Sunspots of area A injected on « solar disk » (data from Royal Greenwich Observatory data)2. Backside emergences introduced stochastically3. Spots fragment stochastically, and erode at boundaries4. Fragmentation/erosion process eventually produces flux tubes, which then disappear with fixed probability5. This result in a time-evolving area distribution N(A;t), which can be convolved with the contrast curve, including center-to-limb variations, to produce a TSI time series.


Observational support

The probability distribution functionof observed sunspot areas has alognormal form over more than twoorders of magnitude in observed areas; successive fragmentationis known to yield such a distribution

Bogdan et al. 1988, ApJ 327, 451

(Necessary but not sufficient!)


Magnetic flux transport

All magnetic structures are carried in the EW direction by(differential) rotation:

…and poleward by meridional circulation:

Bright, small-scale magnetic elements produced by successivefragmentation and erosion accumulate as a « cloud » surroundingeach decaying spot; this is the model’s equivalent to facules

(Komm et al. 1993)

(Charbonneau et al. 1999)


From sunspot and facular areas to TSI

Basic 3-component model: quiet photosphere, spots, faculae:

Irradiance deficit associated with « spots »:

Irradiance excess associated with « faculae »

(Chapman & Meyer 1986)

(Lean et al. 1998; Brandt et al. 1994)


Model parameters

In practice, 6 to 9 free parameters need to be determined

The model involves a number of parameters, some that can be fixed on the basisof observations, others that need to be fitted to the data


Parameter fitting

We need to pick model parameter values that produce best-fitsto both the TSI and sunspot area (SA) time series (multi-objective optimization)

The summed squared residuals between observed and modeled TSI and SAis a statistical function of the model parameters, because of the stochasticnature of the fragmentation process, and statistical treatment of backsideemergences: two model runs with the same parameter values will NOTyield the same TSI and SA time series!

Possible tradeoffs between model parameters make the optimizationproblem multimodal (secondary extrema)

We use the genetic algorithm-based optimizer PIKAIA, with enhancedelitism and metric-distance-based mutation rate adjustment


Genetic algorithms (1)

A class of biologically-inspired, population-based evolutionary algorithms that can form the core of powerful, flexible multimodal optimization schemes

Breed new population from selected members

Select fittest members of the population

Evaluate fitness of new population member

Initialization: build population of random trial solutions; evaluate fitness

Is best of current population good enough? DONE!NO YES



ENCODE:

CROSSOVER:

MUTATE:

DECODE:

1 2 3 4 5 6 7 8 9 0

0 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 0

0 9 8 7 6 5 4 3 2 10 9 3 4 5 6 7 8 9 0

1 2 8 7 6 5 4 3 2 1

3 4 5 6 7 8 9 00 9 0 9 3 4 5 6 1 8 9 0

0 9 3 4 5 6 1 8 9 0

1 2 8 7 6 5 4 3 2 1

( 1.2345 , 6.7890 )

( 0.9876 , 5.4321 )

( 0.9345 , 6.1890 )

( 1.2876 , 5.4321 )



FITNESS is defined in terms of the product of mean-squared residualsbetween the modeled and observed TSI and sunspot area time series:

We use 81-day running boxcar averages of the time series, to avoidlarge contribution to the mean-squared residuals associated withtiming errors in the emergence of large active regions

NOTE: No derivatives of fitness w.r.t. model parameters are required



Different runs converge atdifferent rates, but eventuallyreach similar fitness levels


Results: It Works !!

d41_61_0702

Model run


TSI excess in rising phase

Modelled TSI issystematically belowobservations duringrising phases of cycles…

…even though SAis very well-fitted

RMS(A) = 230 microHem

RMS(S) = 0.202 W/m2


I mean, it really does !!

Bright « facular » component

Dark « spot » component


Optimal parameter values

Conversion efficiency high: Nearly all sunspot flux is converted into small scale elements

Faculae lifetime high: Obs. Suggest tens of days for large facular structures

Facular contrast high: Observational determinations suggest ~ 0.03-0.04

Hint: we are missing an irradiance source unrelated to decay of active regions


Working back to 1874


A TSI downward trend?

Allow for linear trend in quiet Sun irradiance:

Repeating best-fit procedure with additional slope parameter yields an improved fit: fitness in range 1.62-1.81 as opposedto 1.50-1.67 with constant S_Q. Statistically significant!RMS(S) : 0.202 to 0.193 W/m2


Repeating best-fit procedure with additional slope parameter yields an improved fit (fitness in range 1.62-1.81 as opposedto 1.50-1.67 with constant S_Q. Statistically significant!


Optimal parameter values, bis


A cyclically varying contribution to TSI?

Allow for sinusoidal contribution to quiet Sun irradiance,

i.e., unrelated to active region decay:

Repeating fit procedure with additional sinusoidal component yields an improved fit: fitness in range 1.82-2.31 as opposedto 1.50-1.67 with constant S_Q. Statistically significant!RMS(S) : 0.202 - > 0.168 W/m2


How optimal is optimal?

100 best out of 200 GA runs

Some runs remain « stuck »on secondary extrema

Fittest runs have S_QIn range 0.3-0.6 W/m2

Very few runs convergeWith S_Q < 0.3 W/m2

Mean +/- 1 s.d. of100 runs with fixed S_Q


Identifying « bad » local optima

Because fitting parameters have a direct physical meaning, it is possible to assessthe relative merits of globally suboptimal solutions corresponding to local extrema

This solution has a reasonable facular contrast (0.045), but very low lifetime forbright small-scale « faculae » elements (9 days)


Optimal parameter values, coda


Parameter correlations

1.34 < Fitness < 1.84

0.84 < Fitness < 1.34

1.84 < Fitness < 2.34


Conclusions (so far…)

• It works !! We can simultaneously fit, and quite well, both sunspot areas and TSI over the 1978-2007 interval• We find evidence for a brightness source unrelated to active regions in the rising phase of cycles 22 and 23• We find evidence for a slight downward trend in TSI, by -0.0069 +/- 0.0027 W/m^2 per year over 1978-2007• We find evidence for an cycle-phased irradiance source unrelated to active region emergence and decay,

accounting for 40-50% of peak-to-peak TSI cycle variability


What next?

• Introduce and test models for long-term modulation• « Differentiate » bright structures: introduce DLA model

for network and faculae formation• Introduce far-side emergences as inferred helioseismically• Use genetic programming to « evolve » better

fragmentation algorithms, contrast functions, center-to-limb contrast functions for faculae, etc.

• Adapt model for spectral irradiance, with special emphasis on UV range most relevant to atmospheric chemistry

• Use output of dynamo model to « feed » sunspot emergences into the TSI model


Semi-empirical models for long-term modulation of quiet-sun irradiance

K. Tapping et al. 2007, Sol. Phys., 246, 309

Quiet-sun TSIbased on a2-componentmagnetic fluxmodel linkedto TSI via theF10.7 radioflux


DLA model for network formation

[ Crouch, Charbonneau & Thibault, 2007, Astrophys. J., 662, 715 ]

Piece of MDI quiet-sun magnetogram Numerical simulation


DLA model for faculae formation

[ Kim Thibault, UdeM MSc thesis, 2008, in preparation ]

QuickTime™ et undécompresseur codec YUV420

sont requis pour visionner cette image.


FIN


Parameter correlations

Multiple GA-optimizarion runs allow to establish error estimatesand correlations between best-fit parameters.

introduction: tsi and solar activity a tsi model based on active region emergence and decay

Documents