Developing a Proxy Model for Solar EUV Irradiance (1,2)Katherine A. Suess, (1)Marty Snow, (3)Rodney Viereck, (4)Janet Machol Ar'st’s concep'on of GOES satellite, where much of our input data comes from. Photo courtesy NASA and Lockheed Mar'n. 0.0
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Fit to 2012 Reference Data, 90 - 95nm
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Smaller varia'on in large features not captured 01-13
RMS uncertainty larger at longer wavelengths – suggests model performs beuer at shorter wavelengths RMS Uncertainty
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Reference Data TIMED SEE Integrated Spectrum* SDO EVE Time Series TIMED SEE Time Series NOAA GOES XRS-­‐A Channel NOAA GOES XRS-­‐B Channel NOAA GOES EUVS-­‐B Channel (includes He II line) NOAA GOES EUVS-­‐E Channel (includes Ly-­‐α line) Mg II Index from SORCE SOLSTICE 40-­‐day trailing average of EUVS-­‐B 40-­‐day trailing average of EUVS-­‐E 40-­‐day trailing average of Mg II Index Normalized Wavelength
(Wavelength / Wavelength on 1/1/12)
Normalized Wavelength
(Wavelength / Wavelength on 1/1/12)
-­‐  Next, used weights from fi8ng to 2012 to predict 2011 data -­‐  25 – 30 nm (correla'on 0.997) -­‐ 90 – 95 nm (correla'on 0.916) 2011 Predictions, 25 - 30nm
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2011 Predictions, 90 - 95nm
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-­‐ Again, we examine the RMS difference between the model and the data RMS Uncertainty in Model Predictions, 2011
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No clear wavelength dependence like 2012 0.002
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2013 Model Predic'ons -­‐  Used weights from 2012 to predict data from the first half of 2013 -­‐ 25 – 30 nm (correla'on 0.994) -­‐ 90 – 95 nm (correla'on 0.780) 1.0
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2013 Predictions, 90 - 95nm
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RMS Uncertainty
Again, more error in model at longer wavelengths 0.004
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Some inputs add, some subtract to make the total contribu'on 20
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EUV B
EUV B Smooth
EUV E
EUV E Smooth
XRS Short
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MgII
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Contributions of EUVE and Smooth
MgII
MgII Smooth
-­‐  As expected, XRS bands important only at very short wavelengths -­‐  Trends in input and the smoothed input tend to counteract each other: Relative Contributions of EUVB and Smooth
Relative Contributions of MgII and Smooth
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-­‐  This has the effect of making inputs that originally showed limb darkening show limb brightening, which is characteris'c of EUV irradiance Comparison to FISM Model -­‐  FISM (Flare Irradiance Spectral Model) developed as model for solar irradiance 0.1 – 190 nm -­‐  Uses one proxy per 1-­‐nm bin to predict irradiance in that bin -­‐  The use of real-­‐'me EUV measurements from GOES as well as the dependence of each bin on mul'ple proxies may allow our model a higher degree of flexibility and accuracy than FISM -­‐  When comparing the two models, we found that our model had up to 8% higher correla'on at shorter wavelengths, and the FISM model had ~3-­‐4 % beuer correla'on at longer wavelengths Percent Difference Between Models and Data for 2011
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FISM model differs more from data at shorter wavelengths, where our model performs beuer 0.4
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GOES- and SORCE-Based Model
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-­‐  Unclear whether some of the short-­‐wavelength differences between FISM and our model originate from inconsistencies between the reference data sets (SDO-­‐EVE for our model, TIMED-­‐SEE for the FISM model) -­‐  Both models have drops in accuracy past ~50 nm – possible that there is not very good data at this range, or that proxies and inputs are not available in this region Data
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Relative Contributions of Each Parameter
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and Systems XVIII, Quebec, Canada, ASP Conference Series, Vol. 411, p. 251-­‐254. 0.4
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RMS Uncertainty in Model Predictions, 2013
-­‐  (4) Markwardt, C. B. 2009, ‘Non-­‐Linear Least Squares Fi8ng in IDL with MPFIT,’ in proc. Astronomical Data Analysis So0ware 4
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-­‐  RMS uncertainty in model compared to data: XRS EUVS-­‐B EUVS-­‐E -­‐  Fi8ng algorithm: mpfit for IDL -­‐  Developed by Craig Markwardt (4), based on the Levenberg-­‐Marquardt algorithm (damped least-­‐squares method) 0.6
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Most large-­‐ and small-­‐ scale varia'ons captured 2013 Predictions, 25 - 30nm
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90% correlation
-­‐  Correla'on for all three years is above 90% for wavelengths below 50 nm 2012
-­‐  Correla'on then drops, remaining b2011
etween about 60% and 90% for 50 – 105 nm 2013
Solar Cycle
Variability
Relative
Contributions
of Each
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-­‐  However, solar variability has opposite trend – most variable (therefore m
ost i
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model) wavelengths have the best correla'on 1
-­‐  Even at longer wavelengths, model can be used as a guide for EUV irradiance; at shorter wavelengths, it can very accurately predict irradiance 0
Some of large features approximately captured 0.6
2011 Model Predic'ons Input Data Sets 04-12
Normalized Wavelength
(Wavelength / Wavelength on 1/1/12)
0.1 – 6 nm 6 – 40 nm 40 – 105 nm Data
Model
RMS Uncertainty
Wavelength Range Model captures large-­‐
scale varia'on very well 80
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Solar Variability
(Solar Max Irradiance/Solar Min Irradiance
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RMS Uncertainty in Data Fit, 2012
model for aeronomic calcula'ons, J. Geophys. Res., 99, 8981. (2) Tobiska, W. K., T. N. Woods, F. G. Eparvier, R. Viereck, L. Floyd, D. Bower, G. J. Rouman, and O. R. White (2000), The SOLAR2000 empirical solar irradiance model and forcast tool, J. Atmos. Sol.Terr. Phys., 62, 1233. (3) Chamberlin, P. C., T. N. Woods, and F. G. Eparvier (2007), Flare Irradiance Spectral Model (FISM): Daily component algorithms and results, Space Weather, 5, S07005 Data Sets 2
Data & Model Prediction Correlation
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2012
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Solar Cycle Variability
-­‐  Instead of showing graphs of all other bands, we provide a plot of the RMS error between the model and data for each wavelength bin (1) Richards, P. G., J. A. Fennelly, and D. G. Torr (1994), EUVAC: A solar EUV flux -­‐  Recreate the EUV irradiance in each bin by using least-­‐squares analysis to fit observed irradiance from to broadband GOES-­‐15 EUVS & XRS data and current proxies -­‐ Use 2012 measurements to find weights for: observed irradiance in a 5nm band = weight 1 (offset) + weight 2*XRS-­‐A + weight 3*XRS-­‐B + weight 4*EUVS-­‐B + weight 5 * EUVS-­‐B 40-­‐day smooth + weight 6*EUVS-­‐E + weight 7*EUVS-­‐E 40-­‐day smooth + weight 8* SORCE Mg II index + weight 9* SORCE Mg II 40-­‐day smooth -­‐  Fi8ng algorithm returns an array of fi8ng weights; 9 columns of weights by 21 rows of bins -­‐  Use these weights mul'plied by today’s proxy data to obtain a predic'on for the EUV flux 4
Linear Correla'on Coefficient 0.4
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Discussion Percent Contribution
Normalized Wavelength
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Large gap in reference data Fit to 2012 Reference Data, 25 - 30nm
-­‐  One of the least accurate fits (correla'on .73): 90 – 95 nm bin Model doesn’t capture very much small-­‐scale varia'on at all 0.8
Percent Difference
(Model - Data) / Data
-­‐  For 20 5-­‐nm bins between 5 and 105nm, determine a set of weights that will convert a linear combina'on of input data into the desired output data -­‐  Use these weights as a proxy model for EUV that, because it includes EUV data, will be more accurate and dynamic then an F10.7 proxy alone -­‐  Test this model’s effec'veness when compared to other common EUV models and proxies: sunspot number, F10.7 index, EUVAC model (1) , SOLAR2000 model (2) , FISM model (3) Model doesn’t capture all small-­‐scale varia'on 8
Percent Contribution
Objec'ves Fit to 2012 Reference Spectra -­‐  Essen'al for ini'al fit to be accurate, as this is what determines the fi8ng coefficients -­‐  Inaccuracies in ini'al fit will likely produce inaccuracies in the model predic'ons for that band -­‐  One of the more accurate fits (correla'on .98): 25 -­‐ 30 nm bin Normalized Wavelength
(Wavelength / Wavelength on 1/1/12)
Several instruments are able to measure the full EUV spectrum at sufficient wavelength resolu'on for those interested in upper-­‐atmosphere modeling, the effects of space weather, and modeling satellite drag. No missions are planned at present to succeed TIMED and SDO, which currently provide this data source. In order to develop a suitable replacement for these measurements, we use the magnesium core-­‐to-­‐wing ra'o from SORCE SOLSTICE as well as broad-­‐
band EUV measurements made by the NOAA GOES satellite to model the EUV spectrum from 0.1-­‐105 nm at 5 nm resolu'on. Using a Levenberg-­‐Marquardt least squares fi8ng algorithm, we determined a matrix of coefficients that could be mul'plied by our input data 'me series to produce our output data 'me series. As inputs, we used the SORCE Mg II index, the GOES EUVS-­‐B, EUVS-­‐E, XRS-­‐A, and XRS-­‐B channels as well as 40-­‐day backwards smoothed versions of these 'me series to provide opera'onally useful data with the Carrington rota'on dependence removed. We fit to the observed spectrum from TIMED SEE and SDO EVE for the full 2012 year. Applying this model to 2011 and the first six months of 2013, we found that the correla'on between the model predic'ons and the observed spectrum was above 90% for the 0.1-­‐50 nm range, and between 60% and 90% for the 50-­‐105 nm range. These results provide a very promising poten'al source for an empirical EUV spectral model aier direct measurements are no longer available. 1.0
Linear Pearson Correlation
Results Linear Pearson Correlation
Abstract Data & Model Prediction Correlation
Solar Variability
(Solar Max Irradiance/Solar Min Irradiance
(1)Laboratory for Atmospheric and Space Physics, Boulder, CO (2)University of Colorado, Boulder, CO (3) NOAA Space Weather Predic'on Center, Boulder, CO (4) NOAA Na'onal Geophysical Data Center, Boulder, CO 80
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-­‐  All three years suggest that the model is more accurate below ~50 nm Conclusions -­‐  Assuming that EUV irradiance can be modeled as a linear combina'on of input data sets and proxies is both effec've and computa'onally efficient -­‐  Predic'ons for 0.1 – 50 nm could be made with a high degree of accuracy (< 4% difference between data and model predic'ons) -­‐  Predic'ons for 50 – 105 nm could be made, but with less accuracy (6-­‐10% difference between data and model predic'ons) -­‐  Our model compares favorably with the FISM model -­‐  There may be inconsistencies or errors in the reference spectrum for the 60-­‐80 nm range, leading to difficul'es in model predic'ons -­‐  EUV is difficult to measure and degreda'ons in instruments may have not been fully accounted for