Space Weather

Using SDO EVE data as a proxy for GOES XRS B 1–8 angstrom

Authors


Corresponding author: T. N. Woods, Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80303, USA. (tom.woods@lasp.colorado.edu)

Abstract

[1] Solar soft X-ray irradiance measured by the GOES X-Ray Sensor (XRS) is a critical measurement for space weather operations. At present, there is a primary GOES XRS operating with a second XRS in storage on orbit. This configuration results in gaps in critical observational coverage when the primary XRS is nonoperational such as during satellite maneuvers and during the spring and fall eclipse seasons. EUV Variability Experiment (EVE) on NASA's Solar Dynamics Observatory provides near–real-time measurements of the solar soft X-ray irradiances at wavelengths similar to XRS. This study examines the accuracy in using EVE data as a proxy for GOES XRS. Using EVE data, we develop three different solar irradiance index models, which are then tested to determine how well they predict the XRS irradiances and magnitude (GOES class) of solar flares. The best performing index model has been implemented in Version 3 of EVE data and is publicly available within minimal latency through the EVE Science Processing and Operations Center.

1 Introduction

[2] Solar soft X-ray irradiance recorded by the GOES X-Ray Sensor (XRS) is a critical measurement for space weather operations. The GOES soft X-ray irradiance is used by NOAA Space Weather Prediction Center to monitor solar flares [e.g., Garcia, 2000], which cause radio blackouts, decrease the accuracy of GPS, and increase atmospheric drag on satellites. Currently, XRS measurements come solely from the GOES 15 satellite with a second XRS in storage on orbit. During the satellite's semiannual eclipse seasons and other, unplanned, spacecraft outages, EUV Variability Experiment (EVE) on NASA's Solar Dynamics Observatory (SDO) provides the only back-up for XRS data. As we approach the maximum of solar cycle 24, the occurrence of large solar flares is expected to increase and the more frequent interruptions in our ability to monitor the solar activity in near real time could put our nation's assets at risk.

[3] The Solar Dynamics Observatory, launched in February 2010 with a primary mission extending through October 2015, includes EVE, which can serve as a proxy for GOES XRS and expand flare monitoring capabilities. While EVE has several instruments, it includes two channels, the Solar Aspect Monitor (SAM) and EUV SpectroPhotometers (ESP), which measure the solar soft X-ray irradiances at wavelengths similar to GOES XRS. The ability to use EVE data to accurately determine the magnitude of a solar flare with minimal latency provides an invaluable back-up for our current space weather capabilities.

[4] The objective of this study is twofold. First, we describe the development of three solar irradiance index models that use EVE data to estimate the GOES XRS B 1–8 angstrom irradiances. Two of these models use ESP data while the third uses SAM. Second, we calculate how well each of these models performs in predicting both the GOES soft X-ray irradiance and magnitude (GOES class) of flares. Using these results, we are able to determine which index model is best able to reproduce the GOES XRS B 1–8 angstrom irradiances and the limitations in using that model.

2 Data

[5] In this study, we examine the 25 month period from 1 July 2010 to 31 July 2012 to determine how well SDO EVE data perform in specifying the solar soft X-ray irradiance and flare magnitude. Although the primary science mission for SDO started on 1 May 2010, numerous changes were made to the operation of EVE during May and June 2010. While these changes should have, at most, a small impact on the space weather data, we chose to ignore these early observations for the sake of using a consistent data set.

[6] The EUV Variability Experiment is one of three instrument suites on SDO and is designed to measure EUV and soft X-ray solar spectral irradiance. Because Woods et al. [2012] gives a full description of the EVE instrument and science data products, only a brief summary is provided here to highlight EVE observations used in this study. To meet the measurement goals, EVE consists of several instruments. The primary observable, the solar EUV spectral irradiance, is provided by the Multiple EUV Grating Spectrometers (MEGS). MEGS measures the spectral irradiance from 5 to 105 nanometers with 0.1 nanometer spectral resolution at 10 second time cadence. ESP provides broadband irradiances in four channels (0.1–7, 17.1, 25.7, and 30.4 nanometers) with 0.25 second time cadence. A fifth ESP channel centered at 36.6 nanometers does not produce valid solar measurements. SAM is a pinhole camera, which produces images of the Sun in the soft X-rays from 0.1 to 7 nanometers with 15 arcseconds per pixel resolution and 10 second cadence. To increase the solar signal, individual SAM images are added to create 1, 5, or 10 minute images. Finally, MEGS-P is a photodiode that measures the irradiance of the Lyman-α line at 121.6 nanometers with 0.25 second time cadence. Discussions of the preflight calibrations and performance are found in Hock et al. [2012] for MEGS and SAM and Didkovsky et al. [2012] for ESP.

[7] The EUV Variability Experiment produces both “space weather” and “science” data products, available from EVE Science Processing and Operations Center (http://lasp.colorado.edu/eve). Science data products include solar spectral and extracted line irradiances from MEGS and broadband irradiances from ESP. These data products are fully calibrated and generated at full spectral resolution and time cadence. They are generally available within 36 hours of the observation. The space weather data products are available with minimal latency and are generated using simplified processing algorithms and at reduced time cadence. EVE space weather data products are designated either as “Level 0C” or “Level 0CS”, depending on the source of the data. Level 0C data comes from regular science telemetry (Ka-band), which has a 3 minute minimum latency built-in. Level 0CS data, on the other hand, comes from the housekeeping telemetry (S-band). S-band data have a lower latency (approximately 15 seconds) but include diode measurements (ESP and MEGS P) at reduced time cadence (one 0.25 second integration per 10 seconds). Level 0CS contains only data from the ESP and MEGS-P diodes while Level 0C includes data from all EVE channels including SAM.

[8] Here we use two different space weather data products. The first is the Level 0CS counts files. There are two versions of the Level 0CS data: one reports irradiance and the other reports counts (per integration). Here, because we are developing several index models, we want to use the counts files, which is essentially raw data. While the EUV channels in EVE have some degradation, the 0.1–7 nanometers range is not very sensitive to degradation related to contamination, and the ESP and SAM channels in this band have not yet had any measurable degradation. Either the Level 0CS irradiance or counts files can be used, however, for space weather operations because they both include estimates of the GOES XRS irradiances from the preferred index model. Prior to Version 3, the single component model described in section 3.1 was used. Version 3 uses the two-component model described in section 3.2. Level 0CS files, either counts or irradiance version, are ASCII files spanning 24 hours and containing 1 minute averages of either the irradiance or the counts per integration for each of the ESP and MEGS-P diodes. The files also include proxies for GOES XRS A 0.5–4.0 angstroms, GOES XRS B 1–8 angstroms, and SOHO SEM 26–34 nanometers irradiances. The files for the current day are updated every minute and archived at the end of the day.

[9] The second EVE space weather data product we use in this study is the Level 0C SAM 1 minute center of irradiances (SAM_ci_1min). These files contain parameters extracted from SAM images. Like the Level 0CS files, the SAM files are ASCII files spanning 24 hours. They contain among other parameters the average signal on SAM, the center-of-brightness location, the SAM XRS index model, and the location of the brightest pixel. Because of the longer latency of the Level 0C product, the SAM index model has less utility than the models derived from ESP using the Level 0CS data.

[10] To develop and test EVE index models for GOES, we use the 1 minute GOES XRS B 1–8 angstrom irradiances, obtained from NOAA's National Geophysical Data Center (NGDG, http://satdat.ngdc.noaa.gov). These are the measurements that the index models are trying to reproduce.

3 Development of GOES XRS Index Models

[11] The goal of any index model is to use one set of observables to estimate another. Here we want to use the EVE 0.1–7 nanometers data from either ESP or SAM, x, to derive the GOES XRS B 1–8 angstrom X-ray irradiance, y. The simplest index model is where y is a function of x:

display math(1)

[12] More complicated, and potentially more accurate, models can be derived by using more proxies:

display math(2)

[13] In this study, we develop and compare three index models to estimate the GOES X-ray irradiance. The first, a single component model, uses a power law between the ESP 0.1–7 nanometers count rates and the GOES X-ray irradiances. The second, a two-component model, separates both the ESP 0.1–7 nanometers and the GOES time series into a slowly varying background signal and a faster varying flare component. This method attempts to account for differences in the bandpasses of the two instruments by examining the solar variability at those wavelengths. The final model is a single component index model using count rates from SAM soft X-ray images.

3.1 Single Component ESP Index Model

[14] The GOES XRS B 1–8 angstrom index model in the EVE Level 0CS Version 2.1 data products (hereafter, the single or one-component model) is based on a polynomial power law fit between the ESP 0.1–7 nanometers dark-corrected count rates, x, and the GOES XRS B 1–8 angstrom irradiances, IXRS:

display math(3)

[15] The dark-corrected ESP 0.1–7 nanometers counts, x, is given by

display math(4)

[16] The 0.1–7 nanometers channel on ESP is a quadrant diode so C0–7nm is the sum of the counts on each of the quadrants. Because each of the four quadrants is a separate detector, the dark diode signal, Cdark, needs to be multiplied by four. While we use term “dark”, the ESP dark signal is really a deliberate, significant electrometer offset that is much larger than the true diode dark. Here, the corrected count rates are in units of DN (Data Numbers) per integration (0.25 seconds) rather than DN per second.

[17] The coefficients used in the one-component model are given in Table 1. Figure 1a shows the ESP 0.1–7 nanometers dark-corrected count rates versus the GOES XRS B 1–8 angstrom irradiances for every 1 minute interval between 1 July 2010 and 31 July 2012. First, notice that bad data points have not been removed from the figure. The published space weather data from EVE prior to Version 3 includes data taken during calibrations and spacecraft maneuvers. In Version 3, these special data have been excluded. For determining the fits for all the models and calculating any statistics, housekeeping data are used to remove the bad data points. Thus, the bad points do not influence the calculation of the model coefficients or the comparison of the different models and are only shown in Figure 1a to illustrate the presence of bad data in the space weather data products prior to the release of Version 3.

Table 1. Coefficients for the One-Component Model
CoefficientValue
a0–19.6529
a19.52992
a2–2.16084
a30.189092
Figure 1.

Relationship between corrected EVE count rates and GOES XRS B 1–8 angstrom irradiances for each of the three index models. (a) The one-component model, which uses ESP 0.1–7 nanometers dark-corrected counts (black points) and a power law fit (red line), is basis of the one-component model that currently used in the EVE Level 0CS space weather data product. (b) The two-component model (middle) partitions the ESP 0.1–7 nanometers dark-corrected counts into a cool component (blue) and hot component (red). Each component has a separate power law fits (black lines). (c) The SAM index model uses a combination of a linear (blue) and two power law (green and red) relationships between the SAM corrected count rate and GOES XRS B irradiances.

[18] Second, during flares (data points in the upper right of Figure 1a), a hysteresis-like effect is visible. This is due to the differences in the bandpasses of the two instruments. As a result, each instrument has a different response to the thermal evolution of a flare. A critical end result of this effect is that the GOES class of flare can be significantly underestimated using the one-component model. This will be discussed in greater detail in section 4.

3.2 Two Component ESP Index Model

[19] Using a two-component model, it is possible to mitigate the differences in the bandpasses of the two instruments. Here, we have used a “cool” component, represented by the background signal, and a “hot” (flare) component, represented by the excess counts above the background.

[20] The ESP 0.1–7 nanometers channel captures both the soft X-rays from 0.1 to 0.8 nanometers (1–8 angstroms) that GOES XRS measures and an additional component from 3 to 7 nanometers. Overall, the solar irradiance spectrum from 0.1 to 7 nm is dominated by thermal Bremsstrahlung continuum. The region of the spectrum 3 to 7 nanometers is less temperature dependent and thus, varies less with solar activity than the spectrum from 0.1 to 0.8 nanometers. The response of both the ESP 0.1–7 nanometers and GOES XRS B 1–8 angstrom instruments can be construed as consisting of two components: one at shorter wavelengths that increases dramatically during a flare, a “hot” component, and the second at longer wavelengths that is less affected by changes in temperature, a “cool” component. Because the two instruments have different bandpasses, we can expect different power law fits for hot and cool components.

[21] The two-component model is described as the sum of two power law fits

display math(5)

[22] The inputs for the index model, xcool and xhot, are calculated in three steps. First, the dark-corrected count rate is calculated using equation (4). In this model like the one-component model, the ESP 0.1–7 nanometers counts are in units of DN per integration.

[23] Next, the cool component, xcool, is calculated. Figure 2 highlights the steps done in calculating xcool a single data point denoted by the black vertical line using GOES XRS B 1–8 angstroms. For every 1 minute data point, the code finds the previous 23 hours of dark-corrected count rates (1380 data points, shaded region in Figure 2). Then, the median of every 60 points (equivalent to one hour worth of data) is calculated to generate 23 hourly background signals (blue circles in Figure 2). The instantaneous background signal is the minimum of these 23 hourly background signals (horizontal blue line and red circle in Figure 2). Calculating 1 hour medians before finding the minimum removes the effects of any spurious dropouts in the signal. In the final step, the instantaneous background signal (red curve in Figure 2) is smoothed by taking the mean of the previous 2 hours of instantaneous background signals (120 points) to arrive at the cool component signal. This smoothing removes any discrete changes in the background signal that arise.

Figure 2.

GOES XRS B 1–8 angstrom irradiance for a three day period in June 2012 showing how the cool component in the two component model is calculated. See text for a description of the calculation.

[24] Finally, the hot component, xhot, is simply the excess signal above the cool component signal:

display math(6)

[25] The hot component cannot be negative although it can be zero. As a result, this model will overestimate the GOES XRS B 1–8 angstroms irradiance at the lowest levels, approximately 2% of the time.

[26] To calculate the coefficients for the cool component, we calculated xcool for both the ESP corrected counts and the GOES irradiances. The coefficients are then determined by a power law fit between the ESP and GOES cool components calculated for every 1 minute interval between 1 July 2010 and 31 July 2012.

[27] The coefficients for the hot component are calculated to specifically capture the GOES class of flares. The GOES class of a flare is defined based on the maximum of the GOES XRS B 1–8 angstroms irradiance. Using the NOAA event list, we calculated the maximum in both the ESP corrected counts and the GOES irradiances during each flare and subtract the average cool component

display math(7)

[28] Because ESP and GOES have different bandpasses, the peak irradiance during a flare may occur at different times. As the ESP index model is expected to be used when GOES data is not available, using the peak irradiances irrespective of the peak time allows for a fairer comparison. The hot component was calculated for over 4000 flares and the power law fit is then determined.

[29] Statistically, for flares larger than C1.0, ESP peaks on average 0.2 minutes after XRS with a standard deviation is 2.6 minutes. For flares larger than M1.0, ESP peaks on average 0.4 minutes after XRS with a standard deviation of 3.3 minutes.

[30] Although the fits for this model were calculated using peak flare irradiances and the NOAA event lists, this model can be and is run in real time. It does not require any knowledge of when flares occur; it only needs a 23 hour record of the ESP Level 0CS counts.

[31] Figure 1b shows both the data points and the fits for each of the components in this model. The coefficients are given in Table 2. While there is more error in the fitting the cool component, the hot component has little scatter, particularly for larger (>M2.0) flares. As expected, the two components have different power law slopes.

Table 2. Coefficients for the Two-Component Model
CoefficientValue
a0–11.1492
a11.83733
b0–8.57188
b11.16638

3.3 Solar Aspect Monitor Index Model

[32] The Solar Aspect Monitor is a pinhole camera which utilizes an unused portion of one of the MEGS CCDs to produce images of the Sun in the soft X-rays with 15 arcseconds per pixel resolution and 10 second cadence. SAM has a similar bandpass to the ESP 0.1–7 nanometer channel as both have C, Al and Ti filters and Si detectors. SAM, like the ESP 0.1–7 nanometer channel, can be used as a proxy for the GOES XRS B 1–8 angstrom irradiance. Because SAM is intended to be a soft X-ray photon counter, very few photons are measured at low solar activity levels. During flares, however, concentrated large irradiances are observed and persist for minutes to hours. Active regions also persist from image to image.

[33] Like the ESP index models, the GOES XRS B 1–8 angstrom irradiance is estimated using the SAM dark-corrected count rate. As SAM produces images of the Sun, calculating the count rate is done in several steps. First, pairs of raw SAM images are filtered resulting in one lower-noise image at a 20 second cadence. The median of three 20 second images is used to estimate the 1 minute irradiance image. The dark is then subtracted based on nearby pixel values, and the sum of remaining counts is used to generate the SAM dark-corrected count rate in units of DN per second. In this fashion, the SAM image is treated as an energy detector without regard for spatial information. The filtering used in this method biases the signals toward the persistent features such as active regions and flares.

[34] Due to nonlinearities in the XRS and SAM relationship, the SAM index model uses three correlations for different solar activity levels. Figure 1c shows the SAM corrected count rate versus the GOES XRS B 1–8 angstrom irradiances for every 1 minute interval. Table 3 gives the values of the coefficients used in Version 2 and 3 of EVE data processing. The behavior is a simple linear function for lowest levels (B1.0 to B4.9):

display math(7)
Table 3. Coefficients for the SAM Index Model
CoefficientValue
a01.1 × 10–7
a14.0 × 10–11
b0–25.0717
b11.07757
c0–17.0211
c10.50867

[35] This changes to a power law relationship for intermediate levels (B5.0 to M4.9)

display math(8)

and a nearly square root log-log relation for very larger irradiances (greater than M5.0)

display math(9)

[36] The square root behavior is consistent with harder X-rays penetrating the pinhole holder that acts like a larger pinhole camera during larger flares. This behavior provides very robust flare location estimates. Usually, there are few of the shortest wavelength photons to persist through the filtering and median calculations. However, during large flares SAM count rates increase approximately as the square of the XRS in the large flare regime. It is anticipated that extremely large flares (approximately>X5.0) with very small spatial distributions may not follow this function due to excessive saturation of the detector from multiple photon strikes. Values well above saturation can cause charge to bleed outside the defined SAM area and therefore they are not included in the count rate.

4 Comparison of Index Models

[37] To determine which of the three index models produces better results, we compared how the models perform both overall and during large solar flares.

4.1 Comparing Models over the Long Term

[38] Figure 3 shows the 25 month time series for both the single component model (top, blue), two-component model (middle, red), and SAM index model (bottom, green) along with the GOES XRS B 1–8 angstrom irradiance (all three panels, black). Overall, the two-component and SAM index models appear to capture the long-term trends better than the one-component model. The SAM index model has a floor, which could result in over predicting the GOES XRS B 1–8 angstrom irradiances near the minimum between solar cycles 24 and 25.

Figure 3.

Time series from 1 July 2010 to 31 July 2011 of the index models (top: one-component in blue, middle two-component in red, bottom: SAM index model in green) and measured GOES XRS B 1–8 angstrom irradiances (all three panels, black).

[39] To highlight the differences between the models, the residuals, (model-measurement)/measurement, were analyzed. Figure 4 shows the two-dimensional histogram of these residuals for each of the models as a function of the index model irradiance. This figure allows an operational user to understand how common any given model value is and what the uncertainties for the value are.

Figure 4.

Two-dimensional histograms of the residuals, (model-measurement)/measurement, as a function of the index model irradiance for the one-component model (left), two-component model (middle), and SAM index model (right). Color indicates the number of points as a fraction of the total number data points (black/purple few points, orange/red more points).

[40] All three models tend to over predict the GOES XRS irradiances. Both the one-component and SAM index models over predict about 60% of the time while the two-component model over predicts about 75% of the time. However, the two-component model has smaller residuals: on average it over predicts the GOES XRS irradiance by 32% and under predicts it by 14%. In comparison, the one-component model over predicts by 60% and under predicts by 28%. The SAM index model over predicts by 39% and under predicts by 14%.

[41] The two-component model has smaller residuals than the one-component model for GOES levels M1.0 and below. The residuals are larger for the two-component model for GOES levels M5.0 and above; however, the residuals are still small. The SAM index model has large residuals below B4.0 and under predicts the GOES soft X-ray irradiances for the largest flares.

4.2 Capturing GOES Flare Class

[42] Of more interest for space weather operations is how well the models reproduce the GOES class of moderate and large flares. Using the NOAA event list, we calculated the peak irradiance during each flare for each of the index models. Because both SAM and the ESP 0.1–7 nanometer channel have different bandpasses than the GOES XRS 1–8 angstrom, the peak irradiance during a flare may occur at different times. As the index models will be used when GOES XRS data are not available, using the peak irradiance in the index model rather than irradiance at the flare peak time from GOES XRS is preferred for this study.

[43] Figure 5 compares the GOES flare class with the peak modeled irradiance for almost four thousand flares observed by both GOES and EVE from 1 July 2010 to 31 July 2012. Visually, the two component model appears to do better than the single component model or the SAM model. The single component model underestimates the GOES class for M-class flares and overestimates the GOES class for the largest X-class flares. The SAM model overestimates the M-class flares while underestimating the X-class flares. Overall, however, all three models show little scatter for a given flare class. The differences between the model are subtle and reveal systematic trends.

Figure 5.

Comparison (top is the index model currently used in L0CS, bottom is the proposed two-component index model). The grey shaded regions highlight the regions both the model correctly predicts the NOAA radio blackout scale. The red points are flares that the model correctly predicted the NOAA radio blackout scale. The blue points are flares that the model incorrectly predicted the NOAA radio blackout scale. The black points are flares that are too small (<M1.0) to register on the NOAA radio blackout scale.

[44] To quantify the differences between the models, statistical parameters are derived from contingency tables, which are used to display categorical variables. In this case, we used the NOAA radio blackout scale (flare impact scale) to generate categorical variables from the quantitative flare classes. The NOAA radio blackout scale describes disturbances of the ionosphere caused by X-ray emissions from the Sun are defined based on the GOES class of a flare. The scale goes from R1 (minor) to R5 (extreme) and is defined in Table 4. The NOAA radio blackout scale provides one way of testing how the index models will perform when used in operations.

Table 4. NOAA Radio Blackout Scale
NOAA Radio Blackout ScaleRange of GOES ClassesNumber of Events in This Study
R1M1.0-M4.9177
R2M5.0-M9.923
R3X1.0-X9.914
R4X10.0-X19.90
R5X20.0+0

[45] From 1 July 2010 to 31 July 2012, no flares X10.0 or larger were observed so the performance of the models for categories R4 and R5 cannot be tested. For R1 flares (177 events), the one-component model underestimated their radio blackout scale 34% (60 events) of the time and never overestimated it. The two-component model underestimated R1 flares 13% (23 events) of the time and again never overestimated it. The SAM model underestimated R1 flares 19% (34 events) of the time and overestimated them 13% (23 events) of the time.

[46] For R2 flares (23 events), the one-component model underestimated the radio blackout scale for 43% (10 events) of events and never overestimated it. The two-component model underestimated R2 flares 17% (4 events) of the time and overestimated 9% (2 events) of the time. The SAM model underestimated R2 flares for 13% (3 events) of events and overestimated for 26% (6 events) of events.

[47] For R3 flares (14 events), both the one-component and two-component models correctly estimated all the events. The SAM model underestimated one event (7% of the time). For that event, SAM data was of poor quality and the flare does not show up on the plot in Figure 5c.

[48] For each of the three categories (R1 through R3), a basic two-by-two contingency table was created for each model (Table 5). The value found in the upper left (A) is the number of hits or flares where NOAA radio blackout category was correctly predicted by the model. The value in the upper right (B) is the number of false alarms or flares where the NOAA radio blackout category was predicted by the model but not observed by GOES. The value in the lower left (C) is the number of misses or flares where the NOAA radio blackout category was observed by GOES but not predicted by the model. Finally, the value in lower right (D) is the number of correct rejections or flares where the NOAA radio blackout category was neither observed by GOES nor predicted by the model. Contingencies tables like this one do double count missed flares. For instance, a M6.0 flare that is the model estimates as M4.0 will be counted both in cell B for R1 events and in cell C for R2 events.

Table 5. Contingency Tables for NOAA Radio Blackout Scale
Observed Number of Flares
  R1R2R3
  YesNoYesNoYesNo
Predicted Number of Flaresone-component modelYes11714130140
No60380310397103980
two-component modelYes15425170142
No2337926397103978
SAM index modelYes12031423136
No5738149394813974

[49] Table 6 lists various statistical parameters that can be calculated from the contingency tables along with the range of possible values and the perfect score. In Table 7, these statistical parameters for each of the models and each of the NOAA radio blackout scales are shown. For the R1 and R2 events, the two-component model outperforms the other models. For R3 events, the one-component model performed perfectly while the two-component model outperforms the SAM index model. For R3 events, the two-component model, predicts that two high M-class flares should be X-class events.

Table 6. Definition of Statistical Parameters
ParameterDefinitionRangePerfect Score
Bias (B)(A + B)/(A + C)0to1
Probability of detection (POD)A/(A + C)0to11
Probability of false detection (POFD)B/(B + D)0to10
False alarm ratio (FAR)B/(A + B)0to10
Proportion correct (PC)(A + D)/(A + B + C + D)0to11
Critical success index (CSI)A/(A + B + C)0to11
Heidke skill score (HSS)2(AD –BC)/[(A + C)(C + D) + (A + B)(B + D)]–1to11
Table 7. Statistical Parameters for Each Models and Category of the NOAA Radio Blackout Scales
ParameterR1 (M1.0–M4.9)R2 (M5.0–M9.9)R3 (X1.0–X9.9)
One-compTwo-compSAMOne-compTwo-compSAMOne-compTwo-compSAM
B0.7401.0110.6950.5650.7391.6091.0001.1431.357
POD0.6610.8700.6780.5650.7390.6091.0001.0000.929
POFD0.0040.0070.0010.0000.0000.0060.0000.0010.002
FAR0.1070.1400.0240.0000.0000.6220.0000.1250.316
PC0.9810.9880.9850.9970.9980.9921.0000.9990.998
CSI0.6130.7620.6670.5650.7390.3041.0000.8750.650
HSS0.7500.8590.7920.7210.8490.4631.0000.9330.787

[50] The bias (B) is a measure of whether the model under (B < 1) or over (B < 1) predicts the radio blackout category. For R1 flares (small M-class flares), the two-component model over predicts while the one-component and SAM models underpredict. For R2 flares (the larger M-class flares), the SAM index model over predicts and the one- and two-component models under predict. For both R1 and R2 flares, the bias of two-component model is closer to unity than the bias of the other models. Both the two-component and SAM index models over predict and the one-component model perfectly predicts R3 flares (X-class flares).

[51] Looking at the probability of detection, approximately one-third of the R1 flares were not predicted by the one-component or the SAM index models, compared to only one-seventh using the two-component model. For R2 flares, both the one-component and SAM index model captured around 60% while the two-component model captured over 70%. For the R3 flares, both the one- and two-component models correctly predict the 14 observed X-class flares while the SAM index model predicts 13 of the 14 flares.

[52] Both probability of false detection (POFD) and false alarm rate (FAR) describe the frequency of false alarms. When events are rare (like M- and X-class flares), there are a large number on correct rejections. As a result, POFD will be close to zero and FAR is a better measure of the frequency of false alarms. The SAM index model results in fewer false alarms for R1 events but has a higher false alarm rate for R2 and R3 events. Both the one- and two-component models have a FAR of ~10% for R1 flares and 0% R2 flares. For R3 flares, the one-component model has a FAR of 0% and the two-component model has a FAR of 13%.

[53] Like POFD, the proportion correct for rare events is strongly influenced by the number of correct rejections. For all models and radio blackout categories, proportion correct is close to unity. The critical success index (CSI) is similar to the proportion correct but is not affected by correct rejections. The two-component model has the highest CSI for both R1 and R2 events. Although, the one-component model has a perfect CSI for R3 events, the CSI for the two-component model is still higher than any of the CSIs for R1 and R2 events.

[54] Finally, the Heidke skill score (HSS) measures the rate of correct forecasts, after correcting for random chance. Once again, the two-component model outperforms the other proxies for M-class flares (R1 and R2 events). Although, the one-component model has a perfect HSS for R3 events, the HSS for the two-component model is still higher than any of the HSSs for R1 and R2 events. We expect that the statistics of small number of R2 and R3 events can bias these results some.

5 Discussion and Conclusions

[55] In this study, we developed three different index models using data from SDO EVE for the GOES XRS B 1–8 angstrom irradiance. The first two models use data from ESP. One of the models, the one-component model uses a simple polynomial power law relationship between ESP dark-correct counts and XRS B irradiance. This model has a tendency to underestimate the magnitude of M-class solar flares while overestimating the background soft X-ray irradiance. The other ESP index model, the two-component model, attempts to address the different bandpass of XRS B and ESP by modeling the background irradiance (“cool” component) and flare irradiance (“hot” component) separately. While this method is more likely to overestimate than underestimate the irradiance, it accurately captures the magnitude of solar flares. The third and final index model uses data from SAM. This model is good at capturing the overall time series of XRS B but cannot estimate the GOES class for moderate or large flares (M-class and larger).

[56] The two-component index model using ESP data outperformed the other models both in predicting the GOES XRS B 1–8 angstrom irradiances and the GOES class or magnitude of solar flares. As a result, Version 3 of the EVE space weather data uses this two-component proxy in the Level 0CS data products.

[57] While the two-component model is an improvement over the one-component model, there is still some uncertainty in predicting the GOES class of a flare. For a given flare class estimated using the two-component model, Table 8 gives the range of “true” GOES flare classes. For instance, if the two-component model estimates the flare as M1.0, the measured or “true” flare class from GOES could be anything from C6.3 to M1.3. These estimates were done by first partitioning the flares studied to groups (ten intervals within each decade, e.g., B9.5–C1.5, C1.5–C2.5, etc.) based on the model flare class. Then we calculated the mean and standard deviation of GOES flare classes for all events within group and then found the linear fit in log-log space to the mean +/– 2 standard deviations. These curves were then used to populate Table 8.

Table 8. Range of Expected Flare Classes for Two-Component Model
Estimated EVE Flare ClassRange of GOES classes
C1.0B6.2–C1.5
C2.0B9.8–C2.3
C3.0C1.6–C3.7
C4.0C2.3–C5.1
C5.0C3.0–C6.5
C6.0C3.6–C7.9
C7.0C4.3–C9.3
C8.0C5.0–M1.1
C9.0C5.7–M1.2
M1.0C6.3–M1.3
M2.0M1.0–M2.1
M3.0M1.7–M3.4
M4.0M2.4–M4.7
M5.0M3.1–M6.0
M6.0M3.8–M7.3
M7.0M4.5–M8.6
M8.0M5.2–M9.9
M9.0M5.8–X1.1
X1.0M6.5–X1.2
X2.0X1.0–X1.9
X3.0X1.7–X3.2
X4.0X2.5–X4.4
X5.0X3.2–X5.6
X6.0X3.9–X6.7
X7.0X4.6–X7.9
X8.0X5.3–X9.1
X9.0X6.0–X10.3
X10.0X6.8–X11.4

[58] Overall, space weather data from EVE, which is available with minimal latency (<1 minute), has the capability to serve as a proxy for the GOES XRS B 1–8 angstrom irradiance. As there is only one GOES satellite currently monitoring solar activity, having an alternative source for the solar soft X-ray irradiance is critical and EVE provides a good proxy that can capture the time series of XRS B as well as the magnitude of flares (GOES class).

Acknowledgments

[59] This research was performed while R.A.H. held a National Research Council Associateship Award at the Air Force Research Laboratory. The Solar Dynamics Observatory mission and this research are supported by NASA, including NASA contract NAS5-02140 to the University of Colorado.

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