11institutetext:  Laboratory for Atmospheric and Space Physics, University of
Colorado, Boulder, CO, USA 22institutetext: Cooperative Institute for Research
in Environmental Sciences, University of Colorado, Boulder, CO, USA
33institutetext: National Centers for Environmental Information, National
Oceanic and Atmospheric Administration, Boulder, CO, USA 44institutetext:
Space Weather Prediction Center, National Oceanic and Atmospheric
Administration, Boulder, CO, USA

# The GOES-R EUVS Model for EUV Irradiance Variability

G. Wuchterl 11 C. Ptolemy Just to show the usage of the elements in the author
field22 E. M. B. Thiemann 11 F. G. Eparvier 11 D. Woodraska 11 P. C.
Chamberlin 11 J. Machol 2233 T. Eden 11 A. R. Jones 11 R. Meisner 11 S.
Mueller 11 M. Snow 11 R. Viereck 44 T. N. Woods 11

###### Abstract

The Geostationary Operational Environmental Satellite R (GOES-R) series of
four satellites are the next generation NOAA GOES satellites. Once on orbit
and commissioned, they are renamed GOES 16-19, making critical terrestrial and
space weather measurements through 2035. GOES 16 and 17 are currently on
orbit, having been launched in 2016 and 2018, respectively. The GOES-R
satellites include the EUV and X-ray Irradiance Sensors (EXIS) instrument
suite, which measures calibrated solar irradiance in 8 lines or bands between
25 and 285 nm with the Extreme Ultraviolet Sensors (EUVS) instrument. EXIS
also includes the X-Ray Sensor (XRS) instrument, which measures solar soft
X-ray irradiance at the legacy GOES bands. The EUVS measurements are used as
inputs to the EUVS Model, a solar spectral irradiance model for space weather
operations that predicts irradiance in twenty-two 5 nm wide intervals from 5
nm to 115 nm, and one 10 nm wide interval from 117 to 127 nm at 30 second
cadence. Once fully operational, NOAA will distribute the EUVS Model
irradiance with 1 minute latency as a primary space weather data product,
ushering in a new era of rapid dissemination and measurement continuity of EUV
irradiance spectra. This paper describes the EUVS Model algorithms, data
sources, calibration methods and associated uncertainties. Typical model
(relative) uncertainties are less than $\sim$5% for variability at time-scales
longer than 6 hours, and are $\sim$25% for solar flare induced variability.
The absolute uncertainties, originating from the instruments used to calibrate
the EUVS Model, are $\sim$10%. Examples of model results are presented at both
sub-daily and multi-year timescales to demonstrate the model’s capabilities
and limitations. Example solar flare irradiances are also modeled.

##  1 Introduction

Solar extreme ultraviolet (EUV, 10-121 nm) irradiance is the primary energy
input into the Earth’s upper atmosphere at low to mid latitudes and at all
latitudes during geomagnetically quiet periods. By ionizing gases, EUV
radiation creates the ionosphere and heats the thermosphere. The solar EUV
irradiance varies significantly due to the evolving 11-year solar cycle,
27-day solar rotation period and transient solar flares; resulting in
corresponding changes in the density, temperature and composition of the
thermosphere and ionosphere. Additionally, both the solar spectrum and
atmospheric gas absorption cross-sections are highly structured at EUV
wavelengths, influencing the altitudes at which solar EUV radiation is
absorbed. EUV-induced changes in the thermosphere can extend to Low Earth
Orbit (160-2000 km), directly impacting satellite drag, where a hotter, denser
thermosphere exerts a greater drag force on the satellites orbiting within it
(Jachhia, 1959). With regard to the ionosphere, EUV-induced changes modulate
its index of refraction, impacting transionospheric communication and
navigation signals (Davies, 1990). The response of both the ionosphere and the
thermosphere to EUV changes are relatively fast, with the ionosphere
responding near instantaneously and the thermosphere responding in 2-4 hours
(e.g. Mendillo et al., 1974; Qian et al., 2010). As such, near real time solar
EUV spectral irradiance information is needed for accurate space weather
forecasting. To meet this demand, the National Oceanic and Atmospheric
Administration (NOAA) has included an operational (continuous, high time
cadence, low latency) EUV irradiance data product as part of its Geostationary
Operational Environmental Satellite R (GOES-R) series program. The GOES-R
satellites are scheduled to make observations from 2016-2035, providing nearly
two decades of real-time continuous solar EUV irradiance measurements, and
changing the paradigm for the availability and dissemination of spectral EUV
irradiance data.

The NOAA GOES-R series program is the latest iteration of the GOES satellite
constellation, and consists of four satellites, each carrying a suite of
identical instruments designed to monitor terrestrial and space weather
continuously. Once commissioned, the GOES-R series satellites will become GOES
16-19, with the first in the series, GOES-16, having launched on 19 November
2016, and the last in the series, GOES-19, anticipated to launch in the early
2020s and to be operational until at least 2035. The GOES satellites have
monitored solar soft X-ray irradiance in two bands since their inception in
1975 with the X-Ray Sensor (XRS) instruments, and GOES 13-15 have measured EUV
irradiance in several bands with the EUV Sensor (EUVS) instruments (Viereck et
al., 2007). For the GOES-R series satellites, new versions of the XRS and EUVS
instruments have been built as part of the EUV and X-ray Irradiance Sensors
(EXIS) instrument suite. The EXIS instrument suites were built at the
Laboratory for Atmospheric and Space Physics (LASP) at the University of
Colorado at Boulder. Each EXIS suite consists of the EUVS (Eparvier et al.,
2009), which measures solar emissions at 8 lines or bands between 25 and 285
nm, and the XRS (Chamberlin et al., 2009), which measures soft X-ray
irradiance in the legacy 0.1-0.8 nm and 0.05-0.4 nm bands.

The solar atmosphere is comprised of 4 distinct regions, which are (from
nearest to furthest from the surface): the photosphere, chromosphere,
transition region, and corona. They can be equivalently categorized according
to temperature with the photosphere being the coolest ($\sim$5700 K) and the
corona being the hottest ($>$1 MK). Solar radiation emitted from the different
regions of the solar atmosphere tends to vary differently as a result of the
different processes driving the dynamics within them. For example, bright
plasma tends to be concentrated regionally in active region magnetic loops in
the corona, whereas in the chromosphere, bright plasma is distributed more
uniformly across a magnetic network (Antia et al., 2003).

The emission lines observed by EUVS were selected to span a broad range of
emission formation temperatures in the solar atmosphere in order to capture a
broad range of irradiance variability. Specifically, EUVS-A measures the He II
25.6 nm, Fe XV 28.4 nm and the He II 30.4 nm lines; EUVS-B measures the C III
117.5 nm, H I 121.6 nm (Lyman-$\alpha$), C II 133.5 nm and the Si IV/ O IV
(blended) 140.5 nm lines; and EUVS-C measures the Mg II emission line core-to-
wing ratio (Heath and Schlesinger, 1986, hereafter, the Mg II Index) around
280 nm. These 8 fully-calibrated EUVS measurements (hereafter, the EUVS
Measurements) are used as inputs to the EUVS Level 1B solar irradiance model
(hereafter, the EUVS Model), which predicts solar EUV spectral irradiance
continuously at 30 second cadence and 1 minute latency in twenty-two 5 nm wide
intervals from 5-115 nm and a single 10 nm interval from 117-127 nm.

Solar EUV and Far Ultraviolet (FUV, 122-200 nm) irradiance is completely
absorbed in the Earth’s upper atmosphere, requiring it to be measured by
sophisticated space-based instrumentation that is prone to degradation. This
measurement difficulty has resulted in extended periods of time when direct
spectral irradiance measurements are unavailable, necessitating models of
solar EUV and FUV irradiance to bridge the observational gaps. Additionally,
because calibrations often differ from instrument to instrument, models of
solar irradiance provide the capability to estimate irradiance over a long
timespan, while avoiding discontinuities that occur at the edges of
concatenated datasets due to calibration differences.

Hinteregger (1981) proposed the first widely adopted EUV spectral irradiance
variability model, which was based on the Atmospheric Explorer-E EUV
Spectrophotometer (AE-E/EUVS) measurements. In his paper, Hinteregger reported
two models. The first model used the Fe XVI 33.5 nm and H Lyman-$\beta$ 102.6
nm emissions to model coronal and chromospheric variability, respectively,
with a set of regression coefficients that related these two emissions to the
EUV irradiance spectrum. Fe XVI 33.5 nm and H Lyman-$\beta$ 102.6 nm were only
available from AE-E/EUVS during this epoch and therefore this model was of
limited use, but the success of the method laid the foundation for models that
followed, including the GOES EUVS Model described here. The second model
proposed by Hinteregger (1981) used regression coefficients relating the
AE-E/EUVS measurements and the 10.7 cm solar radio flux (F10.7) daily and
81-day mean values to estimate the spectrum. Later, Torr and Torr (1985) re-
partitioned the Hinteregger (1981) model spectra into 37 spectral intervals
based on the absorption cross-sections of major constituent gases in the
Earth’s atmosphere.This repartitioning used twenty 5 nm intervals from 5 to
105 nm and then seventeen narrow intervals to model the irradiance of
individual emissions lines near regions where atmospheric absorption cross-
sections are highly structured. A significant advance occurred when Richards
et al. (1994) introduced the EUV flux model for Aeronomic Calculations
(EUVAC), which was essentially a re-calibration of the Torr and Torr (1985)
model coefficients to be consistent with more accurate rocket measurements.
Later work by Tobiska and Eparvier (1998) and Tobiska et al. (2000) added
space-borne model inputs in addition to F10.7; and incorporated new suborbital
rocket measurements and data from the San Marco 5 satellite into the model
calibration dataset. Regular sub-daily EUV measurements made by the Solar EUV
Experiment (SEE) on board the Thermosphere Ionosphere Mesosphere Energetics
and Dynamics (TIMED) satellite were incorporated into the Flare Irradiance
Spectral Model (FISM) developed by Chamberlin et al. (2007). Chamberlin et al.
(2008) incorporated the capability for estimating solar flare irradiance based
on the GOES/XRS irradiance into FISM. FISM was recently updated by Thiemann et
al. (2017a) to use measurements from the EUV Monitor (EUVM) on board the Mars
Atmosphere and EvolutioN (MAVEN) probe as inputs and included spectral
irradiance data from the EUV Variability Experiment (EVE) on board the Solar
Dynamics Observatory (SDO) in the model calibration dataset. The Solar
Spectral Proxy Irradiance from GOES (SSPRING, Suess et al., 2016) model uses
irradiance measurements from GOES-15 as inputs. The EUVS Model presented here
is an iteration of these preceding empirical models for solar spectral
irradiance, and the first to be implemented in an operational environment.

The long term dataset of EUV spectral irradiance observed by TIMED/SEE
provided an opportunity to rigorously test the idea that solar EUV variability
can be decomposed into groups of emissions which vary similarly depending on
the layer of the solar atmosphere from which they originate. A number of
studies investigated these assumptions statistically (Kretzschmar et al.,
2006; Chamberlin et al., 2007; Dudok de Wit et al., 2008; Amblard et al.,
2008; Lilensten et al., 2007; Dudok de Wit et al., 2009; Cessateur et al.,
2011). Notably, Amblard et al. (2008) used statistical methods to deconstruct
the solar spectrum into elementary components and found that a minimum of 3
elementary spectra are needed to reconstruct the EUV spectral irradiance,
representative of the inactive Sun, cool chromosphere and hot corona.
Chamberlin et al. (2007) used the long-term TIMED/SEE dataset to determine
model error for the integrated 0.1-193 nm band is reduced by $\sim$30$\%$ when
space-borne model-inputs are used in lieu of F10.7. Later, Cessateur et al.
(2011) used statistical methods to analyze the TIMED/SEE dataset and
determined that empirical model error could be reduced by a factor of two
using four spectral pass-bands measured from space rather than the commonly
used F10.7 and Mg II indices.

This paper presents the EUVS Model, its coefficients and the methods used to
derive them, as well as the model uncertainty. In Section 2, the model is
described and the model equations are presented. Section 3 presents the
historical data used to compute the model coefficients, the cross-calibration
between historical and EXIS measurements, and the associated systematic
uncertainty. Sections 4 and 5 present the long- and short-term model
components and their uncertainty; and Section 6 discusses the overall results.

The primary purpose of this paper is to show how the EUVS Model coefficients
and uncertainties are derived, rather than serve as a reference for their
exact values. The coefficients and uncertainties presented here are for
GOES-16 at the time of this writing and may change with updates to the
GOES-16/EXIS calibration. Additionally, the coefficients and uncertainties for
the GOES 17-19 EUVS Models will possibly differ from those presented here. As
such, current values for the EUVS Model coefficients and uncertainties will be
made available via the web address listed in the Acknowledgements section.

##  2 Model Description

The EUVS Model estimates irradiance in the $n^{th}$ wavelength interval,
$E_{n}(t)$, by solving the equation,

$E_{n}(t)=E_{n,0}+\sum_{i=1}^{8}j_{i,n}P_{i}(t)+\sum_{i=1}^{8}k_{i,n}Q_{i}(t),$
(1)

where the summations are over the 8 EUVS Measurements, $E_{n,0}$ is the offset
for the $n^{th}$ wavelength interval, and $P_{i}(t)$ and $Q_{i}(t)$ are the
long- and short-term components of the $i^{th}$ EUVS Measurement, and
$j_{i,n}$ and $k_{i,n}$ are the long- and short-term regression coefficients,
respectively. Note, the EXIS XRS measurements could also be included, but are
not used in practice because their inclusion increases model uncertainty due
to the variability at soft X-ray wavelengths typically being much larger than
that at EUV wavelengths. The long- and short-term components are defined by

$\displaystyle P_{i}(t)=\frac{\left<X_{i}(t)\right>_{T}-X_{i,0}}{X_{i,0}}$ (2)
$\displaystyle
Q_{i}(t)=\frac{X_{i}(t)-\left<X_{i}(t)\right>_{T}}{\left<X_{i}(t)\right>_{T}}$
(3)

where $X_{i}(t)$ is the $i^{th}$ EUVS Measurement with reference offset,
$X_{i,0}$, and (lagging) moving average, $\left<X_{i}(t)\right>_{T}$, over
time, $T$. The fractional units of $P_{i}(t)$ and $Q_{i}(t)$ reduces the
sensitivity to subtle differences between spectral resolution and pre-flight
calibrations of the historical model training data and the EUVS Measurements.

The short-term component is for modeling rapid solar flare induced variability
whereas the long-term component is for modeling more gradual non-flaring
variability. The separation of flaring and non-flaring variability is done
because different emission lines may contribute to the irradiance in a given
spectral band during flares as a result of the significant temperature
difference between flare and non-flare plasma. For example, the EUVS
Measurement at 25.6 nm is primarily due to He II emissions during non-flaring
times but dominated by Fe XIV emission during flares. As such, $T$ is taken to
be 6 hours in order to be significantly longer than most solar flares.
Specifically, T is $\sim$4 times larger than the expected X-class flare
duration as determined by Veronig et al. (2002), who analyzed nearly 50,000
flares and found 90$\%$ of X-class flares last less than 98 minutes. Modeled
irradiance for long duration flares, which can last for several hours, will be
subject to increased error if the flare irradiance contributes measurably to
the 6-hour average.

The offsets and coefficients in equations (1) - (3) are determined from
historical data as follows: $X_{i,0}$ is chosen as the minimum value for the
historical data representing the $i^{th}$ EUVS Measurement. $E_{n,0}$ and
$j_{i,n}$ are found by multiple linear regression fitting of historical data
representing $P_{i}(t)$ and the long-term average (nominally 6 hours) of
$E_{n}(t)$, $\left<E_{n}(t)\right>_{T}$; and $k_{i,n}$ is found by multiple
linear regression fitting of historical data representing $Q_{i}(t)$ and
($E_{n}(t)-\left<E_{n}(t)\right>_{T}$). These methods are described in further
detail in Sections 4 and 5, and the historical data are described in Section
3.

The EUVS Model wavelength intervals are 5 nm wide from 5 to 115 nm (i.e. 5-10
nm, 10-15 nm, …, 110-115 nm), with one 10 nm wide interval from 117 to 127 nm.
This is the official operational wavelength scheme produced in real time by
NOAA and is the focus of this paper.

The cadence of $X_{i}(t)$ (and, hence, the EUVS Model) is 30 seconds, where
$X_{i}(t)$ is a 30-second centered running average of the $i^{th}$ EUVS
Measurement. The EUVS measurements all nominally have a 1-second cadence
except for EUVS-C, which has a 3-second cadence. $\left<X_{i}(t)\right>_{T}$
is a running average of the preceding 6 hours of $X_{i}(t)$. The EUVS Model
latency is 1 minute (i.e., EUVS Model irradiances are publicly available 1
minute after the corresponding EUVS Measurements are made).

The operational nature of the EUVS Model requires the continuous production of
irradiances, even during times when some EUVS Measurements are unavailable.
This requires the derivation of independent sets of coefficients for the most
likely contingencies. For brevity and clarity, we only focus on the nominal
model, which assumes all EUVS measurements are available. The same methods
described here are used to derive coefficients and model uncertainty for
contingency cases, which will be reported on the web link given in the
Acknowledgements Section. The model uncertainty will generally be higher if
the number of inputs is reduced, in particular, if there is no substitute
measurement with a similar formation temperature available as discussed in
Section 1. It is important to note that NOAA plans to maintain redundant
satellites on orbit, reducing the likelihood that the EUVS Model will be
operational at reduced performance for an extended period of time.

##  3 Model Training Data and Cross-Calibration

Figure 1: The time periods and wavelength ranges spanned by the (a) spectral
irradiance and (b) EXIS measurement historical datasets used to determine EUVS
Model coefficients. Wavelengths or bands spanned are on the vertical axis and
time is on the horizontal axis. Table 1 provides details on the datasets used.

###  3.1 Historical Datasets

The historical training datasets used to calculate the EUVS Model
coefficients, and the time and spectral ranges over which they span are shown
in Figure 1, where Figure 1a shows the spectral irradiance datasets used to
create the simulated spectral intervals ($E_{n}$) and Figure 1b shows the
datasets used for the simulated EUVS Measurements ($X_{i}$). Two separate time
intervals of data are used to generate model coefficients, corresponding to
periods when either TIMED/SEE or SDO/EVE are well calibrated. These intervals
are distinguished in Figure 1 with red and blue shading. Note, the TIMED/SEE
dataset is well calibrated through 2011, but the TIMED/SEE (red-shaded)
interval stops at January 1, 2008 to prevent any sampling bias associated with
including a disproportionate amount of data near solar minimum in the training
dataset. Also shown in Figure 1b, with gray shading, is the time period and
measurements used to cross-calibrate the historical training datasets with
GOES-16. The corresponding F10.7 flux is superimposed in the background of
both panels for context. Additionally, Figure 1 indicates cases where a
dataset is only used for either the short or long -term regression
coefficients. For example, in the TIMED-EGS block in Figure 1a the designation
“$j_{i,n}$” implies this dataset is only used to find the long-term regression
coefficient, $j_{i,n}$. Table 1 provides further information on the historical
datasets, including data levels, versions, sampling and accuracy for the
datasets shown in Figure 1. The Purpose column in Table 1 indicates whether
the dataset is used to find the short-term or long-term model regression
coefficients, or for cross-calibrating the EXIS measurements with the
historical datasets.

Table 1: Historical training datasets used to determine the EUVS model coefficients. The Purpose column indicates if the data are used to compute the long-term and/or short-term model coefficients, or to cross-calibrate the historical data with the GOES-16 EUVS Measurements. Data Source | Purpose | Data Level | Version | Wavelength | Sampling | Accuracy
---|---|---|---|---|---|---
SORCE / SOLSTICE a | Long-term, Cross-cal | 3 | 15 | 117-141 nm | 0.1 nm | 5-8%
TIMED / EGS b | Long and Short-term | 3 | 12 | 26-117 nm | 1 nm | 5-20%
TIMED / XPS c | Long-term | 3 | 12 | 5-26 nm | 1 nm | 20%
SDO / MEGS d | Long and Short-term | 3 | 6 | 6-106 nm | 0.1 nm | 1-7%
Bremen Composite Mg II Indexe | Long-term, Cross-cal | Composite | 5 | 275-285 nm | N/A |  0.3%i
FISM-EVE f | Cross-cal | Daily Average | 1 | 28-31 nm | 0.1 nm | 5-10%
GOES-15 / EUVS E g | Short-term | Minute Average | 4 | 121.6 nm |  Lyman-$\alpha$ |  2%h
aSolar Radiation and Climate Experiment / SOLar-STellar Irradiance Comparison Experiment |  |
(McClintock et al., 2005) |  |
bThermosphere Ionosphere Mesosphere Energetics and Dynamics / EUV Grating Spectrograph |  |
(Woods et al., 2005) |  |
c TIMED / XUV Photometer System (Woods et al., 2005) |  |
d Solar Dynamics Observatory / Multiple EUV Grating Spectrographs (Woods et al., 2010) |  |
e http://www.iup.uni-bremen.de/UVSAT/Datasets/mgii |  |
f FISM-EUV Variability Experiment (Chamberlin et al., 2018; Thiemann et al., 2017a) |  |
g https://www.ngdc.noaa.gov/stp/satellite/goes/doc/GOES$\\_$NOP$\\_$EUV$\\_$readme.pdf |  |
h Uncertainty is with respect to scaling to SORCE/SOLSTICE absolute calibration. |  |
i (Woods et al., 2000) |  |

###  3.2 EXIS Cross-Calibration with Historical Datasets

The historical data used to represent the EXIS measurements (shown in Figure
1b) are re-calibrated to best represent the GOES-16/EXIS measurements prior to
finding the GOES model coefficients as follows: For EUVS-A and EUVS-B, the
historical spectral irradiance data are interpolated to match the pixel scales
of the GOES-16/EXIS detectors and then integrated over the same pixel masks
used to compute the GOES-16/EXIS Level 1b line irradiances. These values are
then cross-calibrated against the GOES-16/EXIS Level 1b line irradiances
measured for the first 9 months of its mission using a first order Total Least
Squares fit, which is implemented using the method of Van Huffel (1989). For
EUVS-A, measurements from the EVE/MEGS-A channel do not overlap in time with
GOES-16/EXIS. In lieu of direct measurements for cross-calibrating EVE/MEGS-A
with GOES-16, a version of the FISM model that is calibrated to EVE
(Chamberlin et al., 2018) is used as an intermediary. For EUVS-C, the Bremen
Composite Mg II Index is fit against the GOES-16 Mg II Index native scale. The
Bremen Composite Mg II Index is sourced from the GOME-2B instrument onboard
the MetOp-B satellite for the cross-calibration time period.

Figures 2 \- 4 show the cross-calibration data and fits for EUVS-A, B and C,
respectively. The fit coefficients are given in Table 2 along with the cross-
calibration uncertainty, $\sigma_{CC,i}$. Note that $\sigma_{CC,i}$ only
captures the uncertainty during the period of overlap, and uncorrected
calibration drifts occurring in the training dataset, or future uncorrected
drifts in the EUVS Measurements could increase the systematic error. These
fits are used to simulate the EUVS Measurements using the historical training
data. For all channels except EUVS-A, $\sigma_{CC,i}$ is the uncertainty of
the linear fit . For EUVS-A lines used in the model intervals from 5-35 nm,
$\sigma_{CC,i}$ is the quadrature sum of the cross-calibration uncertainty and
the FISM model uncertainty, where the latter is reported in Thiemann et al.
(2017a). For EUVS-A lines used in the model intervals from 35-127 nm, an
additional error term quantifying differences in the TIMED/SEE and SDO/EVE
calibrations is included in the quadrature sum (in addition to the two
aforementioned terms); this additional term is the uncertainty of the fit of
the EUVS-A line bandpass measured by SDO/EVE to that measured by TIMED/SEE.
Therefore, two values are reported for $\sigma_{CC,i}$ for the EUVS-A lines in
Table 2; the value in parenthesis corresponds with model intervals from 35-127
nm whereas the other corresponds with model intervals from 5-35 nm. There are
also two values reported for the EUVS-B 121.6 nm line; the value in
parenthesis is for the GOES-15/EUVS E channel cross-calibration, whereas the
other value corresponds with SORCE/SOLSTICE.

Figure 2: Scatterplots and best-fits for the EUVS-A line irradiances from FISM (a proxy for historical EVE data) and GOES-16/EXIS on the horizontal and vertical axes, respectively. FISM is used in-lieu of EVE/MEGS-A because EVE/MEGS-A and GOES-16/EXIS did not make measurements contemporaneously. Daily average data from 1 February 2017 through 10 April 2018 are used. Figure 3: Scatterplots and best-fits of the GOES-16 EUVS-B line irradiances and SORCE/SOLSTICE data. Daily average data from 1 February 2017 through 10 April 2018 are used. Table 2: Cross-calibration fit coefficients and uncertainty for the eight EUVS Measurements. The first two columns indicate the EUVS-Channel and line-center wavelength. The slope and offset correspond with the line equation coefficients to estimate the EUVS measurements from the historical data shown in Figure 1, and the corresponding uncertainty is shown in the right-most column. Channel | Wavelength (nm) | Slope | Offset | $\sigma_{CC,i}$
---|---|---|---|---
A | 25.6 | 1.49 | -35.02 $\mu$W | 4.1% (6.2%)
A | 28.4 | 1.33 | 4.04 $\mu$W | 16.8% (18.3%)
A | 30.4 | 1.21 | -92.40 $\mu$W | 1.3% (3.5%)
B | 117.5 | 0.80 | 17.37 $\mu$W | 1.1%
B | 121.6 | 0.99 | 0.09 mW | 0.4% (2.1%)
B | 133.5 | 0.96 | 11.21 $\mu$W | 0.6%
B | 140.5 | 1.03 | 2.65 $\mu$W | 0.7%
C | 280 | 4.52 | -0.88 | 0.4%
Figure 4: Scatterplot and best-fit of the GOES-16 EUVS-C Mg II Index and
Bremen Composite Mg II Index. Daily average data from 1 February 2017 through
10 April 2018 are used. The Bremen Composite Mg II Index source for this time
period is from the GOME-2B instrument onboard the MetOp-B satellite.

###  3.3 Model Uncertainties

The available historical training datasets are partitioned roughly in half,
with one-half used to fit the model coefficients and the other half used to
compute the uncertainties. The uncertainty, $\sigma$, of a linear fit, say,
$\hat{y}=mx_{l}+b$, between two linearly related, N-valued parameters $y_{l}$
and $x_{i}$ with fit coefficients, $m$ and $b$ is given by (e.g. Taylor
(1997))

$\sigma=\sqrt{\frac{\sum\limits_{l=0}^{N}(y_{l}-\hat{y_{l}})^{2}}{N-2}}.$ (4)

Equation 4 is used in this study to compute the absolute uncertainties, with
$\hat{y}_{l}$ corresponding with the $l^{th}$ model output and $y_{l}$
corresponding with the $l^{th}$ observation. In order to account for the
cross-calibration uncertainty ($\sigma_{cc,i}$, listed in Table 2), gaussian
noise with a standard deviation of $\sigma_{cc,i}$ is added to the $i^{th}$
model input prior to being used to compute $\hat{y}$.

It is useful to compare uncertainties in percent units. The percent
uncertainty can be approximated as

$\sigma_{\%}\approx\frac{\sigma}{\left<y_{l}\right>}\times 100\%,$ (5)

An additional useful metric is the percent uncertainty relative to the typical
variability as represented by the standard deviation,

$\sigma_{s}\approx\frac{\sigma}{s}\times 100\%$ (6)

where $s$ is the standard deviation of the observations. It is important to
keep in mind that $\sigma_{\%}$ and $\sigma_{s}$ are relative terms and,
therefore, vary depending on the context in which they are computed.
$\sigma_{\%}$ will be larger (smaller) for lower (higher) irradiance values.
Similarly, $\sigma_{s}$ will be larger (smaller) when computed over a weak
(strong) solar cycle. $s$ and $\left<y_{l}\right>$ are computed over the time
periods spanned by the historical data as shown in Figure 1.

In this study, the Bootstrap method (Efron, 1979) is used to estimate the
model uncertainty. 1000 synthetic datasets are generated by resampling (with
replacement) the available $[y,\hat{y}]$ pairs of values, and values for
$\sigma$ are computed from each synthetic dataset. It is found that the
standard deviation of $\sigma$ is typically $\sim$3$\%$ (i.e. a reported
10$\%$ uncertainty has a spread of $\sim$0.3$\%$) for the long-term model
component and $\sim$15$\%$ for the short term model component. $\sigma$ values
and their standard deviations as determined by Bootstrapping are reported in
Sections 4 and 5.

##  4 6-Hour Average (Long-Term) Model Component

###  4.1 Long-Term Model Formulation

The first two terms on the right-hand side of Equation 1 comprise the long-
term model component. The historical spectral irradiance data are interpolated
to 1-nm sampling for determining the model coefficients, $E_{n,0}$ and
$j_{i,n}$. The regression coefficients are found using the Interactive Data
Language (IDL) multiple linear regression program, regress.pro, via an
iterative scheme: Regressors with negative coefficients or that contribute to
less than 5$\%$ of the fit (as a result of having relatively small
coefficients) are set to zero, and the fits are re-computed until all
coefficients are positive and all regressors contribute to at least 5$\%$ of
the fit. It was found that for particularly noisy intervals, multiple linear
regression can result in model error that is larger than that from single
linear regression using a single EUVS Measurement. To account for this, a
multiple linear regression model using the combined eight EUVS Measurements
and eight single linear regression models using the eight EUVS Measurements
individually are computed. The corresponding model errors, defined as the
quadrature sum of the mean and standard deviation of the model-measurement
difference, are compared, and the model with the smallest error is selected
for each 1-nm interval.

The coefficients for the 1-nm intervals corresponding with a given EUVS Model
interval are then summed over the wavelength range defined by the interval. An
example is given to demonstrate how the fit coefficients determined from the 1
nm wide intervals are combined to correspond with a 5 nm wide interval: The
coefficients for the 5-10 nm interval, $E_{5-10,0}$ and $j_{i,5-10}$ are found
from the five sets of 1-nm sampling coefficients as follows:

$\displaystyle E_{5-10,0}=\frac{1}{5}\sum_{\lambda=5nm}^{9nm}E_{\lambda,0}$
(7) $\displaystyle
j_{i,5-10}=\frac{1}{5}\sum_{\lambda=5nm}^{9nm}j_{i,\lambda}$ (8)

The factor of $\frac{1}{5}$ rescales the coefficients for spectral irradiance
from 1-nm to 5-nm intervals , with units of irradiance per nm. For the 117-127
nm interval, the coefficients are scaled by $\frac{1}{10}$.

###  4.2 Long-Term Model Component Results

In order to more accurately characterize the model uncertainty, the historical
datasets are partitioned approximately in half, with the half corresponding
with lower solar activity being used to compute the model coefficients, while
the half corresponding with higher solar activity is used for model-
measurement comparison to quantify the model uncertainty. The long-term
component _model_ uncertainties, $\sigma_{LTM}$ , for each EUVS Model interval
are reported in Table 3 in absolute units, units of percent uncertainty and
percent variability. Additionally, Table 3 reports the standard deviation of
the uncertainties, $s_{\sigma}$, in absolute units and the long-term component
_instrument_ percent uncertainties, $\sigma_{LTI}$, the latter of which
correspond with the signal-weighted average instrument accuracies of the
historical spectral-irradiance measurements that are used to train the EUVS
Model.

$\sigma_{LTM}$ is the random uncertainty (i.e. the classical precision) of the
EUVS Model long-term component, whereas $\sigma_{LTI}$ is the Model’s
systematic uncertainty (i.e. the classical accuracy). In other words,
$\sigma_{LTI}$ characterizes the magnitude of a constant bias in the model
estimates, while $\sigma_{LTM}$ characterizes the error in the 6-hour
variability estimated by the model. It is important to note the model absolute
accuracy strictly depends on the absolute accuracy of the historical training
data, and for a number of wavelength intervals, the random uncertainty (
$\sigma_{LTM}$) is smaller than the uncertainty of the systematic bias (
$\sigma_{LTI}$).

The sensitivity of the model parameters to the model training period used is
investigated by exchanging the model training and validation periods. When the
model is trained using the dataset half corresponding with higher solar
activity and validated with the less active half, $\sigma_{LTM}$ is smaller
for all intervals except three (the 50-55 nm, 55-60 nm, and 75-80 nm
intervals). The average difference in $\sigma_{LTM}$ is 15$\%$. Additionally,
the model coefficients found from the two different training periods tend to
be different, and the sets of optimal model inputs for a model interval also
tend to differ. This suggests that model error can be reduced by using
training data from periods that have solar activity levels comparable to that
of the period for which the model is being applied.

Sample model measurement comparisons for 6 intervals are shown in Figures 5
and 6 for model intervals derived from SDO/EVE and TIMED/EGS data,
respectively. The modeled and measured irradiances are shown in the left-hand
columns with red and black curves, respectively. The right-hand columns show
time series of the model uncertainty in percent units. Here, the percent
uncertainty is defined as $\sigma_{LT}$ divided by the daily modeled
irradiance multiplied by 100$\%$. The training and validation time periods can
be inferred from Figures 5 and 6: Times when data are shown correspond with
the validation dataset times; times when data are absent between 30 April 2010
and 26 May 2014 (8 February 2002 and 1 January 2008) correspond with the
training dataset times for the SDO/EVE (TIMED/EGS) data interval.

Figure 5: Sample model-measurement comparisons for intervals derived from SDO/EVE data.  Figure 6: Sample model-measurement comparisons for intervals derived from TIMED/EGS data.  Table 3: Long-term model uncertainty in absolute units along with its standard deviation. Uncertainties are also reported in percent units, both relative to the mean and observed variability (as measured by the standard deviation). Model Interval (nm) |  $\sigma_{LTM}$ $(\mu W/m^{2}$-nm) |  $s_{\sigma}$ $(\mu W/m^{2}$-nm) |  $\sigma_{LTM}/<E_{n,L}>$ ($\%$) |  $\sigma_{LTM}/s_{n,L}$ ($\%$) |  $\sigma_{LTI}($%$)$
---|---|---|---|---|---
5-10 | 3.095 | 0.078 | 5.5 | 24.1 | 2.2
10-15 | 1.064 | 0.037 | 5.3 | 30.8 | 2.2
15-20 | 4.817 | 0.122 | 4.3 | 27.6 | 1.1
20-25 | 3.375 | 0.089 | 4.4 | 20.5 | 1.5
25-30 | 4.475 | 0.122 | 8.0 | 32.0 | 2.9
30-35 | 2.737 | 0.069 | 2.0 | 18.1 | 3.0
35-40 | 2.539 | 0.102 | 9.0 | 39.3 | 10.6
40-45 | 0.430 | 0.021 | 5.8 | 40.3 | 10.1
45-50 | 0.429 | 0.018 | 3.4 | 27.2 | 10.4
50-55 | 0.485 | 0.025 | 5.2 | 29.5 | 10.8
55-60 | 0.715 | 0.033 | 3.7 | 42.7 | 13.7
60-65 | 0.925 | 0.045 | 4.4 | 43.0 | 19.1
65-70 | 0.139 | 0.006 | 2.8 | 32.9 | 9.3
70-75 | 0.177 | 0.008 | 3.0 | 41.4 | 9.5
75-80 | 0.483 | 0.026 | 3.4 | 66.0 | 13.5
80-85 | 0.598 | 0.028 | 3.3 | 39.8 | 12.8
85-90 | 1.244 | 0.058 | 3.7 | 34.2 | 12.9
90-95 | 1.030 | 0.048 | 3.6 | 33.2 | 12.7
95-100 | 1.534 | 0.054 | 4.4 | 44.8 | 18.1
100-105 | 1.870 | 0.078 | 3.9 | 35.2 | 18.8
105-110 | 0.439 | 0.015 | 2.3 | 24.5 | 9.5
110-115 | 0.500 | 0.019 | 2.5 | 31.9 | 12.4
117-127 | 2.223 | 0.025 | 0.3 | 2.9 | 10.0

##  5 Minute-Average (Short-Term) Model Component

###  5.1 Short-Term Model Formulation

The short-term model component is the second term on the right hand side of
Equation 1. The model coefficients are found using multiple linear regression
at EUVS Model resolution rather than 1 nm sampling to improve the signal-to-
noise ratio (SNR) of short time scale variability observations. Because the
largest variations in solar EUV variability at short time-scales are due to
solar flares, the regression fitting is done using the peak irradiance
enhancements occurring during solar flares. Typical fits result in a small
constant term, which is collected in $E_{n,0}$ in Equation 1 along with the
constant term from the long-term component. The SDO/MEGS spectral irradiances
are used for the 6-105 nm wavelength range, except for the 35-40 nm interval
where the TIMED/EGS spectral irradiances are used. TIMED/EGS spectral
irradiances are also used for the 105-115 nm wavelength range, and the
SORCE/SOLSTICE irradiance is used for the 117-127 nm wavelength interval, each
of which will be discussed independently in the following paragraphs.

The EVE/MEGS dataset is the most extensive dataset measured to date of EUV
variability at short time-scales, having measured EUV variability at 0.1 Hz
for thousands of flares. MEGS A made measurements near continuously, while
MEGS B has a lower duty cycle for degradation mitigation, resulting in MEGS B
having made fewer flare observations. For every M-class or larger flare
observed by MEGS A, the pre-flare background and flare peak irradiance values
are identified for each 1 nm interval in the MEGS wavelength range. This is
done by manually identifying the time range corresponding with the background
and peak irradiances using the bright flaring 13.29 Fe XXIII line and then
using an automated program to average the background and identify the peak
values. This same process was used by Thiemann et al. (2018), and the reader
is referred to that paper for further details.

A total of 249 (50) flares are identified in the MEGS A (B) wavelength range.
Of these flares, the 100 flares with the largest enhancement at 13.5 nm are
used to compute model coefficients in the MEGS A wavelength range, while 30
flares with the largest enhancement at 97.5 nm are used for finding model
coefficients in the MEGS B wavelength range. The MEGS B sample size is limited
to 30 because including more flares increases the model error across many
intervals as a result of having a low SNR. However, the fit uncertainties
approach an asymptotic value after a sample size of $\sim$10, so 30 flares is
a large enough sample size to accurately characterize the model error. 13.5 nm
and 97.5 nm are used for bright flare identification because they both show
significant enhancement during flares, and hence, have high SNR. The 13.5 nm
interval is dominated by a coronal Fe XXIII line during flares, and hence has
relatively small opacity during flares. Although, it is important to note that
even hot coronal lines, typically considered to be optically thin, limb darken
during flares (Thiemann et al., 2018). On the other hand, the 97.5 nm interval
in the MEGS B wavelength range is dominated by C III and Lyman-$\gamma$, the
latter of which strongly limb darkens due to the high abundance of H in the
Sun’s atmosphere. This inherently biases the sample set of flares in the MEGS
B wavelength range to those having originated away from the limb. As an
alternative, the 49.5 nm interval, which is dominated by the hot coronal and,
hence, less opaque Si XII emission, was also considered for flare
identification. However, it was found that the SNR of the training set greatly
decreased for many intervals in the MEGS B range as a result of their being
dominated by more optically thick transition region emissions. Therefore, it
was decided to use the 97.5 nm interval in order to have higher model accuracy
for flares located nearer to disk center, as they tend to be more geo-
effective (Qian et al., 2010) at a cost of higher model uncertainty for flares
located nearer to the limb. The full set of flares, which includes both disk-
center and limb flares, is used to compute the model uncertainty. As such, the
reported uncertainties are consistent with the average flare, and likely over-
estimated (under-estimated) for disk-center (limb) flares. Figure 7 shows a
histogram of the flare disk-location for all 249 flares considered as well as
those used in the MEGS A and MEGS B wavelength ranges. Note, in both cases,
flares at 80o or further from disk center were discarded to avoid using flares
that may be partially occulted by the limb.

Figure 7: Histograms of all M class flares observed by MEGS A (dotted), flares
used to to compute model coefficients in the MEGS-A (dashed) and MEGS-B
(solid) wavelength ranges.

The MEGS dataset only contains the EUVS-A lines, and there are no
corresponding high time-cadence measurements made for the EUVS-B and EUVS-C
lines except for the 121.6 nm Lyman-$\alpha$ line, which is measured by the
GOES-15/EUVSE instrument. As a result, only simulated EXIS measurements for
the EUVS-A lines and Lyman-$\alpha$ are available for generating the model
coefficients for the intervals ranging from 5 nm to 105 nm (except the 35-40
nm interval).

The model intervals ranging from 105 nm to 115 nm are derived from the TIMED-
SEE dataset. The 35 to 40 nm interval is also derived from the TIMED-SEE
dataset because the MEGS-B flare measurements had very low SNR over this
wavelength range. Flares of magnitude M5 or larger occurring between 30
October 2002 and 18 October 2008 during a SEE observation are used to derive
the model coefficients (where the flare timing is taken to be that reported in
the GOES events list returned by the pr$\\_$gev.pro SolarSoft routine). This
results in a training dataset of 36 flares.

The 117-127 nm interval is derived from the SORCE/SOLSTICE dataset using all
X1 or larger flares that occurred during SOLSTICE observations between
mid-2003 and 2011, resulting in 19 flares. Because SOLSTICE does not measure
short-ward of 117 nm, only simulated EUVS-B lines are used to generate the
model coefficients for this wavelength interval.

###  5.2 Short-Term Model Component Results

Table 4 shows the corresponding short-term model uncertainty ($\sigma_{STM}$)
values in absolute units and their standard deviations (as determined by
Bootstrapping). Values for for $\sigma_{STM}$ are also given in percent units
relative to the mean and standard deviation of the flare peak intensities of
the training dataset. The relative magnitude of the mean flare peak values to
the peak daily average values are given in the right-most column in percent
units for context. As is the case with the long-term model component,
$\sigma_{STM}$ is the random uncertainty, and the short-term instrument
uncertainty ($\sigma_{STI}$, not shown) is the systematic uncertainty of the
short-term model component. The values for $\sigma_{STI}$ are similar to
$\sigma_{LTI}$, but somewhat smaller from 35-105 nm due to the smaller
absolute uncertainty of SDO/EVE relative to TIMED/SEE over these wavelengths.

Figure 8 shows scatter-plots of the measured and modeled peak flare
enhancements from the training data for all 23 EUVS model intervals. From
Figure 8 and Table 4, it is evident that the EUVS model predicted peak flare
enhancements are highly correlated with measurements for most intervals.

In Figures 9 and 10, the short-term EUVS Model predictions are compared with
SDO/EVE measurements for two sample days, beginning at 12:00 UT on 5 July 2012
and 4 August 2011, respectively. Each figure shows measured and modeled short-
term irradiances for a 24-hour period using black and red curves,
respectively, for five wavelength intervals chosen because they tend to show a
relatively large flare enhancement. The curves represent the short-term solar
variability, i.e. the right-most term in Equation 1. Measurement-model
differences are shown in each panel with gray curves. The SDO/EVE and
simulated EXIS measurement data have the 6-hour moving average removed and are
plotted at 10 second cadence with a 30-second ( 3-sample) moving average
applied. The missing SDO/EVE data in Panels e of both figures is because
SDO/EVE reduces its duty cycle at this wavelength range for degradation
mitigation.

Considering first the non-flaring short-term variability that is most
prevalent in Figure 9, the EUVS Model captures this variability well in the
5-10 nm and the 30-35 nm wavelength intervals, but to a lesser degree in the
10-15 nm and 15-20 nm intervals. The EUVS Model is expected to model
variability in the 30-35 nm interval well because it is dominated by the 30.4
nm He II emission and this emission is used as a direct input to the EUVS
Model. The emissions forming from 5-20 nm are formed primarily at hot
temperatures in the solar corona. Therefore, their corresponding emission
measures can be invisible to the EXIS measured emissions, which are formed at
relatively cooler temperatures. The short-term variability in these intervals
is modeled predominantly using the 25.6 nm and 28.4 nm EXIS Measurements. The
reason for the relatively large magnitude of the 25.6 nm measurement
coefficient for these wavelength regions dominated by coronal forming
emissions is because the 25.6 nm EXIS measurement is dominated by an Fe XXIV
emission at 25.53 nm during solar flares. As such, the flare enhancements are
well modeled in the 10-20 nm intervals, when the Fe XXIV emission dominates
the EXIS measurement, but the model performance decreases during non-flaring
periods when the cooler forming He II emission dominates.

Figure 8 quantifies how well the EUVS Model predicts the peak flare emission.
From Figure 8, there appears to be some slight non-linearity between the model
predictions and measurements. For example, in the 5-10 nm panel, the slope is
steeper below 10 $\mu$W/m2 than it is above 10 $\mu$W/m2, resulting in the
model under-predicting enhancements for (less frequent) larger flares.

Figures 9 and 10 provide insight into how well the EUVS Model captures the
time evolution of solar flare emissions. Flare emissions at EUV wavelengths
can pass through a number of phases as they evolve in time (Woods et al.,
2011), including an initial impulsive phase followed by a gradual phase, which
can be delayed in time depending of the emission formation temperature
(Thiemann et al., 2017b); later flare phases typically associated with
eruptive flares include a dimming phase and a late phase. Examples of all
these phases except the late phase can be seen in Figures 9 and 10. Three
impulsive flares are evident in Figure 9, occurring near $6\times 10^{4}$,
$8\times 10^{4}$ and $13\times 10^{4}$ seconds. These are all well-modeled in
the 30-35 nm interval, again due to it being driven by the 30.4 nm EXIS
measurement. The impulsive phase for these flares is modeled poorly in the
15-20 nm interval, where it is under-predicted for the first two flares and
over-predicted for the third flare. This is likely because this interval is
driven predominantly by the Fe XXIV 25.53 nm emission during flares, which
typically lacks an impulsive phase. The model does not adequately capture the
gradual phase delay in the 10-20 nm intervals for the first two flares in
Figure 9. In the 10-15 nm interval, the model over-predicts the gradual phase
delay, whereas in the 15-20 nm interval the gradual phase delay is slightly
under predicted, for both flares. Coronal dimming occurs after both flares in
Figure 10 and is responsible for the emission decrease in panels c and d
following one or both flares. The apparent dimming in Panels a and b is a
result of subtracting off the lagging 6-hour average from the data and the
relatively long duration of the two flares. The dimming is under-predicted in
the 15-20 nm range for both flares because the Fe XXIV emission typically does
not dim. For the second flare, dimming appears in the model but not in the
data because this interval is driven by the 30.4 nm EXIS measurement, which
showed dimming for this flare.

Figure 8: Scatterplots of measured and modeled peak flare irradiances for the flares used to calibrate the EUVS Model short-term component.  Table 4: Short-term model uncertainty in absolute units along with its standard deviation. Uncertainties are also reported in percent units, both relative to the mean and observed flare peak intensity of the training data set. The right-most column shows the mean flare peak intensity relative to the daily average in percent units for context. Model Interval (nm) |  $\sigma_{STM}$ $(\mu W/m^{2}$-nm) |  $s_{\sigma}$ $(\mu W/m^{2}$-nm) |  $\sigma_{LTM}/<E_{n,S}>$ ($\%$) |  $\sigma_{LTM}/s_{n,S}$ ($\%$) |  $<E_{n,S}>/<E_{n,L}>($%$)$
---|---|---|---|---|---
5-10 | 1.739 | 0.197 | 23.6 | 35.9 | 13.2
10-15 | 4.138 | 0.407 | 26.8 | 31.1 | 77.3
15-20 | 0.991 | 0.104 | 14.8 | 20.0 | 6.0
20-25 | 0.844 | 0.077 | 15.8 | 30.0 | 7.0
25-30 | 1.060 | 0.104 | 16.8 | 34.1 | 11.2
30-35 | 3.297 | 0.347 | 12.7 | 21.7 | 19.4
35-40 | 1.840 | 0.252 | 27.0 | 48.5 | 24.2
40-45 | 0.347 | 0.121 | 23.3 | 55.5 | 20.2
45-50 | 0.230 | 0.032 | 12.8 | 20.8 | 14.2
50-55 | 0.186 | 0.026 | 14.0 | 22.6 | 14.2
55-60 | 0.682 | 0.116 | 19.2 | 27.4 | 18.4
60-65 | 0.649 | 0.090 | 26.2 | 38.4 | 11.7
65-70 | 0.303 | 0.033 | 24.2 | 72.8 | 25.5
70-75 | 0.656 | 0.095 | 27.9 | 77.1 | 40.3
75-80 | 1.502 | 0.169 | 30.8 | 57.7 | 34.2
80-85 | 1.765 | 0.227 | 30.9 | 57.2 | 31.8
85-90 | 2.362 | 0.370 | 31.3 | 63.1 | 22.7
90-95 | 2.513 | 0.278 | 31.0 | 65.3 | 28.4
95-100 | 5.459 | 0.807 | 25.0 | 39.3 | 62.1
100-105 | 3.972 | 0.598 | 28.5 | 45.3 | 29.4
105-110 | 1.070 | 0.140 | 19.6 | 17.2 | 28.4
110-115 | 0.943 | 0.123 | 20.0 | 17.8 | 23.3
117-127 | 21.593 | 4.246 | 11.0 | 43.6 | 26.5
Figure 9: A comparison of measured (black) and modeled (red) short-term
variability for a 24 hour period beginning on 5 July 2012 12:00 UT.
Measurement-Model differences are shown in gray. Five intervals are shown that
were selected because they typically show relatively large enhancements during
flares; the interval wavelength range is given on each panel. Figure 10: Same
as Figure 9, but for a period beginning on 4 August 2011 12:00 UT.

##  6 Discussion

All coefficients needed to compute EUVS Model irradiances from the EUVS
Measurements are reported in the Appendix. The EUVS model coefficients
determined here from irradiance measurements made during Solar Cycles 23 and
24 are expected to apply to future solar cycles because the relationship
between EUV emissions and the thermal structure of the solar atmosphere are
expected to be invariant between solar cycles. Because the less (solar) active
half of the available data were used to determine the model coefficients and
the more active half of the data were used to characterize its uncertainty,
the model performance has been validated for periods of higher activity than
that occurring during the period used to compute the model coefficients.
However, the available historical datasets span relatively moderate levels of
solar activity when compared to previous solar cycles (e.g. Solar Cycles
20-22) and the accuracy of the model may decrease during periods when solar
activity exceeds that of the historical datasets. The model performance during
future stronger solar cycles can be improved by recomputing the model
coefficients using the more active half of the historical data.

The EUVS Model uncertainties for the long-term component are comparable to
those from the most recently published FISM update by Thiemann et al. (2017a).
A key difference between the FISM and EUVS models is that FISM uses a single
measurement as an input for each model interval and decomposes the daily
average measurement and spectral irradiance predictions into solar cycle and
solar rotation components, whereas the EUVS Model uses multiple measurements
as inputs for each model interval and does not decompose them according to
longer-term solar variability. This indicates that, at least at 5 nm sampling,
daily average irradiance can be accurately predicted without decomposing solar
variability into solar cycle and solar rotation components if the model inputs
span a broad range of temperatures in the Sun’s atmosphere using model
coefficients derived from multiple linear regression analysis. This has
important implications for real-time solar spectral irradiance estimation,
which does not have the future knowledge required when decomposing solar
irradiance variability into solar cycle and solar rotation components.

On the other hand, the EUVS Model uncertainties for the short-term component
are a significant improvement over those from FISM. For example, Thiemann et
al. (2017a) reported that the FISM-M flare (i.e. short-term) model uncertainty
is 35% and 70% in the 13.5 nm and 30.5 nm (1-nm wide) intervals, respectively.
These values should be compared to the 10-15 nm and 30-35 nm interval
uncertainties of 26.8% and 12.7%, respectively, reported in Table 4. Although
some of the difference in uncertainties is due to the EUVS Model having larger
intervals than FISM, by comparing the model measurement comparisons in Figure
8 with those for FISM-M in Figure 4 of Thiemann et al. (2017a), it is clear
that a significant part of the uncertainty differences are due to FISM using
soft X-ray irradiance variability, which varies by factors of 10-100, to
estimate EUV irradiance variability, which varies by tens of percent. This is
most pronounced in the intervals that contain the He II 30.4 nm emission line.
The uncertainties of the EUVS Model and FISM for the intervals containing the
Fe XXIII 13.3 nm emission line are similar, and likely due to Fe XXIII tending
to evolve similarly to the 0.1-0.8 nm band (Thiemann et al., 2017b). In order
to reduce model uncertainty, future empirical flare irradiance models should
use EUV irradiance measurements as model inputs when possible. However, it is
important to note that Thiemann et al. (2018) showed that the GOES XRS peak
emission measure is linearly proportional to peak EUV irradiance for hot-
forming emission lines ($T>9$ MK) during flares, unlike the XRS irradiances,
which have a highly non-linear relationship with EUV emissions as discussed
above and reported in Thiemann et al. (2017a). As such, the XRS emission
measure is another alternative for reducing flare irradiance model
uncertainty.

The EUVS Model can be improved in a number of ways: An intermediate non-
flaring time-scale could be added to accurately capture variability that
occurs at time-scales of a few hours that is not the result of flares as seen,
for example, in Figure 9. This could be a third term in Equation 1 at an
intermediate time scale, say 2 hours. The current EUVS Model does not
explicitly attempt to model the various EUV emission flare phases. Figures 9
and 10 suggest that the $k_{i}$ coefficients are weighted to capture some of
the flare phases accurately. For example, model intervals that tend to show an
impulsive flare phase are predominantly driven by the impulsive He II 30.4 nm
model input, and those intervals that do not tend to be impulsive tend to be
predominantly driven by the Fe XXIV 25.3 nm (nominally the He II EXIS 25.6 nm
line measurement). Further, from Figure 9, the dimming phase appears to be
accurately modeled for the two flares shown although it is important to note
that a false dimming phase tends to appear in the 10-15 nm interval for long
duration flares. The gradual phase delay is not properly modeled using the
current EUVS Model algorithm. Thiemann et al. (2017b) showed that by applying
a simple differential equation to emission line measurements from hotter EUV
lines, the delay and broadening apparent in cooler EUV lines can be predicted
if the time difference between the line peaks can be determined independently.
Finally, this study did not consider the degree to which the EUVS Model can
reproduce the EUV Late Phase. The Fe XV 28.4 nm EUVS measurement does tend to
show the EUV Late Phase and, as such, could be used to drive model intervals
that also show the EUV Late Phase.

The same methods used to derive the coefficients and uncertainties for the
relatively coarse wavelength intervals presented here can be applied to other
more common wavelength schemes used in upper atmospheric research such as
those introduced in Richards et al. (1994) and Solomon and Qian (2005). The
broadband intervals of Richards et al. (1994) correspond directly with the
broadband intervals presented here, and the remaining work involves finding
coefficients for the 17 emission line intervals. The Solomon and Qian (2005)
intervals do not match those presented here and also include wavelengths below
5 nm. As such, producing coefficients for the Solomon and Qian (2005)
intervals would require re-sampling the source datasets and expanding the
source data to include wavelengths below 5 nm.

The results presented in this paper are for the EXIS instrument on the GOES-16
satellite. The reader should follow the link in the Acknowledgements section
for possible updates, as well as values for other flight models as they become
available. The EXIS dependent model uncertainties, $\sigma_{CC,i}$, are
expected to be similar between EXIS models on GOES- 17-19. As such, it is
expected the EUVS Model uncertainties presented here for GOES-16/EXIS will
hold for the entire GOES-R series EXIS instruments. The EUVS Model
coefficients are expected to be similar between GOES- 16-19 because the EXIS
derived inputs, $P_{i}(t)$ and $Q_{i}(t)$, are independent of absolute
calibration. However, $P_{i}(t)$ and $Q_{i}(t)$ for GOES- 17-19 should be fit
to those from GOES-16 to confirm this, and $k_{i}$ and $j_{i}$ should be
scaled accordingly if the corresponding slopes differ from unity.

###### Acknowledgements.

This work was funded by the NOAA GOES Program contract to the University of
Colorado, NNG07HW00C. The data used in this study are publicly available for
download through the following locations: SDO/EVE data are available at
http://lasp.colorado.edu/home/eve/data/data-access/. TIMED/SEE data are
available at http://lasp.colorado.edu/home/see/data/. SORCE/SOLSTICE data are
available at http://lasp.colorado.edu/home/sorce/data/. Mg II c/w data are
available at http://www.iup.uni-bremen.de/gome/gomemgii.html. Once the EXIS
data have been approved for public release, EUVS Model spectra will be
publicly available through the National Centers for Environmental Information
website, https://www.ngdc.noaa.gov/stp/spaceweather.html. Additionally, future
updates to the model coefficients and uncertainties for GOES-R, as well as
future releases of those parameters for GOES-S through GOES-U will be
available through https://data.ngdc.noaa.gov/platforms/solar-space-observing-
satellites/goes/goesXX/l1b/exis-l1b-sfeu/model$\\_$coefficients/ , where
XX=16-19.

## References

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##  Appendix A EUVS Model Coefficients

Table 5: EUVS Measurement Reference Values. $X_{25.6}$ | $X_{28.4}$ | $X_{30.4}$ | $X_{117.5}$ | $X_{121.6}$ | $X_{133.5}$ | $X_{140.5}$ | $X_{280}$
---|---|---|---|---|---|---|---
2.23e-05 | 2.713e-05 | 3.82e-04 | 8.245e-05 | 5.95e-03 | 1.72e-04 | 1.15e-04 | 0.305
Table 6: Long-Term Model Coefficients. Bin (nm) | $E_{\lambda,0}$ | $j_{25.6}$ | $j_{28.4}$ | $j_{30.4}$ | $j_{117.5}$ | $j_{121.6}$ | $j_{133.5}$ | $j_{140.5}$ | $j_{280}$
---|---|---|---|---|---|---|---|---|---
5-10 | 1.86e-05 | 6.91e-06 | 1.83e-06 | 0.00e+00 | 1.29e-05 | 0.00e+00 | 0.00e+00 | 1.45e-05 | 0.00e+00
10-15 | 9.33e-06 | 2.44e-06 | 0.00e+00 | 0.00e+00 | 2.12e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
15-20 | 5.42e-05 | 1.28e-05 | 1.77e-07 | 0.00e+00 | 0.00e+00 | 1.18e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00
20-25 | 2.51e-05 | 1.03e-05 | 2.06e-06 | 0.00e+00 | 0.00e+00 | 1.37e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00
25-30 | 2.10e-05 | 5.53e-06 | 6.32e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
30-35 | 1.12e-04 | 1.47e-06 | 2.73e-06 | 7.21e-05 | 7.37e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
35-40 | 2.94e-05 | 3.55e-07 | 4.53e-06 | 6.95e-06 | 1.97e-07 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 3.71e-07
40-45 | 6.93e-06 | 2.55e-07 | 2.51e-07 | 2.29e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 4.77e-06
45-50 | 1.15e-05 | 1.96e-07 | 1.77e-07 | 5.69e-06 | 8.95e-07 | 1.10e-06 | 0.00e+00 | 0.00e+00 | 7.74e-06
50-55 | 7.74e-06 | 3.86e-07 | 1.82e-07 | 4.83e-06 | 2.38e-07 | 1.82e-06 | 0.00e+00 | 0.00e+00 | 5.69e-06
55-60 | 1.75e-05 | 2.43e-07 | 0.00e+00 | 2.86e-06 | 4.44e-06 | 9.39e-07 | 0.00e+00 | 0.00e+00 | 1.66e-05
60-65 | 1.91e-05 | 4.46e-07 | 0.00e+00 | 5.78e-06 | 2.32e-07 | 0.00e+00 | 0.00e+00 | 2.63e-06 | 1.51e-05
65-70 | 5.51e-06 | 3.18e-08 | 0.00e+00 | 1.39e-06 | 8.22e-07 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 3.78e-06
70-75 | 7.15e-06 | 2.69e-08 | 0.00e+00 | 3.25e-07 | 1.88e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 5.40e-06
75-80 | 1.56e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 1.50e-05
80-85 | 1.87e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 3.18e-05
85-90 | 3.30e-05 | 2.36e-07 | 0.00e+00 | 8.80e-06 | 0.00e+00 | 5.91e-06 | 0.00e+00 | 0.00e+00 | 4.21e-05
90-95 | 2.95e-05 | 2.09e-07 | 0.00e+00 | 7.91e-06 | 7.31e-07 | 0.00e+00 | 6.60e-06 | 0.00e+00 | 3.08e-05
95-100 | 3.49e-05 | 5.52e-07 | 0.00e+00 | 3.10e-06 | 2.37e-06 | 5.01e-06 | 0.00e+00 | 4.16e-06 | 3.47e-05
100-105 | 4.45e-05 | 5.43e-07 | 8.62e-08 | 1.43e-05 | 2.08e-06 | 0.00e+00 | 2.80e-06 | 7.43e-06 | 4.50e-05
105-110 | 1.67e-05 | 1.08e-07 | 0.00e+00 | 5.26e-06 | 5.59e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 1.85e-05
110-115 | 1.83e-05 | 4.57e-08 | 0.00e+00 | 1.95e-06 | 1.54e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 2.67e-05
117-127 | 6.72e-04 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 6.57e-04 | 0.00e+00 | 0.00e+00 | 0.00e+00
Table 7: Short-Term Model Coefficients. Bin (nm) | $k_{25.6}$ | $k_{28.4}$ | $k_{30.4}$ | $k_{117.5}$ | $k_{121.6}$ | $k_{133.5}$ | $k_{140.5}$ | $k_{280}$
---|---|---|---|---|---|---|---|---
5-10 | 3.66e-05 | 2.12e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
10-15 | 1.12e-04 | 3.97e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
15-20 | 4.36e-05 | 0.00e+00 | 7.74e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
20-25 | 1.27e-05 | 6.16e-06 | 1.12e-05 | 0.00e+00 | 4.76e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00
25-30 | 2.07e-05 | 1.37e-05 | 3.92e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
30-35 | 0.00e+00 | 0.00e+00 | 1.11e-04 | 0.00e+00 | 2.89e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00
35-40 | 0.00e+00 | 1.06e-05 | 2.73e-05 | 0.00e+00 | 2.47e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00
40-45 | 9.23e-07 | 2.93e-06 | 4.41e-06 | 0.00e+00 | 1.47e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00
45-50 | 0.00e+00 | 3.29e-06 | 1.29e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
50-55 | 1.16e-06 | 1.71e-06 | 9.20e-06 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
55-60 | 0.00e+00 | 0.00e+00 | 3.10e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
60-65 | 0.00e+00 | 0.00e+00 | 2.03e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
65-70 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 1.07e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00
70-75 | 0.00e+00 | 0.00e+00 | 2.88e-06 | 0.00e+00 | 1.25e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00
75-80 | 0.00e+00 | 0.00e+00 | 2.02e-05 | 0.00e+00 | 2.25e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00
80-85 | 0.00e+00 | 2.15e-05 | 1.22e-05 | 0.00e+00 | 3.54e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00
85-90 | 1.83e-05 | 7.77e-06 | 7.58e-06 | 0.00e+00 | 5.01e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00
90-95 | 0.00e+00 | 0.00e+00 | 3.23e-05 | 0.00e+00 | 1.79e-05 | 0.00e+00 | 0.00e+00 | 0.00e+00
95-100 | 0.00e+00 | 0.00e+00 | 1.32e-04 | 0.00e+00 | 1.02e-04 | 0.00e+00 | 0.00e+00 | 0.00e+00
100-105 | 0.00e+00 | 0.00e+00 | 1.02e-04 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00
105-110 | 0.00e+00 | 0.00e+00 | 8.16e-06 | 0.00e+00 | 1.00e-05 | 1.57e-05 | 2.87e-06 | 0.00e+00
110-115 | 0.00e+00 | 0.00e+00 | 8.78e-06 | 0.00e+00 | 0.00e+00 | 9.33e-06 | 5.51e-06 | 0.00e+00
117-127 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 0.00e+00 | 7.54e-04 | 0.00e+00 | 0.00e+00 | 0.00e+00