Space Weather

Flare Irradiance Spectral Model (FISM): Daily component algorithms and results



[1] The solar photon output from the Sun was once thought to be constant but is now known to vary considerably over timescales from seconds during solar flares to years due to the solar cycle. This is especially true in the wavelengths shorter than 208 nm (Al ionization edge), where measurements and models of the solar irradiance at these short wavelengths are needed. The time-variant solar irradiance drives physical changes in the Earth's atmosphere that can affect many things including GPS accuracy and satellite drag rates. The Flare Irradiance Spectral Model (FISM) is an empirical model that estimates the solar irradiance at wavelengths from 0.1 to 190 nm at 1 nm resolution with a time cadence of 60 s. This is a high enough temporal resolution to model variations due to solar flares, where few accurate measurements at these wavelengths exist, as well as the solar cycle and solar rotation variations. The modeling of the FISM daily component, including the solar irradiance variations due to the solar cycle and the solar rotation, is the topic of this paper. The daily component algorithms are given, and results and comparisons of the daily component demonstrate that the FISM estimations agree within the stated uncertainties to the various measurements of the solar VUV irradiance. A third type of event that causes sudden changes in the solar irradiance is solar flares. The FISM modeling of the variations in the solar irradiance due to solar flares is the topic of the second paper.

1. Introduction

[2] The large solar cycle, solar rotation, and flare irradiance variations in the X-ray and vacuum ultraviolet (XUV, 0.1–10 nm; VUV, 10–200 nm) wavelengths drive significant deviations in the Earth, Mars, and space environment on similar timescales, some of which include modulations in the atmospheric densities and composition of particular atoms, molecules, and ions of the planets [Lean, 1997; Donnelly, 1976; Liu et al., 2004]. These physical changes in the Earth's atmosphere can then significantly affect many things including satellite drag, radio communications, and navigation accuracy, such as the accuracy in the Global Positioning System (GPS) [Lean, 1997]. Measurements and models of the solar VUV irradiance, covering all timescales from decades to minutes, are therefore needed in order to understand the physical and societal effects that the changing solar VUV irradiance can have on Earth and other planets.

[3] Measurements of solar irradiance a wavelengths shorter than 200 nm represent a valuable data set, with historically extensive sets, as well as several current and planned future observations. This wavelength range includes three other regions of the electromagnetic spectrum and one bright emission line. According to ISO 21348, these regions are the X-ray ultraviolet (XUV, 0.1–10 nm), the extreme ultraviolet (EUV, 10–121 nm), and the far ultraviolet (FUV, 122–200 nm) region, and also include the Lyman-α emission line at 121.57 nm. Despite the numerous measurements throughout these regions of the spectrum, there are still frequent and long-duration data gaps, most notably including the prespace period (prior to 1946), the period from 1980 to 1998 for the EUV range [Donnelly, 1987], and shorter time gaps of minutes to hours that routinely occur between satellite instrument observations.

[4] Four of the most widely used solar VUV irradiance models are the EUV81 model [Hinteregger et al., 1981], the EUVAC model [Richards et al., 1994; Richards et al., 2006], the SOLAR2000 v2.26 model [Tobiska et al. 2000; Tobiska, 2004], and the NRLEUV model [Warren et al., 1998, 2001; Lean et al., 2003]. Another common model, although it only spans the FUV range, is VUV2002 [Woods and Rottman, 2002]. EUV81 and EUVAC are empirical models based on finding relationships of proxies to the Atmospheric Explorer-E (AE-E) data set and several sounding rocket flights. VUV2002 is another empirical model, this time based on the Upper Atmospheric Research Satellite (UARS) Solar Stellar Irradiance Comparison Experiment (SOLSTICE) data [Rottman et al., 1993]. SOLAR2000 is a hybrid model, using both empirical techniques and physics-based models, such as the Mewe algorithm. The NRLEUV model determines the optically thin emissions through a differential emission measure (DEM) technique using data from Skylab. The SOLAR2000 model has been updated to include TIMED SEE data as a reference data set in the XUV-VUV range.

[5] A comparison of the output from these four models to the data from Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) Solar Extreme Ultraviolet Experiment (SEE) [Woods et al., 1998] was given in the work of Woods et al. [2005]. This paper shows the large differences between the modeled irradiances, with SEE being about 70% higher than the EUV81 and NRLEUV values in the 5–25 nm broadband range and EUV81 being about 50% higher in the 50–75 nm range than the SEE measurements over the duration of the SEE mission at the time of the publications (February 2002 to mid-2004). This shows that significant improvements in the models are needed in order to accurately reproduce the solar irradiance for a given day.

[6] These empirical models also lack the ability to accurately represent the center-to-limb variations (CLV) of the EUV emissions, especially the CLV brightening of the coronal emissions. To demonstrate this, Figure 1 shows time series of all four previously discussed models, as well as the SEE data, for two large, colongitudinally located solar active region as they rotate around the solar disk during a 20-day period in January 2004. These active region locations for 3 days in the time period can be seen in the SOHO EIT 30.4 nm images. The SEE data shown is for a 5-nm wavelength bin, from 35.0 to 39.9 nm, which is dominated by coronal bound-bound emissions that have a very strong center-to-limb brightening effect. Figure 1 clearly shows the center to limb brightening in the SEE data, but this is not seen in any of the empirical models. This is the result of the proxies used in the models (e.g., the F10.7 and MgII c/w) that have center-to-limb darkening profiles. The absolute offsets can also be seen in this figure, once again showing the inability for the current models to accurately represent the measurements.

Figure 1.

A time series displaying model and SEE results along with various empirical model results for the 35–40 nm band during a large solar rotation in January 2004. This band is dominated by coronal bound-bound emissions and should show center-to-limb brightening effects. The SOHO images show the two large, colongitudinally located active region location on given days. SOHO images are courtesy of SOHO/EIT (NASA/ESA) consortium.

2. FISM Improvements Over Other Models

[7] The FISM daily component estimates, with respect to other models, provides a more accurate determination of the solar VUV irradiances (0.1–190 nm), showing better agreement with the given measurements. The FISM algorithms, along with the data sets and proxies that are used, resolve most of the discrepancies between the other models and the SEE data, including the large solar cycle offsets and the solar rotation temporal discrepancies.

[8] A significant improvement for FISM over other empirical models is its use of recent, more accurate measurements of the EUV irradiance from the SEE instrument (Version 8 data) on board the TIMED satellite, the FUV irradiance measurements from SEE as well as from the UARS SOLSTICE, and also the XUV and short-wavelengths EUV measurements from both the SEE and Solar Radiation and Climate Experiment (SORCE) versions of the X-ray Photometer System (XPS). SEE has made over 19,000 measurements during the past 4 years and continues to make routine observations. Along with SEE providing a statistically significant improvement in the number of VUV irradiance measurements, it also has a much smaller uncertainty due to the calibration method than previous satellites that have measured the EUV. This calibration method was discussed in more detail in the work of Chamberlin et al. [2006]. UARS SOLSTICE operated for a complete solar cycle, starting in 1991 and concluded its mission in late 2005. Although the long-term degradation of SOLSTICE significantly slowed by 1997, the UARS solar pointing platform lost the capability to measure the calibration stars and to characterize this degradation. Owing to this loss of the ability to correct observations for the long-term degradation after 2001, only the data up to 2001 will be use to base the FISM model on. Nonetheless, over 1700 daily average measurements are available that span a half of a solar cycle, including measurements in both solar cycle maximum and minimum time periods. With the use of the most accurately available data sets for the VUV wavelength range, FISM will be much more accurate than other models based on the measurements from AE-E.

[9] FISM makes use of different proxies that have not currently been utilized in other empirical models, as well as many of the traditional proxies, which are discussed in further detail in section 3. These new proxies include the 0–4 nm band, the 1-nm bin centered at 36.5 nm, and the 1-nm bin centered at 30.5 nm. These emissions are used as proxies in favor of traditional proxies for certain wavelengths in order to more accurately model the solar rotation temporal irradiance changes. These three proxies were made available at a daily time cadence by the SEE data and will be continued into the future by SEE as well as other instruments that are to follow.

[10] FISM also utilizes layers of proxies and is designed to adjust its use of the best available proxy for a given day and a given wavelength if the optimal proxy is unavailable. This allows for continuous modeling of the solar spectrum for all wavelengths as far back as 1947 but does not restrict the current estimates of the solar spectrum to be based on only F10.7, which is not the optimal proxy for most VUV wavelengths.

[11] Another big improvement in FISM is in the algorithm formation that splits the solar cycle and solar rotational components to be optimized separately. As the solar cycle variations range from two times larger in the FUV to 10 times larger in the XUV than the solar rotation variations, any relationships that would be found between the measurements and the proxies without separating the components would then be dominated by the solar cycle variations. This could then lead to inaccurate representations of the solar rotational variations depending on choice of proxy for a given wavelength.

3. Proxies

[12] Six different proxies are used, when available, to represent the solar irradiance variations and provide the most accurate estimation of the solar VUV irradiance for a particular day. These six proxies have different formation temperatures spanning the entire range of solar emissions from the cool chromosphere to the hot corona. The approximate formation temperatures of the proxies, along with the time ranges when the proxies have been measured and are available, are shown in Figure 2. These proxies most accurately represent those emissions with a similar formation temperature and location in the solar atmosphere.

Figure 2.

The location in the solar atmosphere where the six daily average proxies used in FISM are formed, along with the time periods when each proxy was measured and available to use.

[13] The 10.7 cm radio flux, or F10.7, represents the coronal continuum (Bremsstrahlung) emissions and has a long history of calibrated measurements as far back as 1947 [Tapping, 1987]. A more representative proxy for these coronal continuum emissions is the XUV irradiance itself, where the 0–4 nm integrated irradiance from the TIMED SEE instrument will be used, when available. The proxy used for the coronal bound-bound VUV emissions that have a strong center-to-limb brightening effect is the 1 nm bin centered on 36.5 nm from the SEE measurements. This bin contains various coronal bound-bound emissions, including a Fe XVI emission (36.076 nm) formed at 2.5 MK and a Mg IX emission (36.8 nm) that has a slightly lower formation temperature of 1 MK. Another proxy that is used is the 1 nm bin centered at 30.5 nm that is used as a proxy for the upper transition region emissions. This proxy is dominated by the He II 30.4 nm emission line that is formed in the transition region around 25,000 K. The proxy used for the transition region is the neutral hydrogen Lyman-α emission line at 121.6 nm, hereafter referred to as Ly-α [Woods et al., 2000]. The Mg II core-to-wing ratio [Heath and Schlesinger, 1986; Viereck et al., 2001; Viereck et al., 2004] most accurately portrays the chromospheric emissions, along with the continuum emissions in the FUV wavelengths.

[14] FISM can model the solar cycle and solar rotation variations when any one of the six daily averaged proxies is available, with the FISM uncertainties decreasing with the increasing number of available proxies. F10.7 is the only proxy used, as it is the only one available, to model the solar cycle variations from 1947 up until mid-1977 when Lyα started to be consistently measured by the Atmospheric Explorer-E (AE-E) satellite. There are large gaps in the Lyα measurements, as in from early 1989 at the end of the SME mission to late 1991 at the start of the UARS mission, when other available proxies must be used. A third proxy, the MgII c/w index, first became available to use in November 1978, which again increased the ability of FISM to accurately model the VUV irradiance.

[15] The 121.5 nm, 30.5 nm, 36.5 nm, and 0–4 nm emissions have been, and continue to be, measured by the TIMED SEE instrument since its commencement of normal operations in February 2002. A similar XPS instrument on the SORCE satellite is also currently providing a measurement of the 0–4 nm and has been since March 2003. There are also plans for these four proxies, along with Lyα, to be measured in the foreseeable future by the Extreme Ultraviolet Experiment (EVE) that is to be flown on the Solar Dynamics Observatory (SDO), which is set to launch in 2008 [Eparvier et al., 2004]. The SEE and EVE measurements will provide the ability to use the 121.5 nm, 30.5 nm, 36.5 nm, and 0–4 nm emissions as a standard daily irradiance proxy for EUV coronal emissions in FISM, as the measurements will be made with a better than required daily time cadence. There is also the potential to extend this proxy measurement beyond the end of the SDO prime mission in 2013 by either an SDO mission extension or in future NOAA satellites. The GOES EUVS will also begin measurements when the GOES-R spacecraft becomes operational of the 30.5 nm and 121.5 nm emissions, which will provide further redundancy for these proxies.

[16] Time series for each of the daily proxies are shown in Figure 3. This figure shows each of the six proxies as a function of time for a strong solar rotation in January 2004. The active region appeared on the east limb of the Sun on approximately 12 January, was located in the center of the solar disk around day 20, then disappeared from the west limb around 28 January. This plot is in units of normalized irradiance to display the changes that can occur during an approximately 16-day period due to the rotation of an active region across the visible disk of the Sun. Also shown are the various CLV effects that are characteristic of each proxy, which are an important factor in determining the optimal proxy used to represent each 1 nm emission in FISM. The coronal proxies, such as the 36.5 nm bin, show a strong center-to-limb brightening due to these emissions being optically thin, while the optically thick chromospheric proxies, such as the MgII c/w show a center-to-limb darkening profile. More discussion on the optimal proxy selection for each FISM wavelength is discussed in section 4.3.

Figure 3.

Time series for a large active region as it rotates around the solar disk in January 2004. These values are shown normalized to the peak of the solar rotation, so as to portray the relative differences that can occur for each proxy.

4. FISM Concept

[17] The FISM concept to model the daily averaged solar irradiance for a particular wavelength λ on day td, E(λ, td), is to add the contributions from solar variations to a constant minimum irradiance value, Emin(λ). These additional components added to the minimum irradiance value when modeling the daily component are the variations due to solar cycle, ΔESC, and solar rotation of active regions, ΔESR. This relationship is given as:

equation image

[18] For the FUV portion of the FISM solar irradiance minimum spectrum, Emin(119–190 nm), the solar cycle minimum has been observed by UARS SOLSTICE in 1996; therefore the observed 108-day smoothed minimum values are used for these wavelengths. Solar minimum conditions have yet to be observed by SEE, so a different method must be used to determine Emin(0.1–119 nm). The solar irradiance minimum value for these wavelengths was found by using a linear fit for each wavelength from the 108-day averaged SEE data to the respective 108-day averaged proxy value for the duration of the SEE mission. This linear fit was then extrapolated to the proxy minimum value to give the solar irradiance minimum value for each wavelength bin. The values for the FISM minimum reference spectrum are given in Appendix A. A ratio of the FISM minimum reference spectrum to three other measured solar minimum reference spectra, are shown in Figure 4. These are the EUV81 spectrum, SC#21REFW (AE-E measurements) [Hinteregger et al., 1981], in Figure 4a, the VUV2002 (UARS SOLSTICE measurements) [Woods and Rottman, 2002] spectrum in Figure 4b, and the NRLEUV (SOHO Coronal Diagnostic Spectrometer (CDS) and SOHO Solar Ultraviolet Measurements of Emitted Radiation (SUMER) measurements) [Warren, 2005] spectrum in Figure 4c. This shows very large, orders of magnitude discrepancies in the various reference spectra. These discrepancies will hopefully be resolved when various instruments spanning this wavelength region all observe the upcoming solar minimum.

Figure 4.

Ratios of the FISM minimum reference spectrum, FISMref, to (a) the EUV81 reference spectrum (from AE-E data), SC#21REFW [Hinteregger et al., 1981], (b) the VUV2002 reference spectrum (from UARS SOLSITCE data) [Woods and Rottman, 2002], and (c) the NRLEUV minimum reference spectrum (from SOHO CDS and SUMER data) [Warren, 2005]. Note that the EUV81 and VUV2002 spectra span the entire wavelength region covered by FISM, while the NRLEUV reference spectrum spans only 0–120 nm.

[19] FISM models the solar cycle irradiance changes as a relative change above this minimum reference value based on the proxies' relative change above its minimum reference value and is discussed in section 4.1. The irradiance changes due to the solar rotation are modeled as a relative change above the solar cycle value and can therefore be a positive or negative change, which is discussed in section 4.2.

4.1. FISM Solar Cycle Algorithms

[20] The long-term variations above the minimum reference value are the first to be modeled by FISM, and these variations are dominated by the 11-year solar cycle variations. The relative change over the solar cycle is modeled by the linear equation:

equation image


equation image

[21] The 108-day average for the proxy, 〈Pd(td)〉108, is the 108-day mean value centered at day d, and the formulation is similar to find the 108-day average for the irradiance measurements, 〈Ed(λ, td)〉108. A 108-day average, or an average over approximately four solar rotations, is used to eliminate the solar rotation variations, and the choice for this smoothing is discussed later in this section. A linear fit is performed to solve for the constant, C0(λ), and the slope, CSC(λ), terms using the SEE daily average values (Level 3) for the XUV and EUV wavelengths (0.1–119 nm) and the UARS SOLSTICE daily average for the EUV-FUV wavelengths (119–190 nm) on days, td, for Ed(λ, td), and then the corresponding proxy values for these days as Pd(td). This relationship given in equation (2) is useful to understand the relative variations to the proxy. For example, a value of two for CSC(λ) means that the irradiance for that particular wavelength varies from the solar cycle by a factor of two more than the proxy solar cycle variations.

[22] An example of the solar cycle fit is shown in Figure 5 for the 88.5 nm wavelength bin using the Lyα proxy. C0(λ) should be zero, as the relative change in the irradiance measurement should be zero when the relative change in the proxy is zero. C0(λ) only comes out approximately zero due to measurement uncertainties that will cause slight deviations in the fits, which can also be seen in Figure 5. Figure 6 shows CSC(λ) for all FISM wavelengths derived using the MgII c/w proxy in Figure 6a. As can be seen, CSC(λ) is approximately 1 for irradiances of a similar formation temperature, in this case the FUV continuum, meaning the relative solar cycle changes of the proxy and the modeled irradiance are approximately the same. It can also be seen that irradiances with a higher formation temperature than the proxy have a higher relative change, or CSC(λ) > 1. If a proxy with a higher formation temperature is used, then modeled irradiances with a lower formation temperature will have a smaller relative change, or CSC(λ) < 1.

Figure 5.

The solar cycle component linear fit relating the relative change of the 108-day averaged SEE measurements to the relative change of the 108-day averaged proxy value. This is a fit for the 88.5 nm bin using the Lyα proxy. C0(88.5 nm) is approximately zero, while CSC(88.5 nm) is 2.583.

Figure 6.

Results of the fits for (a) CSC(λ) and (b) CSR(λ), using the Mg II c/w proxy, and (c) the ratio of CSC(λ)/CSR(λ).

[23] Once C0(λ) and CSC(λ) are found for each wavelength and for each proxy, the relative change of the irradiance for each wavelength, ΔESC(λ, td)/Emin, can then be found whenever the proxy values are available. To get the absolute change over the solar cycle minimum values, ΔESC(λ, td), the relative change is multiplied by the corresponding Emin(λ). This result can then be used in equation (1) as the solar cycle absolute change contribution, ΔESC(λ, td), to the modeled irradiance. The solar cycle irradiance value, ESC(λ, td) can then be defined as

equation image

[24] ESC(λ, td) represents the solar irradiance with no solar rotation or flare components and is the 108-day smoothed value.

[25] There are several filter techniques to separate out the longer-term variations from the daily time series, and the 108-day average was found to be the most accurate representation of the solar cycle changes. The technique of boxcar averaging is a fast, common algorithm, especially important for near real-time modeling. The averaging centered on the day of interest is usually used, even though it does not have physical meaning in regards to advanced solar variability. This value was found to be the optimal number of days to average by determining the highest correlation between two proxies, the MgII c/w and F10.7, and SEE measurements for various numbers of averaged days. The average correlation for all wavelengths as a function of the averaged number of days is shown in Figure 7, with the centered averages for the two proxies shown as solid lines. The peak is just after 108 days for the correlations using the MgII proxy, and there is not a very significant increase in the correlation function after 108 days for the F10.7 proxy.

Figure 7.

The average correlation values of all n-day averaged SEE 1-nm wavelength bins from 0 to 190 nm and the n-day average proxy values.

[26] Performing center averages does not allow for real-time modeling of the irradiance, in this case, with the minimum time lag of 54 days to make irradiance estimations. To overcome this issue, a 108-day trailing average is used for the real-time FISM version and is an average over the previous four solar rotations. The 108-day trailing average was once again shown to be the optimal number of days for the trailing average in a similar method as was done for the centered average, and the results are shown as the dashed lines in Figure 7. The solar cycle average is then reprocessed daily for the most recent 54 days to include the newly obtained daily values. This is done until the more accurate 108-day centered average can be used. The algorithm to determine the solar cycle average for the day n-days prior to the current day is

equation image

4.2. FISM Solar Rotation Algorithms

[27] The changes in the irradiance due to the solar rotation are given by subtracting the 108-day solar cycle average from the daily value. Dividing this residual by the minimum reference value then gives the relative change of the solar rotation variations above the solar cycle values. A linear relationship is then fit in order to model the relative change of the solar rotation irradiance to the similarly formed relative change of the proxy, or:

equation image


equation image

[28] As with the solar cycle fit, the coefficients are found using SEE daily averaged data (Level 3) for each wavelength in the XUV and EUV wavelengths (0.1–119 nm), and the UARS SOLSTICE data for the EUV-FUV wavelengths (119–190 nm) as Ed(λ, td). The six daily averaged proxies, Pd(td), are considered for each wavelength, and the optimal proxy is determined as discussed in section 4.3.

[29] The solar rotation fit is shown in Figure 8, once again using the 88.5 nm bin and Lyα proxy, as were used in Figure 5. C1(λ) should also be zero for the same reason as C0(λ) in the solar cycle algorithm. The values for CSR(λ) derived using the MgII c/w proxy can be seen in Figure 6b. As is similar to the solar cycle coefficient, those irradiances with larger solar rotation contrast and higher formation temperature than the given proxy will be greater than 1, and the cooler emission with a lower contrast will be less than 1.

Figure 8.

The linear fit of the solar rotation component for the 88.5 nm wavelength bin using the Lyα proxy. C1(88.5 nm) is approximately zero, while CSR(88.5 nm) is 1.87.

[30] Using the proxies, when available, the relative irradiance change for wavelength bin λ on day td can then be found by solving the right side of equation (6) using the known coefficients. The solar rotation relative change on day td is then multiplied by the minimum reference value, Emin(λ), to produce the component that represents the absolute change in the irradiance due to the solar rotation, ΔESR(λ, t). The modeled solar rotation irradiance variations can subsequently be added to the minimum reference values and the solar cycle modeled variations in equation (1) to give the FISM estimated daily component irradiance, Ed(λ, td).

4.3. Optimal Daily Proxy Selection

[31] In order to have an accurate empirical model, proxies that are formed in the same layer of the solar atmosphere as the wavelengths that are to be modeled are needed. If this is not the case, there will be large uncertainties in the model, especially in modeling the solar rotation variations. There are many factors to consider when determining which of the available proxies are best for each of the 1 nm wavelength bins.

[32] One important relationship is the one where the long-term, solar cycle fit coefficient, CSC(λ) from equation (2), equals the short-term, solar rotation fit coefficient, CSR(λ) from equation (6). Therefore the best proxy for each 1 nm wavelength bin in FISM, using this qualifier alone, is the proxy whose ratio of CSC/CSR is closest to 1. This ratio can be seen in Figure 6c for all wavelengths using the MgII c/w proxy, showing that the MgII c/w proxy is best in the FUV wavelengths longward of 122 nm.

[33] Another factor to consider in determining the most representative proxy for a particular wavelength is identifying the proxy that has a similar solar rotation variation, representing a similar center-to-limb variation (CLV) function, as the irradiance measurements. Selecting the optimal proxy based on this condition should provide for a more accurate linear relationship for the solar rotation irradiance variations as described by equation (6). The CLV functions for each wavelength can be derived from irradiance time series using active regions determined from solar images [Worden et al., 2001]. Using a derived CLV function was initially studied for FISM, but it was found to have larger uncertainties than the simpler empirical model. The CLV functions are important for models that use solar images as proxies, as done for the NRLEUV [Warren et al., 2001] and by Worden et al. [2001].

[34] While the final FISM version does not use the CLV functions for modeling daily variations, the effects of CLV on solar rotation variations are important to consider while selecting the best proxies for FISM. Examples of the CLV influence on solar rotational variations are given in Figure 3, which shows all six of the proxies for a large solar rotation in January 2004. It can be clearly seen that the 36.5 nm proxy most clearly represents the center-to-limb brightening temporal profile of the coronal line, while the Lyα bin most accurately represents the center-to-limb darkening profile of the transition region line.

[35] The CSC(λ)/CSC(λ) ratio and the solar rotational variations as related to their CLV functions are the two factors with the highest priority in determining the best proxy for each 1 nm wavelength bin. Another, albeit minor, factor for accessing the best proxy is the correlation given by each of the solar cycle and solar rotational fits from equations (2) and (6). The lowest priority in the optimal proxy determination, although it reconfirms many of the highest priority selection factors, is the standard deviation of the daily component model given by equation (1) using each of the eight daily average proxies. The standard deviation algorithm is discussed in section 4.4. That is, the preferred proxies had to have a high correlation and low standard deviation.

[36] Through these studies, it was found that the best proxy for the chromosphere is the MgII c/w, and the best transition region proxy is the Lyα emission, both of which were expected [Woods et al., 2000]. The 30.4 nm line is the best proxy for the upper chromosphere and lower transition region. The coronal EUV bound-bound emissions were very well modeled by both the 33.5 nm and 36.5 nm emissions. The 36.5 nm emission is selected for FISM as it better fits the coronal emissions in the 32–39 nm range that display strong center-to-limb brightening. The best proxy for the soft X-ray Bremsstrahlung (continuum) emissions is the 0–4 nm integrated irradiance, although the F10.7 or a derived GOES “daily” (actually the third minimum value for the day) proxies are also good for the XUV range. Table 1 lists the proxies that are used in FISM for each 1 nm wavelength bin. The optimal proxy studies have shown that the most representative proxy for each wavelength bin is found to be the one that is formed at a similar formation temperature in the solar atmosphere. When the optimal proxy is unavailable, the next best available proxy is used in its place. Table 2 gives the order in which proxies are used as backups for each of the optimal proxies. F10.7 is continually available, either as a measurement or interpolation between measurements since 1947. As long as F10.7 is available, a complete solar VUV irradiance spectrum can be modeled by FISM. Prior to 1947, a solar spectrum cannot be estimated given this set of proxies.

Table 1. Optimal Proxies Used to Model Each 1 nm Wavelength Bin in FISM
WV, nmProxyWV, nmProxyWV, nmProxyWV, nmProxy
0.50–4 nm49.530.5 nm98.5Lya147.5Lya
1.50–4 nm50.530.5 nm99.5Lya148.5Lya
2.50–4 nm51.530.5 nm100.5Lya149.5Lya
3.50–4 nm52.530.5 nm101.5Lya150.5Lya
4.50–4 nm53.530.5 nm102.5Lya151.5Lya
5.50–4 nm54.530.5 nm103.5Lya152.5Lya
6.50–4 nm55.530.5 nm104.5Lya153.5Lya
7.50–4 nm56.530.5 nm105.5Lya154.5Lya
8.50–4 nm57.530.5 nm106.5Lya155.5Lya
9.50–4 nm58.530.5 nm107.5Lya156.5Lya
10.50–4 nm59.530.5 nm108.5Lya157.5Lya
11.50–4 nm60.530.5 nm109.5Lya158.5Lya
12.50–4 nm61.530.5 nm110.5Lya159.5Lya
13.50–4 nm62.530.5 nm111.5Lya160.5Lya
17.5F10.766.530.5 nm115.5Lya164.5Lya
18.5F10.767.530.5 nm116.5Lya165.5Lya
19.5F10.768.530.5 nm117.5Lya166.5MgII c/w
20.5F10.769.530.5 nm118.5Lya167.5MgII c/w
21.5F10.770.530.5 nm119.5Lya168.5MgII c/w
22.5F10.771.5Lya120.5Lya169.5MgII c/w
23.5F10.772.5Lya121.5Lya170.5MgII c/w
24.5F10.773.5Lya122.5Lya171.5MgII c/w
25.5F10.774.5Lya123.5Lya172.5MgII c/w
26.5F10.775.5Lya124.5Lya173.5MgII c/w
27.530.5 nm76.5Lya125.5Lya174.5MgII c/w
28.530.5 nm77.5Lya126.5Lya175.5MgII c/w
29.530.5 nm78.5Lya127.5Lya176.5MgII c/w
30.530.5 nm79.5Lya128.5Lya177.5MgII c/w
31.536.5 nm80.5Lya129.5Lya178.5MgII c/w
32.536.5 nm81.5Lya130.5Lya179.5MgII c/w
33.536.5 nm82.5Lya131.5MgII c/w180.5MgII c/w
34.536.5 nm83.5Lya132.5MgII c/w181.5MgII c/w
35.536.5 nm84.5Lya133.5Lya182.5MgII c/w
36.536.5 nm85.5Lya134.5MgII c/w183.5MgII c/w
37.536.5 nm86.5Lya135.5Lya184.5MgII c/w
38.536.5 nm87.5Lya136.5Lya185.5MgII c/w
39.536.5 nm88.5Lya137.5Lya186.5MgII c/w
40.536.5 nm89.5Lya138.5Lya187.5MgII c/w
41.536.5 nm90.5Lya139.5Lya188.5MgII c/w
42.536.5 nm91.5Lya140.5Lya189.5MgII c/w
43.536.5 nm92.5Lya141.5Lya190.5MgII c/w
44.536.5 nm93.5Lya142.5Lya191.5MgII c/w
45.530.5 nm94.5Lya143.5Lya192.5MgII c/w
46.530.5 nm95.5Lya144.5Lya193.5MgII c/w
47.530.5 nm96.5Lya145.5Lya194.5MgII c/w
48.530.5 nm97.5Lya146.5Lya  
Table 2. Backup Proxies Used, When Available, When the Given Optimal and Higher-Ranked Backup Proxies Are Unavailable
Optimal ProxyFirst BackupSecond BackupThird Backup
0–4 nmF10.7
36.5 nmLyαMgII c/wF10.7
30.5 nmLyαMgII c/wF10.7
LyαMgII c/wF10.7

4.4. FISM Uncertainty

[37] The FISM daily component uncertainty is found by determining the weighted standard deviation of the FISM daily results from the available SEE Level 3 data, comprising of almost 4 years. This was done using the equation given by Bevington's [1969] analysis of a least squares fit to a line, or:

equation image

[38] A linear fit contains two degrees of freedom, which is why n − 2 is used in the denominator. This is done for the time series of each proxy, EP, and for each wavelength, EMeas, when both components are available.

[39] The standard deviation, or “uncertainty,” throughout this paper refers to the ability of FISM to reproduce the base data set, for example, how well the FISM daily component at 33.5 nm represents the SEE Level 3 daily value at the similar wavelength. The FISM “total uncertainty” is the FISM uncertainties added in quadrature with the measurement uncertainties of the base data set. These uncertainties are discussed in the following sections.

5. FISM Results

[40] FISM has the ability to model the solar cycle and solar irradiance variations as far back as 1947 when the F10.7 record starts, while the uncertainty decreases when the optimal proxies become available. The solar cycle, CSC, and solar rotation, CSR, coefficients that were found to be used in equations (2) and (6) when estimating the solar irradiance are given in Appendices B and C, respectively.

5.1. FISM Solar Cycle Results

[41] The ratio of the FISM estimated spectrum averaged over a 108-day period during the maximum of solar cycle 23 (8 November 2001 to 24 February 2002) to a similar spectrum during the previous solar cycle minimum (16 December 1995 to 2 April 1996) is shown in Figure 9. This figure shows the amount of solar variability estimated by FISM from solar cycle minimum to maximum. The solar cycle variations range from 10% at the long FUV wavelengths to factors of 10 in the XUV wavelengths. These results should be comparable to the solar cycle variations shown in the work of Woods et al. [2005, Figure 14], although the solar cycle variation ratio from Woods et al. was calculated using only a 2-year time period of the TIMED mission when the solar minimum spectrum was not truly at solar cycle minimum.

Figure 9.

The estimated solar irradiance variations that occur as a function of wavelength during between solar cycle maximum and minimum conditions (black) and the maximum and minimum for a strong solar rotation (grey). The solar cycle variation is the ratio (minus 1) of a 108-day averaged spectrum during high solar activity conditions of solar cycle 23 to a similar 108-day averaged spectrum during low solar activity conditions between solar cycles 22 and 23. The solar rotation irradiance variability is for a bright solar rotation in January 2004. This ratio uses a spectrum where a large active region is present in the center of the solar disk (from 19 January 2004) and divides it by a spectrum from 29 January 2004 when this large active region had rotated around the Sun and was no longer visible.

[42] The daily component results for FISM have standard deviations ranging from about 2% in the FUV, from 1% to 10% in the EUV, and then from 1% to 14% in the XUV when all optimal proxies are available, which can be seen in Figure 10. The standard deviation represents how accurately FISM is able to reproduce the SEE and UARS data. The FISM estimations with extremely low standard deviations (<1%) are at wavelengths that are also used as proxies; therefore the FISM irradiances at these wavelengths are essentially the original SEE data and should have a standard deviation of zero. Also shown in Figure 10 is the FISM total uncertainty that is derived as the square root of the sum of the squares of the FISM standard deviation and the measurement accuracy of the base data set used to derive the FISM parameters (SEE and SORCE for wavelengths from 0.1 to 27 nm, SEE for wavelengths from 27 to 119 nm, and UARS SOLSTICE for wavelengths from 119 to 190 nm). The large total uncertainties from 115 to 120 nm are due to the Lyman-α filter in SEE EGS that decreases the statistics around the actual Lyman-α line, leading to larger measurement uncertainties. The increasing total uncertainties with shorter wavelength from 32 down to 27 nm are due to the decreasing reflectance of the gold coating that was used on the EGS detector. There are also large uncertainties associated with the SEE/SORCE XPS algorithm that then leads to the larger measurement errors from 4 to 14 nm. The standard deviations shown in Figure 10 are for the best case when all optimal proxies are available in order to compute the model, where this will increase if using a proxy other than the optimal one.

Figure 10.

The standard deviation for the FISM daily component (black) when all optimal proxies are available, which represents how accurately FISM is able to reproduce the SEE and UARS data. Also shown in grey is the FISM total uncertainty that incorporates the SEE and UARS accuracy with the FISM standard deviation.

[43] The daily averaged irradiances from FISM integrated over all wavelengths (0.1–190 nm) are shown in Figure 11 for the time period from 1947 until present. As can be seen, the standard deviation becomes smaller when the optimal proxies are available, such as in 1977 and 1978 when the Lyα and Mg II c/w proxies, respectively, were first measured. There is then another, more significant decrease in the standard deviation after 2002 when the proxies that are derived from the SEE measurements first became available. The few spikes in the FISM standard deviation that occur after 2002 are from days when the SEE data are unavailable to use as proxies.

Figure 11.

(a) The FISM daily averaged results of the solar irradiance integrated from 0.1 to 193 nm and (b) the associated standard deviation from 1947 until present.

[44] The FISM daily average results for the 34.5 nm wavelength bin is shown in Figure 12, respectively, along with the similar wavelength bin from the TIMED SEE Level 3 data for the days when the respective data are available. There is very good agreement between the FISM results and the SEE data, as the FISM results lie almost directly on top of the measurements. The results shown are also very typical for other wavelengths, which were shown in the FISM standard deviations given in Figure 10. The good agreement between the FISM model and the SEE measurements can also be seen in Figure 12b of the ratio (minus 1) of these two sets. The mean of this ratio is −0.00172, showing that any absolute solar cycle offset in the FISM model is less than 0.2%, while the linear fit slope coefficient of this ratio is −0.00557, showing that the modeling solar cycle changes are accurate for this wavelength to less than 0.6%. Both of these errors are well within the given daily component standard deviation for this wavelength bin of 2.28%. The good agreement is expected for the SEE comparisons, as the SEE measurements are used as the reference for creating FISM at this wavelength.

Figure 12.

(a) FISM results and standard deviation for the 34.5 nm bin that is dominated by coronal EUV bound-bound emissions is shown in grey, while shown in black is the SEE Level 3 data for the same wavelength for comparison. (b) The ratio of the FISM model to the SEE Level 3 data minus 1 for the same 34.5 nm bin shows the deviations of the model irradiance from the observations. The standard deviation for this wavelength is 2.28% when the optimal 36.5 nm proxy is available.

5.2. FISM Solar Rotation Results

[45] Solar rotational irradiance variations are about 2–5 times smaller than the solar cycle variations, but the spectral response is similar with the coronal XUV lines showing more variability than the photospheric and chromospheric FUV emissions. A ratio showing the solar rotational variation for a strong solar rotation in January 2004 can be seen as the grey line in Figure 9. This figure shows the ratio (minus 1) of the spectrum when the active region is in the center of the solar disk to the spectrum when the active region is no longer visible and with no other active regions present. The solar rotation irradiance variations range from 4% in the FUV wavelengths to factors of 2 in the XUV wavelengths.

[46] The results from FISM, along with the SEE Level 3A data (approximately 3-min averages), for the similar wavelength region (35–40 nm) and time period (January 2004) as were shown in Figure 1 are shown in Figure 13. This shows the ability of FISM to accurately estimate the center-to-limb variations for coronal bound-bound emissions that can also be seen in the given standard deviation between the two data sets for this time of 1.44%. The solar rotation results from FISM for this wavelength band containing many coronal bound-bound emissions shows the expected center-to-limb brightening profile, where the two dominant active regions at similar longitudinal locations produced large irradiances both when they first appears on the eastern limb and then again when they disappear on the western limb, while the irradiance had a slight dip as the sunspots traveled across the disk of the Sun.

Figure 13.

A comparison of the FISM daily component results (grey) and the SEE daily median data (black) for the similar wavelength region (35–40 nm) and time period (January 2004) shown in Figure 1 comparing other models to the SEE data.

6. FISM Comparisons

[47] Comparisons between FISM and simultaneous measurements from a few other instruments provide validation of the FISM results. Time series of FISM results have already been shown in Figures 12 and 13 in order to compare this data to the data for which the FISM parameters were derived from. Other data sets are available to produce a more independent validation of the FISM results. As well as the TIMED SEE and UARS SOLSTICE, other measurements that are available for validation of FISM results are from the Solar EUV Monitor (SEM) [Judge et al., 1998] on the Solar and Heliospheric Observatory (SOHO) and the SOLSTICE instrument on the Solar Radiation and Climate Experiment (SORCE). Also available for comparisons are the existing models, including the EUV81, EUVAC, NRLEUV, and SOLAR2000 models that were discussed in section 2, along with another empirical model of the VUV, called VUV2002 [Woods and Rottman, 2002].

[48] As many comparisons of FISM results throughout this chapter will be made to SEM, it is useful to first show the absolute irradiance differences between the SEM data and the SEE data for which FISM is based at the SEM wavelength ranges. SEM data are available since SOHO's launch in 1996, so there are currently data available for almost one entire solar cycle. There are two broadband measurements available from SEM, one ranging from 0.1 to 50 nm and the other ranging from 26 to 34 nm. The SEM data are shown along with the SEE data in Figure 14 for the time period from 2002 to 2005; both include their long-term degradation corrections from rocket calibration underflights. The time series shown in Figure 14a shows that the magnitudes of the solar rotation variations are approximately similar, but the SEM data have an absolute offset that is approximately 10% higher than the SEE data, as seen by the ratio shown in Figure 14b. This offset is propagated to the FISM results, where the 26–34 nm comparisons will show FISM results being approximately 10% lower than the SEM 26–34 nm channel. The SEE and SEM measurements in the other SEM band, 0.1–50 nm, show much better agreement, and there is not the absolute offset that is present in the 26–34 nm channel.

Figure 14.

(a) The TIMED SEE and SOHO SEM time series for the 26–34 nm band for the times where the SEE data are available. (b) The ratio of the SEE to SEM data, showing the SEE data is approximately 10% lower than the SEM data.

[49] The 1 nm bins of FISM are combined in order to make a similar broadband data product as the SEM products. Figure 15 shows the FISM and the SEM daily averaged results for the 0.1–50 nm channel during solar cycle 23. There are many spikes in the SEM data, caused by large increases in the counts due to its sensitivity to high-energy particles, which are not yet removed from the SEM data. There are also significant contributions from large, long-duration flares in the SEM data, as its data set is a daily average, while the FISM data set is based on daily median data with most large flare data removed. There are also large gaps in the SEM data where no data are available. Nonetheless, SEM provides a data set to make comparisons of the FISM results for almost one complete solar cycle. There is good agreement in both channels when the full set of optimal proxies is available to use in FISM, starting in February 2002. The differences between the SEM data and FISM results increase before 2002 due to the loss of the 30.5 nm, 36.5 nm, and 0–4 nm optimal proxies, for which the Lyα and F10.7 proxies are then used in their place.

Figure 15.

The FISM daily-averaged irradiances (black) from 0.1 to 50 nm compared to the broadband measurements from SOHO SEM (grey) over the similar wavelength region for solar cycle 23.

[50] The FISM modeled irradiances seen in Figure 15 are lower than the SEM measurements during the solar cycle minimum around and during 1996 but are in good agreement since 2000. There may be long-term degradation effects that are not correctly being accounted for, in either SEE or SEM. Even though both instruments have underflight rocket calibrations that can eliminate the long-term effects, there are still uncertainties associated with the rocket flight data and the transfer of calibration from the rockets to the satellite instruments. The discrepancies between the FISM and SEM data during solar minimum conditions may also be due to errors in extrapolating the existing SEE data to determine the FISM solar minimum reference spectrum. It is known that some wavelengths “bottom out,” or reach their minimum values, before others, as F10.7 is known to reach its minimum value before Lyα. These wavelength differences introduce nonlinearities in the present linear extrapolation to solar minimum values and also in the linear FISM algorithms near solar minimum. The solar minimum results from FISM are expected to improve in the next 2 years as TIMED SEE, SOHO SEM, and SORCE SOLSTICE all will measure the solar XUV-VUV irradiance during the upcoming solar minimum.

[51] Comparisons can also be performed of the FISM results in the FUV to the SORCE SOLSTICE data from 25 February 2003 to the present, as well as the UARS SOLSTICE and SUSIM data as far back as 1991. Comparisons can also be made to another daily averaged empirical model in the FUV, called VUV2002 [Woods and Rottman, 2002], which is based on the data from UARS SOLSTICE in the FUV wavelengths and exclusively uses F10.7 as its proxy.

[52] Figure 16 shows the standard deviations of the FISM irradiance spectra with the VUV2002 and SOLSTICE (UARS and SORCE) data in the FUV wavelengths for two 54-day periods (two solar rotations), one during low solar activity conditions (mean F10.7 of 70.9) in grey and another during high solar activity conditions (mean F10.7 of 177.0) in black. There is very good agreement between all spectra and models in the FUV wavelengths greater than 150 nm, but the solar cycle variations are also very small, typically 20–40%, for these wavelengths [Woods et al., 2005]. Larger deviations exist in the shorter FUV wavelengths, especially in the strong emission lines formed in the transition region. The transition region lines vary much more during the solar cycle and solar rotation than the underlying FUV continua that are formed mainly in the photosphere and chromosphere and are going to be more difficult to model and have larger uncertainties that are comparable to those in the EUV wavelengths. FISM does agree to within a couple of percent with the UARS SOLSTICE, which is the base data set for FISM, at all FUV wavelengths; therefore FISM accurately represents and models the SOLSTICE results, and the discrepancies between FISM and the other measurements and models in the FUV wavelengths are due mostly to the discrepancies between the UARS SOLSTICE data and the other measurements.

Figure 16.

The FISM standard deviations when compared to (a) the UARS SOLSTICE measurements and (b) VUV 2002 model results at FUV wavelengths. This comparison was done for two 54-day periods, one in 1996 during low solar activity conditions (mean F10.7 of 70.9) shown as the grey lines, and another in 1992 during high solar activity (mean F10.7 of 177.0), shown in black.

[53] A summary table of the standard deviations between FISM as compared to the results from TIMED SEE, SORCE SOLSTICE, and UARS SOLSTICE at 10 nm intervals over the entire overlapping wavelength regions, as well as performing the comparison for all days when data from the respective instruments are available, are shown in Table 3. This comparison shows very good agreement between FISM and SEE in the EUV wavelengths and UARS SOLSTICE in the FUV wavelength region, due to these data sets providing the basis for the FISM parameters. The standard deviations calculated between each of the models and FISM can also be seen in Table 3, which is calculated at 10-nm intervals over the provided wavelengths ranges available for each model, and uses the daily model results from 1996 until 2004, covering almost the entire solar cycle 23.

Table 3. Summary Table of the Standard Deviations of FISM Based on All Other Available Measurements and Model Outputs in 10-nm Wavelength Binsa
  • a

    Note that not all data and models are available at all VUV wavelengths. Also listed are the start and end dates of the data used for each measurement and model in determining the standard deviation.

0–10 nm31.30%———–———–72.10%47.30%27.00%———–
10–20 nm44.50%———–———–41.10%31.90%12.10%26.30%
20–30 nm21.00%———–———–43.00%46.00%16.70%54.20%
30–40 nm2.40%———–———–17.30%37.70%40.90%28.10%
40–50 nm8.31%———–———–21.70%151.30%16.00%18.60%
50–60 nm11.10%———–———–91.00%137.10%24.30%20.80%
60–70 nm10.50%———–———–25.40%142.80%10.30%24.20%
70–80 nm5.77%———–———–41.80%282.50%18.10%26.00%
80–90 nm9.55%———–———–26.70%63.40%22.90%18.80%
90–100 nm8.98%———–———–49.10%62.90%6.91%24.90%
100–110 nm8.54%———–———–51.40%———–———–31.10%
110–120 nm2.32%———–———–63.70%———–———–43.60%
120–130 nm7.13%14.2%2.75%11.70%———–280.20%———–
130–140 nm30.30%8.49%4.36%27.30%———–10.90%———–
140–150 nm3.39%9.27%1.61%20.62%———–12.80%———–
150–160 nm4.00%12.4%1.74%28.20%———–11.20%———–
160–170 nm2.52%12.4%0.87%25.80%———–18.00%———–
170–180 nm3.94%10.5%0.74%36.10%———–16.90%———–
180–190 nm4.06%1.58%1.09%40.80%———–12.60%———–
Start Date2002039200305619920011996001199600119960011996001
End Date2005270200513319963652004365200436520043652004365

7. Conclusion

[54] FISM has made dramatic improvements in modeling the daily average solar irradiance over the currently available models that were discussed in section 2. These improvements involved looking at multiple factors when selecting the optimal proxy for each wavelength, optimizing the solar cycle and solar rotation variation separately, the flexibility to use the best set of available proxies for the given time, and the use of the most accurately available measurements of XUV-VUV irradiance (TIMED SEE and XPS, UARS SOLSTICE, and SORCE XPS) in order to derive the FISM parameters. These improvements provide a more precise representation of the available measurements producing the most accurate solar irradiance model from 0.1 to 190 nm. FISM results may be obtained by contacting the author.

[55] The other models do not reproduce the measured absolute irradiance value correctly, which is mainly due to the modeling of the solar cycle component, but also do not represent the correct solar rotation CLV for the coronal emissions, which is due to the proxies used. It is impossible for any model based on the F10.7 and/or MgII c/w proxies alone, both having a center-to-limb darkening profile, to have the ability to model the center-to-limb brightening function seen in Figure 13 correctly. Also, the FISM includes the spontaneous increases in the irradiance due to the occurrence of a flare, which all other models currently do not have the capability to model. The flare components of FISM will be presented in a separate FISM paper.

[56] FISM can now be used for a wide variety of problems in collaboration with other researchers from different disciplines within space weather. One example includes providing the FISM solar XUV-VUV irradiance over a solar cycle to drive a model of the Earth's thermosphere neutral atmospheric density response. These results can then be convolved with the drag coefficients of various satellites in order to provide estimations for the satellite drag rates. This same type of application may also be applied to Mars' atmosphere in order to assist with the satellite drag estimations during critical aerobreaking procedures.

Appendix A

[57] FISM XUV-VUV minimum reference spectrum, Emin, are shown in Table A1. The irradiance values are in units of W/m2/nm.

Table A1. FISM Solar Cycle Parameters (CSC) for Each Proxy and Wavelengtha
WavelengthMgII c/wF10.730.5 nm0–4 nmLyman Alpha36.5 nm
  • a

    Boldface indicates the optimal proxy for each wavelength.

0.5 nm2.33E + 026.87E + 001.21E + 011.35E + 002.16E + 012.67E + 00
1.5 nm2.03E + 026.14E + 001.04E + 011.13E + 001.87E + 012.32E + 00
2.5 nm1.71E + 025.20E + 008.68E + 009.38E-011.56E + 011.94E + 00
3.5 nm1.24E + 023.79E + 006.26E + 006.76E-011.13E + 011.40E + 00
4.5 nm1.44E + 024.37E + 007.42E + 008.07E-011.32E + 011.65E + 00
5.5 nm7.34E + + 012.23E + 003.78E + 004.11E-016.73E + 008.43E-01
6.5 nm7.93E + 012.40E + 004.08E + 004.44E-017.27E + 009.11E-01
7.5 nm6.53E + 011.98E + 003.36E + 003.66E-015.99E + 007.50E-01
8.5 nm6.57E + 012.00E + 003.39E + 003.68E-016.03E + 007.56E-01
9.5 nm8.70E + 012.64E + 004.48E + 004.87E-017.98E + 001.00E + 00
10.5 nm8.70E + 012.64E + 004.48E + 004.87E-017.98E + 001.00E + 00
11.5 nm8.70E + 012.64E + 004.48E + 004.87E-017.98E + 001.00E + 00
12.5 nm8.70E + 012.64E + 004.48E + 004.87E-017.98E + 001.00E + 00
13.5 nm8.70E + 012.64E + 004.48E + 004.87E-017.98E + 001.00E + 00
14.5 nm3.81E + 011.17E + 001.97E + 002.38E-013.49E + 004.38E-01
15.5 nm2.83E + 028.67E + 001.46E + 011.73E + 002.59E + 013.26E + 00
16.5 nm4.36E + 011.34E + 002.25E + 002.79E-013.99E + 005.03E-01
17.5 nm5.22E + 011.61E + 002.70E + 003.31E-014.78E + 006.02E-01
18.5 nm1.16E + 023.55E + 005.98E + 007.16E-011.06E + 011.33E + 00
19.5 nm3.87E + 021.18E + 011.99E + 012.36E + 003.54E + 014.45E + 00
20.5 nm5.10E + 011.51E + 002.62E + 003.19E-014.70E + 005.83E-01
21.5 nm5.54E + 011.67E + 002.90E + 003.47E-015.13E + 006.43E-01
22.5 nm1.17E + 023.58E + 006.03E + 007.21E-011.07E + 011.34E + 00
23.5 nm8.88E + 012.72E + 004.59E + 005.52E-018.13E + 001.02E + 00
24.5 nm1.23E + 023.77E + 006.35E + 007.59E-011.13E + 011.42E + 00
25.5 nm1.71E + 025.24E + 008.83E + 001.05E + 001.57E + 011.97E + 00
26.5 nm5.41E + 011.63E + 002.80E + 003.35E-015.00E + 006.23E-01
27.5 nm3.67E + 011.12E + 001.89E + 002.26E-013.36E + 004.22E-01
28.5 nm1.97E + 025.97E + 001.02E + 011.15E + 001.80E + 012.27E + 00
29.5 nm3.29E + 019.97E-011.69E + 001.91E-013.01E + 003.78E-01
30.5 nm1.94E + 015.89E-019.98E-011.18E-011.77E + 002.23E-01
31.5 nm2.97E + 019.04E-011.53E + 001.78E-012.72E + 003.42E-01
32.5 nm2.98E + 019.06E-011.53E + 001.80E-012.73E + 003.42E-01
33.5 nm5.19E + 011.54E + 002.69E + 003.03E-014.79E + 005.97E-01
34.5 nm3.97E + 011.21E + 002.04E + 002.48E-013.63E + 004.56E-01
35.5 nm9.63E + 012.93E + 004.96E + 005.87E-018.82E + 001.11E + 00
36.5 nm8.68E + 012.64E + 004.47E + 005.27E-017.95E + 009.98E-01
37.5 nm2.89E + 018.82E-011.49E + 001.81E-012.65E + 003.32E-01
38.5 nm3.34E + 011.02E + 001.72E + 002.10E-013.06E + 003.84E-01
39.5 nm3.26E + 019.97E-011.68E + 002.10E-012.98E + 003.75E-01
40.5 nm2.48E + 017.59E-011.28E + 001.62E-012.27E + 002.85E-01
41.5 nm2.97E + 029.02E + 001.53E + 011.77E + 002.72E + 013.42E + 00
42.5 nm2.97E + 019.08E-011.53E + 001.88E-012.72E + 003.42E-01
43.5 nm1.68E + 015.17E-018.65E-011.12E-011.54E + 001.93E-01
44.5 nm3.78E + 011.16E + 001.95E + 002.35E-013.46E + 004.35E-01
45.5 nm1.92E + 015.90E-019.90E-011.26E-011.76E + 002.21E-01
46.5 nm1.10E + 013.39E-015.68E-017.59E-021.01E + 001.27E-01
47.5 nm1.80E + 015.52E-019.28E-011.18E-011.65E + 002.07E-01
48.5 nm2.47E + 017.55E-011.27E + 001.58E-012.26E + 002.84E-01
49.5 nm1.12E + 023.41E + 005.78E + 006.75E-011.03E + 011.29E + 00
50.5 nm4.06E + 011.24E + 002.09E + 002.57E-013.72E + 004.67E-01
51.5 nm5.99E + 011.82E + 003.09E + 003.72E-015.49E + 006.89E-01
52.5 nm1.78E + 025.41E + 009.16E + 001.09E + 001.63E + 012.04E + 00
53.5 nm3.59E + 011.10E + 001.85E + 002.34E-013.29E + 004.13E-01
54.5 nm3.01E + 019.16E-011.55E + 001.94E-012.75E + 003.46E-01
55.5 nm1.06E + 013.30E-015.44E-018.09E-029.72E-011.21E-01
56.5 nm4.00E + 011.22E + 002.06E + 002.60E-013.66E + 004.60E-01
57.5 nm1.31E + 014.04E-016.71E-019.96E-021.20E + 001.50E-01
58.5 nm3.25E + 019.98E-011.67E + 002.22E-012.97E + 003.73E-01
59.5 nm2.63E + 018.05E-011.36E + 001.75E-012.41E + 003.03E-01
60.5 nm9.73E + 013.02E + 005.01E + 007.44E-018.90E + 001.12E + 00
61.5 nm7.36E + 012.28E + 003.79E + 005.69E-016.74E + 008.47E-01
62.5 nm2.15E + 016.58E-011.11E + 001.40E-011.97E + 002.47E-01
63.5 nm1.84E + 015.71E-019.48E-011.31E-011.69E + 002.12E-01
64.5 nm1.50E + 014.57E-017.73E-019.79E-021.37E + 001.73E-01
65.6 nm1.91E + 015.85E-019.85E-011.27E-011.75E + 002.20E-01
66.5 nm2.21E + 016.77E-011.14E + 001.47E-012.02E + 002.54E-01
67.5 nm2.19E + 016.71E-011.13E + 001.44E-012.00E + 002.52E-01
68.5 nm2.00E + 016.15E-011.03E + 001.36E-011.83E + 002.30E-01
69.5 nm2.67E + 018.17E-011.37E + 001.75E-012.44E + 003.07E-01
70.5 nm1.06E + 013.26E-015.42E-017.41E-029.66E-011.21E-01
71.5 nm1.97E + 016.06E-011.01E + 001.37E-011.80E + 002.26E-01
72.5 nm3.77E + 011.15E + 001.94E + 002.37E-013.45E + 004.34E-01
73.5 nm1.27E + 013.87E-016.53E-018.18E-021.16E + 001.46E-01
74.5 nm1.68E + 015.18E-018.67E-011.15E-011.54E + 001.93E-01
75.5 nm9.59E + 002.96E-014.93E-017.12E-028.78E-011.10E-01
76.5 nm6.61E + 002.03E-013.39E-014.90E-026.04E-017.56E-02
77.5 nm1.89E + 015.87E-019.75E-011.39E-011.73E + 002.18E-01
78.5 nm8.64E + 002.64E-014.44E-015.60E-027.90E-019.91E-02
79.5 nm1.05E + 013.22E-015.40E-016.81E-029.60E-011.20E-01
80.5 nm2.26E + 016.94E-011.16E + 001.53E-012.06E + 002.59E-01
81.5 nm1.28E + 013.92E-016.56E-018.67E-021.17E + 001.46E-01
82.5 nm1.85E + 015.66E-019.55E-011.19E-011.70E + 002.13E-01
83.5 nm1.13E + 013.46E-015.83E-017.48E-021.04E + 001.30E-01
84.5 nm1.75E + 015.39E-019.00E-011.21E-011.60E + 002.01E-01
85.5 nm2.68E + 018.18E-011.38E + 001.67E-012.45E + 003.08E-01
86.5 nm1.78E + 015.45E-019.18E-011.16E-011.63E + 002.05E-01
87.5 nm2.76E + 018.46E-011.42E + 001.84E-012.52E + 003.17E-01
88.5 nm2.86E + 018.77E-011.47E + 001.87E-012.62E + 003.29E-01
89.5 nm1.57E + 014.79E-018.12E-019.88E-021.44E + 001.81E-01
90.5 nm2.30E + 017.05E-011.18E + 001.53E-012.11E + 002.64E-01
91.5 nm2.50E + 017.64E-011.29E + 001.57E-012.29E + 002.88E-01
92.5 nm1.57E + 014.81E-018.07E-011.04E-011.44E + 001.80E-01
93.5 nm2.00E + 016.13E-011.03E + 001.34E-011.83E + 002.30E-01
94.5 nm2.10E + 016.43E-011.08E + 001.38E-011.93E + 002.42E-01
95.5 nm1.90E + 015.88E-019.80E-011.34E-011.74E + 002.19E-01
96.5 nm1.69E + 015.20E-018.69E-011.20E-011.54E + 001.94E-01
97.5 nm1.60E + 014.91E-018.25E-011.02E-011.47E + 001.84E-01
98.5 nm6.93E + 002.18E-013.55E-015.69E-026.33E-017.92E-02
99.5 nm1.64E + 015.01E-018.42E-011.06E-011.50E + 001.88E-01
100.5 nm2.24E + 016.84E-011.15E + 001.43E-012.05E + 002.57E-01
101.5 nm1.87E + 015.76E-019.64E-011.27E-011.71E + 002.15E-01
102.5 nm2.28E + 017.00E-011.17E + 001.48E-012.09E + 002.62E-01
103.5 nm2.28E + 016.98E-011.17E + 001.47E-012.08E + 002.62E-01
104.5 nm1.61E + 014.97E-018.29E-011.13E-011.47E + 001.85E-01
105.5 nm1.39E + 014.30E-017.18E-019.74E-021.28E + 001.60E-01
106.5 nm1.35E + 014.19E-016.94E-019.91E-021.23E + 001.55E-01
107.5 nm1.14E + 013.52E-015.85E-018.21E-021.04E + 001.30E-01
108.5 nm1.81E + 015.55E-019.30E-011.22E-011.65E + 002.08E-01
109.5 nm1.30E + 013.99E-016.67E-018.85E-021.19E + 001.49E-01
110.5 nm1.22E + 013.77E-016.29E-018.51E-021.12E + 001.40E-01
111.5 nm1.28E + 013.94E-016.59E-018.67E-021.17E + 001.47E-01
112.5 nm1.20E + 013.69E-016.16E-018.32E-021.09E + 001.37E-01
113.5 nm9.34E + 002.88E-014.81E-016.51E-028.55E-011.07E-01
114.5 nm2.49E + 007.92E-021.28E-012.84E-022.28E-012.85E-02
115.5 nm2.49E + 007.92E-021.28E-012.84E-022.28E-012.85E-02
116.5 nm2.49E + 007.92E-021.28E-012.84E-022.28E-012.85E-02
117.5 nm8.30E + 002.55E-014.28E-015.98E-027.59E-019.54E-02
118.5 nm2.49E + 007.92E-021.28E-012.84E-022.28E-012.85E-02
119.5 nm5.79E + 001.96E-013.04E-014.55E-025.50E-016.79E-02
120.5 nm1.10E + 013.73E-016.47E-018.56E-021.04E + 001.44E-01
121.5 nm9.90E + 003.36E-015.39E-017.25E-029.40E-011.20E-01
122.5 nm4.80E + 001.63E-012.60E-014.07E-024.62E-015.79E-02
123.5 nm4.97E + 001.68E-012.88E-014.51E-024.69E-016.42E-02
124.5 nm5.17E + 001.76E-012.92E-014.48E-024.95E-016.51E-02
125.5 nm4.20E + 001.45E-012.55E-014.02E-024.26E-015.69E-02
126.5 nm6.98E + 002.40E-014.23E-015.91E-026.90E-019.45E-02
127.5 nm3.73E + 001.30E-012.27E-013.76E-023.85E-015.06E-02
128.5 nm3.49E + 001.19E-011.99E-013.49E-023.39E-014.45E-02
129.5 nm5.49E + 001.91E-015.99E-018.37E-025.53E-011.34E-01
130.5 nm3.90E + 001.32E-012.93E-014.53E-023.70E-016.55E-02
131.5 nm2.47E + 008.46E-025.14E-017.35E-022.45E-011.15E-01
132.5 nm3.45E + 001.17E-014.00E-016.82E-023.31E-018.92E-02
133.5 nm9.27E + 003.18E-015.60E-018.47E-028.79E-011.25E-01
134.5 nm4.10E + 001.39E-018.17E-011.18E-013.87E-011.82E-01
135.5 nm3.70E + 001.25E-012.30E-014.80E-023.50E-015.13E-02
136.5 nm4.21E + 001.43E-013.42E-015.87E-023.97E-017.62E-02
137.5 nm4.03E + 001.36E-013.31E-015.18E-023.76E-017.39E-02
138.5 nm3.69E + 001.24E-013.76E-015.75E-023.44E-018.39E-02
139.5 nm9.68E + 003.30E-016.36E-019.43E-029.14E-011.42E-01
140.5 nm7.10E + 002.44E-014.81E-017.29E-026.74E-011.07E-01
141.5 nm3.90E + 001.32E-012.89E-015.28E-023.65E-016.45E-02
142.5 nm3.45E + 001.17E-012.66E-015.03E-023.24E-015.94E-02
143.5 nm3.51E + 001.19E-012.06E-014.35E-023.29E-014.59E-02
144.5 nm3.40E + 001.16E-012.84E-014.78E-023.20E-016.33E-02
145.5 nm3.31E + 001.13E-013.25E-015.21E-023.09E-017.24E-02
146.5 nm3.12E + 001.08E-011.85E-013.15E-023.05E-014.13E-02
147.5 nm2.50E + 008.62E-021.84E-013.33E-022.42E-014.08E-02
148.5 nm2.58E + 008.80E-022.57E-013.53E-022.43E-015.73E-02
149.5 nm2.58E + 008.87E-021.77E-013.11E-022.48E-013.94E-02
150.5 nm2.47E + 008.47E-021.42E-013.13E-022.37E-013.16E-02
151.5 nm2.42E + 008.33E-023.54E-014.96E-022.33E-017.90E-02
152.5 nm3.15E + 001.08E-012.72E-014.42E-023.03E-016.06E-02
153.5 nm2.78E + 009.59E-022.62E-014.74E-022.71E-015.84E-02
154.5 nm4.70E + 001.61E-014.11E-016.55E-024.48E-019.18E-02
155.5 nm3.64E + 001.25E-012.70E-014.79E-023.44E-016.03E-02
156.5 nm2.48E + 008.50E-022.40E-014.53E-022.33E-015.35E-02
157.5 nm2.57E + 008.80E-022.54E-014.72E-022.40E-015.67E-02
158.5 nm2.48E + 008.50E-022.28E-014.38E-022.34E-015.10E-02
159.5 nm2.18E + 007.46E-022.29E-014.21E-022.05E-015.10E-02
160.5 nm2.51E + 008.59E-021.98E-014.19E-022.37E-014.42E-02
161.5 nm2.45E + 008.42E-021.86E-013.39E-022.34E-014.15E-02
162.5 nm2.42E + 008.33E-022.03E-013.88E-022.33E-014.52E-02
163.5 nm2.62E + 008.96E-022.16E-013.99E-022.50E-014.81E-02
164.5 nm2.56E + 008.76E-021.79E-013.21E-022.46E-014.00E-02
165.6 nm1.80E + 006.15E-022.05E-013.58E-021.71E-014.57E-02
166.5 nm1.15E + 003.89E-021.56E-013.02E-021.06E-013.48E-02
167.5 nm1.95E + 006.64E-021.81E-013.36E-021.83E-014.05E-02
168.5 nm9.84E-013.35E-021.60E-013.43E-029.04E-023.55E-02
169.5 nm1.08E + 003.67E-021.85E-013.66E-021.01E-014.12E-02
170.5 nm1.39E + 004.75E-022.00E-013.96E-021.32E-014.46E-02
171.5 nm1.87E + 006.41E-022.05E-014.01E-021.81E-014.58E-02
172.5 nm1.48E + 005.09E-021.84E-013.77E-021.44E-014.09E-02
173.5 nm1.08E + 003.71E-021.72E-013.78E-021.04E-013.82E-02
174.5 nm9.52E-013.27E-021.84E-013.78E-029.11E-024.10E-02
175.5 nm9.49E-013.24E-022.03E-014.09E-028.93E-024.53E-02
176.5 nm8.42E-012.87E-021.82E-013.87E-027.80E-024.07E-02
177.5 nm9.38E-013.20E-021.92E-014.28E-028.69E-024.27E-02
178.5 nm9.69E-013.30E-021.92E-014.29E-029.04E-024.28E-02
179.5 nm1.14E + 003.88E-022.17E-014.35E-021.06E-014.84E-02
180.5 nm1.91E + 006.51E-021.84E-013.74E-021.85E-014.11E-02
181.5 nm2.41E + 008.26E-022.36E-014.42E-022.35E-015.25E-02
182.5 nm1.65E + 005.59E-022.01E-014.07E-021.58E-014.48E-02
183.5 nm1.73E + 005.85E-021.81E-013.64E-021.65E-014.03E-02
184.5 nm1.59E + 005.37E-021.59E-013.64E-021.52E-013.53E-02
185.5 nm1.54E + 005.22E-021.74E-013.79E-021.48E-013.89E-02
186.5 nm1.62E + 005.48E-021.96E-014.04E-021.55E-014.38E-02
187.5 nm1.51E + 005.13E-021.81E-013.76E-021.45E-014.04E-02
188.5 nm1.51E + 005.10E-021.58E-013.45E-021.44E-013.53E-02
189.5 nm1.61E + 005.47E-021.36E-013.22E-021.54E-013.03E-02

Appendix B

[58] FISM solar cycle parameters, CSC, for each proxy and wavelength to be used in equation (2) are shown in Table B1. The grey boxes indicate the optimal proxy for each wavelength.

Table B1. FISM Solar Rotation Parameter (CSR) for Each Proxya
WavelengthMgII c/wF10.730.5 nm0–4 nmLyman Alpha36.5 nm
  • a

    Boldface indicates the optimal proxy for each wavelength.

0.5 nm3.19E + 028.53E + 002.06E + 011.31E + 002.49E + 014.77E + 00
1.5 nm2.72E + 027.32E + 001.77E + 011.12E + 002.15E + 014.10E + 00
2.5 nm2.32E + 026.28E + 001.50E + 019.46E-011.83E + 013.45E + 00
3.5 nm1.75E + 024.73E + 001.12E + 017.18E-011.37E + 012.58E + 00
4.5 nm1.55E + 024.19E + 001.00E + 016.29E-011.26E + 012.26E + 00
5.5 nm8.47E + 012.28E + 005.44E + 003.47E-016.71E + 001.24E + 00
6.5 nm9.07E + 012.44E + 005.78E + 003.71E-017.19E + 001.32E + 00
7.5 nm7.64E + 012.05E + 004.96E + 003.14E-016.07E + 001.13E + 00
8.5 nm7.69E + 012.07E + 004.99E + 003.15E-016.10E + 001.13E + 00
9.5 nm9.85E + 012.65E + 006.30E + 004.01E-017.83E + 001.44E + 00
10.5 nm9.85E + 012.65E + 006.30E + 004.01E-017.83E + 001.44E + 00
11.5 nm9.85E + 012.65E + 006.30E + 004.01E-017.83E + 001.44E + 00
12.5 nm9.85E + 012.65E + 006.30E + 004.01E-017.83E + 001.44E + 00
13.5 nm9.85E + 012.65E + 006.30E + 004.01E-017.83E + 001.44E + 00
14.5 nm4.14E + 011.13E + 002.69E + 001.75E-013.87E + 006.72E-01
15.5 nm2.71E + 027.45E + 001.75E + 011.19E + 002.59E + 014.43E + 00
16.5 nm5.26E + 011.43E + 003.37E + 002.23E-014.94E + 008.57E-01
17.5 nm6.07E + 011.65E + 003.86E + 002.60E-015.64E + 009.77E-01
18.5 nm1.19E + 023.25E + 007.66E + 005.16E-011.11E + 011.93E + 00
19.5 nm3.65E + 021.01E + 012.37E + 011.61E + 003.49E + 016.01E + 00
20.5 nm4.51E + 011.18E + 002.88E + 001.80E-014.25E + 006.95E-01
21.5 nm4.87E + 011.27E + 003.10E + 001.96E-014.59E + 007.51E-01
22.5 nm1.20E + 023.27E + 007.71E + 005.20E-011.12E + 011.94E + 00
23.5 nm9.34E + 012.57E + 006.02E + 004.07E-018.85E + 001.53E + 00
24.5 nm1.25E + 023.43E + 008.11E + 005.45E-011.18E + 012.04E + 00
25.5 nm1.69E + 024.62E + 001.10E + 017.40E-011.60E + 012.75E + 00
26.5 nm4.74E + 011.25E + 003.03E + 001.91E-014.47E + 007.30E-01
27.5 nm2.23E + 016.33E-011.48E + 001.28E-012.28E + 003.67E-01
28.5 nm1.09E + 023.10E + 007.16E + 006.12E-011.12E + 011.78E + 00
29.5 nm2.07E + 015.85E-011.35E + 001.09E-012.01E + 003.31E-01
30.5 nm1.50E + 014.24E-011.00E + 008.21E-021.49E + 002.42E-01
31.5 nm2.12E + 015.89E-011.38E + 001.12E-011.98E + 003.25E-01
32.5 nm2.30E + 016.40E-011.49E + 001.21E-012.15E + 003.46E-01
33.5 nm3.43E + 019.41E-012.23E + 001.76E-013.33E + 005.39E-01
34.5 nm2.86E + 017.81E-011.80E + 001.63E-012.83E + 004.26E-01
35.5 nm6.70E + 011.85E + 004.25E + 003.84E-016.56E + 001.02E + 00
36.5 nm6.63E + 011.82E + 004.20E + 003.65E-016.40E + 001.00E + 00
37.5 nm2.12E + 015.72E-011.34E + 001.08E-012.02E + 003.21E-01
38.5 nm2.33E + 016.22E-011.47E + 001.21E-012.26E + 003.57E-01
39.5 nm2.26E + 016.18E-011.44E + 001.20E-012.20E + 003.52E-01
40.5 nm1.80E + 014.94E-011.16E + 009.33E-021.79E + 002.79E-01
41.5 nm1.89E + 025.24E + 001.22E + 019.93E-011.83E + 012.99E + 00
42.5 nm2.11E + 015.88E-011.37E + 001.12E-012.11E + 003.38E-01
43.5 nm1.67E + 014.49E-011.09E + 008.75E-021.67E + 002.65E-01
44.5 nm2.76E + 017.65E-011.81E + 001.49E-012.72E + 004.34E-01
45.5 nm1.49E + 014.16E-011.01E + 007.80E-021.45E + 002.36E-01
46.5 nm1.17E + 013.14E-017.71E-016.03E-021.18E + 001.82E-01
47.5 nm1.47E + 014.04E-011.00E + 007.88E-021.47E + 002.36E-01
48.5 nm1.80E + 014.88E-011.21E + 009.40E-021.78E + 002.90E-01
49.5 nm6.83E + 011.85E + 004.48E + 003.55E-016.53E + 001.08E + 00
50.5 nm2.74E + 017.22E-011.76E + 001.39E-012.65E + 004.20E-01
51.5 nm3.78E + 011.05E + 002.54E + 002.06E-013.70E + 006.18E-01
52.5 nm9.90E + 012.68E + 006.30E + 004.83E-019.44E + 001.52E + 00
53.5 nm2.00E + 015.83E-011.43E + 001.13E-012.10E + 003.48E-01
54.5 nm1.90E + 015.36E-011.28E + 001.01E-011.89E + 003.06E-01
55.5 nm9.41E + 002.64E-016.27E-015.86E-029.75E-011.58E-01
56.5 nm2.13E + 015.94E-011.40E + 001.08E-012.06E + 003.33E-01
57.5 nm1.35E + 013.76E-019.12E-017.03E-021.34E + 002.20E-01
58.5 nm2.37E + 016.59E-011.60E + 001.46E-012.33E + 003.88E-01
59.5 nm1.56E + 014.44E-011.05E + 008.48E-021.60E + 002.62E-01
60.5 nm6.04E + 011.69E + 003.78E + 003.48E-016.30E + 009.51E-01
61.5 nm4.64E + 011.29E + 002.92E + 002.66E-014.77E + 007.13E-01
62.5 nm1.59E + 014.61E-011.11E + 001.05E-011.69E + 002.71E-01
63.5 nm1.49E + 014.26E-019.86E-019.36E-021.51E + 002.56E-01
64.5 nm1.24E + 013.41E-018.26E-016.48E-021.22E + 002.03E-01
65.6 nm1.31E + 013.66E-019.04E-016.81E-021.31E + 002.21E-01
66.5 nm1.40E + 013.84E-019.57E-017.04E-021.42E + 002.29E-01
67.5 nm1.58E + 014.26E-011.08E + 008.04E-021.59E + 002.63E-01
68.5 nm1.15E + 013.25E-017.90E-016.45E-021.19E + 001.95E-01
69.5 nm1.70E + 014.76E-011.17E + 009.32E-021.72E + 002.81E-01
70.5 nm8.61E + 002.51E-015.98E-015.42E-029.16E-011.50E-01
71.5 nm1.31E + 013.78E-019.08E-017.91E-021.37E + 002.30E-01
72.5 nm2.62E + 017.36E-011.75E + 001.36E-012.64E + 004.41E-01
73.5 nm1.15E + 013.27E-018.01E-016.44E-021.21E + 001.99E-01
74.5 nm1.13E + 013.16E-018.05E-016.31E-021.19E + 001.97E-01
75.5 nm8.90E + 002.59E-016.46E-015.26E-029.60E-011.59E-01
76.5 nm7.74E + 002.20E-015.35E-015.00E-027.97E-011.36E-01
77.5 nm1.35E + 013.74E-019.15E-017.17E-021.40E + 002.29E-01
78.5 nm1.03E + 012.88E-016.85E-017.93E-021.04E + 001.79E-01
79.5 nm9.86E + 002.82E-016.73E-016.01E-021.00E + 001.82E-01
80.5 nm1.38E + 013.83E-019.62E-017.67E-021.44E + 002.37E-01
81.5 nm1.12E + 013.11E-017.92E-016.47E-021.18E + 001.94E-01
82.5 nm1.35E + 013.80E-019.45E-017.55E-021.40E + 002.34E-01
83.5 nm1.23E + 013.48E-018.47E-018.48E-021.26E + 002.42E-01
84.5 nm1.46E + 014.05E-019.98E-019.34E-021.51E + 002.53E-01
85.5 nm1.83E + 015.09E-011.26E + 001.14E-011.87E + 003.18E-01
86.5 nm1.68E + 014.85E-011.14E + 001.10E-011.71E + 003.33E-01
87.5 nm1.83E + 015.00E-011.26E + 001.12E-011.85E + 003.11E-01
88.5 nm1.86E + 015.24E-011.26E + 001.15E-011.87E + 003.23E-01
89.5 nm1.80E + 015.06E-011.25E + 001.17E-011.83E + 003.72E-01
90.5 nm1.76E + 014.76E-011.18E + 001.10E-011.80E + 002.93E-01
91.5 nm1.72E + 014.73E-011.14E + 001.01E-011.70E + 002.94E-01
92.5 nm1.30E + 013.70E-019.20E-017.38E-021.37E + 002.32E-01
93.5 nm1.36E + 013.87E-019.59E-018.04E-021.43E + 002.40E-01
94.5 nm1.54E + 014.29E-011.05E + 009.20E-021.63E + 002.60E-01
95.5 nm1.38E + 013.93E-019.33E-017.62E-021.43E + 002.46E-01
96.5 nm1.30E + 013.65E-018.96E-017.32E-021.35E + 002.22E-01
97.5 nm1.45E + 014.06E-011.00E + 001.08E-011.50E + 002.55E-01
98.5 nm8.99E + 002.52E-016.30E-015.37E-029.43E-011.59E-01
99.5 nm1.24E + 013.39E-018.21E-016.75E-021.25E + 002.14E-01
100.5 nm1.63E + 014.52E-011.10E + 008.64E-021.69E + 002.68E-01
101.5 nm1.26E + 013.56E-018.37E-016.74E-021.29E + 002.30E-01
102.5 nm1.84E + 015.22E-011.26E + 001.18E-011.84E + 003.25E-01
103.5 nm1.63E + 014.59E-011.10E + 009.42E-021.61E + 002.91E-01
104.5 nm1.39E + 013.89E-019.51E-017.45E-021.40E + 002.46E-01
105.5 nm1.02E + 012.79E-016.97E-015.33E-021.07E + 001.69E-01
106.5 nm9.83E + 002.71E-016.68E-015.16E-021.03E + 001.61E-01
107.5 nm9.13E + 002.52E-016.21E-015.05E-029.64E-011.55E-01
108.5 nm1.41E + 013.82E-019.24E-017.29E-021.43E + 002.35E-01
109.5 nm9.54E + 002.69E-016.48E-015.17E-021.01E + 001.58E-01
110.5 nm1.01E + 012.77E-016.87E-015.49E-021.03E + 001.69E-01
111.5 nm1.01E + 012.82E-016.86E-015.35E-021.03E + 001.72E-01
112.5 nm9.18E + 002.52E-016.27E-014.85E-029.45E-011.57E-01
113.5 nm9.54E + 002.64E-016.46E-014.94E-029.68E-011.67E-01
114.5 nm5.83E + 001.90E-014.09E-017.50E-025.98E-011.23E-01
115.5 nm5.83E + 001.90E-014.09E-017.50E-025.98E-011.23E-01
116.5 nm5.83E + 001.90E-014.09E-017.50E-025.98E-011.23E-01
117.5 nm9.09E + 002.52E-016.12E-015.33E-029.41E-011.64E-01
118.5 nm5.83E + 001.90E-014.09E-017.50E-025.98E-011.23E-01
119.5 nm4.89E + 001.96E-015.05E-015.07E-027.27E-011.40E-01
120.5 nm7.81E + 003.21E-017.83E-016.32E-021.16E + 002.11E-01
121.5 nm7.07E + 003.12E-016.57E-015.84E-021.00E + 001.79E-01
122.5 nm4.90E + 002.01E-014.87E-014.79E-026.93E-011.35E-01
123.5 nm5.80E + 002.15E-016.25E-015.35E-028.34E-011.69E-01
124.5 nm5.99E + 002.22E-015.57E-015.15E-028.81E-011.50E-01
125.5 nm4.18E + 001.63E-014.80E-014.81E-026.31E-011.32E-01
126.5 nm6.22E + 002.49E-015.96E-015.36E-029.07E-011.60E-01
127.5 nm4.17E + 001.65E-015.00E-014.80E-026.25E-011.35E-01
128.5 nm4.20E + 001.61E-014.78E-014.60E-026.14E-011.30E-01
129.5 nm5.34E + 002.10E-016.21E-015.81E-027.51E-011.56E-01
130.5 nm4.96E + 002.00E-014.09E-013.83E-027.04E-011.09E-01
131.5 nm2.99E + 001.25E-014.09E-013.54E-024.52E-011.08E-01
132.5 nm3.48E + 001.47E-014.64E-014.48E-025.03E-011.21E-01
133.5 nm6.37E + 002.64E-016.54E-015.39E-029.18E-011.72E-01
134.5 nm3.46E + 001.49E-016.59E-017.24E-025.01E-011.62E-01
135.5 nm2.86E + 001.15E-012.75E-012.38E-024.04E-017.11E-02
136.5 nm3.31E + 001.37E-013.42E-012.95E-024.76E-019.23E-02
137.5 nm3.02E + 001.26E-013.11E-012.75E-024.36E-017.87E-02
138.5 nm2.83E + 001.23E-013.06E-013.15E-024.21E-018.08E-02
139.5 nm6.06E + 002.31E-015.86E-014.85E-028.66E-011.45E-01
140.5 nm4.71E + 001.83E-014.44E-013.69E-026.68E-011.10E-01
141.5 nm2.68E + 001.13E-012.80E-013.10E-023.92E-017.44E-02
142.5 nm2.41E + 001.05E-012.57E-012.47E-023.59E-016.40E-02
143.5 nm2.45E + 001.01E-012.69E-012.92E-023.60E-017.03E-02
144.5 nm2.53E + 001.08E-012.73E-012.73E-023.73E-017.16E-02
145.5 nm2.38E + 001.06E-012.83E-012.73E-023.59E-017.35E-02
146.5 nm2.41E + 001.02E-012.49E-012.61E-023.54E-016.48E-02
147.5 nm1.95E + 008.38E-022.35E-012.18E-022.84E-016.22E-02
148.5 nm2.01E + 008.74E-022.68E-012.93E-023.01E-016.88E-02
149.5 nm2.22E + 008.52E-022.34E-012.32E-023.23E-015.84E-02
150.5 nm2.13E + 008.20E-022.12E-011.94E-023.13E-015.39E-02
151.5 nm2.20E + 009.12E-022.51E-012.50E-023.14E-016.84E-02
152.5 nm2.71E + 001.12E-012.69E-012.37E-023.97E-016.92E-02
153.5 nm2.62E + 001.09E-012.59E-012.39E-023.71E-016.79E-02
154.5 nm3.49E + 001.35E-014.30E-014.69E-024.95E-011.12E-01
155.5 nm2.77E + 001.16E-012.67E-012.12E-024.09E-017.30E-02
156.5 nm2.31E + 008.79E-022.16E-011.85E-023.46E-015.76E-02
157.5 nm2.16E + 008.52E-022.14E-012.07E-023.17E-015.65E-02
158.5 nm2.06E + 008.50E-022.08E-012.09E-023.05E-015.61E-02
159.5 nm1.84E + 007.99E-022.12E-012.14E-022.67E-015.63E-02
160.5 nm2.04E + 008.59E-021.98E-012.44E-022.84E-015.41E-02
161.5 nm1.88E + 007.64E-021.91E-012.08E-022.76E-015.15E-02
162.5 nm1.91E + 007.65E-022.17E-012.19E-022.89E-015.90E-02
163.5 nm2.29E + 008.77E-022.27E-012.14E-023.31E-015.92E-02
164.5 nm2.35E + 009.28E-022.13E-011.89E-023.51E-015.74E-02
165.6 nm2.11E + 008.81E-022.25E-012.08E-023.09E-015.90E-02
166.5 nm1.67E + 007.28E-021.91E-011.81E-022.39E-015.16E-02
167.5 nm2.30E + 009.30E-022.20E-012.02E-023.40E-015.93E-02
168.5 nm1.55E + 006.24E-021.88E-011.97E-022.28E-014.78E-02
169.5 nm1.58E + 006.34E-021.92E-012.04E-022.35E-015.08E-02
170.5 nm1.69E + 006.87E-021.94E-012.31E-022.47E-015.23E-02
171.5 nm1.83E + 007.55E-021.92E-012.19E-022.74E-015.06E-02
172.5 nm1.77E + 007.09E-021.89E-012.18E-022.59E-015.08E-02
173.5 nm1.64E + 006.79E-021.84E-012.39E-022.48E-015.07E-02
174.5 nm1.66E + 006.74E-021.85E-012.48E-022.43E-015.06E-02
175.5 nm1.72E + 006.98E-021.88E-012.75E-022.57E-015.07E-02
176.5 nm1.60E + 006.45E-021.83E-012.36E-022.36E-014.82E-02
177.5 nm1.80E + 007.22E-021.96E-012.65E-022.69E-015.12E-02
178.5 nm1.74E + 006.95E-021.92E-013.03E-022.63E-015.10E-02
179.5 nm1.94E + 008.22E-021.93E-012.96E-022.70E-015.07E-02
180.5 nm2.18E + 009.31E-022.07E-012.34E-023.17E-015.49E-02
181.5 nm2.50E + 001.05E-012.27E-012.96E-023.71E-015.84E-02
182.5 nm1.95E + 008.43E-021.99E-013.59E-022.82E-015.05E-02
183.5 nm1.94E + 008.57E-021.79E-012.55E-022.81E-014.92E-02
184.5 nm1.69E + 007.26E-021.65E-012.41E-022.39E-014.59E-02
185.5 nm1.60E + 007.02E-021.78E-012.89E-022.27E-014.94E-02
186.5 nm1.75E + 007.60E-021.90E-013.42E-022.53E-015.18E-02
187.5 nm1.70E + 007.43E-021.84E-012.67E-022.47E-015.16E-02
188.5 nm1.73E + 007.60E-021.89E-012.85E-022.48E-015.17E-02
189.5 nm1.72E + 007.48E-021.86E-012.36E-022.48E-015.13E-02

Appendix C

[59] FISM solar rotation parameters, CSR, for each proxy and wavelength are shown in Table C1. The grey boxes indicate the optimal proxy for each wavelength.

Table C1. FISMref VUV Minimum Reference Spectruma
  • a

    Irrradiance is in units of W/m2/nm.

0.5 nm5.23E-0748.5 nm5.90E-0696.5 nm4.23E-06144.5 nm5.04E-05
1.5 nm1.20E-0549.5 nm3.64E-0697.5 nm7.48E-05145.5 nm5.44E-05
2.5 nm3.41E-0650.5 nm6.68E-0698.5 nm1.20E-05146.5 nm6.77E-05
3.5 nm4.78E-0651.5 nm2.38E-0699.5 nm1.20E-05147.5 nm8.56E-05
4.5 nm1.07E-0552.5 nm1.10E-06100.5 nm5.70E-06148.5 nm8.70E-05
5.5 nm2.93E-0553.5 nm2.66E-06101.5 nm7.01E-06149.5 nm7.83E-05
6.5 nm3.07E-0554.5 nm2.17E-06102.5 nm5.86E-05150.5 nm8.78E-05
7.5 nm3.03E-0555.5 nm1.37E-05103.5 nm4.76E-05151.5 nm9.48E-05
8.5 nm3.69E-0556.5 nm2.01E-06104.5 nm1.17E-05152.5 nm1.17E-04
9.5 nm2.77E-0557.5 nm3.95E-06105.5 nm9.52E-06153.5 nm1.31E-04
10.5 nm1.28E-0558.5 nm1.54E-05106.5 nm1.11E-05154.5 nm2.22E-04
11.5 nm4.15E-0659.5 nm3.19E-06107.5 nm1.33E-05155.5 nm1.89E-04
12.5 nm3.17E-0660.5 nm4.03E-06108.5 nm1.86E-05156.5 nm1.97E-04
13.5 nm1.78E-0661.5 nm2.76E-06109.5 nm1.47E-05157.5 nm1.78E-04
14.5 nm1.14E-0562.5 nm1.54E-05110.5 nm1.82E-05158.5 nm1.72E-04
15.5 nm2.03E-0663.5 nm1.12E-05111.5 nm1.58E-05159.5 nm1.73E-04
16.5 nm8.45E-0664.5 nm2.35E-06112.5 nm1.78E-05160.5 nm1.93E-04
17.5 nm5.02E-0565.6 nm1.95E-06113.5 nm1.36E-05161.5 nm2.27E-04
18.5 nm3.13E-0566.5 nm2.00E-06114.5 nm7.46E-06162.5 nm2.61E-04
19.5 nm9.18E-0667.5 nm1.76E-06115.5 nm1.23E-05163.5 nm2.84E-04
20.5 nm4.07E-0568.5 nm3.02E-06116.5 nm1.39E-05164.5 nm3.13E-04
21.5 nm3.74E-0569.5 nm2.22E-06117.5 nm4.75E-05165.6 nm5.00E-04
22.5 nm8.71E-0670.5 nm6.43E-06118.5 nm1.56E-05166.5 nm3.57E-04
23.5 nm7.58E-0671.5 nm2.13E-06119.5 nm4.61E-05167.5 nm4.12E-04
24.5 nm1.53E-0572.5 nm1.60E-06120.5 nm1.24E-04168.5 nm4.71E-04
25.5 nm1.37E-0573.5 nm2.09E-06121.5 nm6.10E-03169.5 nm6.15E-04
26.5 nm1.14E-0574.5 nm2.32E-06122.5 nm5.08E-05170.5 nm7.07E-04
27.5 nm6.09E-0575.5 nm3.74E-06123.5 nm3.54E-05171.5 nm7.00E-04
28.5 nm2.12E-0576.5 nm1.01E-05124.5 nm2.72E-05172.5 nm7.62E-04
29.5 nm4.97E-0577.5 nm6.20E-06125.5 nm2.62E-05173.5 nm7.72E-04
30.5 nm2.27E-0478.5 nm1.19E-05126.5 nm3.59E-05174.5 nm9.51E-04
31.5 nm3.62E-0579.5 nm8.37E-06127.5 nm2.06E-05175.5 nm1.17E-03
32.5 nm2.69E-0580.5 nm4.92E-06128.5 nm1.71E-05176.5 nm1.27E-03
33.5 nm5.20E-0581.5 nm7.14E-06129.5 nm1.90E-05177.5 nm1.53E-03
34.5 nm2.40E-0582.5 nm7.00E-06130.5 nm1.58E-04178.5 nm1.70E-03
35.5 nm1.10E-0583.5 nm1.94E-05131.5 nm2.68E-05179.5 nm1.65E-03
36.5 nm1.41E-0584.5 nm1.08E-05132.5 nm2.00E-05180.5 nm1.96E-03
37.5 nm8.04E-0685.5 nm1.00E-05133.5 nm1.67E-04181.5 nm2.32E-03
38.5 nm4.25E-0686.5 nm1.50E-05134.5 nm1.78E-05182.5 nm2.18E-03
39.5 nm3.15E-0687.5 nm1.45E-05135.5 nm4.09E-05183.5 nm2.33E-03
40.5 nm3.91E-0688.5 nm1.68E-05136.5 nm2.62E-05184.5 nm2.02E-03
41.5 nm7.67E-0789.5 nm2.66E-05137.5 nm2.82E-05185.5 nm2.31E-03
42.5 nm3.10E-0690.5 nm2.74E-05138.5 nm2.83E-05186.5 nm2.64E-03
43.5 nm5.93E-0691.5 nm2.14E-05139.5 nm7.11E-05187.5 nm3.07E-03
44.5 nm3.06E-0692.5 nm8.91E-06140.5 nm6.31E-05188.5 nm3.26E-03
45.5 nm3.65E-0693.5 nm8.20E-06141.5 nm4.06E-05189.5 nm3.66E-03
46.5 nm1.05E-0594.5 nm5.97E-06142.5 nm4.44E-05  
47.5 nm4.63E-0695.5 nm5.13E-06143.5 nm5.16E-05  


[60] This work has been supported by NASA grant NAG5-11408 (TIMED SEE) at the University of Colorado.