Correlations between Total and Spectral Solar Irradiance Variations

We compare short-term (seven solar rotations), wavelength-dependent temporal variations in spectral solar irradiance (SSI) with those from the total solar irradiance (TSI). Using space-based measurements, we empirically find good correlations across most of the visible and near-infrared (NIR) spectral range, suggesting that the TSI time variability can provide a useful estimate of SSI variability. These empirically determined correlations are consistent with physics-based bolometric variations, providing a straightforward wavelength-dependent parameterization of the SSI variability given a known change in the TSI. Using a solar-irradiance model to distinguish the facular and sunspot contributions, which are responsible for nearly all the irradiance variability on timescales longer than a day, we confirm these results and determine the correlation contributions due to each magnetic activity type individually. The correlations determined from the model agree in functional form to those of the empirical data, although we do note differences near opacity minimum (1.6 μm). Our results provide a simple TSI-based estimate of the time dependence of the spectral solar variability across the ultraviolet to NIR spectral regions, with the TSI accounting for 94% of the variability in the SSI over the 400–1200 nm range.


Introduction
The total solar irradiance (TSI) is the spatially and spectrally integrated radiant energy from the Sun incident on the Earth and normalized to one astronomical unit.The TSI provides nearly all the energy input to the Earth's climate system and is therefore important in Earth-climate studies (Lean 1997(Lean , 2010(Lean , 2017;;Lean et al. 2005;Lean & Rind 2008;Gray et al. 2010;Haigh 2011;Solanki et al. 2013;Jungclaus et al. 2017;Matthes et al. 2017;Allen et al. 2013) and energy-balance studies (Trenberth et al. 2009;Loeb et al. 2012;Stephens et al. 2012Stephens et al. , 2023)).Directly measured variations are ∼0.1% over the 11 yr solar cycle, up to 0.3% on solar-rotational (27 days) timescales, and 0.01% on 5-10 minute timescales (Kopp 2016).While seemingly small in a relative sense, these variations alone are greater than all other sources of energy input to the Earth's climate system combined (Kren et al. 2017).Because of the Earth-climate importance of this energy input, the TSI has been monitored from space continually since 1978.Solarirradiance models successfully reconstruct the measured totaland spectral-irradiance variations using image-based indicators of solar-surface magnetic activity (Krivova et al. 2003;Unruh et al. 2008;Ball et al. 2011;Coddington et al. 2016).
The spectral solar irradiance (SSI) provides the spatially integrated but spectrally resolved radiant energy from the Sun.Spectral resolution is necessary to understand the mechanisms whereby solar variability affects climate.These are primarily via absorption or scattering in the Earth's atmosphere (Gray et al. 2010;Haigh 2011;Allen et al. 2013;Jungclaus et al. 2017;Matthes et al. 2017).SSI measurements spanning the visible and near-infrared (NIR) spectral regions, which cover most of the solar radiant energy incident at the top of the Earth's atmosphere, require much more complex instrumentation than the TSI and are therefore not available with the same stability levels or temporal coverage.Thus, the ability to use the TSI as a simple proxy for SSI variability can extend the SSI record, provide validations of its long-and short-term accuracy, and suggest spectral regions of differences warranting further understanding of the causes of solar variability via models.
Since the primary causes of variability for TSI and SSI are common to both, being magnetic activity on the solar surface, the SSI and TSI are correlated across much of the spectrum.In this article, we report on those correlations, giving empirically determined correlation coefficient values and the wavelength sensitivity of relative changes in the SSI for a given TSI change.These correlations are useful for estimating SSI variability at times when only the TSI is available, for providing simple estimates of SSI variability (as desired by some solar-irradiance data users) instead of requiring the more complex SSI data sets, and for understanding the solar physics behind the causes of solar-irradiance variability.In Section 2, we describe the measurements used in this analysis.In Section 3, we compute and discuss the empirically determined spectrally dependent correlations between the TSI and SSI and show that these are consistent with a bolometric temperature change.Section 4 gives modeling-based background on the solar-atmospheric conditions responsible for the irradiance variability and compares the empirically determined correlations with expectations from a SATIRE-like solar-atmospheric model.Section 5 discusses the results of these SSI-to-TSI correlations, identifying the differing contributions from facular and sunspot components.
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Total Solar-irradiance Measurements
The TSI data used in the empirical SSI-to-TSI correlations reported here are from the Total Irradiance Monitor (TIM) instruments on the Solar Radiation and Climate Experiment (SORCE) mission (Rottman 2005) and the Total and Spectral Solar Irradiance Sensor (TSIS-1; Pilewskie et al. 2018).The TIM introduced several new design and measurement approaches, described by Kopp & Lawrence (2005), and provided a much-improved TSI measurement record, particularly regarding absolute accuracy (Kopp & Lean 2011) and intrinsic stability, as summarized by Kopp (2021).The data used are the daily values from the SORCE/TIM's final data version (V.19) and the TSIS-1/TIM's V.3 data.These span the time ranges 2003 February 25-2020 February 25 and 2018 January 11 to the present, respectively.The 17 yr of SORCE/ TIM data are shown in the top plot in Figure 1.

Spectral Solar-irradiance Measurements
The Spectral Irradiance Monitor (SIM), also flown on the SORCE spacecraft and the TSIS-1, provided the SSI measurements used in these analyses and covers the same time ranges as the TSI data.The SORCE/SIM, the first-of-its-kind instrument, is described by Harder et al. (2005) and the improved TSIS-1 version of the instrument by Richard et al. (2020).Both are nonimaging prism spectrometers that span the wavelength range from 240 to 2400 nm.The SORCE/SIM data used are the daily data from V.27, the instrument's final data version, with select bandpasses shown in the lower plots in Figure 1, and the TSIS-1/SIM data are V.9.The instrument spectral resolution varies from 0.25 nm in the ultraviolet (UV) to 33 nm in the NIR.
There are long-term drifts evident in the SIM data, which preclude correlations with the TSI on yearly or longer timescales.On shorter timescales, such as the 5 month period shown in Figure 2, the SSI shows similar variability to the TSI (Ball et al. 2011).There is some community uncertainty about whether the long-term variability in the SORCE/SIM data, as shown in Figure 1, is real (i.e., solar) or instrumental (Ball et al. 2016;Harder et al. 2021).
Because of the uncertainty in the long-term stability in the SIM measurements, those data are detrended.For the analyses presented here, the data are smoothed over seven solar rotations using a 131 days boxcar average applied three times, and then the residuals are analyzed.This smoothing behaves nearly like a 189 day (seven solar rotation) Gaussian filter without the indefinitely extended wings of a Gaussian.For consistency, the same high-pass detrending filter was applied to the TSI data prior to comparisons.This detrending is intended to remove long-term SIM instabilities while allowing the shorter-duration contributions from sunspots and faculae to the SSI and TSI to remain.(Dudok de Wit et al. 2018 found that most of the response to such solar-surface magnetic activity has decayed after seven rotations, which is why that detrending period was chosen.)

Measurement-based Correlations
The average SSI over the SORCE's 17 yr mission is plotted in Figure 3.The SSI is known to have relative variabilities that increase toward shorter wavelengths, and this is apparent in Figure 3.At longer (NIR) wavelengths, the solar variability is expected to continue to decrease.The higher variability shown Figure 2. SORCE short-term TSI and SSI.On short timescales, such as this at longer wavelengths, beginning with the abrupt increase at 1600 nm, is due to SORCE/SIM instrument artifacts associated with a detector change at that wavelength.Also shown is the variability in the detrended SIM data.This variability is the standard deviation of the SIM time-series data at each wavelength after the seven-solar-rotation detrending.It thus includes actual solar variability on these shorter timescales as well as instrument noise.The detrending removes lowfrequency variations due to actual solar variability and instrument artifacts, so they do not contribute to the plotted variability.
The detrended SSI variability shown in Figure 3 is fairly constant from 400 to 1600 nm, at approximately 0.027%.This level of variability is slightly higher than the 0.020% in the similarly detrended bolometric (TSI) variability across the same time range, with the greater SSI variability likely due to additional instrument-induced variability in those measurements.
Spectrally integrating the SSI data (prior to detrending, so as to maintain its absolute value) across the measured spectral range accounts for approximately 97% of the magnitude of the TSI, giving values near 1324 W m −2 instead of the full bolometric (TSI) 1361 W m −2 .Thus, high correlations and a nearly linear scaling relation are expected between the TSI and the spectrally integrated SSI due to solar variability.That comparison is shown in Figure 4 using detrended data.The correlation coefficient, R, of 0.50 indicates the accuracy of this linear-fit correlation.
Such comparisons at each wavelength across the SIM spectral range provide correlations of SSI to TSI as a function of wavelength.Figure 5 shows examples of the comparisons at several representative wavelengths.These correlations are high across the visible and into the NIR.At UV wavelengths, the correlations are lower because sunspots, which cause shortterm decreases in the TSI that dominate facular brightenings at longer wavelengths, are dominated by facular brightenings in the UV, and the SSI is therefore largely unaffected by them.At wavelengths longer than 1600 nm, where the SIM has a detector change and is less stable, the correlations, while expected to be very good from a solar-physics perspective, are poor due to that instrument artifact.
Despite the worsened correlations at UV and > 1600 nm wavelengths, across most of the spectral range, the detrended SSI and the TSI show good correlations.The correlation coefficients from unweighted linear fits between the two are shown as a function of wavelength in Figure 6.This figure indicates that between 400 and 1600 nm, most of the measured short-term SSI variability is well correlated with TSI variability.The relative sensitivities ΔSSI/ΔTSI of the two are indicated by the red curve in Figure 6.At the shortest visible wavelengths, relative SSI variations are approximately twice the relative variability of the TSI.This ratio drops to a one-to-one correlation at 650 nm then continues to monotonically decrease with wavelength such that, approaching 1600 nm, the SSI varies by only half of the TSI in a relative sense.The average correlation coefficient across the 400 to 1200 nm spectral range is 0.80.(The decrease in correlation near 950 nm is due to another detector change in the SIM, although this one is not as pronounced as that at 1600 nm.) Below 400 nm, the correlations markedly decrease on these detrendeddata solar-rotational timescales.Many authors have explored the causes of the UV variability (see Morrill et al. 2001;Shapiro et al. 2016;Berrilli et al. 2020;Lean et al. 2020), explaining the transition from the spot-to the facular-dominated regime occurring in the CN violet system, which amplifies the facular contrast below 400 nm.
Results from the TSIS-1, using TSI and SSI data from that sensor's TIM and SIM, are similar, as shown in Figure 7.This indicates that the SSI-to-TSI variability sensitivity relationship determined is independent of an individual instrument or time range.For this instrument, which suffers from a more pronounced effect at wavelengths immediately below the 900 nm detector change, the correlation coefficient averages 0.68 across the 400 to 1200 nm spectral range.These data do not show the decrease in sensitivity below 400 nm that the  The correlations shown in Figures 6 and 7 indicate that the SSI variability can be well represented using measured TSI variations across the visible and much of the NIR spectral ranges.These correlations are not expected to continue into the UV because of the known higher SSI sensitivity to faculae versus spots at those wavelengths.However, at longer wavelengths, where the correlations shown in Figures 6 and  7 are affected by SIM instrument artifacts, the actual solar-caused correlations are expected to continue smoothly.This is confirmed by the solar-irradiance model presented in Section 4 and the bolometric model comparison in Section 3.3.

Fitted SSI-to-TSI Sensitivity
The empirical SSI variability can be well predicted as a function of wavelength based simply on observed TSI variability, at least across the spectral ranges showing high correlations in Figures 6 and 7, and likely at longer wavelengths, since the low correlations above 1600 nm are due to instrument noise rather than true-solar effects.A weighted geometric fit of the form a a a 0 2 1 l + matches the empirical SSI-to-TSI sensitivity data well for the coefficients given in Table 1 (for wavelength λ in nanometers).These fits to the empirical data allow an estimation of the SSI variability purely from a simple TSI time series for all wavelengths longward of 400 nm.

Bolometric Estimates of SSI-to-TSI Sensitivity
The geometric fits in Table 1 are purely empirical with no physical basis.A more physics-based estimate of the SSI-to-TSI variability sensitivity is nearly as good as these fits and provides a more direct and instrument-independent estimate of the wavelength dependence of the SSI sensitivity to TSI variability.A surprising result from this study is that a small-temperature deviation from the Sun's nominal bolometric temperature matches the empirical SSI-to-TSI sensitivities in Figures 6 and 7.
An idealized solar disk of unity area at blackbody temperature T 0 (nominally 5772 K, per Mamajek et al. 2015 andPrša et al. 2016) emits total and spectral irradiances that vary as where h is the Planck constant, k B the Boltzmann constant, σ is the Stefan-Boltzmann constant, and c is the speed of light.If some portion, a, of the solar disk is an active region at temperature T + ΔT (where ΔT and a can be large or small), This is the physics-based bolometric sensitivity of the SSI-to-TSI variability.Note that variations of both the spectral and total irradiances scale with the areal coverage, so the relative SSI-to-TSI-variability sensitivity is purely a function of the temperatures T 0 and ΔT and is independent of the size of the active region.
From Equation (1), the TSI variability due to a small bolometric solar-temperature change (i.e., 1 and the relative SSI variability The small-temperature bolometric sensitivity of Equation ( 7) is shown by the gray curves in Figures 6 and 7 and agrees well with the empirically determined sensitivities.Note that since hc/(k B T 0 ) = 2.493 μm, the curve varies as ∼1/(4λ) in the UV, visible, and NIR.One of our primary findings from this study is thus that the empirically determined sensitivity of SSI-to-TSI variability very closely matches the bolometric sensitivity for both the detrended SORCE and TSIS-1 data.
This result is surprising, however, in that the Sun's temperature is not changing uniformly or by small amounts due to activity.Sunspots, which are responsible for the majority of short-term irradiance decreases, have temperatures ∼1000 K lower than the quiet-Sun temperature, T 0 , while the spectral dependence of faculae, having much smaller temperature changes, is more sophisticated and cannot be described by either a Planck function or 1D radiative-equilibrium models of a hotter atmosphere (Witzke et al. 2022).The expected wavelength-dependent SSI-to-TSI variability should be a linear combination of the blackbody radiation from each magnetic activity type at its corresponding temperature, but with these large, unequal, nonoffsetting, and temporally different temperature deviations, the individual-region variabilities should differ from the gray curves in Figures 6 and 7.
We thus do not currently have a satisfactory rationale for the close match between the empirically determined SSI-to-TSI variability and the simplistic bolometric sensitivity shown in Figures 6 and 7, when this is instead expected to be caused by a sophisticated dependence of the spot and facular spectral contrasts with wavelength.To further our understanding, we consider the contributions from each magnetic activity type independently via a solar-irradiance model.Correlation coefficients are plotted in green, indicating the degree of linearity in the scatter plots from which the sensitivities are determined, and corresponding sensitivity uncertainties are in blue.Across most of the visible and NIR spectral regions, the correlations are high and the sensitivity of the SSI to a relative change in TSI decreases smoothly from ∼2× at the shorter wavelengths to ∼0.6× at 1600 nm.SIM instrument noise affects the longer SSI measurements, while the lower correlations at UV wavelengths are likely due to solarvariability independence between the SSI and TSI.A geometric fit is plotted in gray and a bolometric-sensitivity model in black (dashed).

Time Ranges of Applicability
The geometric or bolometric fits are derived from data on timescales less than seven solar rotations and greater than 1 day, so can be applied to variability in those ranges.The SSIto-TSI agreement will have the plotted correlation coefficients, indicating agreement to that level.
The results may be limited outside of this time range.The correlations may still hold, but that cannot be ascertained from current measurements.On shorter timescales, no high-cadence (minute or hourly) SSI data are available for great lengths of time.On timescales greater than seven solar rotations, the SIM lacks the stability at some wavelengths to give reliable measurements of true-solar variability, which is why the data are detrended to that timescale.The Sun should behave similarly at longer timescales, suggesting that these results would hold, but that claim cannot be justified based on extant data.
Performing similar analyses in spectral windows where measurements are deemed more reliable may be possible by detrending using timescales that vary with wavelength.While such analyses might improve the time range of applicability for specific spectral regions, the sensitivity and correlation plots would vary with both wavelength and time range, and so would make general application difficult.

SATIRE-based Solar-irradiance Model
The semi-empirical Spectral and Total Irradiance Reconstructions (SATIRE) model (Krivova et al. 2003;Wenzler et al. 2005;Ball et al. 2011) uses sunspot and facular-region areal sizes and positions to estimate total and spectral solar irradiance.To create a solar-irradiance model having longer temporal overlap with the SORCE and TSIS-1 missions for the comparisons presented here, we followed the SATIRE reconstruction methodology of Yeo et al. (2014) using images from the Helioseismic and Magnetic Imager (HMI; Scherrer et al. 2012) to provide the regions of solar activity, thus producing model data from 2010 May to 2021 January.The only semi-free parameter in the model, the facular saturation threshold, B sat , was tuned to a value of 305 G by minimizing the correlation coefficient and slope of the regression of the observed and modeled TSI variability.The solar-irradiance reconstruction was calculated on a 1 hr cadence between HMI images, then daily averages of the model were compared to the daily-averaged TSI observations (see Figure 8).

Causes of Solar-irradiance Variability
Magnetic activity on the solar surface accounts for nearly all solar-irradiance variations on timescales longer than a few hours, with faculae and sunspots being the dominant components determining the variability (Ermolli et al. 2013;Solanki et al. 2013;Yeo et al. 2017;Kopp & Shapiro 2021).Shapiro et al. (2017) break down the contributions from each of these components over different time ranges as follows: Spots and faculae contribute almost equally on timescales of a few days, at the 27 days solar-rotational period, and from about 100 days to 1 yr; at intermediate timescales, spots dominate the variability; and on timescales longer than a year and up to a few 11 yr solar cycles, faculae provide the dominant contribution.The balance between faculae and spots on timescales where they contribute nearly equally depends on magnetic activity levels and spectral passbands (Nèmec et al. 2020).
For the empirical SSI-to-TSI variability sensitivity studies using detrended data analyzed here, the relevant timescales are from 1 day to seven solar rotations, over which range the TSI is generally either spot dominated or equally faculae and spot dominated (Shapiro et al. 2017).The solar-irradiance model helps discriminate between the contributions of each activity type to the sensitivities determined as a function of wavelength.

Modeled Correlations between the TSI and SSI
During the time range in which they overlap, the SSI-to-TSI variability sensitivities from SORCE and the model are plotted in Figure 10(a).The model's sensitivities are smoother with wavelength than those from the empirical determination since the model is not affected by instrument artifacts.For the same reasons, the correlation coefficients are also higher for the model in Figure 10(b).Over the spectral range 400-1200 nm, the average correlation coefficient R is 0.968, indicating the TSI variability can account for 94% of the SSI variations at these wavelengths.At longer wavelengths, the correlations decrease to a minimum of 0.4 just longward of 1600 nm.For the comparisons between the SATIRE model and the instrument data, the model is smoothed to the spectral resolution of the instrument via a Gaussian with a FWHM matching the instrument at each wavelength (Figure 9 shows the TSIS-1/SIM spectral resolution, which varies from 0.28 to 35.5 nm).
Weighting the atmospheric-model spectra from sunspots and faculae by their areal sizes and positions on the solar disk, the SATIRE reconstruction method directly provides the individual wavelength-dependent sensitivities to each magnetic activity type.This enables a determination of the separate contributions to the correlation coefficient and sensitivity of SSI-to-TSI variability from each component, as shown in Figures 10(c) and (d).

Functional Form of Wavelength Dependence of SSI-to-TSI Variability
The major findings of this paper involve the functional form of the wavelength dependence of the SSI-to-TSI variability and are summarized here.Longward of 400 nm, the sensitivity of SSI-to-TSI variability shows a monotonic decrease to at least 1600 nm (see Figure 10(a)) in all three of the empirically determined, bolometrically modeled, and semi-empirical model-based sensitivities.At the shortest wavelengths (near 400 nm), the SSI varies about twice as much as the TSI for short-term (less than seven solar rotations) variations.At 1600 nm, this value is approximately one-half for the SSI variability relative to that of the TSI.The correlation coefficients are high throughout the spectral region 400 to 1200 nm, indicating a robust SSI-to-TSI variability relationship.At wavelengths near and slightly longer than 1600 nm, where the empirical data do not provide a credible relationship, the modeled correlation coefficients reach a minimum of 0.4 Figure 9.The TSIS-1/SIM spectral resolution varies from a minimum of 0.28 nm at 200 nm to 35.5 nm at 1232 nm then decreases at longer wavelengths.
Figure 10.Modeled SSI-to-TSI sensitivities per activity type.The wavelength dependence of the sensitivity of SSI-to-TSI variability from the model is very similar to that of the empirical correlations from SORCE (a) (upper left).The correlation coefficients from the model are higher than those from the data but have similar shape (b) (upper right).This is likely due to noise in the measurements, with known instrument artifacts causing lower correlation at select spectral regions, such as those beginning at 1600 nm and near 900 nm, where the model gives both higher and smoother correlations.The sensitivities and correlation coefficients attributable to activity type (sunspots or faculae) additively give the net values (c) and (d) (lower plots).Comparisons to the TSIS-1 data are similar.
before slowly increasing at longer wavelengths.This nonmonotonic behavior of correlation coefficients in the model with its minimum at 1600 nm is likely simply due to the spectral dependence of the atmospheric altitude that is effectively observed near opacity minimum, which is reached at this wavelength.This is further discussed in Section 5.3, where we consider the independent contributions from faculae and sunspots.

Model Consistency with Empirical Sensitivities
The empirical, bolometric, and solar-model sensitivities and correlations shown in Figures 6, 7, and 10 agree well in functional form up to at least 1200 nm.We find two issues in these results and comparisons: 1.At wavelengths longer than 1200 nm, the model-determined sensitivities decrease faster than the empirical data or the bolometric model.The SATIRE model itself was validated on spectral data primarily from wavelengths below 1 μm (Krivova et al. 2003;Wenzler et al. 2005), so this difference may indicate refinements are needed in the modeling of sunspots, which are poorly represented by 1D representations used in solar-irradiance models, or, possibly, of faculae in the NIR, where various contrasts have been reported (Foukal et al. 1990;Foukal & Moran 1994;Sánchez Cuberes et al. 2002).Being the first such study of these sensitivities, the differences between the modeled and empirical SSI-to-TSI variability in the 1200 to 1600 nm range are another key finding of this paper.Differences at wavelengths longer than 1600 nm are less constrained by the measurements, as the instrument data have higher noise above this wavelength.2. The agreement of the bolometric model to the empirically determined SSI-to-TSI sensitivity is surprisingly good yet physically unrealistic, as the model assumes small thermal deviations from the quiet-Sun temperature, whereas active regions-particularly sunspots-responsible for much of the irradiance variability have much larger localized temperature changes, as mentioned in Section 3.3.
From the modeling side, there is reason to suspect solarirradiance reconstructions may need refining to better account for the observed deviations in sensitivities in the infrared (IR), particularly since, at the time these models were created, regular spectral-irradiance data were unavailable to guide model formulation at these wavelengths.A potential reason for the observed deviation in sensitivities in the IR might be the models' treatments of spot contributions to solar variability.In SATIRE (as well as in most other available models), spot umbra and penumbra are represented by 1D radiativeconvective models of a quiet star having a lower temperature than that of the quiet Sun; that is, spots are treated as cooler, nonmagnetic atmospheres (see Ermolli et al. 2013 for review).This approach allows very precise modeling of the TSI variability as well as the variability of the Sun in the UV and visible domains (see Solanki et al. 2013 and references therein).However, the photons around 1.6 μm come from the deepest layers of the solar atmosphere, where the effects of convection and overshoot, which are not well represented in 1D models, have significant effects.Three-dimensional radiative MHD simulations may offer improvements, as these better describe the transfer of energy in the solar atmosphere without relying on ad hoc parameterizations.In particular, they account for partial ionization, which is crucial for calculating transfer of convective energy in the upper convective zone.They also account for the transfer of radiative energy, which becomes the dominant energy-transport mechanism in the photosphere.The first 3D MHD simulations of sunspots (Rempel et al. 2009) have been followed by recent starspot simulations (Panja et al. 2020) performed with the MURaM code (Vögler et al. 2005).The implementation of such improved, 3D MHD sunspot representations in irradiance models may indicate whether the deviation in the IR sensitivity we report here could be explained by the limitations of 1D spot modeling.(We note there are complementary modeling efforts from stellar-atmosphere models to assess starspot contributions to IR variability in stars, which is important for mitigating contamination of the IR transmission spectra obtained by the JWST in characterizations of exoplanet atmospheres; see Rackham et al. 2023 for review.)

Facular and Sunspot Contributions to Sensitivity Are Additive
The solar-irradiance model used here enables assessments of the contributions to the SSI-to-TSI variability sensitivities independently for sunspots and faculae.These are plotted in Figures 10(c) and (d).The sensitivity contributions from sunspots are always greater than those due to faculae in the visible and NIR.Sensitivities from both activity types decrease monotonically from ∼500 nm to 1600 nm, where faculae provide no modeled contribution to SSI and the only SSI sensitivity to TSI variability comes from sunspots, despite sunspots' decreasing contrast with wavelength.The correlation coefficients from the sunspot component remain relatively high and constant with wavelength; it is only the sensitivities that decrease.
It is profound that the contributions from each component (faculae and sunspots) for both sensitivity and correlation additively give almost the net values.This is an initially surprising finding, since the two components cause opposing behaviors of the solar irradiance, with sunspots causing a decrease in irradiance and faculae an increase.Since the two are both associated with magnetically active surface features on the Sun, they could be expected to give countering effects on irradiance, as explained in power-spectra plots by Shapiro et al. (2017).The reason that they nevertheless additively give the net sensitivity here is likely due to their temporal signatures, with sunspots being of much shorter duration than the corresponding region's faculae, such that the opposing influences do not persist.The opposing effects are thus short-lived and the longer-lasting effects, correlated with both activity types, give positive overall contributions to the irradiance.
Note that near 1600 nm (opacity minimum), the correlation coefficients are negative for the facular contributions (see Figure 10(d)) and the modeled SSI shows very little variability (see Figure 10(c)).At these wavelengths, faculae cause slight decreases in modeled irradiance rather than the increases typical over the remainder of the spectrum.This is consistent with prior, image-based reports (Foukal et al. 1990).

Relations Hold across All Yearly Time Ranges through Solar Cycle
We consider the activity-level dependence of the relationships given in Figure 10, which are determined using the entire available set of overlapping instrument and model values, by analyzing each year during Solar Cycle 24 separately.We do this for both the model (Figure 11) and the observations (Figure 12).
The functional form of the correlation coefficients and sensitivities of SSI-to-TSI variability are similar for all time regions in both the modeled and measured results.demonstrating the additive nature of the individual components and reinforcing the robustness of the SSI-to-TSI variability relationship determined in this study.

Summary
We present a robust wavelength-dependent relationship giving the relative SSI variability corresponding to a given change in the TSI across the UV to NIR spectral region.This relationship is consistent between empirical comparisons, a physics-based bolometric parameterization, and the semi-empirical SATIRE-like solar-irradiance model formulated for this comparison.Such TSIto-SSI correlations have uses at times when SSI measurements are not available or for the simplicity of estimating the SSI at any wavelength from a TSI time series, as can be done directly using Equation (7), with expectations that the TSI can account for 94% of the SSI variability across the 400-1200 nm spectral range.The relative SSI variability decreases with wavelength from being twice that of the relative TSI variability at 400 nm to half that of the TSI variability at 1600 nm.The empirical correlations, determined independently using both the SORCE and TSIS-1 sensors, are high across this spectral region.The model shows a more pronounced decrease in sensitivity with wavelength from 1200 to 1600 nm that is not understood and may indicate refinements needed to the model.This semi-empirical irradiance model enables the separation of the individual contributions from sunspot and facular components, with most of the wavelength dependence being due to sunspots.We confirm that faculae exert a negative contribution to modeled irradiance near opacity minimum at 1600 nm.The contributions of each component additively give the net SSI-to-TSI variability sensitivities and correlation coefficients despite their short-term opposing effects on solar irradiance.This is likely due to the different time regimes over which each contributes, as, instantaneously, they cause opposing effects.We find the presented SSI-to-TSI sensitivity relationship to be independent of the solar activity level through a solar cycle.

Figure 1 .
Figure 1.SORCE mission TSI and SSI.The SORCE measurement records span 17 yr, recording two solar minima and periods of high solar activity near the Solar Cycle 24 maximum.The TSI is plotted in the upper graph (black) while the lower plots show 100 nm binned spectral irradiances at different center wavelengths.The long-term variations in the SSI measurements are likely due to uncorrected SIM instrument effects.Those data are detrended for the analyses in this paper.(The data plotted here have not been detrended.)

Figure 3 .
Figure3.SORCE SSI and SSI variability.The 17 yr averaged SSI measured by the SORCE/SIM (red) is compared to a solar-surface-temperature blackbody (dashed black).The variability, given by the standard deviation of the detrended SSI over the 17 yr time range, is shown at two magnifications (blue and light blue).This variability includes both instrument-caused and truesolar variations, with the former being the likely cause of the long-wavelength variability increases and the latter those at the UV end of the spectral range.The dashed green line shows the bolometric (TSI) variability after a similar detrending.

Figure 4 .
Figure 4. SORCE integrated SSI vs. TSI scatterplot.Spectrally integrated SIM SSI measurements account for 97% of the TSI.This scatter plot of the variability of both over the SORCE's 17 yr data record is therefore expected to show high correlation.An ideal unity correlation is shown in blue.Detrended data are used (although the mean values of the nondetrended data are maintained to give absolute irradiances in watt per square meter on the bottom and left axes).

Figure 5 .
Figure 5. SORCE SSI vs. TSI scatterplots.Scatterplots between the SSI and TSI are shown (red) at seven wavelengths from the UV to the NIR along with computed linear fits of the relative change in the SSI per change in the TSI (green).In the visible and NIR, the SSI and TSI are well correlated.At all wavelengths, differences can be due to either true-solar independence of the SSI and TSI or to instrument effects.The latter are more likely the cause of the lack of correlations at wavelengths greater than 1600 nm, where the SIM has a change in detector used.SORCE data are shown in these plots; TSIS-1 results are similar.

Figure 6 .
Figure 6.SSI-to-TSI sensitivity: SORCE.The relative SSI-to-TSI variation is plotted as a function of wavelength (red) for the detrended SORCE data.Correlation coefficients are plotted in green, indicating the degree of linearity in the scatter plots from which the sensitivities are determined, and corresponding sensitivity uncertainties are in blue.Across most of the visible and NIR spectral regions, the correlations are high and the sensitivity of the SSI to a relative change in TSI decreases smoothly from ∼2× at the shorter wavelengths to ∼0.6× at 1600 nm.SIM instrument noise affects the longer SSI measurements, while the lower correlations at UV wavelengths are likely due to solarvariability independence between the SSI and TSI.A geometric fit is plotted in gray and a bolometric-sensitivity model in black (dashed).

Figure 7 .
Figure 7. SSI-to-TSI sensitivity: TSIS-1.The TSIS-1 SSI-to-TSI sensitivity results are similar to those of the SORCE in Figure 6.The plots use the same colors for each curve.

Figure 8 .
Figure 8. TSI model vs. data.The HMI-based SATIRE-like solar-irradiance TSI model shows similar variability to the SORCE and TSIS-1 TSI data across the time range over which the model was computed.
The measured results show consistent sensitivities and high correlation coefficients for active years of the solar cycle (2012 through 2017).The modeled amplitudes show a similar dependence on activity level.For the modeled results, the year 2018, when very few sunspots existed, nicely shows the actual contributions from faculae alone.These give a negative correlation near opacity minimum (Figures 11(b) and (c)), as mentioned in Section 5.3 for the facular component individually.The overall sensitivity of the SSI-to-TSI variability (Figures 11(e ) and 12) is relatively unchanged regardless of the activity level for each year of this solar cycle for which there is sufficient activity to give high correlations, again

Figure 11 .
Figure 11.Modeled sensitivities and correlations by year.One year segments of the detrended TSI data (top plot) are analyzed individually for correlation coefficients (middle row) and sensitivity of the SSI-to-TSI variability (bottom row) for the SATIRE-based model.

Figure 12 .
Figure 12.Measured sensitivities and correlations by year.The SORCE-measured irradiances are similarly analyzed in 1 yr segments, showing similar sensitivities (left-hand plot; compare to Figure 11(e)) and correlations (right-hand plot; compare to Figure 11(b)) as over the entire record (compare to Figure 6) for years other than those near solar minimum (namely, years 2010, 2011, 2018, and 2019).Instrument noise dominates above 1600 nm.