Last modified on Mar 21, 2024 12:11

Contributors: N. Clerbaux (Royal Meteorological Institute of Belgium (RMIB)), A. Velazquez Blazquez (Royal Meteorological Institute of Belgium (RMIB))

Issued by: RMIB/Clerbaux

Date: 28/11/2023

Ref: C3S2_D312a_Lot1.2.2.5-v1.0_202303_ATBD_ECVEarthRadiationBudget_v1.1

Official reference number service contract: C3S_D312b_Lot1.1.5.1-v2.0_202003_ATBD_ECVEarthRadiationBudget_v1.1

History of modifications

List of datasets covered by this document

Related documents

Acronyms

List of tables

List of figures

General definitions

Scope of the document

This document is the Algorithm Theoretical Basis Document (ATBD) for the generation of the version 3 of the Climate Data record (CDR) and Interim Climate Data Record (ICDR) v3.1 of daily Total Solar Irradiance (TSI) for the Copernicus Climate Change Service (C3S). 

The aim of this ATBD is to provide a full description of the algorithms used to generate the CDR of daily TSI products, including the scientific justification for the algorithms selected to derive the product, an outline of the proposed approach and a listing of the assumptions and limitations of the algorithm. 

Executive summary

The Total Solar Irradiance (TSI) quantifies the amount of solar energy that is received by the Earth. It is defined as the amount of solar power that reaches the Earth’s top of the atmosphere per unit surface perpendicular to the Sun–Earth direction at the mean Sun–Earth distance. It is the most fundamental variable governing the climate system on Earth, and is recognized as an Essential Climate Variable (ECV) by the Global Climate Observing System (GCOS). Within the Copernicus Climate Change Service (C3S), a long composite Climate Data Record (CDR) is constructed from timeseries of daily TSI measured by an ensemble of space instruments. Currently 12 instruments are used in the composite. 

The method can be summarized as follows:

•    First, the 12 individual timeseries are quality checked by comparison with 2 models of the daily TSI (namely SATIRE-S and NRLTSI2 models). 

•    Second, the measurements of the individual instruments are put on a common absolute scale using optimized radiometric correction factors.

•    Lastly, the composite is created as an average of the available measurements, on a daily basis. 

The method is an adaptation of (Dewitte and Nevens, 2016) [ D1 ]. This ATBD fully describes and justifies the successive steps implemented in the data processing. 

The document is presented as follows. Section 1 introduces the measurement principles and the main satellite missions that have been collecting TSI observations. Section 2 contains a detailed description of each of the 12 instruments’ records used to create the composite product. This section also presents important ancillary data such as the models and composites used for evaluation. Section 3 fully describes the algorithm used to create the composite. Finally, Section 4 briefly describes the output format for the TSI composite.

1. Introduction

The first Total Solar Irradiance (TSI) measurements from space were made with the Temperature Control Flux Monitor (TCFM) instrument on Mariner 6 and 7 (Plamondon, 1969). Continuous measurement of the TSI started with the Earth Radiation Budget (ERB) instrument on Nimbus 7 (Hickey et al., 1980). Continuous monitoring with an ageing corrected TSI instrument started with the Active Cavity Radiometer Irradiance Monitor (ACRIM1) instrument on the Solar Maximum Mission (SMM) (Willson et al., 1980).  Since these early missions, TSI measurements have been continued with several space instruments listed in Table 1. 

The instruments used for the TSI measurement are electrical substitution cavity radiometers. Their core detector consists of a blackened cavity in which nearly all incident radiation flowing through a precision aperture is absorbed. The thermal effect of the absorbed optical power is measured by comparison with the thermal effect of known electrical power. When operated in space, any TSI radiometer ages by exposure to solar UV radiation. For ageing correction, a backup radiometer is usually used, for which the UV exposure is kept low such that its ageing is negligible.

As the Sun is nearly a point source, TSI radiometers use a view-limiting mechanism to eliminate the entrance of all except direct solar radiation into the cavity. Early TSI radiometers place a large view-limiting aperture in front of a small precision aperture. In this geometry, scattering and diffraction around the edges of the view-limiting aperture increase the amount of solar power flowing through the second precision aperture. When this effect is not estimated or underestimated, it may lead to an overestimation of the TSI value as in the Earth Radiation Budget Experiment (ERBE) or in the Differential Absolute RADiometer (DIARAD). 

New instruments, like the Total Irradiance Monitoring (TIM) radiometers, use an alternative geometry where the small precision aperture is put in front of the larger view-limiting aperture. In this geometry, scattering and diffraction around the edges of the precision aperture decrease the amount of solar power flowing through the view limiting aperture. When this effect is underestimated it may lead to an underestimation of the TSI. 

Relative variations of the TSI in phase with the 11-year solar cycle of the order of 1 W/m² are now well established, as summarized by Dewitte & Nevens (2016) [D1] and Dewitte & Clerbaux (2017) [D2]. Apart from these true TSI variations, differences in the absolute level well above 1 W/m² are observed between the different instruments indicating limitations of the absolute accuracy. For this reason, multiplicative correction factors are determined to scale all the timeseries to a same radiometric level. These factors are determined by optimizing the consistency over the overlap periods that exist between the different instruments. Still, a reference level must be defined and this is done in this work in such a way that the average of the correction factors for the 5 most accurately calibrated instruments is set to 1.0. These 5 instruments are: Physikalisches und Meteorologisches Observatorium 06 (PMO06), Precision Monitor Sensor (PREMOS), and the TIM instruments on the Solar Radiation and Climate Experiment (TIM/SORCE), on the Total solar irradiance Calibration Transfer Experiment  (TIM/TCTE), and on the International Space Station (TIM/TSIS1).

Table 1: Total Solar Irradiance space instruments (acronyms definitions in footnote). The instruments used in the C3S v3.0 and v3.1 daily TSI composite are highlighted in bold.

2. Input and auxiliary data

This section describes the various daily TSI records used as input to create the C3S composite. In subsection 2.1, we start with the presentation of two different reconstruction models for the TSI: the Spectral And Total Irradiance REconstructions (SATIRE-S) and the Naval Research Laboratory’s solar variability models for Total Solar Irradiance, version 2 (NRLTSI2). These models are used for the quality check of the input satellite records. Then, subsection 2.2 presents and discusses the 12 input satellite records. 

The TSI exhibits large day-to-day variations. The downward spikes in the daily mean values are due to the passage of dark sunspots, temporarily decreasing the TSI values. This is called the sunspot deficit effect. For this reason, it is often interesting to show the 121-day running mean curve. This curve is obtained by replacing the daily TSI value by the average of the daily TSI from 60 days before until 60 days after (thus 121 days in total). The 121-day running mean shows the general increase of the TSI with solar activity due to the increase of long-living bright faculae during high solar activity periods. This is called the facular excess effect.

2.1    TSI reconstruction models 

It is possible to estimate the TSI as a regression against proxies coming from Sun observations such as the Sunspot number. Currently, the most used regression model is: the version 2 of the Naval Research Laboratory’s (NRL) solar variability models for Total Solar Irradiance (NRLTSI2, Coddington et al., 2015, 2016). This dataset is the official daily TSI record of the NOAA CDR program. A semi-empirical approach is also possible, as in the SATIRE-S model (Yeo et al., 2014a and 2014b). Specifically, SATIRE-S derives the distribution of the magnetic features on the solar surface from full-disc solar magnetograms and continuum images, whereby the brightness of these various features is computed using a radiative transfer code from the corresponding semi-empirical solar model atmospheres. In that sense, the TSI variability in SATIRE-S is actually independent of TSI measurements. There are different uses of the SATIRE-S and NRLTSI2 models in this ATBD:

•    They are used for the quality check of the 12 individual timeseries (Section 2.2), in particular to check the record’s temporal stability and, for some records, define observation periods to be excluded from the composite (usually at beginning or end of mission). The models can also help in detecting outliers in early instruments timeseries.

•    The SATIRE-S model is used to interpolate short gaps (up to a maximum of 50 consecutive days) that exist in some of the individual timeseries. The gap filling method is described in Section 3.3. 

•    The SATIRE-S TSI model is finally ingested directly at the very beginning of the CDR, from 01.01.1979 to 06.11.1981. Indeed, before 07.11.1981 the ACRIM1 and the ERB/NIMBUS-7 observations appear significantly overestimated in comparison with the models. Keeping these first months in the C3S record is important for some users or services such as the Satellite Application Facility on Climate Monitoring  (CM SAF) that provides products starting on 01.01.1979.

•    The NRLTSI2 record is explicitly not used when constructing the C3S v3.0 and v3.1 daily TSI composites, so it can be used as independent source for the validation (see methodology and results in PQAD [D3] and PQAR [D5] documents).  

2.1.1    SATIRE-S

The SATIRE-S (Spectral And Total Irradiance Reconstructions, Yeo et al, 2014a and 2014b) is a reconstruction of the TSI over the 1974-present-day period using full-disc magnetograms and continuum images of the Sun. It uses the data from the National Solar Observatory Photospheric magnetogram (NSO KP) (1974-1999), SOHO/ Michelson Doppler Imager (MDI) (1999-2009) and Solar Dynamics Observatory (SDO) Helioseismic and Magnetic Imager (HMI) (since 2010). These observations allow for the estimation of the fractional coverage of: quiet Sun, sunspot umbrae, sunspot penumbrae, faculae and network. A regression between these indices and the TSI is then derived and used in the reconstruction. The SATIRE-S data starts on 23rd August 1974 and provides data until 8th July 2023 (at time of writing). New data are regularly added to the timeseries. 

2.1.2    NRLTSI2

NRLTSI2 is the version 2 of the Naval Research Laboratory’s (NRL) solar variability models for Total Solar Irradiance (TSI). This CDR was created at the Space Science Division of the Naval Research Laboratory (NRL) in collaboration with the Laboratory for Atmospheric and Space Physics (LASP) of the University of Colorado. The NRLTSI2 CDR is published as part of the NOAA CDR Program and is documented by Coddington et al. (2015, 2016).  In this model, the daily TSI is estimated from the observation of the bright faculae and the dark sunspots on the solar disk. A linear regression between these proxies of solar activity and the TIM/SORCE TSI was established and used in the reconstruction. The model assumes a quiet Sun TSI of 1360.45 W/m² (Kopp and Lean, 2011) as estimated from the TIM/SORCE measurement at solar minimum. The reconstruction starts on 1st January 1882 and provides data until 31st December 2022 (at time of writing). New data are regularly added to the timeseries, on a quarterly basis. 

2.1.3    SATIRE-S / NRLTSI2 intercomparison 

Figure 3 shows the SATIRE-S and NRLTSI2 timeseries over the 1975 – 2022 time period. The 2 models show very close agreement over solar cycle 23 (1996 – 2008) but otherwise exhibit significant differences, especially in the level of the solar minima in 1986, 1996 and 2019.

Figure 3: Timeseries of SATIRE-S (red) and NRLTSI2 (black) TSI reconstruction models after 121-days running mean. The daily NRLTSI2 values are shown in grey. Horizontal line at 1360.75 W/m² illustrates the change in solar minima.

2.2    TSI timeseries

Summaries of the 12 instruments used for the C3S daily TSI composite are shown in following tables. Each table specifies the full name, organization responsible of the data/instrument, period of time in which the TSI data is available and period of time used in the C3S composite. The percentages of data availabilities are provided for the original record, as well as after gap filling. The C3S adjustment factor and noise level are also provided (see Sections 3.1 and 3.2). An illustration of the original data is shown, the source of the original data is provided and notes specific to each instrument are listed, including identified “outliers” for some input timeseries.

Note about the graphs in Figure 4 to Figure 15 : the graphs show the timeseries of the satellite record (in green the daily and orange the 121-days running mean) after rescaling to the C3S record (in black). The NRLTSI2 data is also shown (in brown) after a rescaling on the same overlap period. The parts of the satellite record which are discarded in the C3S composite are in red (daily) and blue (121-days running mean).

2.2.1    ERB on NIMBUS7

2.2.2    ACRIM1 on SMM

2.2.3    ERBS

2.2.4    ACRIM2

2.2.5    DIARAD / VIRGO on SOHO

2.2.6    PMO06 on VIRGO

2.2.7    ACRIM3

2.2.8    TIM on SORCE

2.2.9    SOVA on Picard

2.2.10    PREMOS on Picard

2.2.11    TIM on TCTE

2.2.12    TIM on TSIS-1

3. Algorithms

3.1 Radiometric correction factors

The difference in absolute scale between TSI instruments is larger than the intrinsic TSI variability. Therefore, a harmonization to remove the differences is needed. Such a harmonization has been adopted in all the previous TSI composite attempts e.g. by Dewitte and Nevens (2016)[D1], Dudok de Wit et al. (2017), Montillet et al. (2022).

In this work, single correction factors are determined for each of the 12 instruments. The 12 factors  \( (α_i) \)  are determined by minimizing the root mean squared difference between the corrected daily TSI for each pair of overlapping instruments, namely

where the summations are done on all the pairs of instruments  \( (i,j) \) and on all the days d in the CDR record (v3.0 CDR period : from 01.01.1979 to 31.12.2020). The delta function \( δ_i(d) \) has a value of 1 if the instrument i provides a TSI observation for the day \( F_i (d) \) , and a value of 0 otherwise ⁸ .

There is a total of 34 overlapping periods (average length of 1873.3 days) between the 12 input records, which is sufficient to determine the 12 unknowns \( (α_i) \) . During the minimization process, a constraint must be added to avoid that all the correction factors tend to \( ε→0 \) (as in this case the residual error 

would also tends to \( α_i → 0 \)

). This constraint is that the average correction factors for the TIM instruments on SORCE (i=8), TCTE (i=11) and TSIS-1 (i=12), PMO06 on VIRGO (i=6) and PREMOS on PICARD (i=10) is equal to 1, namely:

The minimization is performed using a least mean square software ⁹ . Table 2 summarizes the obtained scaling factors \( α_i \) . The last column gives an estimate of the instruments’ precision as explained in the next section. As shown in the table, a scaling factor is also determined for SATIRE-S that is used in early months of the CDR (1979 and a large part of 1980).

Table 2 : Scaling factors and precision estimates (see Section 3.2) for the 12 input TSI timeseries.

Figure 16 shows the resulting scaled TSI records for the individual instruments. For clarity we use a 121-days running mean to remove the short term solar noise, and to highlight the instrumental differences. After scaling, the instruments agree in general quite well, except at the very beginning of the record and for 2018 onward. Figure 16 also shows that the ERBS instrument is critical to fill the so-called ACRIM gap (15.07.1989 – 03.10.1991), it is the only TSI instrument that was monitoring the TSI during this period.

Figure 16: Timeseries of individual TSI measurements after selection and harmonization. A 121-day running mean is used to remove the short-term solar noise. The 1361 W/m² horizontal line is shown to illustrate the stability between the solar minima.

3.2    Estimating the instrument precision

The precision of the instruments is estimated by the root mean square difference with SATIRE-S, after removing the 365-days running mean for both the instrument and for the SATIRE-S. This RMS difference is given in the column ‘all’ in Table 3. This value is however dependent on the TSI variability when the instrument was operated, as illustrated by the columns ‘max’ and ‘min’ that report the same RMS difference, but respectively over the periods of high (low) solar activity. The high solar activity periods are defined as: 01.01.1984 to 31.12.1987, 01.01.1995 to 31.12.1998, 01.01.2006 to 31.12.2009, and 01.01.2017 to 31.12.2020. The periods of low solar activity are the complement.

As some instruments (PREMOS and SOVAP) have not observed during low activity periods, it is decided to use the ‘RMS max’ column as an estimation of the instrument precision. For the ERBS timeseries, the estimated precision is not realistic (due to the use of SATIRE-S in the gap filling). It is then decided to use the ACRIM1 precision as estimate for the ERBS record, as both missions used the same radiometric cavity.  

Table 3: Instrument precision estimated as root mean square (RMS) difference with SATIRE-S. The columns 'max' and 'min' correspond respectively to periods of high and low solar activity. The column ‘all’ does not involve any selection based on solar activity.

3.3    Gap filling

Many of the input records have gaps in the daily TSI values. It is the case with the ERB (Nimbus7) and ERBS (ERBE) measurements at the beginning of the composite and also of the TSIS-1 instrument at the end of the composite. In the C3S v3.0 and v3.1 daily TSI composite, a gap filling mechanism is implemented as a preprocessing of the original timeseries. A gap is filled provided it extends over less than 50 days.

The gap filling exploits the SATIRE-S reconstruction which is tuned to the observations made just before and just after the gap. In practice, the ratio between the observed TSI and the SATIRE-S reconstruction is evaluated for the last day before the data gap and for the first day following the gap. This ratio is then temporally interpolated for each day within the data gap. The TSI for this day is obtained from the SATIRE-S reconstruction corrected with this interpolated ratio. The gap filling process is illustrated in Figure 17.

Figure 17: Illustration of the gap filling process. The black curve is an original TSI record with many data gaps (in this example the TIM/TCTE in 2014). The green curve is the SATIRE-S model. The red curve shows how the gaps can be filled by mixing the incomplete record with the (complete) SATIRE-S record.

3.4    Construction of the composite timeseries

From the individual time series, the composite daily TSI value \( F(d) \) F(d) for the day d is constructed as the mean of the available TSI values \( F_i(d) \) weighted by the inverse of the estimated accuracy level \( \varepsilon_i \) and homogenized using the factor \( α_i \) :

where the summations are made over the 12 input instruments i.

3.5    Results

The method has been applied on the data described in Section 2.2. Figure 18 shows the resulting TSI composite. The grey curve is the daily value while the red curve shows the 121-days running mean. For evaluation, the 121-days running mean of the (independent) NRLTSI2 record is also shown with an offset of 0.31 W/m² to scale them to the same level. 

Figure 18: C3S composite daily TSI values (grey) and 121-day running mean (red). The NRLTSI2 model, with an offset of 0.31 W/m² to match the curves, is shown in black.

This preliminary C3S composite of daily TSI agrees very well with the corresponding NOAA/NCEI CDR (NRLTSI2), when applying an offset of 0.31 W/m² to the latter. Close agreements are observed as well for the level of the solar minima as for the periods of high solar activity. The CDR stability and accuracy is fully addressed in the PQAD [D3] and PQAR [D5] documents.   

3.6    Limitations and future works

Thermal effect in DIARAD/VIRGO: Since 2010, there is an annual cycle apparent in the DIARAD/VIRGO record. This is likely a thermal effect that could be better corrected using the backup cavity (contact has been taken with the DIARAD science team). In the meantime, an empirical correction has been implemented to limit this effect.

Failure of the DIARAD/VIRGO backup cavity: The aging monitoring cavity failed on 9 Oct 2017 and since then the aging is extrapolated, assuming a constant aging rate. Although “at risk”, the data is kept as it stays as long as it stays in agreement with NRLTSI2. This is justified by the small number of space instruments in the ICDR period (2021 onward).

ACRIM3 apparent aging: The ACRIM3 record shows an apparent aging with respect to the SATIRE-S and NRLTSI2 models (see Figure 10). The impact of this apparent aging on the C3S composite could be investigated.

Overlaps periods: 34 overlap periods exist between pairs of instruments. These periods are used to determine the scaling factors. A comprehensive analysis of these overlaps would be interesting to consolidate this work and possibly estimate the precision and accuracy of the instruments based on these overlaps.

Running mean software: A better handling of the missing data in the running mean software would be welcome. This will not directly impact the C3S composite timeseries but will improve the quality check of the input records.

Gap filling strategy: When there is a data gap, the data for the last day (just before the gap) and the next day (when the acquisition resumes) should be considered “at risk”, in particular because these daily TSI values may be based on only a part of the 24h. The current gap filling strategy (Section 3.3) uses the TSI from these last and next days to scale the SATIRE-S model to fill the data gap. There is therefore a high sensitivity on these “at risk” TSI observations.

SOVAP and PREMOS records on Picard satellite: These are very short records. The interest to keep them in the composite could be assessed.

TIM/TCTE in 2019: From 02.02.2019 (resumption after TIM/TCTE gap) to 15.05.2019 (end of mission) there is a decrease of the TSI that is not supported by the models and the other available observations. Investigations should be carried out to determine if these 100 days should be kept in the C3S composite.

4.    Output data format

The output format is fully described in the Product User Guide and Specifications document [D4] for this data record. Here, only the main characteristics are provided.

 Table 4: General characteristics of the C3S daily TSI composite CDR.

The Total Solar Irradiance is the spectrally integrated total amount of radiant energy coming from the Sun per square meter of surface, perpendicular to the sunlight, at 1 astronomical unit.

 Table 5: Total Solar Irradiance parameter.

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