© R. Crapolicchio et al., Published by EDP Sciences 2025

1 Introduction

This article discusses the development and validation of L-band solar flux derived from the operational ESA Soil Moisture and Ocean Salinity (SMOS) mission launched on November 2nd, 2009, and still in operation, delivering high-quality datasets.

The SMOS mission, originally designed for global observations of soil moisture over land and sea surface salinity over oceans to improve our understanding of the Earth’s water cycle, meteorological and climate predictions (Kerr et al., 2009), has already evolved to include the estimate of sea-ice thickness, freeze/thaw soil state, and high wind speeds at the sea surface (Mecklenburg et al., 2016).

The SMOS payload is a passive L-band 2-D interferometric full-polarization radiometer called MIRAS (Microwave Imaging Radiometer with Aperture Synthesis) operating in the protected 1400 MHz to 1427 MHz band at 1.413 GHz and a wavelength corresponding to approximately 21.2 cm. A detailed description of the MIRAS instrument can be found in Kerr et al. (2000). Since the end of the MIRAS payload commissioning phase in May 2010, Brightness Temperature (BT) images of the full Stokes parameter vector are reconstructed by a cycle of four consecutive acquisitions with an integration time of 1.2 s (Mecklenburg et al., 2012).

The Stokes vector images, due to the MIRAS field of view and satellite orbital geometry, are influenced by the Earth surface emission and surrounding sky, including direct solar intrusion.

The solar signal is the strongest source of contamination (both from direct leakage into the antenna and from solar glitter effects), appearing in almost 97% of the acquired images (Reul et al., 2007). Effective modelling of the Sun’s sources significantly enhances the quality of SMOS-derived products and has thus been a priority for processor improvement (Martin-Neira et al., 2021; Garcìa et al., 2022).

The BT signal derived from the Sun introduces noise affecting SMOS scientific measurements, and it is allocated in the SMOS products as a corrective parameter. But this Sun BT measurement can also represent an opportunity to exploit SMOS measurements to observe the Sun from an unprecedented point of view in terms of bandwidth of observation, temporal resolution, and time coverage. The retrieval of the solar signal from SMOS measurements, presented in this paper, enables new opportunities to exploit the SMOS dataset beyond its original scientific purposes, and may allow for the addition of space weather applications and support to solar science studies to the mission objectives.

The potential of SMOS for space weather applications has already been discussed in Crapolicchio et al. (2016, 2018), Flores-Soriano et al. (2021), where the Solar cycle progression has been compared with F10.7 monthly averages at 10.7 cm, and SMOS solar Radio Burst (SRB) events have been compared with the solar flare events catalogue distributed daily by the NOAA, using data from the soft X-ray sensors of the Geostationary Operational Environmental Satellites (GOES) during the 2010 to 2019 period.

The high temporal resolution solar flux can indeed be used to detect SRBs; as the characteristics of SRB appear to be affected by the detection frequency (Nita et al., 2004; Sato et al., 2019), SMOS data could thus provide an important monitoring and diagnostic tool in the L-band. In addition, since the MIRAS payload works with full polarization data, the full Stokes vector can be reconstructed, allowing to associate the Degree of Circular Polarization (DoCP) to each event.

The usage of the SMOS solar flux data in the solar physics studies gives access to over 15-years of data collected with continuous monitoring at high time resolution. Unlike ground radio-telescopes, since MIRAS is a space-borne instrument, measurements are not affected by day-night cycles. Continuous monitoring is thus not locked behind the need to intercalibrate multiple instruments. Additionally, given its orbit position (at 761 km to 788 km of altitude), MIRAS acquisitions are not affected by atmospheric conditions. Periodic calibration of the instrument’s sensors shows stable performances, making the mission eligible for an additional three-year extension till 2028, with possible future renewals. The L-Band DoCP retrieved by the MIRAS data provides relevant information about the Sun, which is difficult to obtain from an on-ground radio telescope. The state of circular polarization during SRB appears to play a significant role in Global Navigation Satellite System (GNSS) fading events (Kintner et al., 2009), and is an important parameter to study solar storms and emission mechanisms (Morosan et al., 2022; Pulupa et al., 2025).

The work presented in this paper illustrates the theoretical algorithm set up to extract and process the solar signal from the MIRAS measurements and provides its validation with solar flux datasets collected at different frequencies by ground radio telescopes, as well as with solar activity proxies. Additionally, the work addresses the issues identified in Flores-Soriano et al. (2021) regarding Sun BT estimation from SMOS and its biases relative to the Sun position in the MIRAS antenna plane.

This paper makes use of the currently SMOS operational L1B processor v724 dataset, described in Section 2.

Data acquired by selected ground solar radio telescopes provide a reference for the mitigation of the biases, allowing the retrieval and the validation of SMOS L-band Sun BT. To increase the accuracy of the L-Band Sun BT reference, different microwave frequency channels from on-ground radio telescopes have been intercalibrated. Shimojo et al. (2017) report that a linear relation between the base-ten logarithm of the solar flux and the measurements’ frequencies can give a satisfactory fit to most of the microwave spectra when evaluating solar cycle variation through monthly means.

The SMOS solar flux is compared at daily resolution against ground radio-telescopes at different frequencies using data in the 1.0 GHz to 2.8 GHz range (30 cm to 10.7 cm) to assess long-term stability. The spectral content and the presence of seasonal and time drifts are evaluated and discussed using ground data collected at the same frequency of MIRAS. Further analyses are executed on a monthly scale to compare solar cycle progression of the L-band flux with the F10.7, the Wolf sunspot number, and the Mg II proxy. Selected events as detected by the prototype SRB detection algorithm are also shown and discussed, displaying both one mildly polarized event and one with no relevant circular polarization.

This paper is structured as follows: first, the SMOS L1B and validation data are presented in the Dataset section (Sect. 2). Solar flux measurements shown in this paper are all adjusted to a constant Sun-Earth distance; whenever the original dataset is provided prior to this normalization, adjustment to the mean 1 AU of Sun-Earth distance is applied over the source data. Then, the generation algorithm for the SMOS solar flux product is described in the Methods section (Sect. 3), and a great emphasis is put on the calibration step and ground reference definition. The Validation section (Sect. 4) describes the validation procedure used for the daily and monthly estimates; the calibration and validation results are presented and discussed in the Results section (Sect. 5), lastly, the format of the SMOS solar flux product and the potential application for the SRB bulletin is discussed in Section 6.

2 Dataset

This section describes the SMOS input data used to retrieve the solar flux measurements, and the solar activity indicators and ground reference flux data used for the validation.

2.1 Input data: SMOS L1B

Both the SMOS solar flux retrieval algorithm and the SMOS SRB detection algorithm described in this paper require the SMOS L1B v724 data collected by MIRAS, which are available from the SMOS dissemination service portal (https://smos-diss.eo.esa.int/) at: https://doi.org/10.57780/SM1-e20cf57.

Data are sorted by date and (half) orbit and can be downloaded as zipped binary data-block (DBL) and header (HDR) files. These data contain ancillary information on how the Sun appears in the MIRAS antenna, including: timestamp, Sun BT estimate, orbit ID number, orbit type (ascending or descending), start and end time, Sun alias position in the antenna plane, antenna boresight geographical coordinates, and other relevant flags about polarization mode, antenna-lobe (front or back-lobe), Sun-Earth eclipse, Radio Frequency Interference (RFI) contamination.

The Sun appears in the SMOS image as an alias bright spot with a possible tail imprint in the extended alias-free field of view (EAF-FoV) as illustrated in Figure 1. The Y-shaped array of the LICEFs results in a hexagonal sampling of the Discrete Fourier Transformation (DFT) spatial frequency domain. As the antenna distance does not satisfy the Nyquist criterion at L-band, it causes image replicas in the FoV reported in light red. One sample image is represented in the coordinates (ξ, η), which are the direction cosines. These are the components of a unit vector pointing in a specific direction, projected onto the X and Y axes in the antenna plane (Camps et al., 2004). They are defined by the spherical zenith (θ) and azimuth (ψ) angles as: ξ = sinθcosϕ and η = sinθsinϕ. The EAF-FoV area of the image is derived by special processing tasks applied over regions where the sky alias is present, and executed by the L1 processor, an operative algorithm which transforms MIRAS raw data into geolocated brightness temperatures (see Gutierrez et al., 2007). One of the tasks of the L1 processor is the removal of the Sun signal, which is then annotated in the L1B products.

Figure 1 SMOS antenna field of View (FoV). Left panel: Schematic representation of the FoV and geometric configuration of SMOS antennae, as function of Sun position coordinates ξ and η. Image replicas reported in red. Right panel: SMOS image with the solar signal. This signal is removed by the L1 processor, and annotated in the L1B product. Image adapted from Camps et al. (2004).

The SMOS image was initially derived from the visibility function to remove the Sun effect, and the Sun disk was initially modeled as a single source at the center of the image since the Sun is seen at a smaller angle than the angular resolution of the instrument (Corbella et al., 2004).

From the Level 1 Operation Processor (L1OP) version v724 onward, to better remove Sun residuals, the image was derived from the “differential visibility” obtained as the difference between the measured visibility and the visibility associated with the corresponding simulated (artificial) scene and the Sun disk modeled as different distributed brightness sources (Khazaal et al., 2020). The Sun BT, which minimizes the “differential visibility” is used to remove the Sun in the image and is annotated in the SMOS L1B data.

The extracted data derived by the Sun removal algorithm are processed with MATLAB^® scripts to produce the solar flux and SRB bulletin products.

2.2 Validation data

Validation of the derived SMOS solar flux is performed by comparison with multiple ground radio telescopes, using data from the US Air Force Radio Solar Telescope Network (RSTN), the Nobeyama Radio Polarimeters (NoRP), and the solar radio flux at 10.7 cm (F10.7) from the National Research Council of Canada. In addition, the SMOS solar flux is compared with common indicators of solar activity: the Wolf sunspot number (S_N) provided by World Data Center Sunspot Index and Long-term Solar Observations (WDC-SILSO), Royal Observatory of Belgium (Brussels) and the Mg II solar activity proxy provided by the UV Satellite Data and Science Group (UVSAT-UV) of the university of Bremen. Data from 2010 to 2024 are used for solar flux validation.

• The NOAA (National Oceanic and Atmospheric Administration) National Geophysical Data Center (NGDC, now the National Centers for Environmental Information, NCEI) provides daily solar flux bulletins using data collected by the RSTN. These consists of four ground-based observatories located in different parts of the world: Sagamore Hill (Massachusetts, USA), Palehua (Hawaii, USA), Learmonth (Western Australia), and San Vito (Southern Italy), each with three parabolic dish antennas to collect solar flux at 245 MHz, 410 MHz, 610 MHz, 1415 MHz, 2695 MHz, 4995 MHz, 8800 MHz, 15400 MHz¹. The four observatories aim to provide complete daily coverage of the solar flux, but differences in latitude introduce seasonal variations, and differences in longitude lead to different times of day for observations. Data from May 2011 onwards are released at: https://www.ngdc.noaa.gov/stp/space-weather/swpc-products/daily_reports/space_weather_indices/, while older dates are still available at: https://www.ngdc.noaa.gov/STP/space-weather/solar-data/solar-features/solar-radio/noontime-flux/. These are distributed as data adjusted to a constant Sun-Earth distance of 1 AU.

• The Nobeyama Radio Polarimeters (NoRP) are operated by the Solar Science Observatory, a branch of the National Astronomical Observatory of Japan, and their observing data are verified scientifically by the consortium for NoRP scientific operations. The calibration method for NoRP is described in Tanaka et al. (1973); the calibrated daily observatory dataset at 1.00 GHz, 2.00 GHz, 3.75 GHz, 9.40 GHz² is disseminated and updated periodically. Data are accessed at: https://solar.nro.nao.ac.jp/norp/data/daily/TYKW-NoRP_dailyflux.txt and downloaded as solar flux measurements not normalized to a constant Sun-Earth distance.

• The Penticton observatory provides the 10.7 cm solar radio flux (F10.7) and is a widely used index of solar activity. The sources and emission mechanisms, and a full characterization of the measurements are described by Tapping (1987) and Covington (1969); Tapping & Charrois (1994) respectively. Three sets of fluxes are provided: observed, adjusted, and absolute. The observed figures are the least refined and contain fluctuations of up to 7% due to the changing Sun-Earth distance. These are removed in the adjusted flux, which is normalized to the mean Sun-Earth distance. Finally, the absolute flux further reduces errors by multiplying the adjusted value by 0.90 to compensate for uncertainties in antenna gain and waves reflected from the ground. For the scope of this analysis, the data need to be adjusted to the mean Sun-Earth distance. Data used are calibrated from the adjusted to the absolute flux with the calibration factor proposed; see Section 3.6.1. The Solar Radio Monitoring Program is operated jointly by the National Research Council Canada and Natural Resources Canada, with support from the Canadian Space Agency; data were accessed at: https://spaceweather.gc.ca/forecast-prevision/solar-solaire/solarflux/sx-5-en.php.

• Monthly average of the Wolf sunspot number, as provided by WDC-SILSO. It is defined as the arithmetic mean of the daily number of sunspots over all days of each calendar month: with data from 1749 onward, it is arguably the key indicator of solar activity due to the length of the record (Hathaway, 2015). The results presented in this document rely on data from the WDC SILSO, Royal Observatory of Belgium, Brussels, and are available at the SILSO website (https://www.sidc.be/SILSO/datafiles). These data were accessed via the LASP Interactive Solar Irradiance Datacenter (LISIRD) (https://lasp.colorado.edu/lisird/).

• The composite Mg II proxy of solar activity: defined as the core-to-wing ratio associated with the Mg II doublet 280 nm emission. Due to its variability with respect to the natural UV to EUV solar irradiance, it is often used as a proxy for solar activity, showing both the solar cycle and rotation periods, see Viereck et al. (2001). Note that up until 2019 the composite proxy relies on the GOME-2A measurements, while the following years are covered by GOME-2C. The results presented in this document rely on data produced by the Institute of Environmental Physics (IUP) at the University of Bremen (https://www.iup.uni-bremen.de/eng/) and are available at https://www.iup.uni-bremen.de/gome/gomemgii.html. These data were accessed via the LASP Interactive Solar Irradiance Datacenter (LISIRD) (https://lasp.colorado.edu/lisird/).

The aforementioned radio telescope datasets have been used to generate a ground reference for the SMOS calibration Look Up Table (LUT). The only exception is for the RSTN data collected between July 21st and August 2nd, 2021, at times when the NOAA daily reports were not available. This gap has been filled with a local noon estimate based on the 1 s RSTN data following the procedure explained in Section 3.6. The second-by-second RSTN dataset is distributed by the NOAA (https://www.ngdc.noaa.gov/stp/space-weather/solar-data/solar-features/solar-radio/rstn-1-second/), although the Learmonth data update was suspended in 2019, and more recent data are now available from the World Data Centre (WDC) for Space Weather, which is a part of and operated by the Australian Space Weather Forecasting Centre (ftp://ftp-out.sws.bom.gov.au/wdc/wdc_solradio/data/learmonth/SRD/).

3 Methods

Figure 2 describes the algorithm’s theoretical basis of the data processing pipeline that produces the SMOS solar flux product and the required calibration LUT. First, L1B data are selected, extracted, and sorted by solar position. Raw data are filtered to remove corrupted snapshots (with 0 K Sun BT values or affected by solar eclipses or RFI) and less accurate acquisitions (elevation filter). Sun BT values are corrected for the influence of the Sun elevation position in the antenna plane and for the variable Sun-Earth distance and calibrated with a ground reference to remove residual orbital biases. Data are further processed, including conversion to solar flux and data resampling. Note that in the context of this paper, data that have been processed to remove the impact of geometrical factors such as the Sun-Earth distance and the Sun elevation angle in the antenna plane (obliquity factor) are referred to as geometrically corrected data, while the fully calibrated flux nomenclature refers to data also calibrated with a ground reference.

Figure 2 Solar flux (above) and LUT (below) generation pipelines. SMOS data are sorted according to the position of the Sun (in the back (B) or front (F) lobe of the antenna), and the polarization mode (horizontal (HH) or vertical (VV)). Each of these subsets is fully calibrated with a dedicated LUT.

It should be noted that although the solar flux is currently distributed as a semi-orbital average (50 min resolution), higher time resolution data is still available and is used to generate the solar SRB bulletin.

3.1 Ingestion

This step involves input data acquisition and reading. Data sorting is necessary as the front and back lobes acquisitions rely on different elevation thresholds (see Sect. 3.2) and calibration LUTs.

L1B extraction: Data from the L1B SMOS products are downloaded and converted to a binary (.mat) format that is specific to MATLAB^®.

Date-based retrieval: Data selection is based on the input date range, and the selected L1B data are used to initialize the arrays.

Sun position (F/B) sorting: Data are sorted by Sun position flags (Sun in the back or in the front of the antenna plane). The front flag is set to one for front-lobe acquisitions and zero for back-lobe acquisitions.

3.2 Filtering

Data quality is guaranteed by input filtering. The removal is performed using multiple criteria to grant good input data quality.

RFI: RFI flags in the L1B dataset are used to discard corrupted snapshots. Most RFI-affected acquisitions are thus identified, with very few exceptions which are discarded in the outlier removal step by the end of the pipeline.

Sun eclipse: solar eclipse flags are assigned and read from the L1B dataset. These are due to the satellite orbit and follow a seasonal variation. The binary eclipse flags are extended to one minute prior and one minute after the onset and offset of the original eclipsed-flagged period. This time interval was chosen to remove residual impacts of the Sun eclipses which were not flagged by the L1 processor, but were still visible in the form of a signal reduction.

Zero mask: some values of the Sun BT estimates in the L1B data are set to 0 K; the presence of these values is associated with unreliable estimates in the Sun removal algorithm used by the L1 processor to initialize the BT array. These values are thus discarded.

Elevation thresholds: as the Sun elevation angle affects the intensity of the signal (and thus the signal-to-noise ratio), the Sun’s position coordinates in the antenna’s FoV (η and ξ) are used to evaluate its elevation angle (α) above the antenna plane, equation (1).

$$\cos \alpha =\sqrt{{\xi }^2+{\eta }^2}.$$(1)

To ensure high measurement reliability, the elevation angle must satisfy the following constraints:

$$\begin{array}{c}\alpha \ge 0.032 \mathrm{rad},\\ \alpha \le 0.20 \mathrm{rad}\cdot (1-\mathrm{front}).\end{array}$$

The upper elevation limit imposed on the back images is necessary because at high α, the Sun is even further away from the front lobe of the antenna, resulting in a weaker signal. On the other hand, the lower Sun elevation threshold has to be introduced due to issues in the v724 L1OP and will be overcome in the future L1 processor v781 scheduled to be operational in 2026. Threshold values were defined performing a statistical analysis of the data quality as a function of elevation during the initial calibration, see Section 5.1.

3.3 Calibration

The Sun brightness temperature values are corrected, accounting for both the Sun elevation angle over the antenna plane and the Sun-Earth distance variability. Both factors introduce well-known biases which can be easily corrected with analytic equations. As residual biases induced by the antenna pattern are still present even after the geometric correction, data are further calibrated with an inter-calibrated ground reference. The full procedure is detailed as follows:

Elevation correction: the BT values are corrected for the Sun elevation angle, in the form of equation (2).

$$B{T}_{\mathrm{corr}}=\mathrm{BT}/\sin \alpha .$$(2)

Sun-Earth distance correction (1 AU): the data are further corrected for the variable Sun-Earth distance. The corrected BT values are thus normalized to a constant distance, set to 1 AU (Eq. (3)).

$$B{T}_{1\mathrm{AU},\mathrm{corr}}=B{T}_{\mathrm{corr}}\cdot {\left({\Delta }_{\mathrm{Sun}-\mathrm{Earth}}/1 \mathrm{AU}\right)}^2.$$(3)

The current Sun-Earth distance (Δ_Sun–Earth) in AU is a function of the calendar day (n_day), as expressed in equation (4), from Achard & D’Souza (1994). The approximate formula is consistent with Copernicus Sentinel-2 processing with a maximum displacement of about 0.2% mainly induced by the different perihelium reference date (see Eq. (8) from https://sentiwiki.copernicus.eu/web/s2-processing).

$${\Delta }_{\mathrm{Sun}-\mathrm{Earth}}=1-0.01672\cdot \cos \left(0.9856\right(n_{\mathrm{day}}-4\left)\right).$$(4)

The correction factor (f_c) shown in Section 5 is introduced to synthetically refer to the Sun-Earth distance variability factor, and is defined from equation (3) as:

$$f_c={\left({\Delta }_{\mathrm{Sun}-\mathrm{Earth}}/1 \mathrm{AU}\right)}^2.$$

LUT calibration (HH,VV): while the geometrically corrected SMOS data already follow the solar flux trend, a residual offset with respect to the ground-based estimates is still present and requires a calibration step to take into account the residual errors in the image reconstruction and in the Sun removal, mainly driven by uncertainties in the knowledge of the in-orbit MIRAS antenna patterns. The data are linearly calibrated with a Look Up Table that stores different m and q values that are used to calibrate the data as in equation (5).

$$B{T}_{1\mathrm{AU},\mathrm{cal}}=m_{\xi ,\eta ,\mathrm{pol}}{\mathrm{BT}}_{1\mathrm{AU},\mathrm{corr}}+q_{\xi ,\eta ,\mathrm{pol}}.$$(5)

The m and q coefficients depend on the Sun’s position (front or back plane), polarization mode, and the Sun’s position coordinates (ξ and η) in the MIRAS antenna plane. The coefficients are defined by nearest neighbor interpolation with respect to the effective values of ξ and η. A more detailed description of the LUTs generation is provided in Section 3.6 below to improve readability.

3.4 Processing

The brightness temperature values are converted into solar flux estimates. These are used both to generate the solar flux product, and as the data pool for the SRB Bulletin detection (see Sect. 6.2).

Timestamps resampling: as MIRAS operates by sequential measurements of differently polarized components, the horizontally (HH superscript) and vertically (VV superscript) polarized datasets are sampled with different timestamps at 1.2 s resolution. The Sun BT and elevation angle data are thus linearly resampled to a common time frame.

Intensity reconstruction: the first (half) component of the Stokes vector is reconstructed according to equation (6). Similarly, the new elevation angle is defined in equation (7) as the average of the HH and VV components.

$$B{T}_{\mathrm{final}}=(B{T}_{\mathrm{resampled}}^{\mathrm{HH}}+B{T}_{\mathrm{resampled}}^{\mathrm{VV}})/2.$$(6)

$${\alpha }_{\mathrm{final}}=({\alpha }_{\mathrm{resampled}}^{\mathrm{HH}}+{\alpha }_{\mathrm{resampled}}^{\mathrm{VV}})/2.$$(7)

BT to flux conversion: the final conversion to solar flux is obtained (Eq. (8)) by a time-based conversion factor K (Eq. (9)) which is a function of the Sun-Earth distance (Eq. (4)), the solar radius in the L-band (r) and a physical constant which is inversely proportional to the square of the wavelength (λ, which is about 21.2 cm at MIRAS frequency), so that the solar flux is expressed in solar flux units.

$$\mathrm{Flux}=K\cdot B{T}_{\mathrm{final}};$$(8)

$$K=\frac{2\times {10}^{22}\cdot k_{\mathrm{Boltzmann}}}{{\lambda }^2}\cdot \pi {\left(\frac{r}{{\Delta }_{\mathrm{Sun}-\mathrm{Earth}}}\right)}^2.$$(9)

Since the radio emission comes from the lower corona, the transition region, and the chromosphere, the solar radius is larger in the L-band than in the optical, but the exact value of r is difficult to quantify. In this study, the Sun is considered to be circular with a radius of 765 220 km (Reul et al., 2007). This value is higher but still consistent with equation (14) from Oberoi et al. (2017). The solar radius is treated as a constant, despite evidence of a strong variability with the solar activity in the microwave range (Selhorst et al., 2004).

3.5 Solar flux product

Data presented in this study are aggregated into orbital products (i.e., about 100 min). This step reduces the time resolution in the final output but grants complete outlier filtering and eases the implementation in other SMOS products as an orbital parameter, as SMOS orbit period is about 100 min. Actually, since the data collected in the front and back of the antenna are treated as separate datasets, the resolution of the data is 50 min (half-orbital estimates) when considering both antenna planes.

This step reduces the time resolution in the final output but allows both easier comparison with the daily data provided by the ground reference and outlier filtering. However, the solar flux is effectively evaluated for each snapshot that is not corrupted by noise, and higher time resolutions can be achieved, as illustrated in Section 6.

Outliers removal: the moving mean (${\overline{\mathrm{BT}}}_{\mathrm{final}}$) and standard deviation (σ_BT) of the final BT values are evaluated; those that do not satisfy the following condition:

$$|B{T}_{\mathrm{final}}-{\overline{\mathrm{BT}}}_{\mathrm{final}}|<3{\sigma }_{\mathrm{BT}}$$

are considered outliers and are therefore filtered out. Moving averages and standard deviations allow outliers to be identified without losing information about the true flux trend. A centered two-minute sliding window is used.

Orbital aggregation: the orbital values are then provided. The median values of Sun BT and elevation angle are chosen to describe the orbit at a median-defined date, the latter being chosen for the K definition (Eq. (8)) to go from the selected BT to the corresponding solar flux. The median is chosen to further remove out-of-scale values.

3.6 Look Up Tables generation

This section covers the green chain boxes of the LUT generation pipeline described in Figure 2. The input data for the LUTs generation cover the period from June, 2010 (based on SMOS commissioning) to December 31st, 2021. Usage of an external reference is expected to be reviewed in the future in favour of auto-calibration based on data acquired at high Sun elevation angle (see Sect. 5.1). The output of the LUT generation algorithm are the polynomial coefficients m_ξ,η,pol and q_ξ,η,pol shown in equation (5).

3.6.1 Data selection

Data from the ground telescopes are processed to retrieve daily local noon values normalized to 1 AU of Sun-Earth distance. Input data are the 1.415 GHz and 2.8 GHz acquisitions made by the RSTN and Penticton (F10.7) radio-telescopes, and the 1.00 GHz, 2.00 GHz, 3.75 GHz NoRP channels.

Nobeyama normalization: daily values are normalized by evaluating a correction factor based on the current Sun-Earth distance, see Eqs. (3), (4).

RSTN local noon evaluation: daily bulletins provide great coverage of the local noon flux values. Different local noon values have been evaluated only in the July 21st to August 2nd, 2021 period when no bulletin was available. The 1 s resolution RSTN data are turned into local noon estimates by selecting data in the −60 min to 60 min range from local noon time as provided in the bulletins and averaging the selected data-pool. As outliers may shift the effective value, the mean ($\overline{x}$) and standard deviation (σ) are evaluated over the raw data, and solar flux values $|x-\overline{x}|>\sigma$ are discarded before evaluating the final mean value.

F10.7 calibration: the absolute dataset is generated out of the adjusted data following the guidelines provided by the Dominion Radio Astrophysical Observatory (DRAO).

Frequency check: to ensure a reliable modeling of the solar flux frequency dependence, higher frequency flux data need to be greater than the lower frequency flux. Additionally, out-of-scale values need to be removed, depending on the frequency (ν):

$$\begin{array}{c}\mathrm{Flux}>40\mathrm{sfu};\\ \mathrm{Flu}{x}_{\nu >1.415\mathrm{GHz}}<300\mathrm{sfu};\\ \mathrm{Flu}{x}_{\nu \le 1.415\mathrm{GHz}}<250\mathrm{sfu}.\end{array}$$

The valid data are further filtered so that RSTN values need to be greater than solar flux measurements provided by the Nobeyama 1 GHz channel, and lower than every other daily input (as provided at a higher frequency). Nobeyama 2.00 GHz and 3.75 GHz channels are further constrained to be respectively lower and higher than the F10.7 index estimates.

3.6.2 Reference generation

This step involves the radio telescope daily flux inter-calibration. Local noon flux values are thus intercalibrated to generate a daily estimate. These data are then resampled to match the SMOS L1B data time resolution, assuming a slowly varying Sun signal from one day to the other, since transient phenomena like SRB events are discarded during the LUT generation procedure.

Shimojo interpolator: the reference generation is carried out through interpolation of data collected at different frequencies, using the simplified Sun spectrum modeling approach proposed by Shimojo et al. (2017), equation (10), where the solar flux logarithm scales linearly with respect to the frequency.

$${\log }_{10}\left(\mathrm{Flux}\right)=a+\mathrm{b\nu }.$$(10)

For each date, daily flux values are used to fit a and b; these coefficients are then used to generate the ground reference by evaluating equation (10) at 1.413 GHz.

Solar flux to BT conversion: the corresponding ground reference values of Sun BT are thus derived by using a conversion factor (see Eq. (9)) for each calendar day.

Linear resampling: data are linearly interpolated to match the time resolution of the SMOS input data. This timeseries will be referenced as BT_1AU,ref.

3.6.3 LUT fitting

Four datasets for each combination of antenna position and polarization mode are defined. Each subset is processed as follows:

Dataset sorting: the full dataset is sorted by Sun position on the antenna plane and polarization mode so that different LUT coefficients are defined depending on Sun position (in the antenna back or front-lobe) and polarization mode.

Antenna plane binning: each subset is partitioned into ξ and η bins (see Fig. 1). The ξ bins cover −1 to 0.75 with a 0.001 step, while η bins cover −0.6 to 0.6 with a 0.002 step.

Outlier removal: the input data are filtered with the Inter-Quartile Range (IQR) method, discarding data that do not satisfy the inequalities below:

$$\begin{array}{c}{Q}_1-x_i<1.5 \mathrm{IQR};\\ x_i-Q_3>1.5 \mathrm{IQR}.\end{array}$$

The nomenclature Q₁, Q₃ refers to the first and third quartile, and the outlier discard is based on the ratio between SMOS Sun BT and the ground reference ($x_i=B{T}_{1\mathrm{AU},\mathrm{corr}}/B{T}_{1\mathrm{AU},\mathrm{ref}}$). Indeed, while the amount of untagged RFI-contaminated snapshots is very low, ongoing SRB events would artificially shift the data distribution, since calibration is done with a ground reference, which does not account for transient Sun activity events as it is generated through linear interpolation of daily data. The presence of SRB events in these subsets would act as a population of outliers, thus negatively impacting the estimation of the LUT polynomial coefficients. Note that data acquisitions made at elevation angles below 0.032 rad are discarded before outlier evaluation, as they have been proven to be unreliable for the L1 processor v724.

Linear fitting: finally, the m_ξ,η,pol and q_ξ,η,pol calibration coefficients featured in equation (5) are derived through least square fitting of equation (11), which represents a linear relation between the SMOS uncalibrated data and the radio-telescope reference.

$$B{T}_{1\mathrm{AU},\mathrm{corr}}=m_{\xi ,\eta ,\mathrm{pol}}\cdot B{T}_{1\mathrm{AU},\mathrm{corr}}+q_{\xi ,\eta ,\mathrm{pol}}.$$(11)

The results of the calibration step for acquisitions made when the Sun is in the antenna’s front and back planes are depicted in Figures 3 and 4, respectively. The top panels refer to the multiplicative bias with the horizontal and vertical polarization datasets on the left and right plots, respectively; the bottom panels refer to the additive bias. Color bars represent the coefficient value, while x and y axes are representative of the ξ and η coordinates; the Sun elevation angle (Eq. (1)) is represented as dashed lines at iso-elevation.

Figure 3 LUT coefficients across the antenna plane for equation (5). Multiplicative (m) and Additive (q) bias values by antenna plane position and polarization mode for Sun-in-the-front acquisitions, numeric values are featured in the color bar. Dashed lines identify points at the same elevation angle in radians.

Figure 4 LUT coefficients across the antenna plane for equation (5). Multiplicative (m) and Additive (q) bias values by antenna plane position and polarization mode for Sun-in-the-back acquisitions, numeric values are featured in the color bar. Dashed lines identify points at the same elevation angle in radians.

Front-lobe coefficients in Figure 3 feature a semi-ellipse in the lower left part of the frames, which arises due to a partial or total Sun eclipse caused by the Earth in the central winter months. Overall, there appears to be an inverse relationship between high multiplicative and additive bias, with the only significant exception being the outer border of the plane, where low elevation angles require both parameters to be high.

The inner part of the frame is characterized by a striped pattern: most stripes feature a common inclination, however, some stripes with an opposite inclination arise for low ξ and η values in the “bow” region, especially in the horizontal dataset, which further includes a high slope region at high η and mid ξ values. Both the horizontal stripe characterized by high biases and relatively low slopes around η ≈ −0.2 and the ellipse sector near the Sun eclipsed zone have been recognized as coincident with the position of the sky-Earth horizon in one of the Sun aliases and may be due to the Gibbs effect in the image reconstruction, which impacts the Sun BT estimation. As the finite size of the instrument results in limited spatial frequency sampling, and acts like a low-pass filter: near coastlines or Earth-sky sharp transitions, the Gibbs effect results in ripples contaminating the image, as discussed in Corbella et al. (2019).

Figure 4 features the m and q coefficients for back acquisitions. Slope values are strictly lower than those in the front-based LUT, while the additive biases are much higher. The stark contrast between high (above 0.2 rad) and low (below 0.2 rad) elevation angles mark the signal degradation as the signal-to-noise ratio decreases. The horizontal component provides a more stable dataset, with signal degradation ensuing later than in the vertical dataset.

4 Validation

The performance of the LUT calibration is assessed by evaluating the SMOS Sun BT by the Shimojo ground reference ratio and comparing the geometrically corrected and the fully calibrated datasets. If successful, the calibration procedure is expected to remove systematic biases between the SMOS and Shimojo Sun BT values regardless of the Sun elevation angle in the selected dataset. Data uncertainties are evaluated with the coefficient of variation (CV) computed on the orbital dataset, and defined as the orbital flux standard deviation normalized by the average orbital solar flux. Distribution associated with either low or high Sun activity periods is further added to evaluate consistency at different levels of solar activity. The SMOS solar flux defined on a monthly scale is used to distinguish between the two categories: taking April 2014 as the maximum of the XXIV Solar Cycle and December 2019 as the start of the XXV Solar Cycle (Kaplan, 2024), values above the average of the two measurements are classified as high category, while values below the average are classified as low category.

The SMOS daily solar flux is further compared to both the F10.7 index (taking local noon time estimates at 20:00 UTC for the longitude position of the Penticton observatory), the 1 GHz channel from NoRP, and the RSTN daily estimates. The datasets used for the validation of the SMOS solar flux differ from the one selected for calibration, thus allowing the validation process to utilize an independent dataset.

The NOAA Space Weather Daily indexes report the RSTN solar flux values at 04:00, 10:00, 17:00, and 23:00 UTC as measured by the Learmonth, San Vito, Sagamore Hill, and Palehua observatories, respectively, and corresponding to local noon flux measurements. These data are inter-calibrated by selecting the median of the observatory estimates for each date.

Similarly, the SMOS daily reference is defined as the median of the aggregates defined in Section 3.5: as the orbital product can still be affected by strong SRB events, the shift from average to median indicators reduces the influence of SRB activity on the daily data.

The precision of the SMOS solar flux dataset is compared to that one of the F10.7 index, and the RSTN and 1 GHz NoRP data using an auto-regressive model of order eighth (Dudok de Wit et al., 2016). This approach has already been explored for solar flux timeseries in Dudok de Wit & Bruinsma (2017) using both the F10.7 index by Penticton and the 1 GHz NoRP data (F30). The expected precision is expressed as a linear function of the solar flux obtained through fitting of the residuals between the auto-regressive model and the original dataset.

The spectral contents of the SMOS daily solar flux estimates and the F10.7 are compared. The Lomb-Scargle algorithm is used to account for the missing data (Lomb, 1976). Both signals are also decomposed into two components using the Blind Source Separation (BSS) method, as proposed in Dudok de Wit et al. (2014):

• B: the background or quiet component, which indicates the lower envelope of the time series; it is defined as the minimum daily value evaluated with a 21-day moving window.

• S: the rotational modulated component, which shows variability on smaller time scales. This value is obtained by subtracting the B component from the daily value. The width of the moving window has been reported as the best compromise between the solar rotation period and the slowly changing radio flux (Dudok de Wit et al., 2012).

Daily values from SMOS and the RSTN L-band data are compared to check that there are no unexpected seasonal trends or temporal drifts. The F10.7 data and the Nobeyama 1 GHz channel are used as external references.

Then, the calibrated SMOS solar flux trend is compared to the 10.7 cm solar flux, the Mg II proxy, and the Wolf sunspot number using monthly arithmetic means based on calendar months. Pearson correlation coefficients between SMOS (front and back) and each timeseries are evaluated and compared with the corresponding F10.7 correlation coefficients. Spearman correlation coefficients are included to evaluate the hypothesis of linear correlation.

Both the solar flux collected by SMOS front-plane data and the F10.7 are compared and correlated with the Wolf sunspot number and the Mg II proxy.

The Wolf sunspot number correlation with the solar flux at 10.7 cm from Holland & Vaughan (1984) (Eq. (12), with c₁ = 67, c₂ =0.97, c₃ = 17.6, and c₄ = −0.035 as reported by Hathaway (2015) is tuned to reflect the relationship between the L-band solar flux (SMOS front acquisition) and the Wolf sunspot number. Both equation (12) and a linear regression are tested to evaluate the weight of non-linearity effects.

$$F_{10.7}=c_1+c_2{S}_N+c_3\left(e^{c_4{S}_N}-1\right).$$(12)

Correlation between the Mg II proxy of solar activity and the 10.7 cm solar flux has long been used to inter-calibrate different Mg II instruments (see Viereck et al., 2004). Both linear and quadratic fit models have been proposed, showing a better agreement when including the non-linearity effect (Bruevich et al., 2014). A similar approach is tested using the SMOS L-band flux and the F10.7 index.

Monthly averages and the spectral content of the back-based acquisitions are also presented.

5 Results

This section shows the results of the validation procedures illustrated in Section 4 for the calibration LUT (Sect. 5.1), the daily solar flux (Sect. 5.2), and the monthly solar flux (Sect. 5.3).

5.1 Calibration performance

Figures 5 and 6 provide the 2D density charts of the SMOS solar flux by the ground reference ratio for the antenna’s front and back plane, respectively and assess the stability of the calibrated SMOS flux with the Sun elevation angle over the antenna plane. Values below the threshold of 0.032 rad are shown for completeness; however, they display erratic and unstable behavior for the L1OP v724. Preliminary analysis done on the future L1OP v781 expected to become operational by 2026 show that the low α cut-off (see Sect. 3.2) will be removed in the future.

Figure 5 SMOS Sun BT and ground reference Sun BT ratio in the antenna’s front-plane before and after calibration. Comparison between fully calibrated and geometrically corrected data. (a) Horizontal polarization dataset (b) Vertical polarization dataset.

Figure 6 SMOS Sun BT and ground reference Sun BT ratio in the antenna’s back-plane before and after calibration. Comparison between fully calibrated and geometrically corrected data. (a) Horizontal polarization dataset (b) Vertical polarization dataset.

Comparison between calibrated and uncalibrated data shows the removal of the elevation dependency in the antenna’s front lobe. Limited traces are still observed at low elevation angles below 0.05 rad, especially in the vertical dataset. Note that the sharp color discontinuity just before 0.25 rad is induced by the smaller sample size, as high α values are only achieved during some months of the year. On the other hand, compared to the front plane, the antenna’s back plane features a more pronounced elevation dependency both before and after calibration.

The difference between the two polarization modes is evident, with the VV component being by far more dispersed than the HH counterpart; as a consequence, the 0.2 rad threshold mentioned in Section 3 still comes with some caveats since data are expected to feature some degree of bias. As the antenna’s front plane dataset features a much higher accuracy, it is the main SMOS flux reference for the orbital, daily, and monthly solar flux.

While the lower signal-to-noise ratio in the back-lobe dataset requires further improvements in the Sun removal algorithm (L1 processor) and calibration procedure (LUT), accuracy and stability are not expected to meet the levels of the front-lobe dataset. However, back-lobe data are required for continuous monitoring of solar activity.

The enhanced amplitude of the solar signal at times of solar radio bursts eases the process of background removal since the signal-to-noise ratio increases. Many solar radio burst events have already been identified in the back-lobe dataset, thus making it potentially fit for SRB monitoring, see Section 6.2.

Figure 7 shows the histogram distribution of the CV in the 50 min dataset. The data follow right-skewed profiles: this shape is expected, as solar radio bursts may impact the 50 min datasets. Indeed, isolating the high activity years from the low Sun activity periods, the latter show less skewness. Overall, front-lobe data from both polarization components display similar levels of CV, mostly below 0.10. The mode value is around 0.05 of the solar flux; however, the actual relative uncertainty distribution associated with high solar activity measurements is lower, meaning that noise levels are stable with increasing solar signal. Back-lobe data are associated with higher noise levels, with worse performance in the vertical polarization. The mode CV is in the order of 0.13–0.15.

Figure 7 Histogram distribution of the coefficient of variation of the orbital dataset by antenna plane and polarization mode with average, median and mode values (avg, med, mod) of the full dataset.

Overall, CV in the front-lobe is in the 0.05–0.10 range, and 0.13–0.23 range in the back-lobe.

5.2 Daily dataset

Data precision of the SMOS daily solar flux is evaluated and compared with results obtained by the F10.7 and the L-band RSTN and 1 GHz NoRP channels in Figure 8.

Figure 8 Precision of the solar flux datasets as a function of the solar flux in absolute and relative value.

The daily SMOS flux is associated with the lowest error for flux values above 70 sfu; below this threshold, it is the second most precise timeseries behind the F10.7. The latter is associated with the least precise measurements for solar flux values above 100 sfu. On the other hand, the NoRP dataset features very low errors with a trend similar to the one of SMOS. The RSTN is associated with the worst performance at low flux, and the second-worst performance at high flux. Every dataset is still associated with a maximum relative error below 6% in the proposed range, and below 3% for the SMOS solar flux.

These trends are the result of the obtained precision fit coefficients reported in Table 1. Interestingly, results obtained for the fit of the NoRP 1 GHz data are in good agreement with those reported in Dudok de Wit & Bruinsma (2017), while the F10.7 coefficients evaluated show some differences. However, evaluating these coefficients using data from 1957 to 2016, as shown in the reference paper, removes these differences, which can thus be attributable to the different time coverage used in this article, and may be partially explained by the slow drift described in Dudok de Wit & Bruinsma (2017). More analysis will be done in the future to investigate such a trend.

Figure 9 shows the Fourier spectral analysis of the SMOS daily (front and back) and F10.7 (top panel) signals and their BSS components (bottom panels). Each signal shows two peak structures in the daily and rotational (bottom right) panels, associated with the solar activity and rotational periods. Compared to the dashed lines, the effective periods are about 10 years and 27 days long, with the solar rotation peak intensity being higher in the S panel than in the overall signal. On the other hand, the background component shows only the peak of the solar activity period, with a slightly higher intensity and with even smaller differences in the spectral components between the SMOS solar flux and F10.7. The trends found indicate that, despite the need to revisit the LUT calibration of the back acquisitions, the effective trends provided by both the front and the back planes are effectively compatible with those of F10.7. As the mission lifetime increases, the time coverage of the Sun activity cycle by SMOS will increase, and the intensity of the peak corresponding to the solar maximum is thus expected to grow.

Figure 9 Fourier spectral analysis of F10.7 and SMOS daily values, distinguishing between SMOS back and front acquisitions. BSS has been applied to the daily data, and each component has further been analyzed.

A comparison between the F10.7, SMOS, and composite RSTN daily fluxes is shown in Figures 10 and 11. The daily trends show similar structures; due to the higher frequency, the F10.7 index is higher than both the RSTN and SMOS daily flux. Strong spike-like peaks in the F10.7 reference are likely associated with intense solar events still affecting the daily estimates. The panels below show two-year data samples from the low (2018–2019) and high (2023–2024) activity years, to better illustrate the flux structures.

Figure 10 F10.7, composite RSTN, and SMOS (front) daily solar flux time-series over time. Low (left) and high (right) activity years zoomed overview are provided below.

Figure 11 F10.7, composite RSTN, and SMOS (front) daily solar flux comparison. Left-most plots provide seasonal information with respect to the Sun-Earth distance correction. Yearly evolution is represented on the right. Pearson correlation coefficients between each pair and quadrant bisectors are reported on left-most plots.

Periodic structures are associated with solar rotation, with the differences between the F10.7 data and the L-band flux being accentuated in the left panel due to the different scales, as the variability of low activity periods is reduced. The incomplete filtering of the transient activity from the background signal is mostly visible in the right panel, as May 2023 has witnessed several intense events. All three series still show the same structures, although it seems that the RSTN reference slowly drifts towards the end of 2023. Small gaps at the end of August in the SMOS dataset are induced by the low Sun elevation angles below the lower threshold and will be removed in the future v781 L1 processor.

The SMOS and RSTN intensities are in good agreement, with SMOS data providing a higher flux than the RSTN in the 2015–2019 period, while the RSTN flux is higher than the SMOS flux in the remaining years up until 2022. However, the main difference in these years seems to be due to the less spiky and smoother profile of the SMOS data. Data from mid-2022 onwards are systematically lower in the RSTN when compared to those collected by SMOS.

Figure 11 provides a multi-panel overview of how SMOS, the RSTN, and F10.7 datasets compare; similarly, the Nobeyama 1 GHz channel is shown in Figure 12, acting as an external reference. The left and right panels differ only in the color bar information. The leftmost panels are associated with the Sun-Earth distance factor (Eq. (4)) and show no relevant seasonal trend, as the images at different distances mix. However, high f_c values seem to arguably be associated with an overestimation of the Nobeyama dataset when compared to both SMOS and the RSTN, corresponding to data acquisitions made during the month of July.

Figure 12 Nobeyama 1 GHz, composite RSTN, and SMOS (front) daily solar flux comparison. Left-most plots provide seasonal information with respect to the Sun-Earth distance correction. Yearly evolution is represented on the right. Pearson correlation coefficients between each pair and quadrant bisectors are reported on left-most plots.

Each subplot of Figure 11 shows the quadrant bisector: as expected, only the SMOS vs. RSTN (middle) panel shows a mostly symmetric distribution. In the top and bottom panels, SMOS and the RSTN reference are compared to F10.7, and as such the slope of the line is lower than the bisector; however, the latter seems to bend at high solar flux. In some instances, the L-band flux is higher than F10.7, and this discrepancy is due to daily values being vulnerable to transient high activity events; daily measurements are expected to filter out their influence, however, some residual increase may still be present. This effect is very limited, however, the number of points at higher L-band flux than F10.7 is higher in the RSTN reference than in the SMOS dataset. On the other hand, the correlation with Nobeyama should return data distributions consistently below the bisector, with the exception of a subset of acquisitions made during July in the SMOS panels, and more mixed results in the RSTN panels, as additional data other than the same subset seem to underestimate the actual flux. These values are mostly associated with data acquisitions made during 2023 onwards, which correspond to the stray points in the RSTN-SMOS panels.

Moving to the right-most panels, the color bar is representative of the date of acquisition. Different levels of solar activity mean that color variability is expected from the lower left to the upper right. However, for any given Δx or Δy, differently colored points should align with a common slope. The SMOS flux compared to both the F10.7 and NoRP timeseries follows this trend. However, this is not the case when looking at the RSTN panels: comparison with SMOS, the F10.7, and NoRP data shows a different slope from the XXIV to the XXV (current) solar cycle. While the orange and blue dots (solar maxima) overlap in the upper panels (SMOS-F10.7, and SMOS-Nobeyama), two distinct distributions emerge below, with the current RSTN values underestimating the solar flux value, as seen in the high activity panel in Figure 10. This effect is probably related to both the inconsistent number of active radio telescopes featured in the recent daily reports released by NOAA, and due to periodic re-calibration of the RSTN at each new Sun cycle done under the assumption of a constant minimum solar flux value (Giersch & Kennewell, 2022). The greater number of dates at solar flux values below the NoRP 1 GHz estimate and the saturation effect when compared against F10.7 are also induced by this bias.

This is also reflected in the Pearson correlation coefficient. The ideal Pearson correlation coefficient between SMOS solar flux and the RSTN flux should have almost a unitary value, since the frequency of MIRAS and the RSTN L-band channel is mostly the same (Δ ≈ 2 MHz), thus linear correlation would be expected. Non-linear effects between SMOS flux and the F10.7 index, as well as the NoRP 1 GHz channel, are expected to be more pronounced due to the wider frequency gap. However, the correlation coefficient between the SMOS solar flux and the RSTN is lower than the one with both F10.7 and Nobeyama, despite representing mostly the same frequency. Correlation coefficients between the SMOS solar flux and the 1 GHz NoRP flux and F10.7 are higher than those achieved by the RSTN, although they still feature high values. The lower Pearson correlation coefficient evaluated when comparing SMOS flux with the RSTN is attributable to the changing calibration in the RSTN, which introduces non-linearity.

Note that, despite using both the F10.7 index and the Nobeyama data until the end of 2021 to generate the SMOS calibration reference, the difference is effectively attributable to the higher stability of the SMOS timeseries. This is because linear regression is applied over the logarithm of the flux on a daily basis (i.e., different coefficients for each date), and the correlation does not seem to change after the calibration window.

5.3 Monthly dataset

Figure 13 shows the monthly averages trends of the SMOS solar flux (front and back) and the F10.7 index, as well as monthly averages of the Wolf sunspot number and the composite Mg II proxy. All panels show a fairly similar trend and are in good agreement. The top left panel shows SMOS front and back lobes flux averages: further calibration efforts are needed to avoid overestimation during low activity and, to a small extent, underestimation during peak activity. Solar flux progression is still well represented.

Figure 13 Monthly averages of SMOS and F10.7, Wolf sunspot number, and composite Mg II proxy of solar activity. Correlation coefficients (r) are reported in each panel using both Pearson and Spearman (in brackets) methods.

At the monthly scale, the correlation between SMOS L-band flux and F10.7 is close to linear, as highlighted by the extremely high Pearson correlation coefficient with the front-lobe data (above 0.99) and the small increase in the Spearman correlation coefficient. Non-linear effects in the back-lobe datasets are more pronounced when compared to every other solar activity proxy, since it has been shown to systematically underestimate and overestimate high and low Sun activity, respectively. The rank-based Spearman correlation coefficient thus returns higher values, as the linearity assumption is discarded.

Correlation with both the Mg II and Wolf sunspot indicators is similarly high (0.96–0.99) and returns close results for both the SMOS flux and F10.7. The Wolf sunspot number is marginally more correlated to the F10.7, while the Mg II proxy is more correlated to the SMOS flux. Interestingly, the Spearman correlation coefficient between SMOS solar flux and the Mg II proxy is lower than the Pearson correlation coefficient, hinting that at the monthly scale, the correlation between the L-band flux and the Mg II proxy is linear, unlike with the F10.7 data.

Figure 14 further re-establishes the correlation between SMOS solar flux and the Wolf sunspot number, providing a fit model in the same form as proposed in Holland & Vaughan (1984) (Eq. (12)) to correlate the latter with the 10.7 cm solar flux (Hathaway, 2015). The SMOS data appear to be modeled remarkably well by the equation, especially during periods of low activity. The linear fitting model is included in red; overall, the two models are quite similar, however, the introduction of the exponential term better models the low solar activity. On the right panel, the same analysis has been performed over the F10.7 dataset, showing compatible results. The newly fitted data (2010–2024) provide slightly different coefficients than those found in Holland & Vaughan (1984). This discrepancy is expected due to the different datasets used for fitting. The correlation between solar flux and the Wolf sunspot number may change over time as the Sun undergoes different regimes (Hathaway, 2015). Compared to F10.7, the RMSE is only minimally higher under the Holland & Vaughan (1984) modelling assumptions; linear regression is also more effective for the SMOS-based model, as the difference between the RMSE is higher in the F10.7 case study since more significant deviations are also present at high Sun activity.

Figure 14 Monthly Wolf sunspot number and SMOS (left panel) front-plane and F10.7 (right panel) solar flux fitting model according to Holland & Vaughan (1984) (black) compared to linear fitting (red).

Correlation with the Mg II proxy in Figure 15 shows an interesting result. As expected from the higher Pearson correlation coefficient, lower RMSE are achieved by comparing SMOS and the Mg II data rather than F10.7 and the Mg II proxy. More importantly, while the latter benefits from switching to quadratic fitting, the performances of the SMOS-based correlation are stable and do not change when introducing the quadratic term, further reinforcing the idea that the correlation between the SMOS solar flux and the composite Mg II data is mostly linear. This finding may prove to be useful when assessing the reliability of solar activity proxies for atmospheric models.

Figure 15 Monthly composite Mg II solar activity proxy and SMOS (left panel) front-plane and F10.7 (right panel) solar flux fitting model under linear (red) and quadratic (black) regression.

Overall, the SMOS solar flux shows a remarkable agreement with each of the evaluated solar activity proxies, including solar flux measurements in the 1.0 GHz to 2.8 GHz frequency range. Thanks to its stability, the SMOS data are a valuable asset for solar monitoring.

6 The SMOS solar flux product description

This section includes a description of the solar flux product data format, which must be referenced for data distributed at https://doi.org/10.5281/zenodo.15275693 through Zenodo. Daily and monthly data generation follow the procedure described in the previous sections. Additionally, the derived SRB bulletin product is preliminarily described. Note that SRB detection relies on the high temporal resolution solar flux product (i.e., omitting orbital median aggregation). Orbital data are generated and distributed on a daily basis through an FTP connection. Access to this repository is given upon request. For any additional information about any of this data, please feel free to contact the authors. The FTP repository also includes files about SRB detections made with a previous SRB prototype detection algorithm, which is going to be replaced and upgraded in the future.

6.1 Data format description

The solar flux and SRB products are generated on a daily basis by processing data from the previous day. For each calendar date processed, one .txt file is generated, and it includes three sections:

1. A header: it consists of two text lines reporting information about data center, generation time, L1P version, and LUT version. Every file is generated by the RedLab data center, and the generation time is provided in the UTC timezone. The L1 processor version used to generate the L1B data is further specified alongside the LUT version used. For the scope of this dataset, this field is set to 724_2.0, referring to L1OP v724 and LUT (v724) v2. The number of estimates provided for the front (N_front) and back (N_back) antenna planes are included, as well as the number of L1B data originally processed.

2. A body: it is structured as a table with a first row including the name of each parameter, and with front-plane acquisitions being listed first, while back-plane acquisitions are appended below the last front-plane row. Each subset is sorted chronologically and includes information about: median acquisition time, the normalized and calibrated Sun BT (K), the corresponding Sun flux (sfu), the number of snapshots used, Sun BT standard deviation (K), the mean Sun elevation angle α (rad), the Sun-Earth distance factor f_c, a numerical ID used to identify the SMOS orbit, the associated orbit start time, and the acquisition start and stop time of the given entry. Every time-based information refers to UTC time.

3. An annex: listing the SMOS L1B input products used (https://doi.org/10.57780/SM1-e20cf57).

Note that, despite data being meant as half-orbital acquisitions, time steps between different acquisitions may vary due to the presence of RFI contamination, possible outliers, and low Sun-elevation discard.

6.2 Data application for the solar radio burst bulletin

The high time resolution of the SMOS data makes it suitable to detect SRBs. Using SMOS-calibrated flux, a SRB detection algorithm has been designed to improve upon the prototype processor, which has already been implemented. This includes specific modules to address the increasing RFI contamination in the L-band, thereby enhancing SRB detection accuracy. An example of the SRBs bulletin derived from uncalibrated SMOS flux has already been presented in Flores-Soriano et al. (2021).

At the time of this paper’s submission, SRB detection validation has just been completed, using data collected by the RSTN as a reference, and will be thoroughly documented in a forthcoming dedicated publication. To increase the availability of the algorithm, both lower accuracy data collected in the antenna’s back-plane, as well as events with partial RFI corruption, should not be discarded. A relevant feature of the SMOS dataset is its polarimetric nature, which allows the direct association of the event degree of circular polarization on top of the intensity information.

The SRBs detection algorithm needs to:

1. Define a daily solar flux reference to identify possible peaks.

2. Search for high solar flux activity (i.e., above threshold) prolonged over time.

3. Discard false positives induced by either RFI or residual orbital biases.

Figure 16 shows two SRB events as detected by the prototype processor. Black and blue markers represent the SMOS solar flux intensity (top) and the degree of circular polarization (bottom), distinguishing between the Sun in front and back of the antenna, respectively; green markers highlight the SRB detection by the current prototype algorithm, which operates only with data acquired in the front antenna plane.

Figure 16 SMOS SRB detections: solar flux intensity and DoCP. Left panel: SRB event from September 6th 2017. Right panel: SRB event from November 7th, 2022. RSTN references are plotted in red.

The SRB event on the left was associated with significant effects on the GNSS network (Sato et al., 2019). The burst is circularly polarized (negative sign for right circular polarization), and this has been reported as a risk factor for GNSS systems. Interestingly, the DoCP and flux intensity follow a different trend, as the double peak structure of the DoCP, which can be uniquely identified by using the SMOS dataset, is more symmetrical.

A significant part of the event occurs when the Sun is behind the antenna. Detection is limited to the tails, with some data lost during the back-to-front transition. However, both the intensity and degree of circular polarization peaks are captured. It is worth noting that the signal recorded from the back is also consistent with the data obtained from the San Vito station, as the shape and timing of the multiple peaks matches the ground radio telescope with high accuracy. Although the routine does not run over the back acquisition, the unpolarized strong SRBs are still clearly distinguishable. Preliminary tests on a subset of past events suggest that detection of events peaking above 250 sfu during high solar activity periods should not be impaired; detection of events peaking below this value is still to be assessed, but is not excluded. Based on this preliminary analysis further work will be done to extend the routine detection over the back-lobe to increase monitoring availability.

The right panel shows a different unpolarized event recorded by SMOS on November 7, 2022. While this event is listed on many frequencies in the NOAA reports, it was not reported in the L-band by the Learmonth Observatory. This may be due to some measurement inconsistencies later in the day, as the event is well visible in the time series provided. One-second resolution data from MIRAS and Learmonth show the same structures, although peak values in the SMOS solar flux are higher than those visible from the RSTN observatory.

An automatic detection algorithm is under implementation and will be delivered daily through an accessible FTP connection. Preliminary values of precision and sensitivity³ are estimated and compared against the RSTN database performance, using data distributed by NOAA. The detection procedure returns roughly a +20 percentage points sensitivity increase over the RSTN, with the same level of precision.

A dedicated paper discussing the detection algorithm and its performance is in preparation.

7 Conclusions

The MIRAS radio interferometer onboard the SMOS satellite collects high temporal resolution polarimetric data at 1.413 GHz, which can be used to reconstruct the full Stokes vector of the solar flux. Solar flux estimates are derived from ancillary Sun estimation information to enhance the data quality of soil moisture and ocean salinity maps, which are the primary objectives of the mission. The ancillary information annotated in the L1B product has been corrected for the Sun elevation angle on the antenna plane, normalized for a 1 AU Sun-Earth distance, calibrated, and converted to corresponding solar flux values using a novel approach presented and validated in this paper.

Current calibration utilizes an intercalibrated ground-based reference with input data frequency ranging from 1.0 GHz to 3.75 GHz. Future releases may rely on high-quality, high-elevation acquisitions to provide SMOS self-calibrated measurements, removing the need for an external ground reference for the calibration. Regardless, generation of the ground reference will be continued, and it will be used to monitor possible anomalies. The switch to a self-calibrated LUT will prevent SMOS solar flux from being influenced by external factors.

Data calibration successfully removes residual orbital biases induced by the antenna pattern from the antenna’s front-plane with an accuracy estimated by the coefficient of variation ranging between 0.05 to 0.10. On the other hand, back plane acquisition accuracy decreases significantly for Sun elevation angles above 0.2 rad with coefficient of variation values of 0.13–0.23. At a daily scale, the precision of the SMOS dataset is evaluated through auto-regressive modelling and shows excellent performance compared to the radio-telescopes, with relative errors expected to be below 3%.

Daily and monthly solar flux aggregates in the front-lobe demonstrate good agreement with key solar activity indicators (Wolf sunspot number, composite Mg II proxy, 10.7 cm solar flux) as well as with L-band solar flux measurements provided by the RSTN. Unlike the L-Band RSTN dataset, SMOS data exhibit no significant seasonal or temporal drift. Fourier analysis of the SMOS signal reveals clear imprints of the Sun’s rotational period and activity cycle in both antenna plane, compatible with the spectral content of the F10.7.

The stable performance of the SMOS solar flux is also confirmed by the monthly data analysis. Solar cycle progression in the L-band well matches the timeseries of the F10.7 as well as those of the Wolf sunspot number and the composite Mg II proxy. Pearson and Spearman correlation coefficients suggest a mostly linear relationship between the L-band flux and the Mg II solar activity proxy, further confirmed by the better performance of the linear fit model when compared to the F10.7 – Mg II proxy relation. This observation indicates that the SMOS solar flux, measured at a frequency between the F10.7 (2.8 GHz) and the radio flux at 1.0 GHz, could be explored to serve as a solar activity proxy for thermosphere and ionosphere models in specific situations, such as when there is less reliance on decades of solar proxy measurements or particular requirements for temporal resolution and coverage. This consideration arises from the evidence that the radio flux at 1.0 GHz provides certain improvements over the F10.7 (Dudok de Wit et al., 2016; Dudok de Wit & Bruinsma, 2017).

Despite systematic biases (overestimating low solar flux activity and underestimating high solar flux activity) and higher coefficient of variation values, solar flux estimates are still generated even when the Sun is behind the antenna, and correlation with other solar activity proxies at the monthly scale is still very high (above 0.9). Back plane acquisitions remain crucial for SRB detection, as their lower accuracy is counterbalanced by the resulting greater availability of the monitoring.

Indeed, the high time resolution permits the detection of SRBs, allowing events to be characterized in terms of both solar flux intensity and degree of circular polarization. This unique information could prove valuable for GNSS systems, as SRB events with high right-handed DoCP are associated with signal fading and could provide insights into burst emission mechanisms (Flores-Soriano, 2024). Additionally, the low elevation angle threshold intrinsic to the current level 1 operational processor v724 will be overcome with the next operational version of the L1 processor foreseen into operation by the end of 2026, significantly increasing coverage during April, August, and September months when the Sun elevation angle in the antenna is low, and overall increasing data stability with the Sun elevation angle.

The SMOS-derived solar flux has the potential to complement established indicators and contribute to space weather applications and solar physics studies, benefiting from its intrinsic polarimetric properties, high cadence measurements, peculiar bandwidth, and a very stable over fifteen years-long timeseries with strong linear correlations with F10.7 and other solar activity proxies.

Future studies may investigate the quality of products generated with higher temporal resolution and extend the validation procedure to every polarimetric component of the L-band signal, to explore additional potential applications.

The SMOS solar flux dataset is publicly accessible on Zenodo. Details on the SMOS SRB algorithm detection and validation will be presented in a forthcoming paper currently under preparation.

Acknowledgments

We are very thankful to the students of the Space Science and Technology Master’s from the Tor Vergata University of Rome, whose master’s thesis contributed to developing the SMOS solar flux under the supervision of Prof. Francesco Berrilli: Emiliano Capolongo, Nicola Comparetti, Elisa Mantovani. We are very thankful to our colleagues of the Royal Observatory of Belgium: Christophe Marqué, Nicolas Bergeot, and Jean-Marie Chevalier for supporting the exploration of radio-telescopes datasets. Furthermore, we acknowledge the assistance of our former Serco colleagues, Daniele Casella (CNR-ISAC) and Alberto Bigazzi (ASI), for their valuable support during the initial phase of this research work.

We acknowledge the usage of colorschemes taken from the Red Blue Colormap function, available from the MATLAB^® Central File Exchange developed by Adam Auton (2025) (www.mathworks.com/matlabcentral/fileexchange/25536-red-blue-colormap), and the ColorBrewer: Attractive and Distinctive Colormaps 2.0 function accessed through the MATLAB^® Central File Exchange developed by Stephen Cobeldick (Stephen23, https://github.com/DrosteEffect/BrewerMap/releases/tag/3.2.8). The latter includes color specifications and designs developed by Cynthia Brewer (http://colorbrewer.org/), to be perceptually uniform to the eye. The editor thanks Martin Snow and an anonymous reviewer for their assistance in evaluating this paper.

Funding

This work is funded and supported by the ESA contract 4000130567/20/I-BG “Expert Support Laboratory for SMOS level 1 and level 2 over Land, Ocean and Ice”.

Conflicts of interest

The authors declare no conflicts of interest.

Data availability statement

The radio-telescopes’ data used for the validation were taken from different sources. The Nobeyama Radio Polarimeters (NoRP) are operated by Solar Science Observatory, a branch of National Astronomical Observatory of Japan, and their observing data are verified scientifically by the consortium for NoRP scientific operations. Data are downloaded from the webpage: https://solar.nro.nao.ac.jp/norp/data/daily/TYKW-NoRP_dailyflux.txt.

The Radio Solar Telescope Network (RSTN) are run by the United States Air Force. The Radio Interference Measuring Set (RIMS) noon flux radio data were accessed through the National Oceanic and Atmospheric Administration (NOAA) National Centers for Environmental Information (NCEI), as delivered in the daily Space Weather Indices available at https://www.ngdc.noaa.gov/stp/space-weather/swpc-products/daily_reports/space_weather_indices/.

The F10.7 index data used in this paper are provided by the Solar Radio Monitoring Program service operated by the National Research Council and Natural Resources Canada with support from the Canadian Space Agency. Data were accessed through the Space Weather Canada website at https://spaceweather.gc.ca/solar_flux_data/daily_flux_values/fluxtable.txt.

The Wolf sunspot number and the Mg II solar activity proxies were accessed from the LISIRD portal (https://lasp.colorado.edu/lisird/data). The results presented in this document rely on sunspot data from the World Data Center SILSO, Royal Observatory of Belgium, Brussels and are available at the World Data Center SILSO, Royal Observatory of Belgium website (https://www.sidc.be/SILSO/DATA/SN_d_tot_V2.0.txt). The Mg II solar activity proxy data are made available by the Institute of Environmental Physics (IUP) at the University of Bremen at https://www.iup.uni-bremen.de/gome/solar/MgII_composite.dat.

The SMOS L1B data are available from the ESA dissemination server at https://smos-diss.eo.esa.int/oads/access/collection/SMOS_Open_V7/tree. Finally, the solar flux generated using these data as input, documented in this paper, can be accessed through its dedicated Zenodo repository, freely available at https://doi.org/10.5281/zenodo.15275693.

References

All Tables

All Figures

	Figure 1 SMOS antenna field of View (FoV). Left panel: Schematic representation of the FoV and geometric configuration of SMOS antennae, as function of Sun position coordinates ξ and η. Image replicas reported in red. Right panel: SMOS image with the solar signal. This signal is removed by the L1 processor, and annotated in the L1B product. Image adapted from Camps et al. (2004).
In the text

	Figure 2 Solar flux (above) and LUT (below) generation pipelines. SMOS data are sorted according to the position of the Sun (in the back (B) or front (F) lobe of the antenna), and the polarization mode (horizontal (HH) or vertical (VV)). Each of these subsets is fully calibrated with a dedicated LUT.
In the text

	Figure 3 LUT coefficients across the antenna plane for equation (5). Multiplicative (m) and Additive (q) bias values by antenna plane position and polarization mode for Sun-in-the-front acquisitions, numeric values are featured in the color bar. Dashed lines identify points at the same elevation angle in radians.
In the text

	Figure 4 LUT coefficients across the antenna plane for equation (5). Multiplicative (m) and Additive (q) bias values by antenna plane position and polarization mode for Sun-in-the-back acquisitions, numeric values are featured in the color bar. Dashed lines identify points at the same elevation angle in radians.
In the text

	Figure 5 SMOS Sun BT and ground reference Sun BT ratio in the antenna’s front-plane before and after calibration. Comparison between fully calibrated and geometrically corrected data. (a) Horizontal polarization dataset (b) Vertical polarization dataset.
In the text

	Figure 6 SMOS Sun BT and ground reference Sun BT ratio in the antenna’s back-plane before and after calibration. Comparison between fully calibrated and geometrically corrected data. (a) Horizontal polarization dataset (b) Vertical polarization dataset.
In the text

	Figure 7 Histogram distribution of the coefficient of variation of the orbital dataset by antenna plane and polarization mode with average, median and mode values (avg, med, mod) of the full dataset.
In the text

	Figure 8 Precision of the solar flux datasets as a function of the solar flux in absolute and relative value.
In the text

	Figure 9 Fourier spectral analysis of F10.7 and SMOS daily values, distinguishing between SMOS back and front acquisitions. BSS has been applied to the daily data, and each component has further been analyzed.
In the text

	Figure 10 F10.7, composite RSTN, and SMOS (front) daily solar flux time-series over time. Low (left) and high (right) activity years zoomed overview are provided below.
In the text

	Figure 11 F10.7, composite RSTN, and SMOS (front) daily solar flux comparison. Left-most plots provide seasonal information with respect to the Sun-Earth distance correction. Yearly evolution is represented on the right. Pearson correlation coefficients between each pair and quadrant bisectors are reported on left-most plots.
In the text

	Figure 12 Nobeyama 1 GHz, composite RSTN, and SMOS (front) daily solar flux comparison. Left-most plots provide seasonal information with respect to the Sun-Earth distance correction. Yearly evolution is represented on the right. Pearson correlation coefficients between each pair and quadrant bisectors are reported on left-most plots.
In the text

	Figure 13 Monthly averages of SMOS and F10.7, Wolf sunspot number, and composite Mg II proxy of solar activity. Correlation coefficients (r) are reported in each panel using both Pearson and Spearman (in brackets) methods.
In the text

	Figure 14 Monthly Wolf sunspot number and SMOS (left panel) front-plane and F10.7 (right panel) solar flux fitting model according to Holland & Vaughan (1984) (black) compared to linear fitting (red).
In the text

	Figure 15 Monthly composite Mg II solar activity proxy and SMOS (left panel) front-plane and F10.7 (right panel) solar flux fitting model under linear (red) and quadratic (black) regression.
In the text

	Figure 16 SMOS SRB detections: solar flux intensity and DoCP. Left panel: SRB event from September 6th 2017. Right panel: SRB event from November 7th, 2022. RSTN references are plotted in red.
In the text