What to Do When the F10.7 Goes Out?

The solar radio flux at 10.7 cm, known as F10.7, is a critical operational space weather index. However, without a clear backup, any interruption to the service can result in substantial errors in model outputs. In this paper we show the impact of one such outage in March 2022 on the models TIE‐GCM and NeQuick, and present a number of alternative solutions that could be used for future outages. The analysis is extended to the F10.7 time series since 1951 and the approach resulting in the smallest reconstruction error of F10.7 uses the solar radio flux observations at alternative wavelengths (the best giving a percentage error of 3.1%). Alternatively, use of Sunspot Number, a regular, robust alternative observation, results in a mean percentage error of 8.2% and is also a reliable fallback solution. Additionally, analysis of the error on the use of the conversion between the 12‐month rolling sunspot number (R12) and its conversion to F10.7 is included.

Such an interruption occurred on 18 March 2022, when a cyberattack caused a network interruption at the NRC, which resulted in an F10.7 outage that lasted over a month. Without redundant systems, many critical space weather architectures suddenly become unavailable, or, perhaps worse, generate output using "default values" of F10.7 (e.g., an F10.7 of 100 sfu) which can also be used for forcings in forecasts, potentially producing substantial errors without suitable warnings. For example, both the International Reference Ionosphere (Bilitza et al., 2022) and the Empirical Canadian High Arctic Ionospheric Model (Themens et al., 2017) immediately revert to the use of NOAA long-term F10.7 forecasts if measured values are not available. On 18 March 2022, resorting to these forecasts constituted an immediate error of ∼14 sfu, increasing to an error of ∼70 sfu just 10 days later as an active region rotated onto the disk.
In this study we explore the impacts of having to mitigate the F10.7 interruption experienced in March 2022 using a number of methods and investigate their suitability as an F10.7 redundancy.

Models
In addition to DRAO in Canada, the other notable observatory which records solar radio flux is the Nobeyama Radio Observatory in Japan (previously recorded in Toyokawa from 1951(previously recorded in Toyokawa from to 1994, operated by the National Astronomical Observatory of Japan (https://solar.nro.nao.ac.jp/norp/), which makes continuous observations of flux densities at wavelengths of 30, 15, 8, and 3.2 cm (Tanaka et al., 1973). The 30 cm flux (from herein called F30) can be used by the Drag Temperature Model (DTM) and Dudok de Wit and Bruinsma (2017) argue that it is more sensitive than the 10.7 cm flux to longer wavelengths in the UV. Whilst the Nobeyama observatory does not observe the F10.7 flux density, which many space weather models require, the wavelengths measured can be used to generate a proxy for F10.7. A simple expression using just the observation at 15 cm (from herein called F15), which is the observation best correlated with the F10.7, can be found using non-linear least squares to low-order polynomials. For example, by fitting all available data, spanning November 1951 to November 2022, to a second-order polynomial, we find the following expression for adjusted F10.7 using F15: (1) This results in an average root mean square error, compared to the measured F10.7, of ∼7 sfu. This can be further reduced to ∼6 sfu using a more complicated expression that also incorporates F8 (solar flux at 8 cm wavelength): Both expressions enable a value of F10.7 to be used in case of an outage at the Penticton observatory, using observations from Nobeyama.
Additionally, the Collecte Localisation Satellites (CLS) group in France provide a routinely updated file (https:// spaceweather.cls.fr/services/radioflux/) of both the absolute observations and 1 AU corrected observations of F3.2, F8, F15, and F30. This file also contains the observed and interpolated values of F10.7, where an (undescribed) method is used to fill in missing or poor quality F10.7 flux data using measurements at the other solar flux wavelengths. It should be noted that since 1 May 2018, the F10.7 in the CLS database is entirely composed of interpolated values rather than measurements since they gather their F10.7 from the no longer supported NOAA repository which was last updated in May 2018.
More commonly used approaches to estimate F10.7, rather than using additional solar radio flux wavelengths, concern the sunspot number (SN) (Clette, 2021 One equation that was not presented in Clette (2021), which uses the 12-month running SN 1 (R12 1 ), is perhaps the most commonly used equation amongst all of them: This equation is used in both the International Reference Ionosphere (IRI) model (Bilitza et al., 2017) and NeQuick (Nava et al., 2008), as well as in a variety of other places. However, seemingly like the child's game "Telephone" a key term is often missing from Equation 4, F10.7 12 . The equation was designed as a relationship between R12 and the 12-month running mean of F10.7, F10.7 12 (now more commonly referred to as F10.7 365 ; the 365-day running mean) not as a relationship to F10.7 directly (Bilitza, 1990). When using the 12-month running mean of F10.7 the equation is part of the ITU-R Recommendation (ITU-R P. 1999). This misuse may be in part explained by the fact that the relationship in Equation 4 provides a slightly better fit (smaller standard deviation of errors) to the daily F10.7 than the equation specifically designed for that purpose (F10.7 CCIR = 23 −0.05 12 1 + R12 1 + 46 ) also given in Bilitza (1990).
It is important to note that Equation 4, is still used by the IRI and NeQuick, but must use SN 1 since the internal empirical relationships were developed with that version of the SN. However, SN 1 is no longer produced and the recorded values must be "converted" back to version 1. This should be done using the ratio where the 0.6 is due to the change of reference observer and the 1.177 is to offset an inflation factor in the original SN values since 1946 (Clette, 2021). The relationship between SN v2 and SN v1 is roughly linear, and more complex expressions do not significantly reduce the root mean square error (RMSE) between the version 2 and version 1 conversion of approximately 6.2 sunspots.
The use of Equation 4 is not a problem in NeQuick as users input an F10.7 value that is then converted to R12 v1 ; however in the IRI, both F10.7 and R12 v1 are required by various submodules (e.g., F10.7 used by , Shubin (2015), Fejer et al. (2008) and R12 v2 by Altadill et al. (2013) and Scotto et al. (1997) [for a complete list see Table 8 of Bilitza et al. (2022)]). Returning to our previous example of the behavior of the IRI during the March 2022 F10.7 interruption, one could attempt to mitigate the errors caused by the reversion to the NOAA F10.7 forecast by applying one of the many relationships above to determine a synthetic F10.7 that could be manually inputted with the model call. If the IRI is run with no specified options it will use R12 v2 , F10.7, the 81-day centered-mean of F10.7 (Richards et al., 2006) from its internal databases, convert R12 v2 to R12 v1 using Equation 5, and run the model. The 81-day mean F10.7 is used since the average of it with F10.7, PF10.7 = (F10.7 + F10.781)∕2 , correlates well with changes in EUV (Richards et al., 2006). However users can directly specify the daily and 81-day mean F10.7 and/or R12 v2 . If only one is provided then the other is calculated using Equations 4 and 5 (although noting that the IRI uses a value of 0.7 instead of 0.7062). This enables the IRI to mitigate against an F10.7 interruption through the use of R12 v2 ; however, this approach results in a mean absolute percentage error of 14.3% in specification of the F10.7, which is then used in the model; users should eliminate this error when driving the IRI with user inputs by passing both the R12 v2 and F10.7. However, users of IRI cannot manually provide F10.7 365 and the daily or 81-day value is used in its place and Equation 4 is assumed to hold for them. This is particularly problematic in the IRI if using "older" Sub-Models which require F10.7 365 such as that for the E-peak specification (Kouris & Muggleton, 1973) or ion composition Danilov & Yaichnikov, 1985). During an F10.7 outage, other methods, as we will show in the following section, can provide much greater performance than relying on the simple internal relationship to R12 v2 .

Results
During the outage, the observed F10.7 changed by over 50 flux units, an increase of more than 60%. To put this in context, the mean percentage change over a 30-day period is 31% (albeit with a standard deviation of 19%), meaning that the outage period in question is ∼1.5 standard deviations above the average variation that we would expect over such a period. To investigate the impact the replacements for F10.7 in upper atmosphere models, the Thermosphere Ionosphere Electrodynamics General Circulation Model (TIE-GCM; (Qian et al., 2014)) and NeQuick (Nava et al., 2008) has been driven with the observed F10.7 (adjusted to correct for the changing distance between the Earth and the Sun) until the outage on 18 March 2022, at which point each of the above F10.7 models have been used for the remaining runs of TIE-GCM and NeQuick. All other parameters are kept the same. TIE-GCM was run at 5° resolution, with a 30s model timestep and using the observed Kp. These have then been compared to a "true" run using the observed F10.7 values after the outage was fixed. The F10.7 replacement models are: 4. R12 v1 -The ITU-R recommendation for estimating F10.7 from R12 v1 as used by, amongst others, the IRI, Equation 4 5. Constant-The F10.7 is held at a constant value of 97.8 throughout the model run, the last observation before the outage started 6. 27-Day Rotation-The value from 27 days ago is assumed as the current value Figure 1 shows the global mean, absolute percentage error of the total electron content (TEC) in the ionosphere for the six different F10.7 replacement models, as previously described. Absolute percentage error (APE) is defined as: for an observation and truth time series of length . It is clear, and unsurprising, that the models based on closely-related other observation data, F15, F15, and F8 and Clette, do significantly better than the model based on R12 v1 , a constant value and the rotation model for both TIE-GCM and NeQuick. Note that TEC is usually defined as the path integral of electron density from ground to GNSS altitudes (∼20,000 km), however TIE-GCM only provides output to 500-700 km (depending on solar conditions; in this case the model lid is ∼615 km), and so the presented TECs are integrated from ground to 615 km for both TIE-GCM and NeQuick.
Overall both TIE-GCM and NeQuick respond very similarly to the different F10.7 models, with the TIE-GCM absolute percentage errors slightly larger than NeQuick. The largest error, from the R12 v1 method, is approximately 140% for TIE-GCM and 100% for NeQuick. For NeQuick the response in the model is immediate with changes in F10.7, for example, between March 24 and 28. However the TIE-GCM response to changes in F10.7 is delayed, by approximately 24-36 hr . Across the whole time period the model that uses either F15 alone (Equation 1) or both F15 and F8 (Equation 2) performs the best, slightly outperforming the Clette model at the beginning and end of the time period (with a similar performance between all three in the middle of the test period).
In contrast to Figure 1, which shows the overall global absolute percentage error in TEC, Figure 2 gives an example of the global TEC differences in TIE-GCM on March 27 at 1000, nine days after the outage began. It is still clear that the R12 v1 , Constant, and Rotation models give the largest errors, and all of the models have the largest errors around the equatorial anomaly, where TEC values are typically largest.
The results presented thus far only cover the specific outage period from March and April 2022. To perform a more rigorous study of the different approaches, the error statistics of the different F10.7 proxy models have been compared to the observed F10.7 over a 71-year period (from November 1951 to November 2022). In replacement of the "Constant" model used previously an additional model, the average F10.7 across the 71-year time interval (120 sfu) has been used. The overall error statistics shown in Table 1 are in line with the previous example, the models using additional solar flux observations at 15 cm (F15) and 8 cm (F8) wavelengths, and F15 alone, perform best, with a mean absolute percentage error of 3.13% and 3.73% respectively. The Clette model also performs very well with ∼8% error, followed by the Rotation, R12 v1 and the worse performing model (unsurprisingly) is the Average F10.7 model with a 38.5% error. Figure 3 shows a scatter plot comparing the five methods (excluding the "Average F10.7" model), overall each of the models have a strong linear correlation with the observations, with the R12 v1 model performing worst and the F15 and F8 model the best.

Conclusions
The solar radio flux at 10.7 cm, F10.7, is a critical index for space weather modeling and is one of the most commonly applied indices of solar activity used to drive both statistical and first principles models of the ionosphere and thermosphere. A number of operational systems rely on the F10.7; as such, a serious risk is posed by an interruption to the F10.7 data stream. Such an interruption occurred on 18 March 2022 when the F10.7 observations could not be made available due to a cyberattack. Without any clear, redundant system, models can stop working or can rely on default values (often without providing suitable warnings).  This paper has presented a number of proxy models for F10.7, based on flux densities at 15 and 8 cm, sunspot number, 12-month mean sunspot number, 27-day rotations and using a fixed value. The impact of the these different F10.7 proxy models on the physics-based upper atmosphere model TIE-GCM and the empirical NeQuick has been demonstrated. It has been shown using historic F10.7 observations since 1951 that the use of the average F10.7, 12-month mean sunspot number and the 27-day rotation in proxy models causes significant errors in estimating F10.7 (38.5%, 13.9%, and 11.6% respectively, in terms of absolute percentage error) and should be avoided in an operational setting if there is a loss of F10.7. The best performing proxy models rely on using additional wavelength observations at 15 and 8 cm, which can be used to reconstruct F10.7 with just a 3.1% error. Using the best fitting high-order polynomial fit of sunspot number (SN v2 ) to F10.7, as described by Clette (2021), results in an 8.2% error. Whilst this approach clearly performs worse, it has the advantage of being based on a robust observation, with recorded daily observations from 1818, making it a good choice as a redundant option for operational systems or in the backwards reconstruction of F10.7 for events prior to 1947.

Data Availability Statement
The F10.7 observations are recorded at the Dominion Radio Astrophysical Observatory, and freely provided to the space weather community with support from Natural Resources Canada. We are immensely grateful to them for their continued effort in providing this critical resource. The data daily and monthly and rotational averages can be downloaded from https://spaceweather.gc.ca/forecast-prevision/solar-solaire/solarflux/sx-5-en.php. The raw Nobeyama observations of F30, F15, F8 and F3.2 are available from https://solar.nro.nao.ac.jp/norp/data/ daily/. Flare corrected, and Sun-Earth distance adjusted values are provided by Collecte Localisation Satellites (CLS) available from ftp://ftpsedr.cls.fr/pub/previsol/solarflux/observation/radio_flux_adjusted_observation.txt. Finally, the daily Sunspot Number is provided by WDC-SILSO, Royal Observatory of Belgium, Brussels, and can be downloaded from https://www.sidc.be/silso/DATA/EISN/EISN_current.csv.