# Solar Extreme and Far Ultraviolet Radiation Modeling for Aeronomic Calculations
## 3 Results
### Fluvt Model  
For the analysis, we used the daily average data of measurements of the FUV with the SORCE/SOLSTICE apparatus [30] in the 115-242 nm region from the LISIRD database [31]. Measurements corresponding to more than 5500 dates were considered. The web address of the database is [[http://lasp.colorado.edu/lisird/](http://lasp.colorado.edu/lisird/)]([http://lasp.colorado.edu/lisird/](http://lasp.colorado.edu/lisird/)), accessed on 2 March 2021. The dependence of the photon fluxes in different spectral intervals on the flux in the L\(\alpha\) line was studied at different levels of solar activity. The analysis showed that at all levels of activity, the dependence for any wavelength is close to linear. Examples of analysis results are shown in Figure 4 for two wavelength ranges: 130-131 nm and 200-201 nm, located at the edges of the studied FUV interval.  
Figure 3: Comparison of the calculated values of the radiation intensity in the 30.4 nm line with the observed ones.  
The figure shows that the deviations of the measurement data from the approximating straight lines are small and do not exceed a few percent. The analysis shows that approximation using higher order polynomials does not lead to any noticeable decrease in the approximation error.  
The straight lines in the figure correspond to the linear regression equation  
\[\mathrm{N}_{\lambda}=10^{15}\left(\mathrm{B0}_{\lambda}+\mathrm{B1}\lambda \cdot\mathrm{N}_{\mathrm{L}\alpha}\right), \tag{5}\]  
where \(\mathrm{N}_{\lambda}\) is in units of \(\mathrm{m}^{-2}\mathrm{s}^{-1}\), and \(\mathrm{N}_{\mathrm{L}\alpha}\) is the photon flux in the Lyman-alpha line in units of \(10^{15}\)\(\mathrm{m}^{-2}\mathrm{s}^{-1}\). The figure shows that the deviations from the regression lines are small and do not exceed a few percent at any level of solar activity. The average deviation \(\varepsilon\) of the measurement data from the results of the calculation according to the Equation (5) was estimated according to (4). The analysis shows that, when using linear regression, the error \(\varepsilon\) for all wavelengths does not exceed 2.1%, and the average value of \(\varepsilon\) over the wavelengths is \(\sim\)0.8%.  
Relation (5) together with the coefficients \(\mathrm{B0}_{\lambda}\) and \(\mathrm{B1}_{\lambda}\) included in it constitutes the FUVT radiation model. Regression coefficients are determined using standard statistical analysis procedures and are shown in Table 2 for all wavelength intervals \(\lambda\).  
Figure 4: Dependence of photon fluxes in the interval 130–131 nm (dots) and 200–201 nm (circles) on the flux in the Lyman-alpha line.  
It should be noted that earlier the procedure for determining the coefficients of the FUV model was carried out using the previous version of the L\(\alpha\) time series [32]. The values in Table 2 correspond to the latest version of the composite L\(\alpha\).  
The model was verified using measurement data with TIMED/SEE equipment, the calibration of which, as well as methods for eliminating degradation effects, are similar to those used in SORCE/SOLSTICE equipment (see, for example, [24, 25]). Figure 5 shows the comparison of model calculations results with TIMED measurements for epochs of maximum and minimum solar activity in solar cycle 23.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \(\lambda_{\star}\)**nm** & **B0\({}_{\lambda}\)** & **B1\({}_{\lambda}\)** & **\(\lambda_{\star}\)nm** & **B0\  
It can be seen that for the entire wavelength range of 115-190 nm, the results of model calculations practically coincide with measurements at both high and low solar activity. It should be noted that the level of high activity falls on the period when measurements at the SORCE, according to which the model has been developed, have not yet been carried out. It can be assumed that the model adequately describes the changes in the FUV spectrum at any level of solar activity and in any solar cycle.