## 3 Results
The observed differences can be characterized as relatively small, since the primary spectrum model used as input for the respective computations provided the estimation of the galactic component and did not take into account any SEPs which took place during this time period. \begin{table}
\begin{tabular}{c} **Maximum** \\ **Values** \\ \end{tabular} \\ \hline
1996 (SC23 min) & 3.6 & 12.0 & 1.22 & 6.83 \\
2009 (SC24 min) & 3.7 & 13.6 & 1.24 & 7.05 \\
2001 (SC23 max) & 3.4 & 9.1 & 1.18 & 5.49 \\
2014 (SC24 max) & 3.5 & 11.0 & 1.19 & 5.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Minimum and maximum values of CRII and the estimated ambient dose equivalent rate during the minimum and maximum of solar cycles 23 and 24 at FL390. Figure 2: _Cont._  
Time profiles of the yearly values of the CRII and the ambient dose equivalent rate from the year 1996 to the year 2019 (covering the last two solar cycles) are presented in Figures 3 and 4. Four different geomagnetic cut-off rigidity values were selected: 0.1 GV for the polar region (Figure 3a), 3.1 GV (Figure 3b), 8.5 GV, which corresponded to the middle geographic latitudes and specifically Athens, Greece (Figure 4a) and 14.9 GV for the equatorial region (Figure 4b). The results are provided for the three different atmospheric altitudes which corresponded to the usual flight levels of the commercial aircraft: FL310 (9.45 km a.s.l. ), FL350 (10.67 km a.s.l.) and FL390 (11.89 km a.s.l.). The CRII and dH*(10)/dt values for this time period and for all flight levels can be found in the Supplementary Material. It is interesting that both the CRII (left axis, blue lines) and ambient dose equivalent rate (right axis, red lines) followed a long-term modulation, specifically an 11-year one, at all the aforementioned locations, the same way the GCR intensity did [59; 60; 61], since the radiation exposure of aircraft crews was directly linked to the intensity of the cosmic radiation. Furthermore, comparing the time profiles of the three different FLs, it is obvious that the higher the aircraft flew, the higher the CRII and the estimated ambient dose equivalent rates were, since the shielding effect of the atmosphere was reduced and thus the radiation exposure of the aircrew and frequent flyers was higher. It was also observed that the difference among the values at the three FLs was greater as one reached lower rigidities, e.g., polar regions, and became smaller as one reached higher rigidities, e.g., equatorial regions. Since the magnetic field was weaker and more permeable in the polar regions, it allowed even primary cosmic ray particles of lower energies to reach the surface of the Earth, resulting in higher levels of cosmic radiation, unlike in the lower  
Figure 2: Maps of the estimated ambient dose equivalent rate (uSv/h) at FL390: **(a)** during the minimum of solar cycle 23; **(b)** during the maximum of solar cycle 23; **(c)** during the minimum of solar cycle 24; **(d)** during the maximum of solar cycle 24.  
geographic latitudes where the magnetic lines were almost parallel to the Earth's surface, and therefore provided effective shielding. Concerning the CRII, once again, it is noted that during all phases of solar cycle 24, which was a less active solar cycle, the values were greater than those of the respective phases of solar cycle 23, when the solar activity was intense. However, this difference became very small as we moved towards the equatorial regions, which showed that the solar activity mostly affected low-rigidity regions. More precisely, the CRII decreased by 5.6% near the poles and 24.2% near the equator during SC23 and by 5.4% and 19.1% during SC24, respectively. Similarly, the dependence of the dH*(10)/dt on the solar cycle was most evident near the poles (Rc = 0.1 GV) and, to a lesser extent, near the equator (Rc = 14.9 GV), due to the geomagnetic field shielding, which reflected particles of lower energies.