# A High Latitude Model for the E Layer Dominated Ionosphere
## 4 Modeling Results
### NEEM-N: Model for the E Layer Peak Ionization
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{4}{c}{**NmE Model Coefficients North**} & \multicolumn{4}{c}{**NmE Model Coefficients South**} \\ \hline  & **Internal** & \multicolumn{4}{c}{**External**} & \multicolumn{2}{c}{**Internal**} & \multicolumn{2}{c}{**External**} \\ \hline \(MLAT_{0}\) & = & 67.49\({}^{\circ}\) & \(c_{1}\) & = & \(1.07\times 10^{-1}\) & \(MLAT_{0}\) & = & \(-69.03^{\circ}\) & \(c_{1}\) & = & \(6.00\times 10^{1}\) \\ \(\sigma_{MLAT}\) & = & 3.39\({}^{\circ}\) & \(c_{2}\) & = & \(-8.01\times 10^{-2}\) & \(\sigma_{MLAT}\) & = & \(377.96^{\circ}\) & \(c_{2}\) & = & \(1.63\times 10^{-2}\) \\ \(LT_{D}\) & = & 2.94 h & \(c_{3}\) & = & \(6.58\times 10^{-2}\) & \(LT_{D}\) & = & \(6.36\) h & \(c_{3}\) & = & \(5.80\times 10^{-2}\) \\ \(LT_{SD}\) & = & \(-2.36\) h & \(c_{4}\) & = & \(1.92\times 10^{-1}\) & \(LT_{SD}\) & = & \(-1.09\) h & \(c_{4}\) & = & \(-2.50\times 10^{-1}\) \\ \(DOY_{A}\) & = & 165.58 d & \(c_{5}\) & = & \(-6.08\times 10^{-3}\) & \(DOY_{A}\) & = & \(166.77\) d & \(c_{5}\) & = & \(2.45\times 10^{-2}\) \\ \(DOY_{SA}\) & = & \(-113.12\) d & \(c_{6}\) & = & \(7.83\times 10^{-3}\) & \(DOY_{SA}\) & = & \(-70.53\) d & \(c_{6}\) & = & \(-1.07\times 10^{3}\) \\  & & & \(c_{7}\) & = & \(3.80\times 10^{0}\) & & & \(c_{7}\) & = & \(-7.84\times 10^{-7}\) \\  & & & \(c_{8}\) & = & \(8.20\times 10^{4}\) & & & \(c_{8}\) & = & \(-2.19\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coefficients of the E layer peak electron density (NmE) model for the Northern and Southern Hemispheres. As can be seen in the plots of Figure 2, \(NmE\) shows its maximum between 65\({}^{\circ}\) and 70\({}^{\circ}\)\(MLAT\), which is in the main region of the auroral precipitation zone. Furthermore, in local summer and for increased solar activity, the enhanced solar EUV irradiance causes an increased ionization of the entire ionosphere and, thus, also of the E layer. The dependency on \(LT\) shows basically a semidiurnal variation. For an enhanced convection electric field, we observe an increase in the peak ionization of the E layer. This observation could be explained by the fact that the convection electric field magnitude is a measure for the degree of magnetosphere-ionosphere coupling. Its increase indicates an enhanced particle precipitation and, therefore, increased \(NmE\). For both hemispheres, the range of the observed \(NmE\) is largest depending on \(DOY\) (north: 81,000 cm\({}^{-3}\), south: 66,400 cm\({}^{-3}\)). Figure 2: Observed (red) and predicted (black) NmE trends for the modeling dataset. Left column: Northern Hemisphere. Right column: Southern Hemisphere. Last row: root mean square deviation (RMS) and normalized RMS (NRMS) between observation and prediction. Since \(NmE\) determines the critical frequency of the ionosphere in the case of an ELDI event, this quantity is relevant for terrestrial radio wave propagation at high latitudes. As we see in the results, the modelled values of \(NmE\) may reach up to about \(2\times 10^{5}\) cm\({}^{-3}\) at both hemispheres, which corresponds to a critical frequency of about 4 MHz. Considering the derived RMS values, the critical frequency may reach 6 MHz during an ELDI event within this variability range.