# A High Latitude Model for the E Layer Dominated Ionosphere
## 4 Modeling Results
### NEEM-N: Model for the E Layer Peak Ionization  
Equation (3) is the model equation for the peak ionization \(NmE\) of the E layer. The model term accounting for the geomagnetic latitude is based on a Gaussian function. The terms representing the local time and day of year dependencies are given by two \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Interval Index** & **LT** & **DOY** & **F10.7** \\ \hline
1 & [0.0–12.0) & [1–122] & [60–90] \\
2 & [12.0–24.0) & [123–244] & [90–160] \\
3 & & [245–366] & [160–250] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Example interval division for the model drivers LT, DOY and F10.7. superposed cosine functions each, while the dependencies on the solar activity and on the convection electric field magnitude are given by linear functions. Table 2 shows the associated internal and external coefficients for both hemispheres computed as described in Section 3.2. The internal coefficients are given by the phase shift \(MLAT_{0}\) and the standard deviation \(\sigma_{MLAT}\) for the geomagnetic latitude, by the phase shifts \(LT_{D}\) and \(LT_{SD}\) for the diurnal and semidiurnal variations, and by the phase shifts \(DOY_{A}\) and \(DOY_{SA}\) for the annual and semiannual variations. The external coefficients of the equation consist of the amplitudes \(c_{1}\),..., \(c_{7}\) and the bias \(c_{8}\). \[ \begin{split}& NmE(MLAT,\;LT,\;DOY,\;F10.7,F_{Conv})=\\ &\left(c_{1}\cdot\exp\!\left(-\frac{(MLAT-MLAT_{0})^{2}}{2\cdot \sigma_{MLAT}}^{2}\right)+1\right)\\ &\left(\;c_{2}\cdot\cos\!\left(2\pi\cdot\frac{1}{24}\!\cdot\!(LT- LT_{D})\right)+c_{3}\cdot\cos\!\left(2\pi\cdot\frac{2}{24}\!\cdot\!(LT-LT_{SD}) \right)+1\right)\\ &\left(\;c_{4}\cdot\cos\!\left(2\pi\cdot\frac{1}{365.25}\!\cdot\! (DOY-DOY_{A})\right)+c_{5}\cdot\cos\!\left(2\pi\cdot\frac{2}{365.25}\!\cdot\! (DOY-DOY_{SA})\right)+1\right)\\ &\left(c_{6}\cdot F10.7+1\right)\\ &\left(c_{7}\cdot E_{Conv}+c_{8}\right)\end{split}  \tag{3}\]  
In Figure 2, we plot two trends for each hemisphere and each dependency of \(NmE\) on one of the model drivers. One of these trends results from binning the originally observed \(NmE\) values (red), whereas the other is based on binning the \(NmE\) values predicted by our model (black). To highlight the symmetry between the observed trends for the Northern and Southern Hemispheres, in the case of \(MLAT\), we generally plot them depending on the absolute value of the geomagnetic latitude. All the trends are supplemented by error bars indicating the standard deviations of the underlying \(NmE\) values within each bin. In the last row of the figure, we report the root mean square deviation (RMS) between the observed and the predicted \(NmE\) values, averaged for all the dependencies of the respective hemisphere. The normalized root mean square deviation (NRMS) describes the RMS normalized by the mean of the originally observed \(NmE\) values. To estimate which model driver causes the largest variation of the observed \(NmE\), we computed the range of each observed \(NmE\) trend and then determined the model driver that corresponds to the largest range. In this regard, the range of a considered trend was computed as the absolute value of the difference between its maximum and minimum \(NmE\) values.