# A High Latitude Model for the E Layer Dominated Ionosphere
## 4 Modeling Results
### NEEM-W: Model for the E Layer Vertical Profile Width  
As follows, we introduce the model equation (Equation (5)) and its related coefficients (Table 4) for the vertical profile width \(wvE\) of the E layer. The corresponding trends and the RMS are given in Figure 4.  
Figure 3: Observed (red) and predicted (black) hmE trends for the modeling dataset. Left column: Northern Hemisphere. Right column: Southern Hemisphere. Last row: RMS and NRMS deviation between observation and prediction.  
\[\begin{split}& wvE(MLAT,\,LT,\,DOY,\,F10.7)=\\ &(c_{1}\cdot\exp\biggl{(}-\frac{(MLAT-MLAT_{0})^{2}}{2\cdot\sigma_{ MLAT}^{2}}\biggr{)}+1)\\ &\Bigl{(}c_{2}\cdot\cos\bigl{(}2\pi\cdot\frac{1}{24}\cdot(LT-LT_{D}) \bigr{)}+c_{3}\cdot\cos\bigl{(}2\pi\cdot\frac{2}{24}\cdot(LT-LT_{SD})\bigr{)}+ 1\Bigr{)}\\ &\Bigl{(}c_{4}\cdot\cos\Bigl{(}2\pi\cdot\frac{1}{363.25}\cdot(DOY -DOY_{A})\Bigr{)}+c_{5}\cdot\cos\bigl{(}2\pi\cdot\frac{2}{365.25}\cdot(DOY- DOY_{SA})\bigr{)}+1\Bigr{)}\\ &(c_{6}\cdot F10.7+c_{7})\end{split} \tag{5}\]  
As we can see from the plots, the average width of the E layer generally varies between about 15 and 21 km for both hemispheres. This value range is also in the order of magnitude of the E layer thickness observed by [PERSON] et al. [10], who defined this parameter in a similar way to our E layer profile width. They found that at the ESR site, the E layer thickness was about 17 km for most of the EDI events, while it was about 23 km at the EISCAT site. These observed magnitude ranges are quite different from the sporadic E layer thickness of up to 2 km at mid-latitudes [11; 12; 13]. It is interesting to note that the trends show a decrease in \(wvE\) for increasing geomagnetic latitudes. Furthermore, we see a slight enhancement of \(wvE\) around local noon and with increasing solar activity. The \(DOY\) dependency shows a minor semidiurnal variation. For both hemispheres, the range of the observed \(wvE\) is largest depending on \(MLAT\) (north: 5.4 km, south: 4.6 km).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multicolumn{6}{c}{**wvE Model Coefficients North**} & \multicolumn{6}{c}{**wvE Model Coefficients South**} \\ \hline  & **Internal** & \multicolumn{3}{c}{**External**} & \multicolumn{3}{c}{**Internal**} & \multicolumn{3}{c}{**External**} \\ \hline \(MLAT_{0}\) & = & 58.03\({}^{\circ}\) & \(c_{1}\) & = & \(2.84\times 10^{-1}\) & \(MLAT_{0}\) & = & \(-57.66^{\circ}\) & \(c_{1}\) & = & \(2.27\times 10^{-1}\) \\ \(\sigma_{MLAT}\) & = & 4.55\({}^{\circ}\) & \(c_{2}\) & = & \(1.03\times 10^{-1}\) & \(\sigma_{MLAT}\) & = & \(2.53^{\circ}\) & \(c_{2}\) & = & \(8.57\times 10^{-2}\) \\ \(LT_{D}\) & = & 11.70 h & \(c_{3}\) & = & \(-2.68\times 10^{-2}\) & \(LT_{D}\) & = & \(-11.15\) h & \(c_{3}\) & = & \(4.39\times 10^{-3}\) \\ \(LT_{SD}\) & = & 4.87 h & \(c_{4}\) & = & \(7.44\times 10^{-3}\) & \(LT_{SD}\) & = & \(-6.24\) h & \(c_{4}\) & = & \(-2.96\times 10^{-4}\) \\ \(DOY_{A}\) & = & \(-107.25\) d & \(c_{5}\) & = & \(1.36\times 10^{-2}\) & \(DOY_{A}\) & = & \(177.46\) d & \(c_{5}\) & = & \(3.41\times 10^{-2}\) \\ \(DOY_{SA}\) & = & \(-81.82\) d & \(c_{6}\) & = & \(4.02\times 10^{-2}\) & \(DOY_{SA}\) & = & \(-80.45\) d & \(c_{6}\) & = & \(3.36\times 10^{-2}\) \\  & & \(c_{7}\) & = & \(1.45\times 10^{1}\) & & & & \(c_{7}\) & = & \(1.49\times 10^{1}\) \\ \hline \end{tabular}
\end{table}
Table 4: Coefficients of the E layer vertical profile width (wvE) model for the Northern and Southern Hemispheres.