# A High Latitude Model for the E Layer Dominated Ionosphere
## 4 Modeling Results
### NEEM-H: Model for the E Layer Peak Height  
The propagation of HF radio waves also depends on the height of the reflecting layer. In this regard, below, we show the model equation (Equation (4)) and its corresponding coefficients (Table 3) for the peak height \(hmE\) of the E layer. Figure 3 shows the related trends and the RMS values for the peak height. Since we found only a negligible variation of \(hmE\) depending on the convection electric field magnitude in the initial trend analysis, this quantity is not considered as a driver in the model equation.  
\[\begin{split}& hmE(MLAT,\;LT,\;DOY,\;F10.7)=\\ &(c_{1}\cdot\exp\left(-\frac{(MLAT-MLAT_{0})^{2}}{2\cdot\sigma_{ MLAT}}\right)+1)\\ &\left(c_{2}\cdot\cos\left(2\pi\cdot\frac{1}{24}\cdot(LT-LT_{D}) \right)+c_{3}\cdot\cos\left(2\pi\cdot\frac{2}{24}\cdot(LT-LT_{SD})\right)+1 \right)\\ &\left(c_{4}\cdot\cos\left(2\pi\cdot\frac{1}{365.25}\cdot(DOY-DOY_ {A})\right)+c_{5}\cdot\cos\left(2\pi\cdot\frac{2}{365.25}\cdot(DOY-DOY_{SA}) \right)+1\right)\\ &(c_{6}\cdot F10.7+c_{7})\end{split} \tag{4}\]  
As expected, the height \(hmE\) of the E layer is rather stable, varying between about 105 and 112 km for both hemispheres, with the RMS values being extended by about 7 km. These observations fit well with those of [PERSON] et al. (2010). They found that at the EISCAT site (69.9\({}^{\circ}\)N), which is located inside the auroral oval for most of the time, \(hmE\) was about 114 km for the majority of ELDI events. At the ESR site (78\({}^{\circ}\)N), which is mostly located outside the auroral oval, this value was around 108 km. The plots presenting the dependencies of \(hmE\) on \(MLAT\) show a maximum \(hmE\) in the latitude range between 65\({}^{\circ}\) and 70\({}^{\circ}\), indicating the location of the auroral zone. Regarding the dependency on the local time, a minimum \(hmE\) can be found around 8:00 to 12:00 LT. In contrast, the dependency on \(DOY\) shows only a minor semiannual variation. Furthermore, we find that \(hmE\) increases slightly for increasing \(F10.7\). This effect could be explained by the higher amount of EUV irradiance and enhanced heating for increasing \(F10.7\), which causes an expansion of the upper atmospheric layers in general. For both hemispheres, the range of the observed \(hmE\) is largest depending on \(LT\) (north: 7.9 km, south: 6.4 km).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \multicolumn{3}{c}{**hmE Model Coefficients North**} & \multicolumn{3}{c}{**hmE Model Coefficients South**} \\ \hline  & **Internal** & & **External** & & **Internal** & & **External** \\ \hline \(MLAT_{0}\) & = & 69.15\({}^{\circ}\) & \(c_{I}\) & = & \(1.16\times 10^{-1}\) & \(MLAT_{0}\) & = & \(-69.41^{\circ}\) & \(c_{I}\) & = & \(-1.01\times 10^{0}\) \\ \(\sigma_{MLAT}\) & = & 10.82\({}^{\circ}\) & \(c_{2}\) & = & \(2.73\times 10^{-2}\) & \(\sigma_{MLAT}\) & = & \(569.19^{\circ}\) & \(c_{2}\) & = & \(2.12\times 10^{-2}\) \\ \(LT_{D}\) & = & \(-3.71\) h & \(c_{3}\) & = & \(-7.94\times 10^{-3}\) & \(LT_{D}\) & = & \(-1.12\) h & \(c_{3}\) & = & \(2.08\times 10^{-3}\) \\ \(LT_{SD}\) & = & \(-1.79\) h & \(c_{4}\) & = & \(-7.22\times 10^{-3}\) & \(LT_{SD}\) & = & \(-2.27\) h & \(c_{4}\) & = & \(-1.78\times 10^{-4}\) \\ \(DOY_{A}\) & = & \(-171.11\) d & \(c_{5}\) & = & \(4.33\times 10^{-3}\) & \(DOY_{A}\) & = & \(-175.39\) d & \(c_{5}\) & = & \(5.07\times 10^{-3}\) \\ \(DOY_{SA}\) & = & \(-110.35\) d & \(c_{6}\) & = & \(3.25\times 10^{-2}\) & \(DOY_{SA}\) & = & \(-90.90\) d & \(c_{6}\) & = & \(-3.33\times 10^{0}\) \\  & & & \(c_{7}\) & = & \(9.71\times 10^{1}\) & & & \(c_{7}\) & = & \(-1.41\times 10^{4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Coefficients of the E layer peak height (hmE) model for the Northern and Southern Hemispheres.