# Study of an Atmospheric Refractivity Estimation from a Clutter Using Genetic Algorithm
## 3 Estimation of an Atmospheric Refractivity  
Figure 6 shows the shape of the tri-linear model for the atmospheric refractivity estimation method. The artificial tri-linear model consists of three lines with slopes \(d_{1}\), \(d_{2}\), and \(d_{3}\). In addition, the boundaries between the three lines are determined by \(h_{1}\) and \(h_{2}\). Since the slope of the tri-linear model can be changed to negative or positive values, the tri-linear model can express most atmospheric conditions, including normal, super, sub, and duct. Therefore, the tri-linear model can be utilized as an approximate atmospheric refractivity model in refractivity estimation methods. Figure 7 presents the flow chart of the use of the GA algorithm [17, 18] to predict the atmospheric refractivity from the clutter power spectrums. To predict the atmospheric refractivity, a random chromosome is first generated, and then the decoded values from the chromosome are applied to the variables of the tri-linear model. The tri-linear model is used as input to the AREPS EM propagation simulator to calculate the clutter power spectrum. At the same time, the clutter power spectrums are again obtained based on the measured atmospheric refractivity data introduced in Figure 3 using the AREPS simulator. In actual operation, this spectrum of measured reflectivity can be replaced with real-time clutter spectrums collected from radars. Herein, the cost function for the GA is then defined based on the difference between the two calculated clutter power spectrums. In the GA process, the variables of the tri-linear model are adjusted to minimize the cost through the reproduction process. Consequently, the optimum variables of the tri-linear model are  
Figure 5: Clutter power spectrums according to atmospheric conditions: (**a**) using the measured data of Case 1; (**b**) using the measured data of Case 2. Figure 6: The shape of the tri-linear model. determined at a minimum cost in the GA, which means that the estimated atmospheric conditions have been obtained. The GA parameters, such as population size, generations, and mutation ratio, are listed in Table 1.  
Figure 8 provides a comparison of the estimated and measured atmospheric refractivity data based on the clutter powers. Estimation is conducted for the measured data in Figure 3, and the duct slopes and duct thickness of the estimated and measured values are summarized in Table 2. Based on the results shown in Table 2, the estimation errors for the duct slopes and duct thickness are maintained at below 46.1 and 36, respectively. For Case 3, the atmospheric refractivity can estimate with estimation errors for the duct slopes and duct thickness of 29 and 24, respectively. This estimation result of the best case is compared with other studies in Table 3. The results demonstrate that the atmospheric refractivity can be predicted from clutter powers using the proposed method. The proposed method is suitable for actual radar systems because it is possible to obtain more consistent prediction results by analyzing clutter, including land terrain, when operating the actual radar. \begin{table}
\begin{tabular}{c c} \hline \hline
**Option** & **Value** \\ \hline Population size & 30 \\ Generations & 15 \\ Elite count & 6 \\ Crossover ratio & 40\% \\ Mutation ratio & 10\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detailed information of the GA. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & \begin{tabular}{c} **Duct Slopes** \\ **(Esti.)** \\ \end{tabular} & \begin{tabular}{c} **Duct Slopes** \\ **(Mea.)** \\ \end{tabular} & \
\begin{tabular}{c} **Duct Thickness** \\ **(Esti.)** \\ \end{tabular} &
\begin{tabular}{c} **Duct Thickness** \\ **(Mea.)** \\ \end{tabular} \\ \hline Case 2 & \(-74.9\) & \(-121\) & 231 & 200 \\ Case 3 & \(-187.5\) & \(-158.5\) & 176 & 200 \\ Case 4 & \(-168.7\) & \(-121\) & 181.5 & 200 \\ Case 5 & \(-194.3\) & \(-151\) & 264 & 300 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of all estimation results.