# Study of an Atmospheric Refractivity Estimation from a Clutter Using Genetic Algorithm
## 2 Calculation of Clutter Power Spectrums  
Figure 1 presents the propagation of the electromagnetic wave of the shipborne radar systems according to atmospheric conditions, including normal, sub, super, and duct. The atmospheric conditions are classified by the gradient of modified refractive index \(M\) in terms of the altitudes. The modified refractive index \(M\) can be calculated using the following equation [26]:  
\[N=\left(77.6\times 10^{-6}\times\frac{P}{T}+0.373\times\frac{e}{T^{2}}\right) \times 10^{6} \tag{1}\]  
\[M=N+0.157\times h \tag{2}\]  
where \(N\) is the refractive index, \(P\) is the air pressure in millibars, \(e\) is the water vapor pressure in millibars, and \(T\) is the absolute temperature in \(K\). The refractivity of \(N\) is replaced by the modified refractivity of \(M\) to take into consideration the Earth's curvature according to altitude \(h\). Normal refraction occurs when the gradient of the refractivity is \(78\leq\
abla M\leq 157\), which indicates good conditions for radar systems to search for a target. However, when the \(\
abla M\) is greater (sub, \(\
abla M>157\)) or less (super, \(0<\
abla M<78\)) than the normal state, shipborne radar systems find it difficult to observe the exact distance and altitude of the targets due to abnormal refraction of the radio waves. Moreover, in the duct condition (\(\
abla M<0\)), the wave propagation of the radar signal is trapped as if in a waveguide. Therefore, it is important to be able to anticipate atmospheric refractivity to prevent degradation of radar performance depending on the atmospheric conditions. Figure 2 shows the observation area and scan range for obtaining the clutter power spectrum. In our analysis, the shipborne radar is located near Wando, which illuminates the north direction with a scan range of 20\({}^{\circ}\) (\(\varphi\) = 80\({}^{\circ}\)-100\({}^{\circ}\)) to obtain the clutter power spectrums from both the land and sea. Herein, the sea clutter powers are significantly affected by the sea wave height, whereas the land clutter powers do not change substantially as long as the atmospheric environment remains constant. Thus, when the radar obtains the clutter powers by illuminating not only the sea but also the land, atmospheric refractivity can be predicted more accurately. Figure 3 presents the measured atmospheric refractivity data when atmospheric conditions are duct or normal. These data were measured at different times in the Heuksando Meteorological Observatory [27], which is the closest meteorological station to Wando. In this measurement data, Case 5 is the normal condition, whereas Cases 1, 2, 3, and 4 represent duct conditions with duct slopes (\(\
abla M\)) of \(-121\), \(-159\), \(-121\), and \(-151\), respectively. Figure 4 illustrates the propagation factor according to different atmospheric conditions with the measurement data of Case 1 (normal) and Case 2 (duct). The solid black lines indicate the height of the terrain around Wando, and the terrain data are obtained from the NASA earth data center [28]. In this simulation, the radar height is assumed to be 30 m, and the observation range and altitude are 0 to 100 km and 0 to 1000 m, respectively. When the atmospheric condition is normal, radar wave propagation is disturbed by the high topography, so the shaded areas are clearly observed, as shown in Figure 4a. In contrast, when ducting occurs, a strong propagation factor is observed even behind the high terrain. The result means that the radar can have completely different propagation paths depending on the atmospheric conditions. Figure 1: Wave propagation of the shipborne radar according to atmospheric conditions. Figure 2: Observation area and scan range of the shipborne radar systems. Figure 5 shows the clutter power spectrum according to the atmospheric conditions.