## 1 Introduction  
The dramatic advances in long-range radar technologies have resulted in various functional radar applications, such as synthetic aperture radars (SARs) [1, 2, 3], airborne weather radars (AWRs) [4], terrain-following radars (TFRs) [5], and airborne early warning radars (AEWs) [6, 7]. Such radars are usually used to collect a variety of information from the air or from the ground, including weather conditions, storms, volcanoes, target ranges, target movements, and terrain images. In recent years, inverse synthetic aperture radars (ISARs) have been used for space surveillance to ensure the stability and safety of the space environment [8]. Excellent range resolution to display the outline of aircraft and vehicles is achieved using surface movement radars (SMRs) [9]. However, as the attenuation increases, the high resolution of the SAR image and the range resolution of the target distance can no longer be achieved [10, 11]. Moreover, the radio wave radiation from the radar is attenuated by external environmental factors, such as rain scattering, lightning discharges,anthropogenic noise, multi-path effects, clutters, atmospheric gases, and refraction, which can significantly distort the collected information [12; 13; 14; 15; 16]. In particular, the direction of wave propagation for the long-range radar is significantly influenced by the atmospheric refraction, which is mostly caused by the atmospheric conditions, including air pressure, temperature, and relative humidity [17]. These atmospheric conditions can be modeled with the refractive index along the altitude [18]. Then, the wave propagation direction of the long-range radar is bent due to vertical variations in the atmospheric refractive index. These are often classified into four types: sub, super, normal, and duct [19]. Thus, various research studies on modeling the atmospheric refractive index have been conducted by using the sparse measured meteorological data of the atmospheric conditions; observing the global positioning system, phase delay, and path loss [20]; interpolating an observation-based refraction index employing the two-dimensional cubic-polynomial method [21]; and using trilinear lines at the low altitude [22]. In addition, the wave propagation characteristics, including the atmospheric refractive effects, have also been investigated in order to observe the path loss around coastal areas in many countries, i.e., the United States, Australia, China, and United Arab Emirates (UAE) [23; 24; 25; 26]. These studies present an accurate estimation of the refractive index at low altitude and a proper analysis of wave propagation characteristics below the ultra-high frequency band. However, there is still a need for in-depth research into the estimation of the regional radio refractivity at high altitudes as well as the analysis of the radar wave propagation in air-to-ground situations for SAR applications. In this paper, a novel method is proposed for predicting a wide range of two-dimensional radio refractivity using an inverse distance weighted (IDW) interpolation of high-altitude radio refractivity data from multiple meteorological observatories. We obtained a data set of atmospheric conditions along the altitude from twenty meteorological observatories within or nearby the Korean Peninsula [27]. Then, from the sparse refractive data along the altitude, the two-dimensional regional radio refractivity of the entire Korean Peninsula was obtained using the IDW interpolation. In the IDW interpolation, the distance parameters were readjusted to take into account the curvature of the Earth. To validate the interpolation method, we calculated the root-mean-square error (RMSE) between the actual and the interpolated refractivity data at seven observatories and compared the data with other conventional interpolation methods: linear, cubic, and nearest-neighbor. The regional two-dimensional refractivity, using IDW interpolation, was obtained across the Korean Peninsula and compared with the results of other conventional interpolation methods.