Spectral Observation Theory and Beam Debroadening Algorithm for Atmospheric Radar

In order to measure the variance of wind velocity, which is contributed from turbulence, via radar observations, it is necessary to remove the unwanted contribution from strong horizontal velocity components through the finite beamwidth of the radar. This effect is referred to as beam broadening. Although the amount of beam broadening has thus far been calculated based on the approximating assumption that the pattern of the beam is rotationally symmetric and has very low sidelobes, we need to take a more theoretical approach to radar-one that does not have a simple beam pattern like the Antarctic Program of the Antarctic Syowa Station (PANSY) radar (69S, 39E). In this article, we clarify the theoretical relationship in a very simple form between the turbulence spectrum, which is directly associated with the variance of turbulence, two-way beam patterns, and the observed spectrum, using autocorrelation functions (ACFs). The theory is thoroughly universal and applicable to any type of atmospheric radar, such that we can quantitatively analyze radar observation systems. Furthermore, we propose a "debroadening" algorithm based directly on this theory and from calculations of the general maximum likelihood (ML). We performed numerical simulations that validate our theory and the algorithm.