Abstract
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.
Highlights
M EASURING the variance of the velocity of the atmosphere σt2urb, which is proportionally linked to the energy dissipation rate, is a common role given to mesospherestratosphere–troposphere (MST) radar
We develop a mathematical theory that describes how the power spectrum of the radar echoes is formed with respect to the two-way complex-valued beam pattern and the velocity spectrum of the atmospheric turbulence
We further propose a debroadening algorithm that is formed using this relationship, namely an inverse calculation that obtains the true turbulence spectrum given the series of radar echoes or a power spectrum
Summary
M EASURING the variance of the velocity of the atmosphere σt2urb, which is proportionally linked to the energy dissipation rate, is a common role given to mesospherestratosphere–troposphere (MST) radar. It has been known that this can be expressed more in the “correlation domain” as a multiplication of the two autocorrelation functions corresponding to the “beam broadening” and “true” spectra [6]–[9] Following these studies, VanZandt et al [10] proposed a variational technique to estimate σt2urb by taking advantage of two different beam widths. We develop a mathematical theory that describes how the power spectrum of the radar echoes is formed with respect to the two-way complex-valued beam pattern and the velocity spectrum of the atmospheric turbulence. We choose a word of the two that fits more in the context, one would want to replace it by the other when it is confusing
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