Theoretical study of two-frequency coherence of MST radar returns

The theoretical expressions of two-frequency coherence of the MST radar returns from an atmospheric thin layer with sharp boundaries, which embeds within the radar volume and cannot be resolved by conventional radar techniques, are derived in this article. It shows that the derived frequency domain interferometry (FDI) coherence is not only the function of layer thickness and the components of radar wave vector, but also related to the wavenumber power spectrum of refractivity irregularities. A quantitative examination of the derived FDI coherence indicates that the effect of the irregularity power spectrum on FDI coherence is negligible for power law spectral model, while it cannot be ignored for other spectral forms, for example, a Gaussian model. The zenith angle dependence of FDI coherence is also investigated in this article. According to the observations made with Chung-Li VHF radar, it shows that the ratio of the observed FDI coherence at the vertical to that at 17° off-zenith angle is between 1.3 and 2.4. This feature can be illustrated satisfactorily by using the theory developed in this article. The effect of echoing mechanism on FDI coherence is also studied, showing that the expression of FDI coherence derived from the turbulent scattering theory can be treated to be identical to that from the Fresnel reflection theory as long as the condition Δk/k ≪ 1 is met. This result implies that it seems to be impossible to identify the echoing mechanism of MST radar by using FDI technique. The problem of estimating the thickness of a thin layer having sharp boundaries by using a Gaussian function with the expression of exp $(-\Delta k^{2} \sigma_{r}^{2})$ is also discussed. It suggests that the pertinent formula used for layer thickness estimate is L = 2.364σr. A comparison of this work with other results is also made in the text.