Abstract:The criteria suggested by Welsh and Fearing to judge the validity of certain soft-photon amplitudes are examined. We comment on aspects of their analysis which lead to incorrect conclusions about published amplitudes and point out important criteria which were omitted from their analysis.
“…In the accompanying Comment [3] Liou, et al raised two objections to I. While we find these objections invalid, and stand by the conclusions of the original paper, we wish to discuss them, as they reemphasize some of the ambiguities which appear in these generalized SPA's.…”
We respond to the accompanying Comment on our paper, 'Validity of certain soft photon amplitudes'. While we hope the discussion here clarifies the issues, we have found nothing which leads to a change in the original conclusions of our paper.
“…In the accompanying Comment [3] Liou, et al raised two objections to I. While we find these objections invalid, and stand by the conclusions of the original paper, we wish to discuss them, as they reemphasize some of the ambiguities which appear in these generalized SPA's.…”
We respond to the accompanying Comment on our paper, 'Validity of certain soft photon amplitudes'. While we hope the discussion here clarifies the issues, we have found nothing which leads to a change in the original conclusions of our paper.
“…6 of Zhang et al (2005)). Typical targets are storms, mesocyclones and tornadoes; to track them effectively at high resolutions (down to 250m), and with a computational efficiency required by realtime applications, the 2dSA uses a small domain (∼20 × 20 km 2 ) in a moving frame following the tracked feature (Gal-Chen 1982;Zhang and Gal-Chen 1996;Liou 1999;Liu et al 2004). Because the 2dSA has a small retrieval domain, it requires suitable analyses of winds at the meso-β and meso-γ scales, or scales larger than those handled by the small domain of 2dSA analysis, to provide background and boundary constraints.…”
SUMMARYA two-dimensional form of cross-covariance function between the radar radial-and tangential-components (with respect to the direction of radar beam) of background wind errors is derived. Like the previously derived auto-covariance function for the radial component, this cross-covariance function is homogeneous but nonisotropic in the horizontal. The auto-and cross-covariance functions are used with the statistical interpolation technique to perform a vector wind analysis from Doppler radial-velocity observations on a conical surface of low-elevation radar-scans. The structures of the two covariance functions are compared and interpreted in terms of the influence of a single-point radial-velocity observation on the analysed vector wind field. The utility and value of these covariance functions are demonstrated through analysis experiments that use either simulated radialvelocity data from idealized flows or real radar observations. The results of the statistical interpolation scheme utilizing the proposed covariance functions are shown to be superior to the results of traditional VAD technique. The proposed technique can actually be considered a generalization of the traditional VAD technique.
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