Dual-Doppler Analysis in a Single Plane from an Airborne Platform

Abstract

Abstract A modified dual-Doppler analysis technique for use with airborne Doppler radars utilizing two fixed beams is presented. Although the data collected by such a system would ideally lie in the plane defined by the radar beam orientations and the aircraft velocity vector, variations in the aircraft attitude and drift angles lead to displacements between the radar observations and the idealized observation plane. These variations motivated the development of a formal framework in which an a priori velocity estimate is used in conjunction with the two Doppler velocity measurements to form a three-dimensional velocity estimate. Two velocity components, lying within or close to the observation plane, and therefore containing only a small contribution from the a priori velocity estimate, are then extracted from the three-dimensional velocity estimate. Advantages of using the three-dimensional framework include improved accuracy (when an a priori velocity estimate is available) and a framework for assessing the effects of cross-plane contamination on the retrieved velocity components. The velocity fields retrieved using the modified dual-Doppler analysis are affected by errors in the platform motion correction to the Doppler velocities, random noise in the mean Doppler velocity estimates, displacements between the radar beams (and between the radar beams and the idealized observation plane), and meteorological velocity variations about the a priori velocity estimate. Errors in the platform motion correction remain poorly characterized but are believed to be the largest source of error in many cases. However, these errors result primarily in biases (or low-frequency errors) in the retrieved velocity fields and therefore do not interfere with the ability to resolve actual velocity variations. Random noise in the mean Doppler velocity estimates increases dramatically with decreasing signal-to-noise ratio (SNR) (for SNR < 5 dB) and effectively limits the use of the single-plane dual-Doppler (SPDD) analysis to SNR > 0 dB. Displacements between the volumes sampled by the nadir and slanted beams can also be a significant source of error, especially at larger displacements from the aircraft. Errors resulting from meteorological velocity variations about the a priori velocity estimate tend to be small compared to the velocity variations of interest. The dual-Doppler analysis presented in this paper has been applied to retrieve two-dimensional velocity fields with a resolution of ∼50 m using Doppler velocities collected using dual-beam configurations of the Wyoming Cloud Radar. Results are in horizontal and vertical planes for marine stratocumulus, cumulus congestus, and for the clear-air boundary layer.