Coplanar retrieval method for downward pointing, conically scanning airborne Doppler radar

The High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) is a dual-beam, dual-frequency, Doppler radar system designed for operation on board the Global Hawk aircraft unmanned aircraft system. The antennas of HIWRAP point downward and scan conically at two different tilt angles. This scanning geometry, which is unlike previous airborne radar systems, presents unique challenges to retrieving the full three-dimensional wind field. We present a dual-Doppler analysis technique termed the coplanar retrieval method that solves for the wind field in the coordinates natural to the radar's scanning geometry.

We define a cylindrical coordinate system (r,θ,y) centered on a straight level flight track (y coordinate) where r is the distance from the track and θ is the angle from nadir (plane angle). Utilizing scans pointing fore and aft along coplanar beams, two wind components (ur,uy) in each ry-plane (defined by θ) are calculated. The third wind component (uθ) is not sampled by the radar, but it is retrieved using mass continuity and boundary conditions. The first boundary condition is the uθ wind component at nadir, which also comprises the horizontal cross track wind (u). The uθ wind component in this plane is retrieved by combining ur components slightly off nadir on either side, and assuming that the horizontal wind component (u) is linear and the vertical velocity (w) is constant across the span of the ur observations. From this boundary condition, we solve for the uθ field by integrating along constant radii in both directions away from nadir. The unsolved sector of the wind field near the surface is addressed by utilizing the second boundary condition, which assigns the vertical wind component (w) at the surface to be zero. Under this condition, uθ is directly solved at the surface, and uθ elsewhere is retrieved by integrating along constant radii away from the surface. These wind field components (ur,uy,uθ) are then converted into Cartesian coordinate velocities (u,v,w).

We performed tests of the coplanar retrieval method using a radar-scanning simulator on model output in a hurricane environment. A comparison of the retrieved and true Cartesian coordinate velocities revealed low errors throughout most of the field. The cross track (u) and along-track (v) wind components had root-mean-square errors of 1.5 and 0.1 m/s respectively, which were both small compared to the u and v magnitudes. The vertical wind (w) had root-mean-square errors of 0.66 m/s, which mostly results from errors in the uθ nadir boundary condition that spread when integrating. The largest errors occurred along the volume edges which is to be expected from the scanning geometry. This dual-Doppler retrieval method is currently being tested on and calibrated for the actual HIWRAP data collected during the NASA GRIP and HS3 field campaigns.