Prognostic Equation for Radar Radial Velocity Derived by Considering Atmospheric Refraction and Earth Curvature

The prognostic equation for the radial velocity field observed with a Doppler radar is derived to include the effects of atmospheric refraction and earth curvature on radar-beam height and slope angle. The derived equation, called the radial velocity equation, contains a high-order small term that can be truncated. The truncated radial velocity equation is shown to be much more accurate than its counterpart radial velocity equation derived without considering the effects of atmospheric refraction and earth curvature. The truncated equation has the same concise form as its counterpart radial velocity equation but remains to be sufficiently accurate as a useful dynamic constraint for radar wind analysis and assimilation (in normal situations) even up to the farthest 300-km radial range of operational Weather Surveillance Radar-1988 Doppler (WSR-88D) scans where its counterpart radial velocity equation becomes erroneous.