Spaceborne Rainfall Doppler radar measurements: Correction of errors induced by pointing uncertainties Eastwood Im" , Simone Tanelli", Roberto Mascellonib, Luca Facherisb " Jet Propulsion Laboratory, California Institute of Technology, Pasadena CA, USA Dipartimento di Elettronica e Telecomunicazioni, Universith di Firenze, Firenze, Italy ABSTRACT In this paper we present a sea surface radar echo spectral analysis technique to correct for the rainfall velocity error caused by radar pointing uncertainty. The correction procedure is quite straightforward when the radar is observing a homogeneous rainfall field. On the other hand, when NUBF occurs and attenuating frequencies are used, additional steps are necessary in order to correctly estimate the antenna pointing direction. The proposed method relies on the application of Combined Frequency-Time (ClT) technique to correct for uneven attenuation effects on the observed sea surface Doppler spectrum. The algorithm performance was evaluated by Monte Carlo simulation of the Doppler precipitation radar backscatter model, and the high-resolution 3D rain fields generated by a cloud resolving numerical model. Results show that the antenna pointing induced error can be successfullyremoved by the proposed technique. Keywords: Spaceborne weather radar, Doppler 1. INTRODUCTION Knowledge of the global distribution of the vertical velocity of precipitation is important in estimating latent heat fluxes, and therefore in the general study of energy transportation in the atmosphere. Such knowledge can only be acquired with the use of spaceborne Doppler precipitation radars. Although the high relative speed of the radar with respect to the rainfall particles introduces significant broadening in the Doppler spectrum, recent studies have proven that the average vertical velocity in homogeneous rainfield can be measured to the 1 m/s accuracy level by appropriate selection of radar parameters at 14GHz. A suitable configuration for a nadir-looking Doppler precipitation radar (NDPR) is shown in Table 1. For inhomogeneous rainfall in which significant non-uniform beam filling (NUBF) takes place, the vertical velocity estimates are affected by a bias dependent on the along-track displacement of the 'center of mass' of the observed rainfiled with respect to the actual satellite nadir. Such bias can be eliminated by our recently developed Combined Frequency-Time (CFT) processing technique '. In this paper we deal with a further error introduced by the high relative speed vs of the radar: the bias introduced by the off-nadir poiting angle. Figure 1 shows the geometry of the problem and introduces the vector notation used throughout this paper. Specifically, iv is the unit vector in the antenna pointing direction, i, is the unit vector in the satellite motion direction (i.e., the along- track direction) and iz is the unit vector at nadir. Position vectors with respect to a fixed (ground) reference are represented as p = (x,y,z) in which the x- and z-axis of the Cartesian coordinate system are determined by i, and -iz, respectively. ps is the satellite position. Finally, r= (r,e,@) represents the positions with respect to the satellite (i.e., r=p- ps) where iv is the z-axis of the spherical coordinate system (i.e., e*). The center of the resolution volume is indicated by rv = (rv, GO). Using this notation, the radial velocity of a target at positionp and with velocity u = (u,u,uJ can be written as: v, =vsi,.ry +vsi,.(r-ry)-u.r (1) where v, is the satellite velocity. The three terms on right-hand side of (1) are the bias introduced by off-nadir pointing, the bias due to the target position relative to the center of the volume of resolution, and the actual radial velocity of the target, respectively. *Sirnone Tanelli, Jet Propulsion Laboratory, M.S. 300-243 4800 Oak Grove Drive, Pasadena, CA 91 109, U.S.A. E-mail: simne@radar- sci.jpl.nasa.gov