Eiichi Yoshikawa1, N. Matayoshi1, Tomoo Ushio2, V. Chandrasekar3 Japan Aerospace Exploration Agency1, Osaka University2, Colorado State University3
It is essential for meteorological use to retrieve 2-D or 3-D velocities from measurements of radial velocities in a radar or lidar. Volume Velocity Processing (VVP), is a traditional and much-used method for the purpose, in which a linear projection equation connecting 2/3-D velocities to radial velocities of several directions in a defined volume is formulated on the assumption that a linear velocity field inside the volume [1]. In order to solve the linear projection equation, However, it is well known that a large volume with angular width of a few tens of degrees must be defined to accomplish estimation accurate enough for a practical use. This is because enough dependency for orthogonal directions is not extracted by radial velocities within narrow angular width. This independency corresponds to a worse-conditioned coefficient matrix of the traditional VVP formulation. Since the VVP formulation is generally solved by Least Square (LS) method, observational errors in radial velocity measurements highly contaminate LS estimation with a small defined volume. On the other hand, with a large volume, estimated velocities are spatially averaged much, by which it is difficult to detect local phenomena such as a wind shear, downburst, and tornado. In order to estimate 2/3-D velocities accurately and stably, it is proposed in this presentation to apply Minimum Mean Square Error (MMSE) method for considering probabilistic property of velocity measurements. A measurement of radial velocity always includes error, and its probabilistic property of the measurement error is theoretically derived from received power, and radar observational parameters [2]. An accurate and stable solution is provided by applying an MMSE method for the VVP, which can include probabilistic property of measured radial velocity. The MMSE solution for the VVP, its performance evaluation and comparison by numerical simulation, and example of application for observed data will be presented.
[1] R. J. Doviak and D. S. Zrnic, Doppler Radar and Weather Observations, San Diego, CA: Academic, 1993. [2] V. N. Bringi and V. Chandrasekar, Polarimetric Doppler Weather Radar –Principle and applications–, Cambridge, Cambridge University Press, 2001.
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