J. Atmos. Ocean. Tech., 25, 1182-1196, DOI: 10.1175/2007JTECHA1010.1 (2008)

To obtain statistically stable reflectivity measurements by meteorological radars, it is common practice to average over several consecutive pulses during which the antenna rotates at a certain angular velocity. Taking into account the antenna's continuous motion the measured reflectivity is determined by an effective beam weighting function which is different from a single-pulse weighting function, a fact which is widely ignored in applications involving beam weighting. In this paper, the effective beam weighting function is investigated in detail.

The theoretical derivation shows that the effective weighting function is essentially a simple moving sum of single-beam weighting functions. Assuming a Gaussian shape of a single pulse a simple and easy-to-use parameterization of the effective beam weighting function is arrived at which only depends on the single-beam width and the ratio of single-beam width to the rotational angular averaging interval. The derived relation is formulated in the ''radar system'' (spherical coordinate system consisting of azimuth and elevation angles), which is often applied in practice. Formulae for the ''beam system'' (two orthogonal angles relative to the beam axis) are also presented.

The final parameterization should be applicable to almost all meteorological radars and might be used (i) in specialized radar data analyses (ground based or satellite radars) and (ii) for radar forward operators to calculate simulated radar parameters from results of NWP models.