A model for the beam-filling effect associated with the microwave retrieval of rain

Estimating rain rate from environmental microwave emissions is hampered by several difficulties. One of these difficulties is known as the beam-filling effect. Beam filling is the systematic error introduced when the microwave radiometer's field of view is not filled with uniform rain. Beam filling can have dramatic effects on rain-rate estimation, causing rain rates to be underestimated by as much as a factor of 2. The present study derives an approximate expression for beam filling that provides, in principle, a way to estimate this effect. In addition, this study deals only with single-channel microwave rain estimation over the ocean. The final results reveal that beam filling is essentially determined by the freezing level, the mean fraction of the footprint raining, and the footprint-averaged rain rate. Also, the numerical results appear to agree with other empirical studies. Furthermore, the analysis brings to light an interesting connection with rain threshold techniques for estimating area-averaged rain rates.