On averages of radar rain echoes in nonstationary conditions

The authors examine a problem, recently opened up by Jameson and Kostinski (1996), of statistics for radar rain echoes in a nonstationary case such as the observation of rain by a moving antenna beam. The present authors study this problem under the framework of the standard fluctuation theory of Marshall and Hitschfeld (1953). They obtain the exact nonstationary probability density function (pdf) for an average of n mutually independent samples of the received power in the square-law detection, and an approximate nonstationary pdf in the logarithmic detection. They find that the concept of bias does not appropriately describe the effect of antenna beam movement during the sampling. They introduce a new quantity to assess the effect of antenna beam movement on rain observation by radars