MEASUREMENT OF ATTENUATION BY A DUAL-RADAR METHOD - CONCEPT AND ERRORANALYSIS

The authors describe a method for the measurement of specific attenuat ion using two radars operating at virtually the same wavelength al whi ch the attenuation is desired. Use of the same wavelength avoids confo unding between differences in received powers due to attenuation and w avelength dependence of reflectivity factors. A governing equation for the specific attenuation and an analytical solution of the equation a re derived. The analytical solution gives an explicit expression for t he specific attenuation in terms of the specific attenuation at an ini tial point and the second derivative of estimates of the difference be tween ensemble average received powers for the two radars along and ne ar the characteristics of the governing equation. An error analysis sh ows that error in the computed attenuation is due to error in the atte nuation coefficient at the initial point and errors in the estimates o f the ensemble average received powers. Unless the initial point is po orly chosen, the error due to the initial condition is approximately o f the same magnitude as the error in the initial value of the specific attenuation. The error due to errors in estimates of the ensemble ave rage received powers accumulate along the characteristics; the error i ncreases rapidly near the radars and is smaller away from the radars. The error decreases with distance between the radars, the number of in dependent pulses averaged to find estimates of ensemble average power, the number of independent radar pulse volumes used in smoothing the o bserved reflectivities, and the angular intervals used in performing t he numerical differentiation for the calculation of the above-mentione d second derivative. Using typical radar parameters, it is found that the standard error of the two-way specific attenuation can be less tha n a tenth or a few tenths of a decibel per kilometer if the number of independent pulses exceeds about 10, smoothing is performed over hundr eds of independent radar pulse volumes, and the angular intervals for the differentiation are about 3 degrees or greater.