An equation for the rate of rainfall at a given range from the radar is derived. This is expressed in terms of the power level of the received signal (corrected for attenuation by intervening cloud and atmospheric gases) and takes account of radar attenuation due to intervening rain. The equation includes a constant which measures the performance of the radar and is determined by direct calibration.
At attenuating wavelengths (at 3 cm; to some extent at 5.6 cm) a small error in the calibration constant causes a large error in the measured rainfall. This error, which varies with range and may thus cause serious distortion, is, in fact, liable to be more serious than that caused if the attenuation were neglected entirely. Correcting for attenuation is therefore not recommended, unless the calibration error may be held within extremely narrow limits.
Very small calibration errors may be achieved by calibrating the radar by means of a rain gauge located at a point where the attenuation is appreciable. At points of smaller attenuation, a satisfactory degree of accuracy in the calculated rate of rainfall then results.
At wavelengths such as 10 cm, where the attenuation is negligible, errors in the constant still affect the measured rain, but neither so seriously, nor in a manner involving the range, thus causing no distortion.
An examination of the relative importance of the attenuation by gases and cloud at three wavelengths similarly emphasizes the difficulties associated with quantitative work at the shorter wavelengths.