An Inversion Problem on Inferring the Size Distribution of Precipitation Areas from Raingage Measurements

Abstract

Given a long, continuous record of rain rate measured at a point on the ground, it is straightforward to select a threshold value of rate and note the duration of each event in which the threshold is exceeded. The distribution of durations for any prescribed threshold can be transformed to a distribution of linear extents or lengths over which the threshold rate is exceeded by employing the translation velocity of the rain pattern and invoking the time-to-distance conversion, known as Taylor's hypothesis. The conversion from a distribution of lengths to a corresponding distribution of areas in which the threshold rate is exceeded is a more difficult step, but one that can be carried out if the shapes of the rain regions are specified. Using a ten-year record of rain rate at Montreal, we have generated the size distributions of rain regions in which a number of thresholds between 1 and 100 mm h?1 are exceeded, assuming the shapes to be circular. Results were compared with size distributions determined from a large sample of radar records at an altitude of 2 km. It was found that there is reasonable approximate agreement between the observed and computed distributions if an allowance is made for the bias against small echoes in the radar observations arising from limited spatial resolution.