The Alberta Rail Studies Project's AN/FPS-502 radar, equipped with "gray-scale" output circuitry and a broad vertical beam, was employed to study the storm of 18 July 1964. Defining the Total Radar Reflectivity permits the summation of the return from the three antenna beams to produce a composite of the echo through the entire depth of the storm. Time-meaned radar reflectivity profiles are obtained for the first time from this type of radar, and are used to derive equations to calculate the liquid water content of the storm. [...]

Plots of areal coverage as a function of height and intensity have been made for 17 radar echo patches all smaller than 1300 nmi.^2, that were recorded on the constant altitude maps of the 3-cm McGill radar. From these plots, vertical profiles of flux and density of precipitation have been obtained. The profiles generally showed maximum values aloft. The maxima were usually observed to descend or remain at one level. Occasions of ascent were less frequent. [...]

The areal coverage of echoes from snow as a function of height and intensity has been measured using an automated method, for 183 hours of records from the winter of 1963 - 64. The shape of these plots against height averaged over the whole winter season is found to be identical to the shape measured previously for a season of rain echoes whose tops were below 40 thousand feet. [...]

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The intensity returns obtained by a radar from precipitation are well known to fluctuate violently in space and time. We present a systematic study of the resolution dependence time series with overlapping time resolutions spanning 10 orders of magnitude (0.77 ms to 4 months), of the fluctuating radar echo from precipitation. The results undermine the current assumptions of homogeneity of rainfield at scales smaller than the radar resolution, due to Marshall and Hitschfeld (1953), by showing that the only length scales identifiable in the time series are those of the radar pulse volume, the wavelength, and a very small inner scale of the order of millimeters. An analysis of the multiscaling nature of the time series of echo fluctuations reveals multiscaling behaviour at scales down to the resolution or pulse volume scale. Since there are no a priori scales in the rainfield we proceed to model the fluctuating radar echo by assuming a multiscaling model of rainfield variability which extends to sub-resolution scales. A systematic analysis of the statistical behaviour of computed reflectivities from this variability gives a full statistical description of reflectivity originating from multiscaling variability, and solves the scalar multifractal radar observer's problem. Computation of time series of reflectivities from a time-space representation of this variability reveals quantitative and qualitative behaviours consistent with those of observed echo fluctuation time series. We conclude that a multiscaling model of the rainfield which extends to the smallest scales of the rainfield is consistent with observation.

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