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Furthermore, precipitation is too variable for the “coarse” resolution of long-range ground-
based radars (GR). The variability of natural precipitation is so large that the radar beam often
does not resolve it. As a result we find aloft different types of particles and non-homogeneous
reflectivity in the pulse volume, to be compared with rain rate at the ground level. The under-
sampling problem becomes increasingly severe with increasing ranges because the radar
backscattering volume increases with the square of the range; therefore, at longer ranges, small
but intense features of the precipitation system are blurred (non-homogeneous beam filling).
Furthermore, it is more likely to include different types of hydrometeors (e.g., snow, ice, and
rain drops), especially in the vertical dimension. We know that, on average, the radar
backscattered echo from liquid, mixed phase, and frozen hydrometeors decreases with height.
Using several TRMM overpasses, the comparison between the TRMM radar and linearly
averaged GR radar reflectivity, carried out in circular rings around the GR site, has clearly
confirmed a significant range dependence of the TRMM/GR ratio ( Gabella et al. [2006], Gabella
et al. [2011a], Gabella et al.. [2011b]). This well-known problem is caused mainly by the
increasing sampling volume of the long-range GR with range, combined with non-
homogeneous beam filling: e.g., at longer ranges of GR, the lower part of the volume could be
in rain, whereas the upper part of the same pulse can be filled with snow, ice, and mixed phase
particles. Quite often it can be even characterized by an echo weaker than the radar sensitivity
itself (apparently, no backscattered echo). This phenomenon (called “beam overshooting” by
radar meteorologists) is also caused by the decrease of vertical resolution with range, thus
amplifying the influence of the horizon and Earth's curvature. Because of beam overshooting,
strong range degradation has been noticed in several parts of the world when analyzing
weather radar data over a long time period. The reader can refer, for instance, to the 2-year
analysis by Young et al. [1999] in the United States or by Gabella et al. [2005] in the Swiss Alps.
In mountainous terrain, precipitation is even more variable both in space and time because
of orographic effects and interactions of mountains with wind fields. This variability within
the scattering volume is in contradiction with the homogeneously filled pulse volume
assumption usually made when considering the meteorological radar equation. Fulfilling
the assumption of homogeneous beam filling, however, is a prerequisite for a precise
estimate of reflectivity, attenuation and phase shift along the beam.
1.3 Type and width of the distribution of precipitation
Another fundamental problem is the asymmetry and the large variability of precipitation
rates in time and space. In other words, distributions are wide and skewed-to-the-high-end
at the same time. This statement concerns particle type, particle size, number density of
particles as well as derived integral parameters such as reflectivity, rain- and snow-rate. As
a consequence of the distributions in time and space, we find that a small area (say 1/10 of
the “rainy” area, which in turn can be 1/20 of the surveillance area …) during a “short” time
(i.e. smaller than the rainy/cloudy period) contributes a large fraction of the total
precipitation amount. As a direct consequence of this (small “time/space” of significant and
heavy rain rate), the chance of detecting weak rain rate is much larger than high rain rate.
Without careful thinking and without having analyzed large data sets, we may be tempted
to extrapolate the rules of weak rain into strong one. This extrapolation will involve large
errors, because mechanisms producing rain vary with its intensity. In other words, different
mechanisms produce weak and large rain rates.
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