Geoscience Reference
In-Depth Information
4.1.2 QPE evaluation based on the comparison between hourly radar and gauge
rainfall amounts
The evaluation is based by looking at the average value and the dispersion of the errors (we
call error the disagreement between radar and gauge amounts). For such characterization,
we define the two following parameters:
1.
Bias
(in dB). The bias in dB is defined as the ratio between radar and gauge total
precipitation amounts on a logarithmic (decibel) scale. It describes the overall
agreement between radar estimates and ground point measurements. It is averaged
over the whole space-time window of the sample. A positive (negative) bias in dB
denotes an overall radar overestimation (underestimation).
2.
Scatter
(in dB). The definition of scatter is strictly connected to the selected error
distribution from a hydrological (end-user) and radar-meteorological (operational
remotely sensed samples of the spatio-temporal variability of the precipitation field)
perspective. The error distribution is expressed as the cumulative contribution to
total rainfall (hydrologist point of view, y axis) as a function of the radar-gauge ratio
(radar-meteorologist point of view, x axis). Most of the sources of error in radar
precipitation estimates, in fact, have a multiplicative (rather than an additive)
nature. An example of the error distribution is shown in Fig. 2 and 3 of
Germann et
al.
[2004]. The scatter is defined as half the distance between the 16% and 84%
percentiles of the error distribution. The scatter refers to the spread of radar-gauge
ratios when pooling together all volumetric radar estimates aloft and point
measurements at the ground.
From our radar-meteorological point of view the multiplicative nature of the error prevails
with respect to the additive one. For example, water on the radome, a wrong calibration
radar constant, or a bad estimate of the profile all result in a multiplicative error (i.e. a
factor) rather than an additive error (i.e. a difference). This is why bias, error distribution
and scatter are expressed as ratios in dB. A 3 dB scatter, for instance, means that radar-
gauge ratios vary by a factor of 2. If bias is zero, it is interpreted as follows: the radar-
derived estimate lies within a factor of 2 of the gauge estimate for 68% of rainfall while for
the remaining 32% the uncertainty is larger. The scatter as defined above is a robust measure
of the spread. It is insensitive to outliers for two reasons. First, each radar-gauge pair is
weighted by its contribution to total rainfall (y axis of the cumulative error distribution). An
ill-defined large ratio that results from two small values, e.g. 0.4 mm/2 mm ~ −7 dB,
describes an irrelevant event from a hydrological point of view, and only gets little weight.
Second, by taking the distance between the 16% and the 84% percentiles, the tails of the
error distribution are not overrated. Another important advantage of the spread measure is
that it is unaffected by the bias error, hence providing a complementary view of the error in
the estimates. The above definition of the scatter is thus a better measure of the spread than
the less resilient standard deviation.
4.2 Quantitative precipitation estimation for the Palermo radar
The Palermo radar is located on a small hill next to the harbor of the capital of Sicily (blue
triangle, Fig. 5): its latitude is 38°.1139; its longitude is 13°.358; its altitude is 45 m above
Mean Sea Level (MSL). The radar has been installed in autumn 2010.
