The method for the daily monitoring of the differential reflectivity bias for
polarimetric weather radars is developed further. Improved quality control is
applied to the solar signals detected during the operational scanning of the
radar, which efficiently removes rain and clutter-contaminated gates occurring
in the solar hits. The simultaneous reflectivity data are used as a proxy to
determine which data points are to be removed. A number of analysis methods
to determine the differential reflectivity bias are compared, and methods
based on surface fitting are found superior to simple averaging. A separate
fit to the reflectivity of the horizontal and vertical polarization channels
is recommended because of stability. Separate fitting also provides, in
addition to the differential reflectivity bias, the pointing difference of
the polarization channels. Data from the Finnish weather radar network show
that the pointing difference is less than 0.02

Calibration of the radar differential reflectivity (

The active methods are based on polarimetric properties of rain. Differential
reflectivity at vertical incidence is intrinsically zero for raindrops;
hence the measured

The passive methods are based on using the microwave signals from the sun.
The measurements can be off-line measurements, in which the operational
scanning is stopped and the radar antenna is pointing at the sun

In the present paper, we revisit the monitoring of the receiver chain of the

Some properties of the FMI radars relevant to this study. The
columns give the radar name, three letter acronym, latitude and longitude of
the radar, the antenna beam widths for the horizontal polarization (H) and
vertical polarization (V) in elevation and azimuth directions in degrees, the
difference of losses in the transmitter chain (

The Finnish Meteorological Institute (FMI) operates a network of 10 C-band
Doppler weather radars, of which nine radars are polarimetric. Every
15 min the radars perform a 12-elevation volume scan between
0.3 and 45

Solar signals observed simultaneously by four radars in Finland on 25 March 2001 at 04:00 UTC.

The detection of solar signatures in polar volume data of weather radars is
described in

The sun hits have a symmetric distribution around the sun position which is
slightly wider in azimuth than in elevation. A typical example is shown in
the left panel of Fig.

Sun
images based on sun hits collected from the FMI Anjalankoski radar in March 2015. The left panel shows the sun hit power relative to maximum (black
within 1 dB of maximum, red 1 … 3 dB below the maximum, blue 3 … 7 dB
below the maximum, and magenta more than 7 dB below the maximum) and the
right panel the differential reflectivity (magenta less than

As data from different elevations are analysed together, the solar elevation
needs to be corrected for the effects of refraction. We use the analytical
formulas for the atmospheric refraction of radiowaves, which are consistent
with the commonly used

The modelling of the

If the quantities available from the signal processor are

It is also possible to do the analysis directly to

The right panel of Fig.

Calibration of differential reflectivity using polarimetric properties of
rain has first been demonstrated by

For

Statistical estimators in simulated rain with noise. The thick lines
give three estimators of the centre point: mean from 50 km distance (blue),
median from 50 km distance (red), mean from 200 km distance (green). The thin
lines of the respective colours indicate the filtering windows. The second blue
thin line at

The climatological melting layer height in Finland during the summer is about
3 km, which means that most of the data used for the analysis are obtained
from solid precipitation. Snow is not spherical, but the assumption of zero
intrinsic

The quality control of the solar hit data is necessary to get results of good
quality.

The number of sun hits and the statistical accuracy can be increased by
also using data from closer ranges. Then the probability that the data are
contaminated by rain or clutter increases, and one has to devise a method for
removing the contaminated data prior to calculating the solar hit power. One
possible method is a two-stage estimation, in which the first estimate of the
solar hit power is calculated from the full data set, and this power together
with an estimate of the width of the distribution is used to remove non-solar
data. This is illustrated in Fig.

Probability that the solar hit power exceeds the far range power by 0.3 dB. The power determined by mean filtering is denoted by blue, and the power determined by median filtering by red. The green bar indicates solar power determined by the mean filtering when the filtering window is determined from points above 8 km altitude. The probability is given for start altitudes of 2, 4, and 6 km.

Figure

The overall best performance is obtained if the filtering window is first
estimated using data from high altitudes and the final estimate of the mean
is calculated using data also from the lower altitude. Then a biased estimate
is obtained only in very few cases. The median estimator, although nearly as
good, produces biased estimates of the power in some cases. One can reduce
the computational load for real-time analysis of large data sets, e.g. for
the analysis of all European solar hit data within the
OPERA (Operational Programme for Exchange of Weather Radar Information) data centre

The effect of the improved filtering is also noticeable in the fitted
parameters. For the case in Fig.

The filtering of the differential reflectivity

There is a number of different methods to estimate the

Figure

Solar

Elevation and azimuth pointing and image width results for H and V polarizations for 1 month of data of the ANJ radar. In each panel, the median is shown with a thick line at 1st and 3rd quartiles by a box. Whiskers indicate data points closer than 1.5 times the box length from the quartiles, and data points beyond that are marked with circles.

The three fitting methods give comparable results in the FMI case, where the
widths of the two polarizations differ. If the azimuth and elevation widths
are close to each other, the direct fitting to

The additional benefit of doing the fitting to both polarization channels
separately is that one can determine the angle between the pointing
directions of the two polarizations. The two upper panels of
Fig.

The lower panels compare the width values of the two polarizations. There is
a clear difference in the image widths so that for the V polarization the
image is wider in elevation and for the H polarization in the azimuth. This
is a result of the antenna design, and the results are typical for the whole
network and are consistent with the width values given in
Table

Figure

Figure

Both the solar and the zenith methods are based on using an object with
intrinsic zero differential reflectivity. Yet the results are not directly
comparable, because the solar results depend on the receiver biases only,
whereas the zenith results depend both on the receiver and the transmitter
sides. One could, in principle, use the known loss and gain biases to correct
the observations. Any significant deviation of the corrected value from zero
would indicate an error in the loss and gain figures. In systems where both
polarizations are processed using a single radar constant, one needs to
include the

In many operational systems, the zenith

The interpretation of the solar

The differential reflectivity of the quiet sun is zero and constant over the
solar surface but the radar measurements also include the effect of the
antenna and the receiver chain. In case the beam shapes of the horizontal and
vertical polarizations were fully identical, all

The zenith measurements of

The statistical accuracy of the

The numerical analysis and the figures have been prepared using the R software