AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-9-5367-2016An integrated approach to monitoring the calibration stability of operational dual-polarization radarsVaccaronoMattiamvaccar@engr.colostate.eduBechiniRenzoChandrasekarChandra V.CremoniniRobertoCassardoClaudiohttps://orcid.org/0000-0001-5212-3211Colorado State University, Fort Collins, Colorado, USAArpa Piemonte, via Pio VII 9, Turin, ItalyUniversità degli Studi di Torino, via Pietro Giuria 1, Turin, ItalyMattia Vaccarono (mvaccar@engr.colostate.edu)8November2016911536753833February201615February201630September20165October2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/9/5367/2016/amt-9-5367-2016.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/9/5367/2016/amt-9-5367-2016.pdf
The stability of weather radar calibration is a mandatory aspect for
quantitative applications, such as rainfall estimation, short-term weather
prediction and initialization of numerical atmospheric and hydrological
models. Over the years, calibration monitoring techniques based on external
sources have been developed, specifically calibration using the Sun and
calibration based on ground clutter returns. In this paper, these two
techniques are integrated and complemented with a self-consistency procedure
and an intercalibration technique. The aim of the integrated approach is to
implement a robust method for online monitoring, able to detect significant
changes in the radar calibration. The physical consistency of polarimetric
radar observables is exploited using the self-consistency approach, based on
the expected correspondence between dual-polarization power and phase
measurements in rain. This technique allows a reference absolute
value to be provided for the radar calibration, from which eventual deviations may be
detected using the other procedures. In particular, the ground clutter
calibration is implemented on both polarization channels (horizontal and
vertical) for each radar scan, allowing the polarimetric variables to be
monitored and hardware failures to promptly be recognized. The Sun calibration allows
monitoring the calibration and sensitivity of the radar receiver, in addition to
the antenna pointing accuracy. It is applied using observations collected
during the standard operational scans but requires long integration times
(several days) in order to accumulate a sufficient amount of useful data.
Finally, an intercalibration technique is developed and performed to compare
colocated measurements collected in rain by two radars in overlapping
regions. The integrated approach is performed on the C-band weather radar
network in northwestern Italy, during July–October 2014. The set of methods
considered appears suitable to establish an online tool to monitor the
stability of the radar calibration with an accuracy of about 2 dB. This is
considered adequate to automatically detect any unexpected change in the
radar system requiring further data analysis or on-site measurements.
Introduction
Weather radar data are used not only for precipitation monitoring but also for
quantitative applications, such as rainfall estimation, short-term weather
prediction and initialization of numerical atmospheric and hydrological
models. Therefore, the data quality of radars must be continuously monitored,
as for example recommended by the Network of European Meteorological Services (EUMETNET) OPERA
(Operational Programme for the Exchange of weather RAdar Information) program
(; ). Specifically, the
stability of the radar calibration is a mandatory aspect for performing
reliable rainfall measurements. Over the years, many calibration techniques
based on external sources have been developed, e.g., calibration with the Sun,
and ones based on fixed and well-known targets, e.g., calibration with ground
clutter echoes. The calibration using the solar interferences was first
proposed by and has been subsequently applied on operational radars
for the monitoring of the radar receiver chain and antenna pointing
(;
and ). The ground clutter calibration allows
the stability of the radar calibration to be monitored automatically, specifically
the transmitting and receiving chain of both polarization channels, through
statistical analysis of the echo power return from fixed targets
( and ).
For a radar network, the stability of the radar calibration can also be
monitored considering the joint observations in rain medium collected by two
or more radars ( and ).
This intercalibration ensures the consistency and stability of the
precipitation measurements by comparing the radar reflectivity values of two or
more radars in the same area.
In addition, a self-consistency procedure can be performed to evaluate the
absolute radar calibration in the case of heavy rain.
and proposed and
developed a procedure based on the radar reflectivity at horizontal
polarization (ZH), differential reflectivity (Zdr)
and specific differential phase shift (Kdp), known as
self-consistency since these three radar observables lie in a limited
three-dimensional space for rain medium.
The radar calibration is also often monitored using observations collected by
a rain gauge network. However, due to the high spatiotemporal variability
of the Z–R relations, this method is more indicated for the long-term bias
assessment, and it has not been considered in this study.
In this paper we propose an integrated approach to monitoring the calibration
stability of operational radars based on the abovementioned calibration
techniques. The paper is organized as follows. Section
describes the radars and the data on which the proposed approach for the
online calibration monitoring is performed. Section
reviews the self-consistency procedure for the radar absolute calibration and
the calibration monitoring techniques, namely intercalibration, ground
clutter calibration and Sun calibration. The results of each calibration
technique are discussed in Sect. . In
Sect. , the integrated approach to monitoring the
calibration stability of operational radars is discussed, and conclusions
are drawn.
Arpa Piemonte C-band weather radars
The calibration monitoring of the Regional Agency for the Protection of the Environment
(Arpa) of Piemonte C-band weather radars is
evaluated for the period between 28 July and 13 October 2014 on the
operational volume scans. The absolute calibration of the radars is checked
using the self-consistency procedure when precipitation occurs in the radar
domain. During the whole period, the radar calibration is monitored using the
ground clutter calibration, the Sun calibration and the intercalibration
procedures.
The continuous surveillance of the territory in the northwestern region of
Italy is operated by Arpa Piemonte, which manages two C-band weather radars and a mobile X-band radar
for research purposes. The two C-band radars are located at Bric della Croce
hill and at Monte Settepani (Fig. ). The Bric della
Croce radar is located on the hills near Turin, at 736 m above sea level
(a.s.l.). It is placed on the top of a 33 m high tower and covers the
Piemonte region. The east side of the radar domain does not present obstacles
that may block the radar beam, while on the western side of the radar
domain the visibility is limited by the Alps and, on the southern side, by
the Apennines. The radar of Bric della Croce performs a volume scan every
5 min. However, due to different filter settings on the scans starting at
minute 0 and 5, for the purpose of this study only the scan starting at
minute 0 is considered. The scan is composed of 11 elevations between -0.1
and 28.5∘. The volume scan is polarimetric, and the observed
parameters are ZH, Zdr, correlation coefficient
ρhv, differential phase shift Φdp and Doppler
velocity V. Each measure is the result of the integration of about 50
pulses for each polarization. The range of the volume scan is 170 km, and the
range resolution is 340 m. The angular resolution is 1∘. The pulse
time width is 0.5 µs (short pulse). The Bric della Croce radar
operates in dual-PRF (pulse repetition frequency) mode to mitigate the radar dilemma, with frequencies 882
and 588 Hz.
Weather radars in northwestern Italy. The circles correspond to
the scan domains, and the colors are related to the markers on the map. The
red and blue markers represent the two C-band radar locations. The circles
represent the Bric della Croce scan (red) and the Monte Settepani scan
(blue).
The second C-band weather radar is located on top of Monte Settepani
at 1386 m a.s.l., near Savona, in the Ligurian Apennines. This
radar is managed by Arpa Piemonte in collaboration with the Liguria region.
This strategic position allows the precipitation coming from the
Mediterranean Sea to be monitored, which may cause severe hydrological effects. Furthermore,
the Monte Settepani radar has excellent visibility in the north and east
sectors, corresponding to the Po Valley and the mountain areas of Piemonte.
The Monte Settepani radar performs a volume scan every 10 min. The volume scan
is polarimetric and the acquired parameters are the same as for the Bric
della Croce radar. The volumetric scan is composed of seven elevations
between -0.3 and 14.9∘. The range is 136 km, and the range
resolution is 375 m, using short pulses of 0.5 µs and PRF of
1090 Hz.
The specific differential phase shift Kdp is operationally
calculated for both systems using the algorithm. After
Kdp estimation, a hydrometeor classification is performed on the
dual-polarization observations . The output
of the classification is used to select the data for the different
calibration procedures. In order to account for the effects of attenuation
and differential attenuation, the rain profiling algorithm based on
is applied to correct the horizontal reflectivity
for path attenuation, while differential attenuation is linearly estimated
from the horizontal attenuation .
Integrated approach for radar online calibration
The calibration techniques are often investigated separately, and the task of
each technique is the monitoring of a section of the radar system. The Sun
calibration performs the monitoring of the radar receiving chain and the
antenna pointing, using the Sun as a natural radio source. The ground clutter
calibration is able to monitor the calibration stability of the radar
transmitting chain together with the receiving chain. Nevertheless, in the case
of loss of calibration in the radar transmitting chain the ground clutter
calibration is unable to detect whether the loss of calibration affects the
transmitting or receiving chain. By combining and comparing the Sun calibration
together with the ground clutter calibration, it is possible to retrieve
additional information about the eventual calibration change.
Moreover, to monitor the calibration stability of operational radars during
precipitation, the intercalibration may be performed when a radar network is
available. The intercalibration procedure allows the reflectivity
measurements acquired by two radars over the same area to be compared.
The intercalibration, the Sun calibration and ground clutter calibration, however, only
allow monitoring the eventual deviation of the radar calibration from a given
reference value. Hence, it is required to verify the absolute calibration of
the radar by the self-consistency procedure. The integrated approach involves
the following procedures:
intercalibration, performed whenever precipitation is detected in overlapping areas;
self-consistency, performed in the rainfall events selected for the intercalibration;
ground clutter calibration, performed daily;
Sun calibration, performed over the previous 5 days.
Once a reference calibration value is established, e.g., based on the
end-to-end self-consistency method, the two techniques (clutter and
self-consistency) can be combined to provide a more comprehensive monitoring
of the calibration stability:
ΔTR=1σClut(CLUT-CLUTtrend)+1σSC(BIASSC)1σClut+1σSC(dB),
where CLUTtrend is the mean value of the clutter calibration
outputs during the whole study period or, for real-time application, during
the last 4 weeks, while CLUT and BIASSC are weekly averaged.
Each technique is weighted by the inverse of its uncertainty, named σ.
The ΔTR uncertainty is estimated by propagating the
uncertainties of the considered techniques.
Self-consistency
The polarimetric radar measurements of rainfall are self-consistent
, since ZH, Zdr and
Kdp lie in a limited three-dimensional space for rain medium.
For the triplet of measurements ZH, Zdr and
Kdp, the self-consistency technique allows obtaining estimates of
one of the parameters based on the other two. This procedure combines two
methods for the dual-polarization estimate of rainfall: one based on the
reflectivity measurement at horizontal polarization and on the differential
reflectivity, and one based on the specific differential propagation phase
measurement. This latter estimator is assumed to be unbiased, since it is
based on phase measurements, so it is immune to calibration issues
.
The distribution of drop sizes (DSD) and shapes are fundamental for deriving
physically based rain rate algorithms. The raindrop size distribution
describes the probability density (distribution function) of raindrops. A
gamma distribution model (or a similar model such as lognormal distribution)
can adequately describe many of the natural variations in the shape of
raindrop size distributions . For polarimetric
radars, the three radar measurements Z, Zdr and Kdp
can be used in various combinations to estimate rain rate. These estimators
are based on equilibrium shape model, such as the Beard–Chuang ,
which describes the oblate shape of the rain drops. Among the radar rainfall
algorithms discussed in the literature , in this study we used the
Rdr(Z,Zdr) and Rdp(Kdp)
algorithms.
A robust rain rate estimator can be constructed as
Rdr=c1ZHa1100.1b1Zdr,
where ZH is in linear units (mm6 m-3) and Zdr is
in logarithmic scale (dB) . Coefficients a1, b1 and
c1 at C-band (5.45 GHz) are 0.91, -2.09 and 5.8×10-3,
respectively .
Using the specific differential propagation phase and since Kdp
is inversely proportional to wavelength in Rayleigh limit, a general
R(Kdp) estimator can be written using a frequency-scaling
argument in the form Rdp=129Kdpfb2,
where the unit of Rdp is millimeters per hour (mm h-1), Kdp is in
degrees per kilometer (∘ km-1) and f is in gigahertz. At 5 GHz frequency it reduces to
Rdp=32.8(Kdp)0.85.
According to , the absolute calibration bias
can be computed as a function of the slope of the scatterplot between
Rdp and Rdr. Let θ be the angle of the
position vector formed by the coordinates of Rdp and
Rdr. It follows that tan(θ) can be estimated as the slope
of a linear model applied on the rain rate pairs. The system gain bias can be
expressed on a decibel scale as
B(dB)=-10a1Log(tan(θ)),
where 10Log(tan(θ)) is the slope of the linear regression
computed on a decibel scale.
The application of the self-consistency technique requires that
Zdr be properly calibrated . In order
to verify the calibration of Zdr, we considered all measurements
collected matching the following criteria:
observations in liquid phase, as inferred from the application of the
hydrometeor classification ;
ρhv>0.99;
horizontal reflectivity between 10 and 20 dBZ. The lower limit is used
to avoid noise-contaminated observations, while the higher limit correspond to drizzle or light rain conditions.
Using the abovementioned criteria results in selecting echoes from drizzle
composed of nearly spherical droplets and expected differential reflectivity
close to 0 dB or slightly positive.
The self-consistency technique is performed on liquid-phase echoes, inferred
from the hydrometeor classification; rain rates computed from negative values
of Zdr and Kdp are not considered in the analysis,
since these values are unphysical in rain medium.
Intercalibration
The intercalibration ensures the consistency and stability of the
precipitation measurements by comparing the radar reflectivity values of two or
more radars operating in the same frequency band, over the same area and
time. The areas are computed from the intersection of the radar beams with a
theoretical model, considering the normal propagation of the radar beam. The
operational intercalibration of the two C-band radars is performed when
sufficient meteorological echoes (i.e., more than 100 pairs) are available in
the overlapping area. This procedure is able to detect eventual calibration
drifts. In order to compare measurements from different radars, the different
viewing geometry should be carefully considered. The overlapping volumes are
evaluated theoretically for each elevation of both considered radars.
Ideally, the pair of radar cells (∼1∘×0.3 km) should have
similar size in order to obtain consistent results from the intercalibration.
However, to increase the number of radar cells on which the intercalibration
can be performed, some tolerances on the altitude of the main beam center and
on the distance from the radars are set. The height from the ground (or sea
level) of the radar beam is computed by
hbeam=sr2+(h0+RE)2+2sr(h0+RE)sinθ-RE,
where sr is the slant range (i.e., the range along the beam),
h0 the radar height above the sea level and RE the effective
Earth radius. Considering the 3 dB beam width of the Bric della Croce and Monte
Settepani antennas and the distance between the two radars, an example of
vertical section of the two radar beam is displayed in
Fig. a. The displayed elevations are 1.2∘
(Bric della Croce) and 0.7∘ (Monte Settepani), and the direction is
SSE for Bric della Croce and NNW for Monte Settepani.
Intersection (a) of Bric della Croce (red point) and Monte
Settepani (blue point) radar beams for elevations 0.7∘ (Bric della
Croce) and 1.2∘ (Monte Settepani). The overlapping volume is about
halfway between the two radars. Ground projection of the overlapping volume
(b) of the Bric della Croce radar (elevation angle: 1.2∘) and
the Monte Settepani radar (elevation angle: 0.7∘). The Bric della Croce radar
is the northernmost. The colors represent the altitude in meters of the main
beam center axis. The triangle is located halfway between the Bric della Croce
and Monte Settepani radars.
The vertical tolerance is set to 100 m above and below the intersection of
the two main beam axes. To select radar cells with similar volume, a
threshold is imposed on the difference of the distances between the selected
cell and the two radars, i.e., |Δcell,RadarA-Δcell,RadarB|. When projected on the ground, this value must
not exceed 40 km. For each pair of elevations in the scan strategy of the
two radars, intersecting bins in the overlapping area are computed. The beam
height is calculated on a spatial grid with geographical coordinates, and the
cells where the difference between the beam heights is below the tolerance
are selected. The position of the detected cells is then converted from
geographical coordinates to bin-azimuth coordinates of each radar.
The Bric della Croce radar is located at 736 m a.s.l. near Turin, while the
Monte Settepani radar is at 1386 m a.s.l. in the Ligurian Apennines. One of the most
suitable pairs of elevation scans is represented in
Fig. b, where the beam height of the Bric della Croce
scan at 1.2∘ and the Monte Settepani scan at 0.7∘ is shown. Due
to the different radar altitudes, the second elevation scan of Monte
Settepani is combined with the third elevation scan of the Bric della Croce
radar, and the altitude of the main beam center axis is about 2500 m. The
overlapping volume that satisfies the vertical tolerance is displayed in blue
and is located approximately above the Cuneo plain and Asti hills.
Considering all elevation pairs, the total number of intersecting bins that
satisfy the imposed geometrical conditions is about 105.
The intercalibration procedure then requires a statical look-up table (LUT)
to store the polar coordinates of the intersecting bins. For these selected
bins, the corresponding radar observations are extracted from the polar
volumes, which have been preprocessed as reported in Sect. . In
addition to the reflectivity, the correlation coefficient ρhv is also
considered in the analysis to select only rain measurements, associated with
ρhv>0.95. Since different paths inside the melting layer may
experience different attenuation, the data are selected below the freezing
level retrieved from a numerical weather prediction (NWP) model, to reduce the
uncertainty introduced by the melting layer. Furthermore, the radome may
attenuate the electromagnetic radiation during heavy rain; therefore the
reflectivity data measured during rain above any of the two radars are
removed, using a threshold of 20 dBZ on the mean value of the reflectivity
measured close to the radar. Finally, to avoid considering observations in
regions where the radar beam is blocked by the orography, a digital elevation
model (DEM) is adopted to simulate the radar visibility along the radials.
Ground clutter calibration
The aim of the ground clutter calibration is to extract information about the
radar system calibration from well-know targets. The ground clutter
calibration uses a large set of echoes from scans of ground clutter at low elevation
to provide a stable reference empirical cumulative distribution
function (ECDF) of clutter reflectivity. The statistical approach is needed
since clutter echoes may vary over time, e.g., due to anomalous propagation of
the radar beam, wind, vegetation changes or snow coverage. The ground clutter
calibration allows monitoring the stability over time of the radar
calibration considering the value where the ECDF reaches the 95th percentile
. In this paper, this technique has been applied to both
polarization channels of polarimetric weather radars.
Mean reflectivity value and frequency of clutter echoes collected by
the Bric della Croce (figures a and b) and by Monte Settepani
(figures c and d) radars at the lowest elevations:
-0.1 and -0.3∘, respectively. The maximum value exceeds
64 dBZ, and 100 % represents very stable echoes.
The key points of the ground clutter calibration have been stated by
, and the success of the procedure depends on
the ground returns' stability;
the stability of elevation angle at which the clutter echoes are measured;
the rainfall rate: the precipitation echoes must not dominate the clutter echoes.
When these conditions are met, surface clutter echoes can be used in the
ground clutter calibration because of their limited variability over time.
Different samples have a different ECDF, but the values at which the ECDF
reaches 0.95 should not change over time for a given radar system
.
The method of the ground clutter calibration is based on a clutter mask that
is used to select clutter echoes that appear very frequently in the radar
images. This is intended to minimize the possible contamination by
meteorological echoes ( and ). The
radar volumes are processed by the hydrometeor classification algorithm
to identify clutter and meteorological
echoes. Subsequently, empirical thresholds are applied to the volumes in order
to be used for the clutter statistics: the percentage of meteorological
echoes should be less than 1 % and the percentage of clutter echoes greater
than 12 % of the total echoes inside the volume. The radar volume scans
meeting these criteria are processed on a daily basis to calculate a map of
the average clutter reflectivity and a map of the frequency of occurrence of
the clutter echoes. In order to avoid sudden clutter modifications, both maps
are averaged with the corresponding maps from the previous days. The clutter
masks are generated for each elevation of the volume scan and for each
operational radar.
The clutter masks of the Bric della Croce radar at the lowest elevation are
shown in Fig. a and b. Most of the clutter echoes have a
mean frequency above 95 % (Fig. b), meaning that there
were no significant changes in their spatial distribution. The Alps are the
most important source of clutter, whose reflectivity may exceed 65 dBZ in
some areas (Fig. a). The mean value and the frequency of
clutter echoes for the Monte Settepani radar are shown in
Fig. c and d.
It has been observed that the clutter echo ECDF may not have a steep slope
around the 95th percentile, depending on the nature of the clutter echoes.
Especially for the Monte Settepani radar, it has been noted that the limited
slope of clutter echo ECDF yields a high uncertainty of the daily mean
value of the 95th percentile. Therefore, we empirically investigated a
threshold on the clutter reflectivity in order to increase the ECDF slope
around the 95th percentile by removing weak clutter echoes. As a result, the
threshold is imposed at 20 dBZ, corresponding to the best compromise between
the ECDF slope and the amount of clutter echoes.
Sun calibration
The calibration of radar systems using the Sun as a radio source was first
proposed by and developed in several works by
, ,
, ,
, and
. The Sun is used for monitoring the receiver
calibration, the alignment of the radar antenna and checking the antenna gain
. According to and
, the antenna elevation and effective receiver system
gain could be determined within 0.05∘ and 0.2 dB, respectively. The
peculiarities of the Sun as a natural microwave source are
0.57∘ apparent angular diameter;
differential reflectivity about 0 dB, because the radiation is not polarized;
in radar polar plot (azimuth range), the solar interference appears as a uniform signal along one or more
radials.
The Sun calibration is performed on reflectivity and differential
reflectivity data. The method proposed by does not
require stopping the operational radar scans (in contrast, the Sun tracking
task requires stopping the normal radar operations) because it seeks the solar
rays intercepted during the operational scanning. The Sun position is
computed theoretically at the radar location, and then it is converted into
azimuth and range bins. The automated routine scans the rays in the region
(defined by an azimuthal tolerance) where the Sun should be seen by the
radar. If the fraction of valid bins inside the detected ray is higher than
typically 0.9 and the standard deviation of the computed power is less than
1 dB, the ray is flagged as a solar ray .
The Sun elevation is corrected for the atmospheric refraction
. The calculated correction is maximum at zero
elevation and never exceeds 0.5∘. The solar flux is continuously
monitored at S-band by the Dominion Radio Astrophysical Observatory (DRAO) in
Canada. The current solar flux is obtained from the ftp server of DRAO
observatory:
ftp://ftp.geolab.nrcan.gc.ca/data/solar_flux/daily_flux_values/fluxtable.txt.
The solar flux is given in solar flux units:
1 sfu =10-22 W m-2 Hz-1. The S-band solar flux
measurements can be applied to other frequencies with an accuracy of roughly
1 dB. The reference solar flux is converted at the radar band (C-band) by
Eq. () :
FC=0.71×(FS-64)+126(sfu).
The estimated solar power PSun received by the radar is given by
PSun=1210-13ΔfAFC(W),
where Δf is the bandwidth of the radar receiver in megahertz and A is the
effective area of the antenna in square meters (m2). The factor 1/2 takes into
account the unpolarized nature of the Sun, while the radar separately
receives the horizontal and vertical polarized components of the incoming
radiation. The estimated received solar power is compared with the solar
power measured by the radar. The solar power is computed by the radar
equation from the radar reflectivity measured at a given range:
P(dBm)=Z(dBZ)-20Log(R)-2aR-C,
where R is the range (km), C the radar constant (dB) and
a the one-way gaseous attenuation (dB). The received solar power
must be corrected for the gaseous attenuation between the radar antenna and
the top of the atmosphere (TOA), for the imperfect overlap with the antenna
sensitivity pattern and for the averaging of the received power while the
antenna is rotating . The solar power received by the
radar can be fit to a theoretical model in which the received power is
represented by a Gaussian function. The model proposed by
and discussed by is
given by
Pdet=AgasAavgPTOAe-4ln(2)(az-azbias)2Δc,eff2+(el-elbias)2Δc2,
where Δc represents the vertical antenna–Sun
convolution, and Δc,eff the scanning solar width
. The solar power received by the radar, named Pdet,
and the power at the top of the atmosphere, named PTOA, are in milliwatts.
The dimensionless gas attenuation and antenna averaging coefficients are Aavg
and Agas=10(a/10), respectively. The three model parameters
are the power at the top of the atmosphere as seen by the radar
PTOA, the azimuthal bias azbias and the elevation
bias elbias. The biases represent the antenna pointing deviation
and are computed from the difference Δazimuth=azradar-azSun and Δelevation=elradar-elSun. The difference between the radar and Sun elevations is
corrected by
Δelevation=(elradar-elSun)×cos(elradar),
where cos(elradar) projects the incline plane on the
horizontal plane. Operatively, the fit is computed by the nonlinear least-squares
method, whose outputs are the fit parameters, their uncertainties and
the fit residual standard error. The summary of parameters used in the Sun calibration is reported in Table .
Summary of parameters used in the Sun calibration. The radar beam width
refers to the C-band radars managed by Arpa Piemonte.
ParameterValueOne-way gaseous attenuation, a (dB km-1)0.0194/3 of Earth's radius, RE (km)8495Solar beam width, Δs (∘)0.57Radar beam width, Δr (∘)0.94Antenna–Sun convolution, Δc (∘)1Effective antenna–Sun convolution, Δc,eff (∘)1.2Azimuthal bin size, Δx (∘)1Results
The stability of the radar calibration is evaluated for the period between 28
July and 13 October 2014. The self-consistency technique is adopted to ensure
the absolute calibration of the radars during rainfall. In the analyzed
period, when the precipitation data are not suitable to perform the
self-consistency and the intercalibration procedures, the clutter and Sun
calibration allow the stability of the calibration to be monitored.
Radar absolute calibration with self-consistency
Histogram of differential reflectivity echoes satisfying the
selection criteria discussed in Sect. . Bric della Croce
radar, 13 October 2014.
The differential reflectivity calibration is verified, as reported in
Sect. , using observations in drizzle. The results, reported
in the histograms of Figs. and , show a
roughly symmetric distribution, with the most populated class being the one
comprised between 0 and 0.2 dB for both systems. Therefore, Zdr
is considered to be properly calibrated, and the self-consistency technique
may be performed. The rain rates previously described (Eqs. and
) are computed on the 10 min scans at 0.5∘ for Bric
della Croce and 0.7∘ for Monte Settepani for the whole day. The rain
rate estimation based on ZH and Zdr is compared to
the Kdp-based rain rate, which is considered unbiased. The
results are presented as a density scatterplot of the rain rates in
logarithmic scale, with the colors displaying the density of data. A linear
fit with 1:1 slope is computed to estimate the intercept value, which is
then converted to the system bias using Eq. (). Since
Kdp in light rain is noisy, inclusion of these data may affect
the regression results. The standard deviation of estimated Kdp
in drizzle (σdrizzle(Kdp)), where
Kdp is expected to be nearly 0 ∘ km-1, is assumed as the noise level. For both
systems we found σdrizzle(Kdp)≃0.4∘km-1. From Eq. (), the corresponding
rain rate value is
Rmin=32.8(σdrizzle(Kdp))0.85≃14mmh-1.
So, the minimum rain rate, considered for the estimation of the system gain
bias, is 14 mm h-1, equivalent to 11 dBR on a decibel scale for both radars.
The perfect agreement of the two rain rate estimations is represented by the
1:1 line. In the density scatterplot, the total number of data, the
bisector, the fit outputs (uncertainty, intercept and the correlation
coefficient) and the computed bias are displayed. Thus, the self-consistency
technique is performed on 28 July 2014, when thunderstorm cells occurred in
the Piemonte and Liguria regions. Figure shows the
density scatterplot of rain rates calculated on Bric della Croce data. For
rain rates above 11 dBR, there is an overall fair agreement, with the
highest density of data being below the 1:1 line. The computed system gain bias
is slightly negative: -0.9 dB.
As in Fig. but for the Monte Settepani radar, 10
October 2014.
Self-consistency procedure applied on the Bric della Croce radar, 28
July 2014. The Kdp-based rain rate, on a decibel scale, is shown in the
x axis, and the rain rate based on Z and Zdr, on a decibel scale, in
the y axis. The colors represent the density of data from blue (low
density) to violet (high density), as reported in the color bar in logarithmic
units using 1 dBR intervals for both axes. The black and green line display
the 1:1 line and the fit with slope set at 1, respectively, performed on the data with
rain rate greater than 14 mm h-1. The total number of data, the fit
uncertainty, the intercept value (in dB), the correlation coefficient and the
computed system bias are reported in the plot.
Figure displays the density scatterplot of rain rates
calculated on Monte Settepani data. For rain rates above 11 dBR, the higher
amount of data is located above the 1:1 line, pointing out the
overestimation of the Z- and Zdr-based rain rate. The computed
system gain bias is positive: 1 dB.
As in Fig. but for the Monte Settepani radar.
The radar absolute calibration is also checked during the whole study period
and, in particular, on 13 October 2014. During this event, a flood occurred
in southeastern Piemonte (Arquata Scrivia), about 30 km north of
Genoa, with 24 h cumulative precipitation exceeding 400 mm
(Fig. ).
24 h cumulative precipitation in millimeters (color scale) from the Bric della
Croce radar on 13 October 2014. The axes display the east and north distances
from the radar. The black point refers to the city of Genoa.
Figure represents the rain rate density
scatterplot in logarithmic scale for the Bric della Croce radar, showing a
remarkable density pattern around the bisector. The computed system gain bias
is -0.49 dB. For the Monte Settepani radar,
Fig. shows the corresponding rain rate
density plot. Due to the different geometric view of the storm, in this case
the distribution of the observations in the polar domain is dominated by
moderate rain rates, although for heavy rainfall the agreement is quite good,
with a computed system gain of only -0.13 dB.
Monitoring of the radar calibration stability
Between the absolute calibration checks, the radar calibration is monitored
by the ground clutter calibration and the Sun calibration. In addition,
during precipitation, the intercalibration procedure is performed.
Intercalibration
Whenever precipitation is occurring on the overlapping area between the two
radars, the intercalibration is performed as described in
Sect. . The intercalibration results are displayed as
a density scatterplot of all reflectivity data;
a density scatterplot of reflectivity pairs, associated with ρhv>0.95,
acquired below the melting layer and in dry-radome conditions.
For each density scatterplot, a linear fit is compared with a 1:1 slope. If
the radar calibration degrades, the system bias appears as a nonzero
intercept value of the fit. The amount of scatters may vary depending on
several factors, including the temporal and spatial alignment of the
observations and the type of the precipitation (stratiform vs. convective).
In the figures, the total number of data, the residual standard error of the
fit (Sigma), the intercept value and the linear correlation coefficient
R are displayed. In Fig. , the intercalibration performed
on 28 July 2014 is displayed. First, the intercalibration is executed without
thresholds on the copolar correlation coefficient, including all reflectivity
irrespective of the height relative to the freezing level. In
Fig. (left), the highest density of reflectivity pairs,
denoted with warm colors, is located above the 1:1 line (black), and the
total number of reflectivity pairs is about 56 000. A linear fit is applied
on the reflectivity pairs with slope fixed at 1, and the computed intercept
is about 4 dBZ with a fit uncertainty of about 6 dB. Then, the reflectivity
pairs are filtered according to the aforementioned selection criteria. In
Fig. (right), the highest density of reflectivity is closer
to the 1:1 line, and the total number of data is about 4000. Hence, the
selection criteria have reduced the total number of reflectivity pairs by
about an order of magnitude. The intercept is 2.4 dBZ, and the fit
uncertainty has been reduced to about 4 dB. Therefore, the intercept value
is positive, meaning that the Monte Settepani radar overestimates the radar
reflectivity values of rainfall when compared to the Bric della Croce radar.
As in Fig. but for the Bric della Croce radar,
13 October 2014.
Ground clutter calibration
The online hydrometeor classification processing allows selecting the polar
volumes without meteorological echoes for application of the ground clutter
calibration. The output of the daily calibration is the set of the individual
ground clutter ECDFs, from which suitable visualizations may be implemented
for ease of online monitoring. In the current implementation, the image of
the daily ECDFs of horizontal and vertical reflectivity with the enlargement
around the 95th percentile are displayed. In addition, the historical trend
of the daily average 95th percentile is produced as a time series plot.
As in Fig. but for the Monte Settepani radar, 13
October 2014.
Intercalibration between Bric della Croce and Monte Settepani, 28
July 2014. Comparison considering all the reflectivity pairs (left) and the
reflectivity pairs, associated with ρhv>0.95, acquired during
dry-radome conditions and below the melting layer (right). The color bar
displays the number of observations in logarithmic units using 0.25 dBZ
intervals for both axes.
ZH and Zv ECDF with respective enlargements
around the 95th percentile, Bric della Croce radar at elevation 0.5∘,
7 October 2014. Each line represents the ECDF for a single plan position indicator (PPI).
Figure is an example of ground clutter calibration
in normal operational conditions: the 95th-percentile values of
ZH and ZV are very similar, and the spread of the
individual ECDFs around the 95th percentile is quite narrow. When the
enlargement around the 95th percentile is compared, the ECDFs of the horizontal
polarization channel reach the 95th percentile at a value about 0.5 dB
lower than the vertical polarization channel. The historical trend from 28
July to 13 October 2014 shows a remarkable stability of the radar calibration
(Fig. ). The variability of the difference between to
two channels is also quite limited over the study period and always within
the standard deviation of the daily sample. It is interesting to note the
increase of the 95th percentile around 27 September 2014: analyzing the
meteorological conditions and using radio sounding data, we noticed that the
radar beam was likely bent, due to anomalous propagation. Thus, in this
case, the anomalous propagation of the radar beam added about 1 dB to the
trend value of the 95th-percentile mean.
Daily mean values of the 95th percentile of all daily scans of
ZH (top) and Zdr (center) ECDFs. The bottom plot
shows the number of scans used to compute the daily mean values. The error
bars represents the standard deviation.
Sun calibration
Every 5 days, the radar calibration is operatively monitored by the Sun
calibration performed on the previous 5 days. The daily number of
detected solar interferences depends on the season, i.e., on the
ascent / descent rate of the Sun, on the solar activity, on scanning strategy
and on the sensitivity of the radar receiver. This procedure has been applied
to both radars, but in this section only the results for the Monte Settepani one
are discussed.
During September 2014, the Monte Settepani radar collected 130 solar
interferences, represented in the scatterplot of
Fig. . The x axis represents the Δazimuth (see Sect. ), the y axis the Δelevation and the colors the received power in decibel milliwatts (dBm). The isolines show the
value of the received power at a given point on the Δazimuth–Δelevation
plane, computed by the theoretical model fit. It is
evident that the solar interferences are scattered over roughly 1∘ in
both azimuth and elevation around the antenna pointing, the black rhombus in
Fig. . The calculated bias in azimuth and elevation, the mean squared error
and the Zdr bias are reported in the figure.
Scatterplot of solar interferences collected by the Monte Settepani
radar during September 2014. The x axis represents the difference between
the radar and Sun azimuths, the y axis the difference between the radar and
Sun elevations, and the colors the received power in decibel milliwatts (dBm). The isolines show
the value of the received power in a given point on the Δazimuth–Δelevation plane, computed by the theoretical
model fit. The black rhombus is the antenna pointing. The calculated bias in
azimuth and elevation, the mean squared error and the Zdr bias
are reported in the figure.
Daily analysis of the solar interferences detected by the Monte
Settepani radar during July–October 2014. The value of the power at the top
of the atmosphere (PTOA) seen by the radar, computed from the
daily solar interferences, is displayed as red points. The error bars are
calculated, for each day, as the square root of the differences between all
the measured solar powers and the corresponding values computed by the
theoretical model. The blue points display the DRAO reference values of the
solar power. The amount of the collected solar interferences for each day is
shown by the numbers in the plot.
The solar interferences are also analyzed to evaluate the receiver
calibration, in addition to the antenna pointing accuracy during the study
period. The computed power at the top of the atmosphere (PTOA) is
shown together with the reference values form DRAO in
Fig. . The computed value of the power at the top of the
atmosphere seen by the radar from the daily solar interferences is displayed
with the fit uncertainty. The PTOA values have been chosen as the
quantity to be compared with the DRAO reference since it is calculated by the
theoretical model and represents the solar power received by the radar
when the antenna beam is centered on the Sun. The reference values are
considered without uncertainty. The numbers above the x axis represent the
number of interferences on which the mean and uncertainty values are
calculated. The days with missing values are due to a radar hardware failure.
The mean difference between the daily PTOA value and the DRAO
reference is 0.5 dBm, and the correlation is 0.88. The azimuthal and
elevation biases are computed by the three parameters' model inversion
. The azimuth bias and elevation bias from July to
October 2014 are displayed in Fig. . The azimuth and
elevation biases are both slightly negative but approximately constant
during the whole period. The Sun calibration also allows the
values of the differential reflectivity to be monitored. As previously mentioned, the
intrinsic solar Zdr should be 0 since the Sun is an
unpolarized source of microwave radiation. In this work, the observed solar
Zdr is monitored considering its mean value along the solar ray.
The daily value of the observed solar Zdr is shown in
Fig. , where the error bars represent the standard
deviation calculated on the data of the given day. The mean value of the
daily Zdr values deviates significantly from the expected
0 dB value, but no remarkable changes are visible during the study period.
Daily analysis of azimuth bias (top) and elevation bias (bottom) of
the Monte Settepani radar during July–October 2014.
Daily analysis of the differential reflectivity of the solar
interferences detected by the Monte Settepani radar during July–October
2014. The error bars represent the standard deviation of the daily
Zdr values.
Discussion and conclusions
Four different procedures have been considered to operationally monitor the
radar calibration, namely self-consistency, ground clutter calibration,
intercalibration and Sun calibration. The proposed approach for online
monitoring consists in the integration of the results of the discussed
calibration techniques. The study period has been chosen as 28 July–13 October
2014, and the measurements have been acquired by the radars managed
by Arpa Piemonte, Bric della Croce and Monte Settepani located in NW
Italy, considering the operational volume scans with 10 min update
frequency.
The reference absolute calibration is provided by the self-consistency
technique, requiring that Zdr is properly calibrated, which is
verified in drizzle medium. Nevertheless, since the operative scan cannot be
modified to introduce the vertical pointing and since the accuracy of the
Zdr calibration in drizzle is about 0.5 dB, the stability of the
Zdr calibration is monitored using the Sun returns, which shows a
higher accuracy. The self-consistency technique is influenced by the adopted
drop shape model and variability of the DSD: in
particular, different DSDs and drop shape models can produce up to a 3–4 dB
difference in the reflectivity estimates . The
proposed approach considers observations collected over a whole day,
disregarding weak rainfall intensity data, where Kdp is
excessively affected by noise.
Figure provides a comprehensive view of the results achieved
using the calibration monitoring techniques. This combined visualization
represents an effective tool to operationally monitor and detect eventual
drifts in the radar calibration, allowing a quick and efficient
interpretation of the results obtained with the individual techniques.
Monitoring the stability of radar calibration. From the top, Bric
della Croce (blue) and Monte Settepani (red) self-consistency; Bric della
Croce ground clutter and Sun calibrations; Bric della Croce and Monte
Settepani intercalibration (green); Monte Settepani ground clutter and Sun
calibrations. The error bars represent the estimated uncertainty. In the Sun
calibration, the DRAO reference at 20:00 UTC, as reported in
, is subtracted from the observed solar power. The
vertical blue lines divide the study period in three sectors as reported in
the text.
For the Bric della Croce radar, using the self-consistency, a system bias of less
than 1 dB has been found during the selected rainfall events, except for
15 August 2014, when the system gain bias reaches 1.2 dB.
The ground clutter and Sun calibration of the Bric della Croce radar
(Fig. , second panel) show a good stability of the radar
calibration.
For the Monte Settepani radar, the self-consistency calibration allowed a system
gain bias of 1 dB (28 July 2014) and of -0.1 dB (13
October 2014) to be estimated. The step of about 3 dB between 4 August
and 13 August, and of about 4 dB between 23 August and 18 September, is
noticeable, indicating a calibration issue. The self-consistency, the intercalibration
and the Monte Settepani ground clutter calibration (Fig. , top
third and bottom panels) suggest that the study period may be divided into
three sections: from 28 July to 12 August, from 12 August to 17 September and
from 17 September to 13 October. Until 12 August, the mean value of the Monte
Settepani ground clutter 95th percentile is 57 dB, and during rainfalls the
Monte Settepani radar overestimates the radar reflectivity of about 2 dB
when compared to the Bric della Croce radar. On 12 August, a transmitter
module broke down and the radar continued the normal operations with a lower
pulse power, due to a decrease of the Klystron cathode current. In fact, the
ground clutter calibration shows a step between 11 and 12 August, and the 95th
percentile of the reflectivity ECDF decreases at 54.7 dB. In the same period
the intercalibration shows the Monte Settepani underestimation of the radar
reflectivity. On 4 September a second module broke down and the radar
stopped. The radar was repaired on 17 September, when two transmitter modules
were substituted. Nevertheless, the ground clutter calibration from 17
September to 13 October displays a mean value of 56 dB, 1 dB lower than the
mean value until 12 August. This difference is also pointed out by the
self-consistency as a decrease of about 1 dB in the system gain bias between
28 July and 13 October. On the other hand, the receiving-chain Sun calibration
results show a fair agreement between the solar power at the top of the
atmosphere as seen by the radar and the DRAO reference.
The decrease of the Monte Settepani system bias is 1.1 dB. Even if this
value is lower than the self-consistency accuracy, this change is also found
in the ground clutter calibration from the difference between the mean value
of the 95th percentile of clutter echo reflectivity averaged before 12
August and after 17 September. The integrated calibration approach then
suggests that this change in the absolute calibration of the radar should not
be ascribed to the self-consistency uncertainty but may likely be related to
some change in the transmitter subsystem during the corrective maintenance on
17 September.
We can note that the self-consistency trends of the Bric della Croce and Monte
Settepani radars are similar, indicating a correlation in the estimates
obtained using two independent sets of measurements acquired by two different
systems. In fact, the standard deviation of the difference of the
self-consistency biases between the Monte Settepani and Bric della Croce radars
(0.82 dB) is lower than the quadratic sum of the two separate standard
deviations, computed on the two radars separately (1.12 dB). This seems to
indicate a likely role of the specific meteorological conditions and
associated precipitation microphysics .
A more comprehensive monitoring tool, ΔTR, incorporating the
clutter and the self-consistency calibration, is reported in
Figs. and , showing a mean value around 0 for
the Bric della Croce radar and pointing out the calibration issue in the Monte
Settepani radar. In fact, the decrease of the
ΔTR from 0 to -2.5 dB is remarkable. The root mean squared error (RMSE) of the
transmission and reception calibration is evaluated for the Bric della Croce
radar, since no calibration issues were found. The RMSE is 0.38 dB for the
integrated approach; when considering the techniques separately, the clutter
calibration RMSE is 0.45 dB and self-consistency RMSE is 0.79 dB. The
integration of the techniques, which monitor the transmission and reception
calibration, provides a more robust and stable tool with which to detect eventual drifts
in the radar calibration.
ΔTR, as defined in Sect. ,
computed weekly during the study period for the Bric della Croce radar. The
error bars represent its uncertainty.
The impact of a proper calibration is investigated in the QPE product. In
Fig. , we show the comparison between the retrieved rain rate
from radar measurements and the rain rate measured by rain gauges located
within 70 km from the Monte Settepani radar. The radar-based rainfall estimation
is obtained using a Z–R relation with coefficients A=300 and B=1.5. The left-side scatterplot displays the rainfall that
occurred during 28 and 29 July, and 1 and 4 August. This scatterplot is
considered as a reference since no calibration issues were found on those days.
Instead, the right-side scatterplot shows, in blue color, the rain rate
comparison during 13, 15, 19 and 23 August, when the self-consistency and
clutter calibration techniques show a radar miscalibration (about 3 dB).
After correction of the radar reflectivity according to the values found by
the aforementioned procedures (red color in the scatterplot), the magnitude
of the normalized mean bias is substantially decreased.
As in Fig. but for the Monte Settepani radar.
Comparison between rain rates retrieved from radar measurements and
rain rates measured by rain gauges within 70 km from the Monte Settepani radar. The left
panel is assumed as a reference since there was no evidence of calibration
issues. In the right panel, the blue points refer to rain rates retrieved
when the Monte Settepani radar suffered from miscalibration. The radar measurements
are corrected according to the integrated-approach result, and the estimated
rain rates are shown in red. The correlation coefficient, r, and the
normalized mean bias, NMB, are reported.
Each calibration procedure is able to monitor a specific part of the radar
system (e.g., receiving chain, transmitting chain, antenna pointing,
polarization channels), and the self-consistency technique allows
the absolute calibration of the radar to be estimated. The advantages of this integrated
approach are (1) the extensive use of operational routines that do not
require stopping the radar and (2) the integration of the results of several
techniques exploiting different targets (ground clutter, Sun, rainfall) and
based on different measurements (reflectivity only, polarimetric
observations). The self-consistency procedure has been applied, in this
preliminary work, on the precipitation cases selected for the
intercalibration technique. In order to increase the accuracy of the
procedure, more work is needed in particular to derive robust automatic data
selection criteria. The potential limitations of the proposed method could be
related to the winter months, when echoes in the lowest atmospheric levels
are from solid precipitation. The self-consistency and the intercalibration
approach, which are intended for use in the liquid phase, cannot be
performed. In addition, since winter is the driest period in the
considered region, the clutter and Sun calibrations become especially
relevant during this part of the year.
Overall, the integrated approach showed a capability to detect calibration
losses with a high level of confidence derived from the combination of
different techniques, and with an accuracy of about 2 dB. Although a 1 dB
calibration accuracy is in general the ultimate goal, the achieved results
exploiting only the operational radar scans are considered adequate to
automatically detect any unexpected change in the radar system requiring
further data analysis or on-site measurements.
Data availability
The radar data used in this study are available by request from Arpa Piemonte
(www.arpa.piemonte.it).
Acknowledgements
The work has been in part supported by a grant, D.D. no. 1243 of 20 December
2013, by the Italian National Civil Protection. The participation of
V. Chandrasekar was supported by the DOE-ASR program. Edited by: G. Vulpiani Reviewed by: four
anonymous referees
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