AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus GmbHGöttingen, Germany10.5194/amt-7-4151-2014Performance of high-resolution X-band weather radar networks – the PATTERN exampleLengfeldK.katharina.lengfeld@zmaw.deClemensM.MünsterH.AmentF.Meteorological Institute of the University of Hamburg, Hamburg, GermanyMax-Planck-Institute for Meteorology, Hamburg, GermanyK. Lengfeld (katharina.lengfeld@zmaw.de)5December20147124151416625July8August201431October201431October2014This 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://www.atmos-meas-tech.net/7/4151/2014/amt-7-4151-2014.htmlThe full text article is available as a PDF file from https://www.atmos-meas-tech.net/7/4151/2014/amt-7-4151-2014.pdf
This publication intends to prove that a network of low-cost local area
weather radars (LAWR) is a reliable and scientifically valuable complement to
nationwide radar networks. A network of four LAWRs has been installed in
northern Germany within the framework of the Precipitation and Attenuation
Estimates from a High-Resolution Weather Radar Network (PATTERN) project
observing precipitation with a temporal resolution of 30 s, a range
resolution of 60 m and a sampling resolution of 1 ∘ in the azimuthal
direction. The network covers an area of 60 km × 80 km. In this
paper, algorithms used to obtain undisturbed precipitation fields from raw
reflectivity data are described, and their performance is analysed. In order
to correct operationally for background noise in reflectivity measurements,
noise level estimates from the measured reflectivity field are combined with
noise levels from the last 10 time steps. For detection of non-meteorological
echoes, two different kinds of clutter algorithms are applied: single-radar
algorithms and network-based algorithms. Besides well-established algorithms
based on the texture of the logarithmic reflectivity field (TDBZ) or sign
changes in the reflectivity gradient (SPIN), the advantage of the unique
features of the high temporal and spatial resolution of the network is used
for clutter detection. Overall, the network-based clutter algorithm works
best with a detection rate of up to 70 %, followed by the classic TDBZ
filter using the texture of the logarithmic reflectivity field.
A comparison of a reflectivity field from the PATTERN network with the
product from a C-band radar operated by the German Meteorological Service
indicates high spatial accordance of both systems in the geographical
position of the rain event as well as reflectivity maxima. Long-term
statistics from May to September 2013 prove very good accordance of the
X-band radar of the network with C-band radar, but, especially at the border
of precipitation events, higher-resolved X-band radar measurements provide
more detailed information on precipitation structure because the 1 km range
gate of C-band radars is only partially covered with rain. The standard
deviation within a range gate of the C-band radar with a range resolution of
1 km is up to 3 dBZ at the borders of rain events. The probability of
detection is at least 90 %, the false alarm ratio less than 10 % for
both systems. Therefore, a network of high-resolution low-cost LAWRs can give
valuable information on the small-scale structure of rain events in areas of
special interest, e.g. urban regions, in addition to the nationwide radar
networks.
Introduction
Flood forecasting, urban hydrology, hydrometeorological applications and
management of risk and uncertainty require high-resolution spatial and
temporal rainfall estimates near the ground with less than 0.1 km and
1 min, respectively . Therefore, radar systems capable of
producing reliable and accurate quantitative estimates of precipitation at
high temporal and spatial resolution are needed. Rainfall products of
conventional radar systems used in nationwide or even larger networks are
generally based on reflectivity measurements at S- or C-band frequencies with
a temporal resolution of several minutes and a spatial resolution of a few
hundred metres.
To meet present and future demands of resolution, radar observations at
shorter wavelengths are a promising option, as the resolution depends, among
other factors, on the width of the antenna and the wavelength. Therefore,
recent studies support observations at X-band frequencies as an alternative
or an addition to S- and C-bands to fulfil the
requirements of urban drainage system modelling as input for rainfall–runoff models of rural river systems,
hydraulic simulations, insurance proof, detailed information on extreme
events, and many more. Besides higher resolution, radars operating at high
frequencies benefit from lower costs resulting from smaller antenna size
compared to long-wave radars. X-band radars can also derive reliable
precipitation estimates close to the ground due to their relatively short
range. S- or C-band radars measure within a range of hundreds of
kilometres. Therefore, they cannot
observe rainfall near the ground, because the radar beam increases in height
with increasing distance to the radar due to the elevation angle and the
Earth's curvature. Measurements taken at a few kilometres in height above the
Earth's surface need to be extrapolated to give an estimation of rainfall on
the ground. These techniques are limited and imprecise, leading to large
uncertainties in estimated reflectivity.
In contrast to long wavelengths, reflectivity measurements at shorter
wavelengths, especially at X- and K-bands, are significantly attenuated by
liquid water along their paths, where the specific attenuation at any
distance depends on the size distribution of raindrops and their extinction
cross section. The magnitude of attenuation is generally inverse to the
wavelength, and the specific attenuation at the X-band is approximately 2
orders of magnitude higher than at the S-band, according to .
While the effect of attenuation at the S-band is practically negligible, it
becomes increasingly serious as the wavelength is reduced, and corrections
have to be applied to retrieve intrinsic reflectivity. The basics of
microwave attenuation by rain have already been discussed by many authors,
e.g. , , , ,
and , to mention the earliest.
To overcome the apparent drawback of strong attenuation at X-band
frequencies, several authors introduced concepts of overlapping radar
networks consisting of two or more radars. These methods allow for estimation
of attenuation and correction of observed reflectivities simultaneously, if
at least two radars observe a common volume (;
; ; ;
; ). In the last few years, several
networks consisting of different types of X-band radars have been installed
to fill gaps in nationwide networks of C- or S-band radars, e.g. within the
CASA (Collaborative Adaptive Sensing of the Atmosphere) project
(; ), in complex terrain, or in areas
where detailed information on rainfall is of high interest, e.g. near
airports , in mountainous regions (;
; ) or in flood-prone areas
, to name a few of them.
Comparing the existing X-band radar networks, one can distinguish between
three different approaches. On the one hand, there are highly sensitive
X-band weather radar systems featuring dual polarisation as a standard, with
a peak power of about 75 kW and a typical antenna size of 2.5 m in diameter
(e.g. ). The maximum range is of the order of 100 km, with a
range resolution of 20 m. On the other hand, there is an increasing number
of low-cost systems mainly based on conventional nautical radar systems with
a peak power of 25 kW (e.g. ). These systems are
characterised by small antenna diameters of less than 1 m and, in general,
they are not capable of performing measurements in Doppler or
dual-polarisation mode. The maximum range of these low-cost radars is of the
order of 20 km, with a range resolution similar to the former X-band radar
type. Due to their limited range, they are often called local area weather
radars (LAWR). These systems can serve as a sort of magnifying glass in
complementation to C- or S-band radar systems in flood-prone regions or other
areas of interest, because they are affordable not only for weather services,
but also for local authorities or private companies (10–20 % of the
price of dual-polarisation X-band radars). A third approach is systems with a
low peak power of 25 kW that perform dual-polarisation measurements with a
maximum range of the order of 100 km and a range resolution of the order of
250 m (e.g. ).
A network of four LAWRs is installed in northern Germany within the framework
of the Precipitation and Attenuation Estimates from a High-Resolution Weather
Radar Network (PATTERN) project. The goal is to demonstrate that low-cost
radar systems are a scientifically valuable tool for investigating the
spatial structure of precipitation and that a network of LAWRs can enhance
the quality of the retrieved precipitation field. The network approach based
on high-resolution X-band radars has two definite advantages compared to
large-scale C-band radar networks: gain of additional information arises from
high resolution (temporal and spatial) as well as from the wide overlapping
areas of multiple coverage. The former results from the technical
specifications of the X-band radar itself, e.g. wavelength, rotational speed
of the antenna, pulse length and repetition frequency. The latter is based on
the network set-up that is not designed to cover an area as large as possible
like nationwide C-band radar networks, but to create large overlapping areas
covered by multiple radars. Overall, these advantages could not only lead to
better attenuation estimates, but also to improvements in several retrievals
regarding clutter detection, gap filling and, finally, the estimation of
precipitation. Therefore, we will provide high-quality precipitation data in
high temporal and spatial resolution that could be beneficial for
rainfall–runoff simulation, for example. In addition, the X-band radars can
serve as gap fillers and provide precipitation estimates near the ground
in areas far away from C- or S-band radar sites where
the radar beam is several hundred metres above the ground.
The aim of this paper is to identify advantages and disadvantages of the
network as well as single X-band radars and present algorithms making use of
the network approach and the X-band-specific characteristics. The X-band
radars used in this study are described in Sect. . It also
gives an overview of the design of the network. Section
presents the algorithms that are applied to raw reflectivity data in order to
get reliable reflectivity and precipitation fields. First, algorithms are
described that are applied to individual radars, followed by algorithms that
use the advantage of having overlapping areas within the network. A
comparison with a large-scale C-band radar operated by the German
Meteorological Service (DWD) in Sect. gives a first
evaluation of the quality of precipitation fields derived from the PATTERN
network. In Sect. , conclusions are drawn, and
Sect. gives an outlook on future work.
Position of the four network radars: Hungriger Wolf tower (HWT),
Quarnstedt (QNS), Bekmünde (BKM) and Moordorf (MOD) marked in red, the
Hamburg radar marked in blue, and their 20 km range. Reference stations OST,
MST and WST are marked in green.
Radar network
A network of four X-band radars, Hungriger Wolf tower (HWT), Quarnstedt
(QNS), Bekmünde (BKM) and Moordorf (MOD), has been set up to the north of
Hamburg, Germany (Fig. , ), within the
framework of the PATTERN project. Each radar has a range of 20 km in radius
around the site to detect reflectivity. The network spans a region of
approximately 60 km × 80 km. Two radars are at least 11 km, but
not more than 16 km apart. Based on the network design, a large area is
covered by at least two radars at the border and up to four radars in the
centre of the network. Therefore, multiple information from different radars
is available on reflectivity and attenuation in a certain grid cell. This
advantage can be used for clutter detection, gap filling and attenuation
estimation. Additionally, micro rain radars (MRR) at each radar site
complement the network. These vertically profiling K-band radars measure
Doppler spectra of hydrometeors at 31 height levels. From these spectra, drop
size distributions at each height level and, finally, reflectivity as well as
rain-rate profiles are derived . To calibrate the X-band
radars and to evaluate retrieved products, three reference stations (OST, MST
and WST in Fig. ) are set up within the PATTERN area,
consisting of MRR and rain gauges corrected for wind speed at each site. The
whole PATTERN region is covered by a C-band radar operated by the DWD.
Modified ship navigation radar with parabolic dish (a),
typical radar tower in Quarnstedt (b) and radar at Hungriger
Wolf (c).
The LAWRs used in PATTERN are modified ship navigation radars of type GEM
scanner SU70-25E with 25 kW transmit power. Corresponding to technical
specifications, the modified radars are simple backscatter systems and cannot
observe Doppler shift, nor do they perform polarimetric measurements. The
original fan beam antenna is replaced by a high-gain pencil beam antenna; in
order to reduce side lobes, an offset parabolic dish of 0.85 m in diameter
is used (Fig. a). Antenna and scanning drive are protected by a
low-loss radome with air conditioning to avoid condensation within the
radome. Due to the cylindrical shape of the radome, water runs off quickly in
the case of a rain event, and attenuation due to a wet radome is minimised.
Radar control, signal processing and data management is PC based. Technical
details on radar systems and scanning schemes are listed in
Table .
In the PATTERN set-up, LAWRs measure with a pulse width of 0.4 µs
at a pulse repetition frequency of 800 Hz. Repetition frequency as well as
continuous rotation with a speed of about 24 rpm allow for reflectivity
measurements with a temporal resolution of 30 s. The beam width of the radar
is 2.8∘. Received reflectivities are averaged over a sequence of
transmitted pulses with a sampling resolution of 1∘ in the azimuthal
direction. Due to the pulse repetition frequency of 800 Hz and continuous
rotation of the antenna, the average is based on about 5 to 6 pulses per
sweep, corresponding to 67 pulses per 1∘ azimuthal range and an
averaging interval of 30 s. In comparison, the C-band radar operated by DWD
derives reflectivities from only one sweep, with approximately 40 pulses per
1∘ azimuth within about 50 ms of the 5 min interval the measurement
is valid for. Therefore, the X-band radar benefits from a temporal average
over the measuring period, in contrast to a snapshot within the measuring
period as is derived by the C-band radar. The scanning scheme of the X-band
radar is azimuthal only, but fixed elevation angles can be adjusted for
optimum operation according to site conditions. For the X-band radars of the
PATTERN network, a fixed elevation of approximately 2∘ is used.
The standard system installed at the sites consists of the radar mounted on a
two-piece steel tower of 10 m in height screwed onto a steel frame on top of
a container (Fig. b). The complete
structure is 16 m high. In demounted state, the station fits into the container, and
it can be moved easily. With the exception of HWT, all PATTERN radars are
built using this standard installation. Radar HWT is placed on an already
existing radar tower at the Hungriger Wolf former military airport
(Fig. c).
Radars operating in the X-band frequency range benefit from lower costs
resulting from smaller antenna size compared to long-wave radars. The systems
used in this study are simple single-polarised systems that scan horizontally
and do not observe Doppler shift. Therefore, they are inexpensive compared to
dual-polarised Doppler X-band radars. A radar as it is used in this network
costs approximately EUR 60 000 including the data acquisition system and
tower construction. This is less than 20 % of conventional X-band radars.
The network in this study includes four X-band radars, seven MRRs and seven
rain gauges. It was designed for research purposes and consists of more
instruments than necessary for operational precipitation estimation in local
areas. In operational use, it is possible to apply common adjustment
procedures using ground-based precipitation observations by rain gauges or
disdrometers. However, a vertical profiling instrument such as an MRR
provides the opportunity to compare directly observed reflectivity within a
common volume. One additional MRR and rain gauge in the area covered by all
X-band radars of a network would be sufficient to obtain reliable
precipitation data. The overall price of the network depends on the kind of
application and the area that should be observed. In complementation to
larger-scale radars, e.g. C- or S-band radars, one or two X-band radars can
be sufficient. Nevertheless, the network-based algorithms presented in this
study are designed for networks of at least three X-band radars.
Data processing
Weather radars cannot measure precipitation directly; they measure
reflectivity from particles along the radar path. Therefore, a raw
reflectivity signal not only contains meteorological echoes from
precipitation, but also non-meteorological echoes (clutter) and background
noise. Before reflectivities are recorded as 30 s averages, disturbances
caused by other radars and radio links are effectively eliminated by
filtering peaks within adjacent pulses: data of a single pulse at a specific
range gate are omitted if it is 2.5 dBZ larger than both the corresponding
measurements at the previous and following pulses. This filter suppresses
effectively interferences from other X-band sources. The filter is
insensitive with respect to the selection of the threshold, since the
disturbing signals are in general very strong. The value of 2.5 dBZ was
determined by analysing raw pulse-to-pulse radar data output and manual
detection of artificial signals.
Estimating noise level for radar MOD for 15 May 2013, 15:28:30 UTC:
(a) raw reflectivity field, (b) reflectivity field without
background noise, with the red line indicating a 60∘ azimuth, and
(c) noise level and radar signal as a function of the distance to
the radar.
In the following, algorithms for single radars are presented for estimating
background noise, calibrating the X-band radar network with MRR measurements
and correcting for attenuation. Additionally, retrievals are described to
identify non-meteorological echoes using single radar measurements as well as
the advantage of having areas of multiple coverage within the network. The
functionality of the algorithms is demonstrated exemplarily for a rain event
on 15 May 2013 at 15:28:30 UTC observed by radar MOD. The raw reflectivity
field of this event as measured by radar MOD also includes, besides
precipitation, background noise, interferences and clutter
(Fig. a). The rain event covers the western part of the radar
image, with reflectivities of up to 50 dBZ, and stands out clearly from the
background noise. Clutter is mainly evident in the centre close to the radar
site as small-scale disturbances with high reflectivity values.
Noise detection
All reflectivity measurements by radars are affected by noise from internal
electrical circuits used in the receiver chain or by atmospheric noise from
outside the system. An accurate estimation of the background noise is
necessary, especially in the detection of weak weather signals. A detection
algorithm based on received signals has to be implemented in the data
processing, because the used LAWRs cannot measure the noise level directly.
Power P at the output of the GEM scanner SU70-25E system consists mainly of
received power Pr due to weather signals and noise power
PN. Received power Pr for distributed weather targets
can be expressed as a function dependent on the radar system and physical
parameters summarised by the weather radar constant C as
Pr=C⋅Zr2,
which is directly proportional to radar reflectivity factor Z and inversely
proportional to the square of distance r. In contrast,
the power of background noise PN is independent of the distance
to the radar. In a first step, an initial guess of the range-independent
noise level from a rain-free field is used to separate assumed meteorological
signals from noise background. This step is performed only in the very first
time step after system start. If the initial guess is set too low and
underestimates the actual noise level, some noise will remain in the radar
image after subtracting the estimated background noise. Therefore, the
initial first guess overestimates the expected noise level by approximately a
factor of 10. In case of more than 10 % rain-free radar range gates after
subtracting the initial guess from the original reflectivity field, the 10th
percentile of the original reflectivity field is chosen as the next noise
level. Otherwise, the noise level from the last time step is kept. This
estimated noise level is applied as the initial guess for noise estimation in
the next 30 s time step. In order to minimise the influence of radar
artefacts on the algorithm, the average of the recent 10 estimates is used to
correct the measured reflectivity field for background noise. The estimated
noise level is subtracted from each reflectivity field, which is then
multiplied by the squared distance to the radar. The range-dependent received
reflectivity Z field due to weather signals and non-meteorological echoes
remain (Fig. b). Noise level as a function of distance to the
radar (black line in Fig. c) fits the radar signal at 60∘
(red line in Fig. b and red dotted line in Fig. c) for
rain-free areas. At ranges with precipitation, the signal is the sum of noise
and meteorological signal. Therefore, considering the rain field in
Fig. b, the azimuthal mean of the radar signal (blue line in
Fig. c) is always higher than the estimated noise level.
Clutter detection algorithms
Advanced state-of-the-art methods to identify clutter are based on
polarimetric measurements or observations of Doppler shift. The low-cost
radars used in this study do not observe these quantities. Therefore, clutter
detection is only based on temporal and spatial variability of reflectivity.
Distribution of clutter for the period from July to October 2013.
(a) Histogram of the percentage of all clutter range gates (blue)
and the clutter area (magenta). (b) Clutter detected by each
algorithm (static clutter map in blue, SPIN filter in green, TDBZ filter in
brown, spikes and ring algorithm in orange, time-resolution-based algorithm
in blue-green and network-based algorithm in violet) in percentage of all
clutter range gates.
Clutter is characterised by high reflectivity values and can be divided into
two different types: static and dynamic clutter. Static clutter is caused
e.g. by trees, houses and natural reliefs, and is present in almost every
data set at the same radar range gates. Dynamic clutter is caused by moving
objects, e.g. birds and insects, or by other radars operating in the same
frequency range (so-called interferences). It varies from time step to time
step and from range gate to range gate. A number of correction algorithms are
applied to reflectivity data of the PATTERN network in order to detect and
delete clutter and interferences, so that the precipitation signal remains.
Each correction algorithm pursues a different approach: some are
based on common clutter identification methods for single radars,
others use the unique features of high temporal resolution and large overlap
of multiple radars within the network. Many clutter range gates fulfil
detection criteria of more than one of these algorithms and are detected by
multiple algorithms. Features of other clutter range gates can be detected by
only one of the algorithms. In the following, these algorithms are described
in more detail using the exemplary reflectivity field (Fig. b),
and the performance of each algorithm will be investigated over a 4 month
period.
The PATTERN network radar MOD is used exemplarily to investigate the
performance of the clutter detection algorithms from July to October 2013.
Around 30 % of the radar range gates in each radar are classified as
clutter by combining all detection algorithms (Fig. a).
Most of the clutter range gates occur close to the radar. Therefore, about
10 % of the area in the radar image is affected. The distribution is
skewed to the right. This is due to a few disturbances that cannot be
identified by the different clutter and interference detection algorithms,
e.g. wide spikes. In Fig. b, each algorithm is considered
separately. Most clutter range gates are identified by multiple algorithms.
Therefore, the sum of all algorithms is higher than 100 %. The
distribution of each clutter detection algorithm will be discussed in the
following sections. The blue bar at 5 % in Fig. a and
at 100 % in Fig. b corresponds to cases where there
were no radar measurements and the reflectivity field is empty. In these
cases, no clutter detection algorithm is operational but the static clutter
algorithm. Therefore, all clutter (100 %) identified in these cases is
static clutter, which corresponds to approximately 5 % of all range
gates.
All range gates detected as clutter or interference are thresholded and
removed after applying all algorithms. Two different approaches were used to
fill these gates with information:
For individual radars, data gaps are filled by using an inverse
distance weighting interpolation procedure with an area of influence of 50
range bins.
In regions covered by multiple radars within the network, gaps caused
by clutter are filled using the information of at least one other radar or
the averaged information where more than one radar is available.
Clutter detection for radar MOD for 15 May 2013, 15:28:30 UTC:
(a) static clutter map, (b) TDBZ field, (c) SPIN
field. Clutter detection using previous PPIs: (d) dBZ field for
15:27:30 UTC, (e) dBZ field for 15:28:00 UTC, (f) dBZ
field for 15:28:30 UTC.
Static clutter algorithm
The clutter easiest to identify is static clutter, because it is evident in
almost every radar picture at the same range gates. To detect this type of
clutter, a map is generated by counting the time steps at which reflectivity
is higher than 7 dBZ over 10 days, corresponding to 28 800 time steps
(Fig. a). That also includes the precipitation signal and
dynamic clutter. The threshold is set to 7 dBZ, because clutter is
characterised by reflectivity values clearly higher than the background
noise, and to ensure that in the unlikely case of underestimation of
background noise, clutter and the remaining background noise can be
distinguished. A distinction between static clutter and long-lasting rainfall
needs to be made. We assume at least 5 % of the time period of ten days
is rain free. Therefore, range gates that exceed the threshold in more than
95 % of the 28 800 time steps are marked as static clutter. 14–27 %
of the range gates are identified as static clutter for the four network
radars. That corresponds to 8–12 % of the area covered, because static
clutter primarily occurs in the vicinity of the radar where the radar beam is
close to the ground.
The long-term study reveals that for radar MOD, up to 20 % of all clutter
range gates is static clutter (Fig. b). This means that
around 80 % of the clutter range gates are not static, but are dynamic
clutter, and cannot be detected by the clutter map. Therefore, dynamic
clutter algorithms need to be applied. In some images, 100 % seems to be
static clutter. This occurs if there are no measurements for certain time
steps and if the other clutter detection algorithms do not operate.
Dynamic clutter algorithms for single radars
To identify dynamic clutter and interferences, several algorithms are applied
based on the structure of the reflectivity field and a comparison to the last
time steps. First, two common methods for detecting dynamic clutter are used:
the texture of the logarithmic reflectivity (TDBZ) field, and the SPIN field
. The TDBZ field is computed as the average of the squared
logarithmic reflectivity difference between adjacent range gates:
TDBZ=∑iN(dBZi-dBZi-1)2/N
where “dBZ” is reflectivity and N is the number of range gates used. If
the mean of squared reflectivity difference (Fig. b) within five
consecutive range gates is higher than 3 dBZ, the range gate is flagged as
clutter. If the threshold is set too high, some clutter remains undetected;
if it is set too low, small-scale light rain events might falsely be
classified as clutter. The threshold of 3 dBZ is based on several case
studies to optimise the performance of the algorithm. In order to optimise
computing time, the TDBZ field is only calculated in the beam direction
following , and the number of consecutive range gates is
limited to five.
The SPIN field (Fig. c) is a measure of how often the
reflectivity gradient changes sign along the radial direction. Two conditions
must be fulfilled:
sign{Xi-Xi-1}=-sign{Xi+1-Xi}
and
|Xi-Xi-1|+|Xi+1-Xi|2>spinthres,
where Xi+1, Xi and Xi-1 represent three consecutive dBZ values
along a radar radial, and “spinthres” is a reflectivity threshold. The
number of sign changes is calculated within a window of 11 range gates around
the centre range gate in a radial direction, as suggested by
. The reflectivity threshold is set to 5 dBZ in
. Nevertheless, in several case studies, a threshold of
3 dBZ turned out to perform best for the X-band radars used in this study.
If both criteria are fulfilled in more than 10 % of the consecutive range
gates, the centre range gate is flagged as clutter.
Interferences caused by other radars occur in the form of spikes or rings in
the radar image. Spikes are characterised and identified by a sign change in
reflectivity difference between neighbouring radar beams, rings by a sign
change in differences between neighbouring range gates. In order to identify
spikes, the reflectivity difference between range gates of neighbouring radar
beams is calculated and, from that, the sign change in differences is
derived. If Eq. () is fulfilled in more than three cases
within a window of five range gates in radial direction around the centre range gate, it is flagged
as interference. The window of five range gates is chosen in order to be able
to identify spikes that do not affect the entire radar beam.
Equation () needs to be fulfilled for three instead of for
all five range gates within the window to allow for detection of the edges of
spikes, otherwise the first and last two range gates would remain in the
radar image. To detect rings, the same procedure is applied by interchanging
the radial and angular direction.
Despite the application of TDBZ, SPIN as well as spike and ring algorithms,
some clutter remains in the radar image. The unique feature of high temporal
resolution gives additional information for further clutter detection, in
contrast to common radar systems: range gates with high reflectivities that
are present in the current plan position indicator (PPI) image but not in the
two previous ones are most likely clutter or interferences. In
Fig. d–f, the PPI images of reflectivity fields without noise
for 13:28:30 UTC (Fig. f) and the two previous time steps
(13:27:30 UTC in Fig. d and 13:28 UTC in Fig. e)
are shown. Red circles indicate examples of range gates that have
reflectivity values greater than the noise level only at 13:28:30 UTC and
are, therefore, identified as clutter. Clutter caused by moving objects as
well as interferences due to external emitters are present for a short period
of time. Therefore, it appears in only one time step, whereas precipitation
structures remain nearly constant and between two time steps. For radars with
a temporal resolution of the order of a few minutes, this method is not
applicable.
Comparing the performance of the described dynamic clutter algorithms, the
most efficient method is the TDBZ filter (Fig. b). It
detects between 40 and 60 % of all clutter, followed by the SPIN filter
with 20 to 40 %. The algorithm for spike and ring identification can only
detect interferences of other radars. These interferences are more rare than
the static and dynamic clutter that is present in every radar image.
Therefore, the spike and ring algorithms detect only between 15 and 35 %
of all clutter. The algorithm dependent on the advantage of high temporal
resolution of the radar network comparing three time steps (PPI comp) is
designed to identify both, clutter and interferences. It operates in
rain-free areas and is, therefore, not directly comparable to the performance
of the other three algorithms. Despite its limited applicability, it detects
up to 10 % of all clutter.
(a) Sketch of obstacles and precipitation as seen from two
different radars; (b) coverage within the X-band radar network and
(c) clutter range gates detected any clutter algorithm (violet) by
the network algorithm and any other clutter algorithm (yellow), and by the
network algorithm only (red).
Network-based clutter algorithm
In contrast to single radar systems, networks can give multiple information
on reflectivity in overlapping areas. For large-scale radar networks as
operated by the national weather services, the areas of multiple coverage are
minimised in order to cover an area as large as possible with a minimum
number of radars. The X-band radar network in this study is designed so that
a large area is covered by more than two radars. Each radar observes at a
different height above a certain location. Obstacles in the near field of a
radar will occur as clutter, e.g. the house in the image of radar A
(Fig. a). The beam of radar B is higher above the ground at
the same location and, therefore, is not affected. To ensure that a range
gate is affected by clutter, the algorithm is applied in areas covered by at
least three radars. If a range gate of one radar shows reflectivity, but the
corresponding range gates of the other (at least two) radars do not, it is
most likely to be clutter.
The areas covered by more than two radars for the example of 15 May 2013 at
15:28:30 UTC are indicated in dark blue and red in Fig. b.
In this case that amounts to approximately 60 % of the area covered by
the radar. The area around the radar site is of special interest for clutter
detection algorithms because most of the clutter occurs where the radar beam
is close to the ground. This area is mostly covered by more than two radars
and, therefore, the network-based clutter algorithm is applicable using the
advantage of multiple coverage.
The added value of the network-based clutter algorithm is highlighted by the
clutter map in Fig. c. The red area depicts all clutter
range gates that are detected by no others than the network-based algorithm
totals to approximately 30 % of the clutter-affected area. In case of
using a single radar only instead of a network, these disturbed range gates
would remain in the radar image and cause erroneous precipitation estimates.
The long-term study of the performance of the network-based clutter algorithm
shows that this algorithm is the most efficient one
(Fig. b). More than 60 % and up to 80 % of the
clutter range gates are detected by the network algorithm. This is a very
good performance, especially considering the fact that the network algorithm
only works in areas that are covered by more than two radars.
Calibration
In order to calibrate reflectivity measurements of the X-band radar network,
three reference stations are operated in the overlapping area of the PATTERN
network. Each reference station consists of micro rain radar (MRR), a rain
gauge and a wind sensor. The largest sources of error in rain gauge
measurements are wind-induced losses. Thus, wind speed measurements from the
wind sensor are used to correct 3 h averages of rain gauge measurements
within the calibration period from April to October 2013 according to
. These wind-corrected measurements from rain gauges are used
to calibrate the micro rain radars. The MRRs at the reference stations derive
rain-rate and reflectivity observations at 31 height levels from the ground
to 1085 m in height. For measurements in the near field of the MRR, the
relationship between power P and distance r is not valid, because the
height resolution is almost of the order of the measuring height. The MRRs
are operated with a height resolution of 35 m and, therefore, it is common
to omit the two lowest levels. The P–r relation is applicable from the
third level. MRR measurements are corrected for attenuation with the spectral
scheme proposed by based on the classical attenuation
correction scheme of . This scheme avoids the uncertainty
in the relationship between reflectivity Z and rain rate R by calculating
attenuation κ and R from Doppler spectra using the drop size
distribution. Three-hour averages of rain rate are calibrated with rain gauge
measurements. The logarithmic calibration factor for MRR (CMRR)
rain rates R and, therefore, also reflectivities, is the mean difference
between the logarithmic rain rates of MRR (dBRMRR) and the rain
gauge (dBRRG):
CMRR=dBRMRR-dBRRG‾withdBR=10⋅log(R).
The received signals of the MRR are transformed to drop size distributions
(DSDs) using single-particle backscattering cross sections that are
calculated with Mie theory using the code of . Reflectivity
ZMRR is derived from the MRR DSDs using Rayleigh approximation
and, thus, is independent of the wavelength. For the X-band
radar, scattering is assumed to appear mainly as Rayleigh scattering, which
is a good approximation for light and moderate rainfall. For high rain rates,
it is difficult to separate the non-Rayleigh scattering effect from
attenuation completely, due to rain. In this rain intensity range,
attenuation by liquid water is of the same order or outweighs non-Rayleigh
scattering effects. The good agreement between X- and C-band systems that is
found by confirms the applicability of the Rayleigh
approximation for X-band radars.
Sketch of the set-up for calibration of X-band radars with MRR.
Comparison of X-band radar MOD (ordinate) to micro rain radar WST
(abscissa) for April to October 2013. Frequency relative to the highest
frequency is shown in different colours, from low levels in light blue to high levels in dark blue.
The X-band radars are calibrated with reflectivity measurements of MRRs.
Therefore, directly measured reflectivity of the X-band radar is used for
calibration, and not the precipitation product that is used for calibration
with rain gauges. Another advantage of this method is that both systems
observe reflectivity at the same height and, therefore, more or less in the
same volume (Fig. ). This volume is derived for each
combination of X-band radar and MRR individually. The MRRs are between 1 km
and 17.75 km away from the X-band radars. Depending on the distance to the
radar, the radar beam is up to 870 m wide at the MRR sites. Therefore, up to
25 MRR gates are within the radar beam. Reflectivities from all MRR gates
that fall within the radar beam are averaged using a linear weighting
function depending on their distance to the centre of the X-band radar beam,
because the mean received power of the X-band radar comes from the centre of
the beam. A linear fit of the form
ZMRR=a⋅ZX
is applied, where ZMRR is the reflectivity of the MRR, ZX the
reflectivity of the X-band radar, and a is the calibration coefficient:
a=100.1⋅(dBZX-dBZMRR).
As an example, a comparison between radar MOD and reference station WST is
depicted in Fig. a for April to October 2013. Overall X-band
radar MOD fits MRR WST measurements quite well, with a mean bias of
2.34 dBZ. The RMSE of 3.33 dBZ is due to comparison on a 30 s basis. With
a correlation coefficient of 0.95, both systems are in very good agreement. A
list of the calibration coefficients can be found in
Table .
Calibration coefficients a for every possible combination of
X-band radar (HWT, MOD, QNS and BKM) and MRR (OST, MST and WST) and the
average coefficient in dBZ.
As the X-band frequency range is highly influenced by attenuation, parts of
an algorithm especially developed for small single-polarised X-band radars
are used according to , based on .
Attenuation A(r) at a range gate r is multiplicative, and the true
reflectivity profile Z(r) can be calculated with the measured reflectivity
profile Zm(r) and a constant radar calibrationerror δC
(see Table ):
Zm(r)=Z(r)δCA(r).
Attenuation influences the radar beam in both ways, away from and back to the
radar. Therefore, two-way apparent attenuation K is calculated as an
integral along the path from range gate 0 to range gate r and back:
K(r)=2∫0rZm(s)α1βds,
with coefficients α= 132 250 and β=1.2 for the X-band
frequency range . The attenuation factor A for a certain
range gate r is then calculated as
A(r)=1-0.23βKm(r)β.
The determination of attenuation works along a path with undisturbed
measurements. Because of the elimination of clutter-affected range gates,
data gaps occur that need to be filled. A common method for single radars is
interpolation of data gaps. Thereby, information on the small-scale
variability of the rain event gets lost. In the overlapping areas within the
network, the advantages of multiple information from different radars are
used to fill data gaps. Therefore, the structure of precipitation is kept,
and allows for more precise attenuation estimation within the network
compared to single radars. The attenuation factor field is presented in
Fig. a. It is in good agreement with the finding in
. In areas of high reflectivities in the most southern and
western parts of the radar image, the attenuation factor A(r) is higher
than 0.5. The corrected reflectivity field after clutter filtering,
calibration and attenuation correction is shown in Fig. b.
Attenuation correction for radar MOD for 15 May 2013, 15:28:30 UTC:
(a) attenuation factor field and (b) corrected dBZ field.
Composite of network radars
The X-band radar network derives multiple information on reflectivity,
clutter and attenuation, because a large area is covered by more than one
radar. To combine information of all four radars, a composite is calculated
on a rotated Cartesian grid; i.e., the Equator is shifted into the
network-covered area to allow for equidistant grid cells. A grid resolution
of 250 m is used. Each radar range gate is assigned to the grid cell its
centre is located in and the average of reflectivity values of all radar
range gates in a certain grid cell is calculated. In the outer parts of the
radar-covered area, radar range gates are much larger in the azimuthal
direction than grid cells and, therefore, not every grid cell includes a
radar range gate centre. To make sure that grid boxes far away from the radar
sites contain at least one radar range gate centre, the resolution of the
radar is artificially enhanced by dividing each azimuth angle into
0.1∘ steps. In order to determine rainfall rates R of the composite
of reflectivities (Fig. ), a common Z–R relation is applied:
R=aZb,
with coefficients a=320, 200 or 77 and b=1.4, 1.6 or 1.9,
respectively, depending on the strength of the rain event. These coefficients
are used for precipitation estimation in Germany by the DWD, and are adopted
for the X-band radar measurements in order to allow for comparison with
precipitation rates obtained from the C-band radar operated by the DWD. The
result is a nearly undisturbed precipitation field that covers the western
half of the network area.
Composite of the precipitation fields of all four PATTERN radars for
15 May 2013, 15:28:30 UTC.
Comparison to C-band radar
In the last section, it was shown that several algorithms are needed to
obtain nearly undisturbed calibrated reflectivity fields from raw data. In
order to give an estimation on the quality of products from the PATTERN
X-band radar network, reflectivity data are compared to the products of radar
Fuhlsbüttel operated by the DWD in Hamburg 40 km southeast of the network
area. Radar Fuhlsbüttel provides reflectivity measurements in the C-band
frequency range, with a range resolution of 1 km, an azimuthal resolution of
1∘ and a temporal resolution of 5 min. In this study, the
precipitation scan with an elevation angle of 0.7∘ is used for
comparison to X-band radar data. The PATTERN network observes reflectivity
with a temporal resolution of 30 s. Therefore, reflectivity fields obtained
by the PATTERN network are compared to the closest 5 min measurements of
radar Fuhlsbüttel.
A comparison of the composite of reflectivity fields of the four PATTERN
radars (Fig. a) for 15 May 2013, 15:28:30 UTC to the product of
radar Fuhlsbüttel (Fig. b) for 15 May 2013, 15:30 UTC
indicates the high spatial accordance of both systems. Both, geographical
position of the precipitation area as well as its maxima in the western part
of the network area, are displayed well by the PATTERN radars and radar
Fuhlsbüttel. Nevertheless, reflectivity values are slightly higher in the
PATTERN network composite than for radar Fuhlsbüttel. This is due to the
different resolutions of both systems. Maximum reflectivities observed by the
high-resolution X-band radar are smoothed by the C-band radar. Another
possible explanation for the relative bias might be the different
calibrations of both systems. The precipitation field is slightly shifted to
the east in the image derived by radar Fuhlsbüttel. This is due to the time
shift of 1.5 min between Fig. a and b.
(a) Composite of reflectivity fields of all
four network radars
for 15 May 2013, 15:28:30 UTC, and (b) reflectivity field from
radar Hamburg for 15 May 2013, 15:30 UTC.
Comparison of reflectivity values from radar Fuhlsbüttel
(abscissa) and radar MOD (ordinate) from May to September 2013. Frequency
relative to the highest frequency is shown in different colours, from low
levels in light blue to high levels in dark blue. Dashed and dashed–dotted
red lines denote linear fits with radar Fuhlsbüttel and radar MOD as
regressors, respectively. The probability of detection (POD) and the false
alarm ratio (FAR) are also given.
The good agreement between the PATTERN network and radar Fuhlsbüttel in
terms of reflectivity is also evident in a long-term comparison of both
systems shown in Fig. . Reflectivities from the PATTERN network
are averaged on the grid of radar Fuhlsbüttel. All precipitation events
that occur from May to September 2013 are taken into account, and
reflectivity values are divided into 1 dBZ steps. Overall, both systems are
in good agreement. The PATTERN network slightly overestimates measurements of
radar Fuhlsbüttel for reflectivities lower than 15 dBZ, which results in
an intercept of 6.7 dBZ when DWD radar is used as a regressor. For PATTERN
radar as a regressor, the intercept is clearly smaller, at 1.5 dBZ. The
probability of detection (POD) and the false alarm ratio (FAR) give
additional information on the accordance of both systems. One system serves
as a reference, and the other system's ability to observe the same
precipitation events is tested. POD is a measure of how many of all
precipitation events detected by the reference system are also observed by
the test system. It is 90 % for LAWR as a test system, and 93 % for
DWD C-band radar as a test system. This means that at least 90 % of all
rain events are measured by both systems. POD is slightly smaller for the
X-band radar because small-scale structures, especially at the border of rain
events, cannot be resolved by the C-band radar. FAR is a measure of how often
the test system detects rainfall, while the reference does not observe any
precipitation. It does not exceed 10 % for either system. The good
agreement in terms of POD, FAR and reflectivity values between PATTERN and
radar Fuhlsbüttel demonstrates that, overall, the PATTERN network provides
reliable reflectivity data and promising results in terms of higher
resolution.
(a) Percentage of PATTERN network range gates with rain on
the DWD grid and (b) standard deviation of reflectivity in the
PATTERN network on the DWD grid for 15 May 2013, 15:28:30 UTC.
The higher resolution of the PATTERN product compared to radar Fuhlsbüttel
allows for enhanced and more detailed spatial allocation of precipitation. In
order to investigate the variability of reflectivity within a single range
gate of radar Fuhlsbüttel with a range resolution of 1 km and an azimuthal
resolution of 1 ∘, the number of rain range gates from the PATTERN
network is calculated for each DWD range gate (Fig. a).
The lower the percentage of rain range gates, the smaller the rain-covered
area within a certain DWD range gate is. The western part of the network is
completely covered by rain and, therefore, the percentage of rain range gates
from the network is 100 % for almost all DWD range gates. At the edges of
the precipitation field in the centre of the network area, the percentage
drops to less then 10 %. These small-scale structures cannot be observed
with the coarse resolution of radar Fuhlsbüttel. The standard deviation
within each DWD range gate, depicted in Fig. b, stresses
the importance of high-resolution precipitation observations, with values of
up to 3 dBZ at the edges of the rain events.
Conclusions
A network consisting of four X-band radars has been deployed within the
framework of the Precipitation and Attenuation Estimates from a
High-Resolution Weather Radar Network (PATTERN) project that has been
operational since January 2012. The radars provide reflectivity fields with a
range resolution of 60 m, a sampling resolution of 1∘ in the
azimuthal direction, and a temporal resolution of 30 s. Algorithms have been
developed to remove disturbances in raw reflectivity fields of single radars.
The performance of these algorithms is exemplary, as shown for one of the
network radars (MOD). The simple radar systems presented in this study cannot
measure background noise directly. Therefore, noise level is estimated for
each radar using the 5th percentile of the smoothed reflectivity field and
the noise levels of the last 10 time steps.
Approximately 10 % of the radar-covered area is disturbed by reflection
from obstacles such as trees or houses or from other transmitters. In order
to identify clutter range gates, two different types of clutter detection
algorithms are applied: single-radar and network-based algorithms. Some of
the single-radar algorithms are based on classic clutter detection methods,
such as the texture of the dBZ field (TDBZ), sign changes in reflectivity
gradient between neighbouring range gates (SPIN), the shape of disturbances
from other transmitters (spikes or rings), or a static clutter map. The most
efficient of these single-radar algorithms is the TDBZ filter, which detects
up to 60 % of all clutter, followed by the SPIN filter with up to
40 %.
The X-band radars do not perform dual-polarisation measurements, but the
network of X-band radars introduced in this paper has two other features that
are beneficial for clutter detection: high temporal resolution and multiple
coverage by more than two radars within
the network area. The advantage of a high temporal resolution of 30 s is
used for clutter detection by comparing the PPI image of the current time
step to the two previous ones. Range gates with reflectivity values higher
than the noise level that do not occur in the two previous images are flagged
as clutter. This type of algorithm only works for high temporal resolution,
because the spatial shift in the precipitation field is small compared to a
time step of 5 min, which is the common temporal resolution of operational
regional radar systems. Around 10 % of clutter can be detected with this
type of algorithm that operates in rain-free areas. The second type of
clutter algorithm is based on the advantage of having a network of four
radars with high spatial resolution. In areas covered by more than two
radars, range gates with reflectivities higher than the noise level that do
not appear in at least two other radars are flagged as clutter. This
network-based clutter algorithm is more efficient than all single radar
algorithms, with a detection rate of more than 70 %. Therefore, the
network of X-band radars is a very useful tool for clutter filtering that is
also used to fill the gaps resulting from clutter filtering. Thus, smoothing
of the reflectivity field due to interpolation is avoided, and the
small-scale structure of rain events is kept.
Three reference stations are deployed within the network-covered area for
calibration purposes, consisting of a rain gauge, a wind sensor, and micro
rain radar (MRR). Using MRRs for X-band radar calibration has the advantage
of comparing reflectivity measurements at the same height level instead of to
observations at the ground from rain gauges. A slight overestimation of MRR
measurements is detected and corrected for radar MOD. X-band radars are
highly influenced by attenuation from liquid water. Therefore, a simple
single-radar algorithm for attenuation correction is applied to the network
radars. In order to apply this algorithm, a continuous reflectivity field
without data gaps caused by clutter and interferences is needed. Here, the
network benefits again from the large area covered by more than one radar.
Information from other radars is used to fill these gaps and maintain the
small-scale structure of rain events instead of smoothing the precipitation
field by interpolation.
A composite of all four radars is calculated on a 250 m × 250 m
grid by averaging reflectivities from all range gates whose centres fall
within a certain grid cell. A comparison to measurements from a C-band radar
operated by DWD indicates that the PATTERN network slightly overestimates
reflectivity but also displays the spatial structure of rain events very well
in higher resolution than nationwide radar networks can do. This is in good
agreement with case studies conducted by and
, who recommend the use of low-cost X-band radars in
complementation to large-scale C- or S-band networks.
A long-term study showed that both systems are in good agreement for all rain
events that occurred from May to September 2013. It has been shown that,
especially at the border of rain events, where only parts of the C-band radar
range gates are covered by rain, higher resolution of the X-band radar
network provides more detailed information on the structure of the
precipitation. Within a C-band radar range gate, the standard deviation can
be up to 3 dBZ. Due to its low costs compared to other radar systems (less
than 20 % of the price of dual-polarisation systems), a single LAWR or a
network of LAWRs is affordable not only for weather services, but also for
private companies and local authorities, and can be set up in areas of
special interest, e.g. urban areas or mountainous regions. They can serve as
a sort of magnifying glass to investigate the spatial and temporal structures
of rain events in addition to large S- or C-band radar systems.
Outlook
It has been shown in this paper that a network of LAWRs gives reliable
precipitation estimates and can be a useful addition to nationwide radar
networks. For further improvement, the next step will be the implementation
of attenuation correction algorithms that use the advantage of a network
(e.g.).
Better estimation of attenuation can lead to better
precipitation estimates, because the relation between attenuation and
precipitation is more stable than the relation between reflectivity and
precipitation.
Furthermore, the fixed relation between radar reflectivity and precipitation
will be replaced by a dynamic relation determined operationally using
measurements of seven MRRs installed in the PATTERN catchment. This allows
for adaptation of Z–R relations to current weather conditions, e.g. showers
and light or stratiform rain.
High-resolution products of the PATTERN network will also be used as input
for rainfall–runoff simulations. Currently, hydrometeorological models use
products from C- or S-band radars as input, with a resolution of several
minutes in time and kilometres in space. Higher spatial and temporal
resolution of precipitation estimates can be used to improve rainfall–runoff
simulations in areas of special interest, e.g. in small-scale structured
urban areas.
Acknowledgements
The Precipitation and Attenuation Estimates from a High-Resolution Weather
Radar Network (PATTERN) project is a joint project between the University of
Hamburg and the Max-Planck-Institute for Meteorology. It is funded by the
Deutsche Forschungsgemeinschaft (grant AM308/3-1).
The authors thank the German Weather Service (DWD) for making products of
their C-band radar network available for research purposes within the PATTERN
project. Edited by: G. Vulpiani
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