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Keywords:

  • weather radar;
  • quality control;
  • reflectivity

Abstract

  1. Top of page
  2. Abstract
  3. 1. Quality issues in weather radar data
  4. 2. Description of quality control algorithms
  5. 3. Total quality index
  6. 4. Verification on 2-D precipitation radar products
  7. 5. Conclusions
  8. Acknowledgements
  9. References

A set of quality control algorithms developed in the framework of the RADVOL-QC system is described. The algorithms are dedicated to 3-D radar reflectivity data (volumes) provided by a weather radar with single-polarization of the beam. The system consists of two paths of data processing: quality correction and quality characterization. Processing by means of data correction algorithms allows the reduction of uncertainty in the data, whereas quality characterization algorithms generate a map of quality index (QI) that can be attached to the data. The following correction algorithms are included in the proposed scheme: (1) removal of geometrically shaped non-meteorological echoes (from the Sun and other emitters); (2) removal of measurement noise (specks); (3) beam blockage correction, and, (4) attenuation in the rain correction. The list of quality characterization algorithms is longer, as it also includes evaluation of data uncertainty due to technical radar parameters, distance to radar related effects, and ground clutter. All the algorithms have been developed paying special attention to possibility of operational application. The system is planned to be extended successively by other quality factors. Copyright © 2012 Royal Meteorological Society


1. Quality issues in weather radar data

  1. Top of page
  2. Abstract
  3. 1. Quality issues in weather radar data
  4. 2. Description of quality control algorithms
  5. 3. Total quality index
  6. 4. Verification on 2-D precipitation radar products
  7. 5. Conclusions
  8. Acknowledgements
  9. References

1.1. Introduction

Weather radar data have become commonly employed to generate input data in modelling of numerical weather prediction, rainfall-runoff (Rossa et al., 2005, 2010; Zappa et al., 2010) and air pollution dispersion. Increasingly, radar-based products are necessary for efficient civil protection, transport safety, ecology, agriculture and water management (see www.baltrad.eu). However, the number of errors burdening radar data is very high and it is practically impossible to eliminate all the errors satisfactorily (Villarini and Krajewski, 2010). Therefore, information on data uncertainty is becoming essential, especially for end-users, so currently great research effort is focused on quality issues (e.g. Michelson et al., 2005; Rossa et al., 2005; Einfalt and Michaelides, 2008; Zappa et al., 2010). In order to be efficient, information on data quality must be provided to users in a simple way to make it easy to interpret.

Radar data quality control, that includes both correction and quality characterization, is usually applied locally at particular radar networks, however it would be very useful to establish a common standard. The scheme should be an objective procedure, i.e. independent of platform (quality of data from different radar operators could be easy to compare) and the final application of the analysed data (Einfalt et al., 2010). Although it is not possible to make all radar systems identical, it is possible to ensure harmonized technical and software platforms on which each radar data provider can install their preferred (best) modules.

The quality evaluation algorithms should be designed in different ways, dependent on the nature of specific data. In general, the following data types are distinguished (Holleman et al., 2006): volume of 3-dimensional (3-D) radar reflectivity Z data, volume of Doppler velocity V data (3-D), and surface precipitation R (2-D). The aim of the present paper is to describe algorithms for both correction and quality characterization of 3-D reflectivity data, which are employed in the RADVOL-QC system prepared for data generated by the POLRAD weather radar network, operated in Poland by the Institute of Meteorology and Water Management (IMGW).

1.2. Quality control

The schematic chain of 3-D polar data quality control is presented in Figure 1. The employed algorithms are functionally divided into two paths: one for data corrections (QC) and the second for data quality characterization (QI). Particular quality algorithms can be switched on or off in the scheme.

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Figure 1. Weather radar data processing chain in RADVOL-QC system. Radar outputs are the weather radar 3-D polar data as provided by radar system (in HDF5 or other formats)

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In general, algorithms for the 3-D data quality control and characterization can be divided into categories based on analysis of: scan geometry, reflectivity data structure (including vertical profile of reflectivity, VPR), dual-polarization parameters, or external data. In the case of dual-polarization measurements the quality control algorithms constitute a separate category as they offer more possibilities of efficient actions (Bringi et al., 2007) but require different techniques. Thus, these corrections are not considered in this paper.

1.3. Data quality characterization

The aim of quality characterization is to describe uncertainty in the data taking into account potential errors which can be quantified as well as the ones that can only be estimated qualitatively. Because there is no benchmark available for 3-D data (such as rain gauge data for ground precipitation), another method of quality evaluation is needed.

According to OPERA programme (Holleman et al., 2006) the following definitions are employed in the present paper: quality factor is a physically meaningful factor that affects the quality of the data (e.g. radar beam attenuation), quality indicator (Fi) is a generic quantitative descriptor of the data quality (e.g. root mean square error of precipitation rate in mm h−1), and quality index (QI) is a metric providing quality information.

Generally, many of detailed ‘physical’ quality factors are not readable for end-users, so the following quality metrics may be used as more suitable:

  • – total error level, i.e. measured value ± standard deviation expressed by measured physical quantity (radar reflectivity in dBZ, precipitation rate in mm h−1);

  • – quality index, taking value 0 or 1 that means ‘bad’ or ‘excellent’ data (a so called quality flag);

  • – quality index as a unitless quantity related to the data error, expressed by numbers e.g. from 0 to 1 or from 0 to 100. (Einfalt et al., 2010);

  • – ensemble of radar images as equiprobable scenarios of the precipitation field (in size bins, for instance, of 50 members) (Germann et al., 2006, 2009), and,

  • – set of percentiles of precipitation probability density function (e.g. 5, 25, 50, 75, and 95%) (Szturc et al., 2011).

This paper is dedicated to 3-D weather radar reflectivity data. There are few papers focused on quality characterization of such data, e.g. Fornasiero et al. (2005) presented a scheme employed in ARPA, Bologna, (Italy) for quality evaluation of both raw and processed radar data, which is partly dedicated to the 3-D data. The scheme described in the following sections has been developed in IMGW in the framework of the BALTRAD project (Michelson et al., 2010) and its preliminary version was discussed by Szturc et al. (2009) and Ośródka et al. (2010).

For evaluation of radar data quality an idea of a quality index (QI) scheme that ranges from 0 (bad quality) to 1 (excellent quality) is proposed in this paper. The algorithm consists of the following steps (Szturc et al., 2011):

  • – selection of a set of the most significant error sources, i.e. quality factors;

  • – estimation of particular radar data quality indicators Fi related to the factors (where i is the number of the factor);

  • – calculation of individual quality indices QIi, and,

  • – transformation of all the individual indices QIi into one total quality index QI.

In other words, the quality indicators, which are measurable quantities, have to be transformed into n particular indices and then into a total quality one (quality indicators [RIGHTWARDS ARROW] individual quality indices [RIGHTWARDS ARROW] total quality index):

  • equation image(1)

In this chain a determination of all the relationships is required. It can be made empirically using selected form of the formula, e.g. a linear relationship:

  • equation image(2)

where equation image and equation image are the minimal and maximal threshold values, respectively, of the given quality indicator Fi, between which quality is within the range (0, 1), whereas below equation image quality is quite bad (QIi = 0) and above equation image quality is excellent (QIi = 1). The formula QIi = QIi(Fi) must be determined for each quality indicator individually.

The final quality index, QI, which is treated as an overall quality information, is determined from a combination of all quality indices applying one of the formulae such as minimum value, additive or multiplicative operator. The last seems to be the most appropriate for the present aim due to its open form (e.g. changes in the set of quality indicators do not require the scheme parameterization):

  • equation image(3)

where wi are the weights of particular quality indices.

1.4. POLRAD radar network as a testbed

Weather radar data employed in the paper are generated by the Polish radar network POLRAD. The network consists of eight C-band Doppler radars of Selex SI Gematronik (Szturc and Dziewit, 2005). Two of them are dual-polarimetric, the others are going to be upgraded during a next few years. Three- and two-dimensional radar products are generated by Rainbow 5 software (Selex, 2010) every 10 min with 1 km spatial resolution and within a 250 km range. Three measured quantities directly provided by Doppler radar are: reflectivity Z, radial wind velocity V, and spectral width W of the radial velocity measurement (uncorrected reflectivity is unavailable in the POLRAD radars).

A scan strategy currently used in radar network POLRAD is defined by parameters listed in Table 1.

Table 1. Scan parameters currently used in weather radar network POLRAD of IMGW
ParameterValue
Radar beam width
Number of azimuths360
Maximum range from radar site250 km
Distance between sampling 
along radar beam1 km
Number of elevations10
Elevation angles (°)0.5, 1.4, 2.4, 3.4, 5.3, 7.7, 10.6,
 14.1, 18.5, 23.8

The volumes are generated as sets of PPI scans (plan position indicator—one turn of radar antenna) scans from different elevations. In Figure 2 an example of volume data is presented as 10 PPI scans in polar co-ordinates. From the 3-D data various 2-D products are obtained, such as CAPPI (constant altitude plan position indicator), SRI (surface rainfall intensity) and MAX (maximum display). The Marshall-Palmer formula is used for calculation of precipitation rate R (in mm h−1) from the measured reflectivity values Z (in dBZ).

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Figure 2. Example of volume for Legionowo radar, 10 May 2007, 1530 UTC. The polar PPIs are ordered from the lowest elevation to the highest. The panels represent range (y-axis) vs. azimuth (x-axis) displays. This figure is available in colour online at wileyonlinelibrary.com/journal/met

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2. Description of quality control algorithms

  1. Top of page
  2. Abstract
  3. 1. Quality issues in weather radar data
  4. 2. Description of quality control algorithms
  5. 3. Total quality index
  6. 4. Verification on 2-D precipitation radar products
  7. 5. Conclusions
  8. Acknowledgements
  9. References

Quality control algorithms developed for operational use in the Polish radar network are listed in Table 2. Each particular algorithm is discussed in separate sections that comprise a description of the algorithm for data correction and quality characterization, and then an example is demonstrated. Since only the measurement points in 3-D data space, so called gates, are considered here, the data continuity problem is not addressed in the paper.

Table 2. Quality control (correction and characterization) algorithms for 3-D reflectivity (Z) data in order of implementation into the processing chain
CodeTaskCorrection algorithmsQuality factorQuality indicatorReferencesQCQI
  1. QC—quality control algorithm, QI—quality information algorithm,

  2. a

    —correction is made by built-in radar software.

SYSEvaluation of technical radar parametersTechnical radar parametersSet of parametersHolleman et al. (2006) x
BROADAssessment of distance to radar related effectsHorizontal and vertical beam broadeningHorizontal and vertical dimensions of cross-sections of the beam LH and LVSzturc et al. (2009) x
GCGround clutter removalUsing Doppler filter or 3-D clutter mapGround clutterPresence of ground clutterFornasiero et al. (2005) and Selex (2010)xax
SPIKERemoval of geometrically shaped non-meteorological echoes (from sun, emitters, etc.)3-D reflectivity structure used, no external data neededNon-meteorological echoesPresence of the non-meteorological echoesPeura (2002) and Zejdlik and Novak (2010)xx
SPECKRemoval of measurement noise (specks)3-D reflectivity structure usedSpecksPresence of speck gatesMichelson et al. (2000), Peura (2002) and Jurczyk et al. (2008)xx
PBBBeam blockage correctionUsing topography mapBeam blockagePresence of beam blockageFornasiero et al. (2005), Bech et al. (2007), Szturc et al. (2009) and Selex (2010)xx
ATTCorrection for attenuation in rainBased on attenuation coefficientAttenuation in rainBeam attenuated in rain along the beam pathHitschfeld and Bordan (1954), Friedrich et al. (2006), Szturc et al. (2009) and Selex (2010)xx

2.1. Technical radar parameters

This algorithm aims to provide a data quality metric without introducing any correction. As quality factors the set of technical radar parameters that impact on data quality is selected.

A set of such factors, listed in Table 3, is based on EUMETNET OPERA Programme findings (Holleman et al., 2006) and complemented with other parameters. All the quality factors are static within the whole radar range as well as in time (apart from the date of last electronic calibration). The threshold values for which QISYSi become lower than 1 have been set according to the authors' experience.

Table 3. Quality factors related to the radar system technical parameters
Individual quality factorImportanceUnitIndividual QISYSi
Operating frequencyAffects attenuation in precipitationGHz= 0.9 if X-Band
   = 1.0 otherwise (C or S)
Beam widthAffects area of measurement averaging°= 0.9 if > 1°
   = 1.0 otherwise
Pointing accuracy in elevationAffects measurement precision°= 0.9 if > 0.1°
   = 1.0 otherwise
Pointing accuracy in azimuthAffects measurement precision°= 0.9 if > 0.1°
   = 1.0 otherwise
Are statistical clutter map or Doppler-filtered signal used?Allows clutter removal(Flag)= 0.5 if ‘no’
   = 1.0 if ‘yes’
Minimal detectable signal at 1000 mAffects sensitivity to snow and drizzle detectiondBZ= 0.9 if > − 40 dBZ
   = 1.0 otherwise
Antenna speed (in azimuth)Affects measurement precision° s−1= 0.9 if > 15°s−1
   = 1.0 otherwise
Is radome attenuation corrected?Causes measurement overestimation(Flag)= 0.9 if ‘no’
   = 1.0 if ‘yes’
Date of last electronic calibrationAffects measurement precision(Date)= 0.9 if more than 180 days
   = 1.0 otherwise
Time samplingAffects measurement stability(Numeric)= 0.9 if < 30
   = 1.0 otherwise
Range samplingAffects measurement stability(Numeric)= 0.9 if < 5
   = 1.0 otherwise

All the factors affect individual quality index, QISYS, connected with radar system parameters according to formula:

  • equation image(4)

In the cases when some technical parameters employed in the algorithm are missing, the quality of analysed data should be arbitrary decreased. It is assumed that lack of one set of information from Table 3 still allows generation of the QISYS value, but the individual QISYSi connected with the missing information is set as equal to 1.0. If two or more quality factors are missing then the total QISYS is treated as ‘no data’ (as a consequence the total quality index of the analysed data is also set to QI = ‘no data’).

2.2. Horizontal and vertical broadening of a radar beam

Radar measurements are performed along each radar beam at successive gates, which represent certain surrounding areas determined by the beam width and pulse length. Since the radar beam broadens with the distance to the radar site, the measurement comes from a larger volume and related averaging errors increase as well (Figure 3). There is no possibility of correcting this effect. However, it can be determined quantitatively and taken into account in the related quality index QIBROAD.

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Figure 3. Geometry of radar measurement gate

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The horizontal and vertical broadening of the radar beam for each gate can be computed when its polar co-ordinates are known: ε (elevation angle), α (azimuth angle) and l (radial distance to radar site in km), and the two parameters of the radar beam: ϕ (beam width) and PL (measurement gate length in km) calculated from the radar pulse length. The horizontal and vertical broadenings LH and LV are described by the following formulae, calculated from vertical cross-section through radar beam (Figure 3):

  • equation image(5)

The starting point to the investigation of relationships between the quality indicators LH and LV and related quality indices QILH and QILV is the finding of Szturc et al. (2009) that radar data near the ground are not burdened with errors when the distance to the radar site is not longer than 89 km, whereas it is quite wrong when the distance is over 195 km. Threshold values for LH and LV have been estimated from Equation (5) for the two boundary distances assuming PL = 0.3 km, which relates to a standard radar long pulse of 2 µs.

Assuming that the linear shape of Equation (2) can be applied for QILH and QILV determination, from which QIBROAD is calculated, boundary values can be estimated for the both quality indicators LH and LV as:

  • equation image(6)

and finally:

  • equation image(7)

where aLH = 1.1 km, bLH = 2.5 km, and aLV = 1.5 km, bLV = 3.2 km are the boundary values of the radar beam broadening.

In Figure 4 quality index fields related to the indicators for three selected elevations are displayed. It is obvious that the broadening becomes bigger with distance to the radar site and beam elevation. The beam cross-section area is related to spatial averaging of measurement. It can be observed that differences between particular elevations are very small. That is a result of radar volume geometry: the height of the volume is very small in comparison to the horizontal radius (about 20 km against 250 km).

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Figure 4. Maps of quality indices QIBROAD fields related to radar beam broadening. Examples for elevations: 0.5, 7.7, and 23.8° and long pulse (2 µs) are presented. The panels represent range (y-axis) vs. azimuth (x-axis) displays. This figure is available in colour online at wileyonlinelibrary.com/journal/met

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2.3. Ground clutter removal

The correction of radar images due to contamination by ground clutter is commonly made at a level of radar system software which uses statistical or Doppler filtering (e.g. Selex, 2010). In such a situation the information about the correction is not available so an indirect method of generation of a ground clutter map for the lowest (and higher if necessary) scan elevation must be employed, e.g. by using a digital terrain map (DTM).

In order to determine areas contaminated by ground clutter, a diagram of partial beam blockage values (PBB) is analysed. The PBB is defined as a ratio of blocked beam cross-section area to the whole one. A given gate is considered a ground clutter if increase in PBB along the radar beam exceeds 0.005, i.e. 0.5% (Figure 5).

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Figure 5. PBB values along selected radar beam from Ramża radar. The beam (shaded area) hits Gerlach peak in the Tatra Mountains (elevation ε = 0.5°, azimuth 135°)

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Gates where ground clutter was detected should be characterized by lowered quality index. A simple formula for quality index QIGC related to the clutter presence can be written as:

  • equation image(8)

where aGC = 0.5 (Fornasiero et al., 2005). The quality index is decreased in each gate in which ground clutter was detected even if it was removed.

An example of the ground clutter field and related quality index, QIGC, is presented in Figure 6. Areas closer to the radar site, especially, are contaminated by such clutter due to the Earth's curvature, even if higher mountains are noticeable on the DTM at a greater distance.

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Figure 6. Maps of: (a) digital terrain map; (b) ground clutter; (c) quality index QIGC for Ramża radar (elevation ε = 0.5°). The panels represent range (y-axis) vs. azimuth (x-axis) displays. This figure is available in colour online at wileyonlinelibrary.com/journal/met

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2.4. Removal of geometrically-shaped non-meteorological echoes

Apart from ground clutter, other phenomena such as specks, external interference signals (e.g. from the Sun and Wi-Fi emitters), biometeors (flocks of birds, swarms of insects), anomalous propagation echoes (so called anaprop) and sea clutter, are considered as non-meteorological clutter. Effective removal of such echoes is possible while using dual-polarization radars, however correction algorithms must be employed in single-polarization radars as well.

The spatial pattern of the precipitation field is considered as the most essential criterion while developing algorithms for removal of such spurious echoes. In a simpler approach, features of the 2-D radar reflectivity pattern, i.e. considering each elevation, ε, separately, are investigated. Because various types of non-precipitation echoes can be found in radar observations, in practice individual sub-algorithms must be developed to address each of them.

2.4.1. Removal of external interference signals

Signals coming from external sources that interfere with the radar signal have become sources of non-meteorological echoes in radar images more and more often. Their effect is similar to a spike generated by the Sun, but they are observed at all azimuths in any time and mainly at lower elevations and may reach very high reflectivity.

The spurious echoes from the Sun and external interference, so called spikes, are characterized by their spatial structure that clearly differs from the precipitation field pattern. The shape of such echo is very specific: it is similar to a spike along the whole or large part of a single or a few neighbouring radar beams. Commonly, the reflectivity field structure is investigated to detect such echo on a radar image (Zejdlik and Novak, 2010). Recognition of this type of echo is not very difficult unless it interferes with a precipitation field. An algorithm developed for the removal of such artefacts should identify spikes, cut them out from the precipitation field, and replace them with proper reflectivity values.

In the proposed algorithm, three stages of spike removal are introduced: for “wide', ‘narrow’, and ‘high’ types of spikes.

For ‘wide’ spikes an algorithm based on analysis of spatial structure of radar echo is employed. The variability of the echo across and along the radar beam is examined using locally determined reflectivity variances, so a given echo is classified as a potential spike if the first variance is high whereas the latter is low:

  • equation image(9)

where varacross is the variance for a given gate calculated across the radar beam at a distance up to ± 3° in azimuth; varalong is the variance in a given gate calculated along the radar beam at a distance up to ± 15 km; Z is the radar reflectivity expressed in dBZ or mm6 m−3.

If more than 45% of the gates along a radar beam are classified as potential spikes then (1) all the gates with spikes are replaced by reflectivities interpolated from neighbouring beams, and (2) the whole beam is treated as burdened with spike and quality index of all the gates on the beam is decreased.

The next algorithm is employed to recognize and remove ‘narrow’ spikes, i.e. not wider than 7° in azimuth. In the first step, gates with potential ‘narrow’ spikes are detected. This algorithm is applied to each gate (α,l) with echo detected, that means Z(α,l) > − 32 dBZ (which is the lowest reflectivity measured by radar). For these gates, reflectivities at neighbouring beams of azimuth α ± d (where d = 3°) in the same distance to radar l are checked:

  • equation image(10)

The procedure is repeated for d = 2 ° and 1 °. Next, the number of potential gates along a given radar beam is computed and if the number is higher than 25% then (1) all the gates with spikes are replaced by reflectivities interpolated from neighbouring beams, and (2) the quality index of all the gates on the beam is decreased.

‘High’ spurious echoes are all echoes detected at altitudes higher than 20 km where it is not possible for any meteorological echo to exist. All the ‘high’ echoes are removed.

Quality index QSPIKE for the whole radar beam in which spike is detected is given by:

  • equation image(11)

where aSPIKE = 0.5.

2.4.2. Speck removal

Generally, specks are isolated radar gates with or without echo. So called reverse specks are isolated gates without radar echo (Z = − 32 dBZ) surrounded by an echo field. The introduced algorithm is employed to each elevation scan separately. A grid of 3 × 3 gates around a given gate (α,l) is considered. The number of non-echo gates srspeck(α,l) in the grid is calculated from:

  • equation image(12)

where m, n are the polar co-ordinates of gates inside a 3 × 3 grid; Z(m, n) is the radar reflectivity in the gate (m, n) (in dBZ).

The parameter of the algorithm is threshold t for srspeck(α,l) value. If the threshold for (α,l) gate is not achieved then the gate is classified as a reverse speck and its reflectivity is assigned to an average from all precipitation gates inside the grid. The threshold, t, is set to 3.

As opposed to reverse specks, the ordinary ones are gates in which isolated echoes, which can be considered as measurement noise, are observed. The algorithm of speck removal is analogous to the one used for reverse specks. A grid of 3 × 3 gates around a given gate (α,l) is also considered. The number of echo gates sspeck(α,l) in the grid can be calculated from (Jurczyk et al., 2008):

  • equation image(13)

where denotation is the same as for Equation (12).

If the threshold t for a number of surrounding precipitation gates sspeck(α,l) is not achieved then (α,l) gate is classified as a speck echo and the echo is removed, i.e. reflectivity Z = − 32 dBZ is set for the gate. The threshold is set as equal to 3. This algorithm is launched twice to clean the data more thoroughly.

The related quality index QISPECK depends on the presence of a removed speck or reverse speck in the given gate:

  • equation image(14)

where aSPECK = 0.9 (specks are less corrupting of a radar image than spikes because of their isolated character).

Figure 7 shows an example of the performance of the two sets of algorithms launched consecutively: SPIKE (removal of spikes from external interference signals) and SPECK (removal of reverse specks and specks), is depicted for the Legionowo radar, which is the most strongly contaminated with spike echoes within POLRAD network.

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Figure 7. Example of running of the non-meteorological echo removal algorithms: (a) source radar reflectivity data; (b) data after removal of spike echoes and related quality index QISPIKE; (c) data after removal of speck echoes and related quality index QISPIKE × QISPECK (Legionowo radar, 10.05.2010, 1530 UTC, the lowest elevation 0.5° as there are no spikes observed at higher elevations). The panels represent range (y-axis) vs. azimuth (x-axis) displays. This figure is available in colour online at wileyonlinelibrary.com/journal/met

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2.5. Beam blockage

Radar beams can be blocked by ground targets, i.e. places where the beam hits terrain. A geometrical approach is applied to calculate the degree of the beam blockage. This approach is based on calculation of which part of radar beam cross-section is blocked by any topographical object. For this purpose a degree of partial beam blocking (PBB) is computed from a digital terrain map (DTM) taking into account the highest blocked point in the given beam cross-section.

According to Bech et al. (2003, 2007), the partial beam blockage PBB may be calculated using the formula:

  • equation image(15)

where rb is the radius of radar beam cross-section at the given distance from radar, and y is the difference between the height of the terrain and the height of the radar beam centre. The partial blockage takes place when − rb < y < rb, and varies from 0 to 1 (see Figure 8).

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Figure 8. Scheme of partial beam blockage PBB calculation using Bech et al. (2007) algorithm

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The quantity y in Equation (15) and Figure 8 is calculated as an altitude obtained from DTM for the radar gate located in the beam centre, reduced by quantity h involving: (1) altitude of radar antenna, h0, (2) difference of altitude due to the Earth curvature, and (3) difference of altitude due to antenna elevation, ε:

  • equation image(16)

where re is the effective Earth's radius (8493 km) and l is the distance to the radar site.

Correction of partial beam blocking on precipitation rate is made by applying a multiplicative correction factor (Bech et al., 2007):

  • equation image(17)

where b = 1.6 is the exponent in the Marshall-Palmer ZR relationship, and for radar reflectivity (in dBZ):

  • equation image(18)

The correction is introduced if the PBB value is smaller than 0.7. For higher PBB Bech et al. (2007) propose to mark data in such gate as ‘no data’, however in the present paper it is proposed to take reflectivity from neighbouring higher elevations. Only when such data are not available is the ‘no data’ mark is assigned.

A quality of measurement burdened by beam blockage dramatically decreases. The quality index QIPBB of gates where the radar beam is considered as blocked is expressed by the formula:

  • equation image(19)

where the co-efficient aPBB can be set as 0.5 (Fornasiero et al., 2005), or 0.7 (Bech et al., 2007); here the value aPBB = 0.7 is also applied.

If reflectivity in a specific gate has been replaced by reflectivity from higher elevation then QIPBB is taken also from the higher elevation, but multiplied by a factor (1 − aPBB). Finally:

  • equation image(20)

where QIPBB(el + 1) means the QIPBB calculated for the relevant gate in the elevation el + 1, el is the number of elevation (numbered from the lowest to the highest).

In Figure 9 an example for the Pastewnik radar is presented. The Sudety Mountains lying south of the radar site are blocking the southwest sector. The DTM for the Pastewnik radar is depicted with related ground clutter and blocked areas for the lowest elevation 0.5°.

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Figure 9. Example of running of the partial beam blockage correction for Pastewnik radar: (a) digital terrain map; (b) ground clutter map; (c) raw data Z (in dBZ); (d) corrected data Zcor; (e) quality index QIPBB (5 May 2010, 1800 UTC, the lowest elevation 0.5 °). The panels represent range (y-axis) vs. azimuth (x-axis) displays. This figure is available in colour online at wileyonlinelibrary.com/journal/met

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2.6. Attenuation in rain

Attenuation is generally defined as a decrease in radar signal power after passing a meteorological object, which results in an underestimation of the measured rain:

  • equation image(21)

where A is the attenuation (in dB); Zcor is the non-attenuated reflectivity (in mm6 m−3) and Z is the measured one.

The aim of the algorithm is to calculate the non-attenuated rain. Empirical formulae for determination of specific attenuation can be found in the literature. Using 5.7 cm radar wavelength (C-Band radar) the two-way specific attenuation A(i−1, i) (in dB km−1) in precipitation between measurement gates i − 1 and i at 18 °C can be estimated assuming the Marshall-Palmer ZR relationship (Battan, 1973):

  • equation image(22)

where R(i) is the precipitation rate in a measurement gate i (in mm h−1); Z(i) is the radar reflectivity in the gate i (in mm6 m−3).

A reflectivity-based correction made iteratively (‘gate by gate’) is a common technique for correction of attenuation in rain. However, ‘gate by gate schemes are notoriously unstable and very sensitive to small calibration errors’ (Illingworth, 2004). Dual-polarization measurement seems more effective way to estimate the attenuation operationally (e.g. Bringi et al., 2007), but in the case of a single-polarization radar the reflectivity-based algorithm is the sole solution.

The iterative algorithm is also employed in the RADVOL-QC model (Figure 10). Assuming that in the previous algorithm steps the specific attenuations A(0, 1), …, A(i−2, i−1) and their sums PIA(0, 1), …, PIA(0, i−1), called the path-integrated attenuations, were calculated:

  • equation image(23)
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Figure 10. Scheme of estimation of attenuation in rain along the beam

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From reflectivity Z(i) measured in i-gate, PIA(0, i−1) integrated from the radar site to the i − 1-gate, and first guess of attenuation A(i−1, i) between i − 1 and i-gates calculated from Equation (22), the non-attenuated reflectivity Zcor(i) can be obtained according to the formula:

  • equation image(24)

The attenuation A(i−1, i) for the distance between the two neighbouring gates i − 1 and i can then be calculated from Equation (22), and consequently the path-integrated attenuation along the whole distance from the radar site to the given i-gate can be obtained from:

  • equation image(25)

This attenuation value will be applied in the next step of the iterative algorithm.

In order to avoid instability in the algorithm, certain threshold values have to be set to limit the corrections for both specific attenuation A(i−1, i) and path-integrated attenuation PIA(0, i).

The described algorithm is applied only for the gates where echo was detected, otherwise:

  • equation image(26)

The magnitude of the attenuation in precipitation PIA (in dB) (Equation (25)) can be considered as a quality factor for the given measurement gate i. Therefore the relevant quality index QIATT is calculated from the formula:

  • equation image(27)

where parameters aATT = 10 dB and bATT = 5.0 dB are empirically determined.

In Figure 11 an example of the attenuation field for the lowest elevation is presented for the data shown in Figure 2. The corrections are employed only if any echo is observed in the given gate, however for quality characterization the data quality decreases behind any echo area for both echo and non-echo gates.

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Figure 11. Example of running of the attenuation in precipitation correction: (a) raw data Z (in dBZ); (b) corrected data Zcor; (c) quality index QIATT (Legionowo radar, 10 May 2010, 1530 UTC, the lowest elevation 0.5 °). The panels represent range (y-axis) vs. azimuth (x-axis) displays. This figure is available in colour online at wileyonlinelibrary.com/journal/met

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3. Total quality index

  1. Top of page
  2. Abstract
  3. 1. Quality issues in weather radar data
  4. 2. Description of quality control algorithms
  5. 3. Total quality index
  6. 4. Verification on 2-D precipitation radar products
  7. 5. Conclusions
  8. Acknowledgements
  9. References

Computation of the total quality index QI is the final step in estimation of radar volume data quality. According to Table 2 the following individual quality indices QIi characterizing data quality due to:

  • – technical parameters of radar and its configuration (QISYS);

  • – radar beam vertical and horizontal broadening (QIBROAD);

  • – presence of ground clutter (QIGC);

  • – presence of ‘spike’ type echoes (QISPIKE);

  • – presence of ‘speck’ type echoes (QISPECK);

  • – radar beam blocking by ground targets (QIPBB), and,

  • – attenuation of radar beam in rain (QIATT),

are quantitatively determined. The total quality index QI is calculated from all the individual values of QIi employing the multiplicative scheme (Equation (3)) in which all weights are set to one:

  • equation image(28)

It can be noticed that the total quality index QI equals zero if at least one of the individual quality indices QIi equals zero when such a formula is used.

In Figure 12 the final result of running of all quality algorithms is presented as set of QIi images. Only quality indices for the lowest elevation are depicted here, as most often this elevation is burdened with errors in the highest degree. The total quality index (QI) field is shown as well.

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Figure 12. Examples of quality index QI calculated for the lowest elevation 0.5 °: (a) QISYS, (b) QIBROAD, (c) QIGC, (d) QISPIKE, (e) QISPECK, (f) QIPBB, (g) QIATT, (h) total quality index QI (the left hand images for Legionowo radar, 10 May 2010, 1530 UTC, the right hand ones for Pastewnik radar, 5 May 2010, 1800 UTC; distance to radar up to 250 km). The panels represent range (y-axis) vs. azimuth (x-axis) displays. This figure is available in colour online at wileyonlinelibrary.com/journal/met

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Each elevation of raw volume reflectivity data can be compared with the final corrected field. A set of such data for the lowest elevation is presented in Figure 13 along with total quality index field for the two examples from Figure 12. In this figure a strong impact of spike echoes is observed for the Legionowo radar, whereas ground clutter and related blockage on data from Pastewnik radar is evident.

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Figure 13. Example of influence of all correction algorithms for the lowest elevation 0.5 °: (a) raw data Z (in dBZ); (b) corrected data Zcor; (c) total quality index QI (the upper image for Legionowo radar, 10 May 2010, 1530 UTC, the lower for Pastewnik radar, 5 May 2010, 1800 UTC; distance to radar up to 250 km). The panels represent range (y-axis) vs. azimuth (x-axis) displays. This figure is available in colour online at wileyonlinelibrary.com/journal/met

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4. Verification on 2-D precipitation radar products

  1. Top of page
  2. Abstract
  3. 1. Quality issues in weather radar data
  4. 2. Description of quality control algorithms
  5. 3. Total quality index
  6. 4. Verification on 2-D precipitation radar products
  7. 5. Conclusions
  8. Acknowledgements
  9. References

In the case of 3-D radar reflectivity data there is no benchmark to evaluate the data quality, so that only indirect analyses make it possible to characterize the data quality after corrections. The most common approach consists of investigations of the generated 2-D products, such as ground precipitation rate, which are easier to carry out. The efficiency of many corrections described in the previous sections can be evaluated by human experts. However, in order to obtain an objective and comprehensive assessment some quantitative metrics are necessary. Rain gauge data can be used as benchmarks for ground precipitation estimation based on weather radar data, but they are not suitable for all corrections, especially the ones related to small-scale contaminations. Therefore, apart from visual analysis of the effectiveness of corrections, quality metrics based on the spatial pattern of ground precipitation are proposed in order to verify the developed algorithms on monthly accumulations of precipitation.

In this section examples of the performance of the described algorithms are presented on accumulations of 2-D precipitation PseudoCAPPI product at 1 km a.s.l. generated from 3-D volume data. The PseudoCAPPI is a CAPPI product modified by adding data from the lowest available elevation out of the CAPPI range.

4.1. Examples of removal of geometrically shaped echoes

Examples of the effectiveness of the removal of signals from external interference are presented in Figures 14 and 15, for removal of ‘wide’ spikes (with spread of several azimuths) and ‘narrow’ spikes (not wider than a few azimuths) respectively. These examples are presented for the Legionowo radar, which is strongly burdened with spike-type echoes (marked with red ovals). The ‘wide’ spikes in Figure 14 and the ‘narrow’ ones in both Figures 14 and 15 are nearly completely removed. Efficiency of the algorithms depends on spike location in relation to the precipitation field: if the spike is located in the non-precipitation area then the efficiency is very high, especially in cases of ‘narrow’ spikes. On the other hand, the efficiency can be lower for the not very smooth (especially along a beam) pattern of the ‘wide’ spike. The task becomes more difficult if the spike overlaps the precipitation field. In this case the spike can be significantly but not completely removed (Figure 15).

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Figure 14. Example of radar data before and after removal of ‘wide’ external signal (Legionowo radar, hourly accumulation from PseudoCAPPI, 28 May 2010, 2000–2100 UTC). ‘Narrow’ spikes removal is switched on as well. This figure is available in colour online at wileyonlinelibrary.com/journal/met

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Figure 15. Example of radar data before and after removal of ‘narrow’ external signals (Legionowo radar, hourly accumulation from PseudoCAPPI, 5 May 2010, 2100–2200 UTC). This figure is available in colour online at wileyonlinelibrary.com/journal/met

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If the 2-D precipitation data are generated mainly from one elevation, as for products such as CAPPI or PseudoCAPPI, then speck echoes are not significant. Therefore, an example of speck correction is not presented here.

4.2. Example of beam blockage correction

In Figure 16 an example for correction of beam blockage in a mountainous area is presented for the Pastewnik radar where very strong blockages are observed. It can be noticed that the partial and total blockage observed in the southwest is efficiently corrected using the proposed algorithm.

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Figure 16. Example of radar data before and after blocked signal reconstruction (Pastewnik radar, hourly accumulation from PseudoCAPPI, 5 May 2010, 1700–1800 UTC). This figure is available in colour online at wileyonlinelibrary.com/journal/met

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4.3. Example of correction of attenuation in rain

The impact of the correction of attenuation in rain for C-Band radar is depicted in Figure 17, where areas marked with red ovals show places where relatively high attenuation behind intensive precipitation was detected and corrected. The magnitude of this phenomenon in the case of such radar wavelength is not highly significant, but in exceptional cases the attenuation can strongly distort precipitation estimates.

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Figure 17. Example of radar data before and after attenuation in rain correction (Legionowo radar, hourly accumulation from PseudoCAPPI, 17 May 2010, 2200–2300 UTC). This figure is available in colour online at wileyonlinelibrary.com/journal/met

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4.4. Examples of the total scheme performance

The total effect of the corrections on radar-based ground precipitation data is especially noticeable for longer accumulations, optimally one month or even one year. In Figure 18 accumulations generated from PseudoCAPPI products for the whole of May 2010 are presented. The Legionowo radar covers lowland, so that no effects related to beam blockage are observed here. However intense external interferences are detected mostly at the same azimuths, so they become more significant in cases of accumulations.

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Figure 18. Example of radar data before and after all corrections (Legionowo radar, monthly accumulation from PseudoCAPPI, May 2010). This figure is available in colour online at wileyonlinelibrary.com/journal/met

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A similar examination was performed for the Pastewnik radar located near the Sudety Mountains, which result in strong beam blockage (Figure 19). In the southwest part of the radar image a beam is totally blocked, so precipitation is hardly detected here and higher elevation data had to be employed instead. After applying all corrections a significant improvement is noticeable, however it is not quite satisfactory.

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Figure 19. Example of radar data before and after all corrections (Pastewnik radar, monthly accumulation from PseudoCAPPI, May 2010). This figure is available in colour online at wileyonlinelibrary.com/journal/met

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The effect of the Earth's curvature is connected to an increase of the distance between the lowest radar beam and the ground. It results in lower accumulations far away from the radar site because not all hydrometeors are detected. This is strongly noticeable in Figures 18 and 19. Related errors burden surface precipitation products so these must be adjusted at the further stage of 2-D data corrections by means of empirical formulae based on comparison with rain gauge data.

The efficiency of the set of RADVOL-QC correction algorithms has been evaluated by analysis of statistical properties of the monthly accumulations. It was assumed that symmetry and smoothness are proper metrics of the data quality (Joe, 2011).

The symmetry co-efficient is quantified from differences between values x in pixels symmetrical with respect to the centre of the image:

  • equation image(29)

where i is the radar pixel number, i∈(0, …, n − 1); n is the number of pixels in the whole radar image; trunc() means truncation to integer.

Smoothness is evaluated employing a quantity called ENLi (equivalent number of looks) which is calculated locally around i–pixel as ratio of squared mean and variance within smaller grids from the formula:

  • equation image(30)

where j is the number of radar pixel in the i–pixel certain vicinity, j∈(1, …, m), grid 11 × 11 km is considered here (i.e. m = 121).

On this basis, smoothness is defined according to the formula:

  • equation image(31)

The verification using data from May 2010 shows an increase of the symmetry metric from 9.07 to 10.12 for the Legionowo radar and from 2.65 to 3.02 for the Pastewnik radar, and an increase of the smoothness metric for the radars, respectively, from 270 to 324 and from 224 to 250 (Figure 20), so both metrics indicate significantly higher quality of the data after corrections. The impact of a particular correction depends on local conditions, i.e. what kinds of errors a particular radar's measurements are burdened with, especially if spike echoes (such as for Legionowo) or beam blocking (as for Pastewnik) are observed.

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Figure 20. Symmetry (on the left) and smoothness (on the right) coefficients for Legionowo (on the top) and Pastewnik (on the bottom) radars. Legend: 1—no corrections; 2—after SPIKE correction; 3—after SPIKE and SPECK corrections; 4—after SPIKE, SPECK, and PBB corrections; 5—after SPIKE, SPECK, PBB, and ATT corrections

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Generally, specks are not a significant source of errors, especially for accumulated precipitation. The symmetry co-efficient is sensitive to spike and partial beam blocking presence whereas smoothness is sensitive to attenuation.

5. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Quality issues in weather radar data
  4. 2. Description of quality control algorithms
  5. 3. Total quality index
  6. 4. Verification on 2-D precipitation radar products
  7. 5. Conclusions
  8. Acknowledgements
  9. References

The presented studies on quality issues in weather radar data are performed considering mainly practical aspects, as the weather radar data must be disseminated to end-users in real time. As a consequence all the used corrections are to be operationally determinable, employing stable and reliable quality control algorithms. Moreover, the quality information finally attached to the data should be as intuitive and informative as possible. It seems necessary to consult such quality management with end-users of the data in terms of their expectations and requirements.

The radar data quality control and characterization algorithms collected in the paper have been selected having in mind all the above assumptions. At the present stage the quality scheme consists of a few algorithms that deal with the most significant errors in radar measurements. The investigation will be continued, especially towards removal of other error sources and implementation to dual-polarization radars which provide the additional potential for improved quality management. Although dual-polarization weather radars change the methodology of research on quality issues and improve the chance of significant progress, the single-polarization radars still dominate operational networks, so the presented algorithms are still needed. Moreover, part of the algorithms will also be useful for the dual-polarization radars. The work will be performed in the framework of the BALTRAD+ Project and operationally implemented in the RADVOL-QC system at IMGW.

Acknowledgements

  1. Top of page
  2. Abstract
  3. 1. Quality issues in weather radar data
  4. 2. Description of quality control algorithms
  5. 3. Total quality index
  6. 4. Verification on 2-D precipitation radar products
  7. 5. Conclusions
  8. Acknowledgements
  9. References

The paper was prepared in the frame of the ‘An advanced weather radar network for the Baltic Sea Region: BALTRAD’ project (Baltic Sea Region Programme 2007-2013) and partly financed by the Polish Ministry of Science and Higher Education.

References

  1. Top of page
  2. Abstract
  3. 1. Quality issues in weather radar data
  4. 2. Description of quality control algorithms
  5. 3. Total quality index
  6. 4. Verification on 2-D precipitation radar products
  7. 5. Conclusions
  8. Acknowledgements
  9. References
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