Calibrating Ground-Based Radars against TRMM and GPM
1. Introduction
Since their development following the end of the Second World War, ground-based weather radars have become an indispensable tool for studying precipitation systems and associated phenomena on scales ranging from tens of meters to thousands of kilometers. Of particular value is their ability to provide quantitative information about surface rainfall intensity. Such information is used by forecasters to monitor and warn for hazardous extreme-rain events, serves as input data to hydrological models, and allows for areal verification of quantitative precipitation forecasts. However, radar-derived rainfall estimates are subject to significant uncertainties (Villarini and Krajewski 2010). Many of these relate to assumptions that must be made regarding the drop size distribution and its evolution as hydrometeors fall from the level of observation to the surface, but perhaps the most fundamental uncertainty is that associated with errors in radar calibration.
Maintaining a well-calibrated radar system requires regular testing and maintenance of those components that influence the true value of 
The task of comparing reflectivities observed by spaceborne and ground-based radars (hereinafter SRs and GRs, respectively) is complicated by the wildly different sampling characteristics of the two instruments. Operational GRs typically perform volume scans at regular intervals of 5–10 min. These scans consist of 360° radial sweeps performed at multiple elevation angles, ranging from near zero to around 20°–30°. Samples of reflectivity are recorded every 0.5°–1° in azimuth and every 250 m –1 km in range, out to maximum ranges of 150–300 km. By comparison, the TRMM PR and GPM KuPR measure quasi-vertical profiles of reflectivity within ~250-km-wide orbital swaths, with horizontal and vertical sampling intervals of 5 km and 125–250 m, respectively. Sun-asynchronous orbits give rise to quasi-periodic observations at all locations within the satellite’s latitudinal range (±35° for TRMM, ±65° for GPM) with typical overpass frequencies of 1–2 day−1. Another important difference between GR and SR measurements relates to the atmospheric volume sampled by each radar pulse. This volume is proportional to the angular beamwidth and increases with the square of range due to beam broadening. As a consequence, GR sample volumes vary by approximately five orders of magnitude within the instrument’s field of view. In contrast, for SRs the extent of measurements in the range (vertical) direction is limited to the first 20 km above the surface and thus the relative variation in sample volume is small.
To quantitatively compare SR and GR reflectivities, measurements must be associated in time and space. The ground speed of the satellites is sufficiently high that measurements across a typical GR field of view can be treated as instantaneous. Temporal association is thus achieved simply by identifying the GR volume scan closest in time to a given SR overpass. Because of the different sampling geometries, spatial association is much more challenging. Many researchers have taken the fairly simple approach of remapping both observation sets to a common three-dimensional Cartesian grid, using nearest-neighbor or linear interpolation (e.g., Anagnostou et al. 2001; Liao et al. 2001; Bolen and Chandrasekar 2003; Liao and Meneghini 2009b; Wang and Wolff 2009; Park et al. 2015). However, such procedures necessarily introduce errors that may swamp systematic differences in reflectivity associated with GR miscalibration. To overcome this issue, Schwaller and Morris (2011, hereinafter SM11) introduced what will herein be referred to as the volume-matching method (VMM). In this approach, intersections between individual SR beams and GR elevation sweeps are identified and the reflectivity values from both instruments are averaged within a spatial neighborhood around the intersection. Specifically, SR data are averaged in range over the width of the GR beam at the GR range of the intersection, while GR data are averaged in the range–azimuth plane within the footprint of the SR beam. The result is a pair of reflectivity measurements corresponding to approximately the same volume of atmosphere.
The VMM was originally developed as part of ground validation efforts in support of the GPM mission. While the potential of the method as a means to track GR calibration was immediately apparent to the developers, its use in this context has thus far been very limited. Kim et al. (2014) applied the VMM to four GRs in the Korean Peninsula for the period 2006–10, finding time-averaged calibration errors of between −2 and +1 dB. However, they were unable to identify shorter-time-scale variations in GR calibration as a result of the noisiness of the GR–SR comparisons. This characteristic was also noted by SM11 and is believed to result from a combination of factors, including imperfect spatial and temporal matching, differences in radar frequency, and errors in SR attenuation correction.
The present study summarizes our efforts using the VMM to quantify and correct historical calibration errors for three GRs in the vicinity of Sydney, Australia. We first explore how systematic variations in GR–SR reflectivity difference can be related to certain characteristics of the volume-matched sample pair. By isolating samples that are least influenced by these artifacts, it is possible to significantly reduce the noise in GR bias estimates. We then demonstrate how VMM results can be used in combination with radar engineering maintenance records to identify variations in GR calibration on inter- and intra-annual time scales. Finally, we present a simple method for comparing GR observations in regions of overlapping coverage as a means to validate the estimated bias corrections.
2. Methodology
a. Data
The Australian Bureau of Meteorology (BoM) operates a diverse network of over 60 single-polarization GRs comprising a mixture of C- and S-band systems of varying age and make. This study uses data from three S-band radars located close to the cities of Sydney (SYD), Wollongong (WOL), and Newcastle (NEW) in the state of New South Wales (Fig. 1). Together, these sites provide coverage of a densely populated stretch of coastline that is frequently affected by high-impact weather, including damaging hail and extreme precipitation. The characteristics of the radars are listed in Table 1. For each GR, volume scan data for the period 15 May 2009 (the start of operational monitoring at SYD) to 31 December 2015 were extracted from BoM archives and converted from the in-house Radar Picture (RAPIC) format to OPERA (Operational Programme for the Exchange of Weather Radar Information; Köck et al. 2000) Data Information Model–Hierarchical Data Format, version 5 (ODIM-HDF5; Michelson et al. 2014), for processing. Note that all data are subject to on-site processing to mitigate ground clutter and noise (Rennie 2012). No additional quality control was applied for the present analysis.
(a) Map of Australia showing the location of the region of interest (black box). (b) Map of the region of interest showing the locations of the three radars (white diamonds) and nearby major cities (black circles). Dotted lines show the 15- and 115-km range rings around each radar.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
(a) Map of Australia showing the location of the region of interest (black box). (b) Map of the region of interest showing the locations of the three radars (white diamonds) and nearby major cities (black circles). Dotted lines show the 15- and 115-km range rings around each radar.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
(a) Map of Australia showing the location of the region of interest (black box). (b) Map of the region of interest showing the locations of the three radars (white diamonds) and nearby major cities (black circles). Dotted lines show the 15- and 115-km range rings around each radar.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Characteristics of the three GRs used in this study. Listed are the make, wavelength λ, and angular beamwidth ω of the radar, and the range gate spacing Δr, azimuthal beam spacing Δϕ, number of tilts nθ, and elevation angles employed in a volume scan. Note that the WOL radar was replaced in early 2011, with associated changes in λ, ω, and Δr. The set of elevation angles was also updated at this time to be consistent with the SYD radar. The same change was applied to the NEW radar in mid-2013 following a receiver upgrade (from analogue to digital).
BoM engineering staff perform regular (approximately once every 6 months) maintenance work at all GR sites. Relevant to the radar calibration are checks on the transmitted peak power, frequency, and pulse duration, and the receiver gain. Where necessary, these settings are adjusted and the radar constant is updated accordingly. In addition to these routine activities, unscheduled maintenance is sometimes required to deal with system failures or suspected faults. Records of all site visits are maintained on an internal database called SitesDB. While the information contained in these records is minimal, with only a date and a brief description of what was done (e.g., “02/12/2009: 6 monthly maintenance carried out”), it is sufficient to identify dates of possible calibration changes. In theory, calibration accuracy should improve following all maintenance work; however, as we shall demonstrate, this is often not the case.
The characteristics of the TRMM PR and GPM KuPR are listed in Table 2. TRMM operated almost continuously from December 1997 to April 2015, with the PR providing reliable measurements up to September 2014. This study uses data from version 7 of the Level 2 products 2A23 and 2A25 (Table 3). These consist of orbital swaths made up of a large number of individual PR scans that in turn comprise 49 individual rays. Each scan has a unique time stamp, and rays are georeferenced by the latitude–longitude coordinates of their intersection with the Earth ellipsoid. The 2A23 product contains information on precipitation type and the characteristics of the radar bright band2 (where present) for each ray, while 2A25 contains the vertical profiles of attenuation-corrected reflectivity. Precipitation type is determined based on the horizontal and vertical echo structure (Awaka et al. 2007), with three basic classifications: stratiform, convective, and other. The bright band is identified as outlined in Awaka et al. (2009). A hybrid method (Meneghini et al. 2004), combining the approaches of Hitschfeld and Bordan (1954) and Meneghini et al. (2000), is used to correct for attenuation of the SR beam, which can be significant in heavy rainfall. For the GPM KuPR, data are available from March 2014 onward. Version 4 of the 2AKu product is used, which contains the same basic variables as the 2A23 and 2A25 TRMM products (Table 3). All SR data were obtained using the STORM online data-access interface to NASA’s precipitation processing system archive (https://storm.pps.eosdis.nasa.gov). To reduce data volumes, only those sections of orbital swaths corresponding to GR site overpasses were extracted.
Characteristics of the TRMM PR and GPM KuPR. Listed are the satellite orbital altitudes zo, the wavelength λ and angular beam width ω of the radars, and the range gate spacing Δr, cross-track angular beam spacing ΔΦ, and maximum off-nadir angle Φmax of the scans. Note that prior to August 2001, the TRMM orbital altitude was 350 km.
TRMM and GPM parameters extracted for our analysis. Detailed descriptions of these can be found in the file specification documents for the TRMM version 7 2A23 and 2A25 products (NASA 2014, 2015) and GPM version 4 2AKu product (NASA 2016). Array dimensions 
It is noted that at the time of writing, new product versions (version 8 for TRMM and version 5 for GPM) are in the process of being released. These include changes to the SR calibrations, corresponding to reflectivity increases of 1.1 and 1.3 dB for the TRMM PR and GPM KuPR, respectively (NASA 2017; Iguchi et al. 2017). It remains to be seen whether these will be the final adjustments, but for now it must be assumed that the GR calibration errors derived herein are biased low by a little over 1 dB. This serves to illustrate the main limitation of using radar intercomparisons to assess calibration: even the most carefully monitored systems can be in error.
b. Volume-matching method
The VMM allows for a quantitative comparison of SR and GR reflectivities with minimal spatial processing of the two datasets. Intersections between an SR beam and a GR elevation sweep are identified, and the reflectivities from both instruments are averaged to roughly equate the sample volumes. SR reflectivities are averaged along the SR beam (approximately vertically) between the half-power points of the GR sweep. GR reflectivities are averaged in the range–azimuth plane (approximately horizontally) within the footprint of the SR beam. Figure 2 illustrates these averaging procedures for idealized cases at GR ranges of 50 and 100 km. Full details of the procedure are provided in the appendix. Here we note only the key differences between our implementation of the method and the original algorithm as described by SM11 and Morris and Schwaller (2009).
Illustration of the VMM. (a),(b) GR–SR intersection at a GR range of 50 km, azimuth angle of 45°, and elevation angle of 1.3°, and an SR scan angle of 0° (nadir scan). (c),(d) GR–SR intersection at a GR range of 100 km, azimuth angle of 45°, and elevation angle of 2.4°, and an SR scan angle of 17.04° (maximum off-nadir scan). In both cases, the GR has a range gate spacing of 250 m and an angular beamwidth of 1.0°, the SR has a range gate spacing of 250 m, and the SR scan line is perfectly aligned with the intersecting GR azimuth. (a),(c) Vertical cross sections along the SR scan line, with the GR beam boundaries (thick solid blue lines) and center (dotted blue lines), and the SR bin boundaries (thin red lines) and centers (red dots). SR bins contributing to the volume-matched reflectivity are shaded. (b),(d) Horizontal cross sections at the height of the intersection, with the GR bin boundaries (thin blue lines) and centers (blue dots), and the approximate horizontal projection of the SR beam boundary (red circle). GR bins contributing to the volume-matched reflectivity are shaded. In all panels the point of intersection is indicated with a black cross.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Illustration of the VMM. (a),(b) GR–SR intersection at a GR range of 50 km, azimuth angle of 45°, and elevation angle of 1.3°, and an SR scan angle of 0° (nadir scan). (c),(d) GR–SR intersection at a GR range of 100 km, azimuth angle of 45°, and elevation angle of 2.4°, and an SR scan angle of 17.04° (maximum off-nadir scan). In both cases, the GR has a range gate spacing of 250 m and an angular beamwidth of 1.0°, the SR has a range gate spacing of 250 m, and the SR scan line is perfectly aligned with the intersecting GR azimuth. (a),(c) Vertical cross sections along the SR scan line, with the GR beam boundaries (thick solid blue lines) and center (dotted blue lines), and the SR bin boundaries (thin red lines) and centers (red dots). SR bins contributing to the volume-matched reflectivity are shaded. (b),(d) Horizontal cross sections at the height of the intersection, with the GR bin boundaries (thin blue lines) and centers (blue dots), and the approximate horizontal projection of the SR beam boundary (red circle). GR bins contributing to the volume-matched reflectivity are shaded. In all panels the point of intersection is indicated with a black cross.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Illustration of the VMM. (a),(b) GR–SR intersection at a GR range of 50 km, azimuth angle of 45°, and elevation angle of 1.3°, and an SR scan angle of 0° (nadir scan). (c),(d) GR–SR intersection at a GR range of 100 km, azimuth angle of 45°, and elevation angle of 2.4°, and an SR scan angle of 17.04° (maximum off-nadir scan). In both cases, the GR has a range gate spacing of 250 m and an angular beamwidth of 1.0°, the SR has a range gate spacing of 250 m, and the SR scan line is perfectly aligned with the intersecting GR azimuth. (a),(c) Vertical cross sections along the SR scan line, with the GR beam boundaries (thick solid blue lines) and center (dotted blue lines), and the SR bin boundaries (thin red lines) and centers (red dots). SR bins contributing to the volume-matched reflectivity are shaded. (b),(d) Horizontal cross sections at the height of the intersection, with the GR bin boundaries (thin blue lines) and centers (blue dots), and the approximate horizontal projection of the SR beam boundary (red circle). GR bins contributing to the volume-matched reflectivity are shaded. In all panels the point of intersection is indicated with a black cross.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
1) Minimum and maximum ranges
As previously discussed, the volume of atmosphere sampled by a GR varies significantly across the instrument’s field of view as a result of beam broadening. This means that samples considered in the VMM also increase in volume with GR range. Given the limited vertical extent of many precipitating systems, it is appropriate to define a maximum range 
2) Frequency correction
3) Reflectivity thresholds
Both the TRMM PR and GPM KuPR have nominal sensitivities of around 18 dBZ (Hou et al. 2014), although prelaunch tests showed that the KuPR may detect reflectivities as low as 14.5 dBZ (Toyoshima et al. 2015). In the VMM, only SR bins for which 
Another key difference is in our choice of the GR reflectivity threshold. SM11 set 
4) Reflectivity averaging
In the original VMM implementation, reflectivities for GR bins within the SR footprint are averaged using a Barnes Gaussian inverse-distance weighting, where distance is measured horizontally from the center of the SR footprint to the center of the GR bin (Morris and Schwaller 2009). This weighting is designed to account for the nonuniform distribution of power within the SR beam. The algorithm has since been updated to also include linear weighting based on the volume of the GR bins so that larger volumes are weighted more heavily (K. Morris 2015, personal communication). This is justified by the fact that GR bin volumes can vary by up to a factor of 2 within the PR footprint. Our VMM implementation uses this modified weighting scheme. As in the original algorithm, no weighting is applied in averaging the SR reflectivities as a result of uncertainties in the GR beam height associated with nonstandard refraction.
3. Results
a. Comparison examples
Figures 3 and 4 show examples of GR–SR comparisons for the SYD radar. The former shows a comparison with TRMM on 22 November 2013, while the latter shows a comparison with GPM a little over a year later on 27 January 2015. The top row in each figure shows plan views at a particular elevation angle of the (frequency corrected) SR and GR reflectivities and their difference. The middle row shows vertical cross sections along a particular SR scan of the same fields. The bottom row presents a statistical comparison of the reflectivities from the two instruments across all volume-matched samples. Note that samples with 
Example of GR–SR comparison between TRMM and the SYD radar on 22 Oct 2013. Top row shows plan views of (a) SR reflectivity, (b) GR reflectivity, and (c) GR - SR reflectivity for the 1.3° elevation sweep. Each filled circle shows an individual volume-matched sample. Rings show the minimum and maximum GR range. Solid and dashed lines show, respectively, the boundaries and center of the SR swath. Middle row shows vertical cross sections taken across the SR swath (location indicated by dotted lines in top panels) of (d) SR reflectivity, (e) GR reflectivity, and (f) GR - SR reflectivity. Here volume-matched samples are shown as columns of varying depth (note that these overlap for low-elevation sweeps). Solid and dotted lines show, respectively, the center and boundaries of the bright band. Bottom row summarizes the statistics of all volume-matched sample pairs: (g) histogram of SR (black) and GR (gray) reflectivities (2-dB bins); (h) scatter plot of paired SR and GR reflectivities; (i) histogram of GR - SR reflectivity (1-dB bins). Dashed vertical lines in (g) and (h) show the minimum SR reflectivity. Solid and dotted lines in (h) show the line of best fit and one-to-one line, respectively, with the sample size n and Pearson correlation coefficient r given at the top. Mean, median, and modal GR bias are indicated in the top-right corner of (i).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Example of GR–SR comparison between TRMM and the SYD radar on 22 Oct 2013. Top row shows plan views of (a) SR reflectivity, (b) GR reflectivity, and (c) GR - SR reflectivity for the 1.3° elevation sweep. Each filled circle shows an individual volume-matched sample. Rings show the minimum and maximum GR range. Solid and dashed lines show, respectively, the boundaries and center of the SR swath. Middle row shows vertical cross sections taken across the SR swath (location indicated by dotted lines in top panels) of (d) SR reflectivity, (e) GR reflectivity, and (f) GR - SR reflectivity. Here volume-matched samples are shown as columns of varying depth (note that these overlap for low-elevation sweeps). Solid and dotted lines show, respectively, the center and boundaries of the bright band. Bottom row summarizes the statistics of all volume-matched sample pairs: (g) histogram of SR (black) and GR (gray) reflectivities (2-dB bins); (h) scatter plot of paired SR and GR reflectivities; (i) histogram of GR - SR reflectivity (1-dB bins). Dashed vertical lines in (g) and (h) show the minimum SR reflectivity. Solid and dotted lines in (h) show the line of best fit and one-to-one line, respectively, with the sample size n and Pearson correlation coefficient r given at the top. Mean, median, and modal GR bias are indicated in the top-right corner of (i).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Example of GR–SR comparison between TRMM and the SYD radar on 22 Oct 2013. Top row shows plan views of (a) SR reflectivity, (b) GR reflectivity, and (c) GR - SR reflectivity for the 1.3° elevation sweep. Each filled circle shows an individual volume-matched sample. Rings show the minimum and maximum GR range. Solid and dashed lines show, respectively, the boundaries and center of the SR swath. Middle row shows vertical cross sections taken across the SR swath (location indicated by dotted lines in top panels) of (d) SR reflectivity, (e) GR reflectivity, and (f) GR - SR reflectivity. Here volume-matched samples are shown as columns of varying depth (note that these overlap for low-elevation sweeps). Solid and dotted lines show, respectively, the center and boundaries of the bright band. Bottom row summarizes the statistics of all volume-matched sample pairs: (g) histogram of SR (black) and GR (gray) reflectivities (2-dB bins); (h) scatter plot of paired SR and GR reflectivities; (i) histogram of GR - SR reflectivity (1-dB bins). Dashed vertical lines in (g) and (h) show the minimum SR reflectivity. Solid and dotted lines in (h) show the line of best fit and one-to-one line, respectively, with the sample size n and Pearson correlation coefficient r given at the top. Mean, median, and modal GR bias are indicated in the top-right corner of (i).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
As in Fig. 3, but showing a comparison between GPM and the SYD radar on 27 Jan 2015. In this case the 0.5° elevation sweep is shown in the top row.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
As in Fig. 3, but showing a comparison between GPM and the SYD radar on 27 Jan 2015. In this case the 0.5° elevation sweep is shown in the top row.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
As in Fig. 3, but showing a comparison between GPM and the SYD radar on 27 Jan 2015. In this case the 0.5° elevation sweep is shown in the top row.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
From the plan views of reflectivity it appears that the VMM produces good spatial agreement between the reflectivity measurements from the two instruments. This is confirmed by high values of the Pearson correlation coefficient (0.95 and 0.87 for the first and second comparisons, respectively). This agreement allows us to estimate the GR calibration error. In the first case, the error is close to zero (Fig. 3i); however, in the second case the GR shows a substantial negative bias of around 4 dB (Fig. 4i). It is thus apparent that the calibration of the SYD radar changed sometime between late 2013 and early 2015.
It is noteworthy that, on a point-by-point basis, the GR–SR reflectivity difference displays a large degree of scatter. For example, for the first case, the difference varies by more than 10 dB (from <−5 to >5 dB) across the 1.3° elevation sweep (Fig. 3c). Part of this variation will be associated with imperfect spatial matching of the data as a result of a combination of advection and evolution of the precipitation features during the time between measurements (200 s in this case) and beam propagation effects (e.g., nonstandard refraction of the GR beam). However, as we shall demonstrate in the next section, other factors, including the Ku-to-S-band frequency correction and the reflectivity value itself, also strongly influence GR–SR reflectivity differences.
b. Comparison sensitivities
In this section, we investigate the sensitivity of the GR–SR reflectivity difference 
GR–SR reflectivity difference plotted as a function of the minimum fraction of SR and GR bins with reflectivity values above their respective thresholds. Shown are the median (filled diamonds) and IQR (vertical lines) of the ΔZ distribution and the number of sample pairs (open circles; scale on right y axis) for each 
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
GR–SR reflectivity difference plotted as a function of the minimum fraction of SR and GR bins with reflectivity values above their respective thresholds. Shown are the median (filled diamonds) and IQR (vertical lines) of the ΔZ distribution and the number of sample pairs (open circles; scale on right y axis) for each
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
GR–SR reflectivity difference plotted as a function of the minimum fraction of SR and GR bins with reflectivity values above their respective thresholds. Shown are the median (filled diamonds) and IQR (vertical lines) of the ΔZ distribution and the number of sample pairs (open circles; scale on right y axis) for each
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
For the most restrictive case of 
Clearly, it is important to exclude samples with low values of 
We now examine how 
Box-and-whisker plots showing GR–SR reflectivity difference for samples below, within, and above the ML in (top) stratiform and (bottom) convective precipitation for the (left) SYD, (middle) WOL, and (right) NEW radars. Boxes show the median and IQR of the ΔZ distribution; whiskers show the 10th and 90th percentiles. Dark and light gray boxes show values computed using SR data with and without the Ku-to-S-band frequency correction, respectively. The number of samples in each layer is given at the bottom of the panels. Note that all samples whose volume overlaps vertically with the ML are classified as being within it.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Box-and-whisker plots showing GR–SR reflectivity difference for samples below, within, and above the ML in (top) stratiform and (bottom) convective precipitation for the (left) SYD, (middle) WOL, and (right) NEW radars. Boxes show the median and IQR of the ΔZ distribution; whiskers show the 10th and 90th percentiles. Dark and light gray boxes show values computed using SR data with and without the Ku-to-S-band frequency correction, respectively. The number of samples in each layer is given at the bottom of the panels. Note that all samples whose volume overlaps vertically with the ML are classified as being within it.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Box-and-whisker plots showing GR–SR reflectivity difference for samples below, within, and above the ML in (top) stratiform and (bottom) convective precipitation for the (left) SYD, (middle) WOL, and (right) NEW radars. Boxes show the median and IQR of the ΔZ distribution; whiskers show the 10th and 90th percentiles. Dark and light gray boxes show values computed using SR data with and without the Ku-to-S-band frequency correction, respectively. The number of samples in each layer is given at the bottom of the panels. Note that all samples whose volume overlaps vertically with the ML are classified as being within it.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
The frequency correction results in an increase in 
Based on these results we exclude convective precipitation samples and stratiform samples within the ML from all subsequent analysis. This reduces the SYD radar sample size by approximately 62% and the WOL and NEW radar sample sizes by approximately 77% (the larger beam widths of these radars mean that more samples overlap with the ML). It should be noted that in order to mitigate potential biases associated with the SR attenuation correction, only stratiform samples above the ML are used in ground validation of the GPM DPR (W. Petersen 2017, personal communication). However, when combined with the reflectivity criteria introduced below, the exclusion of samples below the ML was found to excessively limit the total number of samples. Testing reveals a slight (typically <0.5 dB) but systematic increase in calibration error estimates when only samples above the ML are used (not shown). This may be indicative of excessive attenuation correction in stratiform precipitation (cf. Wang and Wolff 2009) and/or undercorrection for the frequency difference in snow.
Figure 7 summarizes the influence of two further sample characteristics—GR range 
Bivariate histograms showing GR–SR reflectivity difference as a function of (top) GR range and (bottom) GR–SR time difference for the (left) SYD, (middle) WOL, and (right) NEW radars. Shading shows the sample size for each bin on a logarithmic scale. Black diamonds and vertical lines show, respectively, the median and IQR of the ΔZ distribution for each x-axis bin (not shown for sample sizes < 100). Pearson correlation coefficients r are given in the top-right corner of each panel.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Bivariate histograms showing GR–SR reflectivity difference as a function of (top) GR range and (bottom) GR–SR time difference for the (left) SYD, (middle) WOL, and (right) NEW radars. Shading shows the sample size for each bin on a logarithmic scale. Black diamonds and vertical lines show, respectively, the median and IQR of the ΔZ distribution for each x-axis bin (not shown for sample sizes < 100). Pearson correlation coefficients r are given in the top-right corner of each panel.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Bivariate histograms showing GR–SR reflectivity difference as a function of (top) GR range and (bottom) GR–SR time difference for the (left) SYD, (middle) WOL, and (right) NEW radars. Shading shows the sample size for each bin on a logarithmic scale. Black diamonds and vertical lines show, respectively, the median and IQR of the ΔZ distribution for each x-axis bin (not shown for sample sizes < 100). Pearson correlation coefficients r are given in the top-right corner of each panel.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Turning to the lower row of Fig. 7, it is clear that there is no systematic variation in 
The final sensitivity we consider is to the reflectivity itself. Of course, there are two measures of this quantity and it is important to consider both. The top row of Fig. 8 shows how 
As in Fig. 7, but showing GR–SR reflectivity difference as a function of (top) SR reflectivity and (bottom) GR reflectivity. Vertical dashed lines indicate the SR sensitivity.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
As in Fig. 7, but showing GR–SR reflectivity difference as a function of (top) SR reflectivity and (bottom) GR reflectivity. Vertical dashed lines indicate the SR sensitivity.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
As in Fig. 7, but showing GR–SR reflectivity difference as a function of (top) SR reflectivity and (bottom) GR reflectivity. Vertical dashed lines indicate the SR sensitivity.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
The variations in 
Summarizing the results of this section, we have identified several factors that strongly influence the GR–SR reflectivity difference estimates obtained using the VMM, namely, the percentage of above-threshold reflectivity values within a sample, the height of the sample with respect to the ML, the application of a Ku-to-S-band frequency correction, the precipitation type, and the reflectivity itself. Based on these findings we extract the subset of volume-matched samples for each radar that are expected to most accurately isolate reflectivity differences associated with GR calibration errors. Specifically, samples are included only if they meet the following criteria:
comprise at least 70% SR and GR bins with reflectivities above the respective thresholds;
are located entirely above or below the ML in stratiform precipitation;
have volume-averaged SR and GR reflectivity values between 24 and 36 dBZ.
Statistics of GR–SR comparisons under different sample filtering criteria (see text for definitions): n is the sample size, 
c. Correcting calibration errors
Figure 9 shows the complete 7-yr time series of GR–SR comparisons for the SYD radar. Plotted are the mean reflectivity difference (symbols, colored according to the number of samples) and its standard deviation (vertical lines) for each SR overpass. It is apparent that even with the filtering criteria detailed above there is considerable variability in 
Annual time series of GR–SR reflectivity difference for the SYD radar. Symbols (circles for TRMM comparisons; diamonds for GPM comparisons) and thin vertical lines show, respectively, the mean GR bias and its standard deviation for each SR overpass. Symbols are colored according to the number of volume-matched sample pairs (white for 1–9, light gray for 10–99, dark gray for 100–999, and black for 1000+). Standard deviations are not shown for sample sizes <10.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Annual time series of GR–SR reflectivity difference for the SYD radar. Symbols (circles for TRMM comparisons; diamonds for GPM comparisons) and thin vertical lines show, respectively, the mean GR bias and its standard deviation for each SR overpass. Symbols are colored according to the number of volume-matched sample pairs (white for 1–9, light gray for 10–99, dark gray for 100–999, and black for 1000+). Standard deviations are not shown for sample sizes <10.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Annual time series of GR–SR reflectivity difference for the SYD radar. Symbols (circles for TRMM comparisons; diamonds for GPM comparisons) and thin vertical lines show, respectively, the mean GR bias and its standard deviation for each SR overpass. Symbols are colored according to the number of volume-matched sample pairs (white for 1–9, light gray for 10–99, dark gray for 100–999, and black for 1000+). Standard deviations are not shown for sample sizes <10.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
From the start of operations in May 2009 until the middle of 2014, the calibration appears to be quite accurate and stable, with mean errors generally less than 2 dB. A possible exception is September/October 2012, when several comparisons suggests a negative offset of around 4–5 dB, although the sample sizes for these are small. The period August 2014–May 2015 shows more significant GR errors, with positive offsets of 3–4 dB during the first 3 months and negative offsets of 3–5 dB thereafter. There are no comparisons during June and July 2015 and only one each in August and September; however, toward the end of the year errors return to near zero.
While the VMM does not provide sufficiently precise estimates of GR reflectivity error to identify gradual changes in calibration associated with the degradation of radar hardware, it can pick out sudden jumps that may result from component failures or engineering activities. The problem is that suitable SR site overpasses are rarely frequent enough to determine the exact date of these changes. Fortunately, as discussed in section 2a, the BoM maintains records of all operational GR maintenance work. From these records, the dates of possible calibration changes were identified and used to group the GR–SR comparisons into periods ranging in length from a few weeks to around 18 months. The calibration error ϵ during each period is assumed to be constant and is calculated using the following iterative procedure:
Valid samples (i.e., those meeting criteria 1–3, above) comprising all GR–SR comparisons during the period are grouped, and the mean
The set of valid samples is recomputed, incorporating the estimated calibration error (i.e., with ϵ subtracted from the GR reflectivities) and a new value of ϵ is computed as the mean of the uncorrected
Step 2 is repeated until a stable estimate of ϵ is obtained (to the nearest 0.1 dB). Typically, this takes fewer than five iterations.
As discussed by Protat et al. (2011), an iterative calculation is required when thresholding the reflectivity to account for the fact that, given a nonzero calibration error, samples will be incorrectly included/excluded from the calculation of ϵ. For example, consider a situation where the true ϵ is −3 dB. In the initial estimation (step 1, above), samples with uncorrected reflectivites of 21–24 dBZ (true reflectivities of 24–27 dBZ) will be incorrectly excluded, while those with uncorrected reflectivities of 33–36 dBZ (true reflectivities of 36–39 dBZ) will be incorrectly included. Similarly, if the true ϵ is +3 dB, then samples with uncorrected reflectivites of 24–27 dBZ (true reflectivities of 21–24 dBZ) will be incorrectly included, while those with uncorrected reflectivities of 36–39 dBZ (true reflectivities of 33–36 dBZ) will be incorrectly excluded. In either case, the magnitude of ϵ will be underestimated. By subsetting samples according to the corrected GR reflectivities and recomputing ϵ iteratively, this bias can be eliminated. Figure 10 illustrates the procedure for two consecutive periods (one with positive ϵ, one with negative ϵ) from the SYD radar time series. In both cases, iteration increases the magnitude of the calibration error estimate by 0.6 dB.
Histograms showing SR (thick dotted line) and SYD GR (thick solid line) reflectivity distributions for (a) 29 Jul 2014–27 Nov 2014 and (b) 28 Nov 2014–18 Jan 2015. Thin vertical lines (dotted for SR; solid for GR) bound the portion of each histogram used in the comparison. For the GR, these are colored according to the iteration step (blue for 1, green for 2, yellow for 3, and red for 4) with the corresponding calibration error estimates given in the top-right corner of each panel.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Histograms showing SR (thick dotted line) and SYD GR (thick solid line) reflectivity distributions for (a) 29 Jul 2014–27 Nov 2014 and (b) 28 Nov 2014–18 Jan 2015. Thin vertical lines (dotted for SR; solid for GR) bound the portion of each histogram used in the comparison. For the GR, these are colored according to the iteration step (blue for 1, green for 2, yellow for 3, and red for 4) with the corresponding calibration error estimates given in the top-right corner of each panel.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Histograms showing SR (thick dotted line) and SYD GR (thick solid line) reflectivity distributions for (a) 29 Jul 2014–27 Nov 2014 and (b) 28 Nov 2014–18 Jan 2015. Thin vertical lines (dotted for SR; solid for GR) bound the portion of each histogram used in the comparison. For the GR, these are colored according to the iteration step (blue for 1, green for 2, yellow for 3, and red for 4) with the corresponding calibration error estimates given in the top-right corner of each panel.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Not every single maintenance event will be associated with a change in radar calibration. For example, checks may show the transmitter and receiver settings to be stable with respect to the previous site visit. We therefore test whether the calibration error during each period is statistically distinct from the one that preceded it. Specifically, a difference of means test is performed using the error-adjusted samples from each period. If the difference is significant at the 5% level3 and ≥0.5 dB, then both periods are retained; otherwise, the two are combined and the GR bias estimate is recomputed. Periods are also combined if one contains fewer than two comparisons comprising at least 50 samples each; we consider this the minimum requirement for a robust error estimate. The choice of 0.5 dB as a minimum difference is somewhat arbitrary but reflects the remaining uncertainty in the GR–SR comparisons (i.e., we do not expect the method to reliably detect changes in calibration of less than 0.5 dB).
Figure 11 shows the time series of GR–SR reflectivity difference for the SYD radar following the calculation of calibration error. The dates of possible calibration changes and the mean 
As in Fig. 9, but following the iterative calculation of calibration error. Thick dashed vertical lines show the dates of possible calibration changes. Thick and thin horizontal lines show, respectively, the mean calibration error and its standard deviation during the intervening periods.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
As in Fig. 9, but following the iterative calculation of calibration error. Thick dashed vertical lines show the dates of possible calibration changes. Thick and thin horizontal lines show, respectively, the mean calibration error and its standard deviation during the intervening periods.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
As in Fig. 9, but following the iterative calculation of calibration error. Thick dashed vertical lines show the dates of possible calibration changes. Thick and thin horizontal lines show, respectively, the mean calibration error and its standard deviation during the intervening periods.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Two aspects of these results must be remarked upon. The first is the large magnitude of the calibrations errors, with values frequently >1 dB and occasionally >5 dB. These errors have the potential to mislead forecasters (by suggesting that storms are more/less intense than they really are) and significantly impact radar-derived products, particularly when values are integrated in time (e.g., precipitation accumulations) or space (e.g., vertically integrated liquid water content). The second aspect to remark upon is the change in calibration associated with radar maintenance activities. One would hope that system checks and modifications always act either to maintain an existing good calibration or to improve a poor one. However, our results show that this is often not the case. For example, following preventative maintenance of the SYD radar in July 2014, the calibration error was increased from +0.8 to +3.5 dB (Fig. 11). Further work later that year saw the introduction of an error of roughly the same magnitude but opposite sign (−3.7 dB). It is difficult to ascertain the reason for these changes from the limited textual information contained in SitesDB; however, both human error and miscalibrated test equipment may play a role. Clearly, there is a need for more careful monitoring of radar calibration during operations, an issue we discuss further in section 4.
d. Verification
By combining filtered GR–SR comparisons with radar engineering records, we have been able to quantify historical calibration errors for three GRs in the vicinity of Sydney. We now seek to evaluate the benefits achieved by accounting for these errors. A comparison against ground truth, such as rain gauges, is theoretically one means to achieve this goal; however, as noted in the introduction, radar rainfall estimates are subject to many additional sources of uncertainty. We therefore instead investigate how the consistency of our three radars differs with and without calibration adjustments. Agreement between neighboring GRs is important both from an operational perspective (e.g., forecasters viewing a storm using different radars should obtain the same impression of its intensity) and for the production of multiradar products, such as regional and national rainfall maps. Since we are adjusting the GRs relative to the same SR reference, we would expect the agreement between them to improve.
Following the rationale behind the VMM, we minimize spatial processing (interpolation and averaging) of the measured reflectivities and associated errors by directly matching sample volumes in space and time. The only spatial processing we apply is the averaging of reflectivities in range to achieve a consistent gate spacing (
This GR–GR comparison method is very similar to that used in the original version of the Radar Reflectivity Comparison Tool (RRCT; Gourley et al. 2003), which was developed for monitoring the relative calibration of radars in the U.S. WSR-88D network. Tolerances in the RRCT were 500 m in horizontal distance, 50 m in vertical distance, 5% in volume, and 3 min in time (between volume scans). Note, however, that the method was subsequently modified to use less stringent tolerances (750 m in distance and 6 min in time) while considering only bins within a rectangular region (120 km in length, 20 km in width, and 20 km in height) centered equidistant between the radars to ensure comparable bin volumes (http://rrct.nwc.ou.edu/). The latter approach would not work here because, unlike the WSR-88Ds, our three radars all have different beam widths (Table 1) and thus different bin volumes at a given range.
Figure 12 summarizes the GR–GR comparison results using smoothed kernel density estimation violin plots (Hintze and Nelson 1998). Shown are the distributions of reflectivity difference computed with and without calibration adjustments, together with the sample size and Pearson correlation coefficients. Note that there are over a million samples for each radar pair, with nearly 10 million for the SYD–WOL comparison as a result of the close proximity of these sites (Fig. 1). It can be seen that the agreement of both the WOL and NEW radars with the SYD radar is improved, with smaller values of median difference, smaller IQRs, and higher correlation coefficients for the calibrated reflectivities (Figs. 12a,b). While the latter two changes are also seen in the WOL–NEW comparison, the median difference in this case actually increases in an absolute sense, from −0.1 to +0.5 dB. Taken alone, this would suggest that NEW reflectivities are being overcorrected and/or WOL reflectivities are being undercorrected. However, based on the SYD comparisons, we would expect a difference of only around 0.1 dB between these two radars after calibration adjustments. This discrepancy may be indicative of poorer volume matching between the WOL and NEW radars as a result of the large distance between them (Fig. 1).
Smoothed kernel density estimation violin plots showing bin-matched reflectivity differences between (a) SYD and WOL, (b) SYD and NEW, and (c) WOL and NEW radars before (light gray) and after (dark gray) the application of the calibration corrections derived herein. Thin horizontal solid and dotted lines show, respectively, the median and IQR of the distribution. Sample sizes n and Pearson correlation coefficients (before and after calibration corrections) r are given at the top of each panel.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Smoothed kernel density estimation violin plots showing bin-matched reflectivity differences between (a) SYD and WOL, (b) SYD and NEW, and (c) WOL and NEW radars before (light gray) and after (dark gray) the application of the calibration corrections derived herein. Thin horizontal solid and dotted lines show, respectively, the median and IQR of the distribution. Sample sizes n and Pearson correlation coefficients (before and after calibration corrections) r are given at the top of each panel.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Smoothed kernel density estimation violin plots showing bin-matched reflectivity differences between (a) SYD and WOL, (b) SYD and NEW, and (c) WOL and NEW radars before (light gray) and after (dark gray) the application of the calibration corrections derived herein. Thin horizontal solid and dotted lines show, respectively, the median and IQR of the distribution. Sample sizes n and Pearson correlation coefficients (before and after calibration corrections) r are given at the top of each panel.
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
4. Summary and outlook
In this paper we have presented a method for estimating ground-based radar (GR) calibration errors through comparisons with spaceborne radar (SR) measurements from the TRMM and GPM satellites. This has been developed and tested using data from three Bureau of Meteorology (BoM) operational GRs in the vicinity of Sydney, Australia, for the period 2009–15.
Spatially and temporally coincident GR and SR observations are first obtained using the volume-matching method (VMM) of SM11, which was originally developed to support ground validation efforts for GPM. Following Cao et al. (2013), a precipitation-phase-dependent reflectivity correction is applied to the SR data to account for differences in measurement frequency (S band for GRs, Ku band for SRs). The resulting sample pairs are then filtered to isolate reflectivity differences associated with GR calibration error. Specifically, samples are retained only if they (i) predominantly comprise bins with reflectivities above the respective instrument sensitivities (18 dBZ for the SRs, 0 dBZ for the GRs), (ii) are located in stratiform precipitation outside of the melting layer, and (iii) have moderate reflectivities (24–36 dBZ) that are largely unaffected by the low SR sensitivity or attenuation of the SR beam. It was shown that the application of these criteria on average increases the estimated GR offset by around 2 dB while decreasing its variability.
Time series of the filtered GR–SR comparisons show periods of relatively stable GR calibration separated by sudden jumps of several decibels. However, it is not possible to determine the precise date of these changes because of the low frequency of suitable satellite overpasses. In addition, residual noise in the comparisons, resulting from imperfect volume matching, makes it difficult to detect more subtle changes in calibration. To address these issues, we make use of radar engineering work records maintained by the BoM. Dates of possible calibration changes are identified, between which the GR error is assumed to be constant. The calibration error for each period is then computed as the mean GR–SR reflectivity difference across all contemporaneous samples, using an iterative procedure to account for biases introduced by the reflectivity thresholding (Protat et al. 2011). This method produces results that are consistent with a subjective assessment of the time series while providing precise estimates of calibration error.
Since no ground truth exists to verify the accuracy of our calibration error estimates, we have examined the impact of correcting for these errors on the agreement between the three radars. Following the rationale behind the VMM, a method has been developed where spatially and temporally coincident GR sample volumes are identified and their reflectivities are compared (cf. Gourley et al. 2003). It was found that the calibration corrections in general lead to a robust improvement in the agreement between GRs, with an increase in correlation coefficients and a narrowing and shift toward zero of the reflectivity difference distributions.
In the future it would be valuable to explore ways to further reduce the variability in GR–SR comparisons. One method that is currently being investigated is the use of quality indices to screen out GR samples that may be contaminated by ground clutter, anomalous propagation, or beam blockage (Crisologo et al. 2017). Screening could also be applied in cases where the orientation of the two radar beams leads to poor volume matching (e.g., Fig. 2c). The accuracy of the VMM would likely be further improved by accounting for nonstandard GR beam refraction and the movement of precipitation features between SR and GR scans. Future work could also explore refinements to the Cao et al. (2013) frequency correction in the melting layer, with a view to eliminating the need to filter out volume-matched samples that fall within this layer.
In theory, the approach presented in this paper could be applied to any radar that falls within the coverage of the SRs (±35° and ±65° during the TRMM and GPM eras, respectively). In practice, however, its potential is limited by the requirement for reliable engineering records, as these may not be available for many GR networks. Furthermore, since several months can pass between suitable satellite overpasses, the approach cannot be used for operational calibration monitoring. An alternative method that does not suffer from these issues is the relative calibration adjustment (RCA) technique (Silberstein et al. 2008; Wolff et al. 2015). This uses the statistical properties of ground clutter to provide a precise (±0.5 dB) measure of day-to-day variations in GR calibration relative to some baseline. The problem in this case is identifying an accurate baseline.
Clearly, the two techniques—SR comparison and RCA—are complementary. We are thus exploring the potential of applying them in tandem: using SR comparisons to set and periodically check the baseline reflectivity and the RCA to monitor and correct day-to-day fluctuations in calibration. This approach has already been successfully applied to 16 years of observations from the C-band polarimetric (CPOL) research radar in Darwin, Australia, and work is ongoing to incorporate it into operational radar quality control procedures at the BoM (Louf et al. 2017). Given the near-global coverage of GPM and the ubiquity of ground clutter, we believe that this approach has the potential to improve the accuracy and stability of GR calibration the world over.
Acknowledgments
RAW was funded by an Australian Research Council Linkage Project grant (LP130100679). We are grateful to Walt Petersen for insightful discussions on this work, to Bob Morris for providing details of the VMM implementation, and to Mark Curtis for his assistance with SitesDB. We also thank editor Luca Baldini and two anonymous reviewers for their comments.
APPENDIX
Details of the VMM Algorithm
The VMM algorithm was coded up using Interactive Data Language (IDL) based on the descriptions in SM11 and Morris and Schwaller (2009), with modifications as detailed in section 2b. At the time of writing, work is ongoing to incorporate it into the wradlib Python library (Heistermann et al. 2013). Here we summarize the steps involved in creating the GR–SR comparison for a single SR overpass. The geometry of the GR and SR measurements is illustrated in Fig. A1.
Diagrams showing the geometry of (a) SR and (b) GR measurements (not to scale). In both panels, the main view is from the side in the plane parallel to the radar beam, while the inset shows a plan view. Red lines indicate the radar beam and black circles indicate the location of the bin. Crosses in (a) mark the intersection of the SR beam with the Earth ellipsoid and the blue arrow shows the direction of travel of the satellite. The thin dotted black line in (b) indicates the height of the surface relative to the Earth ellipsoid (i.e., surface orography).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Diagrams showing the geometry of (a) SR and (b) GR measurements (not to scale). In both panels, the main view is from the side in the plane parallel to the radar beam, while the inset shows a plan view. Red lines indicate the radar beam and black circles indicate the location of the bin. Crosses in (a) mark the intersection of the SR beam with the Earth ellipsoid and the blue arrow shows the direction of travel of the satellite. The thin dotted black line in (b) indicates the height of the surface relative to the Earth ellipsoid (i.e., surface orography).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
Diagrams showing the geometry of (a) SR and (b) GR measurements (not to scale). In both panels, the main view is from the side in the plane parallel to the radar beam, while the inset shows a plan view. Red lines indicate the radar beam and black circles indicate the location of the bin. Crosses in (a) mark the intersection of the SR beam with the Earth ellipsoid and the blue arrow shows the direction of travel of the satellite. The thin dotted black line in (b) indicates the height of the surface relative to the Earth ellipsoid (i.e., surface orography).
Citation: Journal of Atmospheric and Oceanic Technology 35, 2; 10.1175/JTECH-D-17-0128.1
The next step is to identify the nearest GR volume scan in time. Each SR scan has a unique time stamp; however, since it takes less than a minute for the satellite to traverse the GR field of view, a single time may be reasonably applied to all scans in the overpass. Specifically, we use the time corresponding to the closest point of approach to the GR 
At this point we have the coordinates of every SR and GR bin in a common reference frame. We now compute the median brightband height and width and apply a Ku-to-S-band frequency correction to the SR data as described in section 2b. The volume matching then proceeds by looping first over SR rays and then over GR elevation sweeps. SR rays are considered only if they (i) contain precipitation (
- Calculate the GR elevation angle of each SR bin [using (A6)] aswhere
Identify the SR bins that fall within the GR beam, that is, for which
- Average the values of
where
Linearly average the reflectivity values (in mm6 m−3) for which
Identify the GR bins that fall within the footprint of the SR beam; i.e., for which
Average the reflectivity values (in mm6 m−3) for which
For every SR overpass, a single file is produced containing data for all volume-matched samples. The variables stored for each sample are as follows:
Cartesian coordinates (
volume dimensions (
GR range (
averaged SR and GR reflectivities [
fraction of SR and GR bins above the respective minimum reflectivity thresholds (
precipitation-type index (
GR–SR time difference (
Note that the quality parameters listed in Table 3 are used at various stages of the algorithm to ensure that all matched samples are accurate. Specifically, SR scans are rejected if 
REFERENCES
Amitai, E., X. Llort, and D. Sempere-Torres, 2009: Comparison of TRMM radar rainfall estimates with NOAA Next-Generation QPE. J. Meteor. Soc. Japan, 87A, 109–118, https://doi.org/10.2151/jmsj.87A.109.
Anagnostou, E. N., C. A. Morales, and T. Dinku, 2001: The use of TRMM precipitation radar observations in determining ground radar calibration biases. J. Atmos. Oceanic Technol., 18, 616–628, https://doi.org/10.1175/1520-0426(2001)018<0616:TUOTPR>2.0.CO;2.
Atlas, D., 2002: Radar calibration: Some simple approaches. Bull. Amer. Meteor. Soc., 83, 1313–1316, https://doi.org/10.1175/1520-0477(2002)083<1313:RCSSA>2.3.CO;2.
Awaka, J., T. Iguchi, and K. Okamoto, 2007: Rain type classification algorithm. Measuring Precipitation from Space: EURAINSAT and the Future, V. Levizzani, P. Bauer, and F. J. Turk, Eds., Advances in Global Change Research, Vol. 28, Springer, 213–224.
Awaka, J., T. Iguchi, and K. Okamoto, 2009: TRMM PR standard algorithm 2A23 and its performance on bright band detection. J. Meteor. Soc. Japan, 87A, 31–52, https://doi.org/10.2151/jmsj.87A.31.
Bolen, S. M., and V. Chandrasekar, 2003: Methodology for aligning and comparing spaceborne radar and ground-based radar observations. J. Atmos. Oceanic Technol., 20, 647–659, https://doi.org/10.1175/1520-0426(2003)20<647:MFAACS>2.0.CO;2.
Cao, Q., Y. Hong, Y. Qi, Y. Wen, J. Zhang, J. J. Gourley, and L. Liao, 2013: Empirical conversion of the vertical profile of reflectivity from Ku-band to S-band frequency. J. Geophys. Res. Atmos., 118, 1814–1825, https://doi.org/10.1002/jgrd.50138.
Chandrasekar, V., L. Baldini, N. Bharadwaj, and P. L. Smith, 2015: Calibration procedures for Global Precipitation-Measurement ground-validation radars. Radio Sci. Bull., 355, 45–73.
Chen, S., and Coauthors, 2013: Evaluation of spatial errors of precipitation rates and types from TRMM spaceborne radar over the southern CONUS. J. Hydrometeor., 14, 1884–1896, https://doi.org/10.1175/JHM-D-13-027.1.
Crisologo, I., R. A. Warren, K. Muehlbauer, and M. Heistermann, 2017: Using data quality to improve comparison between GPM measurements and ground radars. 38th Conf. on Radar Meteorology, Chicago, IL, Amer. Meteor. Soc., 23B.4, https://ams.confex.com/ams/38RADAR/meetingapp.cgi/Paper/321038.
Gourley, J. J., B. Kaney, and R. A. Maddox, 2003: Evaluating the calibration of radars: A software approach. 31st Conf. on Radar Meteorology, Seattle, WA, Amer. Meteor. Soc., P3C.1, https://ams.confex.com/ams/32BC31R5C/techprogram/paper_64171.htm.
Heistermann, M., S. Jacobi, and T. Pfaff, 2013: An open source library for processing weather radar data (wradlib). Hydrol. Earth Syst. Sci., 17, 863–871, https://doi.org/10.5194/hess-17-863-2013.
Hintze, J. L., and R. D. Nelson, 1998: Violin plots: A box plot-density trace synergism. Amer. Stat., 52, 181–184, https://doi.org/10.1080/00031305.1998.10480559.
Hitschfeld, W., and J. Bordan, 1954: Errors inherent in the radar measurement of rainfall at attenuating wavelengths. J. Meteor., 11, 58–67, https://doi.org/10.1175/1520-0469(1954)011<0058:EIITRM>2.0.CO;2.
Hou, A. Y., and Coauthors, 2014: The Global Precipitation Measurement Mission. Bull. Amer. Meteor. Soc., 95, 701–722, https://doi.org/10.1175/BAMS-D-13-00164.1.
Iguchi, T., S. Seto, R. Meneghini, N. Yoshida, J. Awaka, M. Le, V. Chandrasekar, and T. Kubota, 2017: GPM/DPR Level-2. Japan Aerospace Exploration Agency Algorithm Theoretical Basis Doc., 81 pp., http://www.eorc.jaxa.jp/GPM/doc/algorithm/ATBD_DPR_201708_whole_1.pdf.
Jones, D. A., W. Wang, and R. Fawcett, 2009: High-quality spatial climate data-sets for Australia. Aust. Meteor. Oceanogr. J., 58, 233–248, https://doi.org/10.22499/2.5804.003.
Kawanishi, T., and Coauthors, 2000: TRMM Precipitation Radar. Adv. Space Res., 25, 969–972, https://doi.org/10.1016/S0273-1177(99)00932-1.
Kim, J.-H., M.-L. Ou, J.-D. Park, K. R. Morris, M. R. Schwaller, and D. B. Wolff, 2014: Global Precipitation Measurement (GPM) ground validation (GV) prototype in the Korean Peninsula. J. Atmos. Oceanic Technol., 31, 1902–1921, https://doi.org/10.1175/JTECH-D-13-00193.1.
Kirstetter, P.-E., Y. Hong, J. Gourley, M. Schwaller, W. Petersen, and J. Zhang, 2013: Comparison of TRMM 2A25 products, version 6 and version 7, with NOAA/NSSL ground radar–based national mosaic QPE. J. Hydrometeor., 14, 661–669, https://doi.org/10.1175/JHM-D-12-030.1.
Köck, K., T. Leltne, W. Randeu, M. Divjak, and K.-J. Schrelber, 2000: OPERA: Operational programme for the exchange of weather radar information. First results and outlook for the future. Phys. Chem. Earth, 25, 1147–1151, https://doi.org/10.1016/S1464-1909(00)00169-6.
Liao, L., and R. Meneghini, 2009a: Changes in the TRMM version-5 and version-6 precipitation radar products due to orbit boost. J. Meteor. Soc. Japan, 87A, 93–107, https://doi.org/10.2151/jmsj.87A.93.
Liao, L., and R. Meneghini, 2009b: Validation of TRMM precipitation radar through comparison of its multiyear measurements with ground-based radar. J. Appl. Meteor. Climatol., 48, 804–817, https://doi.org/10.1175/2008JAMC1974.1.
Liao, L., R. Meneghini, and T. Iguchi, 2001: Comparisons of rain rate and reflectivity factor derived from the TRMM precipitation radar and the WSR-88D over the Melbourne, Florida, site. J. Atmos. Oceanic Technol., 18, 1959–1974, https://doi.org/10.1175/1520-0426(2001)018<1959:CORRAR>2.0.CO;2.
Louf, V., A. Protat, C. Jakob, S. Rauniyar, and R. A. Warren, 2017: The relative calibration adjustment technique for calibrating Australian operational radars in near real-time. 38th Conf. on Radar Meteorology, Chicago, IL, Amer. Meteor. Soc., 23B.3, https://ams.confex.com/ams/38RADAR/webprogram/Paper320618.html.
Meneghini, R., T. Iguchi, T. Kozu, L. Liao, K. Okamoto, J. A. Jones, and J. Kwiatkowski, 2000: Use of the surface reference technique for path attenuation estimates from the TRMM precipitation radar. J. Appl. Meteor., 39, 2053–2070, https://doi.org/10.1175/1520-0450(2001)040<2053:UOTSRT>2.0.CO;2.
Meneghini, R., J. Jones, T. Iguchi, K. Okamoto, and J. Kwiatkowski, 2004: A hybrid surface reference technique and its application to the TRMM precipitation radar. J. Atmos. Oceanic Technol., 21, 1645–1658, https://doi.org/10.1175/JTECH1664.1.
Michelson, D. B., R. Lewandowski, M. Szewczykowski, H. Beekhuis, and G. Haase, 2014: EUMETNET OPERA weather radar information model for implementation with the HDF5 file format, version 2.2. EUMETNET OPERA Tech. Rep., 38 pp., http://eumetnet.eu/wp-content/uploads/2017/01/OPERA_hdf_description_2014.pdf.
Morris, K. R., and M. R. Schwaller, 2009: An enhanced Global Precipitation Measurement (GPM) validation network prototype. 34th Conf. on Radar Meteorology, Williamsburg, VA, Amer. Meteor. Soc., P7.3, https://ams.confex.com/ams/34Radar/techprogram/paper_155254.htm.
Morris, K. R., and M. R. Schwaller, 2011: Sensitivity of spaceborne and ground radar comparison results to data analysis methods and constraints. 35th Conf. on Radar Meteorology, Pittsburgh, PA, Amer. Meteor. Soc., 68, https://ams.confex.com/ams/35Radar/webprogram/Paper191729.html.
NASA, 2014: Tropical Rainfall Measuring Mission precipitation processing system: File specification 2A23, version 7. NASA GSFC Doc., 21 pp., https://storm-pps.gsfc.nasa.gov/storm/data/docs/filespec.TRMM.V7.2A23.pdf.
NASA, 2015: Tropical Rainfall Measuring Mission precipitation processing system: File specification 2A25, version 7. NASA GSFC Doc., 24 pp., https://storm-pps.gsfc.nasa.gov/storm/data/docs/filespec.TRMM.V7.2A25.pdf.
NASA, 2016: Global Precipitation Measurement precipitation processing system: File specification 2AKu, preliminary version. NASA Earth Observing System Data and Information System Doc., 43 pp., https://storm.pps.eosdis.nasa.gov/storm/data/docs/filespec.GPM.V1.2AKu.pdf.
NASA, 2017: Release notes for the PR Level 1 products. NASA GSFC Doc., 1 pp., https://pps.gsfc.nasa.gov/Documents/ReleaseNote_PU1_productV05.pdf.
Park, S., S.-H. Jung, and G. Lee, 2015: Cross validation of TRMM PR reflectivity profiles using 3D reflectivity composite from the ground-based radar network over the Korean Peninsula. J. Hydrometeor., 16, 668–687, https://doi.org/10.1175/JHM-D-14-0092.1.
Protat, A., D. Bouniol, E. O. Connor, H. Klein Baltink, J. Verlinde, and K. Widener, 2011: CloudSat as a global radar calibrator. J. Atmos. Oceanic Technol., 28, 445–452, https://doi.org/10.1175/2010JTECHA1443.1.
Rasmussen, K. L., S. L. Choi, M. D. Zuluaga, and R. A. Houze, 2013: TRMM precipitation bias in extreme storms in South America. Geophys. Res. Lett., 40, 3457–3461, https://doi.org/10.1002/grl.50651.
Rennie, S. J., 2012: Doppler weather radar in Australia. Centre for Australian Weather and Climate Research Tech. Rep. 055, 42 pp., http://www.cawcr.gov.au/technical-reports/CTR_055.pdf.
Schwaller, M. R., and K. R. Morris, 2011: A ground validation network for the Global Precipitation Measurement mission. J. Atmos. Oceanic Technol., 28, 301–319, https://doi.org/10.1175/2010JTECHA1403.1.
Silberstein, D. S., D. B. Wolff, D. A. Marks, D. Atlas, and J. L. Pippitt, 2008: Ground clutter as a monitor of radar stability at Kwajalein, RMI. J. Atmos. Oceanic Technol., 25, 2037–2045, https://doi.org/10.1175/2008JTECHA1063.1.
Simpson, J., C. Kummerow, W.-K. Tao, and R. F. Adler, 1996: On the Tropical Rainfall Measuring Mission (TRMM). Meteor. Atmos. Phys., 60, 19–36, https://doi.org/10.1007/BF01029783.
Takahashi, N., H. Kuroiwa, and T. Kawanishi, 2003: Four-year result of external calibration for Precipitation Radar (PR) of the Tropical Rainfall Measuring Mission (TRMM) satellite. IEEE Trans. Geosci. Remote Sens., 41, 2398–2403, https://doi.org/10.1109/TGRS.2003.817180.
Toyoshima, K., H. Masunaga, and F. A. Furuzawa, 2015: Early evaluation of Ku- and Ka-band sensitivities for the Global Precipitation Measurement (GPM) Dual-Frequency Precipitation Radar (DPR). SOLA, 11, 14–17, https://doi.org/10.2151/sola.2015-004.
Villarini, G., and W. F. Krajewski, 2010: Review of the different sources of uncertainty in single polarization radar-based estimates of rainfall. Surv. Geophys., 31, 107–129, https://doi.org/10.1007/s10712-009-9079-x.
Wang, J., and D. B. Wolff, 2009: Comparisons of reflectivities from the TRMM precipitation radar and ground-based radars. J. Atmos. Oceanic Technol., 26, 857–875, https://doi.org/10.1175/2008JTECHA1175.1.
Wolff, D. B., and B. L. Fisher, 2008: Comparisons of instantaneous TRMM ground validation and satellite rain-rate estimates at different spatial scales. J. Appl. Meteor. Climatol., 47, 2215–2237, https://doi.org/10.1175/2008JAMC1875.1.
Wolff, D. B., D. A. Marks, and W. A. Petersen, 2015: General application of the relative calibration adjustment (RCA) technique for monitoring and correcting radar reflectivity calibration. J. Atmos. Oceanic Technol., 32, 496–506, https://doi.org/10.1175/JTECH-D-13-00185.1.
Technically, the term reflectivity refers to the quantity 
The bright band is a layer of locally enhanced reflectivities around the melting level that occurs as a result of changes in the scattering properties of snow as it melts.
Other significance levels (10% and 1%) were tested with almost no change in the results.
