a quality control algorithm for the osaka phased array

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48 SOLA, 2015, Vol. 11, 48−52, doi:10.2151/sola.2015-011 Abstract This study develops and tests a quality control (QC) algorithm for reflectivity from the single polarization phased array weather radar (PAWR) in Osaka, with particular focus on clutter detection, in preparation for radar data assimilation into a high resolution numerical model. The QC algorithm employs a Bayesian classi- fication that combines the information from different parameters based on reflectivity and radial velocity. To take advantage of PAWR’s unique high temporal and vertical resolutions, a new parameter based on the temporal variability of reflectivity is included. In addition, clutter probability estimations from pre- vious volume scans are also included. The newly developed QC algorithm performs properly in two events characterized by heavy convective precipitation and stratiform precipitation. (Citation: Ruiz, J. J., T. Miyoshi, S. Satoh, and T. Ushio, 2015: A quality control algorithm for the Osaka phased array weather radar. SOLA, 11, 48−52, doi:10.2151/sola.2015-011.) 1. Introduction In recent years a large effort has been devoted to develop more effective prediction systems for convective-scale severe weather and to provide timely and precise warnings for local severe weath- er events. Weather radars provide valuable meteorological obser- vations with a high temporal and spatial resolution. The phased array radar is the next generation of weather radars and is capable of providing particularly higher temporal and vertical resolutions. These high-resolution data are extremely valuable for monitoring severe weather more precisely, and may also be useful for very short range numerical weather prediction (NWP). Previous studies described quality control (QC) algorithms for radar reflectivity for different purposes such as rainfall estimation and data assimila- tion. These studies focused on the problems that affect the quality of the radar data: blocking by the terrain (Bech et al. 2003), non-meteorological echoes produced by non-weather related targets (Lackshamanan et al. 2007; Steiner and Smith 2002; Li et al. 2013; Hubbert et al. 2009 among others), second trip echoes, and attenuation (Delrieu et al. 1999a, 1999b). However, the previous studies usually assumed conventional parabolic-antenna radars. Based on the previous studies, this study implements and tests a QC algorithm with particular focus on clutter detection for single polarization phased array radars. These radars have stronger side lobes and broader beams which can produce more ground clutter contamination than in conventional parabolic antenna radars. A measure of the temporal variability of reflectivity is used in the QC algorithm to take advantage of the high temporal frequency and high vertical resolution of the phased array radar data. This QC algorithm aims mainly to generate radar reflectivity observations suitable to be assimilated into a high-resolution NWP model with an O(100)-m grid spacing, although in principle, the QC algorithm would be useful for other purposes like precipita- tion estimation. Section 2 describes the data and QC algorithm. Section 3 presents the results. Finally, Section 4 describes the conclusions and planned extensions of the QC algorithm. 2. Data and study method 2.1 Radar data In this study data collected by the first Japanese phased array weather radar (PAWR), installed at the Osaka University, Suita Campus in 2012, is used (Ushio et al. 2014; Yoshikawa et al. 2013). The PAWR is an X-band (3.1 cm wavelength) one-dimen- sional phased array radar which can perform a full volume scan of reflectivity and Doppler velocity at a range resolution of 100 m in 30 seconds with a maximum range of 60 km and with about 100 vertical scan angles, providing a unique dataset with a high temporal and spatial resolution. PAWR radar uses a conventional Fourier digital beam forming technique to scan in the elevation range and a mechanically rotating antenna for the azimuthal scans (Ushio et al. 2014). De-aliased radial velocities in the range (+/− 50 m s −1 ) are obtained through a dual pulse repetition frequency approach. For the development and evaluation of the QC algorithm data from two events are used: a convective heavy-rainfall event on 13 July 2013 that caused a disaster in Kyoto, and a stratiform precip- itation event on 14 August 2012. The temporal scan frequency is 30 seconds for both cases while the number of vertical elevations are 98 (Fig. 1a) and 77 on the convective and stratiform cases, respectively. 2.2 Quality control algorithm Before applying the ground clutter estimation filter, blocking by the topography is estimated using the approach of Bech et al. (2003). Here, all gates that are blocked by more than 60% are rejected and flagged as missing data. The radar beam height is A Quality Control Algorithm for the Osaka Phased Array Weather Radar Juan J. Ruiz 1, 2, 7 , Takemasa Miyoshi 2, 3, 4, 7 , Shinsuke Satoh 5, 7 , and Tomoo Ushio 6, 7 1 University of Buenos Aires, Buenos Aires, Argentina 2 RIKEN Advanced Institute for Computational Science, Kobe, Japan 3 University of Maryland, USA 4 Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan 5 National Institute of Information and Communications Technology, Koganei, Tokyo, Japan 6 Osaka University, Suita, Osaka, Japan 7 CREST, Japan Science and Technology Agency, Kawaguchi, Saitama, Japan Corresponding author: Takemasa Miyoshi, RIKEN Advanced Institute for Computational Science, 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Japan. E-mail: [email protected]. ©2015, the Meteoro- logical Society of Japan. Fig. 1. (a) Vertical scan strategy of the PAWR on 13 July 2013, black lines indicating the elevation angles, (b) ASTER-GDEM topography horizontal- ly interpolated to the lowest elevation radar grid (m).

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Page 1: A Quality Control Algorithm for the Osaka Phased Array

48 SOLA, 2015, Vol. 11, 48−52, doi:10.2151/sola.2015-011

AbstractThis study develops and tests a quality control (QC) algorithm

for reflectivity from the single polarization phased array weather radar (PAWR) in Osaka, with particular focus on clutter detection, in preparation for radar data assimilation into a high resolution numerical model. The QC algorithm employs a Bayesian classi-fication that combines the information from different parameters based on reflectivity and radial velocity. To take advantage of PAWR’s unique high temporal and vertical resolutions, a new parameter based on the temporal variability of reflectivity is included. In addition, clutter probability estimations from pre-vious volume scans are also included. The newly developed QC algorithm performs properly in two events characterized by heavy convective precipitation and stratiform precipitation.

(Citation: Ruiz, J. J., T. Miyoshi, S. Satoh, and T. Ushio, 2015: A quality control algorithm for the Osaka phased array weather radar. SOLA, 11, 48−52, doi:10.2151/sola.2015-011.)

1. Introduction

In recent years a large effort has been devoted to develop more effective prediction systems for convective-scale severe weather and to provide timely and precise warnings for local severe weath-er events. Weather radars provide valuable meteorological obser-vations with a high temporal and spatial resolution. The phased array radar is the next generation of weather radars and is capable of providing particularly higher temporal and vertical resolutions. These high-resolution data are extremely valuable for monitoring severe weather more precisely, and may also be useful for very short range numerical weather prediction (NWP). Previous studies described quality control (QC) algorithms for radar reflectivity for different purposes such as rainfall estimation and data assimila-tion. These studies focused on the problems that affect the quality of the radar data: blocking by the terrain (Bech et al. 2003), non-meteorological echoes produced by non-weather related targets (Lackshamanan et al. 2007; Steiner and Smith 2002; Li et al. 2013; Hubbert et al. 2009 among others), second trip echoes, and attenuation (Delrieu et al. 1999a, 1999b). However, the previous studies usually assumed conventional parabolic-antenna radars.

Based on the previous studies, this study implements and tests a QC algorithm with particular focus on clutter detection for single polarization phased array radars. These radars have stronger side lobes and broader beams which can produce more ground clutter contamination than in conventional parabolic antenna radars. A measure of the temporal variability of reflectivity is used in the QC algorithm to take advantage of the high temporal frequency and high vertical resolution of the phased array radar data.

This QC algorithm aims mainly to generate radar reflectivity observations suitable to be assimilated into a high-resolution NWP model with an O(100)-m grid spacing, although in principle, the QC algorithm would be useful for other purposes like precipita-tion estimation. Section 2 describes the data and QC algorithm. Section 3 presents the results. Finally, Section 4 describes the conclusions and planned extensions of the QC algorithm.

2. Data and study method

2.1 Radar dataIn this study data collected by the first Japanese phased array

weather radar (PAWR), installed at the Osaka University, Suita Campus in 2012, is used (Ushio et al. 2014; Yoshikawa et al. 2013). The PAWR is an X-band (3.1 cm wavelength) one-dimen-sional phased array radar which can perform a full volume scan of reflectivity and Doppler velocity at a range resolution of 100 m in 30 seconds with a maximum range of 60 km and with about 100 vertical scan angles, providing a unique dataset with a high temporal and spatial resolution. PAWR radar uses a conventional Fourier digital beam forming technique to scan in the elevation range and a mechanically rotating antenna for the azimuthal scans (Ushio et al. 2014). De-aliased radial velocities in the range (+/− 50 m s−1) are obtained through a dual pulse repetition frequency approach.

For the development and evaluation of the QC algorithm data from two events are used: a convective heavy-rainfall event on 13 July 2013 that caused a disaster in Kyoto, and a stratiform precip-itation event on 14 August 2012. The temporal scan frequency is 30 seconds for both cases while the number of vertical elevations are 98 (Fig. 1a) and 77 on the convective and stratiform cases, respectively.

2.2 Quality control algorithmBefore applying the ground clutter estimation filter, blocking

by the topography is estimated using the approach of Bech et al. (2003). Here, all gates that are blocked by more than 60% are rejected and flagged as missing data. The radar beam height is

A Quality Control Algorithm for the Osaka Phased Array Weather Radar

Juan J. Ruiz1, 2, 7, Takemasa Miyoshi2, 3, 4, 7, Shinsuke Satoh5, 7, and Tomoo Ushio6, 7

1University of Buenos Aires, Buenos Aires, Argentina2RIKEN Advanced Institute for Computational Science, Kobe, Japan

3University of Maryland, USA4Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

5National Institute of Information and Communications Technology, Koganei, Tokyo, Japan6Osaka University, Suita, Osaka, Japan

7CREST, Japan Science and Technology Agency, Kawaguchi, Saitama, Japan

Corresponding author: Takemasa Miyoshi, RIKEN Advanced Institute for Computational Science, 7-1-26 Minatojima-minami-machi, Chuo-ku, Kobe, Japan. E-mail: [email protected]. ©2015, the Meteoro-logical Society of Japan.

Fig. 1. (a) Vertical scan strategy of the PAWR on 13 July 2013, black lines indicating the elevation angles, (b) ASTER-GDEM topography horizontal-ly interpolated to the lowest elevation radar grid (m).

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49Ruiz et al., Quality Control for the Osaka Phased Array Weather Radar

eters, P(Xk | clutter) is the conditional probability of the k-th parameter given that a pixel is clutter, and P(clutter) is the a priori probability of a pixel being clutter. The conditional probabilities in Eq. (2) can be obtained from the conditional histograms as pre-viously discussed, and the denominator is a scaling factor. The a priori clutter probability is usually considered to be 0.5, but other choices are also possible, such as the probability obtained by the QC algorithm from the previous radar scan. This way, we could take advantage of the high frequency PAWR scanning capability.

Within the framework of the Bayesian classification, using dif-ferent parameters in different regions of the volume is straightfor-ward. In this study, the vertical gradient of reflectivity VGRADZ is used only within 3 km above the terrain because this parameter is designed to detect rapid vertical decrease of reflectivity that occurs near the ground in association with ground clutter.

After the application of the Bayesian classification, another filter is applied to the data to increase the probability of detec-tion of shallow and low echoes associated with ground clutter. The echo top and echo depth corresponding to each pixel are computed. Echo top is computed as the maximum height over the surface, of a particular echo layer, and echo depth as the difference between the maximum height and the minimum height associated with a particular echo layer using a 5-dBZ threshold. Both parameters are computed in a cylindrical coordinate grid and interpolated back to the original spherical coordinate grid using the nearest neighbor interpolation and then averaged over a 5×11×1 box. PAWR’s high vertical resolution allows for a detailed description of the vertical extent of the echo layers even at ranges that are close to the radar location. Pixels with echo tops below 3000 meters and echo depths under 2000 meters are considered as clutter. These values are determined based on the subjective analysis of the conditional histograms of these parameters. The echo depth is used to complement the echo top filter to capture ground clutter that can occur at relatively high altitudes due to beam anomalous propagation.

3. Results

For the validation of the algorithm, the QC algorithm has been applied to radar data from 1400 to 1700 JST 13 July 2013 (charac-terized by heavy convective precipitation) and to radar data from 0711 to 0811 JST 14 August 2012 (characterized by stratiform precipitation), with a total number of 480 volumes.

First, an example of the performance of the algorithm for clut-

estimated by assuming standard refracting conditions (Doviak and Zrnic 1993). The ASTER-GDEM (Advanced Space Thermal Emission and Reflection Radiometer global digital elevation model) terrain data available at http://gdem.ersdac.jspacesystems.or.jp is used to estimate the height of the beam over the terrain (Fig. 1b).

A speckle filter proposed by Zhang et al. (2004) is also applied as part of the QC algorithm. This evaluates the number of pixels exceeding 0 dBZ in a box with a size of 5×11×1 pixels in the azimuth, radial and elevation dimensions. A pixel is detected as speckle if less than 30% of the pixels in the box are above 0 dBZ.

After applying the speckle filter a naïve Bayesian classifica-tion approach (Rico-Ramirez and Cluckie 2008; Li et al 2013) is used to detect the ground clutter based on 4 parameters. A brief description of the parameters used is given below:• Texture of the reflectivity (TEXT, Hubbert et al. 2009): This parameter measures the spatial variability of the reflectivity field.

• Texture of the reflectivity correlation with time (TRCT): The correlation between reflectivity and time is computed over a 5 minute period (10 volume scans in case of the slowest 30-second azimuthal rotation of the Osaka PAWR), and its texture over the neighboring 5×11×1 domain is obtained for each pixel. This parameter shows the spatial coherence of the temporal trend of reflectivity. Clutter exhibits a relatively large value of TRCT (low coherence), while meteorological echoes are characterized by small values of TRCT (high coherence).

• Radial velocity average (RVA): The temporal average of radial velocity over a 5-minute period (10 volume scans in case of 30-second azimuthal rotation scanning mode).

• Vertical component of the reflectivity gradient (VGRADZ, Cho et al. 2006): The vertical component of the reflectivity gradient computed over a height increment of 500 m. The local minimum of this quantity computed over a 5×11×1 local neighborhood of each pixel is used.

To evaluate the skill of each individual parameter in distin-guishing between clutter and meteorological echoes, a training sample containing both types of echoes is created as follows. A clutter mask obtained from a clear sky sample is applied to obtain a training sample for the QC algorithm from 0800 to 1300 JST 13 July 2013. Echoes with the echo tops lower (higher) than 3000 m at locations where the clutter probability is 100% (0%) based on the clutter mask are considered as clutter (meteorological) echoes.

Based on this classification, the different parameters were computed for the clutter echoes and for the meteorological echoes to obtain the conditional histogram of each particular parameter for clutter and meteorological echoes. Histograms with 32 bins for each parameter have been constructed. Then, the difference of the histograms of each parameter for clutter and meteorological echoes is defined as a discrimination index I, such that

IM i P c i

M ii

N

i

N=−

=

=

∑∑

( )( ( | ) . )

. ( ).

0 5

0 25

21

1

(1)

Here, P(c | i ) is the conditional probability of a pixel being clutter given that the parameter value falls within the i-th bin, estimated from the conditional histograms. M (i ) is the total number of times that the parameter value falls within each bin, and N is the total number of bins. The index I = 1 corresponds to the perfect discrimination between clutter and weather echoes, while I = 0 indicates no skill. Figure 2 shows the conditional histograms for the 4 parameters used in the QC algorithm and their correspondent discrimination index.

The Bayesian classification algorithms compute the probabil-ity of a particular pixel being a clutter based on the value of the parameters previously discussed using the following formula:

P clutter X XP clutter P X clutter

P X XKkk

K

K

( | , , )( ) ( | )

( , , )11

1

= =∏ (2)

Where Xk is the k-th parameter, K is the total number of param-

Fig. 2. Conditional histogram for the parameters (a) TEXT, (b) RVA, (c) TRCT, and (d) VGRADZ. The parenthetical numbers on top of each panel indicate the discrimination index values.

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50 SOLA, 2015, Vol. 11, 48−52, doi:10.2151/sola.2015-011

ter detection on the heavy precipitation event is presented. Figures 3a, b show the distributions of the original and quality controlled reflectivity at the second elevation angle. Most of clutter has been eliminated by the QC algorithm, while precipitation echoes are preserved. Precipitation echoes can be recognized in this case with the 30 dBZ reflectivity contour at an elevation angle of 5.3 degrees displayed in Fig. 3b. Figures 3c, d show vertical cross sections at 81 degrees azimuth; this particular azimuth includes a mixture of precipitation echoes and clutter. The QC algorithm detects ground clutter between 0 and 20 km from the radar, but a part of the clutter associated with the mountains around 30 km is not well detected. Meteorological echoes are almost unaffected by the clutter detection algorithm.

Figures 4a, b, c, d show the distributions of the clutter prob-ability computed using each individual parameter as the only classifier. We can see that the RVA, TEXT, TRCT and VGRADZ parameters show a high spatial coherence distinguishing between meteorological echoes and clutter. The TRCT parameter identifies clutter near the ground but it also detects areas with low spatial coherence in the reflectivity trend near the cloud edges, particu-larly away from the radar. The TEXT parameter produces high clutter probabilities not only associated with ground clutter but sometimes near strong reflectivity cores such as the ones near the cell located at 20 km from the radar. This is a known limitation of TEXT discussed by Zhang et al. (2004). The TRCT parameter produces better results in this area indicating low clutter probabil-ity.

Figure 5 shows the case dominated by stratiform precipitation, and here, ground clutter is mixed with precipitation. Most low level clutter is detected in this case although the algorithm fails, for example, to detect clutter contaminated pixels near 34.6°N, 135.4°E. Vertical cross sections (Figs. 5c, d) show a good per-formance of the algorithm to detect ground clutter mixed with precipitation echoes.

Figures 6a, b, c, d show clutter probability using each indi-

vidual parameter as the only classifier for the same cross sections presented in Figs. 5c, d. The TRCT parameter shows a good per-formance in this case, too, detecting high clutter probabilities in an area close to the one detected by the RVA parameter and similar to the area frequently affected by clutter as indicated by the clutter mask (Fig. 6e). Clutter probabilities in the area dominated by weather echoes associated to the TRCT parameter are higher in this stratiform case than in the previous convective case. This might be because reflectivity trends of stratiform precipitation tends to be lower due to the spatial homogeneity of the precipita-

Fig. 5. Similar to Fig. 3, but for the first elevation angle (a and b), the 180° azimuth (c and d) and corresponding to 0721 JST, 14 August 2012.

Fig. 3. PPI display of the (a) original and (b) clutter removed reflectivity (dBz) corresponding to the second elevation angle. The black rings indi-cate the height of the radar beam with a 1000 m interval. In (a) the con-tours indicate probability of clutter greater than 10% as derived from the clear-air clutter mask. In (b), the contours indicate the 20 dBz reflectivity at the 7th elevation angle. RHI display of the (c) original and (d) clutter re-moved reflectivity for the 81° azimuth. The black line indicates the height of the topography. In (b) and (d) dark grey shades indicate pixels blocked by the topography, and light grey shades indicate pixels identified as clut-ter by the QC algorithm. All panels correspond to 1520 JST, 13 July 2013.

Fig. 4. RHI display for the 81° azimuth of clutter probability obtained from each individual parameter (a) RVA, (b) TRCT, (c) TEXT, (d) VGRADZ, (e) clutter probability obtained with the Bayesian classification algorithm, and (f) mean reflectivity in the clear-air clutter mask at 1520 JST, 13 July 2013. The 99% probability of having ground clutter is also indicated by black contours in (f). The black lines displayed in all panels indicate the height of the topography. Dark grey shades indicate pixels blocked by the topography.

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51Ruiz et al., Quality Control for the Osaka Phased Array Weather Radar

tion field, so that the reflectivity trend may be more vulnerable to noise even in weather areas. TEXT performs worse than TRCT in this example, failing to detect low level clutter between 20 and 30 km from the radar.

A statistical verification of the QC algorithm has also been performed. A human expert classification of the echoes has been performed to construct a verification dataset. In both cases the ver-ification dataset is consistent on the identification of two different regions: one dominated by ground clutter and the other dominated by meteorological echoes.

The objective verification has been performed using 5 versions of the QC algorithm:• NOPRIOR: The Bayesian classification is performed by assum-ing a 0.5 a priori probability of clutter for each pixel. The four parameters (RVA, TEXT, TRCT and VGRADZ) are used. No echo top and echo depth filter is applied in this case.

• NOTRCT: Similar to NOPRIOR, but TRCT is not used. This aims to investigate the impact of the TRCT parameter.

• NOTEXT: Similar to NOPRIOR, but TEXT is not used.• PRIOR: Similar to NOPRIOR, but the Bayesian classification is performed using the clutter probability computed in the previous classification as an a priori probability.

• ETOP: Similar to NOPRIOR, but the echo top and echo depth filters are used.

Table 1 shows the probability of detection (POD), false alarm ratio (FAR), critical success index (CSI) and equitable threat score (ETS) for the clutter detection obtained with the different

experiments and for the two verification periods. The results show that the QC algorithm is performing generally well and that verification scores are comparable with the previous studies (Cho et al. 2006; Lakshamanan 2007; Li et al. 2013). Not surprisingly, the QC algorithm is worse when the clutter and precipitation are present simultaneously as in the case dominated by stratiform precipitation. In Table 1, pixels with clutter probability over 0.5 has been classified as clutter. All the scores are sensitive to this threshold. For instance, for NOPRIOR experiment, POD ranges from 0.89 to 0.97 when the threshold goes from 0.1 to 0.9, while CSI reaches a maximum value of 0.94 when the threshold is 0.7 and a minimum of 0.89 for a threshold of 0.1.

Comparing NOTRCT and NOPRIOR suggests that the TRCT parameter reduces FAR. Moreover, NOTEXT shows better results than NOTRCT in both POD and FAR, indicating that TRCT was superior to TEXT in these cases. This coincides with the behavior observed in the examples presented in Figs. 4, 6.

PRIOR uses the clutter probability obtained in the previous scan as an a priori probability for the classification of the next volume and shows the results with lower FAR and larger POD for the convective case, but produces no significant impact in the stratiform case. This approach works as an adaptive clutter mask that might help smooth out random noise in the classification.

The inclusion of the echo top and echo depth filters produces an increase in POD for both cases but a significant increase in FAR, too. The increase in FAR produces a degradation of CSI and ETS which are the lowest. This increase in FAR is produced by weather echoes corresponding to shallow elevated echo layers that are filtered by the echo depth filter.

The significance of the difference in the scores among the different experiments are tested using bootstrapping technique and 1000 realizations indicating that are all significant with a 95% confidence level.

4. Conclusion

A QC algorithm has been developed and applied to the Osaka PAWR data for convective and stratiform precipitation events. The proposed QC algorithm takes advantage of the frequent sampling capability of PAWR by relying on the TRCT parameter that is based on the temporal evolution of the signal. The QC algorithm was also capable to detect ground clutter combining TRCT with 3 additional parameters that describe the 3-dimensional structure and the temporally averaged radial velocity. The TRCT parameter presented in this study shows a promising performance in clutter detection. TRCT also shows low values in the areas of strong re-flectivity, while texture might have problems in separating strong echoes from clutter (Zhang et al. 2004).

The use of a prior based on the result of the QC algorithm for the previous volume was also evaluated. This approach also aims to take advantage of the frequent scanning of PAWR. It has been shown that using a prior, reduces the number of false alarms and increases POD.

Although these results are promising, these are representative of the performance of the QC algorithm for the detection of ground clutter. It would be an important subject of future research to evaluate the performance of the algorithm under other meteoro-logical situations (i.e. anomalous propagation, biological targets, sea clutter, etc.).

Many studies have shown that clutter detection can be im-proved by the use of parameters derived from the phase and power of the signal in the spectral domain (e.g. Li et al. 2013; Hubbert et al. 2009). The combination of TRCT with these parameters would be also an important subject of future research. A minimum mean square error (MMSE) beam forming technique which will help to mitigate clutter contamination is also under development (Yoshikawa et al. 2013) and will be implemented at Osaka PAWR in the near future.

Since the QC algorithm described in this paper is designed for a potential application in operational radar data assimilation, computational efficiency is an important issue. In its current

Fig. 6. Similar to Fig. 4, but for the 180° azimuth and corresponding to 0721 JST, 14 August 2012.

Table 1. Probability of detection (POD), false alarm ratio (FAR), critical success index (CSI) and equitable threat score (ETS) for the QC algorithm for each experiment for the two verification dates.

NOPRIOR NOTEXT NOTRCT PRIOR ETOP

13 July 2013PODFARCSIETS

0.940.3e-30.930.92

0.970.9e-30.930.92

0.940.2e-20.860.83

0.950.6e-40.950.94

1.00.3e-20.880.85

14 August 2012PODFARCSIETS

0.904e-30.900.77

0.935e-30.920.82

0.917e-30.910.79

0.904e-30.900.77

0.914e-20.890.75

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52 SOLA, 2015, Vol. 11, 48−52, doi:10.2151/sola.2015-011

implementation, the algorithm takes approximately 40 seconds to process a single scan in a computer with four 8-core Intel Xeon [email protected] CPUs (total 32 cores). This is slower than the 30-second volume scan, and we keep getting more data than processing. Further optimization to accelerate the computations is necessary for real-time application.

Acknowledgments

This study was supported by CREST, JST.

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Manuscript received 13 December 2014, accepted 23 March 2015SOLA: https://www. jstage. jst.go. jp/browse/sola/