Identifying second trip echoes

To develop a filtering method individual examples of second trip echoes were identified in the COPE data, such as the one shown in Figure 5.4 from 17 August, where widespread rainfall approached from the west, extending from the southern Irish coast to the English Channel as seen in the wider rainfall composite produced by the UKMO (Fig. 5.5). The example shows an alternating reflectivity signal between radials to the west and north west of the radar, as a result of the staggered PRF used and the presence of second trip echoes. Embedded within that region is a first trip rainfall echo, which is visible in both of the lowest elevations and in the UKMO composite.

Although the second trip echoes are clearly identifiable visibly it is beneficial to identify and remove the second trip echoes automatically during processing of the radar data. Dual polarisation was a potential solution to this filtering, provided the second trip echoes had a dual polarisation signature that was distinct from the rainfall signature presented in the preceding section. Figure 5.6 shows six of the available moments for the second trip echo example shown previously in Figure 5.4. On visual inspection the second trip echoes observed have a differential reflectivity comparable to rainfall (panel A), with the first trip echo not being distinct from the second trip echo. There is evidence of

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Figure 5.4: Example of second trip echoes identified in the COPE data, 2013-08-

17 08:16 UTC. A shows the 0.5◦elevation scan and B shows the 1.5◦scan, showing the discontinuity of echoes with increasing elevation. Both panels are 150 km squares centred

on the radar.

differential attenuation impacting the second trip echoes to the west of the radar, which is supported by the high differential phase shift values observed there (panel D), but again the differential phase shift values generally are not unusual for a rainfall event. The correlation coefficient (panel E) for the second trip echoes (≈0.95) is slightly lower than for the first trip (>0.97), which could be useful for filtering. This decrease is expected due to non uniform beam filling, which is more likely at the true range of the second trip echoes than close to the radar where the first trip echoes occur. However non uniform beam filling and therefore decreased CC is possible within the range of the radar (150 km) which may lead to difficulties with a filter based on CC. The specific differential phase shown in panel F is again within the bounds expected for a rainfall echo, with the only distinguishing feature being a strong negativeKDP along the radial boundary of the

first trip echo, caused by the superposition of elevated phase shifts closer to the radar than the first trip echo which then decrease where the first trip echo occurs. The panel also shows that the radar’s internal filtering is removing some but not all of the second trip echoes prior to KDP calculation. The internal filter thresholds the data, removing

segments which contain bad data, with the thresholds being a signal to noise ratio below 3, a CC below 0.8 and a standard deviation of phase shift below 12. Clearly a different filter will be required to adequately remove second trip echoes from the data. Finally panel B suggests the NCP/SQI may be a useful parameter for filtering second trip echoes, with the first trip echo to the north west having values expected for rainfall of 0.9 and

Figure 5.5: UK Nimrod radar composite provided by the UK Met Office for the COPE

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above, while the second trip echoes in that region blend into the background noise data and have a SQI of 0.4 and below.

Figure 5.6: Multiple radar moments for the example shown in Figure 5.4. A shows the ZDR, B the signal quality index (SQI), C the Doppler velocity, D the differential phase shift, E the correlation coefficient and F the specific differential phase. Again these are

150 km squares centred on the radar.

Extending the analysis to multiple radar scans using moment histograms supports these initial findings, with the histograms in Figure 5.7 indicating an overlap of both KDP

and ZDR between rain and second trip echoes, with CC having a broader distribution of moderately high values for second trip echoes (>0.8) than rainfall echoes, which are strongly distributed towards high values (>0.95). However, as 20% of the second trip echo observations have a CC greater than 0.98 there is still significant overlap between

Figure 5.7: Histograms of the dual polarisation radar moments, differential reflectiv-

ity, correlation coefficient and specific differential phase along with normalised coherent power during a rainfall event on the 17 August 2013, from 07:56:03 UTC to 08:56:03 UTC. The data was pre-classified to sample only range gates highly likely to be caused by second trip echoes returning from rainfall beyond the maximum unambiguous range

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the two distributions. In contrast the SQI observations have a very different distribution for second trip echoes than for first trip rainfall echoes, with over 70% of the observations below 0.3 and over 95% below 0.5, compared to the rainfall echoes where 71% of the observations were greater than 0.8 and 91% were greater than 0.5. Dixon and Hubbert (2012) suggested that SQI could be used to filter noise from radar observations, with these results indicating it can also be used to filter second trip echoes. Following the suggestion in that paper, the possibility of using SQI averaged over a window of range gates has been explored. Figure 5.8 shows the variation in SQI when it is taken from an individual range gate compared to taking the mean of the field over a three by three gate window and a five by five gate window, for both rainfall and second trip echoes.

Figure 5.8: Histograms of raw SQI and SQI averaged over a 3x3 and 5x5 gate moving

window centred on the observation range gate. The observations are from the same events shown in Figure 5.1 for precipitation and Figure 5.7 for second trip echoes.

Figure 5.8 shows that as the size of the averaging window increases the distribution of SQI values observed during second trip echoes narrows, while the rainfall distribution varies

only slightly. For second trip echoes the interquartile range is 0.17 when using the raw data, while this decreases to 0.04 when using a 5 gate averaging window, similarly 90% of the data in the later case is within a range of 0.12, while this increases to 0.42 for the raw data. In contrast the 90 percentile range of the rainfall observations only decreases from 0.63 to 0.56, and interquartile range doesn’t vary by more than 0.003 across the three averaging domains. The narrowing of the distribution of second trip echo observations when using an averaging window reduces the overlap between the two distributions, suggesting a better ability to discriminate between the two signals when using averaging windows. Another potentially viable discriminator between the two signals is to generate azimuthal difference fields which take advantage of the dual PRF of the radar producing the alternating signals already seen in the data.

To take advantage of these signals a difference function was developed to calculate the median difference between a radial and its adjacent radials, along a moving five range gate window which is shown in equations 5.2 and 5.2.

xi,j =MdP (5.2)

Where P is the following set andivaries in azimuth and j varies in range:

P ={|xi−1,r−xi,r|,|xi+1,r−xi,r|:xj−2 6r6xj+2} (5.3)

Using equation 5.2 the radial differences of the radar moments were computed for the rainfall and second trip echoes identified previously, with only reflectivity and phase shift showing a noticeable signal difference between the two echo types. Histograms for these two moments are shown in Figure 5.9.

Figure 5.9 shows a stronger signal difference between rainfall and second trip rainfall echoes when using median phase shift compared to median reflectivity, with only 14% overlap compared to 56% overlap. Given the two distributions are largely distinct there is potential for using median azimuthal phase shift difference for identifying and removing second trip echoes.

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Figure 5.9: Histograms of median azimuthal difference in raw reflectivity and phase

shift over a 5 gate window centred on the observation range gate. The observations are from the same events shown in Figure 5.1 for precipitation and Figure 5.7 for second

trip echoes.