## 1. Introduction

The National Center for Atmospheric Research’s (NCAR’s) S-band dual-polarization Doppler radar (S-Pol) was deployed as part of the joint Atmospheric Radiation Measurement (ARM) Program Madden–Julian oscillation (MJO) Investigation Experiment (AMIE)–Cooperative Indian Ocean Experiment on Intraseasonal Variability in the Year 2011 (CINDY2011)–Dynamics of the MJO (DYNAMO) campaigns, which will be collectively referred to as ACDC. For project overview details, refer to Yoneyama et al. (2013). One of the primary goals of ACDC was to thoroughly investigate the moisture structure of the pre-MJO environment in order to assess the likelihood that changes in the lower-tropospheric moisture structure could act as a trigger mechanism for MJO onset. One tool for investigating changes in moisture structure is Bragg scattering layer (BSL) analysis.

BSL analysis is a procedure to extract moisture-structure information from S-band radar by analyzing plan position indicator (PPI) reflectivity factor data (Davison et al. 2013b). Bragg scattering returns are clear-air echoes generated by index of refraction gradients at half the wavelength of the radar. The index of refraction gradients, in turn, is generated by temperature, pressure, and/or moisture gradients (e.g., Doviak and Zrnić 1984), with moisture being the most dominant term (e.g., Knight and Miller 1993; Melnikov et al. 2011, 2013; Davison et al. 2013b). This is especially true in tropical marine environments, where temperature variability is relatively small and moisture variability is high (Davison et al. 2013a). An example time–height diagram of BSL analysis conducted on PPI S-Pol data from ACDC is shown in Fig. 1a. Davison et al. (2013b) showed that BSL bases (blue dots) and tops (red dots) are most commonly associated with local relative humidity (RH) maxima and minima, respectively. Although quantitative RH values are not obtained through BSL analysis, the mesoscale-mean height and Eulerian evolution of moist and dry layers present in the lower troposphere are revealed, providing a structural framework for understanding and interpreting atmospheric behavior. Paired with other datasets such as rawinsonde profiles, a deeper, more accurate understanding of the lower troposphere can be readily achieved (Davison et al. 2013c).

During ACDC, thin, near-perfectly linear BSL edge detections that appear to be artificial were frequently detected in the BSL time–height diagrams (see Fig. 1a). They occur, seemingly regardless of elevation angle, at roughly the same range gate for a given radar volume and often persist for many hours. They are detected intermittently as a function of azimuth but are within roughly the same range gate spans (see Fig. 2). Examination of the original radar data reveals that these false BSL edge detections are produced by regions with radar reflectivity factor values comparable to those from Bragg scattering returns, but they are most likely generated by sidelobe echoes from clutter. Given their presence in PPI data at elevations where BSLs often occur, an objective method to filter out such artifacts is needed. Although identifiable by visual inspection, these spurious lines are not trivial to filter out because their values, shapes, and locations are not steady.

This article describes a filtering method for removing these BSL analysis artifacts without compromising the moisture-structure signal. The method involves modifying the original BSL analysis technique to work for range–height indicator (RHI) data, which has the advantage over PPI data of being sampled at many more elevation angles, each separated by only 0.5° increments. The true and spurious signals are separated by identifying and exploiting their distinct statistical correlations in the RHI BSL data, which then allow for accurate filtering of the spurious signal from both the PPI and RHI BSL data. The adaptation of BSL analysis for use with RHI data is presented first, followed by a description of the statistical filtering technique. The final discussion details both the utility of RHI-generated BSL time–height diagrams when compared with PPI-generated ones and the capability of the statistical filter in removing the clutter problem at hand.

## 2. Data

The data for this paper consist of S-Pol radar scans from ACDC. During ACDC, S-Pol was located on the Addu Atoll, also referred to as the Gan site (see Fig. 3), and took data from 1 October 2011 to 16 January 2012. The radar scanning strategy for ACDC consisted of one PPI volume followed by one RHI volume repeated every 15 min. PPI scans generally had 1° azimuthal resolution over full 360° sectors. For this paper 5°, 7°, 9°, and 11° elevation-angle scans were utilized. The RHI slices were generally taken at 2° azimuthal intervals over the 4°–82° and 114°–140° sectors, with the elevation angle incrementing at 0.5° intervals up to (and down from) 40°. The beamwidth is 0.92°. Data taken at elevation angles lower than 5° were excluded in this analysis 1) for having too shallow a vertical cross section for good identification of BSLs above the one associated with the mixed layer top and 2) due to the presence of significant interfering ground clutter at elevation angles less than 3.5° (Rilling et al. 2013). Note that for the BSL analysis presented here, the quality-controlled in-field version of the data, DBZ_F, is used, rather than the official quality-controlled version, DBZ_S, because the latter contains placeholder values at gates with essentially no echo return, which unduly influence the BSL analysis.^{1}

## 3. RHI BSL analysis

### a. The established BSL analysis technique for PPI data

BSL analysis is an edge-finding technique that locates the mean altitudes of the bases and tops of Bragg scattering layers within individual PPI scans. It employs a modified Haar wavelet technique to produce what is essentially a smoothed first derivative of the data from an individual radar beam, namely, *W*_{m} (Davison et al. 2013b). The degree to which the data are smoothed is controlled by the number of wavelet iterations taken, which dictates the number of data points used in each calculation (Fig. 4). For PPI scans, BSL edge estimates were made using both four- and five-wavelet iterations, with the former more sensitive to shallower BSLs and the latter providing less noisy results.

The *W*_{m} results for a single-elevation-angle scan are averaged over all azimuthal angles. Local maxima and minima in the scan-mean *W*_{m} are located at the mean inflection points, that is, the average location of the BSL edges within the scan. BSL analysis is conducted in radar space in units of range gate number, which is then converted to altitude to produce a time–height diagram of the mean BSL evolution for each elevation angle. Generally, all such time–height diagrams for a given day are shown together on one plot. See the appendix in Davison et al. (2013b) for further details.

As was noted in Davsion et al. (2013b,c), despite the name, there is nothing in the BSL analysis technique that strictly limits the analyses to Bragg scattering–only layers. In point of fact, many of the “Bragg scattering layers” identified are known to include some Rayleigh scattering. It has been shown that cumulus clouds preferentially detrain into preexisting BSLs, since the BSLs are associated with regions of increased static stability. The lowest BSL, which extends from the top of the mixed layer to the top of the transition layer, can also be identified as the (very) shallow cloud layer when such trade wind cumulus are present, and it generally has the highest contribution from Rayleigh scatters of all the layers. However, it was clearly shown in Davison et al. (2013b) that Bragg scattering was the dominant mechanism producing the layers identified by this technique *in this environment*.

For BSL analysis to be effective, knowledge of the local environment and meteorology is key. For the quiescent tropical marine boundary layer sampled during the Rain in Cumulus over the Ocean (RICO) campaign, range gates with reflectivity values higher than 10 dB*Z* were removed from the analysis to minimize the influence of clouds on the BSL results (Davison et al. 2013b). For the more active tropical marine boundary layer sampled during ACDC, a more stringent 5-dB*Z* threshold was necessary. It should be further noted that, because of changes in the NCAR quality-control procedure enacted during the time between these two campaigns (refer to Dixon and Hubbert 2012), the radar variable analyzed was changed from spectral width for RICO to a radar reflectivity factor for ACDC. Refer to the appendix in Davison et al. (2013b) for a discussion of the interchangeability of these two variables with respect to this technique.

### b. Modifications for use with RHI data

The attributes that makes RHI data valuable for this study (i.e., the large number and range of beam-elevation angles) also present complications that require adjustment of the BSL analysis technique developed for PPI data. The complications are twofold: 1) the vertical cross-section lengths sampled at a given range gate vary quite drastically (see Fig. 4) and 2) the uncertainty in beam-to-height conversion is compounded by the necessity of so many conversions. To prevent loss of vertical resolution due to the elevation-angle-dependent differences in vertical cross section, fewer wavelet iterations are carried out on higher elevation angle beams. Based on the geometry and scale used in the PPI BSL analysis, it was decided that four- and five-wavelet iteration results would be used for elevation angles less than or equal to 11.0°, three- and four-wavelet iteration results would be used for elevation angles between 11.5° and 23.5°, and two- and three-wavelet iteration results would be used for elevation angles greater than or equal to 24.0° (see Fig. 4). Thus, when estimating BSL edge altitudes with higher-elevation-angle data, the results are less robust and more noisy, since fewer data points are used in each calculation as fewer wavelet iterations are used.

Despite the differences in sampling geometry, the goal in RHI BSL analysis is to treat the data in an RHI volume as if it came from a PPI volume. As with the PPI BSL analysis, the modified Haar wavelet analysis was conducted on every beam of RHI data. To find the average along-beam location of BSL edges in a given RHI volume, the *W*_{m} results for the same elevation angle from all slices in the volume are first averaged together, then the local maxima and minima in the average are determined, and then the beam-to-height conversion is carried out. As in the PPI BSL analysis, each elevation angle in a given RHI volume provides one set of BSL edge estimates. For robustness, it is required that each RHI volume analyzed contains at least 30 different azimuthal slices (during ACDC most volumes contained 54). Because of the much higher elevation angles in the RHI data, the spherical earth exact geometry beam-to-height conversion is used for the RHI BSL analysis instead of the spherical Earth parabolic approximation used for the PPI BSL analysis (e.g., Murrow 1990). For elevation angles less than or equal to 11°, the height conversion difference between these two methods ranges from a few meters to tens of meters. Both the PPI and RHI conversions are made using the effective Earth radius model, which assumes that the vertical gradient of radio refractivity is constant. This is generally considered a good approximation for weather radar (e.g., Doviak and Zrnić 1984; Murrow 1990). However, it should be noted that, with the high level of moisture variability in the tropical marine boundary layer, it is not difficult to find instances of both large positive and large negative vertical radio refractivity gradients (refer to Fig. 12 in Davison et al. 2013b). These large gradients in radio refractivity will introduce uncertainties in beam-to-height conversion, the magnitude of which will be partially dependent upon the beam’s dwell time in the layers, that is, a function of elevation angle. Rough estimates of the maximum uncertainty in beam-to-height conversion caused by refractivity from such extreme layers were calculated to be on the order of ±50 m for a 7° elevation angle, with the uncertainty decreasing with increasing elevation angle (and vice versa). Given both the high spatial and temporal variability of these moist and dry layers, however, it is impractical to attempt to utilize the available soundings to improve the beam-to-height conversion. Thus, the effective Earth radius model is used. Comparison between the PPI and RHI BSL results for a day that was fairly horizontally homogenous is shown in Fig. 5. Note the consistency in the structure of the mean BSLs mapped out in Figs. 5b–d.

## 4. Data filter

The residual sidelobe clutter in the quality-controlled ACDC PPI data is difficult to objectively separate from true Bragg echoes due to their common proximity in location and value (Figs. 1a, 2a). One example shown in Fig. 2a is the thin strip of enhanced reflectivity that occurs at approximately 1.4 km altitude in the 7° scan, 1.8 km in the 9° scan, and 2.2 km in the 11° scan. This is the same clutter feature—it occurs at a fixed range from the radar and thus, for scans with different elevation angles, it appears at different altitudes once the beam-to-height conversion has been carried out. For a single PPI scan, it appears as a thin yet fairly distinct layer that can be identified by the BSL analysis algorithm, leading to the detection of false BSL edges (Fig. 1a). In the corresponding RHI scans, this same feature appears as the elongated vertical swath of higher reflectivity between 11- and 12-km distance from the radar (Fig. 2b, top) and between gates 70 and 80 (Fig. 2b, bottom), and is clearly distinct from the BSLs. This distinction can be exploited to create an objective statistical filter. The RHI data provide two key advantages: 1) for the higher elevation angle beams, the range gate location of the sidelobe clutter often corresponds to altitudes where BSL detection is less likely; and 2) the large number of elevation angles and dense vertical coverage of the RHI scans make it unlikely to detect a true BSL edge at the same range gate for a large fraction of the elevation angles providing estimates.

For a given RHI volume and number of wavelet iterations, the number of BSL edge detections at each range gate are summed (see Fig. 6). For example, two-wavelet iterations are carried out on beams with elevation angles between 24° and 40°, and with the elevation angles advanced at half-degree increments, a maximum of 33 possible BSL edge detections per range gate is possible (e.g., Fig. 6a). Only range gates 27–120 are included in the edge detection sum. Range gates lower than 27 are excluded, since sampling geometry will cause a higher probability of good detections to occur at the same range gates for multiple low-elevation angles (see Fig. 2b). Range gates higher than 120 were excluded because of the dearth of relevant information. Any range gate with more detections than the mean plus twice the standard deviation for a given RHI volume is then flagged. The same analysis was carried out for the three-wavelet iteration data (beams with elevation angles 11.5°–40°) and the four-wavelet iteration data (beams 5°–23.5°). The flagged gates from these three datasets serve as the basis for constructing the statistical filter.

To filter the false edge lines in the PPI BSL results, each PPI volume is linked with the temporally closest RHI volume for filtering. It is found that the PPI false edge detections are not always at the specific gates flagged using the RHI data but are occasionally off by one gate. Factors that may contribute to this include nonfixed clutter targets, such as a crane that occasionally drove by the radar and nearby ocean freighters, which can drift and tilt (all present during ACDC); overlapping returns of true Bragg signal and sidelobe clutter; edge detections, where one range gate was only slightly preferred over an adjacent gate; and the inclusion of a much larger azimuthal swath (and thus wider sampling area) for the PPI data than for the RHI data. It was therefore decided to filter each PPI BSL edge that falls within plus-or-minus one gate of each RHI-flagged gate. Examples of the statistically filtered data can be seen in Figs. 1b, 5b. Note, for example, the removal in Fig. 5b of the false edge artifacts present just above 2 km between 0600 and 0900 UTC in Fig. 5a. This statistical filter was also applied to the RHI BSL results.

## 5. Discussion

### a. Comparison of RHI versus PPI BSL results

A beneficial by-product of this filter development is the BSL analysis of the RHI volumes, thus making use of the large ACDC RHI dataset. The results show promise for enhancing the PPI BSI retrievals, but in a somewhat mixed fashion. The comparison of RHI to PPI BSL results ranges from quite favorable for the five-wavelet iteration set to somewhat poorly for the two-wavelet iteration set (see Figs. 5b–f). There are many contributing factors that could explain the mixed comparisons. The primary factor results from a combination of the horizontal homogeneity of the BSLs themselves and horizontal data coverage. For instance, the coverage of the azimuthal swaths in the RHI volumes makes up less than one-third of the horizontal area covered by the full 360° PPI sweeps and has half the azimuthal sampling rate (every 2° instead of every 1°). Since the RHI sectors are more commonly over and downwind of the atoll,^{2} any atoll-induced effects likely bias the RHI BSL results. So, too, will smaller-scale transient features (e.g., Davison et al. 2013c) or local cloud detrainment effects have a greater impact on the RHI results, since these are more likely to dominate the RHI swaths than the PPI scans. Conversely, the temporal resolution of the RHI results is much coarser than that of the PPI results, with nearly the full RHI volume time of roughly 9 min contributing to each RHI elevation-angle BSL estimate, in contrast to 37 s of data contributing to each PPI elevation-angle BSL estimate.

The agreement between Fig. 5b and Figs. 5c,d is quite good, as can be expected given the BSL horizontal homogeneity on 4 January 2012. For the two- and three-wavelet iteration sets (Figs. 5e,f), the midlevels (centered around the 3–4-km range) seem to reflect the same good agreement with Fig. 5b but above and below there are issues. The near-surface issues, identified by sparse estimates in Figs. 5e,f, are attributable to a combination of the decrease in smoothing of the two- and three-wavelet iteration sets, which is necessitated by the larger vertical cross section of the higher elevation angles, and smaller range gate volumes when the beam is close to the radar. In other words, beam expansion and the accompanying increase in range gate volume acts to increasingly smooth the data itself the farther the gate is from the radar. So, even though there are fewer data points going into the two- and three-wavelet iteration sets, at a certain distance from the radar, some of the lack of smoothing in the analysis is compensated by smoothing done in the measurements themselves. Before this point is reached, BSL edge detection is much more difficult.

Problems above the midlevels in Figs. 5e,f are largely attributable to the combination of insufficient filtering of systematic noise and the large number of BSL estimates. Figure 5e is a combination of 58 separate time–height diagrams all plotted on the same graph. When a false edge detection makes it past the statistical filter, the elevation angles are only 0.5° apart, and so many elevation angles are providing estimates then false edge estimates can begin to fill the plot. This is more easily seen in the red dots above 6 km in Figs. 5e,f. However, when there are both false BSL base (blue) and BSL top (red) detections (e.g., 0800–1200 UTC near 4.5 km), the results can be very similar to true BSLs. However, the “truth” of the situation is readily apparent when viewing the layering of the time–height diagrams one at a time instead of looking at the net results. Since there are only 33 time–height diagrams being layered in Fig. 5f, there are also fewer false BSL top estimates (red dots) above 6 km than there are in Fig. 5e.

### b. Filter effectiveness

The application of the above-described filter to the PPI BSL results is quite sufficient, as can be seen by comparing Figs. 1a,b and 5a,b as worst-case and best-case scenarios, respectively. With the exception of the false edge line near 2.5 km in Fig. 1b, the majority of the false edge line artifacts have been removed throughout the entire ACDC radar dataset. At times bad data are removed at the expense of good detections, leading to less spread in some BSL edge elevation estimates on the time–height plots. However, thus far, no instances of the complete removal of a viable BSL by the filter have been found. Closer inspection of questionable instances where seemingly bad data was kept or seemingly viable BSL edges were removed revealed that, given the combination of sidelobe clutter and Bragg echoes in these instances, one would tend to subjectively filter the data in the same manner in the majority of cases.

Application of the data filter to the RHI BSL data for the four- and five-wavelet iteration sets also seems quite adequate. However, if the BSL results from the two- and three-wavelet iteration data were to be made direct use of, additional filtering would be required. This is a topic for future work.

## Acknowledgments

Thanks to the reviewers for their insightful comments and suggestions. Special thanks to Scott Ellis for the suggestion of modifying the BSL analysis for RHI data, to Tim Dowling for editorial help, to Stacy Brodzik for getting a copy of the field data to me, and most especially to the NCAR radar group for supplying the S-Pol radar data. This work is supported by NSF Award 1331291. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

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^{1}

The variable DBZ_F refers to DB*Z* after application of the clutter removal filter in the NCAR field version of the DYNAMO S-Pol dataset. DBZ_F does not have beam clipping applied and is not as well calibrated or quality controlled as DBZ_S. Details of NCAR’s quality-control procedures for this dataset can be found in Hubbert et al. (2009a,b) and Dixon and Hubbert (2012).

^{2}

This assertion is based on the rawinsonde-mean wind directions for the depth of the lowest BSL, that is, those associated with the mixed- and transition-layer tops from roughly 450- to 800-m elevation.