This study presents and applies three separate processing methods to improve high-order moments estimated from 35 GHz (Ka band) vertically pointing radar Doppler velocity spectra. The first processing method removes Doppler-shifted ground clutter from spectra collected by a US Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program Ka-band zenith pointing radar (KAZR) deployed at Oliktok Point (OLI), Alaska. Ground clutter resulted from multiple pathways through antenna side lobes and reflections off a rotating scanning radar antenna located 2 m away from KAZR, which caused Doppler shifts in ground clutter returns from stationary targets 2.5 km away. After removing clutter in the recorded velocity spectra, the second processing method identifies multiple separate and sub-peaks in the spectra and estimates high-order moments for each peak. Multiple peaks and high-order moments were estimated for both original 2 and 15 s averaged spectra. The third processing step improves the spectrum variance, skewness, and kurtosis estimates by removing velocity variability due to turbulent broadening during 15 s averaging intervals.
Applying the multiple peak processing to Doppler velocity spectra during liquid-only clouds can identify cloud and drizzle particles and during mixed-phase clouds can identify liquid cloud and frozen hydrometeors. Consistent with previous studies, this work found that spectrum skewness assuming only a single spectral peak was a good indicator of two hydrometeor populations (for example, cloud and drizzle particles) being present in the radar pulse volume. Yet, after dividing the spectrum into multiple peaks, velocity spectrum skewness for individual peaks is near zero, indicating nearly symmetric peaks. This suggests that future studies should use velocity skewness of single-peak spectra as an indicator of possible multiple hydrometeor populations and then use multiple-peak moments for quantitative studies. Three future activities will continue this work. First, KAZR spectra from several ARM sites have been processed and are available in the ARM archive as a principal investigator (PI) product. ARM programmers are evaluating these processing methods as part of future multiple-peak products generated by ARM. Third, MATLAB code generating the Oliktok Point products has been uploaded as supplemental material for public dissemination.
Vertically pointing radars operating in the Ka band (35 GHz) are important remote sensing instruments providing quantitative and high-resolution observations for studying the vertical structure and dynamics of clouds and precipitation (Görsdorf et al., 2015). Vertically pointing radars increase their sensitivity by transmitting multiple pulses and produce Doppler velocity spectra for each range gate and dwell. The temporal evolution and vertical structure of these spectra contain microphysical and dynamical cloud and precipitation information.
Using narrow-beam-width antennas reduces spectrum broadening due to sub-pulse volume turbulence. The resulting recorded spectra are often non-Gaussian shaped and contain multiple peaks due to the presence of different particle size distributions within the radar pulse volume (Kollias et al., 2016). Under certain atmospheric conditions, mixed-phase clouds occur and contain both liquid- and ice-phase particles within the same radar pulse volume (Shupe et al., 2004; Kalesse et al., 2016). Thus, the number of spectrum peaks and their shape provide microphysical information of the particle size distributions. Estimating higher-order spectral moments, including velocity spectrum skewness and kurtosis, extracts microphysical information from the full Doppler spectrum (Luke and Kollias, 2013). These high-order moments are inputs to time–height analyses exploring microphysical and dynamical cloud processes (Maahn and Löhnert, 2017). One caveat for this analysis paradigm is the need for clean radar Doppler velocity spectra void of non-atmospheric signals, including ground clutter. Thus, preprocessing and cleaning of Doppler spectra are often needed before microphysical and dynamical information can be extracted from vertically pointing cloud radar observations.
This study presents three separate methods to improve high-order moments estimated from Doppler spectra. First, Doppler velocity spectra are cleaned by removing ground clutter. Second, multiple peaks are identified within the Doppler spectra. Finally, spectrum skewness estimates are improved by removing turbulent broadening effects at the 15 s scale.
Ground clutter in scanning and vertically pointing radar observations is a pervasive problem (Sato and Woodman, 1982). Ground structures (including buildings, trees, and power lines) act as hard targets reflecting radar waves back to the radar. Since these ground structures are stationary, except for oscillatory trees and power lines swaying due to wind (Barth et al., 1994), the ground clutter has a zero Doppler velocity shift. Bandpass filters can isolate clutter and hydrometeor signals as long as the hydrometeor signal has a non-zero velocity. As the weather signal approaches zero velocity, more sophisticated methodologies are needed to separate clutter from desired weather signals (Siggia and Passarelli, 2004).
For scanning weather radars, both the clutter and weather signals have Gaussian shape peaks that enables removing the clutter signal and recovering any overlapping weather signal. Within the Doppler velocity spectrum domain, the Gaussian model adaptive processing (GMAP) method (Siggia and Passarelli, 2004) uses the saved coherent and quadrature time-series observations (i.e., I and Q voltages) to calculate multiple spectra to adaptively determine the Gaussian-shaped clutter and remove it from the Gaussian-shaped weather signal. The GMAP methodology applied to time-domain calculations (called GMAP-TD) accounts for scanning radars utilizing staggered pulse repetition time (PRT) sequences (Nguyen and Chandrasekar, 2013). Since vertically pointing radars in mixed-phased clouds routinely observe signals from two hydrometeor types (e.g., liquid clouds and falling ice particles, Shupe et al., 2004; Kalesse et al., 2016), the GMAP method cannot be implemented to remove clutter without significantly modifying the GMAP logic. In addition, the time-series I and Q voltages needed to resample the spectra with different amplitude weightings are often not available for reanalysis from vertically pointing radars.
Receiving backscattered energy from moving trees and cars through antenna
side lobes is a common clutter problem with wind profilers (Barth et al.,
1994). Due to the relatively large antenna beam widths in wind profilers
(e.g., 6
Operating parameters for AMF-3 KAZR deployed at Oliktok Point,
Alaska, from 1 October 2015 through 31 October 2017 (at the time of
publishing, the radar was still operating at Oliktok Point, Alaska).
Operating modes included general purpose (GE), medium sensitivity (MD), and
precipitation (PR) modes. Tabulated parameters include pulse repetition
frequency (PRF) (Hz), inter-pulse period (IPP) (
Recent studies have shown that velocity spectrum skewness provides information of drizzle onset (Kollias et al., 2011; Luke and Kollias, 2013; Acquistapace et al., 2017) and for deriving properties of ice clouds (Maahn et al., 2015; Maahn and Löhnert, 2017). Since there is a trade-off between temporal resolution and spectrum noise variance, the spectral moment estimates tend to be noisy for short-duration spectra (Giangrande et al., 2001; Luke and Kollias, 2013; Acquistapace et al., 2017). By shifting spectra to a reference velocity before averaging spectra, Luke and Kollias (2013) showed that spectrum skewness estimates improved and were more coherent in time and height.
There is a long history of estimating multiple peaks in radar Doppler velocity spectra (Clothiaux et al., 1994). These multiple peaks need to be estimated before applying fuzzy logic (Cornman et al., 1998; Cohn et al., 2001; Morse et al., 2002), neural network (Gardner and Dorling, 1998), or wavelet (Lehmann and Teschke, 2001) frameworks to discriminate atmospheric signals from clutter and radio interference. Estimating multiple peaks is a form of data reduction, or feature extraction, that can be used as input to algorithms that estimate boundary layer heights (Allabakash et al., 2017) or horizontal winds (Liu et al., 2017).
This paper has the following structure. Section 2 describes the radar deployment and operating parameters of a US Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program Ka-band zenith pointing radar (KAZR) installed at Oliktok Point (OLI), Alaska. Section 3 describes signatures of clutter and atmospheric signals observed in KAZR velocity spectra. Section 4 develops a clutter identification and mitigation method. This section also discusses how multipath scattering from a nearby scanning radar antenna caused the clutter to have either approaching or receding radial motion. Section 5 describes a method to identify multiple peaks in the spectra and estimate high-order spectral moments. Section 5 also discusses a method of shifting individual spectra to the 15 s mean velocity before averaging. Section 6 provides concluding remarks. For completeness and repeatability, Appendix A provides the equations to estimate high-order spectral moments. The MATLAB code used to perform the analysis is available as supplemental material.
Since the early 1990s, the US Department of Energy (DOE) Atmospheric Radiation Measurement program has deployed atmospheric observing systems around the globe to measure and characterize the radiative properties of the atmosphere (Mather and Voyles, 2013). The radiative properties of clouds are dependent on many factors including cloud composition, cloud thickness, and temperature. Measurements from vertically pointing cloud radars, lidars, and radiometers provide the input observations needed to estimate and to better model the radiative properties of clouds (Clothiaux et al., 2000).
In 2015, DOE installed their third ARM Mobile Facility (AMF-3) at Oliktok
Point, on the North Slope of Alaska (NSA), which is approximately 264 km
east-southeast of the long-term ARM North Slope of Alaska
core-observing site near Utqiaġvik (formally known as Barrow). The AMF-3
instrument suite includes a Ka-band (35 GHz) ARM zenith pointing
radar (KAZR) and a Ka/W-band (
Time–height cross sections of original KAZR Doppler velocity
spectral moments and attributes from 19 June 2016 during hour 12:00 UTC.
The KAZR and SACR at Oliktok Point became operational after an intensive calibration, grooming, and alignment (CGA) field campaign conducted by the ARM Radar Engineering Group in October 2015. The KAZR operates in three modes: general mode (GE), medium mode (MD), and precipitation mode (PR). The initial operating parameters recorded 256-point Doppler velocity spectra. On 16 June 2016, the number of incoherent integrations were reduced in order to record 512-point spectra and maintain the same time-on target (Table 1). Raw spectra used in this study are available on the DOE ARM archive (ARM Climate Research Facility, 2015).
At Oliktok Point, oil refineries, pipelines, and power lines within 2.5 km range are detected by KAZR as backscattered energy reflects back toward the radar and leaks into the radar system through antenna side lobes. To mitigate the ground clutter observed in the KAZR spectra, a temporary clutter screen was installed around the KAZR antenna on 27 August 2016 (Fig. 1b). Thus, there are three different KAZR configurations partitioned by date: (prior to 16 June 2016) 256-point spectra with no clutter screen, (between 16 June 2016 and 26 August 2016) 512-point spectra with no clutter screen, and (after 26 August 2017) 512-point spectra with clutter screen.
Stationary ground clutter will appear in the Doppler velocity spectra near zero velocity. This section examines and quantifies the characteristics, or signatures, of KAZR ground clutter and KAZR atmospheric signals due to clouds and precipitating particles. Appendix A provides details of calculating spectral moments from raw velocity spectra.
Figure 2 shows time–height cross sections of measured radar reflectivity
(Fig. 2a) and mean radial velocity (Fig. 2b, positive values are approaching
the radar) for 1 h of observations starting at 12:00 UTC on 19 June 2016.
For this figure, instead of imposing a user-defined signal-to-noise ratio
(SNR) threshold to discriminate spectra with signal-plus-noise versus spectra with
just noise, moments were estimated only for spectra containing at least three
consecutive spectral points above the noise threshold. While the actual
observations for this precipitation event extend above 6000 m, the vertical
axis in Fig. 2 is limited to 2500 m to show details of the ground clutter
signatures. There are four general areas of interest in this figure: one area
contains atmospheric signals and the other three areas contain clutter
signatures. The atmospheric signals are due to cloud and precipitating
particles that are identifiable by reflectivities greater than approximately
Clutter is visible in Fig. 2a and b within two height ranges prior to minute 20. Clutter signatures are either below 600 m or within 1500–2000 m. In both height regions, the clutter reflectivity is nearly constant at each height and the radial velocity is near zero. Note that the radar continuously detects clutter within these two height ranges throughout the hour. The clutter signature is not visible after minute 20 because signal power from the cloud and precipitation is larger than the clutter power and the spectral-peak-picking routine is selecting the larger atmospheric peak. At a height near 500 m and minutes 30–60, there are intervals when the clutter peak is larger than the atmospheric peak such that the spectral-peak-picking routine has selected the clutter peak instead of the atmospheric peak. These clutter peaks appear near minutes 31 and 50–57 and are distinguished by discontinuities in reflectivity and near-zero radial velocities.
There are significant differences in the characteristics of backscattered return power from distributed targets and from point targets (Mahafza, 2017). In the case of distributed hydrometeor targets, the hydrometeors have different sizes and velocities that are constantly moving within the radar pulse volume. These motions cause the radar-received backscattered power to fluctuate from pulse to pulse (i.e., Swerling type II targets). In addition, there is a distribution of different particle sizes falling at different velocities leading to a broad velocity distribution in the recorded Doppler velocity spectrum.
In contrast, received power return from stationary point targets is nearly
constant from pulse to pulse with small random statistical fluctuations
(i.e., Swerling type 0 or V targets). The constant path length between the
radar and the target results in zero Doppler motion. In an ideal
signal-processing environment, the stationary target in the time domain would
transform into a delta function of finite energy at zero velocity in the
frequency domain. However, in real-world signal processors, the
delta-function energy spreads over several velocity bins following a
In general, distributed hydrometeor targets produce broader velocity spectra than stationary targets. To explore these attributes in the recorded spectra, Fig. 2c shows the drop in received power from the velocity bin with peak magnitude to its directly neighbouring velocity bin expressed in units of dBm (i.e., power relative to 1 mW). Since there are two neighbouring velocity bins bounding the peak value, all calculations use the largest power drop. Figure 2c shows that the power drop for the clutter signal is approximately 6 dBm (i.e., red colours) and occurs prior to minute 25, as well as near 500 m during minutes 31 and 51–57. For the spectra with clouds and precipitation, the drop in power is a distribution of values with a central value near approximately 2 dBm (i.e., blue colours). Figure 2c suggests that the power drop from the peak magnitude to the nearest neighbour is a good indicator of whether the spectrum peak is due to point-target scattering (approximately 6 dBm drop) or due to distributed hydrometeor target scattering (less than 2 dBm drop).
Doppler velocity spectra for profile collected on 19 June 2016 at
12:05:01 UTC.
To explore details of how clutter signals appear in the recorded velocity
spectra, Fig. 3a shows a profile of spectra selected from Fig. 2 at
12:05:01 UTC on 19 June 2016. The radial velocity is on the abscissa and
only extends from 1 m s
The black line at 447 m in Fig. 3a indicates the height of the spectrum shown in Fig. 3c, which contains both a clutter peak and an atmospheric peak due to cloud droplet particles (black line with pluses). An interpolation in linear units is performed across the three points centred about zero velocity and is shown in Fig. 3c with a red line and circles. It is important to note that the three-point interpolation only modifies power recorded at three velocity bins. Figure 3b shows stacked spectra after applying this three-point interpolation to each spectrum. Note that this simple interpolation was sufficient to remove or suppress the clutter near zero velocity such that the atmospheric signal can be resolved.
Time series of radial velocity spectra on 19 June 2016 during hour
12:00 UTC at 447 m range. The first spectrum of the hour is at the bottom of the
panel (minute 0) and last spectrum of the hour is at the top of the panel
(minute 60). Horizontal axis is upward (left side) and downward (right side)
radial velocity.
To illustrate the relatively constant amplitude of the clutter signal with
time, Fig. 4a shows 1774 consecutive spectra at 447 m height for hour
12:00 UTC on 19 June 2016 (which is the same hour shown in Fig. 2). Radial
velocity is on the abscissa with upward motion on the left and downward
motion on the right. Time is on the ordinate with time increasing up the
page. Pseudo-colours represent measured return power in dBm. A clutter peak
near zero velocity is present during the whole hour while there are two
fluctuating atmospheric signals at this height. A liquid cloud is present for
most of the hour with updraft–downdraft magnitudes less than
0.5 m s
Selected spectra to illustrate clutter signal, three-point
interpolation, and residual signal power.
As shown in Fig. 2 during the first 20 minutes of observations, without clutter peak mitigation, standard single-peak-picking algorithms (e.g., Carter et al., 1995) will select ground clutter as a viable peak and will estimate the spectral moments of this clutter peak. If the clutter peak is in the middle of the atmospheric signal as in the example spectrum shown in Fig. 3c, then the estimated reflectivity will be biased high and the mean radial velocity will be biased toward zero velocity. If clutter mitigation is applied to all spectra regardless of whether clutter signals are present, then low-magnitude atmospheric signals centred on zero velocity could be eliminated from the dataset. Thus, this section examines the power drop near zero velocity in order to establish a threshold to determine where and when not to apply clutter mitigation.
To determine whether the spectrum contains point-target signatures, three
statistics are calculated for each spectrum: the drop in power from the zero
velocity bin to the nearest-neighbour velocity bin (
In Fig. 5a, notice the large power drops between the zero velocity bin and
the first and second neighbouring velocity bins. The power drops are
approximately 6 and 25 dBm, respectively. These large power drops are
consistent with the expected
After removing the clutter power using a three-point interpolation (Fig. 5a), the
spectral moments are estimated using the decluttered spectra (Fig. 5b) to
determine whether or not the spectrum contains residual clutter or contains
atmospheric signals. In Fig. 5b, the decluttered spectrum has eight
consecutive spectral points above the noise threshold and is shaded medium
grey. The signal-to-noise ratio of this residual peak is
The spectrum shown in Fig. 5c contains both clutter and atmospheric signals (range 387 m at 17:14:31 UTC on 7 July 2016). The clutter peak is clearly identifiable in the spectrum. A thick dashed line shows the three-point interpolation across zero velocity and the clutter power is shaded in light grey. Figure 5d shows the decluttered spectrum with the residual signal power and noise power indicated with the medium and dark grey shadings, respectively. For this spectrum, the residual peak SNR is 3.3 dB and the peak magnitude velocity (indicated with a filled circle) occurs away from the three-point interpolation velocity bins and is associated with the atmospheric signal.
In order to determine when to apply the three-point interpolation across zero velocity, we need to compare the drop in power in spectra with and without ground clutter. Figure 6 shows a time series of radial velocity spectra at a range of 987 m for the same 1 h interval shown in Fig. 4a. There is no clutter in the raw spectra at 987 m shown in Fig. 6 so it can be used as a reference. Note that there are no saved spectra prior to minute 21 because the automated data reduction and archiving algorithm did not detect any spectral points (clutter or atmospheric signals) with power greater than the Hildebrand and Sekhon (1974) noise threshold.
Similar to Fig. 4a except for 987 m range. In contrast to the range gate at 447 m shown in Fig. 4, this range gate does not contain ground clutter for this hour and does not contain any atmospheric signal before minute 21. Since no signal was detected above the noise threshold before minute 21, the data reduction and storage algorithm did not save any spectra before minute 21.
The power drop from zero velocity to the nearest-neighbour
Time–height cross section of clutter statistics from spectra
collected on 3 July 2016 during hour 20:00 UTC.
Time–height clutter patterns occurred with a repeatable temporal cadence.
Specifically, there were periods of narrow-symmetric clutter and periods of
broader-asymmetric clutter. While the peak magnitude velocity rarely deviated
from zero velocity, the asymmetry caused the mean velocity moment to deviate
from zero velocity. Figure 8 shows an hour's worth of observations on
3 July 2016 (hour 20:00 UTC) when no hydrometeors were above the radar.
Figure 8a shows the clutter-to-noise ratio (dB), Fig. 8b shows the
residual peak SNR (dB), and Fig. 8c shows the residual peak magnitude velocity
expressed in m s
Diagram showing SACR antenna azimuth pointing direction (solid line)
and Doppler shift of residual clutter (shading) for 10 min of observations
shown in Fig. 7. With a rotation rate of 2
Clutter identification and mitigation flow diagram. Processing is performed on individual spectra without knowledge of clutter being identified in neighbouring spectra.
Figure 9 shows the pointing direction of the SACR scanning radar antennas
(solid line) for minutes 20–30 during hour 20:00 UTC on 3 July 2016. During
this 10 min interval, the SACR antennas were rotating at
2
This section describes a clutter mitigation routine that identifies and
removes static and non-static clutter signals from recorded velocity
spectra. Over the course of analysing clutter signatures, several complex
clutter removal routines were developed. After comparing the results from
these routines, the clutter removal methodology was simplified until this
final routine had only three conditions based on two thresholds:
Is power Are there enough spectral points above the noise threshold to estimate
moments? After interpolating across the clutter peak, is the new peak magnitude
velocity at an interpolation edge velocity?
The use of static thresholds is simple to implement, but not easily
transferred to other radar systems that have different clutter statistics.
Thus, the MATLAB code used to process the Oliktok Point KAZR dataset is made
available as supplemental material. Figure 10 shows a flow diagram for the
clutter mitigation routine. Starting with box no. 1, a single spectrum is
loaded into the routine. The power drop from zero velocity to the nearest
neighbour is calculated as
Attributes and integration limits for three spectral peak regimes: single peak, sub-peak, and separate peak. All spectral peaks need at least five consecutive spectral points with magnitudes greater than the noise threshold (Hildebrand and Sekhon, 1974).
Box no. 7 requires that at least five consecutive spectral points have
magnitudes greater than the noise threshold. Note that there are trade-offs
using a fixed number of consecutive spectral points above the noise
threshold. First, increasing the number of spectral points increases the
minimum detected SNR. Second, a fixed number of spectra bins corresponds to a
minimum velocity range, expressed in m s
Similar to Fig. 2 except spectra were decluttered (see Sect. 3)
before estimating
To illustrate the performance of the clutter identification and mitigation
routine, the same spectra used to construct Fig. 2 were processed through the
flow diagram shown in Fig. 10. Figure 11 shows the decluttered spectra
calculations of reflectivity (Fig. 11a), mean radial velocity (Fig. 11b), and
power drop from peak power to nearest neighbour (Fig. 11c). Figure 11 shows a
vertically thin cloud layer just below 500 m that was not visible in Fig. 2
because of the contaminating ground clutter. This is consistent with the
spectra analysis shown in Figs. 3 and 4 that showed an oscillatory cloud
layer near 500 m. In addition to providing the MATLAB code as supplemental
material, the processed Oliktok Point KAZR datasets are available on the ARM
archive (see data availability section for details). These netCDF datasets also
include a 3
After identifying and removing clutter in the effected spectra, this section describes how to identify multiple-peaks in the spectra, how to estimate high-order moments for each spectral peak, and how to construct 15 s average spectra using a “shift-then-average” procedure.
Profile of spectra and moments collected on 15 October 2016 at
11:55:55 UTC. Top row corresponds to single-peak moments and bottom row
corresponds to multiple-peak moments. Top row:
One advantage of processing radar velocity spectra is that different
hydrometeor habits can be identified by their velocity signatures. For
example, Fig. 12a shows a velocity spectra profile when both cloud
particles and ice particles are occurring in the same height between 500 and
800 m. This profile was collected on 15 October 2016 at 11:55:55 UTC with
the pseudo-colours representing received power in dBm. Visually, we can see
two return power patterns in the spectra profile. One pattern is limited in
height between 500 and 800 m and has downward motions between 0 and
0.4 m s
Super imposed on the spectra in Fig. 12a are the mean velocity
Radial velocity spectra on 15 October 2016 at 11:55:55 UTC at
ranges
Identifying multiple peaks (Luke and Kollias, 2013) is a process of identifying boundaries, or integration limits, which will be used in the spectrum moment equations. To help describe how boundaries are identified, Fig. 13 shows how single peaks, sub-peaks, and separate peaks are identified in example spectra pulled from heights 807 and 777 m in Fig. 12. Table 2 provides a description of the three types of peaks. Every spectrum with at least five consecutive spectral points above the noise threshold will have a single peak. However, not every spectrum with a single peak will have sub-peaks or separate peaks.
The spectrum from 807 m (Fig. 13a) has two spectral peaks. The peak on the
right is the most significant peak because it contains the spectral point
with the largest magnitude. The integration limits for the single peak extend
over all consecutive points above the noise threshold. The triangles in
Fig. 13a indicate the single-peak integration limits and
Spectral moments of averaged spectrum after averaging eight spectra using two different methods. All eight spectra were collected during 15 s interval on 15 October 2016 between 11:55:45 and 11:56:00 UTC and are shown in Fig. 14. The averaged spectrum was constructed by averaging individual spectra as shown in Fig. 14a. The mean radial velocity from this averaged spectrum is used as the reference velocity. The shifted-then-averaged spectrum was constructed by first shifting individual spectra to a reference mean radial velocity and then averaging as shown in Fig. 14b.
Figure 13b shows the spectrum from 777 m. The single peak is very broad and
extends from approximately 0.25 m s
After identifying integration limits for all spectral peaks, the high-order moments are calculated for each peak using the equations shown in Appendix A. The spectral moments range from the signal-to-noise ratio (the zeroth moment) to the velocity spectrum kurtosis (the fourth moment).
The scatter-plot profiles on the right side of Fig. 12 show the spectral
moments of reflectivity and velocity skewness for the single, sub-, and
separate peaks. The top row shows only the single-peak moments while the
bottom row shows moments from different peaks. Note that if sub-peaks exist
in a spectrum, then the single-peak moments are not plotted in the bottom
row. The reflectivity vertical structure for the multiple peaks (Fig. 12e)
shows both a continuous pattern with height and two patterns that are limited
in height. The continuous pattern mimics the single-peak reflectivity pattern
shown in Fig. 12b and has a local maximum near 400 m. The two height-limited
patterns occur near 700 and 1400 m where there are two distinct hydrometeor
populations in the spectra profile (Fig. 12d). Near 700 m, the smaller
reflectivity values correspond to the cloud particles with mean velocities
near 0.2 m s
With regard to the velocity skewness, the single-peak estimates (Fig. 12c) show large negative values below 800 m with maximum value near 600 m. A negative velocity skewness indicates that the long distribution tail is on the negative velocity side of the peak, which is upward motion in this dataset. Yet, Fig. 12f shows near-zero velocity skewness for the sub-peaks between 500 and 800 m. This suggests that large-magnitude single-peak velocity skewness could indicate the existence of multiple sub-peaks. Yet, after identifying sub-peaks, velocity skewness represents the asymmetry of each individual spectral peak. Thus, single-peak velocity skewness could be used to identify the existence of multiple sub-peaks and moments from multiple peaks should be used to perform quantitative microphysical analyses.
As discussed in Luke and Kollias (2013), the velocity spectrum skewness can be a noisy estimator due to velocity bin-to-bin spectrum power fluctuations. To improve the velocity spectrum skewness estimate, Luke and Kollias (2013) suggested shifting consecutive spectra to a common reference, averaging the shifted spectra, and then estimating the velocity spectrum variance and skewness. Shifting the spectra before averaging reduces the spectrum broadening and smearing due to vertical air motion variability that occurs during the averaging interval (Giangrande et al., 2001). Several different averaging intervals were tested ranging from 4 s (similar the KAZR-ARSCL resolution) to 60 s. The 4 s interval only contained two profiles, while the cloud system often evolved and changed shape during the 60 s interval. A compromise of 15 s is used assuming that the atmospheric microphysical processes (e.g., evaporation, breakup, and coalescence) are stationary over this interval, yet dynamical processes (e.g., air motions and turbulence) are not stationary.
Eight radial velocity spectra collected on 15 October 2016 during
15 s interval starting at 11:55:45 UTC at 447 m range.
The method of shifting all spectra to line up all peak magnitude velocities
appeared to work well for the maritime drizzle clouds (Luke and Kollias,
2013), but it did not work well with Arctic mixed-phase clouds observed at
Oliktok Point because the peak magnitude sometimes jumped to a different
spectral peak during the 15 s integration interval. To overcome this
occasional issue, the spectra were shifted to the 15 s mean velocity.
Specifically, shift-then-average processing consisted of nine steps performed
at each range gate:
Estimate the single-peak mean velocity for each 2 s spectrum
Incoherently average (no shifting) all spectra within a 15 s interval. Identify the single peak in this 15 s averaged spectrum. Estimate the single-peak mean velocity Shift each 2 s spectrum by Average the shifted spectra. Identify multiple peaks in these shifted-then-averaged spectra. Estimate high-order moments for each identified peak. Save all multiple-peak moments as well as the incoherent averaged spectra
mean velocity
As an example of the shifting process, Fig. 14a shows eight spectra (thin
lines) collected at 447 m on 15 October 2016 during the 15 s interval
starting at 11:55:45 UTC. The average of these eight spectra is shown with a
thick line. The spectral moments of this averaged spectrum are listed in
Table 3. The mean radial velocity
This study is a combined science and engineering effort designed to improve high-order moments estimated from Ka-band (35 GHz) vertically pointing radar Doppler velocity spectra by developing three different signal-processing methods. First, a decluttering method identifies and removes clutter in the Doppler spectra. Hard targets produce narrow spectral peaks. Identifying clutter peaks is based on identifying large power drops between neighbouring velocity bins. In our observations, the narrow clutter peak occurred near zero velocity. After identifying narrow spectral peaks, a linear interpolation is performed to remove the narrow peak from the velocity spectra. All spectra void of clutter and those with mitigated clutter are used in the subsequent processing methods. As an interesting side note, we found that a rotating antenna within 2 m of the Ka-band vertically pointing radar is causing the clutter to be Doppler shifted. We postulate reflected waves bouncing off the rotating antenna cause the path length between the Ka-band antenna feed horn and the stationary targets to change from pulse to pulse, which artificially changes the target range during the 2 s dwell producing a Doppler shift. Note that insects are hard targets and produce narrow peaks in Ka-band spectra with non-zero velocities as shown in Luke et al. (2008). Thus, insect clutter can be removed from spectra by identifying large drops in power between neighbouring velocity bins and then interpolating across these narrow peaks.
The second method developed in this study identifies multiple peaks and calculates high-order moments for each single peak, sub-peak, and separate peak. Identifying multiple peaks is a process of identifying the integration limits that are used in the high-order moment calculations. The high-order moments included velocity spectrum skewness and kurtosis. This work found that spectrum skewness from the single spectral peak is a good indicator of whether two hydrometeor populations are present in the radar pulse volume. Yet, the sub-peak and separate peaks are symmetric with skewness estimates near zero. This suggests a two-step process of using single-peak velocity skewness as an indicator of possible multiple peaks and multiple-peak moments for quantitative studies.
The third method developed in this study is shifting individual 2 s spectra during 15 s intervals to the mean velocity before averaging the spectra. This shift-then-average method improves the velocity spectrum skewness estimates by removing the spectrum turbulent broadening effects at the 2 s temporal scale.
Original raw KAZR spectra are available on the DOE ARM
archive (
The MATLAB code used to generate the Oliktok Point moments
stored on the DOE ARM archive is available in the Supplement and from
GitHub (
This appendix defines the equations used to calculate high-order spectral
moments. The spectral moments are calculated for each recorded radial
velocity spectrum
Noise statistics are determined after sorting the spectrum magnitudes using
the method described in Hildebrand and Sekhon (1974). Essentially, this
method sorts all spectrum values and then determines a threshold that divides
the data into either noise-only data or noise-plus-signal data. Using the
noise-only data, three noise statistics are defined: mean noise
As discussed in the section 5, identifying multiple spectral peaks is a
procedure to identify integration limits for each single peak, sub-peak, and
separate peak. After identifying the left and right indices,
Noise power:
A 3
CRW: clutter filter and multiple-peak code development; MM, JCH, and GB: testing and evaluating products.
The authors declare that they have no conflict of interest.
This research received funding through the DOE Atmospheric System Research (ASR) program under awards DE-SC0013306 and DE-SC0014294. Additionally, this research was supported by the Physical Sciences Division of the NOAA Earth System Research Laboratory. We recognize and appreciate the work of field technicians, especially radar technician Todd Houchens of Sandia National Laboratory, deployed year-round to Oliktok Point and tasked with keeping these instruments running in extremely harsh and challenging weather conditions. This research was supported by the Office of Biological and Environmental Research of the US Department of Energy as part of the Atmospheric Radiation Measurement (ARM) Climate Research Facility, an Office of Science scientific user facility. Edited by: Murray Hamilton Reviewed by: two anonymous referees