Vertical Air Motion Retrieved from Dual-Frequency Profiler Observations

Christopher R. Williams Cooperative Institute for Research in Environmental Sciences, University of Colorado, and NOAA/Earth System Research Laboratory, Boulder, Colorado

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Abstract

The 50-MHz profiler operating near Darwin, Northwest Territory, Australia, is sensitive to both turbulent clear-air (Bragg) and hydrometeor (Rayleigh) scattering processes. Below the radar bright band, the two scattering peaks are observed as two well-separated peaks in the Doppler velocity spectra. The Bragg scattering peak corresponds to the vertical air motion and the Rayleigh scattering peak corresponds to the hydrometeor motion. Within the radar bright band, the Rayleigh scattering peak intensity increases and the downward velocity decreases causing the hydrometeor peak to overlap or merge with the air motion peak. If the overlap of the two peaks is not taken into account, then the vertical air motion estimate will be biased downward. This study describes a filtering procedure that identifies and removes the downward bias in vertical air motions caused by hydrometeor contamination. This procedure uses a second collocated profiler sensitive to hydrometeor motion to identify contamination in the 50-MHz profiler spectra. When applied to four rain events during the Tropical Warm Pool-International Cloud Experiment (TPW-ICE), this dual-frequency filtering method showed that approximately 50% of the single-frequency method vertical air motion estimates within the radar bright band were biased downward due to hydrometeor contamination.

Corresponding author address: Christopher R. Williams, 216 UCB, University of Colorado, CIRES, Boulder, CO 80309-0216. E-mail: christopher.williams@colorado.edu

Abstract

The 50-MHz profiler operating near Darwin, Northwest Territory, Australia, is sensitive to both turbulent clear-air (Bragg) and hydrometeor (Rayleigh) scattering processes. Below the radar bright band, the two scattering peaks are observed as two well-separated peaks in the Doppler velocity spectra. The Bragg scattering peak corresponds to the vertical air motion and the Rayleigh scattering peak corresponds to the hydrometeor motion. Within the radar bright band, the Rayleigh scattering peak intensity increases and the downward velocity decreases causing the hydrometeor peak to overlap or merge with the air motion peak. If the overlap of the two peaks is not taken into account, then the vertical air motion estimate will be biased downward. This study describes a filtering procedure that identifies and removes the downward bias in vertical air motions caused by hydrometeor contamination. This procedure uses a second collocated profiler sensitive to hydrometeor motion to identify contamination in the 50-MHz profiler spectra. When applied to four rain events during the Tropical Warm Pool-International Cloud Experiment (TPW-ICE), this dual-frequency filtering method showed that approximately 50% of the single-frequency method vertical air motion estimates within the radar bright band were biased downward due to hydrometeor contamination.

Corresponding author address: Christopher R. Williams, 216 UCB, University of Colorado, CIRES, Boulder, CO 80309-0216. E-mail: christopher.williams@colorado.edu

1. Introduction

Wind profilers operating at 50 MHz are able to simultaneously observe the motion of hydrometeors and the ambient air motion (Fukao et al. 1985). These radars detect backscattered energy from hydrometeors following Rayleigh scattering theory (Doviak and Zrnic 1993; Rogers et al. 1993). These radars also detect ambient air motion surrounding the hydrometeors from energy being backscattered by gradients of temperature and humidity following Bragg scattering theory (Balsley and Gage 1982; Gage 1990). The ability of 50-MHz profilers to detect both scattering processes enables simultaneous estimation of vertical air motion and raindrop size distributions (DSDs) (Wakasugi et al. 1986, 1987).

One problem with a radar sensitive to both Bragg and Rayleigh scattering processes is the potential for misinterpretation of the observations. If the two signals are not properly identified in the raw observations, then vertical air motion estimates will be biased downward because of contamination from downward-falling hydrometeors. Standard wind profiling processing techniques do not attempt to isolate the two scattering signals (Carter et al. 1995). The purpose of this work is to describe a robust method of using observations from a second radar operating at a different frequency to identify and remove the Rayleigh scattering signal before estimating the vertical air motion.

The standard wind profiling processing technique is described in Carter et al. (1995) and is based on the profiler online processing (POP) routine. This single-frequency method estimates the spectral characteristics of each original spectrum. Specifically, the POP routine estimates the spectrum noise level, the spectrum signal start and end integration points, and the first three moments—power, mean reflectivity-weighted Doppler velocity, and the spectrum width (equal to twice the spectrum standard deviation). The mean Doppler velocity corresponds to the vertical air motion. In contrast, the dual-frequency method prefilters the 50-MHz profiler spectra before using the POP routine to estimate the spectrum moments. The prefiltering uses observations from a second collocated profiler sensitive to hydrometeors to remove the downward hydrometeor motion contaminating the 50-MHz profiler spectra.

The two vertical air motion estimates are then compared to determine if they are greater than the profiler measurement uncertainty. If the difference is less than the measurement uncertainty, then both estimates are valid and either estimate can be retained. If the difference is greater than the measurement uncertainty, then the dual-frequency estimate is retained along with the estimated measurement uncertainty.

Putting the proposed dual-frequency method into context with previous work, the dual-frequency method is a spectral analysis technique identifying and separating multiple signals contained in Doppler spectra. Doppler spectra analysis has enjoyed several decades of research, including the pioneering work of fitting individual cloud droplet spectra to multipeaked millimeter-wavelength profiler spectra (Gossard 1988), and the more recent work of multi-Gaussian feature estimation in 50-MHz profiler spectra (Boyer et al. 2003) or the partitioning of cloud particle liquid and ice phases in 35-GHz cloud profiler spectra (Rambukkange et al. 2010). These highlighted methods use individual spectra to identify multiple physical processes while the dual-frequency method uses two spectra from two radars sensitive to different scattering processes to identify multiple physical processes.

Additional profiler quality control procedures can be performed either before or after applying the dual-frequency method. Before estimating the Doppler velocity spectra, either time series wavelet transforms (Jordan et al. 1997) or Gabor frame expansions (Lehmann and Teschke 2008; Lehmann 2012) can be applied to the complex voltages to remove intermittent nonatmospheric signals. After estimating the dual-frequency method moments, multiple-peak picking routines (Griesser and Richner 1998; Bianco and Wilczak 2002) can be used to identify atmospheric signals extending across neighboring observations in time and height.

The data used to develop the dual-frequency method are described in section 2. Section 3 describes the dual-frequency method. A profiler simulator and a Monte Carlo simulation (MCS) are briefly described in section 4 because they determine the mean Doppler velocity measurement uncertainty needed to evaluate the dual-frequency method. Comparisons and results of the two methods are shown in section 5 and conclusions are stated in section 6.

2. Datasets

Four rain events from 19 to 23 January 2006 occurred over the 50- and 920-MHz wind profilers located near Darwin, Northwest Territory, Australia, during the Tropical Warm Pool-International Cloud Experiment (TWP-ICE; May et al. 2008). These two wind profilers have been used in numerous studies. Rajopadhyaya et al. (1998, 1999) describe their general characteristics and Table 1 lists their TWP-ICE operating parameters.

Table 1.

The 50- and 920-MHz profiler operating parameters during TWP-ICE.

Table 1.

To ensure consistent temporal sampling between the 50- and 920-MHz profilers, both profilers were synchronized to begin their vertical beam observations every 2 min. Because the dual-frequency method will combine observations from both radars, the finer-resolution 920-MHz profiler observations were reduced to match the coarser-resolution 50-MHz profiler data. Specifically, three consecutive 13-s profiles and five consecutive 105-m vertical range gates (for a total of fifteen 920-MHz profiler spectra) were averaged together to match the 50-MHz profiler 41-s dwell by 495-m pulse volume length.

Figure 1 shows 50- and 920-MHz profiler spectra profiles during stratiform rain observed at 0310 UTC 20 January 2006. Colors represent reflectivity power spectral density in decibels {}, where is the reflectivity (mm6 m−3) at each Doppler velocity (m s−1) with resolution (m s−1). Even though the two radars have been cross calibrated (Williams et al. 2005), the colors at each pixel are different due to different Doppler velocity resolutions ().

Fig. 1.
Fig. 1.

The reflectivity spectral density (dB) observed during stratiform rain at 0310 UTC 20 Jan 2006 near Darwin. Spectra from the (a) 50-MHz profiler and (b) 920-MHz profilers are shown. The parameters retrieved from the single- (blue) and dual-frequency (black) methods are indicated, as are the mean Doppler velocity (squares), ±one spectrum width (horizontal lines), and integration limits (pluses) used to determine the spectrum moments. Color scale shows relative intensity (dB).

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/JTECH-D-11-00176.1

Also shown in both panels of Fig. 1 are the POP-derived mean Doppler velocity (blue squares), plus-and-minus one spectrum width SW (blue lines), and integration limits (blue pluses) for each 50-MHz profiler spectrum. No 920-MHz profiler information is used in estimating the spectral moments shown in blue. Below 4 km, POP identifies the Bragg scattering signal near-zero Doppler velocity. Between 4 and 5 km, POP identifies the downward-moving Rayleigh scattering signal as the single, dominant peak. Between 5.25 and 8 km, POP integration limits include both Bragg and Rayleigh scattering signals. This can be seen in the right panel where the blue integration limits include hydrometeor motion. It is interesting to note that the 50-MHz profiler Bragg scattering intensity decreases between 4 and 5.5 km, as previously seen by Rao et al. (1999) and McDonald et al. (2006), increasing the potential for hydrometeor contamination and downwardly biased vertical air motions.

Figure 2 shows the spectra from both radars during convective rain observed at 0000 UTC 20 January 2006. The POP spectral moments and integration limits derived from the 50-MHz profiler spectra are shown in both panels with blue symbols. Because the downward summation limits includes all of the 920-MHz profiler spectra, these downward summation limits include both Bragg and Rayleigh scattering signals in the 50-MHz profiler spectra. Below 4 km, minimum power is observed between the Bragg and Rayleigh scattering signals in the 50-MHz profiler spectra (Fig. 2a). However, only the Rayleigh scattering signal is observed in the 920-MHz profiler spectra (Fig. 2b).

Fig. 2.
Fig. 2.

As in Fig. 1, except during convective rain at 0000 UTC.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/JTECH-D-11-00176.1

Figure 3 shows spectra from stratiform and convective rain profiles to illustrate the Bragg and Rayleigh scattering observed by both profilers. Figure 3a shows spectra taken from the middle of the radar bright band during stratiform rain (at 4.6 km from Fig. 1). Two separate peaks in the 50-MHz profiler spectra (thick line) can be identified above the 50-MHz profiler noise level (thick dashed line). The left-hand peak spans from ~1 m s−1 upward to ~1 m s−1 downward and corresponds to the Bragg scattering peak. The right-hand peak spans from ~1.5 to ~10 m s−1 downward, corresponding to the Rayleigh scattering. The square symbols superimposed on the 50-MHz profiler spectra designate the POP-derived integration limits. As described in Carter et al. (1995), the integration limits are determined by finding the largest magnitude spectral point and working down the spectrum in both directions toward the noise level. The integration limit is the last spectral point before crossing the noise level. From Fig. 3a, we can see that POP has identified the Rayleigh scattering portion of the 50-MHz profiler spectrum. The 920-MHz profiler spectrum (thin line) for this height shows one broad peak corresponding to the hydrometeor Rayleigh scattering but does not detect any Bragg scattering near zero velocity.

Fig. 3.
Fig. 3.

Selected 50- and 920-MHz profiler spectra from profiles shown in Figs. 1 and 2. (a) Spectra in the radar bright band from stratiform rain at 4.6 km and (b) spectra in convective rain at 3.0 km. Each panel shows 50-MHz profiler spectra (thick line), 50-MHz profiler noise level (thick dash), 920-MHz profiler spectra (thin line), and 920-MHz profiler noise level (thin dash). The integration limits for the single-frequency method are indicated (squares) on the 50-MHz profiler spectra.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/JTECH-D-11-00176.1

Figure 3b shows spectra at 3.0 km during convective rain (Fig. 2). The 50-MHz profiler spectra (thick line) show two broad peaks where the minimum between them does not drop below the noise level (thick dashed line). Thus, the POP integration limits span from ~3 m s−1 upward to ~15 m s−1 downward. The 920-MHz profiler spectrum (thin line) confirms that the right-hand peak is due to Rayleigh scattering. The left-hand peak is due to Bragg scattering.

The example spectra shown in Fig. 3 highlight that the POP routines applied to 50-MHz profiler spectra during precipitation do not necessarily provide accurate estimates of the vertical air motion. As shown in Fig. 3a, the POP integration limits could contain just Rayleigh scattering. Or, as shown in Fig. 3b, the POP integration limits could contain a combination of Bragg and Rayleigh scattering. Therefore, if the objective is to estimate vertical air motion during precipitation, the 50-MHz profiler spectra need to be preprocessed before applying the POP routines to remove the downward contamination caused by the Rayleigh scattering signal. The next section describes how the 920-MHz profiler observations are used to suppress the Rayleigh scattering signal in the 50-MHz profiler spectra before applying the POP routines.

3. Dual-frequency method

The dual-frequency method uses three steps to remove the Rayleigh scattering signal in each 50-MHz profiler spectrum. First, the 920-MHz profiler spectrum is used to construct a unitless weighting function that spans from 1 (pure Bragg) to 0 (pure Rayleigh). Second, the weighting function filters the original 50-MHz profiler spectrum to suppress Rayleigh scattering signals. And third, the filtered 50-MHz profiler spectrum is processed using the standard POP routine.

a. Constructing a weighting function

Constructing a weighting function that spans from 1 (pure Bragg) to 0 (pure Rayleigh) using a radar sensitive to Rayleigh scattering requires that first an inverse function be generated. Therefore, the shape of the 920-MHz profiler spectrum is used to construct a Rayleigh scattering probability function that ranges from 0 (no Rayleigh scattering) to 1 (high probability of Rayleigh scattering). Because the 920-MHz profiler mean Doppler velocity is only due to Rayleigh scattering, is set to 1 for all Doppler velocities equal to or more downward than . For the Bragg scattering range, is set to 0 for all Doppler velocities more upward than the POP-derived upward integration limit. Transitioning from 0 to 1 follows a normalized cumulative power distribution. Specifically, at each Doppler velocity is the ratio of accumulated power over the total accumulated power up to . The normalized cumulative power distribution is a robust calculation that smoothly transitions from 0 to 1 even though the spectrum may have local fluctuations, as seen for upward velocities in Fig. 3.

After estimating , the weighting function is related to . To suppress the 50-MHz profiler Rayleigh scattering signal by 20 or 40 dB, the weighting function is scaled by a power of 10, . Figures 4c,d show the weighting functions for the stratiform and convective spectra previously shown in Fig. 3. The weighting function is equal to 1 (or 0 dB; thick solid line) for upward Doppler velocities and then drops in magnitude as the velocity becomes more downward. For reference, the 920-MHz profiler spectra are shown in Figs. 4c,d (offset by −50 dB) with POP-derived mean Doppler velocities (asterisk).

Fig. 4.
Fig. 4.

Dual-frequency method filtered 50-MHz profiler spectra and weighting functions for the selected spectra shown in Fig. 3. (a),(c) Stratiform rain spectra at 4.6 km, and (b),(d) convective rain spectra at 3.0 km. Original (thin line) and filtered (thick line) 50-MHz profiler spectra are shown in (a) and (b). Single- (squares) and dual-frequency (circles) integration limits are shown on the 50-MHz profiler spectra. Bragg (thick line) and Rayleigh (thick dash) weighting functions (dB) are shown in (c) and (d). The 920-MHz profiler spectra are shown in (c) and (d) after shifting downward 50 dB for clarity (thin line).

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/JTECH-D-11-00176.1

b. Prefiltering the original 50-MHz profiler spectra

The Bragg weighting function is designed to retain the Bragg scattering signal and suppress the Rayleigh scattering signal by 20–40 dB. After interpolating the weighting function onto the 50-MHz profiler velocity resolution, the filtered 50-MHz profiler spectra is estimated from the original spectra using .

Figures 4a,b show the original 50-MHz profiler spectra (thin lines) and the filtered spectra (thick lines) for the stratiform and convective spectra previously shown in Fig. 3. Note that the Rayleigh scattering portion of the spectrum is substantially reduced and the filtered spectrum magnitude drops below the mean noise level at smaller downward velocities.

Note that the dual-frequency prefiltering method can be applied to any two collocated profilers operating at different frequencies as long as one radar is sensitive to just Rayleigh scattering and the other is sensitive to both Bragg and Rayleigh scattering. For example, the method could be applied to the 449-MHz and 2.8-GHz profilers deployed in Oklahoma for the 6-week Midlatitude Continental Convective Clouds Experiment (MC3E). Sensitivity tests will be needed for each pair of radars to account for differences in radar performance (e.g., operating frequency, transmitted power, beam widths, and etc.) in order to determine the weighting function transition from 0 to 1.

c. Applying the POP moment estimating routine

New integration limits are determined for each spectrum by passing the filtered 50-MHz profiler spectra through the POP routine. The new integration limits are shown in Figs. 4a,b with circles on the filtered 50-MHz profiler spectra. Note that this dual-frequency method does not require calibrated spectra, but rather, uses the relative contribution from one radar to mask a signal in another radar.

4. Measurement uncertainties

If the difference between the single- and dual-frequency method vertical air motions is greater than an objective measurement uncertainty, then the single-frequency method estimate could be flagged as being potentially biased downward by hydrometeor contamination. One way to determine the objective measurement uncertainty is to develop a profiler simulator that produces realistic simulated Doppler velocity spectra and to construct a Monte Carlo simulation that would estimate the statistics from multiple realistic simulated spectra.

a. Profiler simulator

The profiler simulator takes into account all hardware and signal processing parameters to generate realistic Doppler velocity power spectra to investigate measurement uncertainties. In general, an ideal, noiseless Doppler velocity spectrum is the input to the profiler simulator. The spectrum is broadened because of the finite antenna beamwidth and noise is added at each spectral point following the method described in Zrnić (1975). The spectrum is converted into a time series of heterodyne I and Q voltages, with each sample separated in time by the interpulse period. The I and Q voltages are processed using the same signal processing routines used in a profiler to produce simulated Doppler velocity spectra and include the following: coherent integration, Hanning windowing, fast Fourier transform (FFT) processing, and incoherent integration. The spectral moments are estimated using the POP routine.

b. Monte Carlo simulation

A Monte Carlo simulation (MCS) is used to estimate the mean Doppler velocity measurement uncertainty. For each ideal, noiseless Gaussian-shaped spectrum, the profiler simulator is run 1000 times to generate 1000 mean Doppler velocities. The mean difference from the expected mean Doppler velocity represents the measurement bias, and the standard deviation of the simulated 1000 mean Doppler velocities represents the measurement uncertainty.

The MCS was run using the TWP-ICE 50-MHz profiler operating parameters (see Table 1) and the Gaussian-shaped spectrum had signal-to-noise ratios () and spectrum widths ranging from −20 to 60 dB and from 0.5 to 10 m s−1, respectively. For each simulation, the initial mean Doppler velocity was randomly selected between −1 and +1 m s−1 to avoid quantization errors caused by using the same initial mean velocity. Figure 5a shows a near-zero mean velocity bias for all valid MCSs as a function of and spectrum width. Figure 5b shows the mean Doppler velocity standard deviation, also called the measurement uncertainty, as a function of and spectrum width. For greater than approximately 20 dB, the velocity uncertainty is independent of and depends only on the spectrum width. This dependence is due to noise fluctuations having a greater influence on wide spectra than on narrow spectra. Figure 5b shows that as decreases, noise fluctuations cause an increase in the velocity uncertainty as documented by May and Strauch (1989).

Fig. 5.
Fig. 5.

The (a) mean velocity measurement bias and (b) measurement uncertainty derived from a profiler simulator and a Monte Carlo simulation as a function of signal-to-noise ratio (dB; ) and for selected spectrum width values.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/JTECH-D-11-00176.1

For the TWP-ICE profiler configuration, Fig. 5b indicates that as long as the is greater than a spectrum width–dependent threshold, the 50-MHz profiler velocity uncertainty ranged from approximately 0.05 to 0.25 m s−1. The results shown in Fig. 5b are plotted in Fig. 6 as a lookup table so that each and spectrum width pair corresponds to one mean velocity measurement uncertainty.

Fig. 6.
Fig. 6.

The mean velocity measurement uncertainty as a function of signal-to-noise ratio (dB; ) and spectrum width. Measurement uncertainties have units of m s−1.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/JTECH-D-11-00176.1

5. Improved vertical air motions

The precipitating profiles collected by the 920-MHz profiler during the four rain events from 19 to 23 January 2006 were classified as either stratiform or convective using the objective classification based on the procedure described in Williams et al. (1995). The classification procedure performed on each 39-s profile identifies stratiform rain by an increase in Doppler velocity with decreasing height as a result of ice and snow melting into rain. Figure 7a shows the percent occurrence of valid 50-MHz profiler spectra at each height for the 1172 profiles classified as stratiform rain. The percent occurrence is 100% at low heights and drops off above 7 km.

Fig. 7.
Fig. 7.

Statistics from 1172 stratiform rain profiles observed between 19 and 23 Jan 2006. (a) The number of original observations (circles) and conditional observations (squares) at each range, expressed in percent occurrence, are shown. The (b) single- and (c) dual-frequency mean velocity frequency distributions are shown using box-whisker symbols, which identify the 10th, 25th, 50th, 75th, and 90th percentiles. Observations with mean velocity differences (single-frequency minus dual-frequency methods) greater than the measurement uncertainty are tagged as conditional observations, and (d) the mean velocity difference frequency distributions are shown using box–whisker symbols.

Citation: Journal of Atmospheric and Oceanic Technology 29, 10; 10.1175/JTECH-D-11-00176.1

The mean Doppler velocity frequency distributions derived from the single-frequency method (standard POP processing) are shown in Fig. 7b using 10th–25th–50th–75th–90th percentile box–whisker diagrams. The distribution of single-frequency mean velocities is narrow both below 4 km and above 6 km. Between 4 and 6 km, however, the distribution of single-frequency mean velocities is very broad. At 5 km, the median Doppler velocity is almost 2 m s−1 downward. Figure 7c shows narrow dual-frequency mean Doppler velocity frequency distributions at all heights indicating consistent Bragg scattering signal retrievals, including through the radar bright band.

The difference between the single- and dual-frequency mean velocities is calculated for each profile and range gate. If the velocity difference was greater than the measurement uncertainty estimated from Fig. 6, then that profile range gate was tagged as a “conditional observation” and retained for further analysis. Figure 7d shows the mean velocity difference frequency distribution for the conditional observations. The bias is downward in all heights. The number of conditional observations varied with height. Relative to the 1172 total stratiform profiles, the percentage of observations tagged as conditional observations is denoted with squares in Fig. 7a. Throughout the radar brightband height, from 4.5 to 6 km, over 50% of the observations were tagged as conditional observations and had downward vertical air motion biases (at 5 km, over 75% of the observations were tagged as conditional observations). Between 4.5 and 5 km, the median downward biases were greater than 2 m s−1.

6. Conclusions

During precipitation, a 50-MHz profiler can simultaneously detect both vertical air motion and precipitation motion in the Doppler velocity power spectra. During stratiform rain and within the radar bright band, the precipitation signal has a similar magnitude and sometimes even a larger magnitude than the air motion signal. This similarity in signal magnitude leads to misinterpretation of the observations by the standard wind profiler processing routine. The standard single-frequency processing method either identifies just the precipitation signal or a combination of the two signals. Consequently, the vertical air motions retrieved from this single-frequency method are biased downward because of the hydrometeor motion contamination.

To address downwardly biased vertical air motion estimates, a dual-frequency method was developed that uses a collocated 920-MHz profiler to identify and filter the hydrometeor motion in the 50-MHz profiler Doppler velocity spectra before estimating the vertical air motion. The difference between the single- and dual-frequency method mean velocities was compared against an objective mean velocity measurement uncertainty. Using observations from four rain events collected during the Tropical Warm Pool-International Cloud Experiment (TWP-ICE), over 50% of the single-frequency method vertical air motions in the stratiform radar bright band were determined to be downwardly biased due to hydrometeor contamination. At 4.5 km, the median downward bias was greater than 2 m s−1.

A profiler simulator and a Monte Carlo simulation (MCS) were constructed to estimate mean Doppler velocity measurement uncertainties. Ideal, noiseless spectra were defined as the input to the profiler simulator and realistic noise was added to each spectrum. The input spectrum was processed 1000 times by the profiler simulator to yield a distribution of simulated mean velocities estimates. The velocity spread represented the velocity measurement uncertainty and was used to determine if the single- and dual-frequency methods produced different mean velocity estimates.

Results from this study will lead to improved vertical air motions retrieved from 50-MHz profiler observations. This analysis method can be applied to other profiler frequency combinations [e.g., 449-MHz and 2.8-GHz profilers deployed in support of the 6-week Midlatitude Continental Convective Clouds Experiment (MC3E)]. Also, the profiler simulator and MCS will enable measurement uncertainties to be estimated for each vertical air motion estimate. Therefore, in the future, profiler-derived vertical air motion and its measurement uncertainty can provide the atmospheric science community with the means to study the dynamics and microphysics of precipitating cloud systems.

Acknowledgments

Support for this work was provided by the NASA Precipitation Measurement Mission (PMM) Grant NNX10AM54G.

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  • Fig. 1.

    The reflectivity spectral density (dB) observed during stratiform rain at 0310 UTC 20 Jan 2006 near Darwin. Spectra from the (a) 50-MHz profiler and (b) 920-MHz profilers are shown. The parameters retrieved from the single- (blue) and dual-frequency (black) methods are indicated, as are the mean Doppler velocity (squares), ±one spectrum width (horizontal lines), and integration limits (pluses) used to determine the spectrum moments. Color scale shows relative intensity (dB).

  • Fig. 2.

    As in Fig. 1, except during convective rain at 0000 UTC.

  • Fig. 3.

    Selected 50- and 920-MHz profiler spectra from profiles shown in Figs. 1 and 2. (a) Spectra in the radar bright band from stratiform rain at 4.6 km and (b) spectra in convective rain at 3.0 km. Each panel shows 50-MHz profiler spectra (thick line), 50-MHz profiler noise level (thick dash), 920-MHz profiler spectra (thin line), and 920-MHz profiler noise level (thin dash). The integration limits for the single-frequency method are indicated (squares) on the 50-MHz profiler spectra.

  • Fig. 4.

    Dual-frequency method filtered 50-MHz profiler spectra and weighting functions for the selected spectra shown in Fig. 3. (a),(c) Stratiform rain spectra at 4.6 km, and (b),(d) convective rain spectra at 3.0 km. Original (thin line) and filtered (thick line) 50-MHz profiler spectra are shown in (a) and (b). Single- (squares) and dual-frequency (circles) integration limits are shown on the 50-MHz profiler spectra. Bragg (thick line) and Rayleigh (thick dash) weighting functions (dB) are shown in (c) and (d). The 920-MHz profiler spectra are shown in (c) and (d) after shifting downward 50 dB for clarity (thin line).

  • Fig. 5.

    The (a) mean velocity measurement bias and (b) measurement uncertainty derived from a profiler simulator and a Monte Carlo simulation as a function of signal-to-noise ratio (dB; ) and for selected spectrum width values.

  • Fig. 6.

    The mean velocity measurement uncertainty as a function of signal-to-noise ratio (dB; ) and spectrum width. Measurement uncertainties have units of m s−1.

  • Fig. 7.

    Statistics from 1172 stratiform rain profiles observed between 19 and 23 Jan 2006. (a) The number of original observations (circles) and conditional observations (squares) at each range, expressed in percent occurrence, are shown. The (b) single- and (c) dual-frequency mean velocity frequency distributions are shown using box-whisker symbols, which identify the 10th, 25th, 50th, 75th, and 90th percentiles. Observations with mean velocity differences (single-frequency minus dual-frequency methods) greater than the measurement uncertainty are tagged as conditional observations, and (d) the mean velocity difference frequency distributions are shown using box–whisker symbols.

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