1. Introduction
Accurate measurements of precipitation are essential in our efforts to understand the connection between atmospheric dynamics and storm microphysics. Traditionally, the most identifiable precipitation measurements from scanning weather radar systems are estimates of the rainfall rate and surface rainfall accumulation. Retrievals of these quantities are undeniably challenging as a consequence of scattering (dependency on the sixth power of the raindrop diameter), radar measurement geometry, and several known microphysical limitations (e.g., Sanchez-Diezma et al. 2000; Ryzhkov 2007; Doviak and Zrnić 1993, section 8.4). For a number of applications (e.g., climatology, hydrology), modest instantaneous retrieval errors are acceptable if no long-term bias is introduced. However, detailed process-oriented microphysical studies as well as appropriate characterization of scanning radar measurements (e.g., uncertainty in radar estimates of precipitation) necessitates accurate, high-resolution (space/time), and simultaneous measurements of raindrop size distributions (DSDs), vertical air motions, turbulence, and environmental parameters.
In a vertically pointing mode, radars provide high-resolution measurements of the vertical structure of precipitation and the recorded Doppler spectra offer the distribution of the radar return power as a function of the observed Doppler velocity. Several methods have been proposed for the inversion between a recorded Doppler spectrum and the retrieval of a DSD (or cloud drop distributions; e.g., Battan 1964; Atlas et al. 1973; Gossard et al. 1997; Babb et al. 2000; Kollias et al. 2001, 2002). However, uncertainties in the inversion introduced by the contributions of the vertical air motion to the observed Doppler velocity and Doppler spectra smearing effects as a consequence of turbulence and averaging limit the accuracy of these methods (e.g., Atlas et al. 1973).
Recent studies and the launch of CloudSat that carries the first 94-GHz (λ = 3.2 mm, W band) radar in space have demonstrated the potential value of traditional “cloud” radar systems in precipitation (e.g., Stephens et al. 2002; Kollias et al. 2002, 2007a; Matrosov 2005; Haynes et al. 2009; Ellis et al. 2009). Despite fundamental limitations of radar measurements at shorter wavelengths (notably, attenuation in rain), high-resolution cloud radars operating at 94 GHz can help to overcome the deadlock introduced by radar Doppler spectra-based inversion methods for retrieval of the DSD because of the effects of the vertical air motion. Following a technique first introduced by Lhermitte (1988), it is possible to estimate the Doppler shift in response to the vertical air motion and relate the “quiet air” Doppler velocities in the spectrum to hydrometeor fall velocities. The retrieval technique (briefly described here) capitalizes on the W-band backscattering cross section as a function of raindrop diameter that oscillates because of non-Rayleigh resonance effects (Mie 1908). The oscillations occur within typical raindrop sizes and, under precipitating conditions, are reflected as patterns of maxima and minima in the observed Doppler spectrum. Since raindrop sizes can be reliably mapped to the associated locations of maxima and minima in the observed Doppler spectrum, accurate retrievals of vertical motion are possible. Previous study has suggested there is no rainfall-rate threshold for application of this technique, rather a minimum raindrop size threshold (e.g., Kollias et al. 2002). Although severe attenuation in rain eventually limits the usefulness of W-band radar (e.g., extinction of the signal), velocity retrievals are not immediately tied to the magnitude (spectral density) of the received signal and therefore viable provided relative minima and maxima are observed.
Well-matched observations of the vertical air motions, raindrop sizes, and their fall speeds in two dimensions (time and height) are rare. To date, this resonance-based technique has met with limited application in studies of shallow warm rain (Kollias et al. 1999, 2001), convective (Kollias et al. 2003), and stratiform rain (Firda et al. 1999; Kollias et al. 2002), often in the context of air motion retrievals and simulation-based efforts. In addition to air motion retrievals, this study capitalizes on the accuracy of velocity retrievals for simultaneous retrieval of bulk slope parameter Λ (cm−1) of an exponential DSD. Emphasis has been placed on automated retrieval methods to explore an extended, real-word characterization of W-band retrievals that have not been previously offered in the literature. Establishing connections between W-band radar-based inversions and surface disdrometer platforms are necessary, as all instrument retrievals are impacted by sampling and processing shortcomings (e.g., as in Campos and Zawadzki 2000).
Retrievals in this study utilize the W-band cloud radar (WACR) platform located at the Southern Great Plains (SGP) climate research facility of the Department of Energy’s Atmospheric Radiation Measurement (ARM) program in Lamont, Oklahoma (e.g., Kollias et al. 2007b). These retrievals are drawn from multiple events collected during a climatological peak of convective, warm season precipitation for the SGP region. The SGP central research facility and surrounding north-central Oklahoma region are heavily instrumented and include operational S-band Next Generation Weather Radar (NEXRAD) Weather Surveillance Radar 1988-Doppler (WSR-88D; KVNX) oversight, simultaneous 35-GHz millimeter wave cloud radar (MMCR) measurements, and collocated disdrometer observations available at 1-min temporal resolution for cross-validation of radar-based DSD slope retrievals. Results and discussion for the cumulative performance and a detailed case study for a widespread precipitation event follow a summary of the available instrumentation and formal outline of the automated retrieval techniques.
2. Instrumentation
a. W-band cloud radar
The W-band ARM cloud radar is the primary instrument used for precipitation retrievals in this study. A 95-GHz vertically pointing single antenna Doppler radar is housed at the ARM SGP central facility in Lamont, Oklahoma. At this very short wavelength (λ ≈ 3.2 mm), the radar is highly sensitive to small liquid droplets and ice crystals (−40 dBZ at 2 km, 1-s dwell).
The WACR utilizes a high pulse repetition frequency (10 kHz) that yields an unambiguous Doppler velocity window of ±7.885 m s−1. Current spatial and temporal resolution of the radar data is 43 m vertical and 4.28 s. The 4.28-s temporal resolution accounts for 2.14 s of alternate scanning modes and a 2.14-s temporal scanning window of interest that corresponds to a spectral average of 80 individual 256-point fast Fourier transform (FFT) Doppler spectra. The 2-ft antenna of the WACR provides a narrow beamwidth (0.5°) making the radar suitable for the sampling of small atmospheric volumes at close distances in rain.
b. Supplemental surface instrumentation
The heavily instrumented SGP central facility and surrounding Oklahoma region offers several options for detailed analysis of precipitation and validation of radar retrievals. A Joss and Waldvogel disdrometer (Model RD-80, manufactured by Disdromet, Inc.; Joss and Waldvogel 1967) is collocated with the WACR and serves as the primary source of validation for radar-based DSD slope retrievals. Estimates for the slope Λ and intercept N0 parameter of an assumed exponential DSD (e.g., Marshall and Palmer 1948) are routinely calculated by this system at 1-min accumulation windows.
Complementary radar observations at two wavelengths less attenuated in precipitation are available from the 35-GHz (Ka band) MMCR (λ ≈ 8 mm) collocated with the WACR and the nearby 3-GHz (S band) operational NEXRAD WSR-88D (λ ≈ 10 cm) located at Vance AFB (KVNX, approximately 60 km from the ARM field site). A surface meteorological station and routine atmospheric soundings at the ARM field site provide regular measurements of state variables including temperature, pressure, and rainfall accumulation/rate. The ARM suite of instruments also includes a ceilometer and lidar systems that provide valuable information on the location of cloud base.
3. Retrieval methodology
Resonance effects on the observed W-band Doppler spectrum open several opportunities for the detailed study of precipitation (e.g., Lhermitte 1988). Several studies outline W-band precipitation retrievals (as in section 3a); therefore, in this section emphasis is on the practical implementation and accuracy limitations for long-term automation on the ARM WACR system.
a. Retrieval of precipitation parameters at W band
A combination of characteristics from observed Doppler spectra is useful to retrieve DSD parameters in precipitation. Slope and shape parameter retrievals from a functional form DSD through inversions of (1) have been suggested at W band (e.g., Firda et al. 1999; Kollias et al. 2002). Previous work has been on the results of simulations, with less attention to extended surface validation and automated methods noting constraints in data volume and processing. Nevertheless, it is well-understood that Doppler spectra defined by (1) and associated resonance features also respond to bulk changes of N(D). Figure 1 contains theoretical curves following the expression in (1) with N(D) equal to a constant (dashed lines), the upper dashed curve corresponding to a larger value for N(D) = constant. As an example, for the theoretical curves where N(D) is held constant, spectral density is largely driven by the backscattering cross-section term in (1). Hence, in the simplest case, the location of the first minimum (DM ∼ 1.65 mm), as well as the first and second maxima/peaks (D1 ∼ 1.15 mm and D2 ∼ 2.25 mm, as in Fig. 1, respectively) are reasonably well known.
b. Automated retrievals of precipitation parameters using non-Rayleigh techniques
1) Spectral preprocessing and non-Rayleigh feature identification
WACR Doppler spectra undergo a spectral averaging of the 80 individual spectra collected over a 2-s window. Preprocessing is required to obtain smooth spectra for better identification of bulk spectral features including the primary minimum. For the Nyquist velocity of the WACR, basic velocity dealiasing is required for typical light/moderate precipitation observations. This is accomplished by shifting spectra such that the left edges of the principal peaks are spaced from the left edges of the FFT arrays by a small predetermined offset. We have selected 30 bins (∼1.8 m s−1) as an initial offset. Here, it is noted that the velocity of the principal peak left edge is also viable to determine a cursory starting estimate for the vertical air velocity and applicable for basic self-consistency purposes (assumes small droplets have negligible fall speeds).
After initial processing, a check of the spectral suitability for the techniques is performed. Specifically, resonance-based techniques necessitate the availability of drop sizes sufficiently larger than the diameter of the first non-Rayleigh minimum within the radar resolution volume so as to allow a relative minimum in the Doppler spectrum. In simple terms, one should expect the first resonance valley to be located to the right of the principal peak left edge VL, by the terminal fall velocity VT associated with that resonance drop size. Here, the simplest approach is a width-based screening that rejects all spectra with a principal peak width narrower from the left to right edge than the predicted terminal fall velocity.
Following this basic suitability screening, a second-order Gaussian continuous wavelet transform of scale eight is applied to all remaining spectra (as shown, e.g., in Fig. 2, dashed line).This serves as a bandpass filter suitably matched to the first minima. The continuous wavelet transform (CWT) has been extensively investigated as a tool for robust detection of relevant transient features, such as peaks and edges, within complicated, noisy signals (e.g., Mallat and Hwang 1992; Vetterli and Herley 1992). This method was selected since noisiness and the presence of additional, minor peaks, and valleys in the observed spectra could be confusing to other forms of automated detection.
The number of local minima found in the CWT output is counted. The principal peak left and right edges each produce one CWT output minimum of their own (as in Fig. 2). Thus, when only two local minima are found, no resonance valleys have been designated within the spectrum and no further processing is performed. If three or more local minima are found in the CWT output (as is the case in Fig. 5), the leftmost and rightmost minima are removed from further consideration, as they are presumed to belong to the principal peak left and right edges. On the remaining CWT output local minima, a test is performed to determine the minima that fall within a predetermined velocity acceptance window. In one implementation of the algorithm, the center position of this velocity acceptance window is offset from the principal peak left edge by an expected terminal fall velocity, VC = VL + VT. The width of this window sets a tolerance range within which the actual air velocity offset may be found. We have used a conservative ±70 bins value (or roughly ±4.0 m s−1) with success to mitigate large, instantaneous errors (>1 m s−1). The velocity acceptance window is adaptable; however, wider windows (e.g., allowing minima to be detected at values smaller than 4 m s−1) will increase the probability of incorrect feature detection, particularly when the liquid assumption is no longer valid. For example, melting snow mixed with liquid precipitation within the melting layer will often exhibit secondary peak/valleys of prominence at slower spectral fall velocities and techniques are generally not as straightforward or recommended well within a mixed-phase layer.
For all local CWT minima within the acceptance window, the lowest (i.e., strongest) is identified and the position is an estimate of the first resonance valley. This estimate can still deviate by several velocity bins from the position of the corresponding local minimum in the original Doppler spectrum. A further refinement is attempted by searching the original spectrum for a lower spectral density value within a small neighborhood (e.g., ±3 bins) surrounding the CWT valley velocity estimate (e.g., following Lhermitte 2002). Note it is possible that a spectrum contains no relative minima to the right edge of the spectrum. In these situations, retrievals are not attempted.
2) Spectral alignment (shifting) and additional considerations
Scattering computations from the T matrix approach (e.g., Mishchenko 2000) are used to calculate radar backscattering cross-section values specific for the 95-GHz WACR system. Backscattering cross-section computations depend on several factors including raindrop temperature and shape, as noted by several authors (e.g., Lhermitte 1988; Aydin and Lure 1991; Firda et al. 1999). Raindrop shapes following the axis ratio expression from Brandes et al. (2002) are used for calculations in this study.
Air density and T matrix scattering computations imply regular ingest of atmospheric state variables. Collocated ARM surface instrumentation and regular atmospheric radiosondes (launched at 6-h intervals) provide the necessary thermodynamic profiles and melting layer cutoffs. To improve temporal consistency, ARM merged sounding products (a blend of available ARM and other available radiosondes assimilated with surface observations and various short-term model output) are incorporated at high temporal resolution to better match the temporal sampling of the WACR. Each ARM merged sounding is associated with a fractional value indicating the radiosonde/model contribution to the merged product.
c. Applicability and error characterization of WACR automated techniques
It is important to consider system-based limitations and shortcomings of the automated retrievals for proper comparisons with surface instruments and modeling/precipitation efforts. For the SGP WACR retrieval dataset (Table 1), nearly all (>95%) Doppler spectra collected to 1 km AGL associated with a nonzero surface rainfall rate were suitable for retrievals, indicating the presence of suitable-sized drops for resonance signatures within precipitation sampling volumes. The opportunity to perform retrievals to a typical base of the melting layer (∼2.5 km) was high, often with at least 70% of a column from the surface to the base of the melting layer containing viable spectra (>90% for 1 mm h−1 < rainfall rate <10 mm h−1 and ∼70% for higher surface rainfall rates where attenuation in rain limits retrievals with height). The bulk of the retrieval hours (∼94% of 35 000+ instantaneous retrievals at the lowest gate) were performed for surface rainfall rates <10 mm h−1.
Retrievals of vertical air motions capitalizing on resonance features have been previously reported accurate to within 10 cm s−1 and shown insensitive to a wide range of turbulence intensity parameterizations (e.g., Firda et al. 1999; Kollias et al. 2002; Lhermitte 2002). Accuracy claims are based on the testing of simulated spectra over an extensive range of input DSD parameters and parameterizations for noise and Gaussian-form subvolume turbulence. Of interest is a weak relationship between the location of the first resonance minimum and the bulk slope of the DSD (as in Fig. 1, to within 5 cm s−1 for an exponential form with 0 < Λ < 65 cm−1). Specific to the WACR, a constraint is imposed by the resolution of the Doppler spectrum (Δυ ∼ 6 cm s−1), which is coarser than the reported accuracy under most simulated conditions. Testing of the CWT method revealed detected minima typically to within a single misplacement of a velocity bin (Δυ ∼ 10 cm s−1). A pronounced presence/absence of particular drop sizes in response to isolated-intense drop sorting (e.g., along strong updraft/downdraft interface) or melting particles could also obscure prominent spectral features. Efforts to ensure the consistency of CWT minima with corresponding spectral features (left edge offset check, spacing relative to predicted peak locations) mitigate gross errors; however, limited instantaneous misplacements on the order of a few spectral bins are unavoidable.
Beyond these considerations, the accuracy of velocity retrievals is mapped to an assumed fall speed relation and corrections at altitude. GK49 measurements do not describe precipitating conditions and limited references exist for fall speeds at altitude (e.g., Lhermitte 2002). From (3) and (4), modest air density variability within precipitation can impact retrieval accuracy through the estimates of fall speed velocities to the same order as the stated retrieval accuracy (∼10 cm s−1). The combined uncertainty in placement and fall speed mapping may argue for a more conservative stance on velocity retrieval accuracy in operational settings than previously reported, perhaps to within 10 to 20 cm s−1.
Slope parameter retrieval accuracy is challenging as this is coupled with velocity retrievals and methods for fitting an assumed DSD form (system/retrieval noise). Previous simulation studies using traditional exponential and gamma forms report an accuracy of W-band inversion methods typically to within 3 cm−1 of simulated inputs provided spectral noisiness and turbulence do not obscure prominent spectral features (e.g., Kollias et al. 2002). Inversion techniques following (1) also imply sampling errors within small and large drop regimes as computational limitations, for example, as in the consequence of a rapidly increasing dD/dV term at larger sizes.
To offer a different perspective on retrieval errors, this study explores the automated retrieval performance through comparisons with collocated surface disdrometer observations performing a similar parameter fit. Here, we perform an exponential slope parameter fit using nontruncated estimates of the third and sixth moments (e.g., Waldvogel 1974), similar to the ARM reference Joss–Waldvogel disdrometer standard calculation. These efforts offer an initial reference for WACR retrievals against a familiar standard. The subject of a more appropriate or optimal slope parameter fit for validation, especially as it pertains to known disdrometer instrument limitations for sampling of small and large drops, is not well resolved (e.g., Smith 2003; Smith et al. 2009). Retrieval intercomparison and expectations therein are also clouded by similar temporal and spatial sampling limitations of platforms (e.g., Zawadzki 1975; Campos and Zawadzki 2000). Additional factors, including noisiness as a consequence of variability within a physical process (sorting effects, as described for Joss–Waldvogel 1-min disdrometer efforts; Lee and Zawadzki 2005), will introduce additional uncertainty between the “instantaneous” retrievals from both platforms.
4. Automated retrieval observations from May to June 2007
As listed in Table 1, the events from May and early June 2007 were selected to assess automated retrieval performance covering a total of 14 cases and 85 h of measurable precipitation recorded by the WACR system. Many events featured extended observations in isolated convective systems, as well as classical mesoscale convective system (MCS) squall-line convective storms followed by extended trailing stratiform regions. As a consequence of severe attenuation in rain, WACR retrievals through the strongest precipitation cores are often limited to within 1.5 km AGL. As described in the previous section, the bulk of the retrieval hours is associated with lower surface rainfall rates and stratiform regions trailing strong convective lines. Cumulative statistics for these events are offered, as well as a case study from the 1 May 2007 event for a detailed look at the automated retrieval fields.
a. Cumulative automated retrievals, velocity
For each W-band range gate, instantaneous retrievals are conducted without any information from surrounding gates (independent) and exhibit high spatial correlations in time–height with adjacent retrievals (∼0.8). Instantaneous vertical velocity measurements (convention is positive downward) predominantly range from ±3.0 m s−1, within kinematic definitions of bulk stratiform precipitation found in the literature (e.g., Yuter and Houze 1995a,b). Approximately 5% of the instantaneous velocity retrievals for the events exhibited magnitudes greater than 1 m s−1. Figure 3 (top) shows a cumulative two-dimensional histogram [height and velocity cumulative frequency with altitude display (CFAD); e.g., Yuter and Houze 1995a,b] for velocity retrievals with rainfall rate >1 mm h−1 and radiosonde fractions >50% (indicative that ingest sounding data reasonably matched in time with the observations). The bulk of retrievals in Fig. 3 (top) are obtained in lower rainfall rates, exhibiting a downward net air motion profile beneath the melting layer (downward offset ∼0.04 m s−1). The bulk of observations are between ±0.3 m s−1 with a standard deviation of 0.24 m s−1. As the quality of velocity retrievals are potentially linked to factors including regime (concatenation of convective and stratiform events) and sounding viability, we have isolated retrievals for only lower rainfall rates <2 mm h−1 and at the times of highest radiosonde fraction (>90%) to approximate well-observed, light widespread precipitation conditions (Fig. 3, bottom). For this subset, the CFAD reveals similar net downward motion and overall standard deviation as before (0.05 and 0.3 m s−1, respectively).
b. Cumulative radar–disdrometer slope parameter comparisons
Slope retrievals for the lowest available range gate from the W-band radar (300 m AGL) are compared with measurements from the collocated surface disdrometer (Fig. 4). For the scatterplot in Fig. 4 (∼24 000 instantaneous radar observations with rain rate >1 mm h−1), radar-based instantaneous slope retrievals are paired with the closest matched instantaneous 1-min disdrometer estimate. Although instantaneous retrieval comparisons assume system, spatial, and temporal mismatch, the results demonstrate a mean bias of −1.48 cm−1 (radar underestimation) and an rms error of 4.36 cm−1. Similar bias and rms errors were observed for a rain-rate threshholding of >2 mm h−1 (−1.38 and 4.26 cm−1 for 16 500+ points not shown, respectively). Instantaneous radar slope retrievals as a function of surface rainfall rate indicate slope measurement variability decreases at higher rainfall rates and associated with lower slopes (Fig. 5). Instantaneous retrievals fall within expectations for Λ–R model relations following the N0 value of Marshall–Palmer (N0 = 0.08 cm−4, dashed line) and bounded by a spread of light rain and thunderstorm conditions (N0 = 0.3 cm−4 and N0 = 0.014 cm−4, top and bottom solid lines, respectively; following Lhermitte 2002). A decreasing correlation is also noted between the time series of slope retrievals performed at a surface reference height to those performed immediately aloft (Fig. 6). These observations provide an indication for the consistency of these independent instantaneous retrievals from one gate to the next, but also the variability (sorting effects) of the DSD slope parameter with height.
c. Example observations of 1 May 2007 storm
During the early overnight hours through midafternoon of 1 May 2007, an upper-level low pressure system tracked from west Texas through the state of Oklahoma. Favorable thermodynamic conditions in the region contributed to widespread cloud cover and precipitation development over the ARM central facility in Lamont. Initial precipitation was in the form of light, stratiform rain (rain rate ∼1–3 mm h−1) developing in advance of the center of low pressure or surface boundary. Moderate precipitation rates (rain rates >10 mm h−1) were recorded as the center of the low approached the field site. The strongest precipitation band to pass over the field site is associated with a weak segment of a developing convective line.
Time–height plots of the equivalent radar reflectivity factor Ze for the 1 May 2007 event are provided for three radar systems (KVNX, WACR, and MMCR) in Fig. 7. The S-band reflectivity measurements as from KVNX are well associated with the changes in precipitation-sized particles and precipitation intensity (e.g., Doviak and Zrnić 1993). Although attenuation in rain is negligible at S band, finescale insight from KVNX in its current operational mode is limited by the coarse resolution volume (∼1 km3 at 50 km), beam broadening, signal-to-noise (SNR) thresholds, and the effect of the earth’s curvature. Nevertheless, these measurements provide context for several situations for which cloud radar systems are heavily attenuated in rain and therefore unavailable to higher altitudes.
The precipitation as viewed by surveillance radar matches several classic stratiform characteristics from the literature (e.g., Steiner et al. 1995). A brightband signature is observed around 3.3 km throughout most of the event, in agreement with freezing level heights recorded by radiosondes regularly launched at the ARM facility. The brightband enhancement is observed at S band and an isolated enhancement is also visible for this event in MMCR Ka-band measurements that are sensitive to select precipitation-sized melting particles. Although a pronounced enhancement is not apparent in WACR measurements, Doppler spectra multimodality features infer some presence of melting snowflakes down to heights of 2.5–2.8 km (e.g., bottom of the melting layer, not shown). KVNX Ze measurements at low levels are in agreement with field site observations of light/moderate rainfall rates of 1–5 mm h−1. A weak convective line (Ze ∼ 45 dBZ) forms over the site after 1800 UTC and surface observations indicate a shift to moderate/heavy rainfall rates of 10–30 mm h−1. The increase in the precipitation intensity may also be inferred from cloud radar Ze measurements that exhibit severe bias due to attenuation in rain and are unavailable above 2 km during the most intense convective cells.
Hourly time–height cross sections of retrieval segments of vertical velocity and slope parameter as in Fig. 8 (1300–1400 UTC) and Fig. 9 (1815–1915 UTC) also match with the expectations based on larger-scale event features. Slope parameter retrievals trend with large-scale changes in the precipitation patterns as inferred by the reflectivity factor fields at the multiple wavelengths. For example, the lowest values of slope often correspond to extended regions beneath pronounced brightband enhancements that are most likely associated with the presence of additional and larger melting particles (sizes that the current methodology of slope retrieval is most sensitive).
A closer inspection of retrieved precipitation fields of air velocity and slope reveal finescale structures. It is quite common to observe small, but intense embedded structures a few hundred meters in depth with periods of oscillation on the order of 1–2 min. Slope retrievals feature trails or streaks of Λ in time/height. Most often, slope parameter signatures are consistent with large particles originating from the melting of large snow aggregates reaching the surface first because of the differential fall speed of raindrops. Retrievals performed near the end of the event (Fig. 9) reveal pronounced structures in time–height. These structures possibly indicate isolated regions of strong horizontal wind shear, waves, and additional size sorting of the largest particles.
Slope retrievals for the lowest available range gate from the W-band radar (solid black lines) are compared with measurements obtained from the collocated surface disdrometer (solid blue line) in Figs. 8 and 9 (bottom panels). The rainfall rate observed by the disdrometer during the 1-min collection period has been included on the images for an additional reference (solid green line). The temporal sampling of the instruments has been taken into account and radar-based retrievals have been smoothed in time to better match 1-min disdrometer sampling and mitigate instantaneous instrument scatter as was observed in Fig. 4. For this event, the mean bias (radar–disdrometer) is again near 1.0 cm−1.
5. Discussion and conclusions
This study demonstrates the applicability of an automated, 94-GHz radar Doppler spectra-based technique for the retrieval of precipitation parameters in low-to-moderate rainfall rates (1–30 mm h−1). In a vertically pointing mode, the techniques are performed for range gates in which the radar signal is not fully attenuated in rain and requires the presence of particular sized raindrops within the resolution volume. When these conditions are satisfied, the methods have been automated and are of use for detailed retrieval of vertical air motions and inversions of the Doppler spectra for simultaneous information on the slope of the DSD in time and height. It is suggested that techniques require minimal signal processing using a continuous wavelet transform methodology for the location of relative features in the Doppler spectra. This automation is important if one considers the long-term ARM program plans to deploy W-band systems at all ARM climate research facilities. For this validation effort, known surface instrument limitations motivated the selection of exponential DSD fitting for the intercomparison. However, the authors do not exclude investigations of gamma or other retrievals parameters (including at altitude) provided capable surface disdrometer instruments are collocated.
Results for the monthlong application indicate viable retrievals in the Oklahoma warm season for a wide range of rainfall rates (e.g., Kollias et al. 2002). For the SGP dataset, retrievals are demonstrated viable to heavy surface rainfall rates, as in the case-study event recorded near 1834 and 1847 UTC (15–30 mm h−1). It is noted that less than 6% of the valid retrievals for the SGP May 2007 dataset were obtained for rainfall rates in excess of 10 mm h−1. During these intense precipitation intervals, retrievals are only available from the surface to heights below 2 km AGL before the beam is attenuated in rain. Retrievals performed during moderate surface rainfall rates <10 mm h−1 are typically available from the surface to the base of the melting layer or slightly above. Retrieval availability may not project similarly to other precipitation regimes with an absence of moderate drop sizes.
Long-term averages and frequency histograms of velocity retrievals fall within expected ranges for central Oklahoma weak convective and stratiform-type systems. This includes air motion averages in stratiform precipitation that feature a net downward air motion of 0.05 cm s−1 and a standard deviation of 25–30 cm s−1. High temporal/spatial resolution plots of retrievals from automated techniques also reveal several complex structures in precipitation fields. Retrieved velocity patterns exhibit various scales of motion embedded within the precipitation field to scales of a few hundred meters and a few minutes in time. Instantaneous air motions are recorded with magnitudes to 3 m s−1, with 5% of the observations exceeding 1 m s−1.
Within this study, it was suggested that poorly matched environmental soundings carry the potential to introduce significant retrieval bias. An advantage of the ARM climate research facility for W-band retrievals is in an availability of sounding launches and merged model-sounding products at high temporal resolution that lessens these sorts of biases. CFAD segregation revealed only subtle differences in cumulative statistics for retrievals that included possibly lesser-matched ARM merged sounding products. However, as radiosonde launches are often aborted in heavier precipitation and/or launched in advance of oncoming systems, even frequent air density profile availability may not best represent the environment and occasionally introduce detrimental biases for individual event studies. Merged soundings products are also not immune in situations with model failure to capture initiating or ongoing precipitation.
Long-track slope retrievals at low levels are in agreement with surface disdrometer measurements, and error characteristics are in line with statements in the existing literature for W-band retrievals. Known system limitations of the Joss–Waldvogel disdrometer and spatial/temporal retrieval mismatch including physical process noise/sorting effects may help explain additional bias and spread of instantaneous slope retrievals (e.g., Sheppard and Joe 1994; Tokay et al. 2001; Campos and Zawadzki 2000; Lee and Zawadzki 2005). In general, an undersampling of small and larger particles by the impact disdrometer is consistent with the reported offset (bulk radar underestimation, as in Fig. 4) between surface disdrometer observations and the inversion-based radar retrievals following a method of third and sixth moments. That is, WACR-based retrievals feature a larger sampling volume more sensitive to the presence of low concentration larger drops. It is suggested small raindrops are also better sampled by the WACR as compared with the impact disdrometer platform. This disdrometer sampling limitation is consistent with a reversal of the slope retrieval offset (overestimation) at higher values of slope.
Collocation of W-band systems can serve as a strong complement to various ground-based radar and profiler measurements. The W-band systems could be a valuable tool for validation of other forms of radar-based wind retrieval and improving our understanding of precipitation processes with appropriate averaging. Here, interpretation of offered instantaneous retrievals of the slope parameter may be suitable within a remote sensing context, analogous to median large drop sensitivity of polarimetric differential reflectivity factor ZDR and extend toward exploration of small-scale DSD variability on polarimetric measurements (e.g., Miriovsky et al. 2004). Note that slope parameter retrieval is representative of the particles present in the illuminated volume (weighted toward the contribution of larger drop sizes according to the method of moments), but not relevant for tracing the paths traversed by all particles contributing to that volume. Averaging in time and height is necessary for microphysical insight into various physical processes (as with the 1-min disdrometer observations; Lee and Zawadzki 2005).
Acknowledgments
Support for this research was funded by the Office of Biological and Environmental Research, Environmental Sciences Division of the U.S. Department of Energy as part of the Atmospheric Radiation Measurement program (Grant DE-FG02-08ER64573). The authors would also like to thank Isztar Zawadzki, Frederick Fabry, and Mark Berenguer of McGill University for helpful discussions, as well as the anonymous reviewers who have greatly improved the quality of this manuscript.
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Examples of Doppler spectra from the ARM WACR W-band cloud radar. The Doppler spectra were collected at the same altitude and 3 min apart (thick and thin solid lines). Spectral density curves for N(D) = constant are shown for two different constant values (dashed lines). The inset contains spectral density curves for an exponential distribution using different values of the slope parameter (cm−1). The diameters associated with the first two resonance maxima (D1 and D2) as well as the first minimum (DM) are plotted as reference.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Examples of Doppler spectra from the ARM WACR W-band cloud radar. The Doppler spectra were collected at the same altitude and 3 min apart (thick and thin solid lines). Spectral density curves for N(D) = constant are shown for two different constant values (dashed lines). The inset contains spectral density curves for an exponential distribution using different values of the slope parameter (cm−1). The diameters associated with the first two resonance maxima (D1 and D2) as well as the first minimum (DM) are plotted as reference.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Examples of Doppler spectra from the ARM WACR W-band cloud radar. The Doppler spectra were collected at the same altitude and 3 min apart (thick and thin solid lines). Spectral density curves for N(D) = constant are shown for two different constant values (dashed lines). The inset contains spectral density curves for an exponential distribution using different values of the slope parameter (cm−1). The diameters associated with the first two resonance maxima (D1 and D2) as well as the first minimum (DM) are plotted as reference.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Example of an observed Doppler spectrum (solid line) and its continuous wavelet transform performed at a scale of eight (thick dashed line). Locations of the peaks and first minimum are denoted by dotted vertical lines.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Example of an observed Doppler spectrum (solid line) and its continuous wavelet transform performed at a scale of eight (thick dashed line). Locations of the peaks and first minimum are denoted by dotted vertical lines.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Example of an observed Doppler spectrum (solid line) and its continuous wavelet transform performed at a scale of eight (thick dashed line). Locations of the peaks and first minimum are denoted by dotted vertical lines.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
(top) CFAD of radar-based velocity retrievals for all events and rainfall rates >1 mm h−1 and radionsonde fraction >50% (positive downward). (bottom) CFAD for retrievals over surface rainfall rates <2 mm h−1 with radiosonde fraction >90%.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
(top) CFAD of radar-based velocity retrievals for all events and rainfall rates >1 mm h−1 and radionsonde fraction >50% (positive downward). (bottom) CFAD for retrievals over surface rainfall rates <2 mm h−1 with radiosonde fraction >90%.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
(top) CFAD of radar-based velocity retrievals for all events and rainfall rates >1 mm h−1 and radionsonde fraction >50% (positive downward). (bottom) CFAD for retrievals over surface rainfall rates <2 mm h−1 with radiosonde fraction >90%.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Scatterplot of radar-based slope retrievals vs disdrometer slope estimates for SGP May 2007.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Scatterplot of radar-based slope retrievals vs disdrometer slope estimates for SGP May 2007.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Scatterplot of radar-based slope retrievals vs disdrometer slope estimates for SGP May 2007.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Scatterplot of radar-based slope retrievals vs disdrometer rainfall rate estimates for SGP May 2007. The top solid line represents a model slope–rainfall rate curve for light rain N0 = 0.3 cm−4 and the bottom solid line for a thunderstorm N0 = 0.014 cm−4. The dashed line is a model curve for the Marshall–Palmer N0 = 0.08 cm−4.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Scatterplot of radar-based slope retrievals vs disdrometer rainfall rate estimates for SGP May 2007. The top solid line represents a model slope–rainfall rate curve for light rain N0 = 0.3 cm−4 and the bottom solid line for a thunderstorm N0 = 0.014 cm−4. The dashed line is a model curve for the Marshall–Palmer N0 = 0.08 cm−4.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Scatterplot of radar-based slope retrievals vs disdrometer rainfall rate estimates for SGP May 2007. The top solid line represents a model slope–rainfall rate curve for light rain N0 = 0.3 cm−4 and the bottom solid line for a thunderstorm N0 = 0.014 cm−4. The dashed line is a model curve for the Marshall–Palmer N0 = 0.08 cm−4.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Correlation of radar-based slope retrieval time series as a function of the distance from a surface reference height.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Correlation of radar-based slope retrieval time series as a function of the distance from a surface reference height.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Correlation of radar-based slope retrieval time series as a function of the distance from a surface reference height.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Time–height mapping of the reflectivity factor at (top) 3, (middle) 95, and (bottom) 35 GHz for the 1 May 2007 event.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Time–height mapping of the reflectivity factor at (top) 3, (middle) 95, and (bottom) 35 GHz for the 1 May 2007 event.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Time–height mapping of the reflectivity factor at (top) 3, (middle) 95, and (bottom) 35 GHz for the 1 May 2007 event.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
(top) Precipitation parameter retrievals for the time frame between 1300 and 1400 UTC and (bottom) the time series of observed (disdrometer) and radar-retrieved slope Λ for the same time interval (velocity is positive downward). The black line is the radar-based retrieval, solid blue line is the 1-min disdrometer measurements. The green line indicates the rainfall rate observed by the disdrometer.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
(top) Precipitation parameter retrievals for the time frame between 1300 and 1400 UTC and (bottom) the time series of observed (disdrometer) and radar-retrieved slope Λ for the same time interval (velocity is positive downward). The black line is the radar-based retrieval, solid blue line is the 1-min disdrometer measurements. The green line indicates the rainfall rate observed by the disdrometer.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
(top) Precipitation parameter retrievals for the time frame between 1300 and 1400 UTC and (bottom) the time series of observed (disdrometer) and radar-retrieved slope Λ for the same time interval (velocity is positive downward). The black line is the radar-based retrieval, solid blue line is the 1-min disdrometer measurements. The green line indicates the rainfall rate observed by the disdrometer.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
As in Fig. 8, but for the time interval between 1815 and 1915 UTC.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
As in Fig. 8, but for the time interval between 1815 and 1915 UTC.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
As in Fig. 8, but for the time interval between 1815 and 1915 UTC.
Citation: Journal of Atmospheric and Oceanic Technology 27, 9; 10.1175/2010JTECHA1343.1
Listing of SGP events and the hours of observation.
