The ARM SGP Central Facility RWP was a Vaisala Meteorological Systems Inc. LAP-3000 wind profiler (Muradyan and Coulter, 2020) and is a commercial version of the NOAA UHF wind profiler developed under an industry–government 1991 Cooperative Research and Development Agreement (CRADA). From 22 March 2011 to 31 March 2014, the RWP operated in a precipitation mode observing only in the vertical direction. The precipitation mode sampled the atmosphere with a short and long pulse, yielding low-sensitivity short-range measurements and high-sensitivity long-range measurements, respectively. On 1 April 2014, a wind mode was added to the RWP and consisted of transmitting pulses in three different directions in order to estimate the horizontal wind as a function of height. The RWP collected data in both precipitation and wind modes for 5 years. On 11 March 2019, the wind mode operating parameters changed, and on 19 August 2019, the RWP hardware failed and was eventually replaced with a wind profiler produced by a different radar manufacturer. The LAP-3000 RWP can only collect data in one beam direction with one pulse configuration at a time. Thus, during the 2011 to 2014 period, the radar alternated between two vertically pointing precipitation mode radar beams, requiring approximately 5 s to collect both beams of data. During the 2014 to 2019 period, the radar sequentially collected data in five unique radar beams (i.e. two precipitation mode beams and three wind mode beams), requiring approximately 25 s to complete one observation cycle. Table 1 lists pertinent RWP operating parameters for both modes.

The ARM RWP uses the manufacturer's default processing routines (Muradyan and Coulter, 2020). For each mode, the RWP transmits a sequence of pulses and performs coherent integrations, fast Fourier transforms (FFTs), and spectra averages. Using the precipitation short-pulse mode as an example, the RWP transmits 56 radar pulses (represented by Ncoh) and integrates the in-phase and quadrature voltages (also called I and Q voltages) to produce one in-phase and one quadrature voltage (i.e. Icoh and Qcoh). After collecting 128 (represented by Npts) coherently averaged Icoh and Qcoh voltages, a von Hann window is applied to the time series and a complex FFT is performed to produce a Doppler velocity power spectrum. Another sequence of 7168 pulses (calculated as NcohNnpts) is transmitted and processed to produce another Doppler velocity power spectrum. After producing three power spectra (represented by Nspc), the three power spectra are averaged and saved to disc. The option of calculating a median spectrum or statistically averaging the three spectra (as discussed in Merritt, 1995) in order to remove transient signals (e.g. birds or other flying objects passing through the radar beam) was not implemented. A total of 21 504 pulses (NcohNptsNspc) are transmitted per dwell and a 100 µs inter-pulse period yields a 2.2 s dwell. For each Doppler velocity spectrum, the first three spectrum moments (i.e. signal-to-noise ratio, mean radial velocity, and spectrum width) are estimated using the manufacturer's single peak processing routine with integration limits bounded by the Nyquist velocities ± VNyquist. The average spectra and the moments are saved to disc.

Between 2011 and 2019, the RWP had two hardware failures. In 2015, the phase shifter module controlling the beam-pointing direction failed due to age and overuse. A new phase shifter module was installed. In 2017, the final amplifier in the transmitter module failed, and several relays failed in the phase shifter module. The transmitter module was replaced with a used Vaisala unit scavenged from a newer RWP, and the relays were replaced. Since calibration constants change with ageing and changing hardware, the RWP dataset is divided into five calibration periods as listed in Table 2.

A 2-dimensional video disdrometer (VDIS) manufactured by Joanneum Research in Graz, Austria (Schönhuber et al., 2008), was deployed about 100 m from the RWP at the SGP Central Facility (Wang et al., 2021; ARM, 2011). The VDIS uses two orthogonal pointing cameras in the horizontal plane to detect raindrops falling through a 10 cm square opening and then estimates the raindrop number concentration with a 1 min temporal resolution (Tokay et al., 2001, 2013). Radar reflectivity factors assuming Rayleigh scattering were calculated using PyDisdrometer routines (Hardin and Guy, 2014), as used in previous studies using VDIS observations (Giangrande et al., 2019).

The calibration procedure uses the 1 min surface disdrometer radar reflectivity factor to estimate a RWP calibration constant for the precipitation short-pulse mode using 1 min averaged RWP observations at 500 m altitude. The other RWP modes could be calibrated directly with the 1 min surface disdrometer observations, but to increase the number of samples, the other RWP modes are calibrated using the precipitation short-pulse mode as a reference and using multiple range gates and nearest-in-time observations. The calibration procedure described herein is only valid for RWP modes that collect data while it is raining. If the RWP is adaptive and collects precipitation mode data when it is raining and wind mode data otherwise, then there are not any nearest-in-time precipitation mode observations nor surface disdrometer observations available to calibrate the wind mode observations. In this situation, the precipitation mode data can be calibrated, but the wind mode data cannot be calibrated with the disdrometer observations.

This subsection describes three processing steps: (1) spectrum adjustments due to Nyquist velocity aliasing, (2) spectrum adjustments due to coherent integration, and (3) recalculating the spectrum moments. Appendix A presents a flow diagram illustrating how these processing steps are applied to a profile of radar observations.

Signal power is estimated relative to the estimated mean noise power and is quantified with the signal-to-noise ratio SNR. If the noise power estimate is too large, then the signal-to-noise ratio and the inferred signal power are underestimated. The a0 processed noise power Pnoisea0 shown in Fig. 1c had increased magnitudes at nearly all range gates during the convective rain event between approximately 11:35 and 12:10 UTC. This increased noise power is not expected for RWPs because the gain is constant with range so that noise power should be independent of range. Also, Fig. 2 shows signal power spread over a large fraction of the velocity spectrum. These two features are linked: the broad signal spectra are causing increased noise power estimates. Specifically, as the signal velocity power spectrum broadens and occupies more of the velocity spectrum, the noise estimator is biased by the inclusion of signal power. The RWP online signal processing uses the Hildebrand and Sekhon (1974) noise level estimator to separate noise-only spectral bins from signal-plus-noise spectral bins based on the statistical properties of both populations (for more details see Merritt, 1995, and Wilfong et al., 1999). If the signal-plus-noise spectral bins are included in the noise-only population, then the noise level estimate will be biased high, leading to an underestimated SNR. To correct for this low SNR bias, a reference noise power Pnoisereference (dB) is determined and an adjusted SNR is estimated using 5SNRadjustedrevised=SNRrevised+Pnoiserevised-Pnoisereference(dB), where SNRrevised and Pnoiserevised are moments calculated in Sect. 3.1.3.

The noise power for every spectrum is estimated using the method outlined in Hildebrand and Sekhon (1974). The reference noise power Pnoisereference is the median noise power derived from all spectra collected on a given day. Figure 5 shows the daily median noise power for the precipitation short pulse (black plusses) and long pulse (red crosses) for the 8-year dataset. The jump in daily median noise power in mid-2017 corresponds to replacing the transmitter with a used, yet updated version, from the same RWP vendor. It is interesting to note that the seasonal noise variation decreased with the updated transmitter and not when the equipment shelter air conditioning system was updated in mid-2016.

Figure 6 illustrates the impact of adjusting the signal-to-noise ratio with the reference noise power. Figure 6a shows the real-time estimated SNRa0 (thick line) and Pnoisea0 (thin line) profiles. The large variations in Pnoisea0 between 4 and 5 km appear as large and inverse variations in SNRa0. Figure 6b shows the adjusted signal-to-noise ratio using two methods. The method described in Tridon et al. (2013) uses the real-time moments (SNRa0 and Pnoisea0) to estimate the adjusted signal-to-noise ratio SNRadjusteda0 (thick blue line in Fig. 6b). The method described herein recalculates the moments and then estimates the adjusted signal-to-noise ratio SNRadjustedrevised using Eq. (5) (thin red line). The profile offset in Fig. 6b is due to different reference noise powers used in the two methods. The SNRadjusteda0 has more variability than SNRadjustedrevised, indicating that the revised spectra reprocessing method produces smoother, more vertically consistent SNR vertical profiles than the Tridon et al. (2013) method.

The precipitation short-pulse beam is defined as the RWP reference beam, and the radar reflectivity factor ZPrecipShort (dBZ) for this beam is estimated from the adjusted signal-to-noise ratio SNRadjustedPrecipShort using 6ZPrecipShort(r)=SNRadjustedPrecipShort+20log(r)+CPrecipShort(dBZ), where r (m) is range from the radar, and CPrecipShort (dB) is the calibration constant. To estimate the calibration constant CPrecipShort, an initial value of CPrecipShort equal to 0 dB is selected, and Eq. (6) is used to estimate the RWP reflectivity factor at all range gates. These initial RWP reflectivity factors at 500 ma.g.l. are averaged into 1 min quantities and then compared with the 1 min surface disdrometer radar reflectivity factors. Using only disdrometer reflectivity factors between 20 and 40 dBZ, the reflectivity factor differences are calculated for RWP lags between ± 4 min. Both positive and negative lags are needed because the two instruments are separated by approximately 100 m, and the horizontal wind speed and direction can cause the surface rain observations to occur before the radar observations at 500 m altitude. Figure 7 shows scatter plots and statistics of mean, SD, and Pearson's correlation coefficient for the 7 June 2018 rain event at nine different lags. For this rain event, the distribution in Fig. 7d is selected for calibration because it has the highest Pearson's correlation coefficient of 0.95.

Using the calibration constant and lag determined from Fig. 7d (i.e. CPrecipShort = -49.5 dB and -1 minlag), Fig. 8a shows the time–height cross-section of calibrated RWP precipitation short-pulse mode radar reflectivity factor. Figure 8b shows a time series of RWP reflectivity factor at 500 m (red crosses) and the surface disdrometer reflectivity factor (black plusses). The thin blue lines in Fig. 8b at 20 and 40 dBZ indicate the reflectivity factor range used for calculating the RWP and disdrometer differences, which are shown in Fig. 8c. Also shown in Fig. 8c are the statistics for this lag, including lag, number of samples, calibration constant, SD, and Pearson's correlation coefficient. Figure 8d shows surface disdrometer rain rate RR and mass-weighted mean diameter Dm. The SD of 1.9 dB for this event is due to spatiotemporal mismatch between the surface disdrometer and radar sample volume as well as measurement uncertainties of both instruments and is comparable to 1 to 2 dB measurement uncertainties of side-by-side surface disdrometers (Tapiador et al., 2017; Wang et al., 2021). Note that the lag is only used in the calibration procedure and not used as a time offset for any other purpose.

Figure 9 shows improved moments and calibrated reflectivity factors for the same rain event shown in Fig. 1. The top panel (Fig. 9a) shows the revised adjusted signal-to-noise ratio (SNRadjustedPrecipShort), and the middle panel (Fig. 9b) shows the revised mean radial velocity (VmeanPrecipShort). Compared to the a0 real-time processed moments, the reprocessed moments in Fig. 9a and b show improved data quality and uniformity. The calibrated radar reflectivity is shown in Fig. 9c.

The radar sensitivity can be adjusted by changing the transmitted pulse length, the number of coherent integrations, and the number of averaged Doppler velocity spectra. Using the precipitation short-pulse mode as the reference beam, the expected relative change in sensitivity for the other four radar beams can be estimated using 7CrelativeOtherMode=20logΔRMUTΔRPrecipShort+10logNcohMUTNcohPrecipShort+5logNspcMUTNspcPrecipShort+20log[sin⁡(θel)], where ΔR is the range resolution, Ncoh is the number of coherent samples, Nspc is the number of averaged power spectra, θel is the elevation angle from the horizon, and the superscripts PrecipShort and MUT represent the precipitation short-pulse mode and the mode under test (MUT), respectively. Using the values from Table 1 and Eq. (), Table 3 lists the expected relative sensitivities for the precipitation long-pulse mode and the wind mode. The last term in Eq. () represents the decrease in gain associated with beam-pointing direction in phased-array antennas (Balanis, 1997). As the beam-pointing direction deviates from broadside (a.k.a. vertical direction in the RWP), the projected antenna area decreases, causing the gain to decrease and beam width to increase (Balanis, 1997; Palmer et al., 2022). System losses and variations in antenna gain cause the measured relative sensitivities to deviate from the expected values listed in Table 3.

The reflectivity factor for the other four radar beams follows Eq. (6) with the addition of the relative calibration constant CrelativeOtherMode (dB) and is estimated using 8ZOtherMode(r)=SNRadjustedOtherMode+20log(r)+CPrecipShort-CrelativeOtherMode(dBZ).

The negative sign in the bracketed term is because a positive CrelativeOtherMode indicates that this mode is more sensitive than the precipitation short-pulse mode and will produce a larger SNRadjustedOtherMode for the same radar reflectivity factor. Note that weaker radar reflectivity factors will be detected at further ranges at the expense of possible receiver saturation from large reflectivity factor targets at close range.

To estimate relative sensitivities between the other beams and the reference beam, reflectivity factors are estimated at all profiles and range gates using Eq. (8) with CrelativeOtherMode set to zero and then estimating the differences from nearby precipitation short-pulse mode observations. Figure 10 shows scatter plots and histograms of reflectivity factor differences for the precipitation long-pulse beam during the 7 June 2018 rain event. Valid observations are constrained to be within the height interval of 800 and 2100 m and precipitation short-pulse reflectivity factors greater than 30 dBZ. Over 13 000 valid samples are used from this event to calibrate the precipitation long-pulse beam. The mean relative offset is 15.5 dB for this event, with a SD of 1.3 dB. The relative calibration constant CrelativePrecipLong is set to 15.5 dB and implies that the long-pulse mode is more sensitive and produces a larger signal-to-noise ratio for the same radar reflectivity factor as expressed in Eq. (8).

Figure 11a and b show the time–height cross-sections of cross-calibrated precipitation short- and long-pulse reflectivity factors at their native resolution for the 7 June 2018 rain event. Figure 11c shows the precipitation long-pulse relative calibration offset for each matched short- and long-pulse observation. The relative calibration offsets shown in Fig. 11c are the same samples used to produce Fig. 10 and indicate the limited height interval used in the comparison to avoid large reflectivity gradients near the radar bright band caused by melting particles.

Estimating the relative calibration offsets for the three wind beams follows the same procedure used for estimating the precipitation long-pulse beam relative calibration offset. As expected, the calibration offsets for the oblique beams have more event-to-event variability than the vertically pointing wind mode beam and will be discussed further in the next section and shown in Fig. 14.

From 22 March 2011 to 18 August 2019, the precipitation short-pulse beam calibration constant CPrecipShort was estimated on 340 d, each having at least 120 min of surface disdrometer reflectivity factor greater than 20 dBZ. Figure 12 shows CPrecipShort for every valid precipitation event using black plus symbols. The calibration constant is approximately -50 dB at the beginning of this record in 2011 and then increases to about -35 dB near the beginning of 2015. There is an abrupt drop in calibration constant near the end of 2015, and then the calibration constant steadily increases until the end of this dataset in 2019. Snow events were not included in the calibration procedure.

An increase in calibration constant, without changing operating parameters, indicates the radar sensitivity is degrading. Referring to Eq. (6), if the reflectivity factor is constant and the measured SNR decreases because of ageing radar hardware, then the calibration constant must increase. Thus, from early 2011 to mid-2015, the calibration was stable until early 2013, then increased approximately 15 dB over the next 2 years, indicating a rapid change in calibration. There was a hardware failure in mid-2015.

The gaps in measurements in mid-2015 and early 2017 are when the radar was not operating. A new antenna phase shifter module was installed in September 2015, and the calibration constant dropped by about 10 dB relative to the old hardware. In mid-2017, a new radar transmitter and receiver module was installed, and the mean noise level dropped by about 7 dB (see Fig. 5), but the short-pulse beam calibration constant did not change significantly. The steady increase in calibration constant from 2016 through 2019 suggests an approximate 3 dByr-1 decrease in sensitivity for this modified radar. Though not documented publicly, similar decreasing sensitivity rates have been estimated in other NOAA UHF wind profilers and have been attributed to delamination of the fibreglass patch antenna (Ecklund et al., 1988).

The slow change in calibration constant between precipitation events suggests that the disdrometer-to-RWP calibration procedure could be performed using fixed time intervals instead of individual rain events. To test this hypothesis, calibration constants were determined using all rain events during 1-month and 3-month intervals (i.e. months of JFM, AMJ, JAS, and OND). The 1- and 3-month calibration constants are plotted in Fig. 12 using blue squares and red triangles, respectively. The vertical blue and red lines represent 1- and 3-month calibration constant SDs, with mean SDs over the 9-year record equal to 3.6 and 2.9 dB, respectively. These SDs represent variations due to spatiotemporal mismatch of surface disdrometer and radar measurements, instantaneous measurement uncertainties of both instruments, and ageing hardware over the sampling interval.

Since the radar operating parameters did not change during the 2011 to 2019 interval, variations in relative calibration constants will depend on changes to the radar hardware. This section examines how the precipitation long-pulse and wind mode relative calibration constants evolved with hardware changes.