1. Introduction
Continuous development and evolution of polarimetric weather radar have been going on for about four decades and have reached the time for operational applications. Some countries, like the United States, are implementing dual linear polarization on the existing network [i.e., Weather Surveillance Radar-1988 Doppler (WSR-88D)]; other countries, like Germany, are acquiring new polarimetric radars [i.e., Doppler Weather Surveillance Radar-5001C/Simultaneous Dual Polarization/Conformity with European safety regulations (DWSR-5001C/SDP/CE) see Frech et al. 2011]. The benefits of dual polarization have been documented through scientific investigations (e.g., Bringi and Chandrasekar 2001) and semi-operational applications (Ryzhkov et al. 2005). Most of the reported impressive results have been achieved on data that were scrutinized and calibrated by specialists.
Calibration of the weather radars is essential for accurate measurement of precipitation. Reflectivity factor remains the most difficult and elusive to calibrate although several methods to do it have existed for a long time (Atlas 2002). Recently it has been demonstrated that check of consistency between reflectivity and polarimetric variables from rain can identify bias in reflectivity of more than 1 dB (Ryzhkov et al. 2005; Gourley et al. 2009). The consistency method needs specific differential phase and calibrated differential reflectivity ZDR, which presents a new challenge in an operational environment.
Calibration of operational radars should be continuously maintained and be as automated as possible. To achieve precision in measurements of reflectivity on the WSR-88D, automatic calibration of the receiver is performed between volume scans. Transmitter power is measured at 8-h intervals (the frequency could be increased and it is in principle possible to monitor the stability of the transmit–receive path from the existing sample of the transmitted pulse). The procedure does require built-in signal generator and control circuits; hence, on many types of radars it is not feasible.
An alternative monitoring of deviation in radar parameters affecting calibration was suggested by Rinehart (1978) who used peak cross sections of ground scatterers to check variations in Z. Silbertstein et al. (2008) computed daily cumulative distribution function of combined ground clutter and precipitation reflectivity irrespective of whether precipitation was present or absent over the clutter area. In their data the values of reflectivity at the 95th percentile and higher were exclusively due to ground returns. Hence, daily change in the 95th percentile was attributed to variation of sensitivity (failure of components, change in receiver gain, transmitted power, etc.). The baseline 95th percentile was set to 50 dBZ because it exceeded reflectivities of rain at Kwajalein (Republic of the Marshall Islands) where measurements were made.
Differential reflectivity needs accurate calibration to control bias in rainfall estimates and classification of precipitation; the rainfall estimator tested by Ryzhkov et al. (2005) has a bias error of 18% if the bias of ZDR is 0.2 dB. Therefore, a smaller bias is desirable (a value of 0.1 dB is specified for the WSR-88D network). Confining bias uncertainty to such a small value is necessary for maintaining precision, which is a prerequisite to accurate measurement.
Herein we exploit ground clutter differently than Silbertstein et al. (2008) to monitor stability of reflectivity and differential reflectivity and thus quantify temporal changes in bias. We consider polarimetric radars that operate by transmitting simultaneously horizontal and vertical (SHV) polarization and likewise receive these. This mode is susceptible to variation in ZDR imposed by changes in gains of the receivers (in horizontal and vertical channels). Thus to maintain precision, continual adjustment of differential reflectivity is needed, and a method relying on internal generator has been proposed for the WSR-88D network (Zrnic et al. 2006).
Absolute calibration of ZDR must be established if relative calibration (precision) is to be useful. Use of data for that purpose is preferred compared to intrusive measurement with power meters; hence, few data-based calibration methods have been devised. Among these the ZDR calibration at vertical incidence is common. It entails observing precipitation at vertical incidence while the antenna rotates about its axis (Gorgucci et al. 1999; Bringi and Chandrasekar 2001). Precipitation particles have no preferential orientation in a horizontal plane (crystals are randomly oriented and rain drops present the circularly symmetric side) therefore differential reflectivity should be zero. Departure from zero captures the overall bias of the radar system. But, on some weather radars (e.g., WSR-88D) the antenna cannot be pointed to 90°. A way to achieve absolute calibration in such cases has been devised by Ryzhkov et al. (2005). It uses dry aggregates at high-elevation angles and claims accuracy better than 0.2 dB for the complete transmit–receive calibration of ZDR. The ZDR calibration based on properties of rain returns (Bechini et al. 2008) compares measured ZDR profile in elevation with the theoretical profile. Several hours of uniform precipitation within 20–30 km from the radar are needed to achieve a bias smaller than 0.1 dB and an rms error of less than 0.01 dB. Hubbert et al. (2003) propose a sun scan through precipitation-free region to account for the receiving path, and cross-polar measurements from precipitation (or other scatterers) to account for the transmit path. The method is suited for radar that can measure all elements of the backscatter covariance matrix. Although sun scan is an excellent source for calibrating differential bias of the receiving path, it must be supplemented by calibration of the transmitting path (Hubbert et al. 2003; Zrnic et al. 2006). Moreover, because the effective antenna aperture size is proportional to the product of directivity and wavelength squared, a 3-cm wavelength radar has a disadvantage in sensitivity compared to a 10-cm wavelength radar of equal beamwidth. Although the solar flux (of quite sun) is about 2.5 time stronger at the X band (Edelson 1962), the wavelength dependence puts its sensitivity to about 7 dB below the sensitivity of the S-band radar (the same receiver noise powers and beamwidths are assumed). Therefore, the solar flux at the 3-cm wavelength is marginally detectable and, hence, might not be suitable for monitoring calibration. Thus other viable alternatives are highly desirable.
This paper describes use of urban ground clutter to monitor calibration of the radar reflectivity factor ZH and differential reflectivity ZDR.
2. Calibration of reflectivity and differential reflectivity
We evaluate the stability of ZH and ZDR on data obtained from 21 November 2009 to 17 January 2010 in Bonn, Germany, and on 3.5 consecutive days (2–5 July 2011) in Norman, Oklahoma. The Bonn data contain 17 rainy days, 7 snow days, and 3 days with mixed snow and rain. It has been collected with a polarimetric X-band radar (BoXPol) belonging to the Meteorological Institute of the University of Bonn. The radar wavelength is 3.213 cm, peak power is 200 kW, pulse repetition time is 1 ms, and two-way pulse depth is 100 m. The 3-dB beamwidth (one way) is 1.06° and the radar has no radome. BoXPol uses the SHV mode and records reflectivity factors at horizontal and vertical polarizations ZH and ZV, differential reflectivity ZDR, differential phase ΦDP, and correlation coefficient between horizontally and vertically polarized returns ρHV. These polarimetric variables are estimated from a long dwell time side (90 contiguous time samples at a pulse repetition time of 1 ms).
The Oklahoma data were obtained with the WSR-88D (KOUN) recently upgraded to dual polarization by the National Weather Service. The radar operates in the SHV mode and has an automatic measurement and correction of differential reflectivity bias at the end of each volume scan.
a. Absolute calibration of reflectivity and differential reflectivity
A brief description of absolute calibration of the BoXPol radar is presented as a preamble to the main theme. The ZH was calibrated by comparison with reflectivities from nearby German Weather Service radars. This revealed a bias of −5 to −7 dB (Borowska et al. 2011), which herein has been corrected.
On 4 days of observations (8–11 December 2009) a vertical scan (i.e., elevation of 90° and rotation over 360° in azimuth) had been incorporated at the end of each volume scan and the update time equaled 5 min. The ZDR plot at the height of 1.3 km (Fig. 1) is typical, and statistical values are mean = −1.7 dB, median = −1.7 dB, and standard deviation = 0.1 dB or 6% of the mean. The scatter is homogeneous with no visible periodicities or other oddities possibly because the radar has no radome. The vertical profile of median ZDR (Fig. 2, left column) indicates a stable −1.7-dB value from ~1 km above ground to the bottom of the melting layer (marked with a dip in ρHV at 1.5 km in Fig. 2, left column) and from the top of the melting layer (1.7 km) to about 6 km.
Differential reflectivity ZDR at a height of 1.3 km obtained while antenna was vertically pointing and rotating in azimuth. The rain event occurred on 10 Dec 2009. The median of ZDR is −1.7 dB and the standard deviation is 0.1 dB or 6%.
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
The vertical profiles of ZDR and ρHV from the rain event at 0324 UTC 10 Dec 2009. Each value of ZDR and ρHV represents a median over 360° in azimuth.
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
b. Clutter detection
In Bonn and Norman data there were no ZH precipitation values larger than 49 dBZ. Thus for detecting ground clutter, we set a threshold to 50 dBZ. We use measurements from 0.5° elevation angles and constrain the range to 20 km for Bonn data and to 7 km for Norman data. Clutter is strongest at a close range, and the effects of beam bending due to refractive index gradients are smaller at short distances (see section 3b). Another advantage of close range is that a good portion of nearby clutter is from urban structures. Therefore it is more likely to have a very stable ZH and ZDR. Clutter from rural areas (trees or fields) might introduce variability to ZH and ZDR due to variations in foliage (i.e., presence, absence, wet, dry, etc.) and relative motion of vegetation.
In the case of our data, the simple threshold applied to reflectivity was sufficient for identifying a significant ground clutter because precipitation was light to moderate. We examined the Doppler velocities from clutter in Bonn and found these to be at the smallest quantized levels next to zero (0.12 or −0.12 m s−1, hardware does not allow exact zero values). We added for the X-band data the additional constraint that data passing the ZH threshold must have velocities of 0.12 or −0.12 m s−1. In Norman data, the Doppler velocity measurements were made on a separate scan from the scan for ZH and ZDR. The radials of the two scans were not precisely aligned. Therefore, the zero velocity from the Doppler scan was not suitable for discriminating clutter.
There are more powerful ways to identify ground clutter (e.g., Passarelli and Siggia 1983; Hubbert et al. 2009; Warde and Torres 2009) even in heavy precipitation. Moreover scientists, attempting to measure changes in refractive index, have developed algorithms to identify stable returns from rigid objects (Fabry 2004; Cheong et al. 2008). Similar techniques are directly applicable and highly recommended. Implementation of these requires conceptually simple changes in basic signal processing. For example, operational radars have cancellers to remove ground clutter. Therefore the removed power would need to be kept for processing. Furthermore, if the radar beams can be pointed at exactly the same azimuths from scan to scan (precise indexed beams), a clutter map can be generated and used for locating strong clutter. We created a clutter map and made an attempt to use it, but found that the detected positions varied slightly because of imperfect assignment of antenna pointing. Thus, the map would need to encompass up to 3° in azimuths to cover all possible shifts. Hence, we settled for the much simpler detection based solely on the reflectivity and velocity thresholds.
3. Data analysis
First part of this section deals with the analysis of data from the BoXPol. In the second section, the results obtained from the newly modified KOUN radar are presented.
a. Analysis of X-band radar data
We start by examining the median values of ZH, ZV, and ZDR plotted at 5-min increments for days with rain (Fig. 3). The median ZDR has an advantage over the average value in a practical radar system whereby the word size matters; the represented ZDRs are typically confined within a range that is smaller than the span of clutter ZDR. On the BoXPol this range is −6.25–6.25 dB. The out-of-range values do not occur in precipitation and most clear-air conditions. The values within a relatively small range can be quantized in sufficiently fine increments to make good quantification and classification of precipitation. Clutter ZDR spans a larger range than allowed by the word size and therefore the average of clutter ZDR would always be biased toward 0 whereas the median estimate is not biased unless the true median is out of the digital range. In our case about 16% of clutter ZDR values are smaller than −6.25 dB and about 2% are larger than 6.25 dB mostly because the V channel yields higher returns than the H channel. Thus, the median values of ZDR contain a bias of −1.7 dB, which has not been compensated because our interest here is in the trend and stability. From measurements at vertical incidence on 10 December 2009 we conclude that the correct clutter median value is −0.5 dB.
(top) Medians of ZH, ZV, from ground clutter; ZH > 50 dBZ and Doppler velocity v = ±0.12 m s−1 within a range of <20 km, elevation 0.5°, and full 360° scans in azimuth. (middle) As in (top), but it is the median ZDR. (bottom) Difference between the total number of clutter detections M and the average number of clutter detections 〈M〉 = 4865. The dataset (17 days between 21 Nov and 30 Dec 2009) consists of 3103 samples spaced 5 min apart on days when rain fell somewhere within the radar coverage. The thin vertical lines indicate temporal discontinuities between contiguous samples. The durations of the continuous measurements are written in (middle) hours and the beginning of each episode is indicated in (bottom) UTC. The thick marks on the time axis are in increments of 500 min.
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
Noteworthy is the stable and consistent median ZH for rainy days (Fig. 3) and for snow days (not shown); we computed the standard deviation of the medians to be 0.09 dB for rainy days and 0.11 dB for days with snow. A quick look at the median ZH and ZV (Fig. 3) reveals their excellent stability. The majority of ZH are 56 dBZ with a much smaller occurrence of 55.5 dBZ. As the quantization increment of the data is 0.5 dB, we conclude that the true median is close to 56 dBZ and the variation of the radar system gain (H channel) and/or environmental conditions affecting strength of reflected signals is within the quantization interval. For the most part the temporal change of the median ZV (Fig. 3) is within 0.5 dB similar to the change of median ZH (Fig. 3) except it exhibits faster fluctuation between the two quantized levels. This prompted a more detailed look at the characteristics of the dataset.
We examine the number M of clutter detections (ZH > 50 dBZ and v = ±0.12 m s−1) within 20 km of the radar as function of time (from scan to scan at 5-min intervals). The number varies within contiguous time periods by less than 1.6% as can be seen in Fig. 3 where for visual clarity the difference M − 〈M〉 is plotted, and 〈M〉 = 4865 is the average for the whole span of data with rain. The vertical lines bracket uninterrupted data episodes and abrupt changes occur at each transition (i.e., coincide with the gaps in data). The largest steps (~10%–15% of the total number) occur on 28 November, 3 December, and 30 December. These largest changes correlate with the decrease in the average values of clutter ZH (Fig. 4, top and middle) and ZV (not shown) suggesting that a common cause influenced both channels. It could be a small systematic decrease (about 0.1 dB, Fig. 4) in transmitted power or some environmental factor. Thus, we submit that the number of detections can serve a useful role in identifying the times of the onset of change. Attribution of this change to a definite cause is difficult, but the fact that such a small change is detectable implies that larger changes (~0.5 dB) should be easy to monitor.
As in Fig. 3, but (top) average ZH of ground clutter; (middle) 30-point running average of ZH and ZV (2 dB is added to ZH for visual clarity); and (bottom) 30-point running average of ZDR.
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
The average values of ZH (Fig. 4, top) have definite trends not seen in the median due to coarse quantization. Superposed to the slower variations are rapid fluctuations suggestive of noise. To quantify and separate the two we analyzed the autocorrelations of averaged ZH, ZV, and ZDR. This we did for each episode (separated by thin vertical lines in Figs. 3 and 4). The examples in Fig. 5 illustrate the autocorrelation coefficients and are typical for most of the episodes. The time it takes the autocorrelation coefficient to reach 0 is 250 min.
Autocorrelation coefficients rZH, rZV, and rZDR of ZH, ZV, and ZDR, respectively, of average values. Data are from 21 Nov 2009 (the ZH data from which rZH was computed are in the first episode in Fig. 4). The thick marks correspond to lag of 50 min (10 points, 5 min apart).
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
The SNR corresponding to the vertical polarization is larger in Fig. 5 and in all other episodes we examined. In few correograms of the ZH the correlated part was almost nonexistent as it had no continuity in the lag domain and could not be separated from the background fluctuation; the correogram consisted of a noise peak at 0 lag and uniformly fluctuating values at other lags. This was not the case with the ZV correograms and consequently was also not seen in the ZDR correograms. These correograms always had a well-defined decreasing trend with a lag up to a zero value. The time to zero correlation varied between about 50 min and 15 h, but most values were about 2–3 h.
Further quantitative evaluation is listed in Table 1 for all episodes of rain and snow. The variances (i.e., signal) of ZV are mostly 4 or more times larger than corresponding variances of ZH. Also the SNRs of the ZV are larger by a similar factor. The correlation coefficients (lag 0) between the average ZH and ZV are low with only three values exciding 0.5 suggesting that the environment is not a major cause of variations.
BoXPol: signal variances, SNR of 〈ZH〉, 〈ZV〉, and 〈ZDR〉, correlations of 〈ZH〉, 〈ZV〉, and noise variances for each contiguous part (rain means rain or no rain days; sn means snow or no snow days).
The changes in the noise variances (power in the jargon of electrical engineers) are within about ±25% of mean values, which are 13 × 10−4, 30 × 10−4, and 16 × 10−4 dB2 for the Var(ZHN), Var(ZVN), and Var(ZDRN) as can be seen from the last row and last column in Table 1; corresponding standard deviations are 0.036, 0.055, and 0.04 dB.
Figure 6 illustrates the histogram of change {i.e., med[ZDR(i + 1)] − med[ZDR(i)], i is time index} of the median ZDR value between the consecutive scans for the data in Fig. 3 (258.6 h). The plot clearly indicates most changes (73%) between scans are within the quantization interval (0.05 dB) of the recorded data. The standard deviation of the changes is 0.07 dB, slightly higher than the standard deviations of averages in ZDR likely due to quantization noise and relatively low correlation between adjacent median ZDRs. The changes are sufficiently small to justify some temporal filtering followed by compensation of the corresponding bias in ZDR over the rest of the volume subsequent (or prior) to the lowest-elevation scan.
Histogram of the difference of median ZDRs from ground clutter between two consecutive scans. The values are obtained from the data in Fig. 3.
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
Data indicate correlation times of few hours hence we averaged over 2.5 h (30 points) and plotted the values of filtered ZH and ZV in Fig. 4 (middle) and ZDR (bottom). Stability and consistency of filtered average ZH is in contrast to the more variable ZV, which could be due to significant gain variations in the V chain. Otherwise, the dominant influence of ZV on ZDR is quite visible as anticorrelation in the variations of the two. This is expected because the ZV is linearly related to ZDR (computation of ZDR in the radar signal processor is from powers prior to conversion into reflectivities).
In Fig. 7 are the time dependencies of filtered average ZH and ZV, median ZDR and the deviation of the number of detection from the average (which this time was 4653 points) for the 7 days in which snow fell within the radar coverage area. A pulselike swing of M by 1200 (26%) in the fifth episode is unusual. Associated with it are drops in filtered-averaged ZH and ZV, which cause significant increase in the signal variances (see Table 1) and a spike in ZDR. The zoomed view of M − 〈M〉 (Fig. 8, bottom) shows the leading and trailing edges lasting about 25 min and 35 min and the duration of the deep decrease in between is 80 min. Clearly the change is slow and subtle and thus could not be due to an abrupt failure of hardware. The relatively monotonic drop and rise in the number of detected points might have been caused by environmental conditions. This hypothesis prompts the following more detailed analysis.
(top) The 30-point running average of ZH and ZV with 1.5 dB added to ZH for visual clarity. (middle) Median ZDR. (bottom) Difference between the total number of clutter detections M and the average number of clutter detections 〈M〉 = 4653. The dataset consists of 1827 samples spaced 5 min apart from 7 days (between 22 Dec 2009 and 9 Jan 2010) on which snow fell somewhere within the radar coverage. The thin vertical lines indicate temporal discontinuities between contiguous samples. The thick marks on the time axis are in increments of 500 min.
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
(top) Median values of ZH and ZV from snow obtained at 4.4° elevation between 5 and 20 km from the radar. (middle) Median ZDR. (bottom) Difference between the total number of clutter detections M and the average number of clutter detections 〈M〉 = 4653. Time (UTC) is indicated. The vertical dotted lines bracket the sharp drop and sharp rise in the number of detections. The thick marks on the time axis are in increments of 25 min.
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
From 0400 to 0830 UTC temperature in Bonn (100 m from the radar site measured at 5-min intervals) was between −0.5° and 0.7°C. It is doubtful that this variation by itself could have caused the drop in clutter detections. But a physical change of some kind seems to have occurred on the radar system. We speculate that the effect might have been due to snow falling on the antenna and the antenna-mounted receiver both of which are exposed to the environment. Thus, we examined the reflectivity fields and found that significant snow started falling over and around the radar at 0430 UTC. The median reflectivity factor of snow within 20 km from the radar and obtained at 4.4° elevation is plotted as function of time in Fig. 8 (top). By 0530 the uniform snow field broke in two small bands one of which crossed the radar at about 0543 UTC. The temperature from the start of snowfall (Fig. 8, top) until 0454 UTC was consistently at 0.7°C and gradually fell to reach 0.4°C at 0538 (it stayed at that value until 0738 UTC, thereafter it was gradually dropping again). During all this time the air was calm. It could be that the small fall in temperature at 0538 UTC was amplified at the antenna, which is on a building top 18 m above ground. Perhaps wet snow was freezing on the dish and/or the feed horn assembly both of which likely experienced increased radiative cooling. Although the change in clutter ZH and ZV is modest, ~0.3- and 0.4-dB decrease (Fig. 7), the tell-signal in the number of detections is remarkably distinct and strong. Whatever condition the environment caused it remained unaltered until just after sunrise (0733 UTC) by which time and coincidentally the snowfall was completely gone. Whereas the slow increase starting with the sunrise might be fortuitous the steep reversal starting at 0741 UTC is not accidental. It took similar amount of time as in the drop of the number of detection to restore the radar status (by 0816 UTC). It could be that the sun caused warming of the dish and elimination of the ice/snow. Accumulation of ice precipitation on the dish and or feed can distort the antenna pattern and cause change in directivity.
Consistent with the episodes in which rain fell somewhere (Fig. 4 and Table 1) are the results for the snow cases: the variability of ZV is larger whereas that of ZH is within 0.2 dB until the time when the number of samples M drops.
b. Analysis of S-band radar data
The modified KOUN radar was used to collect data on 3.5 consecutive days (2–5 July 2011). Clutter filter (which normally operates in real time) had been disabled and volume scans were accomplished in approximately 10-min intervals (average separation was 9.73 min). Radials of overlapped data spaced 0.5° apart in azimuth were collected at the elevation of 0.5°. Two consecutive scans at 0.5° elevation were made: a surveillance scan for ZH and ZDR measurements (pulse repetition frequency of 326 Hz and 64 pulses for averaging) and a Doppler scan for estimating the first and second spectral moment.
In between volume scans (while the antenna is descending) an automatic calibration procedure is used to estimate noise powers and bias in ZDR (Zrnic et al. 2006); these are applied to correct data in the subsequent volume scan. Therefore, the imbalances in the transmitter and receiver part of the radar do not induce variations in ZDR from ground clutter making it easy to determine the influence of the environment on the stability of this measurement. A significant environmental factor turns out to be the refractivity profile. It induces differences in the differential reflectivity from clutter because the beamwidths (in elevation) of the main lobes at horizontal and vertical polarizations are not necessarily equal (see the appendix). Thus, the change in elevation and/or beam bending causes a change in ZDR. At close range the changes due to beam bending are relatively small and so is the number of clutter targets. We found that a good compromise is 7 km, which we use on this dataset.
In Fig. 9 the system ZDR is defined as the measured bias that is automatically taken out from the data. The very well-defined periodicity of 1 day is related to the temperature in the radome, suggesting that the primary cause of the bias is the difference in gains of the H and V amplifiers. The extreme variation is within 0.1 dB justifying the need for automatic correction.
(top) System ZDR obtained automatically at the end of volume scans using signal generator and a prior initial calibration. Dotted vertical lines indicate beginning of a day (UTC time); the dates and minutes of the beginning are indicated along the abscissa. (middle) Median ZDR. (bottom) The difference between the number of points M and its average value (〈M〉 = 2742). Data obtained with the preproduction model of the WSR-88D. The thick mark on the abscissa corresponds to 10 consecutive volume scans (accomplished in 9.73 min).
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
The variation in the median ZDR from clutter (Fig. 9) has also a diurnal periodicity; the same is very clearly seen in the average ZH (Fig. 10). The surface temperature excursion on these 3 days was ~13°C (Fig. 10) and the average ZH from clutter has a minimum slightly lagging the time of maximum temperature. (The number of clutter detections has a similarly positioned minimum.) Because the boundary layer becomes well mixed after the time of maximum surface temperature the beam will be least bent at that time. Hence, its weaker lower part would illuminate clutter.
(top) Average ZH from clutter. (middle) Surface temperature. (bottom) Average elevation angle of the lowest (commended to be 0.5°) scan. Times and thick marks are as in Fig. 9.
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
The median ZH varies within the quantization interval (i.e., 53 and 53.5 dBZ) suggesting that monitoring of power calibration within 0.5 dB would be viable (just as in the case of BoXpol). The average ZH exhibits small variations caused by radar and its environment.
As stated the median ZDR exhibits diurnal trend, which would preclude its use for routine automatic calibration at the end of volume scans. But if measurements are made at the same time (i.e., under similar environmental conditions) a check of calibration to within ~0.1 dB appears possible. Note that quantization interval of ZDR on the KOUN radar is 0.0625 dB compared to 0.05 on the BoXPol. The autocorrelation coefficients of average ZH and ZDR (Fig. 11) show that the diurnal periodicity and superposed higher-frequency variations are especially visible in the rZH plot. The high-frequency variations have a period of approximately 50 min and are caused by periodic variation of the antenna elevation angle (Fig. 11, bottom). Examination of the scanning process (recorded in the data) reveals that every volume scan begins at an azimuth angle on the average 66° larger than the previous one (the position varies randomly between 60° and 75°). Thus, at the end of the fifth scan the antenna is positioned ~30° behind in azimuth from the first scan. For other scans relatively close to the batch of the five, the starting position of the antenna is farther away from the first scan. This basic periodicity of the five is highly correlated with the antenna elevation variations that are within 0.04° of the mean (not shown). Such small variations cause less than 0.1 dB change (not shown) in the ZH. The change in elevation with the starting azimuths of volume scans might be coincidental; some other factor such as periodic drift in the servo control might have caused it. We add that the KOUN pedestal is one of a kind (it is the preproduction model of the WSR-88D). Hence, we do not know if a similar effect is present on other WSR-88Ds as these have larger and more robust units.
(top) Autocorrelation coefficient of ZH. (middle) Autocorrelation coefficient of ZDR. (bottom) Autocorrelation coefficient of average elevation angle. The thick marks are at lag 10 corresponding to 10 scans separated by 9.73 min. The linear tapers with lag are caused by the linear decrease in the number of points normalized to the total number of points in computation of the autocorrelations.
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
The variances of ZH are within the values of ZH variances estimated on BoXPol data and the SNRs (Table 2) are comparable. The noise powers are a little higher possibly due to larger quantization and superposed high-frequency oscillations in the data from Norman.
KOUN: Signal variances, SNRs, and noise variances of 〈ZH〉 and 〈ZDR〉.
Next we concentrate on the time ~0400–0700 UTC 4 July when the number of detections increased significantly (500–1000 more). The increase is by a factor of 2 (from ~6000 to ~12 000) if clutter up to 20 km in the range is included. We examined the data and found that a storm moved over the radar at 0400 UTC and stalled. At 0500 UTC it begun to dissipate rapidly, extinguished by precipitation embedded in a downdraft. The ensuing cool air (see the sharp temperature drop after ~0250 UTC, Fig. 10) spread and created an inversion conducive to beam bending toward ground hence the increase in the number of detections (Fig. 9, bottom) and average ZH (Fig. 10, top). Note that the increase in median ZDR (Fig. 9, middle) precedes the increase in ZH, likely due to wetness as opposed to contamination by precipitation as there is no increase in the number of detected points. The rain came after many days of extremely hot dry weather, hence, it could have influenced clutter reflectivity.
4. Discussion
Analysis of data suggests that the average of ground clutter reflectivities is sufficiently stable over a 1-month period in a cool environment (Germany) that it can be used to monitor radar calibration. In 3.5 days of a hot summer environment in Oklahoma the reflectivities of clutter were similarly stable. Combined with the number of detections, measurements of clutter ZH can point to changes that affect calibration. The following is a list of influences on measurements of Z and ZDR from clutter:
changes in transmitted power;
changes in receiver transfer function (mainly gains);
antenna settling in elevation from scan to scan;
differences in beam pointing (azimuth) at subsequent scans;
variation of clutter reflection coefficient;
refraction of the beam; and
changes in attenuation due to precipitation.
Some of the changes can be isolated and related to radar problems, but for monitoring calibration the changes in the transmitted power and the receiver transfer function need to be quantified. Influence of transmitted power variation on Z calibration is resolved with direct power measurements. On occasions there can be other impediments such as accumulation of snow on the radome; monitoring of ground clutter can alert engineers about these. One can set a threshold (say 0.5 dB) and take action if the threshold is exceeded. If one of the Zs from clutter stays constant (say within 0.1 dB) as ZH in Fig. 3 (within each episode), but the other exhibits variations, it suggests the transmitter power is stable and the likely cause is in the receiving chain and a correction to ZDR bias would be warranted. If both reflectivities exhibit significant correlated variations, it would suggest a common cause such as transmitted power change or environmental influence.
Consider antenna settling at slightly different elevations from scan to scan. For Bonn data the midrange of clutter contribution is 10 km, and if 0.05° variation in elevation occurs there would be a corresponding vertical displacement of the beam by 8.7 m. The extent of the main lobe from center to the null is more than 1°. Therefore at 0.5° elevation the principal contribution of clutter is through the steep part of the main lobe. Furthermore, the change in antenna pattern value over a 0.05° (at 1° off axis) is 2.5 dB. Clearly this large variation would be seen in the plots of ZH or ZV. The fact that it is not seen implies that the variations are much smaller or not present. We would expect these to be random, but not systematic as observed in the Fig. 3 (average ZH, ZV).
In data from the polarized KOUN (preproduction WSR-88D) the variations in elevation (0.04° peak to peak) are periodic and correlate with the corresponding variations (0.2-dB peak to peak) in ZH from clutter. These are due to the azimuthal dependence of antenna settling at the beginning of volume scans. Although very small, the variations are easily detected because of the large number (few thousand) of ground clutter points.
If the main lobes for the H and V polarizations differ slightly in width, the ZH and ZV would be positively correlated. If antenna position changes (up or down) then both reflectivities would decrease if the antenna has moved up and increase if it moved down. The ZDR would increase if the antenna moves up and the H pattern is wider (larger than the V pattern at the same distance from beam axis) because the difference of patterns at places the beam hits ground increases. If the H pattern is narrower, the ZDR will decrease. On the KOUN radar the changes in elevation and ZDR are out of phase indicating that the beamwidth at V polarization is broader than at H polarization (see the appendix) by about 0.04°.
Imperfect beam positioning in the azimuth can also cause variation in Zs and ZDR from scan to scan. The effect is similar to the one from beam settling in elevation and it might have a periodic component. Briefly the exact position in the azimuth is not in perfect sync with the timing of samples for computing estimates of polarimetric variables. Thus, the position of the beam at the center of dwell time differs from scan to scan. The value of ZH and ZV would be affected just the same as in case of settling in elevation. An increase in both occurs if in the subsequent scan the effective beam center is pointing closer to the dominant ground scatterer. Otherwise, a decrease in both follows. The differential reflectivity would be influenced by the difference in azimuthal beamwidths just as it is in case of elevation changes.
We do have evidence of change in the effective pointing direction of the antenna on the BoXPol which manifested itself in a smaller number of clutter detections due to decrease in the reflectivities. Also occasional changes in the range location were noted.
Short-term changes in the reflection coefficient from urban clutter can be caused by wetness. We expect these to be similar for ZH and ZV; hence, the two would be highly correlated and perhaps not affect ZDR. But we have circumstantial evidence that wetness after a dry period in Oklahoma might be a reason for increased ZDR; the clutter environment in Norman is a mix of suburban houses and open rolling prairie with small trees, which might make a difference. Long-term changes (due to presence or absence of leaves on trees) might also affect ZDR.
Banding of the beam due to change in the profile of refraction can have a significant influence on Zs and ZDR. In the cool regime like winter in Bonn no diurnal trends are evident as the refraction profile changes little throughout the day. Nonetheless, a change due to passage of a cold front correlates well with the increase in the number of detections and the average values of ZH, and ZDR. Diurnal periodicity is evident in the data from Oklahoma and is highly correlated with the surface temperature. Moreover, an episode of cool outflow from a dissipating storm cell created a stable layer that caused significant beam bending and an increase in ZH. Although small (few tenths of a dB) the changes are very well defined.
Change due to attenuation can be significant and in heavy precipitation would preclude calibration of Z and ZDR from clutter returns. Perhaps the amount of attenuation could be diagnosed and cautiously used for corrections of reflectivities and differential reflectivities caused by these effects, but systematic correction of biases by drifts in the hardware would be very difficult in cases of heavy precipitation. Still ground clutter returns between episodes of heavy precipitation might suffice to monitor the radar status.
5. Conclusions
The possibilities of using median and average values of ground clutter reflectivity and differential reflectivity for monitoring polarimetric radars’ calibration have been explored. For that purpose two sets of data have been examined: over 1 month from the X-band polarimetric radar (Bonn, Germany) and 3.5 days from the preproduction polarimetric WSR-88D radar (Norman, Oklahoma). Very simple (but satisfactory) clutter detection by restricting the range close to the radar and accepting values larger than a threshold of 50 dBZ was used. More sophisticated techniques are available for operations, but were not needed in this proof-of-concept study. We constrained the range of clutter to 20 km in Bonn and 7 km in Norman. That way the effects of beam bending under significant temperature variations in Norman were reduced.
We have determined that ZH and ZDR from clutter can have a role in checking calibration (bias) in these two variables. However, because both the environment (including temperature and precipitation) and the radar system influence ZH and ZV, it is important to determine if the changes due to the environment are within acceptable calibration errors.
We conclude that median and average reflectivities of urban ground clutter are good indicators of radar stability. In 3.5 days of S-band radar data the median stayed within a quantization interval of 0.5 dB, which is the same as found in data from Bonn over a much longer period of time. This is deemed acceptable for routine monitoring of power calibration. Thus, the average ZH can be used to see subquantization effects and sound an alarm if these become unacceptable. The variation of average ZH in Oklahoma had a diurnal periodic change within about 0.2 dB. The periodicity is caused by the pronounced diurnal cycle of refractivity profile driven by surface temperature (~13°C diurnal change). No such periodic variation existed in Bonn data likely because of the cool season, but amplitude of the average variation was similar.
On one occasion in Oklahoma the change in ZH was predicated by a cool-air storm outflow. An increase in the number of clutter detections as well as ZH followed. Thus, the variation in the average number of clutter detections can be a proxy for reflectivity variation.
The effects of the environment on ZDR are significant and might be difficult to routinely separate from the changes in the system. Nonetheless, monitoring ZDR from clutter has merit on three accounts. 1) If changes are within tolerable limits (say 0.2 dB) unnecessary calibration work would be avoided regardless of the cause. 2) Changes correlated with signals from the environment such as temperature, the presence of outflows, and storms indicate the system is most likely functioning properly and need not be tended for. 3) On days with similar periodic environmental conditions one can use ZDR quantitatively to estimate the system bias by choosing the time for calibration when conditions are most similar and stable. We suggest that a low correlation coefficient between ZH and ZV might indicate a problem in one of the receiver channels. This was apparently the case in the data from Bonn.
Other factors can be uncovered by observing clutter returns. Once in the Bonn data the number of detections dropped significantly apparently from the effect of snow accumulation on the antenna. In the case of the Oklahoma radar, periodicities of average ZH pointed to small (0.04°) periodic variations of the elevation angle. Inadvertently, from these variations, we were able to determine the difference of beamwidths in the vertical direction between the patterns for horizontal and vertical polarization. These agreed well with independent pattern measurements.
Because of its ubiquitous presence and stability ground clutter offers possibilities to continuously monitor the state of a radar system. The scheme is amendable for real-time applications and can be made more robust if the reflectivity threshold applied herein is augmented with a sophisticated clutter recognition procedure. Tests of the technique at locations with different clutter type (forests, prairies, mountains) need to be made during various seasons to determine the extent of its applicability.
Acknowledgments
We thank the Meteorological Institute at the University of Bonn for the X-band radar data. We thank Prof. Simmer for establishing and leading the radar program. Richard L. Ice and Darcy Saxion from the Radar Operation Center, Norman, Oklahoma, arranged data collection on the polarimetric WSR-88D (KOUN). Dan Suppes and John Krause from CIMMS, Norman, Oklahoma, provided these data to us. We appreciate the suggestion of one reviewer to explore the clutter map and examine data from the WSR-88D radar, and the suggestion by the other reviewer to plot the number of clutter detections. Funding for Dr. Borowska was provided by the National Research Council (NRC) sponsored by NOAA/Office of Oceanic and Atmospheric Research Grant N-0940760.
APPENDIX
Patterns at Horizontal and Vertical Polarizations
The usual assumption in computing the polarimetric variables is that the radar resolution volume is uniformly filled with scatterers, and the beam cross section is circular. Herein we demonstrate that the cross-section areas of the main lobes for horizontal and vertical polarizations are equal, but the beamwidths in the vertical (or horizontal) planes are inherently different. The difference can be obtained from measurements of ground clutter.
The main reason for the elliptical shape of the pattern cross sections is the distribution of currents on the dish. It is obvious that the distribution of the currents created by the V polarization would match the distribution created by the H polarization if the dish is rotated by 90°. A consequence is that the pattern cross sections are ellipses of equal area but “orthogonal” to each other. Therefore, the resolution volumes of the two patterns are equal and so are the gains, and if the beam is uniformly filled with scatterers, the difference in patterns would not bias the polarimetric variables.
The geometry of the KOUN radar. The elevation angle is θ, the average along a ray distance to clutter is 4.5 km, and a flat earth is assumed.
Citation: Journal of Atmospheric and Oceanic Technology 29, 2; 10.1175/JTECH-D-11-00036.1
If one of the beamwidths is known then the other can be computed from (A4). Measurements on an open-antenna range of exactly the same type of antenna and at the same frequency (2.700 GHz) indicate that the beamwidth at horizontal polarization in the vertical (E-electric field plane) was 0.95°. The beamwidth at horizontal polarization in the same plane (i.e., vertical, magnetic field plane for H polarization) is not available. But beamwidths along both planes are available for the vertical polarization (0.94° in the E plane, which is now horizontal and 0.9° in the H plane). Therefore, assuming that the beamwidth at horizontal polarization in the E (vertical plane) is 0.9° (as theory suggests) we estimate the difference in beamwidth of 0.04°. This estimate coincides with the value obtained here (0.04°) from the average magnitude of Δθ and 0.03° obtained from the average in the maximum swing.
As indicated, the periodicity in variation of the elevation angle and ZDR were obvious in the time plots but their phase relation could not be clearly seen. Thus, we plotted the cross correlation and saw that its periodicity was offset by half a period from the variations in ZDR and elevation. This indicates that the elevation beamwidth at horizontal polarization is smaller than the elevation beamwidth at vertical polarization. We stress that this estimate is not biased by the possible difference in gains at the two polarizations.
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