In-Place Estimation of Wet Radome Attenuation at X Band

Transcription

1 MAY 2013 F R A S I E R E T A L. 917 In-Place Estimation of Wet Radome Attenuation at X Band STEPHEN J. FRASIER Microwave Remote Sensing Laboratory, University of Massachusetts Amherst, Amherst, Massachusetts FADELA KABECHE, JORDI FIGUERAS I VENTURA, HASSAN AL-SAKKA, AND PIERRE TABARY Centre de Meteorologie Radar, Direction des Systemes d Observation, Meteo-France, Toulouse, France JEFFREY BECK AND OLIVIER BOUSQUET Centre National de Recherches Meteorologiques, Meteo-France, Toulouse, France (Manuscript received 10 July 2012, in final form 3 January 2013) ABSTRACT The effect of wet radome attenuation is estimated on a French operational X-band weather radar deployed in the Maritime Alps of southeastern France. As the radar is deployed in a remote location, the reflectivity factor in the immediate vicinity of the radar is used as a proxy for rain rate at the radar and by extension, to the radome wetting. By means of intercomparison with a neighboring radar that lacks a radome, a wet radome correction is deduced. The correction is reasonably consistent with theoretical expectations and with other evaluations done, for example, via disdrometer. The improvement is evaluated by comparison to a Micro Rain Radar located under the point of comparison, and the impact on quantitative precipitation estimation (QPE) retrievals is positive. The intercomparison of such observations permits a routine means of monitoring radome attenuation. 1. Introduction Operational and research weather radars are often covered by radomes that serve several purposes. They protect the antenna and pedestal from the elements, provide a consistent environment, and provide a directionindependent wind load. In addition to these technical reasons, radomes also mitigate the visual impact of operational weather radars by hiding the moving parts. Radomes also have the deleterious effect of disrupting the transmitted and received signals. Rain and ice on the radome will degrade the signals beyond the nominal dry radome attenuation. For frequencies below C band, these impacts can usually be ignored. However, at higher frequencies, and in particular at X band, the impact of radome attenuation can be significant. As research and operational networks begin to incorporate X-band polarimetric radars for weather and hydrological applications (Matrosov et al. 2005; Wang Corresponding author address: Stephen J. Frasier, Microwave Remote Sensing Laboratory, University of Massachusetts Amherst, 151 Holdsworth Way, Amherst, MA frasier@ecs.umass.edu and Chandrasekar 2010; Kabeche et al. 2010, 2011), the impact of radome attenuation must be considered. Wet radome attenuation (WRA) has been studied at several frequencies. Early studies focused on satellite communications systems (Gibble 1964; Blevis 1965; Anderson 1975), while weather radar studies by Merceret and Ward (2002) and Kurri and Huuskonen (2008) reviewed prior work with focus on performance at S and C bands. Thompson et al. (2012) have recently illustrated techniques to estimate attenuation at C band through observing the radar system noise. At X band, Trabal et al. (2008) devised a formula for radome attenuation using area-averaged quantitative precipitation estimations (QPEs) over a rain gauge network and simultaneous observations by a nearby Weather Surveillance Radar Doppler (WSR-88D). Bechini et al. (2010) made simultaneous X-band radar measurements at close range with a collocated video disdrometer to provide unattenuated reflectivity factor estimates. In this paper we compare near-simultaneous observations of a common volume by two X-band radars: one with a radome and one without. The radars comprise the first two installations of the Risques Hydrometeorologiques en Territoires de Montagnes et Mediterraneens DOI: /JTECH-D Ó 2013 American Meteorological Society

2 918 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 30 (RHYTMME) network, an operational and research network to improve hydrological measurement and forecasting in the French Maritime Alps. The observations are stratified by the observed reflectivity factor nearest to the radar with the radome. This near-radar reflectivity is used as a proxy for the rain rate on the radome. In the following section, we describe the siting and characteristics of the X-band radars. Section 3 describes the methodology and observations used to derive the correction. In section 4, we compare the correction to both theory and other available X-band wet radome attenuation corrections. 2. Theory In the absence of precipitation, a radome is designed to be as transparent as possible while retaining sufficient structural integrity to support itself and to withstand weather hazards (rain, snow, hail, high winds). Typical dry radome one-way attenuation is a few tenths of a decibel. Radomes may be inflatable, in which case they are very thin, or they may be self-supporting. A sandwichtype construction is typical with thin laminates as outer layers separating a low-dielectric, rigid foam within. A foam-layer thickness of a quarter wavelength (within the foam material) minimizes the total reflection from the two laminate layers and thereby maximizes transmission. Alternatively, a uniform, single layer of dielectric of halfwavelength thickness (within the dielectric medium) achieves a similar minimization of total reflection. Large or multiband radomes may employ more sophisticated multilayer structures. The presence of water on the surface can significantly impact radome performance. Radomes are usually treated with a hydrophobic coating to suppress the collection of water on the surface. Water droplets bead on the surface and run off when they achieve sufficient mass. When the hydrophobic coating is lost or degraded, however, sheeting of water will occur. This latter case is easier to treat analytically, since the layer of water is uniform. The transmission loss for a specific radome with a layer of water on its surface can be treated as a multilayer dielectric. Here, we assume a two-layer model consisting of a uniform dielectric radome and a uniform layer of water. For this simple model, the overall transmission loss through the two-layer structure can be expressed as L db 5 T 210 log 1 T 2 T 3 e 2j(u 1u r w ) 2 11G 1 G 2 e 2j2u r 1G 2 G 3 e 2j2u w 1G 1 G 3 e 2j2(u 1u r w ), (1) where u r and u w are the electrical thicknesses of the radome and water layers, respectively, defined as pffiffiffiffi pffiffiffiffiffi u r 5 k 0 rdr, u w 5 k 0 wdw, (2) where k 0 is the free-space wavenumber; r and w are the complex relative dielectric constants of the radome material and of water at X band, respectively; and d r and d w are the physical thicknesses of the radome and water layer, respectively. Also, T 1,2,3 and G 1,2,3 are the respective transmission and reflection coefficients for the electric field at the 1) air radome, 2) radome water, and 3) water air interfaces, defined as G p ffiffiffiffi r p 1 1 ffiffiffiffi, r pffiffiffiffi pffiffiffiffiffi G 2 5 r 2 w pffiffiffiffi p ffiffiffiffiffi, 1 r w pffiffiffiffiffi G 3 5 w 2 1 pffiffiffiffiffi, and w 1 1 T 1,2, G 1,2,3. (3) Note that the numerator of the expression in (1) represents the cumulative transmission and one-way propagation through the two-layer structure, while the denominator represents the multiple internal reflections and associated two-way propagation through the structure. For multilayer structures, an analytical expression becomes unwieldy due to the many possible combinations of internal reflections. Although these can be treated via the method described in Kurri and Huuskonen (2008), this simple model is sufficient for evaluating radome wetting effects. The radome s dry attenuation is the most important property to capture, and precisely how this is modeled is secondary. We therefore choose to model the radome as a uniform dielectric layer with the same dry attenuation as that quoted by the radome manufacturer. We assume a low-loss fiberglass material ( r j072) such that the dry, one-way attenuation is 0.3 db. We use the dielectric constant for water at X band from Meissner and Wentz (2004). The thickness of the water layer can be related to rain rate through Gibble s formula (Gibble 1964; Anderson 1975), 3mk ar 1/3 d 5, (4) 2g which assumes a spherical radome, and where m k is the kinematic viscosity of water, a is the radome radius, R is the rain rate, and g is gravitational acceleration (all

3 MAY 2013 F R A S I E R E T A L. 919 TABLE 1. Comparison of the two X-band radars. Parameter Vial Maurel Make Novimet Selex-Gematronik Model Hydrix Meteor 50DX Peak power (kw) Frequency (GHz) Pulse width (ms) 2 2 Polarization Dual simultaneous T/R Dual simultaneous T/R Antenna Offset parabolic Center-fed parabolic Beamwidth (8) Range resolution (m) Radome No Yes FIG. 1. Predicted transmission loss at 9.4 GHz through a 2.5-m-diameter spherical radome covered with a laminar sheet of pure water at the given temperature as a function of rain rate. Solid lines: water-covered radome. Dotted lines: water layer alone. expressed in MKS units). Both the viscosity and the dielectric constant vary with temperature, and both vary so as to reduce transmission loss with increased temperature. Solid lines in Fig. 1 show the predicted one-way transmission loss through a 2.5-m-diameter radome covered with a uniform water layer of thickness given by (4) as a function of rain rate. Dotted lines show the effect of the water layer alone (i.e., assuming r 5 1 for the radome). The figure suggests two-way attenuations of more than 3 db can occur for even modest rain rates. This error can have a major impact on quantitative precipitation estimates. Radomes with a hydrophobic coating that inhibits the sheeting of water may be expected to perform significantly better than this theoretical prediction, especially at lower rain rates. However, the beading of water on the surface and the formation of rivulets that run down the radome surface result in a spatially varying effect that is less straightforward to model. It may also impact polarimetric performance, as one may expect rivulets to be vertically oriented in the absence of significant wind. Over time, as the hydrophobic properties of the radome surface are lost, the theoretical prediction of (1) is more applicable. 3. The RHYTMME network The French Southern Alps area of southeastern France is a mountainous region prone to heavy rain and flash-flood events in the summer and autumn months. Because of the complex terrain, radar coverage by France s terrestrial network in this area is poor. Meteo- France along with regional partners has established a project entitled RHYTMME that is deploying a network of four X-band polarimetric radars to improve the coverage in this region (Westrelin et al. 2010). At present, two radar sites are operational. One of these is a preexisting installation located near Nice on Mont Vial. It is a Novimet Hydrix radar owned by the Centre National de la Recherche Scientifique (CNRS) and operated under contract by Novimet. This radar employs an offset parabolic reflector with no radome. The other radar, owned and operated by Meteo-France, is located 52 km to the northeast on Mont Maurel. It is a Selex-Gematronik X-band radar employing a centerfed parabolic antenna with a radome. Characteristics of the two radars are listed in Table 1. Of comparable size, power, and capability, the principal difference between the two radars is the presence or absence of a radome. Between these two sites, in the village of Puget- Theniers in the Var valley, a Metek K-band (24 GHz) Micro Rain Radar (MRR) was installed and operated for most of 2011 by the Centre National de Recherches Meteorologiques (CNRM). The MRR is a small, frequencymodulated continuous-wave radar that provides vertical profiles of the Doppler spectrum due to precipitation. From the Doppler spectra, assuming drops fall at their terminal velocity, a variety of parameters are deduced. These include drop size distribution, rain rate, and reflectivity factor. Deriving these properties from the Doppler spectrum necessarily neglects the impacts of vertical air motion. Thus, the estimates obtained in convective precipitation may be subject to some error. Figure 2 shows the relative locations of the three radars and the regional topography. The two X-band radars are separated by 52 km. The K-band MRR is located 22 km from Mont Vial and 30 km from Mont Maurel and nearly along the baseline between the two radars. While not equidistant from both X-band radars, the differing beamwidths of the two radars partially offset this effect (the MRR site is closer to Mont Vial,

4 920 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 30 FIG. 2. (top) Topography in the vicinity of the Mont Maurel, Mont Vial, and MRR locations. (bottom) Terrain profile along the dotted lines in (top) (solid line). Beam elevations as indicated (dashed lines) intersect over the vertically pointed MRR. Pictures of the (left) Maurel and (right) Vial radars are shown as insets. which has the wider beam). Thus, the sampling volumes of the two radars at this location are quite similar. Figure 2 also shows the respective deployment elevations and beams used in this study over the MRR location. Above the MRR site, the 0.58-, 1.58-, and 2.78-elevation beams from the Maurel radar nearly align with the respective 1.28-, 2.48-, and 4.08-elevation beams from the Vial radar. The lowest beam from Mont Maurel is subject to some partial beam blockage by a ridge approximately 8 km from the radar. A correction for this blockage of 4.6 db was deduced from adjacent tilts of the radar in this region. 4. Methodology and dataset For this study we compare near-simultaneous observations by the two X-band radars over the MRR location. While the sampling volumes are nearly spatially matched, the differing scan patterns of the two radars yield time differences of up to 2.5 min (the tilts analyzed herein are repeated at 5-min intervals). Thus, fastmoving features may be present in one radar s pixel and absent in other s pixel. This temporal mismatch results in additional scatter of the comparison beyond that due to inherent fluctuation of the weather echo, but it should not affect relative biases observed between the radars. Observations from the MRR during 2011 were surveyed for reflectivity factors exceeding 45 dbz at the altitudes of interest. Then, collocated observations from the Maurel and Vial radars were analyzed. A total of 14 days were selected, each day consisting of 288 observations by each tilt of each of the X-band radars. While both X-band radars employ pulse widths yielding an intrinsic range resolution of 300 m, Maurel and Vial employ 240- and 300-m range-bin spacing, respectively. Along the radials passing over the MRR site, we select nine range bins at four-bin (Vial) or five-bin (Maurel) intervals for comparison. Only reflectivities exceeding 0 dbz are considered. Figure 3 shows a histogram of all available observations. These are calibrated and attenuation-corrected X-band reflectivities processed through the Meteo- France dual-polarization processor (Boumahmoud et al. 2010; Figueras i Ventura et al. 2012). The attenuation correction assumes a linear relationship between pathintegrated attenuation (PIA) and the differential propagation (DP) phase,

5 MAY 2013 F R A S I E R E T A L. 921 FIG. 3. Histogram of attenuation-corrected reflectivities observed over the MRR location by the Vial and Maurel radars. The solid line is Vial 5 Maurel, and the dotted line is a least squares fit. An average bias over all observations is 3.63 db. PIA 5 0:28F DP. (5) This relationship was derived experimentally using the Vial radar (Kabeche et al. 2010) and the nearby S-band radar at Nimes. The two radars observations exhibit a correlation coefficient of 0.69 and a relative bias (Vial/Maurel) of 3.63 db. Since both axes are measurements subject to similar uncertainty, the regression line is that which minimizes the mean square error (MSE) along the direction orthogonal to the regression. The less-than-unity slope of the regression line indicates a reduced sensitivity to higher reflectivities by Maurel. This is suggestive of wet radome attenuation impacting the Maurel observations. The histogram of Fig. 3 does not take into account the effect of the radome on the Maurel radar. Since the radar is deployed in a remote location at high elevation, reliable monitoring of the true rain rate at the radar site is diffcult. We use the reflectivity factor observed at the nearest usable range bins to the Maurel radar as a proxy for the rain rate on the radar, and hence the relative wetting of the radome. In this case, we use the sixth range bin (between 1.5 and 2 km) along the radial passing over the MRR site. Denoting this value Z M,wethenstratifythe observations of Vial and Maurel subject to Z M within a prescribed range. While this is clearly an imperfect measure of radome wetting, it is the most straightforward to derive from routine observations. Figure 4 shows histograms similar to Fig. 3, except they are now conditioned on particular ranges of Z M as indicated. One can observe an increasing bias between the two radars measurements as Z M increases. Performing this over a number of ranges of observed Z M yields the curve of Fig. 5. This curve shows the average bias (Vial/Maurel) over all observed reflectivities as a function of the measured reflectivity Z M at Maurel. To construct this curve, all observations for Z M within 65 db of a given threshold are selected. The mean Z M for these points is chosen as the abscissa, while the observed bias is the ordinate. The threshold is increased in 5-dB steps. Averaging the observed bias is done in the log domain (on dbz values), which yields a mean bias representing the geometric mean of the ratios of Z values (Vial/Maurel). The geometric mean is the appropriate measure of the average when data are ratios or span large dynamic ranges (Hines 1983). A second-order polynomial fit is indicated, which can be used directly as an empirical correction. For low values of Z M, we assume a dry radome. Here, we observe a bias between the two radars of approximately 2.5 db. This difference includes an inter-radar calibration error (note: based on this and other observations, including QPE retrievals, the calibration constant of the Maurel radar has since been adjusted by 2 db). More importantly, bias in excess of this amount for larger values of Z M is attributed to the 2-way attenuation through the (wet) radome. Because the measured Z M is also subject to this attenuation, we must add this bias to the measured Z M to obtain the intrinsic Z M, which may then be related to rain rate. 5. Results Radome performance is commonly specified by manufacturers in terms of one-way attenuation. Symbols in Fig. 6 show the derived one-way attenuation versus rain rate assuming Marshall Palmer (Z 5 200R 1.6, diamonds) and WSR-88D (Z 5 300R 1.4,triangles)Z R relations. The dotted line is a fit to the observations, yielding the empirical relation A db 5 0:2 1 0:85R 1/3, (6) where A is the one-way attenuation in decibels and R is expressed in millimeters per hour. The dashed line shows the result obtained by Bechini et al. (2010) performed on a similar X-band radar. In their study, they used a collocated disdrometer to obtain intrinsic reflectivities to compare to radome-attenuated X-band measurements at very close range. The solid line is the theoretical attenuation from (1) at 208C. The

6 922 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 30 FIG. 4. As in Fig. 3, but for (clockwise from top left): 25, Z M, 5dBZ,5, Z M, 15 dbz,15, Z M, 25 dbz, and 25, Z M, 35 dbz. Larger values of Z M yield larger mean differences between Vial and Maurel observations. dashed dotted line is the relation obtained by Trabal et al. (2008). They studied area-extensive X-band reflectivies over a rain gauge network and used nearby WSR-88D (S band) observations over the X-band radar site as the indicator of local rain rate. They found a relation between observed differences of X- and S-band observations as a function of S-band reflectivity over the X-band radar. We have divided Trabal et al. s (2008) result by two to obtain one-way attenuation, and we have added 0.3 db to include dry radome attenuation. We find our result falls somewhat below the theoretical prediction and well below the result of Bechini et al. (2010). In their study, they noted the radome in use was old and had lost its hydrophobic properties. The Maurel radar was installed in October 2010 and so was in its first year of service for the data collected in this study. It may be expected to exhibit better hydrophobic properties, though it has been indicated that radomes may begin to lose their hydrophobic properties within the first 6 months to a year of service (Bechini et al. 2010). Over time, one may expect that the radome attenuation will increase as the hydrophobic coating degrades. In the absence of any knowledge of the radome condition, a theoretical correction would seem to be an improvement on no compensation at all. Finally, we see the comparatively low radome attenuation obtained by Trabal et al. (2008). The data used in their study were collected in summer 2007, which was the first year of the Collaborative Adaptive Sensing of the Atmosphere (CASA) radar network s observations. The radomes may have better retained their hydrophobic properties. The difference of the analysis approach (i.e., using wide areal averages as

7 MAY 2013 F R A S I E R E T A L. 923 FIG. 5. Mean difference between Vial and Maurel radars as a function of measured Z M. Numbers above each data point are the number of samples averaged to obtain the given mean bias. Error bars indicate the standard deviation of the estimate of the mean. opposed to more local measurements) may also contribute to the difference. Finally, we repeat the comparison of Fig. 3 applying the WRA correction. The result is shown in Fig. 7. The comparison now shows a near-unity slope and a slightly improved correlation coefficient (from 0.69 to 0.72). In addition, the RMS difference between Vial and Maurel observations is reduced from 8.2 dbz without correction to 7.1 dbz with the correction. Though reduced by this process, the scatter in the observations remains dominated by effects of the nonsimultaneous observation and inherent fluctuations of the radar signal. a. Comparison with the MRR An independent evaluation of the correction is afforded by comparison to the K-band Micro Rain Radar. Figure 8 shows a rain event of nearly six hours duration from the MRR. The top panel is reflectivity computed from the DSD estimated from the Doppler spectrum (METEK 2005), and the bottom panel is the vertical velocity. Pairs of horizontal lines denote the altitudes of the 0.58, 1.58, and2.78 tilts of the Maurel radar. It is evident in this case that the highest tilt is above the freezing level. Although the MRR employs an attenuation correction scheme on a spectral bin-by-bin basis, it does not differentiate between ice and water. Often, the highest altitudes above the bright band may be extinguished completely. Such cases are excluded from the comparison. Figure 9 shows histograms of Maurel versus MRR reflectivity, both before and after applying the wet radome correction. Improvement is evident in the (slight) increase of the correlation coefficient, the reduction of bias, and the increase in the slope. The slope remains less than unity (Maurel, MRR). Possible explanations FIG. 6. One-way radome attenuation as function of rain rate R, using Marshall Palmer (diamonds) or WSR-88D (triangles) Z R relationships. The dotted line is (6). Other results as indicated. for this include the differing attenuation correction methodologies employed by the two radar systems; the influence of Mie scattering on the X-band observations, which have necessarily assume Rayleigh scatter; or the effects of vertical air motions on the K-band observations. b. Impact on QPE retrieval Finally, we can assess the impact of the WRA on QPE retrievals. These are summarized in Fig. 10,which shows the normalized bias (NB) in retrievals of hourly rainfall accumulation over six rainfall events in The normalized bias is defined as FIG. 7. As in Fig. 3, but with wet radome attenuation correction applied to Maurel observations. Slope of the fit is near unity, and the correlation coefficient has increased.

8 924 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 30 FIG. 8. (top) Reflectivity factor and (bottom) vertical velocity estimated from the MRR on 27 Jul Pairs of horizontal lines indicate the regions sampled by the three elevations from Maurel. NB 5 hri 2 1, (7) hgi where hri is the average of radar-estimated accumulations and hgi is the average of rain gauge estimates collocated with the nearest radar pixel. Radar observations within 60 km of Mont Maurel coincide with approximately 40 rain gauges. The Meteo-France rain gauge network consists of tipping-bucket gauges with a bucket resolution of 0.2 mm, that is, the minimum hourly rainfall accumulation that can be measured is 0.2 mm. All rain gauge data are routinely quality controlled. Results are shown for various intervals of hourly rain accumulation. With the exception of the lowest accumulation interval, where the WRA correction overcorrects, the WRA correction reduces the normalized bias for the two Z R relation-based retrievals considered. We note that the QPE using these relations remains systematically low partly due to other complications in this mountainous terrain (brightband effects, partial beam blockage, etc.). FIG. 9. Histograms of Maurel vs MRR reflectivities (left) without wet radome attenuation correction and (right) with the correction.

9 MAY 2013 F R A S I E R E T A L. 925 FIG. 10. Normalized bias in hourly rainfall accumulation intervals without WRA correction (solid lines) and with WRA correction (dashed lines) for Marshall Palmer Z R relation (asterisks) and WSR-88D Z R relation (diamonds). 6. Discussion Assigning all the observed bias to the wet radome involves a few assumptions. First, it neglects the effects of path attenuation between the radar and the range bin (s) used as a proxy for the rain rate at the radar. These initial range bins are not corrected for attenuation by the radar processor. Given that these observations are made at close range (approximately 1.5 km), it is hoped that this path attenuation is negligibly small compared to the radome effect, except possibly in the heaviest rain. In developing the relationship, the true local reflectivity will be underestimated, resulting in an undercorrection for the given rain rate. By reversing the study, one can mitigate the concern of uncompensated path attenuation. This is done by stratifying observations based on the local reflectivity near the Vial radar (denoted Z V ) instead of Maurel. Since the Vial radar lacks a radome, we expect that there should be no dependence of the Vial/Maurel bias on the value of Z V. In doing so, we obtain a near-constant bias of approximately 4 db (not shown) for Z V from 0 to 40 dbz. If path attenuation were a significant factor, then it would be evident here as an increasing bias with Z V. We note that this bias is larger than the 2.5-dB minimum bias when observations were conditioned on Z M ; that is, even for small values of Z V, there are possibly large values of Z M, which will yield wet radome attenuation inducing more bias. Another assumption is neglect of the time required for the radome to dry after being wetted. This will also lead to an undercorrection, as the local (and now possibly low) reflectivity will be underestimated. A third assumption is the assumption of a uniform film of water on the FIG. 11. The Z dr bias (Vial/Maurel) vs intrinsic reflectivity factor at Maurel. radome for a given rain rate. Thompson et al. (2012) have illustrated that the radome attenuation is often nonuniform depending upon the wind direction. Their WRA correction method requires detailed analysis of the radar system noise, which in our case is not readily available in the operational processor. Some refinement of this assumption may be possible by incorporating wind direction in the future. a. Differential attenuation Using the same methodology, it is possible to investigate the impact of wet radome differential attenuation on Z dr. Frech (2009) observed a Z dr bias with rain rate at C band for an aged, orange-peel-type radome. For a uniform film of water on the radome, we expect both polarizations will be affected identically, in which case there should be no impact on Z dr. However, if the radome surface has hydrophobic properties, then water will tend to bead on the surface, remaining as droplets. These have a lesser impact on transmission loss than does a uniform film. As water droplets coalesce, they can form rivulets that flow down the face of the radome. These rivulets also present a lower transmission loss than a uniform film, but they tend to attenuate the vertical polarization more than the horizontal (assuming they are vertically oriented). Thus, one might expect an overestimate of Z dr when there is rivulet flow present on the radome. Figure 11 shows Vial/Maurel Z dr bias versus the intrinsic reflectivity at the Maurel radar, Z M. It reveals a Z dr bias between the two radars of 20.2 to 20.1 db. This curve was constructed by considering those observations exceeding 0 dbz and classified as hydrometeors by both radars. To first order, we can conclude the two polarizations experience the same transmission loss through the radome. There is insufficient knowledge at

10 926 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 30 present of the detailed properties of the radome along the viewing direction (i.e., presence and/or orientation of seams or joints) to conclude anything further about the average bias. It is known that the Z dr does fluctuate with azimuth angle, depending upon the beam s interaction with the radome and support structures (Figueras i Ventura et al. 2012). The slight reduction of the bias for moderate rain rates (possibly indicating an increase in Maurel s Z dr ) might be explained by the presence of rivulet flow on the radome, but this is somewhat speculative. The bias is reversed at the highest values of Z M. These may be impacted by errors in the differential attenuation correction. At present, Meteo-France does not use Z dr for QPE, as the uncertainty in its value has not (yet) been reduced below 0.2 db. The observed bias between the radars indicated in Fig. 11 lies within this uncertainty. b. Path-integrated attenuation correction With a wet radome attenuation correction in hand, it is possible to investigate the relationship between pathintegrated attenuation and the propagation differential phase F DP. We do so by conditioning our observations on minimal PIA from the Vial radar and examining Vial/ Maurel bias (after wet radome correction) as a function of F DP measured from Maurel. If the Vial observations are unattenuated, then the Vial/Maurel bias is equal to the PIA from Maurel, which can then be plotted versus F DP. Figure 12 shows the PIA, so estimated as a function of the propagation differential-phase from Maurel. The condition for minimal attenuation from Vial is F DP, 58. The latter is estimated from the measured differential phase by applying a 25-point (6 km) median filter to the measured differential phase as described in Figueras i Ventura et al. (2012). A least squares fit to the points in Fig. 12 yields a line with a slope very near 0.28, which is indeed the value used in the Meteo-France attenuation correction scheme for X band. We note that while the methodology used to derive the WRA correction employed attenuationcorrected observations with this coefficient, it does not necessarily guarantee that this result is obtained. This is because the WRA estimation approach included applying a common (but possibly incorrect) path-attenuation correction for both radars. Since the pathlengths from the radars to the common volume are comparable, errors in the path-attenuation correction are a common-mode error in the mean. Averaged over a large number of observations, the derived WRA correction is not sensitive to the particular path attenuation correction. That the two radars employed the same correction scheme was the most critical factor in deriving the WRA correction. FIG. 12. (top) PIA from Maurel (obtained from Vial/Maurel bias after wet radome attenuation correction and conditioned on F DP, 58 from Vial) vs F DP from Maurel. Dotted line indicates a slope of 0.28 db deg 21. (bottom) As in (top), but for PIDA from Maurel. Dotted line indicates a slope of 0.04 db deg 21. Wet radome attenuation is assumed common to both polarizations. The same approach is used to consider the differential attenuation effect on Z dr. In this case, the same procedure yields a slope of 0.07, which is substantially different from the value proposed by Bringi and Chandrasekar (2001) of or by Snyder et al. (2010) of The initial value adopted by Meteo-France is essentially the average of these two (Kabeche et al. 2010). We note the values from the literature were derived from scattering simulations. To our knowledge, this relation is the first based purely on field observations at X band. Gourley et al. (2007) performed an empirical study at C band and found significant variability (up to a factor of 2) in the relationship between differential attenuation and differential phase. Returning to the concern of possible differential attenuation by the radome, we note that such would tend to increase the Maurel Z dr, resulting in a reduced slope. The fact that we observe a larger slope suggests that this should not be a significant contributing factor. Thus, we conclude that a value

11 MAY 2013 F R A S I E R E T A L. 927 of 0.07 appears to be a more appropriate coefficient, at least for the precipitation encountered in this mountainous region of southeast France. We further note that obtaining this value does not impact our earlier conclusions as Z dr, while calculated, is not yet used in Meteo- France s polarimetric processing or QPE. 7. Conclusions In this paper we have devised a correction for wet radome attenuation through direct comparison of observations made by the subject radar and a similar X-band radar without a radome. The derived WRA correction appears reasonably consistent with prior experimental observations and with theory. When applied, it improves the correlation of observations between the two X-band radars, as well as an independent K-band Micro Rain Radar. It also reduces the normalized bias of QPE retrievals based on Z R for hourly rain accumulations exceeding 1 mm. The same methodology applied to investigate differential reflectivity shows possible evidence of rivulet flow on the radome. Finally, after accounting for WRA correction, intercomparison of the two X-band radars enables direct investigation of the PIA and PIDA and their relationship to the differential phase. Acknowledgments. This work was done while the first author was on sabbatical at the Centre National de Recherches Meteorologiques (CNRM) and the Centre de Meteorologie Radar, Meteo-France, in Toulouse. The authors and their organizations wish to acknowledge the support of the European Union, the Provence Alpes C^ote d Azur region, and the French Ministry of Ecology, Energy, Sustainable Development and Sea, who cofinanced the RHYTMME project. REFERENCES Anderson, I., 1975: Measurements of 20-GHz transmission through a radome in rain. IEEE Trans. Antennas Propag., 23, Bechini, R., V. Chandrasekar, R. Cremonini, and S. Lim, 2010: Radome attenuation at X-band radar operations. Proc. Sixth European Conf. on Radar in Meteorology and Hydrology, Sibiu, Romania, ERAD, P15.1. [Available online at ERAD2010_0346_extended.pdf.] Blevis, B., 1965: Losses due to rain on radomes and antenna reflecting surfaces. IEEE Trans. Antennas Propag., 13, Boumahmoud, A.-A., B. Fradon, P. Roquain, L. Perier, and P. Tabary, 2010: The French operational dual-polarization processing chain. Proc. Sixth European Conf. on Radar in Meteorology and Hydrology, Sibiu, Romania, ERAD, 6 pp. [Available online at radpol2/3_erad2010_0272.pdf.] Bringi, V. N., and V. Chandrasekar, 2001: Polarimetric Doppler Weather Radar: Principles and Applications. Cambridge University Press, 494 pp. Figueras i Ventura, J., A.-A. Boumahmoud, B. Fradon, P. Dupuy, and P. Tabary, 2012: Long-term monitoring of French polarimetric radar data quality and evaluation of several polarimetric quantitative precipitation estimators in ideal conditions for operational implementation at C-band. Quart. J. Roy. Meteor. Soc., 138, , doi: / qj Frech, M., 2009: The effect of a wet radome on dualpol data quality. Preprints, 34th Conf. on Radar Meteorology, Williamsburg, VA, Amer. Meteor. Soc., P [Available online at ams.confex.com/ams/34radar/techprogram/paper_ htm.] Gibble, D., 1964: Effect of rain on transmission performance of a satellite communication system. IEEE International Convention Record, Part VI, IEEE, 52. Gourley, J. J., P. Tabary, and J. P. du Chatelet, 2007: Empirical estimation of attenuation from differential propagation phase measurements at C band. J. Appl. Meteor. Climatol., 46, Hines, W. G. S., 1983: Geometric mean. Faa di Bruno s Formula to Hypothesis Testing, S. Kotz and N. L. Johnson, Eds.,Vol. 3, Encyclopedia of Statistical Sciences, John Wiley & Sons, Kabeche, F., J. Figueras i Ventura, B. Fradon, R. Hogan, A. A. Boumahmoud, A. Illingworth, and P. Tabary, 2010: Towards X-band polarimetric quantitative precipitation estimation in mountainous regions: The RHYTMME project. Proc. Sixth European Conf. on Radar in Meteorology and Hydrology, Sibiu, Romania, ERAD, 6 pp. [Available online at ERAD2010_0113_extended.pdf.],,, A. A. Boumahmoud, P. Dupoy, S. Westrelin, and P. Tabary, 2011: Quantitative precipitation estimation in the French Alps with a dense network of polarimetric X-band radars. Preprints, 35th Conf. on Radar Meteorology, Pittsburgh, PA, Amer. Meteor. Soc., P [Available online at ams.confex.com/ams/35radar/webprogram/paper html.] Kurri, M., and A. Huuskonen, 2008: Measurements of the transmission loss of a radome at different rain intensities. J. Atmos. Oceanic Technol., 25, Matrosov, S. Y., D. E. Kingsmill, B. E. Martner, and F. M. Ralph, 2005: The utility of X-band polarimetric radar for quantitative estimates of rainfall parameters. J. Hydrometeor., 6, Meissner, T., and F. Wentz, 2004: The complex dielectric constant of pure and sea water from microwave satellite observations. IEEE Trans. Geosci. Remote Sens., 42, , doi: / TGRS Merceret, F. J., and J. G. Ward, 2002: Attenuation of weather radar signals due to wetting of the radome by rainwater or incomplete filling of the beam volume. NASA Tech. Memo. NASA/TM , 16 pp. METEK, 2005: MRR physical basics, version Meteorologische Messtechnik GmbH, 22 pp. Snyder, J. C., H. B. Bluestein, G. Zhang, and S. Frasier, 2010: Attenuation correction and hydrometeor classification of high-resolution, X-band, dual-polarized mobile radar measurements in severe convective storms. J. Atmos. Oceanic Technol., 27,

12 928 J O U R N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L O G Y VOLUME 30 Thompson, R., A. Illingworth, T. Darlington, and J. Ovens, 2012: Correcting attenuation in operational radars from both heavy rain and the radome using the observed microwave emission. Proc. Seventh European Conf. on Radar in Meteorology and Hydrology, Toulouse, France, ERAD, 8A.5. Trabal, J. M., I. Zawadski, and D. J. McLaughlin, 2008: A method to correct for wet radome attenuation in CASA radars by the use of a contiguous WSR-88D radar. Proc. Fifth European Conf. on Radar in Meteorology and Hydrology, Helsinki, Finland, Wang, Y., and V. Chandrasekar, 2010: Quantitative precipitation estimation in the CASA X-band dual-polarization radar network. J. Atmos. Oceanic Technol., 27, Westrelin, S., S. Diss, P. Meriaux,andJ.-L.Cheze, 2010: Hydrometeorological risks in Mediterranean mountainous areas. Proc. Sixth European Conf. on Radar in Meteorology and Hydrology, Sibiu, Romania, ERAD, 4 pp. [Available online at 05_ERAD2010_0363.pdf.]