Unusually High Differential Attenuation at C Band: Results from a Two-Year Analysis of the French Trappes Polarimetric Radar Data

Transcription

1 OCTOBER 2009 T A B A R Y E T A L Unusually High Differential Attenuation at C Ban: Results from a Two-Year Analysis of the French Trappes Polarimetric Raar Data PIERRE TABARY AND GIANFRANCO VULPIANI Direction es Systèmes Observation, Météo France, Toulouse, France JONATHAN J. GOURLEY NOAA/National Severe Storms Laboratory, Norman, Oklahoma ANTHONY J. ILLINGWORTH AND ROBERT J. THOMPSON University of Reaing, Reaing, Unite Kingom OLIVIER BOUSQUET CNRM/GAME, Météo France, Toulouse, France (Manuscript receive 14 May 2008, in final form 1 April 2009) ABSTRACT The ifferential phase (F DP ) measure by polarimetric raars is recognize to be a very goo inicator of the path integrate by rain. Moreover, if a linear relationship is assume between the specific ifferential phase (K DP ) an the specific attenuation (A H ) an specific ifferential attenuation (A DP ), then attenuation can easily be correcte. The coefficients of proportionality, g H an g DP, are, however, known to be epenent in rain upon rop temperature, rop shapes, rop size istribution, an the presence of large rops causing Mie scattering. In this paper, the authors extensively apply a physically base metho, often referre to as the Smyth an Illingworth constraint, which uses the constraint that the value of the ifferential reflectivity Z DR on the far sie of the storm shoul be low to retrieve the g DP coefficient. More than 30 convective episoes observe by the French operational C-ban polarimetric Trappes raar uring two summers (2005 an 2006) are use to ocument the variability of g DP with respect to the intrinsic threeimensional characteristics of the attenuating cells. The Smyth an Illingworth constraint coul be applie to only 20% of all attenuate rays of the 2-yr ataset so it cannot be consiere the unique solution for attenuation correction in an operational setting but is useful for characterizing the properties of the strongly attenuating cells. The range of variation of g DP is shown to be extremely large, with minimal, maximal, an mean values being, respectively, equal to 0.01, 0.11, an B Coefficient g DP appears to be almost linearly correlate with the horizontal reflectivity (Z H ), ifferential reflectivity (Z DR ), an specific ifferential phase (K DP ) an correlation coefficient (r HV ) of the attenuating cells. The temperature effect is negligible with respect to that of the microphysical properties of the attenuating cells. Unusually large values of g DP, above 0.06 B 8 21, often referre to as hot spots, are reporte for 15% a nonnegligible figure of the rays presenting a significant total ifferential phase shift (Df DP. 308). The corresponing strongly attenuating cells are shown to have extremely high Z DR (above 4 B) an Z H (above 55 BZ), very low r HV (below 0.94), an high K DP (above 48 km 21 ). Analysis of 4 yr of observe rainrop spectra oes not reprouce such low values of r HV, suggesting that (wet) ice is likely to be present in the precipitation meium an responsible for the attenuation an high phase shifts. Furthermore, if melting ice is responsible for the high phase shifts, this suggests that K DP may not be uniquely relate to rainfall rate but can result from the presence of wet ice. This hypothesis is supporte by the analysis of the vertical profiles of horizontal reflectivity an the values of conventional probability of hail inexes. Corresponing author aress: Dr. Pierre Tabary, Centre e Météorologie Raar, Direction es Systèmes Observation, Météo France, 42 Ave. Coriolis, Toulouse, France. pierre.tabary@meteo.fr DOI: /2009JAMC Ó 2009 American Meteorological Society

2 2038 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME Introuction Attenuation by rain may be a serious source of errors when estimating rainfall rates with C-ban an X-ban raars. Iterative approaches base on horizontal reflectivity (Z H ) have only been propose (Hitschfel an Boran 1954) but they are known to be unstable ue to miscalibration of the raar an/or inaequacy of the assume rop size istribution (DSD). The avent of ual polarization clearly offers new perspectives in this respect. Theoretical works [see the comprehensive review in Bringi an Chanrasekar (2001)] an observations (e.g., Carey et al. 2000; Gourley et al. 2006b, hereafter referre to as G06) suggest that the relationships between specific ifferential phase (K DP ) an specific attenuation an specific ifferential attenuation (A H an A DP,respectively) are almost linear in rain at C ban: A H 5 g H K DP an (1) A DP 5 g DP K DP, (2) where A H an A DP are expresse in ecibels per kilometer, g H an g DP in ecibels per egree, an K DP in egrees per kilometer. The coefficients of proportionality, enote by g H an g DP in (1) an (2), are, however, known to be epenent in rain upon the temperature, rop shape (oblateness), an DSD characteristics of the attenuating cells with Carey et al. (2000) quoting a typical range for g H of B 8 21 an for g DP of B Ryzhkov an Zrnić (1995) foun that both coefficients increase because of Mie scattering by the larger rops at S ban. Keenan et al. (2001) rew attention to the effect of the large rops on the attenuation coefficients at C ban, while Carey et al. (2000) showe that at C ban this effect became important once Z DR. 2B.G06havepropose an empirical metho to objectively buil the curves of path integrate attenuation (PIA) 5 f(f DP ) an path integrate ifferential attenuation (PIDA) 5 g(f DP ). In their Fig. 2, G06 present the results obtaine for seven cases of intense convection observe by the French operational C-ban polarimetric raar locate in Trappes near Paris (Gourley et al. 2006a). All curves are remarkably linear an within the expecte theoretical bouns but their slopes [i.e., the g H an g DP of (1) an (2)] appear to be variable from episoe to episoe. G06 trie to relate the variability of g H an g DP to characteristics of the attenuating cells, such as rop temperature an percentage of cells containing large iameter rops leaing to Mie scattering at C ban. Mie scattering effects were assume when the percentage of attenuating cells with 3, Z DR, 5 B became.15%. In this paper, we propose to revisit that empirical stratification for g DP only using a physically base approach for etermining intrinsic Z DR in the stratiform region behin convective cells (Smyth an Illingworth 1998) to provie an estimate for the value of PIDA. The analysis is carrie out using the same French C-ban operational polarimetric raar as in G Data an methoology a. Step-by-step escription of the methoology Smyth an Illingworth (1998) suggeste using a Z DR 0 constraint in the stratiform region behin convective cells to estimate the PIDA an correct raar measurements for ifferential attenuation. The stratiform region is efine as a low-reflectivity region where the ifferential phase plateaus. This constraint cannot be use for an operational algorithm because it is not always possible to fin such a region for each ray. This limitation is not a problem for the present work since we are essentially intereste in characterizing the g DP variability an we can affor not to process the unsuitable rays. The application of the Smyth an Illingworth constraint (hereinafter referre to as the S&I constraint) is one as follows: Select all rays that have at least 308 of ifferential phase shift (DF DP ). This threshol value is justifie in the following. Correct the polarimetric measurements for low signalto-noise ratio (SNR) biases, nonmeteorological echoes, calibration biases, azimuthal interferences, an ifferential phase aliasing an offsets (Gourley et al. 2006a). Filter F DP an estimate K DP. In the present analysis, we simply use a running, centere, meian filter of length 1.68 km, corresponing to seven 240-m gates. At least 50% of the F DP measurements have to be available (i.e., classifie as precipitation) within the filtering winow to valiate the K DP estimate. Otherwise, the K DP estimate is set to a missing value. The rather short path over which K DP is estimate is relate to the fact that K DP will essentially be use in convective rain. Correct Z H for PIA using F DP assuming a given g H : Z H,correcte 5 Z H,measure 1 g H F DP. (3) Actually, as explaine below, the choice of g H is couple with the g DP estimation. For each selecte ray, search for light, stratiform precipitation in regions behin convective cells from the raar s vantage point. A so-calle stratiform region is efine in this stuy as a series of at least 20

3 OCTOBER 2009 T A B A R Y E T A L consecutive 240-m gates below the freezing level with (correcte) horizontal reflectivity less than 45 BZ an no ifferential phase shift. The freezing-level height is retrieve from the brightban ientification technique propose by Tabary et al. (2006). The stanar eviation of the ifferential phase (F DP ) over the 20 gates also has to be less than 58 [i.e., slightly more than the typical gate-by-gate noise foun with the Trappes raar ifferential phase measurements in Gourley et al. (2006a)]. That value was etermine subjectively by examining a large number of profiles. A stratiform region is more simply ientifie as a smooth plateau on the F DP profile. If the intrinsic horizontal reflectivity (Z H,intrinsic )is known, then the intrinsic Z DR,intrinsic can be obtaine using an empirical relationship. For instance, Bringi et al. (2001) have propose the following formula: Z DR,intrinsic (B) Z H,intrinsic (BZ) if Z H,intrinsic 20 BZ, (4) Z DR,intrinsic (B) 5 0 if Z H,intrinsic, 20 BZ. (5) Figure 1 helps to assess the relevance of (4) an (5). The ata have been obtaine from a large number of close-range, nonattenuate, nonshiele, high-snr ata in rain collecte by the French polarimetric operational Trappes raar [see Gourley et al. (2006a) for a thorough evaluation of its quality]. The mean Z DR an its stanar eviation have been compute for each 1-BZ class of Z H ranging from 0 up to 45 BZ. The Bringi et al. (2001) moel [(3) an (4) above] has been superimpose (iamons). The agreement is remarkable even though the moel tens to overestimate the intrinsic Z DR by aroun 0.1 B for Z H between 15 an 20 BZ an to unerestimate it by the same amount (0.1 B) for Z H between 40 an 45 BZ. For the present analysis, a linear-by-part moel was fitte to the empirical ata. It has been represente by a light straight line on Fig. 1. Here are the corresponing relationships: Z DR,intrinsic (B) 5 0 if Z H,intrinsic, 10 BZ, (6) Z DR,intrinsic (B) (Z H,intrinsic 10) 10 if 10, Z H,intrinsic, 20 BZ, (7) Z DR,intrinsic (B) (Z H,intrinsic 20) 10 if 20, Z H,intrinsic, 30 BZ, (8) FIG. 1. Empirical (Z H, Z DR ) scatterplot. The mean (iamon) 6 st ev of Z DR has been compute for each class of Z H. The bin size for Z H was 1 BZ. The Bringi et al. (2001) simplifie relationship (crosses) an the linear-by-part fitte moel use in the analysis (light straight line) have been superimpose. Also shown is the number of ata use for each class of Z H. Notice that for that variable the vertical scale is expresse in 10 5 units. Z DR,intrinsic (B) (Z H,intrinsic 30) 10 if 30, Z H,intrinsic, 40 BZ, (9) Z DR,intrinsic (B) (Z H,intrinsic 40) 5 if 40, Z H,intrinsic, 45 BZ. (10) Figure 1 also helps in setting the minimum value DF DP require in the first step of the processing (first item above). The scatter of the intrinsic Z DR (Z DR,intrinsic ) aroun the linear-by-part fitte moel is typically 60.2 B. If we assume a typical g DP value of 0.03 B 8 21, then a 308 ifferential phase shift (which is the value that was retaine) correspons to a PIDA of about 1 B, which is 5 times larger than the uncertainty on the intrinsic Z DR. As a consequence, setting DF DP to 308 guarantees that the g DP estimation has a precision better than 20%.

4 2040 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 Once the intrinsic ifferential reflectivity (Z DR,intrinsic ) is estimate for each of the 20 gates, then the simple arithmetic mean is taken (Z DR,intrinsic,mean ) an the slope g DP can be compute as follows: g DP 5 (Z DR,intrinsic,mean Z DR,measure ) F DP. (11) If the g H value assume initially to correct horizontal reflectivity measurements was not aequate, then the intrinsic Z DR,intrinsic an, subsequently, the g DP estimation may be biase. In the appenix, however, we show that given the typical range of variation of g H (between 0.07 an 0.13 B 8 21 ) the relative error on the estimate g DP is aroun 5%. Even though that amount of error may be consiere to be fairly acceptable, a refinement has been introuce to solve for g H an g DP simultaneously. The approach relies on the assumption that g H an g DP are proportional in rain. Using numerical simulations, Vulpiani et al. (2008) have shown that the following relationship (see their Fig. 1), g DP 5 0.3g H, (12) was fairly stable for a large range of temperatures, N W, m, and 0. Later we will present an analysis of 4 yr of observe rainrop spectra that supports this relationship. Similarly, G06 have empirically foun ratios g DP /g H equal to 0.37, 0.27, 0.5, 0.34, 0.42, 0.46, an 0.56 (their Table 1). Those results reveal some variability but part of this variability is ue to the uncertainty in the estimate g DP an even more g H an also to the fact that hail is likely to be present in several of the situations analyze by G06. The propose iterative approach assumes an initial value for g H (say g H0 ), corrects Z H for attenuation using (3), estimates the intrinsic Z DR,intrinsic via (6) (10), retrieves g DP with (11), an finally computes a new g H with (12). Convergence is achieve when two successive values of g H iffer by less than 0.01 B Because of the nonlinear form of the (Z H, Z DR ) relationship [(6) (10)], the solution for g H an g DP cannot be obtaine in one step. In the couple retrieval, which relies on the important assumption that precipitation is pure rain, unusually large retrieve g DP will be translate into unusually large g H. In this example, if the coupling is eactivate an a climatological g H value (g H B 8 21 )is use, then Z H an subsequently Z DR [(6) (10) values in the stratiform region will be unerestimate an the g DP estimation will be biase negatively. The impact of using or not using a coupling between g H an g DP will be presente an iscusse in section 3. Once the optimal g H an g DP have been retrieve, all Z H an Z DR measurements along the ray between the raar an the stratiform region are correcte for attenuation using filtere F DP. Finally, the characteristics of the attenuating cells are extracte using weighte averages of the various relevant parameters (Z H, Z DR, r HV, K DP, an T), the weights being the attenuation-correcte Z H values (expresse in linear units) at each gate: Z Z r K attenuating cells H attenuating cells DR attenuating cells HV attenuating cells DP 5 S raar!stratiform region z H Z H S raar!stratiform region z H, (13) 5 S raar!stratiform region z H Z DR S raar!stratiform region z H, (14) 5 S raar!stratiform region z H r HV S raar!stratiform region z H, (15) 5 S raar!stratiform region z H K DP S raar!stratiform region z H, (16) T attenuating cells 5 S raar!stratiform region z H T S raar!stratiform region z H. (17) In (13) (17), z H is equal to 10 Z H/10 an Z H is the attenuation-correcte horizontal reflectivity (BZ). The summation symbols in (13) (17) (i.e., S raar/stratiform_region ) simply mean integration over all gates along the ray between the raar an the stratiform region through the convective cells. To extract the characteristics of the attenuating cells, the proper weights to use in (13) (17) shoul be the specific ifferential attenuation (A DP ) or the specific attenuation (A H ) both expresse in ecibels per kilogram. Those two quantities, however, are not known so we use linear horizontal reflectivity (mm 6 m 23 ) as a proxy [as in Ryzhkov et al. (2007)]. Notice that in rain, the relationship between linear horizontal reflectivity an specific attenuation is close to linear (see Table 1 of Testu et al. 2000). The temperature profile has been reconstructe uner the assumption of a constant km 21 lapse rate from the freezing-level height retrieve by the brightban ientification algorithm (Tabary et al. 2006). Even though this is rarely allue to, one has to concee that it is extremely ifficult to obtain a very accurate estimation of the roplets temperature insie the attenuating cells because it is highly variable in space an time an may iffer significantly from ambient air temperatures. The space time resolution of the raiosone ata is clearly not

5 OCTOBER 2009 T A B A R Y E T A L operational services to iagnose the presence of hail at groun level. As will be seen later, a central question for the present work an more generally for all attenuation correction methos at C ban (Ryzhkov et al. 2007) is whether the attenuating cells contain hail, a rain/hail mixture, or pure rain. The scan strategy for the Trappes raar for the years 2005 an 2006 is presente in Fig. 2. The elevation angles are scanne on a 15-min basis an range from 1.58 to 98 (9.58 for the year 2006). Two aitional low-elevation angles (0.48 an 0.88) are actually revisite every 5 min, but they were consiere to be too much affecte by beam blockage an raome interferences for use in the present analysis. Because of this limite number of elevation angles, the vertical structure coul only be recovere for ranges between 40 an 80 km. To reconstruct the vertical profile, horizontal reflectivity ata were synchronize using a stanar cross-correlation avection fiel at the en of the 15-min perio an correcte for attenuation using filtere F DP an the appropriate g H (i.e., the one retrieve following the approach escribe previously). The vertical profile was then extracte at the range of maximum Z H. b. Examples FIG. 2. Scan strategy of the Trappes raar in (a) 2005 an (b) The vertical bars at 40 an 80 km inicate the area where the retrieval of the vertical profile can be one. sufficient while mesoscale moel forecasts of the wetbulb temperature fiels may not be relevant for the inner part of the convective cells, where significant latent heat release is expecte. Jameson (1992) has suggeste that the g H an g DP parameters are typically multiplie by a factor of 1.5 when the temperature ecreases from 208 own to 08C. In aition to characterizing the attenuating cells in terms of Z H, Z DR, temperature, K DP,anr HV,wealso consiere the vertical profile of reflectivity in the most intense part of the attenuating cells, as this is wiely use to inicate the presence of hail at groun level. Several inicators [Z H. 55 BZ, vertically integrate liqui content, probability of hail (POH), etc.] have been propose an valiate to ientify the presence of hail within convective cells (Walvogel et al. 1979; Eilts et al. 1996; Witt et al. 1998; Joe et al. 2004; Delobbe an Holleman 2006). While it is recognize that those conventional methos typically o not attempt to estimate the height or the size of the hailstones, they have proven to be efficient enough to be use by many Figure 3 shows an example of the application of the metho on a particular ray. Data were taken at 1.58 uring a convective situation (1630 UTC 23 June 2005). The raw Z H an Z DR profiles are represente by thin lines an their attenuation-correcte counterparts by thick lines. Profiles of raw f DP (noisy thin line), sevengate, meian-filtere f DP (thick line), K DP, an r HV are also plotte in Fig. 3 an show that the total ifferential phase shift is more than The PIA an PIDA are in this case respectively equal to 10 an 3 B, an g DP was estimate at B 8 21, a typical value (Carey et al. 2000; G06; Ryzhkov et al. 2007). In the most intense part of the attenuating cell (in terms of Z H, see the vertical bar), Z H reaches 51.5 BZ, Z DR reaches 2.78 B, an K DP of reaches 3.98 km 21. It is noteworthy that r HV ecreases own to 0.93; r HV normally ecreases in convective cells when hyrometeors with a large variety of shapes are present. This occurs in heavy rain when large an small rops are both present (e.g., Keenan et al. 2001, their Fig. 10) an when there are rain/hail mixtures, particularly when the hail is large enough to Mie scatter. In aition, low values of r HV can occur when there are high graients of reflectivity within the resolution volume (e.g., Ryzhkov 2007). The vertical reflectivity profile steaily ecreases from 53 BZ at the lower levels to 33 BZ at 10 km. The 45-BZ level is reache approximately at the height (H 45BZ ) of 7 km.

6 2042 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 FIG. 3. Range profiles of raw an filtere F DP, K DP, raw an correcte Z DR an Z H, an r HV. Those profiles have been obtaine at the elevation of 1.58 at 1630 UTC 23 Jun The values of the g DP parameter an the properties of the attenuating cells (Z DR, temperature, Z H, r HV ) are given. All profiles have been correcte for nonprecipitation echoes. Z H an Z DR were correcte for attenuation using the proceure escribe in section 2. The F DP profile has been correcte for the system ifferential phase, the value of which F DP0 is given on the graph. Two f DP profiles are presente on the graph: the raw profile (thin noisy line) an the meianfiltere profile (thick smooth curve). Also inicate are the st ev of F DP (stevf DP ) in the stratiform region an the range of the maximum of K DP (r attenuating_cells ). The vertical profile of (horizontal) reflectivity was retrieve from the set of PPIs of the volume scan. The 08C isotherm height (H 08Cisotherm ) for that ay was at 3.5 km above sea level. Using Delobbe an Holleman s (2006) formula to assess the probability of hail (POH), POH (H 45BZ H 08Cisotherm ), (18) we get a POH of Even though (18) has not been tune specifically for the Trappes region, one can say that there is presumption of hail in that cell. We recall here that comparisons with surface reports have shown that the conventional POH estimator is fairly successful at preicting hail at groun level. Since in this work we are mainly using ata from low-elevation angles at short istances from the raar (i.e., close to the groun), it is fair to assess the presence of hail in the plan position inicator (PPI) using the conventional POH estimator. Figure 4 is taken from the same episoe as Fig. 3 (23 June 2005) but at a slightly ifferent time (1600 UTC) an in another azimuth. The amount of total ifferential phase shift is about the same as in Fig. 3 (a little more than 1008). Yet in that case, the attenuation is much more severe; the PIA an PIDA values are respectively equal to 20 an 5 B. The estimate g DP is equal to B 8 21 (i.e., more than twice as large as in the previous example). Figures 3 an 4 clearly illustrate the fact that the coefficient of proportionality between A DP an K DP in (2) oes not epen solely upon temperature.

7 OCTOBER 2009 T A B A R Y E T A L FIG. 4. As in Fig. 3 but at a slightly ifferent time (1600 UTC) an in another azimuth. The central question is then to know whether the attenuating cells have significantly ifferent characteristics in the two cases. The r HV pattern is rather similar in both cases. A careful examination though reveals a tenency in the secon case (the one with high g DP )to have slightly lower values of r HV, with some spikes even below 0.9. Likewise, the K DP profiles are comparable, though higher in the high g DP case, in terms of maximum (;48 km 21 ) an range extension (20 km). On the other han, there is a very sharp contrast between the Z H an even more between the Z DR profiles. In the high g DP case, Z H reaches 58.5 BZ an Z DR 4 B over almost 10 km. The vertical profile of reflectivity is almost vertical an beyon 60 BZ up to 6 km. Given the limite vertical coverage, the top of the cell cannot be etermine with a high egree of accuracy but one can expect that the POH woul probably be beyon 1. Before moving on to the analysis of all the observations, Fig. 5 illustrates one limitation of the present approach. In this situation, two attenuating cells are clearly visible on the profile: the first one prouces a ifferential phase shift of 208 (maximum Z H of 50 BZ) an the other prouces 1008 (maximum Z H of 58 BZ). A stratiform region was ientifie between 50 an 55 km an the properties of the attenuating cells were automatically extracte using (13) (16). Given the linear Z H weighting use in the equations, basically only the secon cell was consiere when retrieving Z H, Z DR,temperature, K DP, an r HV. A better approach woul have consiste of splitting the ray into two parts, analyzing the first part, retrieving the appropriate g H an g DP, correcting Z H an Z DR for attenuation, an then processing the secon part. This refinement has not been introuce mainly because a subjective overview of all the profiles showe that, in the vast majority of the cases, attenuation was ue to a well-efine single attenuating cell. 3. Results a. Introuction The metho propose in the previous section has been applie to more than 30 convective an mixe cases observe uring 2005 an All tilts between 1.58

8 2044 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 FIG. 5. As in Fig. 3 but for another episoe (0930 UTC 26 Jun 2005). an 98 were consiere. The freezing-level height varies between 1 an 3.5 km above mean sea level (MSL), the raar being locate at 191 m MSL. However, most of the attenuating cells correspon to summer events with freezing-level heights typically at 3 km MSL. For each suitable ray, the following parameters were compute an store: PIA (B), PIDA (B), g DP (B 8 21 ), g H (B 8 21 ), T attenuating_cells (8C), Z attenuating_cells attenuating_cells DR (B), Z H (BZ), r attenuating_cells attenuating_cells HV (imensionless), K DP (8 km 21 ), r attenuating_cells (km), system ifferential phase (F DP0 ), an stanar eviation of the ifferential phase in the stratiform region (st evf DP ). Overall, the ataset comprises profiles. We have calculate that the S&I constraint coul only be applie to 20% of all attenuate rays (efine by F DP. 308). For 80% of the rays having a significant ifferential phase shift (F DP. 308), no suitable stratiform region coul be ientifie, either because a plateau of F DP coul not be foun in the rain region, the stanar eviation of F DP was too high (.58), Z H was too high, or the SNR too low. This means that the S&I constraint oes not qualify for operational attenuation correction of ual-polarization measurements. Also store in the atabase are the vertical profiles of horizontal reflectivity (Z H ) for the attenuating cells locate between 40 an 80 km. This information was only available for 10% of all the attenuating cells present in the atabase. Figure 6 introuces the quantitative analysis. It simply represents the mean 6 1 /10 (for visibility purposes) of the stanar eviation of the PIDA (B) as a function of the total ifferential phase shift (Df DP ; 8) for a narrow range of temperature (12.58, T, 17.58C) an for ifferent values of Z attenuating_cells DR (i.e., the Z DR value of the attenuating cells). All curves in Fig. 6 are approximately linear, which establishes the relevance of (2). Also noteworthy is the fact that their slopes (i.e., the g DP attenuating_cells, parameter) seem to be increasing with Z DR consistent with previous works (Carey et al. 2000; Bringi an Chanrasekar 2001; G06). The subsequent analyses aim at precisely assessing the relationship between g DP an the polarimetric values of the attenuating cells.

9 OCTOBER 2009 T A B A R Y E T A L FIG. 6. PIDA (B) as a function of the normalize ifferential phase (f DP, 8) for ifferent values of Z attenuating_cells DR an for a fixe temperature (12.58,T, 17.58C). Vertical bars correspon to 6 1 /10 (for visibility purposes) of the st ev. b. Stratification of the observe attenuating cell properties with g DP Figure 7 presents a stratification of the results accoring to the estimate g DP, with an without the coupling between g H an g DP being activate in the retrieval in (12). For clarity, no stanar eviation bars are presente. We shall first comment on results obtaine with the coupling activate. The basic iea of that first stratification is to characterize the properties of the attenuating cells leaing to high g DP values. First of all, Fig. 7a presents the overall an ay-by-ay occurrence frequency of the estimate g DP. The vertical scale is logarithmic. The maximum frequency is centere at B 8 21, which is a value that compares quite well to previously reporte results. The istribution is rather broa an values beyon 0.06 B 8 21 occur for 15% a nonnegligible figure of the rays presenting a significant ifferential phase shift (.308). Several episoes lea to such high g DP values. This is a convincing emonstration that the variability of the g DP coefficient has to be accounte for in any operational

10 2046 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 FIG. 7. Overall an ay-by-ay occurrence frequency of (a) g DP an characteristics of the attenuating cells in terms of (b) Z DR, (c) Z H, () r HV, (e) K DP, an (f) T as functions of the S&I retrieve g DP. Panels (b) (e) can be consiere as stratifications at a fixe temperature (158C) while (f) is a stratification at fixe Z DR (Z DR B). The bin size for g DP is 0.01 B For each parameter, the mean (iamon) 6st ev is plotte. Also shown in (b) (f) are the histograms of the attenuating cell characteristics. Results without the coupling activate correspon to crosses. attenuation correction proceure. More recently, Ryzhkov et al. (2007), using inepenent ata from the two SIDPOL C-ban polarimetric raars in Alabama an in Canaa an a rather ifferent methoology to estimate g DP, also foun a large variability of g DP (see their Table 1). The typical meian values they obtaine for Alabama were 0.01 (tropical rain), 0.02 (rain with hail), an 0.01 (tornao) B In Canaa, the typical meian values of g DP were (small hail), 0.01 (rain), 0.08 (hail), an (rain with hail) B Figures 7b e show respectively the mean Z DR, Z H, r HV, an K DP values of the attenuating cells as a function of g DP. To avoi confusion an competing effects between temperature an DSD characteristics an shapes, these plots are for ata all having similar temperatures (T attenuating_cells between an 17.58C). Therefore, one can say that temperature plays a negligible role in the trens observe in Figs. 7b e. There is a clear linear relationship between g DP an each of the four above-mentione variables (Z attenuating_cells DR,

11 OCTOBER 2009 T A B A R Y E T A L Z attenuating_cells H, r attenuating_cells HV, an K attenuating_cells DP ). Larger g DP values statistically correspon to larger Z DR, larger Z H, smaller r HV, an larger K DP. In particular, the unusually high g DP values (say beyon 0.06 B 8 21 ) that we will show are very unlikely in rain are cause by cells with Z DR beyon 5 B, Z H beyon 60 BZ, r HV below 0.94, an K DP above 48 km 21. Those cells are likely to contain frozen particles (hail or graupel) mixe with rain since such low values of r HV are unlikely in rain. Interestingly, the high g DP regime (above 0.06 B 8 21 ) seems simply to be the linear extrapolation of the low regime (below 0.06 B 8 21 ). Among all the storms that were inclue in the atabase, some are known to have been hail proucing (Vulpiani et al. 2008). The presence of ice leas to an expecte increase in values of Z H, but also more surprisingly, increases in Z DR an K DP. This seriously questions the usability of K DP to retrieve rain rate in the presence of ice. Finally, Fig. 7f presents the relationship between T attenuating_cells an g DP.Similarly to what was one to remove any temperature impact on Figs. 7b e, Fig. 7f was built from ata having all the same Z DR (Z attenuating_cells DR between 1 an 2 B). Figure 7f oes not reveal any clear relationship between g DP an T attenuating_cells. This may be explaine by the fact that the range of T attenuating_cells present in the atabase is rather moest (say between 108 an 208C). Climatologically speaking, the majority of attenuating precipitation systems occur in France at the same season in about the same temperature conitions (158C). Operational attenuation correction algorithms shoul try to take into account the temperature effect but it is clearly secon orer compare with the impact of the microphysical characteristics of the attenuating cells. The presence of ice in the attenuating cells calls into question the application of a coupling between g H an g DP. Inee, the 0.3 factor between g H an g DP was establishe using scattering simulations an isrometer observations in pure rain an little is known about the evolution of the proportionality factor in the presence of ice. This is the reason why a no coupling analysis has been carrie out where g H is set to a climatological value (0.1 B 8 21 ). Results of this experiment are inicate by crosses on Fig. 7. As expecte, the variable that is mostly affecte is Z attenuating_cells H. In the coupling experiment, it reaches the unrealistic value of 72 BZ (for g DP equal 0.1 B 8 21 ) while in the no coupling experiment, it peaks at 60 BZ, still an extremely high value that woul be consistent with the presence of wet ice. Because it is very likely that unusually high g DP leas to unusually high g H (in a proportion that is unknown), it is fair to amit that the no coupling curve stans as the minimum boun of Z attenuating_cells H while the coupling curve can be consiere as its maximum boun. The Z attenuating_cells DR curve (Fig. 7b) changes a little bit towar slightly lower values for extremely high g DP, which is the logical consequence of lower g H, hence lower Z H an Z DR values in the stratiform region an lower estimate g DP. The r attenuating_cells HV (Fig. 7) an K attenuating_cells DP (Fig. 7e) are also slightly altere because of the change of the attenuation-correcte Z H values that are use as weights in the extraction of the properties of the attenuating cells [(13) (17)]. Overall, the coupling an no coupling curves can be regare as uncertainty bouns attache to the estimate polarimetric variables of the attenuating cells. The conclusions regaring the surprisingly very high values of g DP, K DP,anZ DR an the likelihoo of (wet) ice remain whether the coupling is consiere or not. c. Comparison with simulations base on Chilbolton isrometer ata Figure 8 is another way to look statistically at the results. The stratification of the raar observations is one this time accoring to the properties of the attenuating cells (Z attenuating_cells DR, Z attenuating_cells H, r attenuating_cells HV, K attenuating_cells DP ) an for various temperature ranges. In aition, on the left-han sie of Fig. 8, we present computations of these variables using rainrop size spectra obtaine with a Joss Walogel isrometer over the perio June 2003 June 2008 (i.e., 4 yr) site at Chilbolton (Hampshire, Unite Kingom). Chilbolton is locate less than 400 km northwest of Trappes. Chilbolton is the closest site to Trappes where long time series of reliable isrometer ata are available. Both sites have a maritime climate with similar total annual rainfall istribute throughout the year but with a very slight tenency to more convective precipitation at Trappes. Table 1 gives the seasonal statistics of rainfall accumulations compute over the perio for Paris an Lonon. It is thus fair to assume that the rain systems affecting both sites have, on average, similar microphysical properties. Because we are intereste in events with unusually high attenuation, extreme care is neee to ensure that the isrometer is operating reliably uring the heaviest rain, which occurs only for brief perios. Analysis of the ata reveals occasional very short perios of apparently heavy rain compose of only very large rops; closer examination of other gauges showe no rain was falling an that the large rops were probably spurious an cause by crows attacking the Styrofoam cover of the isrometer. To remove such spurious ata, the isrometer ata were compare with three gauges each recoring the iniviual rops (equivalent to mm of rain) forming at the base of the gauge funnel; each 30-s isrometer spectrum was only accepte when two of the three rop

12 2048 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 FIG. 8. The g DP as a function of (a),(e) Z attenuating_cells DR, (b),(f) Z attenuating_cells H, (c),(g) r attenuating_cells HV, an (),(h) K attenuating_cells DP. Panels (a) () correspon to observations an panels (e) (h) correspon to simulations base on Chilbolton observe spectra. Different temperature ranges are analyze. counting gauges recore some rainfall. The isrometer calibration was monitore by comparing weekly rainfall totals with those from a conventional gauge an any perios of questionable calibration were rejecte. After this rigorous quality control, a total of spectra were accepte. The next stage of the isrometer analysis is to compute values of Z H, Z DR, K DP, r HV, g H, an g DP at 08C using the T-matrix solution technique (Mishchenko 2000) to account for any Mie scattering an resonance at C ban an the rainrop axis ratio relationship propose by Branes et al. (2002), which has been confirme as appropriate for rain observe in northern France (Gourley et al. 2009). The spectra with a Z H above 25 BZ (rain rates above about 1 mm h 21 ) were selecte an the values of Z DR, Z H, r HV, an K DP plotte as a function of g DP in Figs. 8e h, respectively, where the iniviual points are in gray an the mean values are crosses. Analysis for values of Z H above 45 BZ (not shown) showe a linear relationship between g H an g DP with a very high correlation an a slope of 0.3, thus justifying our funamental assumption in (12). In the heaviest rain, the upper limit of 5 mm for the isrometer may be truncating the spectra an eliminating the largest rops, which may be contributing significantly to the attenuation an the polarization parameters. To account for the truncation, we consier the TABLE 1. The rainfall amount statistics in Paris an Lonon. Mean rainfall amount Paris Lonon January March April June July September October December Total

13 OCTOBER 2009 T A B A R Y E T A L counts in the last bin (bin no. 127), which provies the total number of rops above 5 mm. Because of saturation of the instrument, rops with a iameter beyon that threshol cannot be accurately size. The last bin count was nonzero for 201 spectra an reache 23 in the heaviest rainfall cases. To extrapolate the spectra to inclue the larger rops we fitte our observe truncate spectra to a normalize gamma function of the form N(D) 5 N W (D/D 0 ) m exp[2( m)d/d 0 ] using the metho of moments as escribe by Kozu an Nakamura (1991). The fitte values obtaine are very reasonable. The mean value of log(n W )is 3.8 mm 21 m 23 with a stanar eviation of 5 B, D 0 peaks at 1.1 mm with a tail extening to 4 mm, an the m istribution is quite skewe with a meian of 5 an a long tail of positive values. To recreate the missing large rops the full untruncate spectrum was compute from the fits, an the number of rops.5 mm that the isrometer woul have classifie in its last bin (bin no.127) was calculate. A scatterplot of the number of preicte rops above 5 mm with those observe was very encouraging. For 218 spectra the extrapolate fit preicte one or more rops.5 mm, an the maximum number of preicte large rops.5 mm was 22. On average the extrapolate preicte count was within 3 counts of the observe number. The values of Z H, Z DR, r HV, K DP, A H, an A DP were compute from the spectra fitte to a gamma function an the mean values of Z DR, Z H, r HV, an K DP plotte in Figs. 8e h as a function of g DP for 08 an 208C. The impact of the extrapolate large rops is, as expecte, really only significant for Z DR, where for Z DR. 3 B the inclusion of the extrapolate large rops increases Z DR by about 1 B. This change oes, however, lea to a much better agreement with the raar observations in Fig. 8a. Note also that the computations using the isrometer spectra preict a very slight increase in attenuation at the lower temperature, also in agreement with the raar observations. A maximum size of 10 mm was assume for the extrapolate spectra in Fig. 8, but reucing this to 8 mm i not change the plots significantly; most of the fitte spectra ha a positive m, which introuces a natural truncation of the spectrum. The plot of Z DR against g DP at 208C for Z DR. 5 B is shown otte in Fig. 8e because there are only three ata points. We note that the highest value of g DP in nearly all naturally occurring rainfall is 0.06 B 8 21 an the minimum value of r HV erive from the spectra is 0.96, which may be reuce by raar imperfections to In their analysis of a large ataset of tropical rainrop spectra, Keenan et al. (2001) foun a similar minimum (their Fig. 10). In their Fig. 9, the vast majority of spectra ha a g DP below 0.06 B 8 21, with just a very few tropical spectra above this value when a maximum rop size of 2.5 D 0 was assume but not for an 8-mm maximum rop size. This suggests that values of r HV lower than 0.95 an g DP above 0.06 B 8 21 foun in hot spots in northwest Europe are only rarely ue to pure rain but usually inicate targets that inclue some wet ice. We now consier the implications of Fig. 8. Figure 8a (mean g DP value as a function of Z attenuating_cells DR ) shows that Z attenuating_cells DR is an excellent preictor of the g DP value. The corresponing isrometer calculations (Fig. 8e) reprouce the Z DR epenency very well but only up to 5 B an g DP of 0.06 B 8 21 inicating that values above these limits are likely to be ue to partially frozen particles. Figures 8b an 8f reveal an excellent agreement between the observe an simulate g DP 5 f(z attenuating_cells H ) relationships, with both preicting, for example, values of g DP of 0.02 an 0.04 B 8 21, for a mean Z H of 50 an 60 BZ, respectively. There again, however, the isrometer preicts no values of g DP above 0.06 B Figures 8c an 8g show r HV plotte as a function of g DP. Lower values of r HV are clearly associate with higher values of g DP both on the observations an on the simulations. However, simulations o not yiel r HV values below 0.96 (corresponing to g DP equal to 0.04 B 8 21 ). This can be interprete as further evience that the attenuating hyrometeors are most unlikely to be pure rain in the low r HV high g DP regime. We note that the melting moel of hail presente by Rasmussen an Heymsfiel (1987), whereby a torus of water forms aroun the equator of a melting hailstone leaing to a stable nontumbling fall moe, is consistent with the hot spots having very high Z H an Z DR, low r HV, an very large total an ifferential attenuation. Finally, observe an simulate g DP 5 f (K attenuating_cells DP ) curves (Figs. 8,h) both show the same increasing tren, but the isrometer curves are rather flatter with K DP values approximately halve. The raar observations ten to show a much clearer increase of g DP with increasing K attenuating_cells DP, consistent with Fig. 7e. We recall here that observe K DP have been estimate using a very short path (1.68 km) an shoul therefore be very close to intrinsic K DP. The isagreement between observations an simulations can be interprete as further evience that ice is contributing to the high values of K DP an to the attenuation in the hot spots.. Vertical profile analysis To better assess the potential presence of frozen particles in the cells causing unusually high g DP,an analysis of the vertical profiles of horizontal reflectivity has been carrie out. Figure 9 presents an analysis of

14 2050 J O U R N A L O F A P P L I E D M E T E O R O L O G Y A N D C L I M A T O L O G Y VOLUME 48 FIG. 9. Mean vertical profiles of reflectivity (Z H ) in two contraste cases: (a) g DP, 0.06 B 8 21 an (b) g DP B The histogram of Z H for each height level between 1 an 10 km MSL is plotte. The vertical thick line correspons to Z H 5 55 BZ. those vertical profiles in two contrasting cases: g DP, 0.06 B 8 21 (Fig. 9a) an g DP B 8 21 (Fig. 9b). Two profiles are presente on each graph: the one retrieve with coupling between g H an g DP (thick line) an the one retrieve without coupling (thin line). In Fig. 9a, the coupling an the no coupling curves overlap completely an are harly iscernible. In Fig. 9b, the no coupling profile is about 5 B smaller than the coupling profile. In all cases, the mean Z H profiles are typical of convective cells. The profiles are almost vertical in the lowest layers (say up to 4 km), then ecrease at the rate of 21.5 B km 21. The high g DP profile, however, is shifte by about 5(10) B in the no coupling (coupling) case towar higher Z H than the low g DP profile. The low g DP profile is less than 55 BZ at all heights whereas the high g DP profile excees that typical hail threshol up to 4(6) km MSL in the no coupling (coupling) case. The 45-BZ contour is reache at about 4 km in the low g DP case an at some height above 7 km in the high g DP cases (with an without coupling). Assuming a 08C isotherm height at 3 km, Eq. (18) gives values of POH of 0.45 (low g DP case) an a value above 0.85 (high g DP cases). This strongly supports that hail, possibly combine with rain, is present in the high g DP case. 4. Conclusions This paper has ocumente the variability of the coefficient g DP between the specific attenuation (A DP )anthe specific ifferential phase (K DP ) retrieve from a 2-yr, C-ban polarimetric ataset through the application of a physical constraint referre to as the Smyth-an- Illingworth (S&I) constraint. This constraint consists at first orer in assuming that the intrinsic Z DR in the lowreflectivity stratiform region behin convective cells is approximately equal to 0 B. An empirical Z DR 5 f(z H ) istribution was built using a large number of nonattenuate, close-range, an high-snr ata an showe excellent agreement with the linear moel propose by Bringi et al. (2001). The empirical Z DR 5 f(z H )relationship an a first guess of the attenuation-correcte Z H were use to improve the estimation of Z DR in the stratiform region. The S&I constraint has been implemente with an without a coupling between g H an g DP. A thorough analysis of raar observations in Trappes (Gourley et al. 2009) inicate that the Branes et al. (2002) rainrop shapes are appropriate with no evience of oscillations in the heavier rain leaing to unusual shapes; the self-consistency of the polarization parameters inicate that the rainrop spectra were well represente by normalize gamma functions a conclusion confirme by the analysis of four years of spectra in southern Englan. Accoringly, we are reasonably confient that in this stuy in northwest Europe a large majority of the highly attenuating hot spots that are accompanie by low r HV o not result from rainrops alone. From the extensive analysis, which can very easily be reprouce for any other

15 OCTOBER 2009 T A B A R Y E T A L polarimetric raar ataset, the following conclusions can be rawn: The S&I constraint, implemente as escribe above, coul only be applie to 20% of all attenuate rays (efine by DF DP. 308). This means that operational ifferential attenuation correction algorithms cannot exclusively rely on the S&I constraint an that other correction techniques have to be use as an alternative. Any operational ifferential attenuation correction scheme shoul inclue a basic check on the sign of the correcte Z DR values because no negative values are expecte in rain. The range of variation of g DP is large an has to be accounte for in any operational algorithm. The minimum, maximum, an mean values are respectively equal to 0.01, 0.11, an B This is fully consistent with inepenent results obtaine by Ryzhkov et al. (2007) in Alabama an Canaa with the two SIDPOL raars. Another lesson of this work is that the impact of temperature on attenuation (hence on attenuation correction schemes) is clearly negligible compare to the impact of microphysical properties of the attenuating cells, as reveale by the values of the polarimetric variables. In aition to that, the majority of attenuating cells of the Paris area evelop at the same season in the same thermal environment (T 5 158C). Surprisingly, g DP appears to be remarkably correlate (linearly) across its entire range of variation [0.01; 0.11] B 8 21 with the values of the polarimetric variables of the attenuating cells: Z DR, Z H, an K DP (positive correlation) an r HV (negative correlation). For the sake of simplification, we have istinguishe in the paper two g DP regimes: high g DP regime (.0.06 B 8 21 ) an low g DP regime (,0.06 B 8 21 ). Extremely high g DP values (.0.06 B 8 21 ) occur for 15% a nonnegligible figure of the rays presenting a significant ifferential phase shift (.308). Those extremely high g DP values are cause by attenuating cells having unusually high (intrinsic) Z DR. 4 B, Z H. 55 B, an K DP. 48 km 21, an unusually low r HV, This low r HV regime is only very rarely reprouce by scattering simulations in pure rain using normalize gamma rop size istributions or by computations base on observe rainrop spectra. The corresponing vertical profiles of horizontal reflectivity show very high values (above 55 BZ)upto3 km, then a steay ecrease at a rate of 1.5 B km 21. The probability of hail erive from the classical comparison between the 45-BZ height an the 08C isotherm height is close to 1. Those facts strongly suggest that ice is present in the attenuating cells. Ryzhkov et al. (2007), using an inepenent ataset (from the SIDPOL C-ban raars from Alabama an Canaa) an a somewhat similar methoology to estimate g DP, obtaine very similar results an conclue that the ifferential attenuation hot spots were cause through resonant Mie scattering by a mixture of large rainrops an melting hail. Such hot spots can be ientifie by values of r HV below 0.94, which, combine with high values of Z H, can be consiere a signature of the presence of wet ice. Such wet ice appears to be associate with high total an ifferential attenuation an also accompanie by high values of Z DR an K DP. If this is the case then we may have to question the suggestion that K DP respons only to the presence of oblate rainrops an thus can provie accurate estimates of rainfall rates in the presence of hail. Among all the numerous intense convective cells (Z H. 55 BZ) that were analyze in this work, only an extremely small percentage show the typical hail signature (low Z DR an K DP ). The conclusion surrouning that is that pure (ry) hail is very rare in the Paris area an that the ominant precipitation type in intense convective systems is wet ice, the forwar an backscattering of which are completely ifferent from pure hail or pure rain. Operational correction of ifferential attenuation create by the so-calle hot spots is clearly not a trivial task, especially if one consiers that the accuracy of the correction has to be better than 0.1 B for Z DR to be usable in subsequent rainfall rate estimation an we cannot be confient of a simple link between g H an g DP. If the hyrometeors in the hot spots are inee a mixture of rain rops an melting or wet ice then it will be very ifficult to obtain a unique solution from the available polarization parameters for the sizes an shapes of both the rain rops an the wet ice particles. A more practical solution may be to flag any erive rain rates in such hot spots as error prone. It will also be very ifficult to correct the ray profiles behin the hot spot for attenuation; in this case one strategy coul be to use a secon, probably more istant raar in the network, which is unlikely to suffer from hot spot attenuation in the same location. Acknowlegments. The authors are inebte to Laurent Périer, Patrick Roquain, an Kim Do Khac from Météo France who evelope the French CASTOR2 raar processor an mae the polarimetric ata collection possible. Julien Desplats (Météo France) kinly provie the seasonal statistics of rainfall accumulations for Paris an Lonon.