1. Introduction
The backscatter differential phase δ (°) is defined as the contribution of backscattering from objects within the radar resolution volume to the difference between the phases of horizontally and vertically polarized components of the wave—the total differential phase ΦDP (°)—observed at the radar. Accurate rainfall measurements based on specific differential phase KDP rely on the propagation component of ΦDP and thus require an effective filtering of the backscattered component (e.g., Matrosov et al. 1999, 2002; Otto and Russchenberg 2011; Schneebeli and Berne 2012). Until recently, this troublesome characteristic of δ has been the primary target of researchers while its potential utilization (e.g., for hydrometeor and process typing) has not been well explored.
In this study, we focus on the potential information content of δ in mixed-phase conditions. Berenguer and Zawadzki (2009) report correlations between brightband intensity and ZDR near the surface, which hints at big melting snowflakes in the ML creating big raindrops below. These findings suggest that δ and ZDR measurements and the analysis of their relationship in the ML may open a new avenue for improved Z–R relationships (where Z and R represent the linear radar reflectivity and rain rate, respectively) for utilization near the ground. For example, for a given reflectivity in the rain layer, the presence of rimed snow in the ML is manifested by lower ZDR and δ both in the ML and in the rain below relative to unrimed snow (e.g., Ryzhkov et al. 2008). Since δ increases with the dominant size of raindrops or wet snowflakes and its vertical profile thus hints at microphysical processes leading to their formation, the quantification of δ together with other polarimetric variables in the ML might allow for a better microphysical characterization of the bright band. Such information can then be exploited for both improving microphysical models of the ML and quantitative rainfall estimation. An improved ML characterization including its temporal evolution could also be utilized in object-based approaches to precipitation system analysis, which use the ML evolution for system identification and prediction (e.g., Trömel et al. 2009; Trömel and Simmer 2012).
In section 2, the method recently introduced by Trömel et al. (2013) to reliably measure δ in the ML is summarized. In section 3, we report on recent analyses of δ in the ML, together with reflectivity at horizontal polarization ZH, differential reflectivity ZDR, and cross-correlation coefficient ρhυ (where h and υ represent horizontal and vertical, respectively) observed at X band in Germany and at S band in the United States. Dual-frequency observations at X and C bands in Germany and dual-frequency observations at C and S bands in the United States are also compared in order to explore the regional frequency dependencies of the δ signatures. Section 4 presents simulations of the backscatter differential phase δ in the ML and elucidates the potential microphysical processes, which might be responsible for generating the observed values of δ. A summary and outlook are given in section 5.
2. Method
The measured total differential phase ΦDP routinely exhibits characteristic “bumps” within the ML, which may be associated with either δ or nonuniform beam filling (NBF) (Ryzhkov 2007). Within the ML, ρhυ can vary from 0.8 to 0.97 and variations of ΦDP (caused by reduced ρhυ) may become so overwhelming that δ cannot be reliably estimated solely from individual radials. Trömel et al. (2013) suggest a reliable method for estimating δ in the ML; they use azimuthal averaging of ΦDP measured at high antenna elevations (>7°) to suppress statistical fluctuations of ΦDP that are attributed to low ρhυ. Their method allows for better separation of the effects of δ and KDP and for minimization of the impact of NBF. In cases of uniform stratiform precipitation, averaging may extend over all azimuths prior to δ detection along the range. Values of ΦDP just above and below the ML are then connected with a straight line, and the difference between the actual average profile of ΦDP along the range and the straight line is used to derive the maximal azimuthally averaged δ. For more heterogeneous precipitation fields only an azimuthal sector containing subjectively identified uniform brightband characteristics is averaged [see also Trömel et al. (2013) for the required extent of the averaging].

3. Observations of δ in the melting layer
a. δ measurements at X band in Germany
A total of 480 snapshots from 13 precipitation events in Germany observed with the polarimetric X-band radars in Bonn (BoXPol) and Jülich (JuXPol) between July 2010 and June 2013 have been analyzed. Every 5 min both radars take 10 plan position indicator (PPI) scans at different elevation angles, including one scan at 37° for the JuXPol radar. Table 1 provides a list of all events considered together with their respective elevation angles and radial resolutions. The azimuthally averaged profiles of ΦDP, ZDR, ρhυ, and ZH measured by BoxPol at 2140 UTC 20 June 2013 (Fig. 1) indicate that the ML is at around 3.2-km height by increased ZH and ZDR and a decreased ρhυ. The increase of ΦDP across the ML is obviously almost exclusively attributed to δ. According to the method described in section 2, the estimated δ is about 3.6°, while the maximum δ observed during all 13 events is about 8.5°.
Radar wavelength, name, date, radial resolution, and elevation angle of the PPIs analyzed in Germany and the United States (single-frequency observations only). Information about the dual-frequency observations is provided in Table 5, below.
Quasi-vertical averaged profiles of ZH, ZDR, ρhυ, and δ in the ML observed with the BoXPol X-band radar in Bonn at 28° elevation on 20 Jun 2013.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
For all events the relative heights and magnitudes of the polarimetric moments in the ML have been investigated. The polarimetric theory of the melting layer as described by Giangrande (2007), Ryzhkov et al. (2008), and Trömel et al. (2013) predicts the δ maximum above the ZDR maximum (which is confirmed by our observations; see Fig. 2). The theory is, however, not clear regarding the relative heights of the δ maximum and the ρhυ minimum. Our X-band observations position the δ maximum above the ρhυ minimum. The observations show also that the height levels of maximum ZH and δ approximately coincide, which is unexpected. The S-band observations (see section 3b), however, are in agreement with theoretical simulations concerning the relative heights of maximum ZH and δ. These discrepancies have to be further explored.
Relative heights of the (left) ρhυ and δ extrema, ZH and (center) δ, as well as (right) ZDR and δ in the ML observed with the X-band radars BoXPol in Bonn and JuXPol in Jülich.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
To investigate the relationship between different polarimetric variables in the ML, the anomalies ΔZH, Δρhυ, ΔZDR, and δ for all events are determined and correlated with each other. The method introduced by Trömel et al. (2013) is applied to generate azimuthally averaged quasi-vertical profiles based on single PPI scans measured at high antenna elevations prior to this analysis. The anomalies are determined as the difference between the maximal values of the respective polarimetric variable in the ML and the one in rain immediately below the bottom of the ML. The bottom of the ML is defined by the intersection of the radial profile with its straight-line fit. The scatterplots in Fig. 3 summarize the magnitudes of the anomalies observed on 4 December 2011. Note that the maximal Δρhυ is around −0.2 and maximal ΔZDR is 1.5dB, which is close to the maximal anomalies Δρhυ = −0.23 and ΔZDR = 1.7dB observed during all 13 of the precipitation events investigated. Both absolute values are higher than expected from simulations, which ignore aggregation and accretion processes (Trömel et al. 2013; Ryzhkov et al. 2008). Table 2 compares Pearson correlation coefficients between the different anomalies in the ML based on all events with the correlations based on the snapshots observed on 4 December 2011, only. The magnitudes of δ and ΔZH in the ML are, as expected, not significantly correlated both on average (left side of Table 2) and for individual cases (e.g., right side of Table 2 and Fig. 3), because δ does not—contrary to ZH—depend on particle concentration. A stronger—negative—correlation exists between δ and Δρhυ, which is however dominated by only a few events like the 4 December 2011 case (see also Trömel et al. 2013). Thus, the generally weak correlation of δ with other polarimetric variables suggests independent information about the ML carried by δ, which may hint at specific microphysical processes.
Correlations between anomalies in the ML observed on 4 Dec 2011, from the 7°-elevation-angle PPI taken by the BoXPol radar in Bonn.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
Pearson’s correlation coefficients r between the anomalies of observed polarimetric moments in the ML based on all events observed in Germany at X band and based on observation on 4 Dec 2011, only.
Larger aggregates above the ML are generally expected to produce larger δ. Hence, in the absence of riming, for example, associated with higher cloud tops (i.e., deeper subfreezing parts of the storm), intense dendritic growth, indicated by the presence of a fake bright band aloft, makes subsequent aggregation more likely. Thus, a link between intense dendritic growth and higher δ values may exist. No clear correlation between δ and the depth of the cloud has, however, been identified so far. Some link may exist, however, between an intense dendritic growth zone aloft and δ within the ML. Dendritic growth is often observed in the region near −15° along with a sharp vertical increase in ZH in this region and local maxima in KDP and ZDR in stratiform clouds (e.g., Kennedy and Rutledge 2011; Bechini et al. 2013). Below the layer of dendritic growth, ZH increases toward the surface while KDP and ZDR decrease due to aggregation. The signatures above the freezing level observed in several of the investigated cases in Bonn can be identified as the layers of dendritic growth. Figure 4 shows the composite PPI of ZH, ZDR, and ρhυ observed with BoXPol at 2141 UTC 4 December 2011 at 8.1° elevation. The first layer of enhanced ZDR and reduced ρhυ associated with a high vertical gradient of ZH above the freezing level is likely the area of dendritic growth. Although the connection between the presence of the layer of pronounced dendritic growth aloft and the δ enhancement within the ML seems to be present in some cases, it is not always the case.
PPIs of ZH, ZDR, and ρhυ observed with BoXPol at 2141 UTC 4 Dec 2011 at 8.1° elevation, showing a dendritic growth signature.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
b. δ measurements at S band in the United States
The data for 13 precipitation events spanning both warm and cold seasons of the year observed at S band with the Weather Surveillance Radars-1988 Doppler (WSR-88Ds) in the United States were analyzed (Table 1). Figure 5 shows as an example of the PPIs of ZDR, ρhυ, and δ in the ML observed with the Jacksonville, Florida (KJAX), radar at 9.9° elevation on 26 June 2012. The ML is quite pronounced across the entire azimuthal range, and all variables shown (all 360° have been averaged in order to derive the quasi-vertically averaged profiles shown in Fig. 6) clearly indicate the ML. All rain events exhibit well-pronounced δ in the melting layer ranging from 3° to 42° at 9.9° elevation with an average value of about 25°. The values of δ measured at higher elevation angles can be stunningly high in some cases (up to 70°; see Table 3).
PPIs of ZH, ρhυ, and δ in the ML observed with the S-band KJAX WSR-88D in Jacksonville at 9.9° elevation on 26 Jun 2012.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
Quasi-vertical averaged profiles of ΦDP, ZH, and ρhυv in the ML observed with the S-band KJAX WSR-88D in Jacksonville, at 9.9° elevation on 26 Jun 2012.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
Maximal reflectivities Zmax and anomalies ΔΦDP in the ML for different elevation angles observed with the KJAX radar in Jacksonville on 26 Jun 2012.
Such high values of δ measured in the melting layer at S band are quite surprising at first glance and considerably exceed the theoretical expectations put forward in Trömel et al. (2013) that were based on the model of ML without accounting for accretion/aggregation (Szyrmer and Zawadzki 1999; Battaglia et al. 2003; Zawadzki et al. 2005;). In all 13 of the events examined at S band, the maximum of δ coincides very well with the minimum of ρhυ. The corresponding minimum ρhυ varies between 0.87 and 0.96 and does not show an obvious correlation with the magnitude of the δ maximum. The δ maximum–ρhυ minimum is always below the maximum of ZH and above the maximum of ZDR in the S-band observations. Again, as in the X-band cases, we did not find any pronounced correlation between the magnitude of the δ maximum and the maximal value of ZH and its enhancement in the ML. In approximately half of the examined cases in the United States, the increase in δ with increasing elevation angle within the interval from 6.0° to 19.5° was documented. Examples of these elevation dependencies are shown in Tables 3 and 4 for the cases in Florida and Oklahoma. Beam smearing is the most likely explanation for this effect. Indeed, for the height of the ML at 4.6 km in the Florida case, the width of the radar beam (or vertical resolution of the radar) is about 0.75 km at 6.0° elevation angle and more than 3 times smaller at 19.5° elevation angle. The melting layer is usually a few hundred meters deep and the layer of enhanced δ inside the ML is shallower by a factor of 3–4. Hence, an inevitable degradation of the δ signature occurs for poorer vertical resolutions at lower antenna elevations. This is consistent with the decrease of the maximal value of ZH measured in the ML at lower elevations (see Tables 3 and 4).
Maximal reflectivities Zmax and anomalies ΔΦDP in the ML for different elevation angles observed with the KTLX radar in Oklahoma City on 30 Jul 2013.
c. Dual-frequency observations
Since all analyzed X-band observations are from Germany and all S-band observations are from the United States, part of the observed differences between the X and S bands may be attributed to climatic differences. Thus, dual-frequency observations of δ in individual storms have been included for both regions in order to corroborate the unexpected high δ observations at longer wavelengths (Table 5).
Radar wavelength, name, date, radial resolution, and elevation angle of the PPIs analyzed in Germany and the United States for the dual-frequency observations.
In Germany, dual-frequency observations are obtained at the X and C bands for single events observed with BoXPol and JuXPol and adjacent C-band radars from the German Weather Service (Deutscher Wetterdienst, or DWD) network. On 22 June 2011, thunderstorms occurred ahead of a cold front in the region observed by the radars. The BoXPol observations in the stratiform region following the front show δ values around 5° while somewhat smaller δ values around 3° and below are observed by the C-band radar in Essen in accordance with the expectations of Trömel et al. (2013). On 1 November 2013, however, a day with warm-air advection and large-scale rainfall, δ observations at X band around 3° at 28° elevation angle approximately collocate with δ of 25° at 25° elevation angle at C band. At 12° elevation angle the Essen radar even showed δ magnitudes of around 35°.
The most impressive German event analyzed, however, occurred during 20 June 2013. A prefrontal convergence line generated high instability and heavy thunderstorms, which caused a host of flooded basements and ended a heat wave in Germany. Intense lightning activity was reported on 20 June 2013; the international LINET lightning detection network (Betz et al. 2009) measured 854 872 lightning strikes across Germany. Observations from the DWD radar in Essen at 12° and 24.9° elevation are compared now with BoXPol and JuXPol observations at 28°. Figure 7 shows the quasi–vertically averaged profiles of ZH, ZDR, ρhυ, and ΦDP observed with the Essen DWD radar at 12° elevation (top) and 24.9° elevation (bottom) at 0908 and 0914 UTC, respectively. At 12° elevation angle δ reaches 60° and at 24.9° elevation angle is reaches 84°. These large δ values remained stable for at least 35 min. BoXPol and JuXPol, however, show very small δ values between 1° and 4° during the same time period.
Quasi-vertical averaged profiles of ZH, ZDR, ρhυ, and ΦDP observed with the Essen DWD radar at (top) 12° and at 0908 UTC and (bottom) 24.9° elevation at 0914 UTC 20 Jun 2013.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
Similar dual-frequency observations have been performed with a C-band polarimetric radar and two operational WSR-88D S-band radars in the United States. Figure 8 compares the quasi-vertical profiles of ΦDP, ZH, and ρhυ from the WSR-88D S-band radar at Fort Rucker, Alabama (KEOX); the WSR-88D S-band radar at Eglin Air Force Base (AFB), Florida (KEVX); and the C-band radar at the Enterprise Electronics Corporation (EEC) in the city of Enterprise, Alabama, observed around 2216 UTC 13 January 2014. The elevation angles range from 14.6° to 15.6°. It is interesting that although the ZH enhancements within the ML are very similar for the S- and C-band radars, the C-band ρhυ is much lower than ρhυ at S band, whereas the C-band δ is almost invisible.
Quasi-vertical profiles of ΦDP, ZH, and ρhυ from dual-frequency observations with the KEOX and KEVX WSR-88D S-band radars, and the C-band EEC radar, observed around 2216 UTC 13 Jan 2014.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
4. Theoretical simulations of the backscatter differential phase in the melting layer
The model of the ML without accretion/aggregation, which was used in a number of previous studies (Szyrmer and Zawadzki 1999; Battaglia et al. 2003; Zawadzki et al. 2005) and in the recent paper by Trömel et al. (2013), suggests values of δ below 1°, 3°, and 5° at S, C, and X bands, respectively (see Fig. 8 in Trömel et al. 2013). The model also obviously does not reproduce the observed large values of differential reflectivity ZDR enhancement and the cross-correlation coefficient ρhυ reduction in the ML (Ryzhkov et al. 2008). The model assumes that snowflakes gradually turn into raindrops by melting. While the density of the melting snowflake increases with fall distance, its size decreases. This assumption creates the largest particles at the very top of the melting layer and contradicts the observations by Stewart et al. (1984), Willis and Heymsfield (1989), Barthazy et al. (1998), and Goeke and Waldvogel (1998), which position the maximal particle size within the ML. This is illustrated in Fig. 9, adapted from the study of Barthazy et al. (1998), who measured the maximal size of snowflakes of 7 mm with an optical spectrometer at the top of the ML. In the middle of the ML or slightly below the maximum of ZH, the maximal measured particle size reaches 23 mm and then rapidly decreases toward the bottom of the ML.
Particle size distributions, velocity distributions, and vertical profiles of radar reflectivity within the (a) upper and (b) lower parts of the ML. The two curves indicate the fall velocities for raindrops (dashed line; Atlas et al. 1973) and for unrimed aggregates (dotted line; Locatelli and Hobbs 1974). [Adapted from Barthazy et al. (1998).]
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
The further increase of particle size, when falling below the melting point can be explained and eventually modeled by the following mechanisms. Large partially melted snowflakes generated at the top of the ML collect smaller liquid drops originating from smaller completely melted snowflakes below via accretion. Aggregation occurs if partially melted snowflakes collect other partially melted snowflakes. Both processes are believed to be dominant in the upper part of the ML (Goeke and Waldvogel 1998). As the size and water content of large wet snowflakes increase, the snowflakes become unstable and prone to spontaneous breakup and breakup caused by collisions. The processes of accretion, aggregation, and breakup can be described by the stochastic collection equation (e.g., Mitchell 1988), which is, however, very difficult to solve within the ML where the microphysical information necessary to parameterize all three processes is very limited. The process of accretion though is relatively easy to model without resorting to solving a full-fledged stochastic collection equation.
The dependence of the maximal size of liquid drops on the fall distance from the top of the melting layer is illustrated in Fig. 10 for the case of unrimed snow (frim = 1), temperature lapse rate of 6.5°C km−1, and relative humidity of 100%. The terminal velocities of hydrometeors are very different for rain and snow with raindrops falling much faster. Figure 11 shows that at 400 m below the top of the melting layer, where the maximal size of raindrops is about 2 mm, the difference between terminal velocities of raindrops Ur and wet snowflakes Us can be as large as 5 m s−1, which favors accretion of partially melted snowflakes.
Maximal diameter of raindrop originated from melted snowflake as a function of fall distance from the top of the melting layer for unrimed snow, with a temperature lapse rate of 6.5°C km−1 and relative humidity of 100%.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
Terminal velocities of raindrops and partially melted snowflakes at the top of the melting layer (bottom curve) and at the levels 200, 400, and 600 m below the top. Unrimed snow aloft, temperature lapse rate of 6.5°C km−1, and relative humidity of 100% are assumed.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
At any given height level, raindrops originating from fully melted snowflakes and partially melted snowflakes have very distinct size distributions, as Fig. 12 demonstrates. Size distributions shown in Fig. 12 are calculated assuming that the size distribution of melted diameters of snowflakes is of Marshall–Palmer type corresponding to a rain rate of 5 mm h−1. It is clear from Fig. 12 that the size distribution of hydrometeors is close to exponential only at the top and bottom of the ML. Inside the ML, it is close to biexponential, which agrees with the observations of Barthazy et al. (1998) and Goeke and Waldvogel (1998).
Size distributions of raindrops and partially melted snowflakes at the top of the ML (upper curve) and at the levels 200, 400, and 600 m below the top of the ML. The Marshall–Palmer distribution of melted diameters with equivalent rain rate 5 mm h−1 is assumed.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
The size dependencies of the volume water fraction on the diameter of melting snowflakes at 400 m below the freezing level were computed using the microphysical model and Eqs. (6)–(9) (Fig. 13) for the absence (thin line) and presence (thick line) of accretion. Following Goeke and Waldvogel (1998), it was assumed that the collection efficiency E is equal to 1 in the upper part of the melting layer. At 400 m, the maximal size of liquid drops is about 2 mm (Fig. 10). Beyond this size, the volume water fraction decreases rapidly with increasing size of partially melted snowflakes. Accretion redistributes the water fraction across the size spectrum from the lower end toward its higher end. In other words, larger snowflakes get more water at the expense of the “liquid” part of the spectrum. Although accretion makes larger snowflakes wetter, it does not significantly change their size. The increase of the maximal size of the snowflakes occurs due to aggregation when two large partially melted snowflakes collide and stick together. The combined effect of accretion and aggregation reduces the concentration of smaller-size particles and boosts the concentration of larger-size snowflakes, as the conceptual plot in Fig. 14 shows.
Volume fraction of water in a melting snowflake as a function of its equivolume diameter at the height level 400 m below the freezing level. Thin and thick lines are for the absence and presence of accretion, respectively.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
Conceptual plot illustrating the modification of the size spectrum of partially melted snowflakes via accretion and aggregation. The solid line represents the size spectrum before and the dashed line the size spectrum after the interaction processes.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
Backscatter differential phase δ as a function of the melting hydrometeor diameter at S, C, and X bands. Dotted lines indicate dry snow at the top of the melting layer, dashed lines indicate partially melted snowflakes in the middle of the melting layer (400 m below the top), and the solid line is pure water spheroids. The aspect ratio of particles is equal to 0.7.
Citation: Journal of Applied Meteorology and Climatology 53, 10; 10.1175/JAMC-D-14-0050.1
It is not surprising that δ of dry snowflakes is very close to zero at all three radar wavelengths (dotted lines in Fig. 15). A thin film of water at the surface of a snowflake makes its δ comparable to that of a giant pure liquid drop with the same shape and orientation. The simulated values of δ for larger diameters are consistent with the results of the polarimetric radar observations. Both positive and negative values of δ are possible although the positive cases are certainly prevalent. The observed δ results from the integration over the full size spectrum. It is quite possible that large negative δ within the size range of 1.5–1.6 cm at X band may cancel out the contribution of hydrometeors with positive δ and this may explain why the observed magnitudes of δ at X band are generally smaller than those at C and S bands.
Very high values of the backscatter differential phase δ are likely attributed to the presence of large partially melted snowflakes, which grow by accretion and aggregation within the ML. If the microphysical model of the ML does not include any interaction between particles (i.e., no accretion/aggregation), then it cannot produce the large observed values of δ. It can be shown that the magnitude of δ increases with the amount of accreted water. Hence, microphysical factors favoring accretion help to boost δ. The degree of riming frim has a strong effect on the volume of accreted water and the magnitude of δ. Indeed, as Eq. (6) indicates, the factor |Us – Ur|/Us decreases with increasing frim due to the decrease of the numerator and the increase of denominator. Therefore, the magnitude of δ can be used for an indirect estimation of the degree of riming of snow above the ML.
5. Summary and outlook
Backscatter differential phase δ within the ML is a reliably measurable parameter, which exhibits high variability. A method recently introduced for estimating δ in the melting layer has been applied to polarimetric radar observations at X band in Germany and S band in the United States. Model simulations that assume spheroidal shapes for melting snowflakes in the absence of accretion and aggregation within the ML yield much lower values of δ than observed, especially at S band (Trömel et al. 2013). Contrary to our expectations, δ observations at S band showed much higher magnitudes than the δ observations at X band. The maximal observed δs at X band are 8.5° and 42° at elevation 9.9° at S band. Single measurements at higher elevation angles (19.5°) exhibit even higher δ values up to 70°. Dual-frequency observations of δ in the same events have been included to verify the unexpectedly high δ observations at longer wavelengths. Measurements from the Essen C-band radar in Germany again show δ signatures around 30° and even 60° in one intense thunderstorm case, while the two strongly overlapping X-band radars provide δ values only around 5°. Dual-frequency observations with a C-band EEC radar and two WSR-88D S-band radars (KEOX and KEVX) also confirm larger δ at S band compared to C band.
Theoretical simulations that do not account for any interactions between particles in the ML are not able to reproduce the results of the observations. The observed very high values of the backscatter differential phase δ are likely attributed to the presence of large partially melted snowflakes. Theoretical simulations using a two-layer T-matrix code and a simple model for the representation of accretion are able to explain the origin of the observed pronounced signatures at S and C bands. To simulate the observed large δ magnitudes, the presence of very large water-coated snowflakes with diameters exceeding 1 cm has to be assumed. The accretion of small liquid droplets originating from smaller size, quickly melted snowflakes by larger, partially melted snowflakes leads to significant increases of the water content of larger snowflakes. Both positive and negative values of δ are possible; large negative δ values are expected at X band for hydrometeor melting diameters of around 1.5–1.6 cm. Since the measured δ result from integrating over the particle size spectrum, large negative δ may compensate to a large extent the contribution of hydrometeors with positive δ, which may partially explain the observed small δ magnitudes at X band compared to C and S bands.
We believe that the effects of nonuniform beam filling are negligibly small at elevation angles exceeding 6°–8°. However, the impact of beam smearing resulting in the degraded vertical resolution of the radar within the melting layer can be quite significant and result in the decrease of the observed δ at lower antenna elevations, which has to be taken into account in the microphysical interpretation of the backscatter differential phase.
In summary, very high values of the backscatter differential phase δ are likely attributed to the presence of large partially melted snowflakes within the ML. If the microphysical model of the ML does not include any interaction between particles (i.e., no accretion/aggregation), then it cannot produce the large observed values of δ. The backscatter differential phase δ varies in a wide range, particularly at S and C bands, and definitely contains very important microphysical information about accretion and aggregation processes in the ML, as well as the degree of riming of the snowflakes above the melting layer.
In the future, measurements of δ can probably be utilized as an important calibration parameter for improving microphysical models of the ML. Larger δ can be associated with larger size aggregates above the ML. Additionally, unrimed snow seems to produce much larger δ than rimed snow; thus, δ may be used to estimate the degree of riming aloft. Some link may exist between the appearance of the zone of dendritic growth aloft and δ within the ML. Signatures for dendritic growth have already been identified in several of the German events shown and need further investigations.
Acknowledgments
The research of S. Trömel was carried out within the framework of the Hans-Ertel-Centre for Weather Research (http://www.herz-tb1.uni-bonn.de/). This research network of universities, research institutes, and the Deutscher Wetterdienst is funded by the Federal Ministry of Transport, Building and Urban Development (BMVBS). Alexander Ryzhkov and Pengfei Zhang were supported via funding from NOAA–University of Oklahoma Cooperative Agreement NA11OAR4320072 under the U.S. Department of Commerce and from the National Science Foundation (Grant AGS-1143948). We gratefully acknowledge the support of the German Weather Service for providing the radar data for Essen, the support of the Terrestrial Environmental Observatories (TERENO) project funded by the Helmholtz-Gemeinschaft in providing the JuXPol observations, and finally the support of the Transregional Collaborative Research Centre 32 (SFB/TR 32) funded by the German Research Foundation (DFG) for travel funds for A. Ryzhkov to Germany and for providing the BoXPol data. The authors are thankful to the Enterprise Electronics Corporation and to Dr. Qing Cao, in particular, for providing C-band polarimetric data in Alabama.
APPENDIX
Melting of Snowflakes
REFERENCES
Atlas, D., R. C. Srivastava, and R. S. Sekkon, 1973: Doppler radar characteristics of precipitation at vertical incidence. Rev. Geophys., 11, 1–35, doi:10.1029/RG011i001p00001.
Barthazy, E., W. Henrich, A. Waldvogel, 1998: Size distribution of hydrometeors through the melting layer. Atmos. Res.,47–48, 193–208, doi:10.1016/S0169-8095(98)00065-9.
Battaglia, A., C. Kummerow, D.-B. Shin, and C. Williams, 2003: Constraining microwave brightness temperatures by radar brightband observations. J. Atmos. Oceanic Technol., 20, 856–871, doi:10.1175/1520-0426(2003)020<0856:CMBTBR>2.0.CO;2.
Bechini, R., L. Baldini, and V. Chandrasekar, 2013: Polarimetric radar observations in the ice region of precipitating clouds at C-band and X-band radar frequencies. J. Appl. Meteor. Climatol., 52, 1147–1169, doi:10.1175/JAMC-D-12-055.1.
Berenguer, M., and I. Zawadzki, 2009: On the relationship between Z-R, the bright band intensity and ZDR. Preprints, 34th Conf. on Radar Meteorology, Williamsburg, VA, Amer. Meteor. Soc., 4A.3. [Available online at https://ams.confex.com/ams/pdfpapers/155482.pdf.]
Betz, H.-D., K. Schmidt, P. Laroche, P. Blanchet, W. P. Oettinger, E. Defer, Z. Dziewit, and J. Konarski, 2009: LINET—An international lightning detection network in Europe. Atmos. Res., 91, 564–573, doi:10.1016/j.atmosres.2008.06.012.
Brandes, E. A., G. Zhang, and J. Vivekanandan, 2002: Experiments in rainfall estimation with a polarimetric radar in a subtropical environment. J. Appl. Meteor., 41, 674–685, doi:10.1175/1520-0450(2002)041<0674:EIREWA>2.0.CO;2.
Brandes, E. A., K. Ikeda, G. Zhang, M. Schoenhuber, and R. Rasmussen, 2007: A statistical and physical description of hydrometeor distributions in Colorado snowstorms using a video-disdrometer. J. Appl. Meteor., 46, 634–650, doi:10.1175/JAM2489.1.
Giangrande, S., 2007: Investigation of polarimetric measurements of rainfall at close and distant ranges. Ph.D. dissertation, University of Oklahoma, 236 pp.
Goeke, S., and A. Waldvogel, 1998: Studies of snowflake aggregation efficiencies within the melting layer. Preprints, Conf. on Cloud Physics, Everett, WA, Amer. Meteor. Soc., 458–461.
Kennedy, P. C., and S. A. Rutledge, 2011: S-band dual-polarization radar observations of winter storms. J. Appl. Meteor. Climatol., 50, 844–858, doi:10.1175/2010JAMC2558.1.
Locatelli, J. D., and P. V. Hobbs, 1974: Fall speeds and masses of solid precipitation particles. J. Geophys. Res., 79, 2185–2197, doi:10.1029/JC079i015p02185.
Matrosov, S. Y., R. A. Kropfli, R. F. Reinking, and B. E. Martner, 1999: Prospects for measuring rainfall using propagation differential phase in X- and Ka-radar bands. J. Appl. Meteor., 38, 766–776, doi:10.1175/1520-0450(1999)038<0766:PFMRUP>2.0.CO;2.
Matrosov, S. Y., K. A. Clark, B. E. Martner, and A. Tokay, 2002: X-band polarimetric radar measurements of rainfall. J. Appl. Meteor., 41, 941–952, doi:10.1175/1520-0450(2002)041<0941:XBPRMO>2.0.CO;2.
Mitchell, D. L., 1988: Evolution of snow-size spectra in cyclonic storms. Part I: Snow growth by vapor deposition and aggregation. J. Atmos. Sci., 45, 3431–3451, doi:10.1175/1520-0469(1988)045<3431:EOSSSI>2.0.CO;2.
Otto, T., and H. W. J. Russchenberg, 2011: Estimation of specific differential phase and differential backscatter phase from polarimetric weather radar measurements of rain. IEEE Geosci. Remote Sens. Lett., 8, 988–992, doi:10.1109/LGRS.2011.2145354.
Ryzhkov, A., 2007: The impact of beam broadening on the quality of radar polarimetric data. J. Atmos. Oceanic Technol., 24, 729–744, doi:10.1175/JTECH2003.1.
Ryzhkov, A., S. Giangrande, A. Khain, M. Pinsky, and A. Pokrovsky, 2008: Exploring model-based polarimetric retrieval of vertical profiles of precipitation. Extended Abstracts, Fifth European Conference on Radar in Meteorology and Hydrology, Helsinki, Finland, ERAD, P6.1.
Ryzhkov, A., M. Kumjian, S. Ganson, and A. Khain, 2013: Polarimetric radar characteristics of melting hail. Part I: Theoretical simulations using spectral microphysical modeling. J. Appl. Meteor. Climatol., 52, 2849–2870, doi:10.1175/JAMC-D-13-073.1.
Schneebeli, M., and A. Berne, 2012: An extended Kalman filter framework for polarimetric X-band weather radar data processing. J. Atmos. Oceanic Technol., 29, 711–730, doi:10.1175/JTECH-D-10-05053.1.
Stewart, R. E., J. Marwitz, J. Pace, and R. Carbone, 1984: Characteristics through the melting layer of stratiform clouds. J. Atmos. Sci., 41, 3227–3237, doi:10.1175/1520-0469(1984)041<3227:CTTMLO>2.0.CO;2.
Szyrmer, W., and I. Zawadzki, 1999: Modeling of the melting layer. Part I: Dynamics and microphysics. J. Atmos. Sci., 56, 3573–3592, doi:10.1175/1520-0469(1999)056<3573:MOTMLP>2.0.CO;2.
Trömel, S., and C. Simmer, 2012: An object-based approach for areal rainfall estimation and validation of atmospheric models. Meteor. Atmos. Phys., 115, 139–151, doi:10.1007/s00703-011-0173-5.
Trömel, S., C. Simmer, J. Braun, T. Gerstner, and M. Griebel, 2009: Toward the use of integral radar volume descriptors for quantitative areal precipitation estimation: Results from pseudoradar observations. J. Atmos. Oceanic Technol., 26, 1798–1813, doi:10.1175/2009JTECHA1203.1.
Trömel, S., M. Kumjian, A. Ryzhkov, C. Simmer, and M. Diederich, 2013: Backscatter differential phase: Estimation and variability. J. Appl. Meteor. Climatol., 52, 2529–2548, doi:10.1175/JAMC-D-13-0124.1.
Willis, P. T., and A. J. Heymsfield, 1989: Structure of the melting layer in mesoscale convective system stratiform precipitation. J. Atmos. Sci., 46, 2008–2025, doi:10.1175/1520-0469(1989)046<2008:SOTMLI>2.0.CO;2.
Zawadzki, I., W. Szyrmer, C. Bell, and F. Fabry, 2005: Modeling of the melting layer. Part III: The density effect. J. Atmos. Sci., 62, 3705–3723, doi:10.1175/JAS3563.1.