Airflow and Precipitation Properties within the Stratiform Region of Tropical Storm Gabrielle during Landfall

Dong-Kyun Kim Department of Atmospheric Science, University of Alabama in Huntsville, Huntsville, Alabama

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Kevin R. Knupp Department of Atmospheric Science, University of Alabama in Huntsville, Huntsville, Alabama

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Christopher R. Williams Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado

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Abstract

Kinematic and microphysical characteristics of a stratiform rainband within Tropical Storm Gabrielle during landfall on 14 September 2001 were investigated using data from a collocated 915-MHz wind profiler and scanning Doppler radar. The curved 60-km-wide rainband was relatively intense with mesoscale updrafts and downdrafts exceeding ±1 m s−1. The bright band is classified as strong, as indicated by reflectivity factors in excess of 50 dBZ and rainfall rates below the bright band peaking at 10–20 mm h−1. The melting layer microphysical processes were examined to understand the relation between brightband processes and precipitation intensity and kinematics (mesoscale downdraft in particular) below the melting layer. The profiler and Doppler radar analyses, designed to maximize vertical resolution of flows within the melting layer, disclose a striking convergence–divergence couplet through the melting layer that implies a prominent cooling-induced finescale circulation. Melting-driven cooling initiates midlevel convergence in the upper part of the melting region, while weak convergence to positive divergence is analyzed within the lower melting layer. A melting-layer parameter study indicates the significance of the level of maximum reflectivity that separates convergence above from divergence below and also reveals a mixture of aggregation and breakup of ice particles, with aggregation being dominant. In this vigorous rainband case, the presence of strong mesoscale downdrafts cannot be ignored for accurate retrievals of raindrop size distribution and precipitation parameters from the Sans Air Motion model. When downdrafts are included, retrieved rainfall estimates were much higher than those under the zero vertical air motion assumption and were slightly less than those from a power-law ZR relation. The rainfall estimates show a positive correlation with reflectivity factor and brightband intensity (i.e., aggregation degree) but less dependence on brightband height.

Corresponding author address: Dong-Kyun Kim, Department of Atmospheric Science, University of Alabama in Huntsville, 320 Sparkman Dr., Huntsville, AL 35805. Email: dkkim@nsstc.uah.edu

Abstract

Kinematic and microphysical characteristics of a stratiform rainband within Tropical Storm Gabrielle during landfall on 14 September 2001 were investigated using data from a collocated 915-MHz wind profiler and scanning Doppler radar. The curved 60-km-wide rainband was relatively intense with mesoscale updrafts and downdrafts exceeding ±1 m s−1. The bright band is classified as strong, as indicated by reflectivity factors in excess of 50 dBZ and rainfall rates below the bright band peaking at 10–20 mm h−1. The melting layer microphysical processes were examined to understand the relation between brightband processes and precipitation intensity and kinematics (mesoscale downdraft in particular) below the melting layer. The profiler and Doppler radar analyses, designed to maximize vertical resolution of flows within the melting layer, disclose a striking convergence–divergence couplet through the melting layer that implies a prominent cooling-induced finescale circulation. Melting-driven cooling initiates midlevel convergence in the upper part of the melting region, while weak convergence to positive divergence is analyzed within the lower melting layer. A melting-layer parameter study indicates the significance of the level of maximum reflectivity that separates convergence above from divergence below and also reveals a mixture of aggregation and breakup of ice particles, with aggregation being dominant. In this vigorous rainband case, the presence of strong mesoscale downdrafts cannot be ignored for accurate retrievals of raindrop size distribution and precipitation parameters from the Sans Air Motion model. When downdrafts are included, retrieved rainfall estimates were much higher than those under the zero vertical air motion assumption and were slightly less than those from a power-law ZR relation. The rainfall estimates show a positive correlation with reflectivity factor and brightband intensity (i.e., aggregation degree) but less dependence on brightband height.

Corresponding author address: Dong-Kyun Kim, Department of Atmospheric Science, University of Alabama in Huntsville, 320 Sparkman Dr., Huntsville, AL 35805. Email: dkkim@nsstc.uah.edu

1. Introduction

Stratiform precipitation within tropical cyclones (TCs) is significant because of its relatively large aerial coverage and contribution to the total water budget and associated latent heating (Gamache et al. 1993; Schumacher and Houze 2003). The microphysics and dynamics within stratiform regions of TCs must be understood within the context of vertical air motions that account for the hydrometeor growth and size distribution evolution above, within, and below the melting layer. As an important part of water phase transitions, the melting layer can affect stratiform dynamics and TC intensity.

Willis and Heymsfield (1989) noted that the 0°C isothermal layer formed by melting produces a transition layer that separates dynamics above and below the melting layer. They observed vertical wind fluctuations due to the pressure and buoyancy changes produced by melting-driven cooling. Using a mesoscale model, Szeto et al. (1988) indicated that melting-driven cooling can have large impacts on the circulations near the melting layer by perturbing thermal and dynamic fields. Since this cooling is concentrated in a narrow melting zone, cooling by melting of snow particles may be more significant in producing mesoscale downdrafts than evaporational cooling from raindrops (Srivastava 1987). Enhanced mesoscale downdrafts can transport low-valued θe air downward and decrease the temperature within the boundary layer (Yang et al. 2007). Such downdrafts processes require close examination in view of the potential impact on TC intensity (Barnes et al. 1983; Powell 1990).

Two important microphysical processes around the melting layer are snow aggregation in the upper portion of the melting layer, and breakup within the lower part of the melting layer (Klaassen 1988; Yokoyama et al. 1985). The bright band is an important radar feature since changes in precipitation rate and raindrop size distribution (RSD) are closely related to brightband intensity and its dependence on aggregation and breakup. However, only a limited number of studies have used a vertically pointing wind profiler to examine the melting layer microphysics and dynamics within stratiform precipitation (Drummond et al. 1996; Fabry and Zawadzki 1995; Huggel et al. 1996; Zawadzki et al. 2005). To our knowledge, such studies in stratiform precipitation of TCs have not been conducted.

As a different aspect from a recent study of Tropical Storm (TS) Gabrielle (Knupp et al. 2006), we focus on the dynamical and microphysical properties around the melting layer. The primary goal of this study is to investigate the microphysical and kinematic properties of the melting layer and its impact on mesoscale downdrafts and precipitation properties below the melting layer. This paper is organized as follows. In section 2 we describe the instruments and Doppler radar techniques utilized to derive vertical air motion and horizontal divergence. In section 3, the evolution and environmental features of TS Gabrielle are addressed. In sections 4 and 5, we examine the dynamical and microphysical properties around the melting layer based on a quantitative parameter analysis and various radar analysis techniques described in section 2. These sections also investigate the temporal and vertical variations of the RSDs and discuss their characteristics via the RSD parameters, particularly during aggregation and breakup-dominant periods. A discussion and conclusions follow in sections 6 and 7, respectively.

2. Instrumentation and analysis techniques

Primary instruments used in this study were the 915-MHz wind profiler of the Mobile Integrated Profiling System (MIPS), the Shared Mobile Atmosphere Research and Teaching Radar (SMART-R), and the Tampa Bay Weather Surveillance Radar-1988 Doppler (WSR-88D) (TBW). The 915-MHz wind profiler sampled from five beams: one vertical and four orthogonal beams with an off-vertical angle of 23.6°. The dwell time for each beam was about 30 s and the range gate spacing was 105 m with high-height mode. The vertical beam measurement was sampled every 60 s. The SMART-R is a mobile C-band Doppler radar (Biggerstaff et al. 2005), which sampled volumes consisting of 17 elevation angles from 1.8° to 44.3° over 5-min intervals during the 0545–0648 UTC period. The TBW radar located 70 km north of the SMART-R was used to analyze the horizontal and vertical structure of TS Gabrielle (see Fig. 1).

a. Analysis techniques

Four different methods were used for obtaining vertical air motion: 1) reflectivity–fall speed relationships, 2) extended velocity azimuth display (EVAD), 3) quasi-velocity azimuth display (Q-VAD), and 4) Sans Air Motion (SAM) model (discussed in section 2b). The EVAD, Q-VAD, and the divergence theorem were used to determine horizontal divergence. Vertical air motion (w) is estimated using the reflectivity–fall speed relations for rain (Ulbrich and Chilson 1994) and for snow (Atlas et al. 1973):
i1520-0493-137-6-1954-e1
and
i1520-0493-137-6-1954-e2
where Zrain and Zsnow are radar reflectivity factors (mm6 m−3) for rain and snow, respectively; w is the vertical air motion; and Wdop is the mean Doppler velocity at vertical incidence measured by the wind profiler. Both w and Wdop are negative downward. The term (ρ0/ρ)0.4 is the atmospheric density correction (Beard 1985), where ρ is air density parameterized by ρ(z) = ρ0 exp(−z/9.58) and z is altitude in kilometers. The two relationships were applied to pure snow and rain regions separated by the snow and rain levels defined at the maximum curvature in the Z profile. For the intermediate layer between the snow and rain levels, w was acquired by performing a linear interpolation between the values within the rain and overlying snow levels.
The EVAD provides profiles of w, terminal fall velocity, and horizontal divergence by processing data at horizontal rings in all elevation cones per layer (Matejka and Srivastava 1991). The EVAD performs a linear regression using the equation
i1520-0493-137-6-1954-e3
where div is horizontal divergence, Wdop is Doppler velocity, α is the elevation angle, r is the radius of the VAD circle, and ao is the zeroth harmonic coefficient as a function of the radius and elevation angle. Two unknowns, div (intercept) and Wdop (slope), per layer are determined by the linear regression between the x and y terms (i.e., y = aX + b) in (3). After a div profile is obtained from the regression, a w profile is produced by performing a variational integration of the mass continuity equation. One important assumption is that the wind field over the analysis domain is horizontally linear. Also divergence and terminal fall velocity for a given layer are considered as homogeneous over the maximum horizontal range of the rings.
The Q-VAD computes the wind gradient using two opposite beams of the 915-MHz profiler. The vertical air motion, assumed to be identical over all five beams at the same time, is derived from downward integration of the anelastic continuity equation starting with EVAD vertical air motion as the top boundary condition (wtop):
i1520-0493-137-6-1954-e4
where div is the sum of Δux and Δυy, the east–west and north–south gradients of the winds divided by a horizontal distance between the off-vertical range gates of the two beams. Divergence estimates become increasingly noisy at low levels because the horizontal distance between the opposite beams decreases with decreasing height. Thus, div and w from the Q-VAD technique are not displayed below 2 km AGL.
The divergence theorem was utilized to estimate div using the highest elevation angle (44.2°) of the SMART-R. This technique has been used to diagnose diabatic div profiles in tropical mesoscale convective systems (MCSs) using aircraft radar measurements (Mapes and Houze 1993, 1995). This highest elevation angle was selected to most closely match the sampling volume of the 915-MHz profiler. The horizontal divergence over an area A is equal to the closed line integral of the normal component of Doppler radial velocity (Vr) shown by
i1520-0493-137-6-1954-e5
where Vh is a horizontal component of Vr and dl is a length element along the circular boundary. The horizontal component (Vh) of Doppler radial velocity is calculated by
i1520-0493-137-6-1954-e6
where Vf is the terminal fall speed expressed with positive values for upward motion to match the vertical air motion sign convention.

b. The SAM model—The nonzero vertical air motion

The RSDs and their integral parameters such as rain rate and liquid water content can be retrieved from the Doppler velocity power spectrum of wind profiler radars. In doing this, w, turbulence, noise level, and deviation of Rayleigh scattering need to be taken into account. In this study, the SAM model (Williams 2002) is used to retrieve the RSDs below the melting layer in the stratiform rainband. The retrieved RSDs are approximated by the gamma size distribution of the following form:
i1520-0493-137-6-1954-e7
where N(D) is the number concentration of particles which diameters range between D and D + dD. Here N0 (m−3 mm−1), μ, and Λ (mm−1) are the intercept, shape, and slope parameters, respectively, of the size distribution. The SAM model retrieves the hydrometeor spectrum by comparing the observed Doppler spectrum with many modeled spectra with the final retrieved spectrum minimizing a least squares difference cost function. The modeled Doppler velocity spectrum is formed by convolving the clear-air spectrum with the modeled hydrometeor spectrum. The shape of modeled hydrometeor spectrum is varied by changing the mean mass-weighted diameter (Dm) and μ, and the clear-air spectrum by changing the clear-air mean vertical air velocity (w) and spectral broadening (σair). The rainfall rate is calculated from the three parameters {N0, Dm [or Λ using Λ = (4 + μ)/Dm], and μ} of the gamma RSD by using
i1520-0493-137-6-1954-e8

To account for different vertical air motions, the SAM model uses a two-step process. The first step estimates the best hydrometeor spectrum (N0, Dm, and μ) and spectral broadening (σair) for a fixed vertical air velocity (w) by minimizing the squared difference between the modeled and observed spectra. The first step is then repeated for many different vertical air motions. Values of w are acquired by shifting the observed spectrum along the velocity axis in one spectral bin increment (Δυ = 0.169 m s−1) removing the effects of updrafts or downdrafts on the observed spectrum. As shifting the observed spectrum by a spectral bin increment, the best-fit hydrometeor spectrum with the final estimate of w, as a multiplication of the increment, is determined with the minimum cost function between the observed spectrum and the modeled spectrum. Shifting the observed spectrum to account for updrafts decreases rainfall rates, whereas shifting the observed spectrum to account for downdrafts increases rainfall rates (Rajopadhyaya et al. 1998).

3. Tropical Storm Gabrielle

a. Storm evolution and environment

Gabrielle was first classified as a tropical depression at 1800 UTC 11 September 2001 and attained a tropical storm status at 1200 UTC 13 September over the western Gulf of Mexico (Lawrence and Blake 2002; Molinari et al. 2006). Gabrielle then moved northeastward after 0000 UTC 14 September. A continuous intensification was observed for the next 12 h, particularly between 0600 and 1200 UTC, the time of landfall (Molinari et al. 2006). The MIPS, SMART-R, and TBW radar sampled an extensive stratiform rainband between 0430 and 0700 UTC. The storm circulation center was located southwest (upshear) of center of the stratiform rainband. During this period Gabrielle became more organized, as the deep convection (bottom part of Fig. 1) intensified near the circulation center. The arc-shaped stratiform rainband (Fig. 1) appeared at around 0400 UTC and persisted until 1100 UTC. This rainband exhibited an arc length of ∼250 km and a mean width of ∼60 km.

A pronounced brightband signature was observed by the 915-MHz profiler and the TBW radar between 0500 and 0650 UTC. In Fig. 2, vertical sections of reflectivity factor and radial velocity at 0601 and 0656 UTC from the TBW radar, located 70 km north of the MIPS, show an extensive bright band near 4 km AGL. The increase in magnitudes of radial velocity, and vertical gradients in radial velocity near and above 6 km AGL reveal large vertical wind shear within the ice region at 0656 UTC, consistent with the findings of Molinari et al. (2006). Fig. 2e depicts a cyclonic flow of about 15 m s−1 magnitude along the rainband in the dual Doppler analysis at 3.5 km AGL.

Two soundings were taken at 0000 and 0600 UTC from Tampa Bay (KTBW) within the stratiform precipitation (Fig. 3). At 0000 UTC, the 650–950-hPa layer is nearly saturated. The 0600 UTC sounding released near the leading edge of the rainband shows a slightly subsaturated layer (RH = 85%) centered near 850 mb. This relatively unstable layer is between 770 and 850 hPa where mesoscale downdrafts are likely maintained by evaporational cooling. The extended saturated layer down to 770 hPa (2.2 km) at 0600 UTC could be ascribed to heat and moisture transport, supported by increased winds from the southeast direction (see the wind barbs on the right).

At 0600 UTC, it should be noted that an increase in temperature and wind speed occurred in the 500–800-hPa layer for the 6-h period. Cooling within and below the melting layer is probably counteracted by heat and moisture transport from the south and southeast at these levels. Comparison with the 0000 UTC sounding reveals that cooling at low levels was associated with the offshore easterly flow. Knupp et al. (2006) noted that an extensive region of cool air at the surface preceded landfall and that the surface cold air exerted large effects on the ABL, and apparently on storm intensity changes. This cooling and its association with rainfall evaporation, mesoscale downdrafts, and precipitation properties is a primary motivation for this study.

b. Overview of 915-MHz profiler measurements

In Fig. 4a, the 915-MHz profiler-derived reflectivity factor (Z) patterns show a prominent and continuous brightband signature whose height oscillated by ∼200 m from a mean height of 4.3 km. Rainfall rates up to 23 mm h−1 and low-level Z maxima approaching 40 dBZ were measured within this rainband. Within the melting layer near 4.2 km AGL, Z values exceeded 50 dBZ. These observations indicate that this was a relatively intense stratiform rainband. In Fig. 4b, the larger Wdop regions reaching about 10 m s−1 located particularly just below the stronger bright band, were well correlated with the regions of higher Z streaks around 0550, 0610, 0625, and 0635 UTC. A positive correlation between Wdop and Z and an increase in their magnitudes over several kilometers above the melting layer, particularly around 0550, 0625, and 0635 UTC, indicates a substantial increase in snow aggregation close to 0°C level.

In Fig. 4c, spectral widths show a notable contrast between the rain and ice regions except for thin layers of large spectral width near the bright band. The large spectral widths exceed about 4.5 m s−1 and are centered near 4.7 km, which appears to be a consequence of wide distributions in fall speeds of snow aggregates. The narrow region of small spectral widths less than 2 m s−1 near the level of maximum Z (4.0–4.5 km) between 0535 and 0645 UTC suggests much less breakup and more uniform distributions of fall speeds relative to that at the top of the melting layer. The w patterns and precipitation characteristics of this rainband are examined in greater detail in the following sections.

4. Mesoscale flows

The SMART-R sampled the stratiform rainband with 13 full-volume scans from 0545 to 0650 UTC. During this period, horizontal winds over the SMART-R location (x = −4 km and y = 0 km in Fig. 2e) were sufficiently uniform from the east-southeast so that the EVAD could be applied. The radius of the EVAD circle was set to 25 km.

In Fig. 5, w from the EVAD and 915-MHz profiler show similar structures. The profiler w, estimated from w915 = WdopVf , where Vf was derived from Eqs. (1) and (2), shows stronger up- and downdrafts exceeding ±1 m s−1. Both the EVAD and w915 exhibit a lowering of the w = 0 level during the period. Houze (1989) observed that the height of zero vertical air motion can vary from 0 to 2 km above the 0°C level, depending on location of the mean w profiles within stratiform regions. The lowering of the w = 0 may be related to the increase in sampling the edges of the arc-shaped stratiform region as time progresses. Hence, irregularities in w increase in upper levels (i.e., above 8 km AGL in Fig. 5b). The greatest w915 downdraft magnitudes (−1.5 m s−1) were analyzed below the melting layer from 0555 to 0610 UTC, earlier than those in the EVAD analysis (Fig. 5a). The slight mismatch in downdraft location between the two w fields may be attributed to the large difference in spatial resolution between the SMART-R (radius of 25 km) and the 915-MHz profiler.

Figure 6 shows the div and w profiles from the EVAD, Q-VAD, and divergence theorem averaged over the 0545–0631 UTC period. All the div profiles show good agreement above the melting layer. Particularly, the div profiles from the Q-VAD and the divergence theorem are in better agreement despite a difference in the sampling domains between the profiler and the SMART-R at the maximum 44.2° elevation angle. The horizontal diameter for the divergence theorem at 10 km AGL at this angle is 19.5 km, more than 2 times the 8.7-km distance between opposing beams in the Q-VAD at the same level. Since the divergence theorem utilizes the highest elevation angle (44.2°), the divergence error becomes larger at low altitudes. For this reason, the convergence magnitudes increase rapidly below 2 km AGL.

The composite div profile from the divergence theorem was a useful supplement to the composite Q-VAD divergence to examine small-scale variations in airflow around the melting layer. In Fig. 6a, the convergence–divergence couplet in the Q-VAD div profile is notable between the 0°C level (4.8 km AGL) and 3.5 km AGL. Mapes and Houze (1995) attributed the couplet to a warm–cold–warm temperature anomaly due to melting, suggesting that the convergence–divergence couplet is a result of a response to cold temperature perturbations within and warm temperature perturbation below the melting layer. The latter might be associated with adiabatic warming induced by subsidence. In addition, as melting-driven cooling strengthens midlevel convergence, weak convergence, near-zero, or even positive divergence beneath it may occur to fulfill a mass balance in the vertical.

The div profile from the theorem shows a similar pattern but its variation is narrower than that of the Q-VAD. The difference in the div profiles between the Q-VAD and the divergence theorem near levels exhibiting a local maximum in divergence (e.g., near 3.7 and 2.5 km AGL) may be influenced by the terminal fall speed bias based on the ZVf relations and the decrease in range. The discrepancy is also a consequence of the difference in the sampling volumes of the two techniques. On the other hand, the EVAD div profile from the largest sampling volume shows better agreement with two other profiles above the melting layer, than below the melting layer. The vertical air motions from the three methods are in better agreement above the melting layer. The w915 profile reveals larger magnitudes above 6.5 km AGL, which is most likely due to the small sample volume.

5. Precipitation properties

a. Melting layer and brightband signatures

In Fig. 7a, the contoured frequency by altitude diagram (CFAD; Yuter and Houze 1995) of almost constant Z in the rain layer is shown with a strong bright band above during the 0530–0648 UTC period. Particularly, the Z CFAD shows a slight increase below 2 km AGL. The almost constant Z profiles are often measured in tropical stratiform regions (Cifelli et al. 2000; Schumacher and Houze 2003; Tokay et al. 1999) as a result of the compensation between breakup of large drops and continuous collection of small drops, which maintain a constant Z (Huggel et al. 1996). Figures 7a,b show a narrow distribution in both Z and Wdop from the top of the melting layer (4.8 km) to about 5.5 km AGL, suggesting that aggregation, accretion, and deposition processes at these levels compose equilibrium in snow size spectra. The CFAD of Wdop shows relatively high frequencies centered near 2 m s−1 over a 1-km depth above the melting layer, implying that the mean fall speeds are independent of particle size and shape. However, as snow aggregates start melting, their size and fall velocity distributions become wider because the probability of collision rapidly increases at the same time. It is noted that an increase in the vertical gradients of Wdop is smaller in the upper part of melting layer than in the lower part because of a slower increase in melted fraction of snow in the upper part.

Spectral widths for snowflakes are narrower than those for raindrops since the range of fall speeds of snowflakes is smaller. But this range of fall speeds rapidly broadens as snow particles aggregate near the 0°C level where collision efficiency is relatively high. Large spectral widths near the top of the melting layer (Fig. 7c) are attributed to broader distributions of fall speeds of melting snow aggregates and perhaps to small-scale turbulence triggered by melting-driven cooling. However, an uncertainty still exists in the spectral width values obtained from the 915-MHz profiler observations as the spectra above the melting layer are more asymmetric with smaller peak values than those below the melting layer. One or both edges of the spectrum may be too steep, the spectral peak may be off-center, or the number of spectral peaks may be greater than 1 (Janssen and Van der Spek 1985). The increase in vertical wind shear (not shown) may have played a role in very asymmetric shapes (including some noise) of spectra near the top of the melting layer.

The CFADs for spectral widths and wind speeds (Figs. 7c,d) show a slow increase from 5 km AGL to near the 0°C level. The heights of high spectral widths and large horizontal winds are almost identical near the top of the melting layer, suggesting that the increase in spectral widths is partially due to increased horizontal wind speed and wind shear.

The smallest spectral width values near the level of maximum Z (i.e., 4.4 km in Fig. 7a) suggest a minimum in breakup and a maximum in collection efficiency. Right below the levels of the Z maxima, the spectral widths rapidly increase, indicating that collisional breakup becomes more significant since the range of particle fall speeds in the lower half of the melting layer is, on average, larger due to partly or completely melted particles than in the upper half (Barthazy et al. 1998). Higher collision efficiency due to a larger range of fall speeds may produce more efficient breakup in the lower half of the melting layer. The second peak in the CFAD for spectral widths near 3.8 km may be attributed to increased instability associated with cooling (i.e., increased lapse rate of air temperature) as well as mixed distributions of raindrops and partially melted particles near the bottom of the layer.

b. Melting layer parameters

Melting layer microphysics is quantitatively analyzed by using various melting layer parameters defined at the top and bottom of the melting layer. The top of the melting layer is defined as a height of the maximum curvature in the Z profile (Drummond et al. 1996). The snow reflectivity expressed in equivalent reflectivity factor (Zesnow) is an averaged Z value (in order to reduce the noise) over two successive range gates above the top of the melting layer (Fig. 8). The bottom of the melting layer is also determined at the height of the maximum curvature in the Z profile. The rain reflectivity also expressed in equivalent reflectivity factor (Zerain) is taken as an averaged value over three successive range gates below the bottom of the melting layer. The basic eight parameters, Htop, Hbottom, Hpeak, Zesnow, Zepeak, Zerain, Wsnow, and Wrain, and their extended parameters, γ, ΔZ = ZepeakZerain, and ΔH = HtopHbottom, are estimated during the 0530–0648 UTC period when the Z profiles had distinct curvatures. The parameter γ is defined as the ratio of the products of Z and Wdop at the top (Htop) and bottom (Hbottom) of the melting layer (Drummond et al. 1996) by
i1520-0493-137-6-1954-e9
where Zesnow and Zerain are the equivalent reflectivity factor (mm6 m−3) and Wsnow and Wrain are the mean Doppler velocity of snow and rain at the top and bottom of the melting layer, respectively, which are shown in Fig. 9a. We assume a 1:1 relationship of the snowflake mass entering the melting layer and the raindrop mass leaving it, implying an absence of aggregation and breakup in the melting layer. Therefore, the deviation of the ratio of the two masses from unity indicates aggregation or breakup in the melting layer.

Aggregation- and breakup-dominant periods are determined by using smaller γ values and larger γ values, respectively. Drummond et al. (1996) suggested a threshold of γ = 0.23 to separate aggregation and breakup-dominate periods. Additional reflectivity constraints of Zepeak > 49 dBZ and Zerain > 38.3 dBZ are used for reliably determining aggregation-dominant periods since Zepeak and Zerain tend to be proportional to the degree of aggregation. In this study, the period (0600–0608 UTC, a time when Hpeak descends as shown in Fig. 9a) is identified in order to examine the relationship of the descending bright band with the microphysics below the melting layer. In Fig. 9b, breakup is suggested over a limited time period between 0612 and 0618 UTC when γ values are largest, and aggregation is suggested for the other times. It is shown that the dominance of breakup or aggregation is solely determined by the Z ratio at the two levels. For breakup-dominant periods, the Z ratio is relatively higher due to smaller Zerain than for aggregation-dominant periods when smaller γ values are due to higher Zerain. It is found that the Doppler velocity ratio is inversely proportional to the Z ratio during aggregation-dominant periods, indicating that snow aggregates are probably denser, more rimed, and even larger in size.

c. Quantitative analysis

In Fig. 10a, the scatterplot of Zepeak with brightband height (Hpeak) and thickness (ΔH) shows that ΔH is proportional to Zepeak (Fabry and Zawadzki 1995; Klaassen 1988), but Hpeak is inversely proportional to Zepeak. During breakup-dominant periods, ΔH is especially small. The inverse relationship is probably due to melting-driven cooling because the downward propagation of cooled air would lower the brightband height as indicated in Durden et al. (1997). Fig. 10a shows that the average ΔH for aggregation-dominant periods is about 30% larger than that for breakup due to melting of large snow particles at a long fall distance.

Figure 10b shows a slightly positive correlation between ΔZ and Zepeak, and a negative correlation between ΔZ and Zerain. Both Zepeak and Zerain are larger and less scattered for aggregation-dominant periods than those for breakup. Since all ΔZ values (9.5–15 dB) in Fig. 10b are greater than 7 dB, the threshold that Huggel et al. (1996) used following Fabry and Zawadzki (1995) to discriminate weak and well-defined bright bands, the bright band within this TC is classified as strong and well-defined throughout the 80-min analysis period. For breakup-dominant periods, the average ΔZ value is 2 dB larger than that for aggregation periods. This is due to a large reduction of Zerain at the bottom of the melting layer, which contributes more to an increase in ΔZ, indicating active breakup in the lower half of the melting layer during breakup-dominant periods. In this study, ΔZ for breakup-dominant periods is larger (ranging from 11 to 15 dB) than aggregation-dominant periods (ranging from 10 to 13 dB). However, the large ΔZ does not necessarily indicate the dominance of breakup because both periods have ΔZ, which includes the range of 11–13 dB. Thus, the parameter ΔZ alone cannot be used for diagnosing the aggregation or breakup dominance, especially for the strong brightband case. On the whole, the average ΔZ and ΔH during the descending brightband period are between those during aggregation- and breakup-dominant periods, implying that the microphysical properties would be between the two distinguishable periods.

In Fig. 11a, the rain rate (R) retrieved from the SAM shows positive correlations with both the Zepeak and ΔH, particularly during aggregation-dominant periods. That is, R is proportional to brightband intensity. Since brightband intensity is highly dependent on the characteristics of the largest particles (Stewart et al. 1984), this is attributed to stronger precipitation produced by melting of larger snow aggregates over a longer fall distance (Fabry and Zawadzki 1995). In Fig. 11b, overall R shows little dependence on Hpeak, indicating that for a given Hpeak, there can be a wide range of R. Thus, a higher Hpeak does not always imply a higher R (or larger ΔH). However, it is shown that the larger R during aggregation-dominant periods corresponded to lower Hpeak, relative to other RHpeak pairs. A primary cause for this is melting-driven cooling, which plays a role in lowering Hpeak (Durden et al. 1997) and producing negative buoyancy for downdrafts at rather small temporal and spatial scales. It seems that the large-scale variation in Hpeak is probably more associated with other physical factors like temperature change, vertical air motion, and so on, besides melting-driven cooling.

d. Raindrop size distributions

Figure 12 shows the time–height sections of Z, R, Dm, and N0. As proportional to Z, it is evident that R is higher during aggregation-dominant periods when the bright band was strong. Overall, Dm tends to be inversely proportional to R above 2 km AGL, and it is proportional to R below 2 km, particularly during aggregation-dominant periods. The R is positively correlated with N0, indicating that the increase in R is related to narrow spectra having a large number of small raindrops, thereby increasing the RSD slope and decreasing Dm. The notable increase in N0 particularly below 2 km AGL is attributed to raindrop breakup. (Evaporation would be small, given the nearly saturated sounding.) During aggregation-dominant periods, Z profiles are nearly uniform or decrease with height, indicating that collision–coalescence produces moderate to large raindrops and balances or even dominates over breakup (around 0540 and 0640 UTC). It appears that breakup is more dominant than collision–coalescence when R increases as Dm decreases, but collision–coalescence is more dominant than breakup when R increases as Dm also increases, intermittently shown below 2 km AGL. During the descending brightband period, both Z and R are smaller than those during aggregation-dominant periods. During this period, the slight increase in Z with decreasing height, along with a slightly larger Dm and smaller N0 indicates a relative increase in the number of moderate to large drops. Relatively stronger mesoscale downdrafts were measured below 2 km AGL during this period. Evaporation may decrease the number of smaller drops the most and collection of large and midsize drops may increase. Both the sporadic increase in R and Dm below 2 km AGL probably indicates the possibility of raindrop growth within the mesoscale downdrafts. On the other hand, during breakup-dominant periods, the smallest Z and Dm are shown among the sampling periods.

In Fig. 13, the correlation between R from the SAM and ZR relation (Z = 367R1.3; Tokay and Short 1996) shows better agreement when vertical air motions are included. The increase in R for a given Z in Fig. 13a is due to the fact that corrected downdrafts shift the spectrum to smaller fall speed and smaller drop diameter range. In Fig. 13a, the R derived from the ZR relation exceeds the SAM-retrieved R values. We interpret this as raindrops in this case are, on average, larger than those for a given Z. The inference of larger than average raindrops is consistent with the stronger bright band. In Fig. 13b, the overall underestimation in SAM-retrieved R is due to the absence of downward air motions, which were estimated below the melting layer.

Figure 14 shows the composite RSDs retrieved from the SAM model at 3472 m AGL during three periods. We chose this height closest to the bottom of the melting layer in order to minimize uncertainties or errors by horizontal advection of particles. Each RSD is an average of the five successive RSDs. The composite RSD during aggregation-dominant periods shows larger number concentrations at almost all drop sizes, corresponding to high reflectivity streaks shown in Fig. 12a. During breakup-dominant periods, the RSD shows a larger number of small drops and smaller number of large drops. This may be evidence of small raindrops resulting from melting of smaller snow particles produced by more active breakup in the melting layer. The RSD during the descending bright band shows smaller number concentrations at the small to midsize drop range when compared with those during the two other periods. The Dm is a little larger during this period than during aggregation-dominant periods. The contributions of the number concentration of large drops on Z and Dm are relatively larger than at least those during breakup-dominant periods when Dm was smallest.

Since these composite RSDs were obtained near the bottom of the melting layer, the properties of snow size distributions near the top may be deduced from the RSDs. For aggregation-dominant periods, as expected, large snow aggregates were present just above the melting layer as aggregation dominates breakup within the melting layer, increasing the brightband intensity. Small and dense rimed particles may be present as well in terms of large number concentration of small drops in Fig. 14 and large Doppler velocity ratio in Fig. 9b. During breakup-dominant periods, snow aggregates are expected to be relatively smaller and less dense. The smallest Zerain suggests substantial breakup in the lower part of the melting layer during these periods. During the descending brightband period, presumably less efficient breakup within the melting layer and larger Dm indicates that on average, large and dense hydrometeors are probably present in terms of small γ values in Fig. 9b. However, their sizes seem to be smaller than those during aggregation-dominant periods since their Zerain values are about 3 dB less.

6. Discussion

a. Kinematics

Similar to this study, mesoscale up- and downdrafts above and below the melting layer in stratiform regions of hurricanes have been observed by Marks and Houze (1987) and Black et al. (1996). The mean range of w915 (from −1 to 1.5 m s−1) in this study is larger than the mean w range from −0.3 to 1.3 m s−1 from Marks and Houze (1987) and the mean w range from −0.5 to 1.0 m s−1 in Fig. 8 of Black et al. (1996) in stratiform regions. Particularly, the mean downdraft velocity of −1 m s−1 at low levels in this study is relatively large. It is likely that the strong downdrafts below the melting layer are overestimated by an underestimation of fall speeds of hydrometeors.

A convergence–divergence couplet within the melting layer has been documented in a limited number of papers (Cifelli et al. 1996; Mapes and Houze 1993, 1995; Steiner et al. 2003; Szeto et al. 1988; Szeto and Cho 1994). However, finding the convergence–divergence couplet within such an intense stratiform rainband of TC is unprecedented to our knowledge. Szeto and Stewart (1997) indicated that melting-driven cooling can produce mesoscale circulations that enhance horizontal convergence around the melting layer. In this study, the convergence–divergence couplets both in the div profiles from both the Q-VAD and divergence theorem are probably indicative of cooling-induced circulations. (Although the couplet is not as obvious in the divergence theorem profile, the trend in strong convergence to weak convergence near the 4-km height is similar to that indicated in the Q-VAD profile.) The convergence above and divergence below the levels of Z maxima within the melting layer implies indirect finescale circulations of airflow as a coupling of the upper and lower half of the melting layer.

b. Melting layer studies

Huggel et al. (1996) used a ΔZ threshold of 7 dB to determine weak or well-defined bright bands and showed a prominent negative correlation between ΔZ and N0 particularly for the R range of 1–10 mm h−1. However, in this study, all ΔZ values (9.5–15 dB) were greater than 7 dB and an overlapping range of ΔZ was found for both the aggregation- and breakup-dominant periods. The average ΔZ for breakup-dominant periods was 2 dB greater than that for aggregation-dominant periods. But the average Zepeak for aggregation was rather higher than that for breakup (ΔZ = ZepeakZerain), suggesting that there are larger numbers of large particles (i.e., larger Dm, see Fig. 14) during aggregation-dominant periods. Therefore, one should exercise caution in interpreting the inverse relationship between ΔZ and N0 (or Λ), proposed by Huggel et al. (1996), if the bright band is strong with moderate precipitation. This is because a large ΔZ does not always indicate a large number of large particles (i.e., small N0) as we found that the average ΔZ was larger during breakup-dominant periods when Dm is comparatively smaller.

c. Precipitation properties regarding brightband intensity

During aggregation-dominant periods, the increase in number concentrations at all drop sizes was shown in Fig. 14. Such wide distributions have dependence on snow properties (size and habit) near the top of the melting layer. Yuter et al. (2006) indicated that the standard deviation of fall speeds of wet (i.e., partially melted) snow aggregates is larger than that of dry snow aggregates. The collision efficiency for aggregation-dominant periods would be higher because of the larger standard deviations of fall speeds of wet snow aggregates. A higher R during aggregation-dominant periods (Fig. 12b) as proportional to Z implies higher collection efficiency since R increases as the number concentration of large drops increases (Hu 1995; Low and List 1982). Considering that the largest factor to the decrease in Z below the melting layer is raindrop breakup (Stewart et al. 1984), a slow increase in Z and Dm with decreasing height suggests that moderate to large raindrops are still produced while breakup proceeds, even within the mesoscale downdrafts that were present below the melting layer throughout the analysis period. The almost constant or slightly increasing Z CFAD (Fig. 7a) indicates the raindrop growth by collection (particularly below 2 km AGL), suggesting relatively less breakup and evaporation in this particular stratiform rainband. During the descending brightband period (i.e., strong downdraft period), the collection efficiency is probably not as large as that during aggregation-dominant period because of smaller Zerain and smaller numbers of small and large drops. However, relative to aggregation-dominant periods, evaporation associated with the strong downdrafts may come to play a more important role in decreasing R near the surface during the descending brightband period.

It is found that the effects of mesoscale downdrafts cannot be neglected for interpreting all dynamics and microphysics in and below the melting layer, particularly for intense stratiform rainbands of TCs as in this case study. Therefore, the accurate estimation of w is more significantly required for this case. Even though the w variation would be larger with shorter periods (about 80 min) and the ZVf relations for snow and rain might not work well just below and above the melting layer, w from the profiler and the SAM showed good agreement. The RSD retrievals from the nonzero w assumption gave rise to less errors or biases than from the zero w assumption.

Errors in determining the top and bottom heights and the parameter values (e.g., γ) based on these levels can lead to false interpretation. Since the determination of snow and rain levels using the reflectivity curvatures can never be perfect, a secondary constraint such as the Doppler velocity would be auxiliary to make the levels be more accurate. Also, one should keep in mind that an increase of breakup in this study is a relative increase over aggregation within the melting layer, even during breakup-dominant periods.

7. Conclusions

This study examined the kinematic and microphysical characteristics of an unusually intense stratiform rainband within Tropical Storm Gabrielle. Mesoscale updrafts and downdrafts with an average range from −1 to +1.5 m s−1 were relatively strong. During a short analysis period of about 80 min, the rainband exhibited more variability in w and div profiles, compared with previous studies. The important findings from this study are as follows:

  1. The prominent convergence–divergence couplet both from the Q-VAD and divergence theorem implies the existence of prominent cooling-induced finescale circulations near the melting layer, primarily due to melting of large snow aggregates in association with strong brightband intensity. Near-zero or positive divergence beneath the narrow convergence peak is probably representative of a physical behavior to satisfy a mass balance in the vertical.

  2. It is the levels of reflectivity maxima where convergence above and divergence below is approximately separated and a minimum of spectral width is located, suggesting the smallest breakup and the largest snow aggregates within the melting layer.

  3. Rainfall estimates retrieved from the SAM under the nonzero w assumption increase with Zepeak and brightband intensity, particularly during aggregation-dominant periods. A higher R as proportional to Z implies higher collection efficiency since R increases as the number concentration of large drops increases. Strong precipitation under strong brightband intensity is produced by melting of large snow aggregates over a long fall distance.

  4. Rainfall estimates at the bottom of the melting layer show a positive relation with ΔH, but less dependence on Hpeak. However, the higher R during aggregation-dominant periods corresponded to lower Hpeak. This is probably associated with melting-driven cooling that plays a principal role in lowering Hpeak during this period, rather than in small temporal and spatial scale. The large-scale variation in Hpeak is probably more associated with other physical factors like temperature change, vertical air motion, and so on, except melting-driven cooling.

  5. The almost uniform Z CFAD below the melting layer indicates the balance between raindrop growth by collection and breakup/evaporation. This feature, in turn, implies a possibility of raindrop growth even within strong mesoscale downdrafts, which were persistently measured below 2 km AGL. In support of this, a slight increase in Z and Dm with decreasing height suggests that large and midsize raindrops are produced while breakup advances. However, breakup and evaporation are probably more effective than collection close to the ground particularly during strong downdraft periods.

Aggregation and riming contributions to brightband intensity are related to vertical profiles of temperature, relative humidity, cloud water content, and w around the melting layer. Hence, collocated thermodynamic soundings along with high-resolution Z measurements are necessary for in-depth brightband studies. Since the RSDs near the bottom of the melting layer show a close connection with brightband intensity (i.e., aggregation degree), this study proposes an implication of retrieving snow size distributions near the top of the melting layer using the relationship between fall speeds, masses, and size spectra of snow and rain suggested by Leary and Houze (1979). The possibility of a wind profiler application into melting layer studies (i.e., the small-scale variations in precipitation, airflow, and heating/cooling, especially around the melting layer) is significantly reemphasized in this study. To build up quantitatively generalized relations of the melting layer parameters with precipitation properties, other case studies with more radar data will be conducted in the near future.

Acknowledgments

This research was sponsored by the National Science Foundation under Grant ATM-0533596 and by the National Oceanic and Atmospheric Administration under Grant NA06OAR4600156.

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Fig. 1.
Fig. 1.

Horizontal plane of reflectivity at 3.5 km AGL from the TBW radar at 0656:14 UTC 14 Sep 2001. The stratiform rainband considered in this study extends from the left-center to the right-center part of the figure. The red circle shows the location of the TBW radar and the thick black line represents the land boundary.

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 2.
Fig. 2.

(a),(c) Vertical sections along x= 0 of radar reflectivity (dBZ) and (b),(d) radial Doppler velocity (m s−1) at 0601:05 and 0656:14 UTC from the WSR-88D at Tampa Bay (KTBW). The arrow at y= 0 km represents the location of the SMART-R and MIPS. (bottom) A horizontal plane of reflectivity with horizontal wind vectors (storm relative) over it on 0656:14 UTC at 3.5 km AGL. The wind vectors were acquired by dual-Doppler radar process using the CEDRIC software. Upper and lower circles show the locations of the TBW and SMART-R, respectively.

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 3.
Fig. 3.

Upper-air soundings at (left) 0000 and (right) 0600 UTC 14 Sep 2001 at KTBW.

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 4.
Fig. 4.

Time–height sections of (a) radar reflectivity (dBZ), (b) Doppler velocity (m s−1), and (c) spectral width (m s−1) derived from the 915-MHz profiler.

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 5.
Fig. 5.

Time–height sections of vertical air motions (a) from the EVAD and (b) the 915-MHz profiler. The horizontal line in (a) shows the top of the section in (b) at the same scale for the comparison and the dashed line shows the approximate level of the 0.0 m s−1 contour.

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 6.
Fig. 6.

Composite profiles of (a) horizontal divergence and (b) vertical air motions derived from various methods between 0545 and 0631 UTC. In (a), the thin line the EVAD divergence profile, the thick line the Q-VAD divergence profile, and the middle thick line represent the divergence profile from the theorem. A three-point running average with regard to heights was performed for Q-VAD and the divergence theorem. In (b), each vertical air motion profile derived from EVAD (thin), the divergence theorem (middle thick), Q-VAD (thick), and the reflectivity–fall speed relations (dashed) is shown. The vertical air motions derived from the reflectivity–fall speed relations were also three-point smoothed. The horizontal line at 4.8 km shows the approximate top of the melting layer.

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 7.
Fig. 7.

CFADs for (a) reflectivity (bin: 1.25 dB), (b) Doppler velocity (bin: 0.25 m s−1), (c) spectral width (bin: 0.15 m s−1), and (d) wind speed (bin: 1.0 m s−1) during 0530–0648 UTC. The top horizontal line at 4.8 km represents the approximate top of the melting layer and 0°C level. The bottom horizontal line at 3.47 km shows a height where the SAM performed for the RSD retrievals.

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 8.
Fig. 8.

Schematic diagram for the parameters (see the text for more details).

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 9.
Fig. 9.

(a) Time–height section of the reflectivity near the brightband region. The black-colored pixels represent reflectivity greater than 50 dBZ. The thick solid line indicates Hpeak and upper and lower thin lines indicate Htop and Hbottom, respectively. The symbols of rectangle and circle represent the breakup and aggregation-dominant periods, respectively. (b) Time variations of the γ parameter (solid line), reflectivity ratio (dashed line), and Doppler velocity ratio (dotted line). The circle and rectangle symbols represent aggregation- and breakup-dominant periods, respectively. The triangles indicate the period of a prominent decrease in brightband height. The horizontal line indicates the threshold of 0.23 (suggested by Drummond et al. 1996).

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 10.
Fig. 10.

(a) Scatterplot between Zepeakand the brightband height (top group; left axis) and brightband thickness (bottom group; right axis). (b) Scatterplot between ΔZ and Zepeak (top group) and Zerain (bottom group). The symbols are as defined in Fig. 9b with solid dots representing all other observations.

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 11.
Fig. 11.

(a) Scatterplot between rain rate (mm h−1) and Zepeak(top group; left axis) and ΔH (bottom group; right axis). (b) Scatterplot between rain rate and Hpeak. Rain rate is retrieved at 3472 m AGL. The symbols are as defined in Figs. 9b and 10.

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 12.
Fig. 12.

Time–height sections of (a) reflectivity (dBZ), (b) rain rate (mm h−1), (c) Dm (mm), and (d) N0 (m−3 mm−1). For each section, smoothing using the eight nearest values was performed in time and height. The symbols are as defined in Fig. 9b.

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 13.
Fig. 13.

(a) Comparison between R (mm h−1) from the SAM with vertical air motion accounted, and ZR relation and (b) the comparison R (mm h−1) from the SAM with vertical air motion not accounted, and ZR relation.

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

Fig. 14.
Fig. 14.

Comparison of the averaged RSDs during the three major periods at 3472 m AGL. The black solid line represents the RSD during the first aggregation-dominant periods (0548 UTC), the red line the RSD during the breakup-dominant periods, and the blue line the RSD during the descending brightband height periods. The thick lines are those retrieved from the SAM model with vertical air motion accounted and the thin lines are those from the measured profiler spectra. The number in bracket indicates the mean mass-weighted diameter (mm).

Citation: Monthly Weather Review 137, 6; 10.1175/2008MWR2754.1

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  • Fig. 1.

    Horizontal plane of reflectivity at 3.5 km AGL from the TBW radar at 0656:14 UTC 14 Sep 2001. The stratiform rainband considered in this study extends from the left-center to the right-center part of the figure. The red circle shows the location of the TBW radar and the thick black line represents the land boundary.

  • Fig. 2.

    (a),(c) Vertical sections along x= 0 of radar reflectivity (dBZ) and (b),(d) radial Doppler velocity (m s−1) at 0601:05 and 0656:14 UTC from the WSR-88D at Tampa Bay (KTBW). The arrow at y= 0 km represents the location of the SMART-R and MIPS. (bottom) A horizontal plane of reflectivity with horizontal wind vectors (storm relative) over it on 0656:14 UTC at 3.5 km AGL. The wind vectors were acquired by dual-Doppler radar process using the CEDRIC software. Upper and lower circles show the locations of the TBW and SMART-R, respectively.

  • Fig. 3.

    Upper-air soundings at (left) 0000 and (right) 0600 UTC 14 Sep 2001 at KTBW.

  • Fig. 4.

    Time–height sections of (a) radar reflectivity (dBZ), (b) Doppler velocity (m s−1), and (c) spectral width (m s−1) derived from the 915-MHz profiler.

  • Fig. 5.

    Time–height sections of vertical air motions (a) from the EVAD and (b) the 915-MHz profiler. The horizontal line in (a) shows the top of the section in (b) at the same scale for the comparison and the dashed line shows the approximate level of the 0.0 m s−1 contour.

  • Fig. 6.

    Composite profiles of (a) horizontal divergence and (b) vertical air motions derived from various methods between 0545 and 0631 UTC. In (a), the thin line the EVAD divergence profile, the thick line the Q-VAD divergence profile, and the middle thick line represent the divergence profile from the theorem. A three-point running average with regard to heights was performed for Q-VAD and the divergence theorem. In (b), each vertical air motion profile derived from EVAD (thin), the divergence theorem (middle thick), Q-VAD (thick), and the reflectivity–fall speed relations (dashed) is shown. The vertical air motions derived from the reflectivity–fall speed relations were also three-point smoothed. The horizontal line at 4.8 km shows the approximate top of the melting layer.

  • Fig. 7.

    CFADs for (a) reflectivity (bin: 1.25 dB), (b) Doppler velocity (bin: 0.25 m s−1), (c) spectral width (bin: 0.15 m s−1), and (d) wind speed (bin: 1.0 m s−1) during 0530–0648 UTC. The top horizontal line at 4.8 km represents the approximate top of the melting layer and 0°C level. The bottom horizontal line at 3.47 km shows a height where the SAM performed for the RSD retrievals.

  • Fig. 8.

    Schematic diagram for the parameters (see the text for more details).

  • Fig. 9.

    (a) Time–height section of the reflectivity near the brightband region. The black-colored pixels represent reflectivity greater than 50 dBZ. The thick solid line indicates Hpeak and upper and lower thin lines indicate Htop and Hbottom, respectively. The symbols of rectangle and circle represent the breakup and aggregation-dominant periods, respectively. (b) Time variations of the γ parameter (solid line), reflectivity ratio (dashed line), and Doppler velocity ratio (dotted line). The circle and rectangle symbols represent aggregation- and breakup-dominant periods, respectively. The triangles indicate the period of a prominent decrease in brightband height. The horizontal line indicates the threshold of 0.23 (suggested by Drummond et al. 1996).

  • Fig. 10.

    (a) Scatterplot between Zepeakand the brightband height (top group; left axis) and brightband thickness (bottom group; right axis). (b) Scatterplot between ΔZ and Zepeak (top group) and Zerain (bottom group). The symbols are as defined in Fig. 9b with solid dots representing all other observations.

  • Fig. 11.

    (a) Scatterplot between rain rate (mm h−1) and Zepeak(top group; left axis) and ΔH (bottom group; right axis). (b) Scatterplot between rain rate and Hpeak. Rain rate is retrieved at 3472 m AGL. The symbols are as defined in Figs. 9b and 10.

  • Fig. 12.

    Time–height sections of (a) reflectivity (dBZ), (b) rain rate (mm h−1), (c) Dm (mm), and (d) N0 (m−3 mm−1). For each section, smoothing using the eight nearest values was performed in time and height. The symbols are as defined in Fig. 9b.

  • Fig. 13.

    (a) Comparison between R (mm h−1) from the SAM with vertical air motion accounted, and ZR relation and (b) the comparison R (mm h−1) from the SAM with vertical air motion not accounted, and ZR relation.

  • Fig. 14.

    Comparison of the averaged RSDs during the three major periods at 3472 m AGL. The black solid line represents the RSD during the first aggregation-dominant periods (0548 UTC), the red line the RSD during the breakup-dominant periods, and the blue line the RSD during the descending brightband height periods. The thick lines are those retrieved from the SAM model with vertical air motion accounted and the thin lines are those from the measured profiler spectra. The number in bracket indicates the mean mass-weighted diameter (mm).

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