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  • View in gallery

    Schematic of the observational facilities for the offshore phase of the IMPROVE field studies.

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    Infrared satellite image at 0000 UTC 2 Feb 2001.

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    One hour pressure changes (in hPa) and surface winds on 2 Feb 2001 at (a) 0000, (b) 0100, (c) 0200, (d) 0300, (e) 0400, (f) 0500, (g) 0600, and (h) 0700 UTC. Surface- and upper-level fronts are shown in the conventional manner. Winds at select stations that experienced significant wind shifts are highlighted.

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    Synoptic map for 0300 UTC 2 Feb 2001. Isobars are labeled in hPa. Surface- and upper-level fronts are shown in the conventional manner. Precipitation intensity, measured by the NCAR S-Pol radar at Westport, WA, and the NWS radars at Portland and Medford, OR, and Eureka, CA, are shown by shading.

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    Radar PPI reflectivity factor measured by the NCAR S-Pol radar located at Westport, WA, on 2 Feb 2001 at (a) 0136:46 UTC at 0.5° elevation scan and (b) 0138:39 UTC at 2.4° elevation scan. The white and black dashed lines show the locations of the subbands of the wide cold-frontal rainband. The solid black line indicates the 250° azimuth along which the UW Convair-580 flew vertically stacked horizontal legs.

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    Radar RHI reflectivity factor measured by the NCAR S-Pol radar located at Westport, WA, on 2 Feb 2001 in the wide cold-frontal rainband at (a) 0054:01 UTC at 240.0° azimuth from radar, (b) 0156:19 UTC at 270.0° azimuth from radar, (c) 0125:02 UTC at 240.0° azimuth from radar, and (d) 0256:41 UTC at 240.0° azimuth from radar. The dashed arrows indicate generating cells in the cirrus clouds, and the solid arrows indicate generating cells in the altocumulus clouds.

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    Some crystal types recorded by the CPI aboard the UW Convair-580 research aircraft on 1–2 Feb 2001. (a) Radiating assemblage of plates, (b) plate with sheaths growing on face of plate, (c) assemblage of capped bullets, (d) sideplanes, (e) assemblage of sideplanes, (f) broad-branched crystal, (g) assemblage of bullets, (h) capped column, and (i) sheaths. The scale is the same for each crystal image.

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    Vertical cross section of storm-relative flight track (thin line with arrowheads) of the UW Convair-580 research aircraft through the wide cold-frontal rainband. (left) The horizontal legs for the flight are numbered. The dominant crystal types observed in situ for each minute of the flight are shown by symbols (see Table 1 for key to symbols). The temperature zones for the formation of several crystal types are indicated by the large crystal symbols within the white circles on the right and the associated shading. (left) The bracketed regions indicate saturation levels inferred from dominant particle habits. (right) The bracketed regions indicate growth regions inferred from crystal imagery, liquid water contents, and crystal concentrations. The generating cell and fallstreak structure are inferred from S-Pol radar measurements. The hatched circles along the top flight leg indicate areas where the aircraft passed through generating cells.

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    Radar RHI polarimetric particle classification from the NCAR S-Pol radar located at Westport, WA, on 2 Feb 2001 in the wide cold-frontal rainband at 0156:02 UTC at 250.0° azimuth from radar. The arrow indicates the location of the UW Convair-580.

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    Particle size spectra measured by the 2D cloud probe and HVPS aboard the UW Convair-580 research aircraft in (a) flight leg 7 (6.5 km, T ≈ −21°C), (b) flight leg 6 (5.5 km, T ≈ −15°C), (c) flight leg 4 (3.7 km, T ≈ −7°C), and (d) flight leg 2 (2 km, T ≈ +0.7°C).

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    Radar reflectivity (in dBZ) derived from the airborne in situ measurements and measured by the S-Pol radar. The range is defined as one std dev from the average value. Flight legs are numbered alongside the derived radar reflectivity values. (right) The dominant crystals encountered on each flight leg are indicated (see Table 1 for key to symbols).

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    Range and average values of the air-relative vertical precipitation mass flux derived from airborne measurements (expressed as a precipitation rate, in mm h−1, by dividing Ft by the density of liquid water). The range is defined as one standard deviation from average. Flight legs are numbered alongside the derived values. (right) The dominant crystals encountered on each flight leg are indicated (see Table 1 for key to symbols).

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    Some microphysical variables measured aboard the UW’s Convair-580 research aircraft from 0238:00 to 0239:09 UTC 2 Feb 2001. (a) FSSP-100 total particle concentration. (b) PVM-100A liquid water content. (c) PMS 2D cloud probe total particle concentration.

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    (a) Pressure trace at Westport, WA, on 1–2 Feb 2001. (b) The time of the passage of the upper-level cold front, shaded region indicates the region of the pressure trace are enlarged, also enlarged view of the segment of the pressure trace within the shaded region in (a), showing the pressure perturbation and the resulting surface convergence.

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    (a) Schematic depicting the extent of the enhanced (−2 to 64 dBZ) radar reflectivity (shading) associated with the wide cold-frontal rainband. Fronts (taken from Part I) are overlaid. (b) Schematic showing the extent of the enhanced (−2 to 64 dBZ) radar reflectivity (shading) of a portion of the wide cold-frontal rainband. Schematics of a fallstreak from the cirrus cloud and a generating cell and fallstreak from the altocumulus cloud are overlaid. Regions of formation of various crystal types are shown on the left side (see Table 1 for key to symbols).

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The IMPROVE-1 Storm of 1–2 February 2001. Part II: Cloud Structures and the Growth of Precipitation

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  • 1 Department of Atmospheric Sciences, University of Washington, Seattle, Washington
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Abstract

On 1–2 February 2001, a strong cyclonic storm system developed over the northeastern Pacific Ocean and moved onto the Washington coast. This storm was one of several that were documented during the first field phase of the Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE). In the 1–2 February case, soundings and wind profiler measurements showed that a wide cold-frontal rainband was coincident with the leading edge of an upper-level cold front in a classical warm occlusion. Ground-based radar observations revealed the presence of subbands within the wide cold-frontal rainband and two layers of precipitation generating cells within this rainband: one at 5–7 km MSL and the other at 9–10 km MSL. The lower layer of generating cells produced fallstreaks that were traced from the cells down to the radar bright band at 2 km MSL. Observations suggest a connection between the subbands and the lower layer of generating cells.

A research aircraft, equipped for cloud microphysical measurements, passed through at least two generating cells in the 5–7-km region. These cells were in their formative stage, with elevated liquid water contents and low ice particle concentrations.

The microphysical structure of the wide cold-frontal rainband was elucidated by particle imagery from a Cloud Particle Imaging (CPI) probe aboard the research aircraft. These images provide detailed information on crystal habits and degrees of riming throughout the depth of the rainband. The crystal habits are used to deduce the temperature and saturation conditions under which the crystals grew and, along with in situ measurements of particle size spectra, they are used to estimate particle terminal fall velocities, precipitation rates, radar reflectivities, and vertical air motions. The radar reflectivity derived in this way generally compared well with direct measurement. Both the derived and directly measured parameters are used to determine the primary particle growth processes in the wide cold-frontal rainband. Above the melting layer, vapor deposition was the dominant growth process in the rainband; growth of ice particles by riming was small. Significant aggregation of ice particles occurred in the region just above the melting layer. A doubling in the air-relative vertical precipitation mass flux occurred between the region where sheath ice crystals formed (−3° ≤ T ≤ −8°C) and the surface. Substantial amounts of liquid water were found within the melting layer where growth occurred by the accretion of cloud droplets and also by condensation. Growth by the collision and coalescence of raindrops was not significant below the melting layer.

Corresponding author address: Professor Peter V. Hobbs, Box 351640, Dept. of Atmospheric Sciences, University of Washington, Seattle, WA 98195. Email: phobbs@atmos.washington.edu

Abstract

On 1–2 February 2001, a strong cyclonic storm system developed over the northeastern Pacific Ocean and moved onto the Washington coast. This storm was one of several that were documented during the first field phase of the Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE). In the 1–2 February case, soundings and wind profiler measurements showed that a wide cold-frontal rainband was coincident with the leading edge of an upper-level cold front in a classical warm occlusion. Ground-based radar observations revealed the presence of subbands within the wide cold-frontal rainband and two layers of precipitation generating cells within this rainband: one at 5–7 km MSL and the other at 9–10 km MSL. The lower layer of generating cells produced fallstreaks that were traced from the cells down to the radar bright band at 2 km MSL. Observations suggest a connection between the subbands and the lower layer of generating cells.

A research aircraft, equipped for cloud microphysical measurements, passed through at least two generating cells in the 5–7-km region. These cells were in their formative stage, with elevated liquid water contents and low ice particle concentrations.

The microphysical structure of the wide cold-frontal rainband was elucidated by particle imagery from a Cloud Particle Imaging (CPI) probe aboard the research aircraft. These images provide detailed information on crystal habits and degrees of riming throughout the depth of the rainband. The crystal habits are used to deduce the temperature and saturation conditions under which the crystals grew and, along with in situ measurements of particle size spectra, they are used to estimate particle terminal fall velocities, precipitation rates, radar reflectivities, and vertical air motions. The radar reflectivity derived in this way generally compared well with direct measurement. Both the derived and directly measured parameters are used to determine the primary particle growth processes in the wide cold-frontal rainband. Above the melting layer, vapor deposition was the dominant growth process in the rainband; growth of ice particles by riming was small. Significant aggregation of ice particles occurred in the region just above the melting layer. A doubling in the air-relative vertical precipitation mass flux occurred between the region where sheath ice crystals formed (−3° ≤ T ≤ −8°C) and the surface. Substantial amounts of liquid water were found within the melting layer where growth occurred by the accretion of cloud droplets and also by condensation. Growth by the collision and coalescence of raindrops was not significant below the melting layer.

Corresponding author address: Professor Peter V. Hobbs, Box 351640, Dept. of Atmospheric Sciences, University of Washington, Seattle, WA 98195. Email: phobbs@atmos.washington.edu

1. Introduction

Comprehensive field measurements and enhanced physical understanding are needed to improve cloud microphysical schemes used in mesoscale models. During the Improvement of Microphysical Parameterization through Observational Verification Experiment (IMPROVE) field studies, in situ and remotely sensed measurements of meteorological and microphysical variables were collected to quantify cloud and precipitation processes under a variety of conditions (Stoelinga et al. 2003). The focus of IMPROVE-1, which took place from 4 January to 14 February 2001 off the coast of Washington state, was frontal forcing as a precipitation generating mechanism.

This paper focuses on data collected on 1–2 February 2001, during the passage of an occluding frontal system and the main rainband associated with this system which, in the terminology proposed by Hobbs (1978), was a wide cold-frontal rainband (WCFR). Following a brief description of the observational facilities, the synoptic and mesoscale structure of the frontal system are described. Airborne in situ measurements of cloud structures are then used to deduce the primary precipitation producing mechanisms in the WCFR. Locatelli et al. (2005, hereafter Part I) give a detailed description of the development of the forward-tilted upper-level cold front and warm occlusion that drove the WCFR studied here.

2. Observational facilities

In the field phase of IMPROVE-1, simultaneous measurements were obtained from ground stations, radar, and aircraft. This provided detailed information from the synoptic scale down to the microscale. A schematic diagram of the study area and the observational facilities used in IMPROVE-1 are shown in Fig. 1.

The National Center for Atmospheric Research (NCAR) S-Band, dual-polarization Doppler radar (S-Pol) was located at Westport, Washington, where it had an unobstructed view of the offshore study area. This radar was used in real time for weather surveillance and short-term forecasting, as well as guidance of the research aircraft into precipitation features. The polarimetric capabilities provided information on particle types and rainfall rates. In addition, Doppler velocity measurements were collected using the S-Pol radar and two bistatic receivers to retrieve 3D wind fields (Wurman 1994).

In situ measurements of meteorological state variables (temperature, dewpoint, relative humidity, and wind speed and direction) and cloud microphysical variables (liquid water content, particle size spectra, and crystal type) were obtained from the University of Washington’s (UW) Convair-580 research aircraft. The Particle Measuring System (PMS) Forward Scattering Spectrometer Probe (FSSP)-100 was used to detect cloud particles. The FSSP-100 sizes particles up to 47 μm in diameter by measuring the amount of light scattered into the collecting optics as a particle passes through a focused laser beam (Knollenberg 1976). The PMS 2D cloud particle imaging probe, which uses a linear photodiode array and high-speed electronics to record 2D images of particles, was used to measure the size spectra of drops from 25 to 3000 μm in diameter (Heymsfield and Parrish 1978). Liquid water content measurements were made with a Particle Volume Monitor (PVM)-100A, which uses the diffraction of light by cloud particles to obtain a particle size spectrum of which the third moment is liquid water content (Gerber 1991). The primary instrument used for ice crystal identification was the Stratton Park Engineering Company, Inc. (SPEC), Cloud Particle Imager (CPI; Lawson and Jensen 1998). The CPI uses a pulsed laser to produce detailed 2D images of cloud particles from 5 μm to 2.5 mm in size. The SPEC High Volume Particle Spectrometer (HVPS), which has a resolution of 200 μm, was used to measure the size spectrum of particles from 3 mm to 1.5 cm (Lawson et al. 1993).

Vertically stacked horizontal flight legs were flown through rainbands to provide vertical cross sections of microphysical parameters. In the 1–2 February 2001 case study, the flight path was along the 250° azimuth from the Doppler radar, allowing the superposition of the flight track over a vertical cross section (or RHI scan) by the radar.

Special rawinsondes were launched by the National Weather Service (NWS) from Quillayute, Washington, and from Westport by the U.S. Navy and the UW. Other instrumentation and observational facilities included a National Oceanic and Atmospheric Administration (NOAA)/Environmental Technology Laboratory (ETL) wind profiler at Westport and numerous rain gauges along the Washington coast (Fig. 1). Stoelinga et al. (2003) provide further information on the instrumentation.

3. Synoptic analysis

On 1 February 2001, a warm occluding frontal system approached the coast of the Pacific Northwest. Infrared satellite imagery taken at 0000 UTC 2 February 2001 shows the entire midlatitude cyclone with a classic comma-shaped cloud and cold-air advection behind the system (Fig. 2). The NCEP analysis for 0000 UTC 2 February 2001 soundings (see Fig. 2 in Part I) indicates the presence of a tipped-forward baroclinic zone ahead of the surface occluded front. This corresponded to the location of the upper-level cold front. The tipped-forward structure of the upper-level cold front is also clearly visible in Fig. 1 of Part I, where it is described in some detail.

Passage of the nose of the upper-level cold front produced a surface wind shift, a slight rise in surface pressure at Westport, and the beginning of the precipitation associated with the WCFR. The movement of the upper-level cold front, after it came ashore, is shown by the hourly changes in the mean sea level pressure readings at Westport between 0000 and 0007 UTC (Fig. 3). A slight rise in pressure, followed by a fall in pressure, accompanied the passage of the upper-level front at many locations. Wind shifts from easterly to south/southwesterly occurred behind the upper-level front at the stations highlighted in Fig. 3. A second rise in pressure occurred as the surface occluded front came ashore.

The WCFR in which the Convair-580 flew was associated with the upper-level cold front seen in Fig. 4. An overlay of radar reflectivity measurements from the radar at Westport, Washington, and a composite of NWS radar reflectivity data at 0300 UTC, confirm the coincidence of the upper-level front with the leading edge of the WCFR. Observed cloud base for the WCFR was at ∼1.5 km, which was below the freezing level (T ∼ 0°C) found at ∼2.3 km.

4. Mesoscale features

The WCFR moved with a speed of 12 m s−1, it was oriented perpendicular to the 250° azimuth, and it was ∼120 km wide. Within the WCFR (Fig. 4), were subbands of more intense precipitation, as seen in the radar reflectivity values shown in Fig. 5a. The subbands were oriented in a northwest–southeast direction, they were ∼30 km apart, and they moved with a speed of 17 m s−1. The subbands are still visible in the higher radar elevation angle scan (2.3°) shown in Fig. 5b, even in areas where no precipitation reached the ground. This indicates that the subbands were generated somewhere between 3 and 6 km.

To investigate the generation of the subbands, we examined areas of more intense precipitation, called precipitation cores by Hobbs and Locatelli (1978). Vertical cross-sectional scans from the S-Pol radar show two layers of generating cells (Fig. 6), that is, areas of shallow, weak convection aloft. We will refer to the layer of generating cells located between 9 and 10 km as cirrus generating cells, and the layer between 5 and 7 km as altocumulus generating cells. Distinct altocumulus generating cells and their accompanying fallstreaks can be seen in the leading edge of the WCFR (Fig. 6c). Fallstreaks from both the cirrus and altocumulus generating cells can be seen within the WCFR itself (Figs. 6b and 6d, respectively).

The vertical wind profile within the WCFR, as measured by the Convair-580 and by the 0200 UTC sounding from Quillayute, show a deep layer, from ∼2 to 6.5 km MSL, with relatively uniform winds of 28 m s−1 from 210°. This layer was capped by a layer of vertical shear, where the wind speed increased by 3 m s−1 over a depth of ∼0.5 km. This wind profile is consistent with the shapes of the fallstreaks from the altocumulus generating cells. The cells themselves were vertically oriented, indicating vertical mixing of momentum due to convective overturning. Immediately beneath the cells, the fallstreaks curved sharply within the shear layer. Within the deep layer of relatively uniform wind, the fallstreaks were not curved.

A comparison of the slopes of the subbands seen in a series of conical plan position indicator (PPI) scans and the slope of fallstreaks associated with altocumulus generating cells seen in RHI scans, yielded similar values. The radar reflectivity was approximately 20 dB greater in the fallstreaks from the altocumulus generating cells than outside of the fallstreaks. Therefore, it is likely that the precipitation cores were produced by the altocumulus generating cells.

Previous research has shown that the contribution of generating cells to precipitation mass at the ground is ∼20% to 35% depending on the magnitude of the vertical air motions within the cells (Hobbs et al. 1980; Houze et al. 1981). Rutledge and Hobbs (1983) artificially inserted the effects of generating cells in model simulations. In ongoing studies we are investigating if mesoscale models can resolve generating cells, or if generating cells have to be parameterized to improve quantitative predictions of precipitation.

5. Cloud and precipitation microphysics

a. Crystal identification and size spectra

Ice crystal types can provide important information on the temperature zones where precipitation growth occurs, particle growth mechanisms, regions of water and subwater saturation, and the fall speeds of crystals. Imagery from the CPI was used for ice crystal identification in the 1–2 February 2001 case study. Examples of these images are shown in Fig. 7. Over 99 000 crystal images were analyzed to determine the dominant crystal types and degrees of riming for each minute of the Convair-580 flight on 1–2 February 2001. Using this information we deduced the location where each crystal type formed (Fig. 8; Table 1).

The polarimetric capabilities of the S-Pol radar provide some information on hydrometeor types (Vivekanandan et al. 1994, 1999). An RHI polarimetric particle classification scan from the S-Pol radar at Westport, Washington, is shown in Fig. 9. The particles shown in this scan are representative of the stratiform precipitation found within the wide cold-frontal rainband. Above the melting layer, the majority of the precipitation is classified as irregular ice crystals, where irregular ice crystals are defined as small ice crystals with no orientation discernable by the radar. This agrees with the imagery of sideplanes, assemblages of plates, assemblages of bullets recorded by the CPI aboard the UW Convair-580 in the upper regions of the rainband (between 4.5 and 6.5 km). Immediately above and through the melting layer, the precipitation classification from the radar is predominantly dry snow and wet snow, respectively. The snow classification refers to aggregates of crystals and is divided into dry and wet categories depending upon temperature and reflectivity. The in situ observations in this region indicate the presence of a large number of aggregates from ∼4 km through the melting layer. Overall, the precipitation classification from the S-Pol radar appears to be correct, but the current classification scheme is too coarse to provide much useful information for the present study.

Particle size spectra, together with knowledge of crystal types, also provided information on the main regions of particle growth and on the fall speeds of the crystals (Locatelli and Hobbs 1974; Brown 1970). A particle size spectrum for each flight leg was derived from the measurements provided by the PMS 2D cloud probe and the HVPS aboard the Convair-580 aircraft (Fig. 10). The 2D cloud probe was used to measure particles ranging in sizes from 25 μm to 3 mm in diameter, while the HVPS covered particle diameters from 3 mm to 1.5 cm.

From the crystal types and particle size spectra, we derived the average radar reflectivity, particle mass concentration, terminal fall speeds of particles, and the air-relative vertical precipitation mass flux for each flight leg. Calculations of ice particle mass were made from particle size spectra averaged over 30-s intervals for flight legs 1–6 and over 5-s intervals for leg 7 and from dominant crystal types determined by CPI imagery. The methods used for calculating the average reflectivity factor per flight leg are described in Löffler-Mang and Blahak (2001). The mass–diameter relationships for various crystal types used in calculating the reflectivity factor and fall speeds were taken from Locatelli and Hobbs (1974) and Brown (1970). Using the temperature and pressure dependencies implied by the fall speed expression given in Heymsfield et al. (2002), the ice crystal fall speed relationships given by Locatelli and Hobbs (1974) and Brown (1970) were adjusted from the altitudes at which they were measured in those studies to the altitudes of the aircraft flight legs in the present study. To a very close approximation, this adjustment factor is equal to the cube root of the ratio of pressure at which fall speeds were measured to the pressure at flight leg altitude.

b. Growth processes

It can be seen from Fig. 8 that the region of altocumulus generating cells corresponded to the temperature zone where side planes and assemblages of plate crystals grow. Crystals in the form of bullets grew above the flight level of 6.5 km MSL, most likely in the region of the cirrus generating cells. In the region where dendritic ice crystals grow, and where one expects the most vigorous crystal growth to occur under water-saturated conditions, only a few broad-branched and sectorlike crystals were observed. This indicates that the air in this region was subwater saturated. This conclusion is supported by the fact that liquid water contents were below detectable limits during this leg. By this we mean that measured values of liquid water content of ≤0.04 g m−3 were consistent with values seen throughout the flight at temperatures below freezing, and attribution of these liquid water measurements to ice particles was supported by consistently weak, flat particle spectra measured by the FSSP-100 (Gardiner and Hallett 1985). Furthermore, riming did not significantly contribute to precipitation growth.

Reflectivity measurements from the S-Pol radar were compared with the values derived from the in situ airborne measurements. For this purpose we used radar reflectivity measurements in an RHI scan taken at 0226:36 UTC on 2 February along the 250° azimuth flown by the Convair-580. The 0226:36 UTC RHI scan occurred when the aircraft was approaching its final flight leg at ∼6.5 km and was at its nearest point to shore. There was no significant change seen in S-Pol radar reflectivity values during the passage of the rainband through the field study area, thus we feel the 0226:36 UTC RHI scan is representative of the area of the band in which measurements were obtained from the Convair-580. The area covered by this scan was 10 km (vertical) × 10 km (range) on a 0.5-km horizontal grid. An average radar reflectivity was calculated for this region over height intervals of 0.5 km, which yielded a vertical profile of radar reflectivity (Fig. 11). The reflectivity derived from the airborne in situ measurements of particles along each of the flight legs was averaged over 30-s intervals with a resolution of ∼3 km; they generally compared well with those measured by the S-Pol radar (Fig. 11). However, in the lowest flight leg (200 m) the derived reflectivity was greater than that measured by the S-Pol radar.

Several key aspects concerning the growth of precipitation can be derived from the comparison of the derived and measured radar reflectivities. Between 6.5 and 5.5 km (flight legs 7 and 6) there was a significant increase in radar reflectivity; this corresponds to the altocumulus generating cells (Fig. 11). An increase in reflectivity is also seen between 5.5 and 4.5 km (flight legs 6 and 5) when caps began to appear on the bullet and column crystals that fell from above (Fig. 7h). Only a slight increase in reflectivity occurred from 4.5 to 3.7 km (flight legs 5 and 4) where no new crystal types were seen on the CPI imagery. Below the region where sheaths form, from 3.5 to 4 km, there was a sharp increase in reflectivity, which was maintained down to the bright band. This was produced by the rapid aggregation of crystals.

To facilitate the analysis of precipitation growth, we define a quantity that we will refer to as the air-relative vertical precipitation mass flux (units: kg m−2 s−1)
i1520-0469-62-10-3456-e1
where Vt is the mass-weighted mean terminal fall speed, and C the mass concentration, of the precipitation particles. The equation for the local time tendency of C can be written as
i1520-0469-62-10-3456-e2
where ▿ is the three-dimensional gradient operator, V the three-dimensional air velocity, and G a source term for precipitation mass that includes all growth processes (vapor deposition, riming, etc.). Under approximately steady-state conditions, the left-hand side of (2) vanishes. Furthermore, for typical vertical air velocities within convectively stable, frontally driven precipitation bands (∼0–50 cm s−1), it can be shown that the flux divergence term due to air motions [the first term on the right-hand side of (2)] is an order of magnitude smaller than the flux divergence term due to particle fallout [the second term on the right-hand side of (2)]. Thus, under the above assumptions, the precipitation mass growth (G) is approximately equal to the vertical convergence of Ft
i1520-0469-62-10-3456-e3

The vertical profile of Ft (expressed as a precipitation rate by dividing Ft by the density of liquid water, and shown in Fig. 12) is similar in pattern to that of the radar reflectivity (Fig. 11). While we do not have any independent measure of Ft that can be used to verify the aircraft-derived profile, the previously discussed comparison of aircraft- and radar-derived reflectivity is a more stringent test of the aircraft data, because of the strong dependence of reflectivity on the particle size distribution. Therefore, the favorable reflectivity comparisons bolster our confidence in the aircraft-derived Ft profile. Calculations of Ft in and below the melting layer were higher than surface measurements of precipitation rate at Westport, Washington. The calculations of Ft were made as the WCFR approached the coast, while the surface measurements were taken 2 h later when the WCFR reached Westport. A comparison between S-Pol reflectivity scans and rain gauge measurements at Westport also indicate that evaporation was occurring as the rainband made landfall, which could have had an effect on the average precipitation rate at Westport. Regardless of which quantity is used for comparison (the calculated Ft or the measured surface precipitation rate), significant growth occurred between leg 4 (3.7 km, T ≈ −7°C) and the ground (Fig. 12).

Increases in the value of the aircraft-derived Ft are seen in the same regions above the melting layer where increases in reflectivity were present (Figs. 11, 12). These regions include the altocumulus generating cells and the region of plate growth (where caps grew on bullets and columns). This confirms that significant particle growth occurred in these two regions.

Our estimates of particle growth between flight leg 4 (3.7 km, T ≈ −7°C) and leg 2 (2 km, T ≈ 0.7°C) are questionable because of the scarcity of in situ data from leg 3 (3.7 km, T ≈ −7°C) caused by a malfunction of the 2D cloud probe. Wide variations are seen in the values of Ft calculated along flight leg 2. This is due, in part, to using the Heymsfield and Parrish (1978) reconstruction method, which is designed for spherically symmetric particles, to obtain size spectra from the 2D particle imagery, since asymmetric aggregates were the dominant particles on leg 2 (2 km, T ≈ 0.7°C). Possible particle growth mechanisms in this region are discussed in the next section.

If it is assumed that the term G in Eqs. (2) and (3) is entirely due to growth by deposition (which is consistent with the observations), it is possible to estimate the vertical air velocity above the melting layer from the derived values of Ft (see appendix for methodology). The estimates of vertical air velocity (Table 2) are within the range of vertical velocities expected within WCFR, namely, tens of centimeters per second (Matejka et al. 1980). These estimates of vertical velocity should be useful for future comparison with mesoscale model simulations.

c. Altocumulus generating cells

During flight leg 7 (6.5 km, T ≈ −21°C), the aircraft intersected an altocumulus generating cell at least twice, from 0238:20 to 0238:40 UTC and from 0238:45 to 0239:02 UTC (Fig. 13). In the initial growth stage of a generating cell, the updrafts should produce an abundance of cloud droplets. This was seen in both penetrations of the generating cell by the FSSP-100, which measures droplets from 4- to 60-μm diameter (Fig. 13a). The PVM-100A, which measures cloud liquid water content, recorded spikes in the generating cell that exceeded the expected signal from ice particle contamination (i.e., a few hundredths of a gram per square meter), confirming the presence of cloud droplets (Fig. 13b). At the same time, there was a decrease in the concentration of ice crystals measured by the PMS 2D cloud probe (Fig. 13c). Apparently the cell was too young to produce large numbers of large ice particles.

6. Discussion

a. Mesoscale structure of the wide cold-frontal rainband

Numerous studies (e.g., Browning 1974; Harrold and Austin 1974; Hobbs 1978; Matejka et al. 1980; Sanders 1986; Byrd 1989; Sienkiewicz et al. 1989; Martin et al. 1990) have shown that mesoscale rainbands are an important part of the organization of precipitation in midlatitude cyclones. Mesoscale rainbands have been classified into six categories, depending on their relation to frontal and airmass structure (Hobbs 1978). The rainband studied in the 1–2 February 2001 case was associated with an upper-level cold front within an occluded cyclone and can be classified as a WCFR with a width of ∼120 km.

b. Structure of the generating cells and subbands

Observations of generating cells and their associated fallstreaks, and mechanisms for their formation, have been described by Wexler and Atlas (1959), Marshall (1953), Carbone and Bohne (1975), and Syrett et al. (1995). These structures have been observed in both cirrus clouds (e.g., Heymsfield and Knollenberg 1972; Ludlam 1956; Sassen et al. 1990) and altocumulus clouds (Henrion et al. 1978). Two regions of generating cells, in cirrus and altocumulus clouds, were observed in the present case.

The formation of generating cells has been linked to the lifting of potentially unstable layers of air (Wexler and Atlas 1959). Several studies of precipitation events have found generating cells in potentially unstable regions (e.g., Hobbs and Locatelli 1978; Matejka et al. 1980; Herzegh and Hobbs 1981). Since the generating cells within the rainband discussed here were located above the cold front, frontal lifting could have released potential instability and formed convective cells.

Generating cells play a significant role in precipitation generation in warm-frontal rainbands (Hobbs and Locatelli 1978; Matejka et al. 1980), prefrontal surges (Matejka et al. 1980), and WCFR (Herzegh and Hobbs 1981). In the present case, fallstreaks associated with generating cells in the cirrus region were tracked in radar RHI scans until they reached the altocumulus region (Fig. 6b). Fallstreaks associated with generating cells in the altocumulus region were tracked to the melting layer and below. The reflectivity of the fallstreaks from the altocumulus generating cells and the precipitation they produced beneath the melting layer was ∼20 dBZ greater than outside of the fallstreaks. Thus, generating cells in the altocumulus region played a significant role in enhancing the growth of precipitation particles.

Since the fallstreaks at cloud base (∼1.5 km) had a width of ∼10 km, which were similar to the widths of the subbands, and the subbands and fallstreaks had similar slopes in the vertical, we attribute the subbands seen in the radar PPI scans (Fig. 5a) to the fallout from the generating cells. The subbands propagated perpendicular to the 250° azimuth at 17 m s−1. The component of the wind speed along the 250° azimuth, taken from the 0200 UTC Quillayute sounding, ranges from 15 to 19 m s−1, which corresponds to the wind speeds at the altocumulus generating cell level between 5.5 and 7 km.

c. Rainband enhancement

The passage of an upper-level cold front is characterized by “a slower rate of [pressure] decrease or only a slight rise in the barometer” (Holzman 1936). Surface convergence induced by the change in the horizontal pressure gradient associated with the passage of an upper-level cold front produces vertical velocities on the order of tens of centimeters per second (Locatelli et al. 1997). Stratiform precipitation within stably stratified warm occlusions, such as that which occurred in the 1–2 February case study discussed here, may be enhanced by this type of convergence.

The nose of the upper-level cold front passed over Westport, Washington, between 0200 and 0230 UTC on 2 February 2001 (see Fig. 1 in Part I). The pressure at Westport, Washington, started to increase at ∼0200 UTC (Fig. 14). This increase lasted until ∼0330 UTC, after which the pressure decreased until the passage of the occluded front between 0600 and 0700 UTC. Using the method described by Locatelli et al. (1997), the surface convergence, and resulting maximum vertical velocity, were calculated during the 1 h of passage of the upper-level cold front (Fig. 14b). The resulting maximum vertical velocity at a height of 1 km MSL was 28 cm s−1, which could significantly augment stratiform precipitation.

The maximum vertical velocity of 28 cm s−1 at 1 km MSL is considerably larger than those estimated above the melting layer (Table 2). However, the maximum surface convergence occurred over ∼15 min, which translates to ∼11 km on a horizontal scale, whereas the values of Ft used to estimate the vertical velocity above the melting layer were averaged over entire flight legs, which were ∼65 km in length. Thus, the difference between the values of vertical velocity derived for above and below the melting layer is likely due to differences in the representative horizontal scales.

d. Microphysics and growth processes

Within the generating cells in the cirrus region, bullets, which form at T ≤ −40°C and supersaturation with respect to ice ≥20% (Bailey and Hallett 2002), grew by vapor deposition (Fig. 15b). Columnar crystals that form below −25°C, such as bullets, provide an efficient path for the growth of precipitable particles (Mason 1994). Because of their large volume-to-surface ratio, columnar-type crystals should sublime only slowly after leaving generating cells and falling into unsaturated air. This accounts, in part, for the deep fallstreaks that are commonly seen emanating from generating cells in cirrus clouds. Also, because of shape differences and aerodynamic effects, a columnar-type crystal falls 1½–2 times faster than a platelike crystal of the same mass. Therefore, columnar-type crystals collect more supercooled water than platelike crystals (Mason 1994). In the WCFR discussed here, the bullets fell into air that was at least ice saturated, so sublimation was not an issue; also riming was not seen at these altitudes. From the crystal imagery, we know that the bullets survived and grew down through the altocumulus generating cells.

The growth of side planes and assemblages of plates within the altocumulus generating cells was entirely by vapor deposition. Except in newly formed cells (Fig. 13), liquid water contents along flight leg 7 (6.5 km, T ≈ −21°C) were below detectable limits, and probably zero, as discussed previously for the dendritic region in section 5b. In addition, no riming was detected along this leg. Below the altocumulus generating cells, in a region of subwater saturation, caps (i.e., plates) begin to grow by deposition onto the columns and bullets. These various types of growth are reflected in the increase in Ft seen between legs 7 (6.5 km, T ≈ −21°C) and 5 (4.5 km, T ≈ −9°C) in Fig. 12.

Another region for the efficient growth of ice particles is between −12° and −16°C where dendrites grow. Dendrites aggregate more readily than plates and can more easily capture supercooled cloud droplets (Hobbs et al. 1974). In the WCFR discussed here, the −12° to −16°C zone was below water saturation, and only a few broad-branched and sectorlike crystals were observed. Instead, plate growth on other crystal types appeared to dominate (Fig. 7h).

In the temperature region between −3° and −8°C, Mason (1994) proposed that needles and columns are the most efficient means for precipitation growth because they have a larger collection efficiency than platelike crystals and they are more likely to survive sublimation. Also, during riming at temperatures between −3° and −8°C needles and columns can produce copious ice splinters (Hallett and Mossop 1974). The UW research aircraft passed through the temperature region −3° and −8°C on leg 3 (2.7 km, T ≈ −3°C) and leg 4 (3.7 km, T ≈ −7°C). However, the liquid water content was only ∼0.07 g m−3 (much of which may have been due to ice particles), and laboratory experiments indicate that more liquid water is required to produce splintering (Hallett and Mossop 1974). Little growth of ice was seen on flight leg 4 (3.7 km, T ≈ −7°C), and significant growth was not detected again until between flight legs 4 and 2 (2 km, T ≈ 0.7°C) where sheaths were present (Fig. 12). Sheaths began to grow both singly and on the faces of platelike crystals (Figs. 7i and 7b, respectively) between flight legs 4 and 2. The crystals at the top of the melting layer on flight leg 2 (2 km, T ≈ 0.7°C) were primarily aggregates, some as large as 14.5 mm.

As the sheath aggregates and other crystals fell through the melting layer, further growth occurred. Two growth processes, accretion and condensation, appear to have been responsible. The FSSP-100, PVM-100A, and Johnson–Williams probes independently measured significant concentrations of cloud droplets throughout the depth of the melting layer; the liquid water contents measured by the PVM-100A approached 0.4 g m−3 several times along flight leg 2 (2 km, T ≈ 0.7°C), which was well above the values caused by ice particle contamination in other parts of the flight, and sufficient for accretion to take place. Cloud liquid water can be produced in the melting layer by frontal forcing (Stewart et al. 1984; Lin and Stewart 1986; Houze 1993). In the present case, the melting layer was coincident with the warm-frontal boundary, which is typically characterized by widespread ascent. Therefore, it is possible that melting particles grew by the accretion of cloud liquid droplets as they fell through the melting layer. A melting particle can also grow by condensation if the environment is above freezing and a large temperature gradient exists between the particle and its environment (Stewart 1992). Therefore, it is possible that in the WCFR discussed here growth by condensation occurred within the melting layer.

Some cloud liquid water was observed below the melting layer, but visual observations did not indicate any significant cloud in this region. Therefore, the growth of raindrops by collisions with cloud drops was probably not substantial in this region. Also, because the particle size spectra along both the flight leg 1 (300 m) and the climbing leg (600 m to 1.1 km) up to the melting layer were virtually identical, collisions between raindrops must have been negligible.

7. Summary

The occluding cyclone studied off the Pacific Coast on 1–2 February 2001 during the IMPROVE-1 field project is typical of those that make landfall in the Pacific Northwest in winter. Analyses of a comprehensive dataset for this cyclone, collected in the IMPROVE-1 field project, shows the main precipitation feature was a wide cold-frontal rainband associated with an upper cold front. Within this rainband were several subbands of more intense precipitation on the scale of ∼10 km; the subbands were probably produced by similarly spaced bands of altocumulus generating cells and their associated fallstreaks.

Ice crystals in the form of bullets formed in cirrus generating cells; some of these crystals fell through altocumulus generating cells. Side planes and assemblages of plates, which form at water or subwater saturation, were the primary ice crystal types formed in the altocumulus generating cells. In the region of dendritic crystal formation and growth (5 to 5.5 km, −12° ≤ T ≤ −16°C), where the greatest growth is expected under water saturated conditions, only a few broad-branched and sectorlike crystals, which form under subwater-saturated conditions, were detected. The greatest growth occurred as crystals from aloft fell through the sheath formation region (3.5 to 4 km, −6° ≤ T ≤ −8°C) where they provided substrates for sheath growth. Thus, there was a doubling in the precipitation rate between the sheath formation region and the ground. We attribute this rapid growth of precipitable particles to deposition, some riming, and condensation and accretion of cloud droplets as crystals fell through the melting layer. Collision and coalescence of raindrops in the short distance (∼1.5 km) between the melting layer and the ground, was not a significant growth process.

Vertical air motions were estimated within the upper subfreezing part of the rainband from the measured vertical profile of precipitation mass, and were found to range from 0 to 11 cm s−1 averaged over the width of the aircraft flight stack (∼65 km). Vertical air motions at 1 km above the surface, estimated from the moving surface pressure pattern associated with the upper cold front, were ∼28 cm s−1 within a region 11 km in width beneath the upper cold front.

Future work will focus on comparing the mesoscale and microscale features of the wide cold-frontal rainband described here with high-resolution modeling results using the MM5 model. The driving mechanism behind the formation of the generating cells and their alignment will be investigated, and measured microphysical fields described here will be compared to model outputs to test the accuracy of the parameterization of clouds and precipitation microphysics in the model.

Acknowledgments

We thank all those who participated in IMPROVE-1 for help in collecting data. This research was supported by Grants ATM-9908446 and ATM-0242592 from the Mesoscale Dynamic Meteorology Program, Atmospheric Sciences Division, NSF (Program Manager: Stephan Nelson).

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APPENDIX

Estimation of Vertical Air Velocity from Microphysical Measurements

The vertical velocity can be estimated from the microphysical data if it is assumed that the growth of precipitation mass above the freezing level is primarily due to vapor deposition, and that such growth occurs near ice saturation. For the rainband discussed in this paper, both of these assumptions are supported by a general lack of cloud liquid water or rimed particles above the freezing level, as well as by the measured relative humidities, which were generally closer to ice saturation than water saturation. Under these conditions, the vertical velocity, w, is equal to a value that reduces the saturation concentration of water vapor with respect to a plane surface of ice, Csi, at a rate equal to the growth rate of precipitation mass, G, in Eqs. (2) and (3). This can be written as
i1520-0469-62-10-3456-ea1
Solving for w and substituting Eq. (3) into (A1) yields
i1520-0469-62-10-3456-ea2
The term (∂Ft /∂z) is estimated from the vertical profiles of Ft; (∂Csi/∂T) and Γi are determined from the airborne measurements of pressure and temperature as discussed below.
The saturation concentration of water vapor is related to the saturation vapor pressure with respect to a plane surface of ice, esi, by
i1520-0469-62-10-3456-ea3
where ε is the ratio of the molecular weight of water to that of dry air, esi is the saturation, and R is the gas constant for dry air. An empirical expression for the saturation vapor pressure with respect to ice is given by Reisner et al. (1998)
i1520-0469-62-10-3456-ea4
where esi0, A, and B, are constants equal to 6.11 hPa, and 22.514 and 6150 K, respectively. Substituting (A4) into (A3) yields
i1520-0469-62-10-3456-ea5
and taking the partial derivative of Csi with respect to T yields
i1520-0469-62-10-3456-ea6
An expression for the water-saturated adiabatic lapse rate is given in various texts (e.g., Rogers and Yau 1989). If the saturation mixing ratio with respect to liquid water is replaced with that with respect to ice and approximated as RTCsi/p, and the latent heat of condensation is replaced with the latent heat of fusion, Lf , the following expression for the ice-saturation adiabatic lapse rate, Γi, is obtained
i1520-0469-62-10-3456-ea7
where cp is the specific heat of dry air at constant pressure, and g the acceleration due to gravity.

Using (A2), the vertical air velocity can be estimated, with Csi, (∂Csi/∂T), and Γi given by (A5), (A6), and (A7), respectively. Only temperature, pressure, and the estimate of −(∂Ft /∂z) are required.

Fig. 1.
Fig. 1.

Schematic of the observational facilities for the offshore phase of the IMPROVE field studies.

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 2.
Fig. 2.

Infrared satellite image at 0000 UTC 2 Feb 2001.

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 3.
Fig. 3.

One hour pressure changes (in hPa) and surface winds on 2 Feb 2001 at (a) 0000, (b) 0100, (c) 0200, (d) 0300, (e) 0400, (f) 0500, (g) 0600, and (h) 0700 UTC. Surface- and upper-level fronts are shown in the conventional manner. Winds at select stations that experienced significant wind shifts are highlighted.

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 4.
Fig. 4.

Synoptic map for 0300 UTC 2 Feb 2001. Isobars are labeled in hPa. Surface- and upper-level fronts are shown in the conventional manner. Precipitation intensity, measured by the NCAR S-Pol radar at Westport, WA, and the NWS radars at Portland and Medford, OR, and Eureka, CA, are shown by shading.

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 5.
Fig. 5.

Radar PPI reflectivity factor measured by the NCAR S-Pol radar located at Westport, WA, on 2 Feb 2001 at (a) 0136:46 UTC at 0.5° elevation scan and (b) 0138:39 UTC at 2.4° elevation scan. The white and black dashed lines show the locations of the subbands of the wide cold-frontal rainband. The solid black line indicates the 250° azimuth along which the UW Convair-580 flew vertically stacked horizontal legs.

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 6.
Fig. 6.

Radar RHI reflectivity factor measured by the NCAR S-Pol radar located at Westport, WA, on 2 Feb 2001 in the wide cold-frontal rainband at (a) 0054:01 UTC at 240.0° azimuth from radar, (b) 0156:19 UTC at 270.0° azimuth from radar, (c) 0125:02 UTC at 240.0° azimuth from radar, and (d) 0256:41 UTC at 240.0° azimuth from radar. The dashed arrows indicate generating cells in the cirrus clouds, and the solid arrows indicate generating cells in the altocumulus clouds.

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 7.
Fig. 7.

Some crystal types recorded by the CPI aboard the UW Convair-580 research aircraft on 1–2 Feb 2001. (a) Radiating assemblage of plates, (b) plate with sheaths growing on face of plate, (c) assemblage of capped bullets, (d) sideplanes, (e) assemblage of sideplanes, (f) broad-branched crystal, (g) assemblage of bullets, (h) capped column, and (i) sheaths. The scale is the same for each crystal image.

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 8.
Fig. 8.

Vertical cross section of storm-relative flight track (thin line with arrowheads) of the UW Convair-580 research aircraft through the wide cold-frontal rainband. (left) The horizontal legs for the flight are numbered. The dominant crystal types observed in situ for each minute of the flight are shown by symbols (see Table 1 for key to symbols). The temperature zones for the formation of several crystal types are indicated by the large crystal symbols within the white circles on the right and the associated shading. (left) The bracketed regions indicate saturation levels inferred from dominant particle habits. (right) The bracketed regions indicate growth regions inferred from crystal imagery, liquid water contents, and crystal concentrations. The generating cell and fallstreak structure are inferred from S-Pol radar measurements. The hatched circles along the top flight leg indicate areas where the aircraft passed through generating cells.

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 9.
Fig. 9.

Radar RHI polarimetric particle classification from the NCAR S-Pol radar located at Westport, WA, on 2 Feb 2001 in the wide cold-frontal rainband at 0156:02 UTC at 250.0° azimuth from radar. The arrow indicates the location of the UW Convair-580.

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 10.
Fig. 10.

Particle size spectra measured by the 2D cloud probe and HVPS aboard the UW Convair-580 research aircraft in (a) flight leg 7 (6.5 km, T ≈ −21°C), (b) flight leg 6 (5.5 km, T ≈ −15°C), (c) flight leg 4 (3.7 km, T ≈ −7°C), and (d) flight leg 2 (2 km, T ≈ +0.7°C).

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 11.
Fig. 11.

Radar reflectivity (in dBZ) derived from the airborne in situ measurements and measured by the S-Pol radar. The range is defined as one std dev from the average value. Flight legs are numbered alongside the derived radar reflectivity values. (right) The dominant crystals encountered on each flight leg are indicated (see Table 1 for key to symbols).

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 12.
Fig. 12.

Range and average values of the air-relative vertical precipitation mass flux derived from airborne measurements (expressed as a precipitation rate, in mm h−1, by dividing Ft by the density of liquid water). The range is defined as one standard deviation from average. Flight legs are numbered alongside the derived values. (right) The dominant crystals encountered on each flight leg are indicated (see Table 1 for key to symbols).

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 13.
Fig. 13.

Some microphysical variables measured aboard the UW’s Convair-580 research aircraft from 0238:00 to 0239:09 UTC 2 Feb 2001. (a) FSSP-100 total particle concentration. (b) PVM-100A liquid water content. (c) PMS 2D cloud probe total particle concentration.

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 14.
Fig. 14.

(a) Pressure trace at Westport, WA, on 1–2 Feb 2001. (b) The time of the passage of the upper-level cold front, shaded region indicates the region of the pressure trace are enlarged, also enlarged view of the segment of the pressure trace within the shaded region in (a), showing the pressure perturbation and the resulting surface convergence.

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Fig. 15.
Fig. 15.

(a) Schematic depicting the extent of the enhanced (−2 to 64 dBZ) radar reflectivity (shading) associated with the wide cold-frontal rainband. Fronts (taken from Part I) are overlaid. (b) Schematic showing the extent of the enhanced (−2 to 64 dBZ) radar reflectivity (shading) of a portion of the wide cold-frontal rainband. Schematics of a fallstreak from the cirrus cloud and a generating cell and fallstreak from the altocumulus cloud are overlaid. Regions of formation of various crystal types are shown on the left side (see Table 1 for key to symbols).

Citation: Journal of the Atmospheric Sciences 62, 10; 10.1175/JAS3547.1

Table 1.

Symbols and descriptions of crystal habits classified according to the scheme proposed by Magono and Lee (1966).

Table 1.
Table 2.

Vertical air velocity estimates derived from air-relative vertical precipitation mass flux (Ft). The vertical velocity at 4.1 km is zero because no increase in Ft was seen between flight legs 5 and 4 (4.5–3.7 km).

Table 2.
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