Thermodynamic and Kinematic Structure of a Snowband and Freezing

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Thermodynamic and Kinematic Structure of a Snowband and Freezing Rain Event during STORM-FEST HUNTER COLEMAN

AND

JOHN MARWITZ

Department of Atmospheric Science, University of Wyoming, Laramie, Wyoming (Manuscript received 2 October 2000, in final form 10 July 2001) ABSTRACT A unique wintertime storm occurred on 12 February 1992 during the Stormscale Operational and Research Meteorology-Fronts Experiment Systems Test (STORM-FEST) field project. This storm consisted of a narrow east–west-oriented snow swath (max 20-cm snow depth) with an extensive area of freezing rain to the south. The event was well observed by various networks and systems. Included in these systems were about twice the normal sounding sites, which released rawinsondes every 3 h, single- and dual-Doppler capabilities, and NCAR King Air and Wyoming King Air aircraft. Four aspects of the storm were investigated: the temporal evolution of the low-level jet, the vertical stability of various layers, the development of isothermal layers, and the dynamical effects resulting from melting. The freezing rain related to this storm was a result of an overrunning situation, and the snow swath was produced from conditional symmetric instability with respect to the ice process in the overrunning cloud layer. The warm frontal layer was dynamically unstable in terms of the Richardson number and contained some shearinduced gravity waves. A convective boundary layer was present near the surface. A low-level jet was present at the top of the convective boundary layer and along the snow–freezing rain interface. Isothermal layers developed just below the bright band as a result of diabatic cooling because of melting. The diabatic process of melting appears to have enhanced the speed of the low-level jet and triggered and focused the release of the thermodynamic instability so that an enhanced precipitation rate occurred over the snow–freezing rain interface.

1. Introduction Freezing rain is a meteorological event that occurs during the winter months in parts of the United States and southern Canada. Freezing rain poses a serious threat to surface transportation and electric power transmission (e.g., Martner et al. 1993; Bendel and Paton 1981; Regan 1998). The synoptic conditions that produce freezing rain have been studied previously and are fairly well understood (e.g., Bernstein et al. 1998; Cortinas 2000). Freezing rain usually results from a layer of warm (T . 08C) air overriding a shallow layer of cold (T , 08C) air with subfreezing temperatures at the surface. Typically, snow falls into the warm layer of air and melts. When the melted snowflakes fall through the layer of subfreezing air just above the surface, they do not refreeze, but rather become supercooled. The drops freeze upon contact at the surface. The depth of the cold layer is critical in determining the precipitation type observed at the surface. If the depth of the cold layer is sufficiently deep, that is, .400 m, the supercooled drops may refreeze to become ice pellets (Zerr 1997; Cortinas 2000). Corresponding author address: Dr. John Marwitz, Dept. of Atmospheric Science, University of Wyoming, Laramie, WY 82071. E-mail: [email protected]

q 2002 American Meteorological Society

It is uncertain whether the effects of diabatic cooling from melting are sufficient to significantly modify the thermodynamics and kinematics of a winter storm when it occurs over homogeneous terrain. A case (12 Feb 1992) will be diagnosed and examined in terms of its thermodynamics and kinematic structure. This case was chosen because it occurred over the relatively homogeneous terrain of northern Kansas and western Missouri during the Stormscale Operational and Research Meteorology-Fronts Experiment Systems Test (STORM-FEST), was an especially well documented freezing rain event because of the enhanced observing network, and it produced a narrow band of snow with a maximum depth of 20 cm (Fig. 1). There was a large region of freezing rain along the south side of the snowband. The locations of many of the observing systems during STORM-FEST are also illustrated in this figure. The track of the surface low pressure system over a 12h period is shown across northern Oklahoma. A warm front extended from the low toward the east as the low moved eastward at ;10 m s 21 . The heaviest precipitation in this winter storm, as well as many other winter storms in the central United States, occurred along the snow–freezing rain interface. When there is a topographic feature such as a mountain barrier (Marwitz and Toth 1992) or a large lake like Lake Erie

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WEATHER AND FORECASTING

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FIG. 1. Map of STORM-FEST observing systems, with locations of surface observations (dots) and track of surface low on 12 Feb 1992. Triangles (D) are locations of rawinsonde sites, crosses (3) are locations of CP-3 and CP-4 radars, and wide solid lines are flight tracks of the aircraft. Total snowfall (cm) where hatched areas represent snowfall of 8–12 cm. Dashed line represents area reporting freezing rain.

(Martner et al. 1993), it is easy to show that the topographic feature can act to focus the heaviest precipitation parallel to the topographic feature. One question this paper will attempt to answer is the following: Why does the heaviest snowfall typically occur along the snow–freezing rain (SN–FZRA) interface? The warmest thermodynamic soundings in a winter storm that results in surface snowfall are along the SN– FZRA interface. They contain the highest precipitatable water and, therefore, can produce the heaviest snow. These soundings are also typically the most thermodynamically unstable and, therefore, will allow convectively enhanced snowfall rates. Thermodynamic instability requires a trigger mechanism to initiate its release. Although upper-level divergence is normally associated with winter storms, one cannot argue a priori that the strongest upper-level divergence will occur directly over the SN–FZRA interface and, therefore, upper-level divergence is not the explanation. Is there a mechanism associated with the diabatic process of melting that can act to focus the release of thermodynamic instability over the SN–FZRA interface? This paper will investigate and describe the detailed kinematic and thermodynamic structure of the SN– FZRA interface region that produces the heaviest snow and freezing rain. In particular, four aspects of the storm were investigated: the temporal evolution of the lowlevel jet (LLJ), the vertical stability of the various layers, the development of isothermal layers, and the dynamical effects resulting from melting. The logical order of this article is as follows. A literature review of melting effects and the SN–FZRA interface are presented in section 2. Section 3 consists of a description of the STORM-FEST domain and observing networks, as well as the data collected by the

FIG. 2. Observed isothermal layers near 08C (from Findeison 1940). The numbers at the top of each sounding are the day, month, and year.

network. The analysis procedures are also described in this section. The synoptic overview of the storm and the thermodynamic, radar, and aircraft analyses are described and discussed in section 4. Section 5 contains a description of the temporal evolution of the LLJ. Section 6 contains a summary of the results. Finally, section 7 describes the applicability of these results to forecasting. 2. Literature review a. The effects of melting Freezing rain is a phenomenon that most often occurs when a layer of subfreezing air at the surface is overridden by warm moist air aloft. When precipitation occurs in this area, the snowflakes fall into this warm (T . 08C) air and melt, causing cooling in the melting layer. This process sets the stage for the formation of 08C isothermal layers. Findeison (1940) provided early documentation of 08C isothermal layers and presented these layers on a thermodynamic diagram (Fig. 2). He asserted that these layers were formed by diabatic cooling through the removal of the latent heat of fusion from the air by melting snowflakes. Wexler et al. (1954) examined an East Coast storm over the Boston area and observed significant surface cooling, the eventual change of rain to snow, and that the area of phase change coincided with the area of heaviest precipitation. The authors concluded that diabatic cooling occurred because of melting snowflakes,

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which created an unstable lapse rate below the 08C isothermal layer, thus resulting in overturning and allowing the cold air to be transported toward the surface. This conclusion was supported by the observation that a radar bright band that was initially over the radar descended from approximately 0.2 km to the surface and became undetectable. The precipitation at this station also changed from rain to heavy snow. Evaporation was eliminated as a possible cause for cooling because the temperature fell below previous dewpoints. Atlas et al. (1969) modeled the effects of diabatic cooling by melting and concluded that a significant pressure perturbation would form beneath the melting layer. The authors showed that mesoscale wind perturbations are correlated with variations in precipitation rates. An area of peak precipitation results in an area of peak cooling because of melting snowflakes and thus creates a local high pressure center. Winds in the vicinity of this local high pressure adjust and flow outward from the area of melting if this melting is short lived. The perturbation flow becomes tangential about the melting area if there is enough time for the Coriolis force to act. These perturbed wind vectors produce local minimum and maximum winds when added to the background winds and move approximately with the speed of the precipitation band. Atlas et al. (1969) created a theoretical model relating the mass of melted snow, the pressure perturbation, and the depth of the 08C isothermal layer. The model was compared to the observed velocity azimuth display (VAD) radar analysis of a case in which melting occurred and the observations roughly agreed with the model results. Pace (1980) modeled the diabatic cooling rate caused by melting and evaporation and discussed the effect that melting had on the evolution and depth of 08C isothermal layers. Using this model he showed that significant isothermal layers could develop by melting a small amount of ice. These layers can also form fairly quickly. For example, a 100-m-deep layer can be formed from ;0.1 mm of water. At a precipitation rate of 1 mm h 21 the layer will form in approximately 6 min. Pace also investigated the effects of variations in the initial lapse rate, pressure, and the degree of saturation of the atmosphere. He found that the depths of isothermal layers significantly depend on the initial lapse rate and degree of saturation of the atmosphere, while pressure did not have much effect on the depth of isothermal layers. His results showed that the depth of an isothermal layer would be smaller when the initial lapse rate is greater for a given amount of melted snow. His results also showed that in unsaturated conditions the combined effects of melting and evaporation due to the removal of latent heat from the atmosphere can be substantial, producing deeper isothermal layers than would occur under saturated conditions. Most isothermal layers are limited to a depth of approximately 200–300 m in the atmosphere because dissipative forces, such as embedded convection, act to

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inhibit layer development (Pace 1980). Moore and Stewart (1985) discussed feedback mechanisms that prevent isothermal layers from becoming very deep and maintain a quasi-steady state. As an isothermal layer increases in depth, the lapse rate just below this layer becomes unstable and creates convection, which acts to reduce the depth of the layer. When the depth of an isothermal layer decreases, air beneath this layer becomes more stable and reduces convection, allowing the layer to deepen. Likewise, changes in convection will be counteracted by changes in isothermal layer depth in order to maintain a balance. However, Stewart (1984) observed 08C isothermal layers with depths up to 1 km within two different precipitation bands over southern Ontario. The reason for these unusually deep isothermal layers was likely from evaporative effects as each of the soundings taken from the precipitation bands showed subsaturated conditions in the lower levels. Szeto et al. (1988b) created a model to simulate the formation of 08C isothermal layers and showed that at a prescribed precipitation rate of 1 mm h 21 and an initial lapse rate of 68C km 21 , a 1.5-km-deep isothermal layer could be formed in 100 min. The authors attribute warm air advection at levels above the initial melting level and low-level cold air advection beneath the melting level to the production of deep isothermal layers near 08C. b. The rain–freezing rain–snow interface Stewart and colleagues began an extensive series of field studies and numerical simulations of the SN–FZRA interface in southeastern Canada in the 1980s (e.g., Stewart 1984, 1992; Stewart and King 1987; Stewart and McFarquhar 1987). Also, particularly notable papers in that series were Szeto et al. (1988a,b). The model developed by Szeto et al. (1988a) was used to investigate the dynamic effects of cooling from melting snow in relation to the SN–FZRA interface. Initial conditions in the model consisted of an existing temperature gradient and uniform precipitation rate. Szeto et al. (1988b) concluded based on a simple twodimensional model that melting in the vicinity of an SN–FZRA interface produces a thermally indirect circulation that could lead to further intensification of precipitation near the SN–FZRA interface. The thermally indirect mesoscale circulation resulted from diabatic cooling caused by melting. Descending air occurred on the rain (warm) side of the SN–FZRA interface and ascending air occurred on the snow (cold) side of the SN–FZRA interface. An instrumented aircraft and Doppler radar documented two freezing rain events that occurred near Kansas City, Missouri, and a preliminary algorithm for detecting freezing rain was developed (Prater and Borho 1992). Two features were recognized in these events: a bright band in the melting layer and a distinct top of the veering wind layer. The top of the veering wind layer was assumed to be the top of the warm frontal

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FIG. 3. Timeline of dataset used in this study for 12 Feb 1992.

layer, that is, the level of maximum temperature. These two features along with the surface temperature were incorporated to produce a preliminary algorithm for detecting freezing rain. If the following conditions are present, 1) surface temperature is below 08C, 2) there is a bright band present, and 3) the top of the veering wind layer is above the bright band, then a freezing rain warning is issued. Thomas and Marwitz (1995) identified several features associated with freezing rain events including the storm presented herein, 12 February 1992. This case will be discussed in detail in a later section. The authors noted five distinct layers associated with freezing rain soundings: (a) an ice cloud layer (cloud top to melting level), (b) a melting layer (melting level to height of maximum temperature Tmx ), (c) a warm frontal layer [Tmx to top of the convective boundary layer (CBL)], (d) a convective cloud layer (top of CBL to cloud base), and (e) a subcloud layer (cloud base to the surface). More recently, Szeto et al. (1999) modeled a severe ice storm, which affected the east coast of Canada, with a hierarchy of cloud-resolving model simulations. The authors conclude that an intensification of cross-frontal circulation because of changing surface characteristics from ocean to land leads to the development of an extensive above-freezing layer in the model storm. Depending on the depth of the subfreezing surface layer, surface precipitation may be observed as ice pellets (deep subfreezing layer) or freezing rain (shallow subfreezing layer). Potential instability and conditional symmetric instability were likely responsible for the observed banded precipitation in the model storm. 3. Data and data analysis a. STORM-FEST analysis area The data used in this research were collected during the STORM-FEST field project (Szoke et al. 1994). This

project was coordinated and funded by several agencies. The field project focused on studying the dynamics and structure of fronts associated with winter storms and the resulting precipitation over the central United States. STORM-FEST was operational from 1 February through 15 March 1992. The study area of STORMFEST covered several states in the central United States with most of the focus on Kansas, Missouri and Oklahoma. This study area can be seen in Fig. 1. Many facilities were used in the STORM-FEST domain including five research aircraft, six Doppler radars complementing eight National Weather Service (NWS) radars, numerous surface observing networks, as well as supplemental rawinsondes and rawinsonde sites. This extensive observing network provided an unparalleled dataset for mesoscale phenomena occurring in this region during winter storm events. A 4-h timeline of the data systems used in this case study is shown in Fig. 3. The Wyoming King Air landed at 0709 UTC and, therefore, does not appear in Fig. 3. b. Upper air data The National Center for Atmospheric Research (NCAR) and National Severe Storms Laboratory deployed 12 special fixed Cross-chain Linked Atmospheric Sounding System stations to supplement the NWS soundings. Soundings were taken at 3-h intervals during the period of this research and consisted of 10-mb vertical resolution of temperature, pressure, wind speed, and direction and relative humidity up to 100 mb. Dropsondes from the NCAR King Air were used to add to the sampling of data, consisting of 10-mb vertical resolution of temperature, pressure, wind speed, wind direction, and relative humidity. The Topeka, Kansas (TOP); Seneca, Kansas (62K); Omaha, Nebraska (OMA); and Arkansas City, Kansas (AKZ), soundings were of particular interest in this

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FIG. 4. Location and unit of resolution map for observing systems used in this study. The dual-Doppler lobes are drawn at 308 crossing angles.

study because of their location relative to the observed SN–FZRA band. The NCAR King Air dropsondes also provided useful data along its flight track as key data were obtained north and south of the SN–FZRA band. c. Aircraft data Data collected by the NCAR King Air and Wyoming King Air were used in this research. Figure 4 shows a plan view of the flight path flown by the NCAR King Air and the descent sounding made by the Wyoming King Air. The data from the NCAR King Air were plotted as 20-s averages and those from the Wyoming King Air as 10-s averages. Temperature, equivalent potential temperature, components of the wind, wind speed, wind direction, and turbulence were used. Both aircraft were based at Richards-Gebaur Air Force Base (GVW), which is located about 30 km south of Kansas City, Missouri. The Wyoming King Air descent sounding to

GVW was the only portion of that dataset used. The NCAR King Air flew back and forth over the same track at 1.0-km intervals in the vertical below 5.5 km between approximately 0255 and 0541 UTC. The legs were through the SN–FZRA band. Two dropsondes were released during the 4.5-km leg. Table 1 shows the units of resolution for the observing systems utilized in this case study. The lobes used in the dual-Doppler analysis are located SE and NW of the radar baseline. The spatial locations of the observing systems within the study area can be seen in Fig. 4. d. Single-Doppler radar data Several ground-based radars were operated during the STORM-FEST project but only two were used in this research—the two NCAR mobile research Doppler radars: CP-3 and CP-4. These radars are C band (5-cm wavelength). Both radars operated on a pulse repetition

TABLE 1. Units of resolution for instruments. Instrument

Shape

NCAR King Air UW King Air Dropsonde Radiosonde VVP technique BVP technique Dual-Doppler Bin volume at 7 km

Horizontal line Horizontal line Vertical line Vertical line Disk Slab Square block Disk

Horizontal, vertical, and temporal resolution 2100 m, 1 mb, 1 s 2100 m, 1 mb, 1 s —, 10 mb, — —, 10 mb, — 26-km radii, 50 m, — x9 5 6 km, y9 5 640 km, 200 m, — x9 5 4 km, y9 5 4 km, 400 m, — diameter 5 100 m, range 5 150 m

Cycle time 2.5 h 17 min — 3h 5 min 5 min — —

Volume (km 3 ) — — — — 106 96 6.4 0.000 015

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frequency of 1080 s 21 leading to a maximum unambiguous range of 138 km and Nyquist velocity of 14.8 m s 21 . The primary variables that were retrieved were radar reflectively and horizontal velocity. These radars were positioned in northeast Kansas, which was an ideal location for dual-Doppler analysis. Note from Fig. 1 that CP-4 was located at the northern edge of the snowband and CP-3 was located near the SN–FZRA interface. Note from Fig. 3 that CP-4 was down from 0352 to 0512 UTC because of the freezing rain. The Doppler velocity data were unfolded using the radar editing software package SOLO (Oye et al. 1995). 1) VVP

SINGLE-DOPPLER RADAR ANALYSIS TECHNIQUE

The first analysis technique applied to the unfolded radar volume scans was done using the volume velocity processing technique (VVP; Waldteufel and Corbin 1979). The major advantage of the VVP technique is that it utilizes all the Doppler data within a cylinder centered over the radar. The VVP, therefore, provides results from a single volume scan for units of resolution, which are invariant with height rather than altitude-dependent units of resolution as with the VAD. The VVP unit of resolution is a disk centered on the radar, which is 6 km in radius and 50 m in vertical thickness. This results in a sample volume of 106 km 3 . Time—height cross sections may be obtained by compositing VVP results, assuming steady-state conditions. The main assumption in the VVP technique is spatial linearity of the wind field. Waldteufel and Corbin (1979) noted that errors in this technique occur more from irregularities in the wind field than from random errors in the velocity data. Error analysis shows that fall speed and its vertical gradients can be retrieved with high confidence but are sensitive to irregularities in the velocity field and, therefore, should not be used. A small analysis radius helps to reduce errors from nonlinearities with large spatial scales while a larger analysis radius smoothes the effects of inconsistencies because of small-scale nonlinearities. An intermediate analysis radius should be chosen to minimize both of these problems. Nonetheless, an accurate vertical wind profile can be obtained and displayed as a hodograph by the VVP technique. 2) BVP

SINGLE-DOPPLER RADAR ANALYSIS TECHNIQUE

The other single-Doppler analysis technique applied to the unfolded radar data was the band velocity processing technique (BVP; Johnston et al. 1990). This technique is very useful and an excellent complement to the VVP technique because it offers a finer scale of resolution, thus providing a more accurate and complete structure of the kinematics in the storm. BVP also avoids the limitation of nonlinear attributes and produces x–z

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cross sections from just one volume scan reducing the limitation of the steady-state assumption. The BVP technique is based on the assumption that the kinematics of the airflow is two-dimensional. This assumption is required in order to minimize the vorticity contamination by the y component of the winds. The two-dimensional assumption can be tested by comparing the cross-band divergence (]u/]x) to the along-band divergence (]y /]y). When ]u/]x k ]y /]y or when ]y /]y ; 0, then the two-dimensional assumption is valid. When this condition is not valid, then the flow field is three-dimensional and this results in vorticity contamination of the u and y fields. The two-dimensional assumption is utilized by selecting a coordinate system transformation that is parallel to the precipitation band. Other assumptions made in BVP are time invariance and linearity of the wind field. The linearity and twodimensional assumptions are applied on the scale of the analysis slab rather than locally. These assumptions state that the alongband derivatives and the wind fields do not vary systematically from linearity. BVP uses a least squares technique applied to a seven-variable model1 in order to estimate the vertical profiles of the alongband averages of the various kinematic parameters. BVP does have some disadvantages such as bias and variance errors and BVP gives unreliable results over the radar in the ‘‘cone of silence’’ (Johnston et al. 1990). Bias errors occur because of the removal or neglect of some of the terms in the model and if there are irregularities in the wind field. However, accounting for the bias error, horizontal velocities are accurate to 1.0 m s21, horizontal derivatives to 10 24 s 21 , and the vertical shears are accurate to 10 23 s 21 . Variance errors occur because of ambiguities in the data or improper data editing and these errors are usually small compared to the nonlinearities in the wind field. e. Coordinate system transformation The conventional Cartesian coordinate system (x, y, z), for the purposes of this study, will be transformed into x9, y9, and pressure altitude. The purpose of this coordinate transformation is to utilize the two-dimensionality of the ‘‘banded like’’ structure that was observed in this storm. The 0543 UTC full-volume plan position indicator (PPI) scan of reflectivity at the 0.48 elevation angle is shown in Fig. 5. Note the bandedlike structure oriented along ;1008 in the plot. The movement of the band was examined using several PPI and sectors scans and found to be stationary. This band was the primary reason the NCAR King Air flew through this region and CP-3 and CP-4 performed sector scans through this region. It will be shown later that the northern edge of this band is the SN–FZRA interface. The transformed coordinate system is centered over 1 The seven variables are u, y , ]y /]x 1 ]u/]y, ]u/]x, ]y /]y, ]u/]z, and ]y /]z (from Johnson et al. 1990).

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FIG. 5. The 0.48 elevation PPI of reflectivity (dBZ ) for CP-3 at 0543 UTC on 12 Feb 1992. The grayscale was adjusted to enhance the SN–FZRA–RA band oriented along 1008 azimuth. The minimum detectable reflectivity was attenuated to about 25 dBZ.

the CP-3 radar with the x9 axis oriented toward the warm air (1908) and perpendicular to the SN–FZRA interface and the y9 axis parallel to the band (1008) and along the wind shear vector. This transformed coordinate system will be used for all remaining analyses and presentations. The vertical coordinate will be pressure altitude

in order to utilize the aircraft data more easily. The pressure altitude is related to geometric altitude above the ground and to mean sea level through the hypsometric equation. Since the soundings are near the International Civil Aviation Organization Standard Atmosphere, the difference between pressure altitude and geometric altitude above sea level was ,50 m. 4. Analysis of 12 February 1992 winter storm a. Synoptic overview of the winter storm

FIG. 6. Surface chart for 0600 UTC 12 Feb 1992. Solid lines represent pressure in mb. Dashed lines represent temperature in 8C. The surface low, warm and cold front, and 08C isotherm are highlighted. Small circles are NWS surface stations.

This winter storm is particularly interesting in that heavy snowfall accumulations (20-cm maximum) occurred across most of northern Kansas and into Missouri. The heavy snowfall was about 400 km north of the surface low located in central Oklahoma. Figure 6 shows the location of the weak surface low at 0600 UTC with the associated fronts and contours of isotherms and isobars. A warm front extended east-northeast from the low pressure center with southerly winds flowing behind it. A cold front extended southward from the low center and wrapped back to the west through the panhandle of Texas with northerly winds behind it. The fronts were analyzed using pressures, temperatures, and wind data from NWS surface stations. A north–south-oriented temperature gradient was observed across eastern Kansas. The 08C isotherm was located across central Mis-

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TABLE 2. Various locations within the study area reporting FZRA, PE, or neither (2). Time (UTC)

0200

0300

0400

0500

0600

0700

0800

0900

Garden City, KS Dodge City, KS Salina, KS Manhattan, KS Topeka, KS Kansas City, KS Warrensburg, KS

FZRA FZRA PE PE — — —

— FZRA FZRA — PE — —

FZRA FZRA FZRA PE PE FZRA–PE —

FZRA FZRA — PE PE FZRA PE

— FZRA FZRA — PE FZRA–PE FZRA–PE

— — — — FZRA FZRA–PE FZRA–PE

— — FZRA — FZRA — FZRA–PE

— — FZRA — FZRA — FZRA–PE

souri and extended into Kansas and dipped south into the Oklahoma panhandle. The low pressure system moved slowly (;10 m s 21 ) toward the east from near the Oklahoma panhandle at 0000 UTC to the Missouri– Arkansas border by 1200 UTC (Fig. 1). An analysis of the upper-level dynamics indicated that the upper-level support for this storm was very weak. There was no significant upper-level jet core in the area, for example. The extended period of overrunning warm air aloft over the cold subfreezing surface air resulted in this storm. It will be shown later that the precipitation rate was ,2 mm h 21 , which is consistent with a dynamically weak storm. Several stations south of the snowband in central and southwestern Kansas and westcentral Missouri reported FZRA and/or ice pellets (PE). Table 2 shows a sample of stations that reported FZRA and/or PE and the time they occurred. All of the stations experienced at least one period of time where freezing rain or ice pellets fell in consecutive hours with TOP observing seven continuous hours of FZRA and/or PE. b. Vertical instability Figure 7a2 shows the vertical profile of temperature, equivalent potential temperature (Qe ), and turbulence as measured by the Wyoming King Air during its final descent into GVW. The turbulence is based on a Meteorological Research, Inc. (MRI) indicated turbulence meter (MacCready 1964) and the parameter is the cube root of the eddy dissipation rate. The first important feature to note from this sounding is the presence of the CBL. The CBL consists of a convective cloud layer and a subcloud layer and extends from the surface up to ;0.7 km. The top of the CBL is marked by the minimum temperature (Tmn 5 22.98C). Further support for a CBL is the presence of a well-mixed boundary layer. Measurements of equivalent potential temperature Qe show a nearly constant value of 284 K up to ;0.7 km, the same height as Tmn . Turbulence is also shown in this figure. The highest values of turbulence are seen closest to the surface up to the top of the CBL. Above the CBL, the turbulence values are quite small compared to those 2 Figure 7 and the following discussion were adapted and derived from Thomas and Marwitz (1995). The figure and discussion are presented herein because of their direct relevance and because the original reference is rather obscure.

near the surface. An LLJ is also located at the top of the CBL (Fig. 7b). Maximum winds of.17 m s 21 are observed near 0.7 km. Strong wind shear is observed from the surface to the top of the CBL and beyond. The CBL is convectively unstable (]Qe /]z 5 0) from the sensible heat transfer because the surface was still warm from the previous warm days (T . 108C). The height of the low-level jet (Vmx ) and/or the height of the minimum temperature (Tmn ), henceforth, will identify the top of the CBL in other soundings. The layer above the CBL and extending up to the level of maximum temperature (Tmx ) is the warm frontal layer (WFL). This layer displays a thermal inversion, as temperatures increase from Tmn (22.98C near 0.7 km) up to Tmx (1.68C near 1.3 km), where Tmx will identify the top of the WFL. Both Tmn and Tmx will identify the WFL in other soundings. It was not possible to uniquely identify the top of the WFL by its kinematic properties [as suggested by Prater and Broho (1992)] because there was significant warm air advection and hence vertical wind shear in the overrunning warm air. The thermodynamic stability of the WFL can be seen from the plot to increase rapidly with height. The final layer identified in this sounding is the overrunning cloud layer (OCL). This layer consists of the ice cloud layer and the upper part of the melting layer. Temperature decreases rapidly just above the top of the warm front because of diabatic cooling from melting. There may be convective instability near the bottom of a melting layer, if the sounding becomes convectively unstable from the diabatic cooling effects of melting. The fluctuating values of turbulence near the bottom of the overrunning layer and just beneath the melting layer may be indicative of this instability (Fig. 7a). These same layers can also be identified in the 0600 UTC TOP sounding (Fig. 8). The sounding was saturated throughout (Fig. 8a). The top of the CBL (Tmn 5 23.18C) is located at 920 mb (;0.8 km). The top of the WFL (Tmx 5 1.18C) is located at 880 mb (;1.3 km). A ;500-m deep 08C isothermal layer was present from 860 to 820 mb (1.3–1.8 km). Figure 8b shows a hodograph of the winds for this sounding. Strong veering occurred from the surface through the WFL. The lowlevel jet (Vmx ) was located at 920 mb (0.8 km). The top of the WFL (880 mb) was at the top of the strong veering. Winds through the isothermal layer were from the

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FIG. 8. (a) Topeka, KS (TOP), vertical sounding at 0600 UTC 12 Feb 1992 of temperature and dewpoint. (b) Same as in Fig. 7b except at 0600 UTC at TOP. Height is marked every 100 mb.

FIG. 7. (a) Vertical profile of temperature, equivalent potential temperature, and turbulence measured by the Wyoming King Air during its descent into Richards-Gebaur AFB. The 08C isotherm is marked by a vertical line for reference. [Adapted from Thomas and Marwitz (1995).] (b) Hodograph of winds measured by Wyoming King Air. The surface geostrophic wind at 0600 UTC is plotted as Vgo . Temperatures (8C) are enclosed by a circle. Height is marked every 300 m. [Adapted from Thomas and Marwitz (1995).]

southeast, indicating the flow of warm, moist air in this OCL. The vertical profiles of temperature and winds from one of the NCAR King Air dropsondes (0342 UTC) are shown in Fig. 9. This dropsonde was made near the southern edge of the SN–FZRA band. The sounding was saturated from the surface through the top of the sounding. The top of the CBL (Tmn 5 23.18C) is located at

920 mb (;0.8 km). The top of the WFL (Tmx 5 2.78C) occurs at 860 mb (;1.3 km). Melting occurred in the bottom of the overruning cloud layer and is evident by the presence of the near 08C isothermal layer between 800 and 820 mb. The temperature profile above 750 mb is parallel to the ice-bulb potential temperature (Qi ).3 The low-level jet (V 5 20 m s 21 ) was at the top of the CBL (Fig. 9b). The top of the WFL corresponded to the top of the strong veering winds. The dynamic instability within various layers can be examined using an approximate form of the gradient Richardson number:4 Ri ; g/Qe 3 (]Qe /]z)/(]V/]z) 2 . 3 For soundings through typical snowbands, the lapse rate of Qe compared to the lapse rate of Qi from 800 to 500 mb is about 18C less. 4 This form of the gradient Richardson number is a good approximation when the saturated static stability is large, as in this case (Durran and Klemp 1982).

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FIG. 9. (a) Same as in Fig. 8a except at 0342 UTC dropsonde. The triangle just below 700 mb and 08C is the calculated amount of diabatic cooling by melting. (b) Same as in Fig. 8b except at 0342 UTC dropsonde.

The WFL was examined for dynamic instability (Ri , 0.25) because of the strong vertical windshear. Although inversion layers are very stable, when there is strong vertical wind shear, these layers can be dynamically unstable. The data from the Wyoming King Air were analyzed for the descent sounding from 0.85 down to 0.75 km (Fig. 10). This layer is within the warm front where the sounding is absolutely stable. One would normally expect to observe a very flat field of Qe , which increases rapidly in the vertical. The thin solid line is the track of the aircraft. The Qe structure displays a significant vertical displacement. Since the calculated Richardson number from 0.85 to 0.75 km was ;0.5, it is logical to conclude that these data indicate that a shear-induced gravity wave was present. The pilot had a very difficult time flying on the glide slope because of the odd wind shear profile and because of the varying

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updraft structure associated with the shear-induced gravity wave. The amplitude and wavelength of the vertical variation was ;80 m and 4 km, respectively. A shearinduced gravity wave was also observed within the WFL of a freezing rain case in Oklahoma (Damiana and Marwitz 1995). The geostrophic wind based on the surface pressure gradient (Vgo ) over northeast Kansas was calculated from the pressure gradient of altimeter settings on the 0600 UTC surface map (not shown). The altimeter settings where calculated for all the Automated Weather Observation System, Automated Surface Observing System, Portable Automated Mesonet, and NWS stations. The value5 of Vgo was ;1158 at 19.5 m s 21 . Given the 600-m well-mixed CBL shown in Fig. 8a, the geostrophic wind varies ,1 m s 21 within this layer.6 The value of Vgo was, therefore, plotted on each of the hodographs (Figs. 7b, 8b, and 9b) and compared to the value of Vmx . In each case the value of Vgo was about the same as Vmx indicating that the winds in the lowlevel jet were quasigeostrophic. The strong veering of the winds with height within the CBL was caused by surface friction. The turning of the winds toward the south caused the surface winds in the CBL to flow across the isotherms producing the observed cold air advection near the surface. The observed winds above the CBL and within the WFL veered with height indicating warm air advection and/or ascending motion. The thermodynamic instability of the OCL above the SN–FZRA band was examined using cross sections through the band (Fig. 11). The cross sections were based on the 0600 UTC soundings from TOP and 62K. Temperature and wet-bulb potential temperature (Qw ) are shown in Fig. 11a. The locations of the top of the WFL and the top of the CBL are indicated. The most significant feature in this cross section is the double folding of the 08C isotherm. This folding of the 08C isotherm is the primary reason for the observed freezing rain at many locations just south of the heavy snowband. The isotherms kink near 910 mb (the top of the CBL) and near 840 mb (the top of the WFL). Cold air advection occurs near the surface with northeasterly winds in the CBL and warm air advection occurs in the WFL with southerly wind flowing up the warm front. The southerly winds brought warmer moist air into the region, thus, setting up the scenario for freezing rain. The Qw is also plotted to diagnose the convective instability (CI) and conditional symmetric instability (CSI) of the 5 This value of Vgo is significantly greater than the Vgo one derives from the gradient of sea level pressure shown in Fig. 6. The advantages of using altimeter settings is that more surface stations can be utilized to compute altimeter settings than can be used to compute surface sea level pressure and the gradient of altimeter settings provides a much truer estimate of the pressure gradient force. 6 Given the north–south thermal gradient and pressure gradient near GVW (Fig. 6) and an adiabatic atmosphere, the vertical change in the geostrophic wind for a 1-km well-mixed boundary layer is ,1 m s 21 .

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FIG. 10. Cross section along x9 of Qe (solid lines, K) from Wyoming King Air data. Note the shear-induced gravity wave with an amplitude of ;80 m and wavelength of ;4 km. The dashed line represents temperature (8C). The light solid line represents the Wyoming King Air flight track.

system (Schultz and Schumacher 1999). If ]Qw /]z , 0, then the air within that layer is convectively unstable and may give rise to upright vertical convection. The atmosphere is absolutely stable with respect to CI. CSI is another possible mechanism of releasing thermodynamic instability. CSI is diagnosed by following along an angular momentum surface (M). If Qw decreases along an M surface, then there is CSI and slantwise convection will occur (assuming saturation, of course). An examination of CSI with respect to water (CSIw ) revealed absolute stability conditions. Figure 11b presents a similar cross section of icebulb potential temperature (Qi ), M surfaces, and the y 9 component of the winds. Since Qi increased with height (]Qi /]z . 0), the layer was also absolutely stable in terms of convective instability with respect to ice (CIi ). CSI with respect to ice (CSIi ) revealed that CSIi was stable below 760 mb but was slightly unstable above this level. It appears that the weak banded-like structure of the SN–FZRA band was likely a result of CSIi and not CSIw . c. VVP single-Doppler analysis A series of CP-3 volume scans were analyzed using the VVP software. The top of the cylinder volume was 5 km above ground level. Hodographs derived from the software are presented at hourly intervals from 0353 to 0852 UTC in Fig. 12. The hodographs show a very smooth and continuous representation and evolution of the wind structure in the vicinity of the radar. The height of the LLJ and, hence, the top of the CBL, was ;0.8 km. Note the strong veering of the winds throughout all

FIG. 11. (a) Vertical cross section along x9 of temperature (solid, 8C) and wet-bulb potential temperature (dashed, 8C) from 62K to TOP. The heavy dashed lines represent the top of the CBL and the top of the WFL. (b) Same as in (a) except ice-bulb potential temperature (solid, 8C), angular momentum (dashed, m s 21 ), and y 9 component of the winds (heavy dashed, m s 21 ).

of the hodographs. The veering below the LLJ is indicative of surface friction in the CBL. Strong veering above the LLJ occurs within the WFL whose top is near the level with light (,5 m s 21 ) winds that occurred between 2 and 3 km. The direction of the mean wind shear through the WFL is approximately 1008 corresponding to the orientation of the observed snowband. Time–height plots (Fig. 13) of (a) reflectivity, (b) wind speed, (c) wind direction, (d) u9 component, and (e) y 9 component are presented. Figure 13a shows how the reflectivity field evolved during the 6-h period from 0300 to 0900 UTC. A bright band became detectable at 0400 UTC. The precipitation falling prior to this time

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FIG. 12. Wind hodographs derived from the VVP software from 0400 to 0900 UTC 12 Feb 1992. Each hour is offset along x9 (1908) and 15 m s 21 .

was snow but when the bright band appeared, the surface temperature was observed to be subfreezing and, thereafter, freezing rain was inferred to be the dominant precipitation type. This bright band occurred at approximately 1.3 km, intensified over the next 2 h to a maximum value of 34 dBZ, and descended ;200 m during this time. The 200-m descent of the bright band was caused by the diabatic melting process. By 0700 UTC, the reflectivity values began to decrease at all levels and over the next 2 h the level where the maximum reflectivity occurred ascended back to the original level of 1.3 km. Based upon the reflectivity profile, it appears that the freezing rain changed back to snow by 0800 UTC. Applying the Marshall–Palmer Z–R relationship (Rogers and Yau 1989) to the reflectivity beneath the bright band, the precipitation rate during the freezing rain was calculated to be 1.3–1.5 mm h 21 . An analysis of the wind speed field (Fig. 13b) indicates strong low-level winds over the entire period with an LLJ becoming established between 0.7 and 0.9 km at 0400 UTC. This jet intensified over the next 2 h, with a maximum wind speed of .20 m s 21 , and then weak-

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ened to 17 m s 21 by 0900 UTC. Note from Fig. 3 that there were no full volume scans for either radar at 0530 UTC. It is important to note that this jet intensified during the period of heaviest precipitation (0400–0600 UTC) as indicated in the reflectivity plot. It is also interesting that at 0300 UTC there was a deep layer of moderate winds (.12 m s 21 ) and at 0600 UTC the depth of the strong winds (.20 m s 21 ) was only ;100 m. Figure 13c is a plot of wind direction. The winds within the dashed line were nearly constant in direction (,88 change). The strongest veering is present within the lowest kilometer, with winds above this level nearly constant in direction. Note how the depth of the veering layer decreased with time. The LLJ between 0500 and 0600 UTC was from the east at ;1108. Warm air advection occurs above the CBL in the WFL and also well into the OCL. Figure 13d is a plot of the u9 component of the winds (cross band). Note the presence of a strong shear layer between 0.5 and 0.9 km. The winds in the CBL (below 0.7 km) have a northerly component (positive u9). This again is a reflection of the influence of frictional effects in the CBL. The winds above the CBL (above 0.7 km) have a southerly component and this is consistent with the fact that warm, southerly air ascended along the warm front. Winds near the 1.8-km level gradually decrease with time from 210 to 4 m s 21 . Figure 13e is a plot of the y 9 component of the winds (alongband). The most prominent feature is the presence of the low-level jet from the east (negative y 9) and located near 0.8 km, as verified by the previous wind direction plot. Also consistent with previous plots is the establishment of the LLJ around 0400 UTC with its maximum winds occurring between 0500 and 0600 UTC. Note that the winds throughout the entire 6-h period have an easterly component up to 2.3 km. d. BVP single-Doppler analysis The CP-3 data were also analyzed using the BVP single-Doppler technique. The dimensions of each analysis slab were set to 6 km in the x9 direction, 640 km in the y9 direction, and 0.2 km in the vertical (Fig. 4). Figure 14 presents cross sections of the BVP analysis for the 0552 UTC volume scan. Each dot represents an analysis slab from which valid kinematic data were obtained. The reflectivity profile (Fig. 14a) shows the presence of a bright band at ;1.2 km extending from ;24 km south of the radar to ;12 km north of the radar. The bright band is confined to a shallow layer with maximum reflectivities slightly exceeding 32 dBZ. The bright band appears to descend slightly toward the surface 14 km north of the radar, representing the SN–FZRA interface and the northern extent of the 08C isotherm at 1.2 km. The region beneath the bright band corresponds to the region of freezing rain. The southern edge of the freezing rain was determined by the location of the 08C isotherm from the 0600 UTC surface map. The data between 1.5

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FIG. 13. (a) VVP time–height plot of reflectivity (dBZ ) at approximately hourly intervals from 0300 to 0900 UTC on 12 Feb 1992. The dashed line represents height of the bright band (BB). (b) Same as in (a) except for wind speed (m s 21 ). (c) Same in (a) except for wind direction (8). Above the dashed line, wind direction is almost constant. (d) Same as in (a) except for u9 component of the wind (m s 21 ). (e) Same as in (a) except y 9 component of the wind (m s 21 ).

and 2.5 km above the radar indicate that two ‘‘bands’’ may have been present. The northern band was centered ;10 km north of the radar and the southern band was centered ;15 km south of the radar. The two ‘‘snowbands’’ were about 25 km apart.

Figure 14b shows a plot of the wind speed with the LLJ at ;0.8 km with the southern edge over CP-3 and northern edge 14 km north of the radar. The maximum winds associated with the LLJ slightly exceed 18 m s21. The height of the LLJ marks the top of the CBL. The LLJ

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occurs within the strong low-level veering winds (Fig. 13c). Note the increased vertical wind shear above the LLJ and below 2.3 km. This may be a result of dynamical influences caused by diabatic cooling from melting. The u9 component of the winds is presented in Fig. 14c. The positive winds below 0.8 km are representative of winds with a northerly component while the negative winds have a southerly component. There is a strong wind shear in the lowest kilometer. The strong shear within the CBL (z , 0.8 km) is because of frictional effects. The arrow shows the motion of airflow from the south that ascends along the warm front advecting warm moist air. Figure 14d shows the y 9 component of the winds. The LLJ is distinct and over and north of the radar at ;0.8 km. e. Analysis of dual-Doppler data The dual-Doppler scans at 0348 and 0538 UTC were analyzed. The horizontal and vertical structure of the LLJ was not resolved by the resulting wind data. Consequently, results from the dual-Doppler analysis are not shown. The interpolation and smoothing used in the dual-Doppler analysis is assumed to have filtered out the finescale structure of the LLJ. It may be possible to tune the interpolation and smoothing procedure so as to resolve the finescale structure of the LLJ. f. Analysis of aircraft and dropsonde data The NCAR King Air data, dropsondes, and Wyoming King Air data were plotted in vertical cross sections along x9. Figure 15 shows cross sections of various parameters measured by the two aircraft and the two dropsondes. The thin solid lines represent the flight path of the aircraft. The CBL and WFL are displayed in all cross sections. The temperature profile (Fig. 15a) shows the folding of the 08C isotherm. A thermal inversion was present in the WFL. Temperatures above ;1.5 km are fairly uniform and decreasing with height. The Qe profile is shown in Fig. 15b. The 284-K contour is near the top of the CBL. Note the rapid increase with height of Qe within the WFL. In all locations Qe increases with height above the WFL and below 4 km indicating that the atmosphere is absolutely stable to upright moist convection. Note that there are two wavelike patterns along the 1-km leg between x9 5 20 and 250 km. These wavelike patterns correspond to the two bands that were indicated in Fig. 14a. Figure 15c shows the observed y 9 component of the winds measured by the aircraft. The y 9 component of the winds near the surface was fairly strong, about 10 m s 21 . The strongest y 9 component of the winds occurred in the bands at an attitude of ;0.8–1.0 km.

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5. Temporal evolution of the LLJ The temporal evolution of the LLJ as measured by a variety of STORM-FEST instruments is shown in Fig. 16. The various STORM-FEST instruments included the rawinsondes, the dropsondes, the NCAR King Air, the Wyoming King Air, and the CP-3 Doppler radar. Each of these instruments and analysis techniques has different units of resolution (Table 1). The heavy dashed line, thin dashed line, and solid line in Fig. 16 are the maximum individual bin values of Doppler velocity in the LLJ, the maximum velocities from the VVP technique, and maximum velocities from the BVP technique, respectively, as a function of time. The unit of resolution for the individual bin value technique is the bin volume of the radar. These radial velocities were corrected for hydrometeor fallspeeds and LLJ orientation. The bin volume at 7-km range where the 58 scan intercepted the LLJ was 150 m in range and 120 m in diameter. The VVP analysis technique consistently measured winds that were about 1 m s 21 greater than the BVP technique and, therefore, fell between the BVP and bin values. The peak wind speed values for the two analyzed dual-Doppler scans are also plotted in Fig. 16. The values are just slightly greater than the VVP values. Recall that the unit of resolution for the VVP technique was a disk centered over the radar, which was 50 m in vertical thickness and 26 km in radius. The unit of resolution for the BVP technique was a slab oriented parallel to the band with x9 5 6 km, y9 5 640 km, and z 5 0.2 km. The maximum winds observed by the aircraft and sondes are also plotted in Fig. 16. The unit of resolution for these instruments is much smaller than the radar techniques and it was strictly serendipitous that these measurements were made at the right time and location. The LLJ began developing in the vicinity of the CP3 radar after 0300 UTC. During the next 3 h the LLJ strengthened from 15 to 22 m s 21 . The peak precipitation rate of 2.7 mm h 21 (discussed later) occurred at 0600 UTC. By 0900 UTC the peak winds in the LLJ had decreased to ,18 m s 21 and the precipitation rate decreased to ,1 mm h 21 . The maximum jet core wind speeds measured by a variety of techniques were within 3 m s 21 of each other during the evolution and passage of this LLJ. The differences were systematic and functions of the location, shape, and size of the various units of resolution. 6. Summary of results a. Vertical stability CBLs are a common feature of freezing rain cases when there is significant sensible heat flux from the surface. Significant sensible heat flux will occur when subfreezing air flows over warm water or warm land. The Qe profile in this STORM-FEST case had a nearly constant value from the surface to ;0.7 km, represen-

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FIG. 14. (a) BVP cross section of reflectivity (dBZ ) at 0552 UTC 12 Feb 1992. The heavy dashed line represents the bright band. (b) Same as in (a) except for wind speed (m s 21 ). (c) Same as in (a) except for u9 component of the wind (m s 21 ). The heavy dashed arrow highlights the southerly flow of air. (d) Same as in (a) except for y 9 component of the wind (m s 21 ).

tative of a well-mixed CBL. The CBL consisted of both a subcloud layer in which there were no supercooled cloud droplets and a convective cloud layer, which contained both cloud droplets and raindrops. The turbulence profile showed high turbulence at the surface and decreased upward to the top of the CBL, consistent with strong downward turbulent momentum flux. A low-level jet was present at the top of the CBL and the core of the jet was located near the SN–FZRA interface. The minimum temperature (Tmn ) and the level at which the LLJ was observed (Vmx ) also marked the top of the CBL. The winds in the core of the LLJ are quasigeostrophic and can be estimated using the surface pressure gradient derived from altimeter setting data. This procedure is valid because the vertical variation of the geostrophic wind is ,1 m s 21 for a CBL whose vertical depth is ,1 km. Strong veering winds are present within the CBL because of surface frictional effects. Cold air ad-

vection was only present in the lowest 100–200 m of the CBL in this case. Otherwise, either warm air advection and/or ascending motion was occurring within the CBL. Shear-induced gravity waves are sometimes observed within the WFL confirming that dynamic instability is present within this layer. The identification of the WFL for this STORM-FEST case was also consistent across the observing platforms. Here, Tmn and Tmx bound the lower and upper boundaries of the WFL, respectively. Strong veering was present throughout the WFL. Some weak veering often continues in the OCL. The WFL is characterized by a thermal inversion for freezing rain cases; therefore, the layer is absolutely stable with respect to upright convection. However, because of the strong wind shear in this layer, dynamic instability (Ri , 1) may be present. The microphysical process in OCL associated with

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FIG. 15. (a) Vertical cross section of temperature (8C), using NCAR King Air data, Wyoming King Air data, and dropsonde data. The heavy dashed lines represent the boundaries of the CBL and the WFL. (b) Same as in (a) except for equivalent potential temperature (K). (c) Same as in (a) except for wind speed (m s 21 ).

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TABLE 3. Accumulated diabatic cooling across the bright band. x9 (km) 24 18 12 6 0 26 212

z (dBZ)

u9 (m s21 )

R (mm h21 )

25 26 26 27 27 29 30

27.0 27.5 28.2 29.0 29.0 28.2 28.0

1.35 1.54 1.54 1.80 1.80 2.40 2.73

Dt (h) 0.24 0.22 0.20 0.18 0.18 0.20 0.21 S 5 1.43

SR (mm) 0.32 0.66 0.97 1.29 1.62 2.10 2.67

dq qT (LR 2 c p Ry T ) 5 s 3 3 ( pgw). dt p (c p Ry T 2 1 q s L 2 )

FIG. 16. Subjectively hand-drawn analysis of the temporal evolution of the LLJ measured by various systems. Triangles represent the maximum Doppler velocity in a single bin from the 58 PPI scan (corrected for fallspeed and scan angle), small dots represent VVP, 3’s represent BVP, and squares represent dual-Doppler value.

SN–FZRA interfaces is primarily the ice process. Thermodynamic instability with respect to upright CI and slantwise CSI is often present in the OCL. The thermodynamic instability in the OCL is typically not properly evaluated because of the assumption of a water process. The CI and CSI must be evaluated with respect to ice and not water, as is typically done. A simple rule of thumb is that the ice process results in an additional 18C of buoyancy for a parcel that ascends from 800 to 500 mb. In this STORM-FEST case the CI with respect to water and ice was stable. The CSI with respect to water was neutrally stable but was unstable with respect to ice. Therefore, the snowband observed in this case appears to have been caused by the release of convective symmetric instability with respect to the ice process.

Therefore, the precipitation that fell during this storm was constant with the release of CSIi as the warm moist air ascended along M surfaces. The amount of melted equivalent precipitation that caused diabatic cooling by melting will be estimated using the radar data. Data shown in Table 3 are the BVP slab averages for reflectivity (dBZ) beneath the bright band and the u9 component of the winds (m s 21 ) within the bright band (Fig. 14). The reflectivity values were used in estimating the rainfall rate, R, using the Marshall–Palmer Z–R relationship (Rogers and Yau 1989). The u9 components of the winds are representative of values at each of the locations along x9 at the brightband level from Fig. 14c. The amount of time it takes a parcel to traverse the width of a BVP slab (6 km) is Dt. The total accumulated melted equivalent precipitation in millimeters (SR) is shown in the last column of the table. The total accumulated precipitation, ;2.7 mm, will produce an approximately 400-m-thick isothermal layer (Pace 1980). Using the method outlined by Pace, one can estimate the amount of diabatic cooling that occurs because of melting. The amount of diabatic cooling that resulted from melting in this case is represented as the triangle just below 700 mb in the 0342 UTC dropsonde (Fig. 9a).

b. Development of isothermal layers by melting The development of isothermal layers by melting is evident in this case study. These layers develop as snowflakes fall into the melting layer. The melting process removes sensible heat from the environment, which in turn causes the temperature in the layer to decrease toward 08C. The estimated precipitation rate based on ascent along the angular momentum surfaces (M) displayed in Fig. 11b and using the observed horizontal wind speed (5 m s 21 ), provided enough lift (w 5 0.3 m s 21 ) and, hence, condensation supply rate to produce the estimated precipitation rate. Assuming the condensation supply rate is equal to the precipitation rate, the precipitation rate was calculated to be 1.5 mm h 21 . The condensation supply rate was estimated using Eq. (9.11) from Haltiner (1971):

c. Dynamical effects caused by melting Melting can have significant effects on the thermodynamic structure of the atmosphere as well as creating changes in the winds. Atlas et al. (1969) have documented some dynamic effects caused by melting. When the 08C isotherm is folded, as was observed in this STORM-FEST case, precipitation falling as snow encounters the melting layer, producing diabatic cooled air because of the extraction of latent heat of melting. The diabatic cooling is accumulated across the SN–FZRA7 band within the bright band or melting layer. Winds in 7 When there is no freezing rain, either because the folded 08C isotherm at the surface in Fig. 17 extends all the way to the snowline or because there is no thermal inversion in the WFL, the snow–rain interface is similar to the SN–FZRA interface.

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FIG. 17. Schematic showing the dynamical effects caused by melting from diabatic cooling.

this melting layer are from the southeast. The simplest explanation of the dynamical effects caused by melting is that the increased thermal gradient across the SN– FZRA band results in increased vertical wind shear via the thermal wind equation. The thermal wind equation assumes geostrophic balance. A more complicated explanation is fundamentally the same but is the geostrophic adjustment process. When this diabatic cooling occurs, the air contracts and thus creates a series of dynamic responses (Fig. 17). The initial response to this cooling and contracting is subsidence of the air above where the cooling occurred. This initial response does not change the mass of air in the vertical column and, hence, results in no change in surface pressure above the interface. Air above this region where melting occurred flows into the region to replace the air that subsided. This influx of air into the subsided region results in more mass and, hence, a positive pressure perturbation beneath the bright band, that is, below the melting level.8 The positive pressure perturbation results in both a thermally direct secondary circulation in the warm air south of the interface and a thermally indirect secondary circulation in the cold air north of the interface. The thermally direct secondary circulation is much stronger than the thermally indirect secondary circulation. Portions of the thermally direct secondary circulation can be seen in Fig. 14. In Fig. 14c the u9 winds above the bright band are observed to increase. As the secondary circulation continues, the flow turns to the right resulting 8 This explanation is similar to that presented by Atlas et al. (1969). The difference is that the process has been partitioned into two steps.

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in the LLJ and increased vertical wind shear. The increase in the LLJ is shown in Fig. 14d and was ;5 m s 21 . The location of the LLJ core coincided well with the position of the bright band (Fig. 14a). The dynamical response caused by melting also creates a positive feedback upon the precipitation. The warm air ascending along the warm front must ascend additionally in order to overrun the pool of diabatic cooled air. This cooled air accumulates beneath the bright band. This ‘‘thermal mountain’’ increases the ascent rate and hence the precipitation rates along the SN– FZRA interface. The ascent portion of the thermally direct secondary circulation has another important role in winter storms. The diabatic process of melting produces the thermally direct secondary circulation, which acts to trigger and focus the release of CSI i (or CI i , if present) resulting in the heaviest precipitation directly over the SN–FZRA interface. Another dynamical response caused by melting is the gravity waves within the WFL. The increased vertical wind shear resulting from melting in the WFL decreases the dynamic stability in terms of the Richardson number below the critical value of one (Ri , 1), thus allowing gravity waves. 7. Applicability of results to forecasting The applicability of these results to forecasting can best be described by referring to the schematic diagram shown in Fig. 17. This is a vertical cross section located ahead of a surface low of a severe winter storm, which has rain, a band of freezing rain, and a band of snow. The cross section is oriented normal to the SN–FZRA interface. The warm air is to the right and the cold air is to the left. The strong winds aloft are primarily into the diagram and the LLJ is primarily out of the diagram. The 08C isotherm is folded and labeled. The top of the warm front corresponds to the maximum temperature (Tmx ) level and the top of the corresponds to the minimum temperature (Tmn ) level. The top of the warm front and the top of the CBL are both indicated as wide lines. The WFL is located between these two levels. The OCL is above the warm front. Most of the condensate (and, hence, precipitation) results from the ascent of air in the OCL. The precipitation process in the OCL is primarily an ice process. Therefore, in evaluating the thermodynamic instability in the OCL, one must consider the additional buoyancy due to the latent heat of fusion. Because the warm front is typically near the 800-mb level and near 08C, a simple rule of thumb is that the latent heat of fusion results in about 118C of buoyancy for an air parcel lifted from the top of the warm front to 500 mb. If the convective instability with respect to ice (CIi ) indicates upright convection, then an evaluation of the conditional symmetric instability with respect to ice (CSIi ) is not needed. In many cases the additional buoyancy will support updrafts of sufficient strength to produce lightning—a not uncommon, but often per-

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plexing phenomenon—in freezing rain cases (Rauber et al. 1994). The diabatic cooling resulting from melting snow occurs beneath the 08C isotherm and sometimes extends into the top of the warm front. This diabatically cooled air is advected and accumulated as it moves across the band of RA and FZRA. The presence of melting is unambiguously indicated by the presence of a bright band in radar reflectivity data. Noting the reflectivity beneath the bright band and using a Z–R relation, such as the Marshall–Palmer relation, to estimate the rainfall/ melting rate, one can estimate the magnitude of the diabatic cooling. The effects of melting are as follows: 1) The soundings across the RA and FZRA bands are modified. The modification occurs beneath the 08C level. If the sounding beneath the 08C level is saturated and neutrally buoyant, that is, follows a saturated adiabat (Qw ), then a 08C isothermal layer will develop with an unstable layer beneath. The unstable layer will mix not by rising thermals, as assumed by Moore and Stewart (1985), but rather by sinking thermals. The sinking thermals are likely initiated by nonhomogeneous precipitation/melting elements. The thermals will sink until they reach a level of equilibrium. If the thermals sink into the top of a very stable layer, such as a warm frontal layer, they will quickly reach a level of equilibrium. If, as was the case in Wexler et al. (1954), the saturated adiabat extended all the way to the ground, then the diabatically cooled parcels will sink to the ground, as stated by Wexler et al. (1954). 2) An LLJ develops. The LLJ develops at the top of the CBL and near the SN–FZRA interface. The LLJ develops as a direct response to the increased baroclinicity from the diabatic cooling. The LLJ is in quasigeostrophic equilibrium. The LLJ can be most easily understood by means of the thermal wind equation. By increasing the thermal gradient from diabatic cooling across the FZRA band (Fig. 17), the vertical wind shear is increased. The magnitude of the LLJ is 5–10 m s 21 . This LLJ is small in vertical and horizontal extent and, therefore, difficult to identify. An LLJ distinctly appeared in the data presented by Martner et al. (1993), but was not recognized as such. From their Fig. 9, it may be noted that at 1520 UTC and at 0.5 km, the u and y components of the wind were 15 and 10 m s 21 , respectively. The magnitude of the LLJ was ;18 m s 21 . This location corresponds to the SN–FZRA interface and the top of the CBL. The most effective way to identify the LLJ is using the BVP single-Doppler analysis technique described by Johnston et al. (1990). The juxtaposition of the bright band and LLJ can be easily identified up to, maybe, 10 km from the radar. Since SN–FZRA interfaces typically move rather slowly,

using the BVP technique may provide up to a 1-h lead time for the arrival of the SN–FZRA interface. 3) Shear-induced gravity waves develop. The increased vertical wind shear through the WFL decreases the dynamic stability within this layer. The Richardson number is an indicator of the dynamic stability. A shear-induced gravity wave was observed in the PPI display by Damiana and Marwitz (1995) in an Oklahoma freezing rain case and by aircraft in this case. 4) Positive feedback develops between melting and precipitation. A secondary direct circulation develops in response to melting effects. The increased ascent above the warm front results in increased condensation and, hence, increased precipitation/diabatic cooling. Also the increased diabatic cooling causes the precipitation to increase, which is a positive feedback process. One can visualize the increased ascent being caused by an increased ‘‘thermal mountain’’ above which the air must rise. The significant result is that melting effects act to focus the release of CIi and CSIi over the SN–FZRA interface, thereby explaining the typical observation that the greatest snowfall rate typically occurs immediately north of the SN–FZRA interface. Acknowledgments. The authors’ participation in STORM-FEST was funded by NSF Grants ATM9014763, ATM-9308409, and ATM-9527434. REFERENCES Atlas, D., R. Tatehira, R. Srivastava, W. Marker, and R. Carbone, 1969: Precipitation-induced mesoscale wind perturbations in the melting layer. Quart. J. Roy. Meteor. Soc., 95, 544–560. Bendel, W., and D. Paton, 1981: A review of the effect of ice storms on the power industry. J. Appl, Meteor., 20, 1445–1449. Bernstein, B., T. Omeron, M. Polotivich, and F. McDonough, 1998: Surface features associated with freezing precipitation and severe in-flight aircraft icing. Atmos. Res., 46, 57–73. Cortinas, J., 2000: A climatlogy of freezing rain in the Great Lakes region of North America. Mon. Wea. Rev., 128, 3574–3588. Damiana, T., and J. Marwitz, 1995: Development of a gravity wave event during an Oklahoma blizzard. Preprint, 27th Conf . on Radar Meteorology, Vail, CO, Amer. Meteor. Soc., 314–316. Durran, D., and J. Klemp, 1982: On the effects of moisture on the Brunt–Va¨isa¨la¨ frequency. J. Atmos. Sci., 39, 2152–2158. Findeison, W., 1940: The formation of the 08C-isothermal layer and fractocumulus under nimbostratus. Meteor. Z., 57, 49–54. Haltiner, G., 1971: Numerical Weather Prediction. Wiley, 317 pp. Johnston, B., J. Marwitz, and R. Carbone, 1990: Single-Doppler radar analysis of banded precipitation structures. J. Atmos. Oceanic Technol., 7, 866–875. MacCready, P., 1964: Standardization of gustiness values from aircraft. J. Appl. Meteor., 3, 439–449. Martner, B., J. Snider, R. Zamora, G. Byrd, T. Niziol, and P. Joe, 1993: A remote-sensing view of a freezing-rain storm. Mon. Wea. Rev., 121, 2562–2577. Marwitz, J., and J. Toth, 1992: The front range blizzard of 1990. Part I: Synoptic and mesoscale structure. Mon. Wea. Rev., 120, 402– 415. Moore, G., and R. Stewart, 1985: The coupling between melting and

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convective air motions in stratiform clouds. J. Geophys. Res., 90, 10 659–10 666. Oye, R., C. Miller, and S. Smith, 1995: Software for radar translation, visualization, editing, and interpolation. Preprint, 27th Conf. on Radar Meteorology, Vail, CO, Amer. Meteor. Soc., 359–361. Pace, J., 1980: Microphysical and thermodynamic characteristics through the melting layer. M.S. thesis, Dept. of Atmospheric Science, University of Wyoming, 204 pp. Prater, E., and A. Borho, 1992: Doppler radar wind and reflectivity signatures with overrunning and freezing-rain episodes: Preliminary results. J. Appl. Meteor., 31, 1350–1358. Rauber, R., M. Ramamurthy, and A. Tokay, 1994: Synoptic and mesoscale structure of a severe freezing rain event: The St. Valentine’s day ice storm. Wea. Forecasting, 9, 183–208. Regan, M., 1998: Canadian ice storm 1998. WMO Bulletin, 47, 250– 256. Rogers, R., and M. Yau, 1989: A Short Course in Cloud Physics. Butterworth-Heinemann, 290 pp. Schultz, D., and P. Schumacher, 1999: The use and misuse of conditional symmetric instability. Mon. Wea. Rev., 127, 2709–2732. Stewart, R., 1984: Deep 08C isothermal layers within precipitation bands over southern Ontario. J. Geophys. Res., 89, 2567–2572. ——, 1992: Precipitation types in the transition region of winter storms. Bull. Amer. Meteor. Soc., 73, 287–296.

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——, and P. King, 1987: Rain–snow boundaries over southern Ontario. Mon. Wea. Rev., 115, 1894–1907. ——, and G. McFaquhar, 1987: On the width and motion of a rain/ snow boundary. Water Resour. Res., 23, 343–350. Szeto, K., C. Lin, and R. Stewart, 1988a: Mesoscale circulations forced by melting snow. Part I: Basic simulations and dynamics. J. Atmos. Sci., 45, 1629–1641. ——, R. Stewart, and C. Lin, 1988b: Mesoscale circulations forced by melting snow. Part II: Application to meterological features. J. Atmos. Sci., 45, 1642–1650. ——, A. Tremblay, H. Guan, D. Hudak, R. Stewart, and Z. Cao, 1999: The mesoscale dynamics of freezing rain storms over eastern Canada. J. Atmos. Sci., 56, 1261–1281. Szoke, E., J. Brown, J. McGinley, and D. Rogers, 1994: Forecasting for a large field program: STORM-FEST. Wea. Forecasting, 9, 693–705. Thomas, M., and J. Marwitz, 1995: Droplet spectra in freezing rain. Preprint, Sixth Conf. on Aviation Weather Systems, Dallas, TX, Amer. Meteor. Soc., 253–256. Waldteufel, P., and H. Corbin, 1979: On the analysis of single-Doppler radar data. J. Appl. Meteor., 18, 532–542. Wexler, R., R. Reed, and J. Honig, 1954: Atmospheric cooling by melting snow. Bull. Amer. Meteor. Soc., 35, 48–51. Zerr, R., 1997: Freezing rain: An observational and theoretical study. J. Appl. Meteor., 36, 1647–1661.