Forcing, instability and equivalent potential vorticity in a Midwest USA convective snowstorm

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1 Meteorol. Appl. 10, (2003) DOI: /S Forcing, instability and equivalent potential vorticity in a Midwest USA convective snowstorm Department of Atmospheric Sciences, University of Missouri-Columbia, 387 McReynolds Hall, Columbia MO marketp@missouri.edu This paper investigates a case of convective snow that was observed with an occluded-type cyclone. Cross-section and plan-view analyses show that convection resulted from the release of elevated, potential instability by isentropic uplift associated with an easterly trowal airstream (a western extension of the warm conveyor belt) located between 700 and 850 hpa. Forcing for ascent was supplied by low-level frontogenesis, as well as an intensifying 500hPa tropopause fold and its associated potential vorticity anomaly. The latter not only provided a source of very cold, dense air, but also was responsible for lower tropospheric cyclogenesis and subsequent trowal generation. 1. Introduction The occurrence of convective snowstorms has been and continues to be a significant forecasting problem for operational meteorologists. Holle et al. (1998) revealed that there were 628 hourly observations of snow with thunder and lightning (hereafter, thundersnow) across the contiguous United States from 1982 to 1990, an average of approximately 70 per year. Similar events occur the world over (see, for example, Canovan 1972; Takeuti et al. 1978). Of the 628 observations in the study by Holle et al. (1998), 156 occurred at temperatures at or below freezing, with moderate or heavy snow occurring in 62% of those observations. That thundersnow can produce localised areas of heavy snow accumulation shows that it should be treated as an important forecast issue. Working from the assumption that thundersnow is often banded snow, researchers have been focusing on the nature and source of this banded structure for the past two decades. Forecasting such convective snow events is made even more difficult by the meso-β scale banding (with halfwidths of approximately 100 km) that is usually observed in these events. Moore & Blakely (1988), Weismuller & Zubrick (1998), Nicosia & Grumm (1999), and Martin (1998a, 1998b) have all presented case studies in which meso-β bands of heavy snowfall fell in regions of otherwise light to moderate snowfall, likely in the presence of either potential instability (PI), conditional symmetric instability (CSI), or weak conditional symmetric stability (CSS). PI is a state of the atmosphere where a lifted layer achieves a statically unstable lapse rate, resulting in upright convection. CSI exists in a saturated environment, which is statically stable for purely vertical parcel displacements and inertially stable for purely horizontal perturbations. With the appropriate slantwise displacement in such an atmosphere, the parcel will continue to accelerate upward (e.g. Bennetts & Hoskins 1979; Sanders & Bosart 1985). This paper presents a case study of a convective winter storm that occurred on the morning of 9 December 1999, at Lubbock, Texas (LBB), and produced 18 cm (7 inches) of snow and sleet in a 5-hour period. This event was characterised by a 98-minute episode of thundersnow, which was mixed at times with sleet and persisted from 0912 UTC to 1050 UTC. While originally expecting accumulations of only 2.5 cm (1 inch) or so, National Weather Service discussions at the time of the event attributed the convection to the release of CSI, although Lubbock was to the northwest of a mature, occluding cyclone, and in a cyclonically sheared environment, which is typically more prone to potential instability (see below). It is our intention to show that the convection in this case occurred in response to the release of PI, not CSI. Furthermore, we intend to examine the various methods by which equivalent potential vorticity (EPV) is calculated as a diagnostic tool for CSI. One method, described by Moore & Lambert (1993) and McCann (1995), employs the equivalent potential temperature (θ e ) in the calculation of EPV. The other, described by Schultz & Schumacher (1999), employs the saturated equivalent potential temperature (θ es ) in the calculation. Following Schultz & Schumacher (1999), the use of θ e in the EPV calculation permits assessment of potential symmetric instability (PSI), while employing θ es in the calculation of EPV allows one to diagnose CSI. 273

2 2. Background CSI can be described as instability that arises from the release of latent heat during the slantwise ascent of an air parcel (Bennetts & Sharp 1982), a condition that obviously implies a saturated environment. CSI is favoured under conditions of strong anticyclonic shear, strong vertical shear and low static stability (Bluestein 1986; Moore & Lambert 1993), conditions that are most likely to be observed north of a warm front, east of a surface cyclone. When released by a forcing mechanism, CSI may produce mesoscale bands of locally heavy precipitation. Potential instability can also produce banded precipitation when released; its diagnosis is simple. If θ e decreases with height either on analysis of cross-section or by analysis of a θ e vertical profile, then PI is present in the layer. Because vertical motions associated with PI are much greater than those associated with CSI, PI can create periods of very heavy precipitation, and will likely dominate over CSI when the two occur simultaneously. It is our hypothesis that PI is preferred in cyclonically sheared environments, such as to the northwest of a mature surface cyclone, in which the trowal airstream (a westward branch of the warm conveyor belt in older extratropical cyclones; see Martin 1999) interacts with colder, dryer air at higher levels to produce negative lapse rates of θ e and elevated convection. The methodology related to the diagnosis of CSI has become a source of debate in recent years, with the threshold of saturation being the major hurdle. Most studies have used the threshold given by Bennetts & Hoskins (1979), which assumes saturation occurs in an environment with relative humidity greater than 80%. Practical reasons for this practice are to account for sensor error as well as that introduced by objective analysis. It has also been noted that relative humidity is measured with respect to a flat water surface, and that 80% so defined at a temperature of 15 C (the preferred temperature for dendrite growth) is in excess of 100% with respect to ice. Therefore, CSI may be diagnosed via a cross-section normal to the orientation of the thermal wind in which lines of θ e slope more steeply than lines of absolute geostrophic momentum (M g ) and where relative humidity (RH) values are above 80%. The cross-section line must be oriented perpendicular to the direction of the thermal wind in order to satisfy the requirement of geostrophy, because M g is used. Schultz & Schumacher (1999) adhere to the true threshold of saturation, at which the relative humidity is 100%. As a result, θ es is used instead of θ e to diagnose CSI, while cross-sections utilising θ e are said to diagnose PSI. We prefer to employ θ e with RH (> 80%) in order to concur with the majority of the existing literature, while striving to meet the more stringent criteria of more recent investigations. Moreover, we believe 274 that the use of θ es overmoistens a cross-section, lending no clues to the spatial distribution of moisture. With this approach, we preserve the need to diagnose CSI in a saturated environment, while avoiding the assumption that the RH everywhere is 100%, which is implied with the use of θ es. Another method of diagnosing CSI is through the analysis of EPV in cross-section, again drawn perpendicular to the thermal wind direction. However, McCann (1995) expresses EPV, which is given as EPV gη g θ e (1) in its three-dimensional form θ v u v u e g θ e g g g θe EPV = g + fk (2) x p y p x y p where f k = 2Ω sinφ, and the final units are given as 1 PVU or m K Pa 1 s 3. The inclusion of u g and v g instead of M g into the equation allows any crosssection line to be used to analyse EPV, not just one that has been positioned perpendicular to the thermal wind field. In an otherwise stable (i.e. no PI) atmosphere, if EPV < 0 and the atmosphere is saturated, then CSI is present. If EPV > 0, then the atmosphere is symmetrically stable. Again, Schultz & Schumacher (1999) suggest substituting θ es for θ e into the three-dimensional equation for EPV, thus making it a calculation for moist potential vorticity (MPV). 3. Methodology Surface and mandatory level data were plotted and analysed both subjectively and objectively. Surface analyses were performed at 3-hour intervals from 0000 UTC to 1200 UTC on 9 December The mandatory level data were analysed at 0000 UTC and 1200 UTC. Output from the Rapid Update Cycle (RUC) short-term numerical model initial fields was then analysed at 3-hour intervals between 0000 UTC and 1200 UTC to deduce heights, temperatures and winds. Analyses of absolute vorticity, θ e, and thickness were also performed. Using the analysis of the hpa thickness, a cross-section line was established from Clovis, New Mexico (CVS), to Dallas-Fort Worth, Texas (DFW), in order to assess moist symmetric instability. Crosssections were then constructed in order to deduce the underlying instability present, and to compare two methods for diagnosing CSI. One cross-section consists of θ e, M g, and relative humidity, one of EPV, one of θ es and M g, and one of MPV. Finally, an isentropic analysis of pressure contours on the 294K surface was overlain on an analysis of stormrelative moisture transport vectors, in order to deduce the possible effects of the trowal airstream on the

3 Forcing, instability and EPV in a convective snowstorm thundersnow event in LBB. The storm motion vector (C) was calculated by determining the motion of the 500 hpa vorticity maximum associated with the event. This vector value was then subtracted from the total wind (V) to gain the storm-relative motion (V-C), upon which the moisture transport vectors were based. New Mexico Texas 4. Case study 4.1. Synopsis The analysis at 0000 UTC (Figure 1) shows a 1005 hpa open wave cyclone over southwestern Texas. A weak warm front extended from the low across west Texas into Oklahoma and Missouri, while a cold front extended from the low into Mexico. At 500 hpa, a pronounced short-wave trough was digging into New Mexico, in combination with a s 1 absolute vorticity maximum (not shown). A 90-knot curved jet streak was emerging from the base of a 300 hpa trough over west Texas, placing LBB in the weakly divergent (< s 1 ) left exit region, while a 100-knot jet streak was diving southwestward behind the trough axis (Figure 1). By 0900 UTC, the time of thundersnow initiation at LBB, the surface cyclone had moved to near DFW and weakened to 1010 hpa. RUC initial field analysis shows that the 850-hPa low has moved into northwestern Figure 1. Composite chart valid at 00 UTC 9 December The surface low and front are depicted, as are the jet cores at 300 hpa (heavy bold arrows), the 500-hPa trough axis (bold dashed line), and the 850 hpa warm advection (>10 4 K s 1 ; shaded region). Cross and bold LBB denote location of Lubbock, Texas. Texas, while a knot wind field was creating a warm-cold pool couplet (Figure 2). This type of thermodynamic structure is characteristic of a cyclone that is intensifying and beginning to occlude (Martin 1998b). A closed 500-hPa circulation was now evident to the southwest of LBB and the associated vorticity maximum had intensified to s 1, while 300-hPa divergence continued to be very weak (< s 1 ), which suggests that lower to middle tropospheric forcing was primarily responsible for this event (not shown). Figure hpa Rapid Update Cycle initial field valid at 09 UTC 9 December Solid lines depict heights contoured at 30 gpm intervals. Dashed lines depict temperature at 5 C intervals. 275

4 By 1200 UTC, the surface cyclone (1010 hpa) was centred over northeastern Texas and was occluding. At this time, convection had ended at LBB and 13 cm (5 inches) of new snow had now accumulated. Mandatory level analysis shows the vertical, untilted nature of the system at and above 850 hpa over southwestern Oklahoma, again indicative of a mature system Isentropic analysis/cross-sections Isentropic analysis of RUC initial fields at 0000 UTC indicates a θ e ridge extending into eastern Texas below 700 hpa, with a second θ e ridge present at 850 hpa over northern New Mexico (not shown). By 0900 UTC, the θ e ridge remained over eastern Texas, while high θ e air was being advected into the Texas Panhandle by easterly winds. This feature is most evident at 700 hpa (Figure 3), which clearly displays a trowal feature that originates over the western Gulf of Mexico, and is then wrapped cyclonically into the Texas Panhandle. The western nose of the trowal was located directly to the north of the cold pool, which again is a sign of an intensifying, occluding system. However, the trowal was completely absent at 500 hpa, where negative θ e advection was occurring over western Texas (not shown). At Figure hpa Rapid Update Cycle initial field of θ e (solid, every 2K) valid at 09 UTC 9 December a b Figure 4. (a) 300 hpa Rapid Update Cycle initial field, valid at 09 UTC 9 December 1999, of height contours (solid; every 120 gpm) and temperatures (dashed; every 2 C); (b) Rapid Update Cycle initial field valid at 09 UTC 9 December 1999 depicting tropopause pressures (solid; every 100 hpa) and the hpa potential vorticity (dashed; every m K s 3 Pa 1 ). 276

Forcing, instability and EPV in a convective snowstorm Figure 5. Rapid Update Cycle initial field valid at 09 UTC 9 December 1999 depicting 700-hPa ω (every 2 µb s 1 ). Figure 6.

5 Forcing, instability and EPV in a convective snowstorm Figure 5. Rapid Update Cycle initial field valid at 09 UTC 9 December 1999 depicting 700-hPa ω (every 2 µb s 1 ). Figure 6. Rapid Update Cycle initial field valid at 09 UTC 9 December 1999 depicting 850 hpa Petterssen surface frontogenesis (every 10 1 K 100 km 1 3 h 1 ). 300 hpa (Figure 4a), a warm air pool was co-located with a K m 1 Pa 1 s 3 PV maximum, which appears to be directly related to a stratospheric intrusion that was producing 500 hpa tropopause heights over southwestern New Mexico (Figure 4b). Significant upward vertical motion (ω 700 < 10 µb s 1 ) was diagnosed to the north of the potential vorticity anomaly (Figure 5), inferring that the tropopause fold probably played a direct role in the production of forced ascent near LBB. Plan view analysis shows a strong frontogenesis frontolysis couplet (Figure 6) over the Texas Panhandle, with the orientation of the frontogenetical 277

6 Figure 7. Rapid Update Cycle analysis of the 294 K isentropic surface valid at 09 UTC 9 December Solid contours depict isobars (every 50 hpa), while arrows depict storm-relative moisture transport vectors, q (V C), in units of m s 1 g kg 1. C is calculated here to be from 257 at 13.7 m s 1. Heavy bold line denotes cross section line for Figures 8 and 9. field being almost perfectly aligned with that of the trowal structure evident on the 294K isentropic surface (Figure 7). The orientation of the storm-relative moisture transport vectors [q (V-C)] illustrates that isentropic uplift is occurring in a region of appreciable moisture inflow (Figure 7). The presence of confluent flow likely acted to promote frontogenesis (Figure 6) while moisture convergence was evidenced by the along stream decrease in the moisture transport vector field. The CVS to DFW cross-section analysis of θ e, M g, and RH (Figure 8a) at 0900 UTC shows a sloping region of potential instability between 750 and 550 hpa over LBB, in a region of high RH. While not a diagnostic tool for CSI in this case, Figure 8b shows negative EPV between 700 and 500 hpa, in association with the region of potential instability. This is due to the final term in the expression for EPV (Eq. 2), where large PI leads to θ a positive value for p e, but a negative term when multiplied by the absolute geostrophic vorticity. The relatively strong gradient of EPV is illustrative of a strong vertical moisture gradient, which may have aided in convective overturning. Finally, Figure 8c shows that the strongest vertical motion (ω = 10 µb s 1 ) is occurring near 750 hpa, just above a region of frontogenesis, again implying the influence of the trowal. In the interest of assessing the practical, operational benefit of calculating and analysing moist symmetric instability with θ es, the previous cross-section analyses were duplicated using θ es as the thermodynamic variable. Comparative cross-sections (Figures 9a and 9b) of θ es and MPV show nearly identical patterns to those observed in Figures 8a and 8b. The only real exception is that the gradient that was evident on the EPV crosssection is absent when MPV is calculated. This occurs because MPV assumes that the atmosphere is saturated everywhere, which is not a true representation of the environment near LBB at 0900 UTC. Given the minor differences between EPV and MPV shown here, several points emerge which are of operational significance. First, continued use of θ e in the search for CSI is valid, provided that RH is also used in the process. This practice allows forecasters to isolate operationally significant areas near saturation (RH > 80%), especially when snow is anticipated (due to the definition of RH with respect to a flat water surface). Second, while a three-dimensional method of EPV calculation exists (McCann 1995), cross-section analysis may still aid in the diagnosis of CSI, a point advanced by Schultz & Schumacher (1999). However, cross-sections of EPV must still be used with the θ e, M g and RH analyses in order to diagnose regions of PI, where gravitational instability may be released. 5. Discussion and conclusions The episode of convective snow and sleet associated with this event was clearly due to the release of elevated potential instability by isentropic uplift and frontogen- 278

Relative humidity is shaded where it exceeds 80% (light grey) and 90% (dark grey).

7 Forcing, instability and EPV in a convective snowstorm a b c Figure 8. (a) Cross-section from Clovis, NM (CVS), to Dallas Fort Worth, TX (DFW), of Rapid Update Cycle initial fields valid at 09 UTC 9 December Relative humidity is shaded where it exceeds 80% (light grey) and 90% (dark grey). Solid contours depict θ e (every 2 K) and dashed are geostrophic pseudo-angular momentum (M g ; every 10 m s 1 ); (b) Threedimensional EPV (every 10 6 m K s 3 Pa 1 ) based upon θ e. Values < 0 are shaded. (c) Petterssen surface frontogenesis (solid; every K 100 km 1 3 h 1 ) and ω (dashed; every 1 µb s 1 ). LBB is near the second tick mark from the left. esis within the strong, easterly trowal airstream. As in the study by Nicosia & Grumm (1999), a region of dry air superimposed over the moist tongue associated with the trowal acted to make EPV more negative, therein making the lower to middle troposphere more unstable in terms of PI. Indeed, another look at the last term in Eq. 2 will reveal that when the atmosphere is potentially unstable, then EPV < 0. In order to make the atmosphere more potentially unstable, one must dry the atmosphere above and/or moisten it below. The latter is happening over western Texas in this case. In addition, although the surface cyclone actually filled over time, it is likely that large values of PV associated with a tropopause undulation were responsible for weak to moderate cyclogenesis above the surface, and for the generation of the wind field that created the trowal. Hakim et al. (1996) illustrated that tropopause undulations are often precursors to cyclone intensification, particularly in the presence of a warm cold pool couplet. Furthermore, tropopause undulations decrease 279

Acknowledgements The authors would like to thank Dr Don McCann and Dr Dave Schultz for their suggestions and extended discussions on instability and the calculation of moist potential vorticities.

static stability and increase absolute vorticity near the level of the tropopause, thus implying the generation of a more intense wind field.

8 Acknowledgements The authors would like to thank Dr Don McCann and Dr Dave Schultz for their suggestions and extended discussions on instability and the calculation of moist potential vorticities. References Figure 9. (a) As in Figure 8a, but without relative humidity and with solid contours depicting θ es ; (b) as in Figure 8b, but using θ es. static stability and increase absolute vorticity near the level of the tropopause, thus implying the generation of a more intense wind field. In this case, the generation of large amounts of absolute vorticity at the level of the tropopause not only generated more wind, but also acted as an indicator of upward increasing positive vorticity advection, which acted to further enhance upward vertical motion near LBB. Overall, this case study illustrates the importance for the accurate diagnosis of either PI or CSI for the purposes of forecasting. Because vertical accelerations associated with PI are much more intense than those associated with CSI, snowfall rates (LBB totalled 18 cm/7 inches in 6 hours) with this event were likely to be much heavier than would have been observed in a CSI environment. Finally, minimal differences were encountered between two methods for the diagnosis of PSI and CSI. 280 a b Bennetts, D. A. & Hoskins, B. J. (1979) Conditional symmetric instability a possible explanation for frontal rainbands. Q. J. R. Meteorol. Soc. 105: Bennetts, D. A. & Sharp, J. C. (1982) The relevance of conditional symmetric instability to the prediction of mesoscale frontal rainbands. Q. J. R. Meteorol. Soc. 108: Bluestein, H. (1986) Fronts and jet streaks: A theoretical perspective. In Peter Ray, ed., Mesoscale Meteorology and Forecasting, Am. Meteorol. Soc., Canovan, R. A. (1972) Snow accompanied by thunder. Weather 27: Hakim, G. J., Keyser, D. & Bosart, L. F. (1996) The Ohio Valley wave merger cyclogenesis event of January Part II: Diagnosis using quasi-geostrophic potential energy inversion. Mon. Wea. Rev. 124: Holle, R. L., Cortinas, J. V. & Robbins, C. C. (1998) Winter thunderstorms in the United States. Preprints, 16th AMS Conf. on Weather Analysis and Forecasting, Phoenix, AZ, Am. Meteorol. Soc., Martin, J. E. (1998a) The structure and evolution of a continental winter cyclone. Part I: Frontal structure and the occlusion process. Mon. Wea. Rev. 126: Martin, J. E. (1998b) The structure and evolution of a continental winter cyclone. Part II: Frontal forcing of an extreme snow event. Mon. Wea. Rev. 126: Martin, J. E. (1999) Quasi-geostrophic forcing of ascent in the occluded sector of cyclones and the trowal airstream. Mon. Wea. Rev. 127: McCann, D. W. (1995) Three dimensional computations of equivalent potential vorticity. Wea. Forecasting 10: Moore, J. T. & Blakely, P. D. (1988) The role of frontogenetical forcing and conditional symmetric instability in the Midwest snowstorm of January Mon. Wea. Rev. 116: Moore, J. T. & Lambert, T. E. (1993) The use of equivalent potential vorticity to diagnose regions of conditional symmetric instability. Wea. Forecasting 8: Nicosia, D. J. & Grumm, R. H. (1999) Mesoscale band formation in three major northeastern United States snowstorms. Wea. Forecasting 14: Sanders, F. & Bosart, L. F. (1985) Mesoscale structure in the megalopolitan snowstorm of February Part I: Frontogenetical forcing and symmetric instability. J. Atmos. Sci. 42: Schultz, D. M. & Schumacher, P.N. (1999) The use and misuse of conditional symmetric instability. Mon. Wea. Rev. 127: Takeuti, T., Nakano, M., Brook, M., Raymond, D. J. & Krehbiel, P. (1978) The anomalous winter thunderstorms of the Horurika coast. J. Geo. Res. 83: Weismuller, J. L. & Zubrick, S. M. (1998) Evaluation and application of conditional symmetric instability, equivalent potential vorticity, and frontogenetic forcing in an operational forecast environment. Wea. Forecasting 13:

THE MAP ROOM. BAND ON THE RUN Chasing the Physical Processes Associated with Heavy Snowfall

THE MAP ROOM. BAND ON THE RUN Chasing the Physical Processes Associated with Heavy Snowfall THE MAP ROOM BAND ON THE RUN Chasing the Physical Processes Associated with Heavy Snowfall BY CHARLES E. GRAVES, JAMES T. MOORE, MARC J. SINGER, AND SAM NG AFFILIATIONS: GRAVES, MOORE, AND NG Department