242 WEATHER AND FORECASTING VOLUME 21

On the Classification of Vertical Wind Shear as Directional Shear versus Speed Shear

PAUL MARKOWSKI AND YVETTE RICHARDSON

Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania

(Manuscript received 31 December 2004, in final form 30 June 2005)

ABSTRACT

Vertical wind shear is commonly classified as “directional” or “speed” shear. In this note, these classi- fications are reviewed and their relevance discussed with respect to the dynamics of convective storms. In the absence of surface drag, storm morphology and evolution only depend on the shape and length of a hodograph, on which the storm-relative winds depend; that is, storm characteristics are independent of the translation and rotation of a hodograph. Therefore, traditional definitions of directional and speed shear are most relevant when applied to the storm-relative wind profile.

1. Introduction file containing vertical wind shear—the “Ekman spi- ral”—can be derived by assuming the presence of The Glossary of Meteorology defines vertical wind boundary layer friction and no ambient baroclinity shear as the “local variation of the wind vector or any of (e.g., Holton 2004, 127–129). Large accelerations of the its components in a given direction” (Glickman 2000). horizontal wind also can contribute to vertical wind Vertical shear is a required presence in the geostrophic shear in ways not predicted by the thermal wind rela- wind profile in a hydrostatic, baroclinic atmosphere. tion given in (1). For example, near jet streaks or rap- The relationship between the vertical shear of the geo- idly moving and/or intensifying cyclones, the observed strophic wind and the temperature gradient is given by vertical wind shear can differ substantially from the the thermal wind relation: geostrophic vertical wind shear. A more lengthy discus- Ѩ Ѩ vg 1 R sion of the processes contributing to vertical wind shear T, ͑1͒ ١ ⌽ͪ ϭ k ϫ ١ Ϫ ϭϪ ͩ k ϫ Ѩp Ѩp f p fp p is provided by Doswell (1991). Although the definition of vertical wind shear makes where p is the pressure (used here as the vertical coor- no distinction regarding whether the shear is associated ⌽ ⌽ ١ ϵ ϫ dinate), vg (1/f ) k p is the geostrophic wind, with variations in wind direction and/or speed with is the geopotential height, R is the gas constant for dry height, the literature abounds with classifications of ١ air, pT is the temperature gradient on a pressure sur- vertical wind shear as being either “directional” or face, k is the unit vector in the vertical, and f is the “speed” shear. However, a survey of the literature in- Coriolis parameter. dicates that the classifications have not always shared Vertical wind shear also can be present in the ab- the same meaning from one study to the next. As class- sence of large-scale baroclinity. For example, friction room instructors, we have found the possible ambiguity plays a role in creating vertical wind shear within the in the wind shear classifications to be a source of con- boundary layer, owing to the fact that the effects of fusion on occasion. The purpose of this note is to pro- friction decrease with height, becoming negligible at vide some clarification on wind shear classifications. the top of the boundary layer. An analytical wind pro- Although vertical wind shear exerts important controls on many atmospheric phenomena (e.g., boundary layer rolls, lake-effect snowbands, gravity waves), our forth- Corresponding author address: Dr. Paul Markowski, Dept. of Meteorology, The Pennsylvania State University, 503 Walker coming discussion primarily will focus on the relevance Bldg., University Park, PA 16802. of wind shear classifications to the structure and evo- E-mail: [email protected] lution of convective storms.

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2. Popular definitions of directional shear and Weisman and Klemp 1982, 1984) demonstrated the dy- speed shear namical importance of the shape and length of the hodograph characterizing the storm environment, Probably the most popular usage of the term “direc- rather than the orientation of the hodograph relative to tional wind shear” has referred to the changing of the the ground. Only the shear and its variation with height angle of the wind velocity vector with height, expressed have dynamical importance—the variation of the in degrees per vertical distance. “Speed shear” corre- ground-relative wind direction (or speed) with height spondingly has been defined as the variation of wind has no dynamical relevance to thunderstorm structure, speed with height. To the best of our knowledge, these at least for simulations in which a free-slip lower are the only definitions that have been used outside of boundary is prescribed (almost universally the case the severe storms community. For example, these defi- throughout the 1970s and 1980s).1 Indeed, some re- nitions have been used by investigators of lake-effect cently developed storm motion predictors have recog- snow (e.g., Cooper et al. 2000; Steenburgh et al. 2000), nized the approximate invariance of gross storm dy- boundary layer convection (e.g., Balaji and Clark 1988; namics to hodograph rotation and translation (Rasmus- Redelsperger and Clark 1990; Weckwerth et al. 1997; sen and Blanchard 1998; Bunkers et al. 2000). Atkins et al. 1998; Kristovich et al. 1999), gravity waves A rotation or translation of a hodograph in the real (e.g., Kim and Mahrt 1992; Hauf 1993; Shutts 2003), atmosphere is complicated somewhat by surface drag, and tropical convection (e.g., Halverson et al. 1999; which tends to extend a hodograph toward the origin Rickenbach 1999). Even within the severe storms com- [(u, ␷) ϭ (0, 0) m sϪ1, where u and ␷ are the zonal and munity, these definitions frequently have been em- meridional wind components, respectively]; that is, the ployed in the past (e.g., Schlesinger 1975, 1978; Johns surface layer often contains strong vertical wind shear 1984; Giordano and Fritsch 1991; Hagemeyer and due to the requirement that wind speeds approach zero Schmocker 1991). at the ground. Stated another way, because of surface On the other hand, an alternative meaning of “direc- drag, a hodograph generally cannot be rotated or trans- tional” shear also has been used or implied within the lated without an attendant modification of the context of severe local storms, whereby directional hodograph length and shape. It currently is not known shear is the change in direction of the wind shear vector, what importance the vertical wind shear within this rather than the horizontal wind vector, with height relatively shallow layer may have on storm dynamics, (e.g., Cotton and Anthes 1989, 515–520; Houze 1993, principally because this layer has not been well resolved 289–291). Moreover, the terms “unidirectional” or in past numerical simulations. In spite of the complica- “one-directional” shear commonly have been used to tions arising from surface drag, the gross characteristics describe a shear vector that does not change direction of convective storms are largely independent of the with height, in contrast to a “directionally varying” magnitude and degree of veering of the ground-relative shear vector. These classifications of the vertical wind winds as long as the hodograph length and shape out- shear, which describe whether a hodograph is curved side this layer are held constant. (directional or directionally varying shear) or straight The fact that it is the hodograph shape and length (unidirectional shear), have been used extensively that dictate the structure and evolution of a convective within the severe storms community (e.g., Toutenhoofd storm is related to the fact that hodographs dictate the and Klemp 1983; Peterson 1984; Klemp 1987; characteristics of the storm-relative wind profile. The Wakimoto et al. 1998; Cai and Wakimoto 2001), espe- importance of storm-relative winds has been stressed cially in modeling studies of thunderstorms (e.g., since the early days of severe storms research (e.g., Klemp and Wilhelmson 1978a,b; Wilhelmson and Browning 1964), as well as in climatological (e.g., Mad- Klemp 1978; Weisman and Klemp 1982, 1984, 1986). dox 1976; Darkow and McCann 1977) and theoretical (e.g., Davies-Jones 1984) studies of severe storms envi- 3. Importance of hodograph shape and length ronments. Davies-Jones (1984) applied the traditional definitions of directional and speed shear to storm- It probably is not coincidental that the severe storms relative wind profiles. This correctly implies that it is community has had to develop terminology to describe the hodograph shape and length that matter; a given the variation in the direction of the wind shear vector with height. The seminal three-dimensional numerical 1 It is entirely possible that the profile of ground-relative winds simulations of supercell thunderstorms in the late 1970s could be relevant in considering the likelihood of thunderstorm and early 1980s (Schlesinger 1975, 1978; Klemp and initiation. A detailed discussion of this matter is beyond the scope Wilhelmson 1978a,b; Wilhelmson and Klemp 1978; of this paper.

Unauthenticated | Downloaded 09/28/21 05:27 PM UTC 244 WEATHER AND FORECASTING VOLUME 21 hodograph will be associated with the same amount of directional and speed shear of the storm-relative wind regardless of how the hodograph is oriented, assuming that storm motions are affected only by internal storm dynamics and not by external forcings, such as terrain or an inhomogeneous environment. On the other hand, hodograph translation and rota- tion lead to changes in the variation of ground-relative wind speed and direction with height. Directional and speed shear defined by such ground-relative wind varia- tions ultimately depend on the mean wind velocity, which governs hodograph translation with respect to the origin. One would not expect such quantities to be dynamically relevant. Directional and speed shear de- fined by ground-relative wind variations also depend on the orientation of the thermal wind, which largely con- trols the orientation of a hodograph. The hodographs shown in Fig. 1, which very roughly have similar shapes, span a variety of mean wind velocities and deep-layer shear orientations. Hodographs that are confined to the first quadrant (i.e., u, ␷ Ͼ 0 at all levels) are commonly observed in eastern United States severe weather out- breaks [Figs. 1a and 1b; e.g., Kaplan et al. (1998)], whereas hodographs commonly span the first and sec- ond quadrants (i.e., ␷ Ͼ 0 at all levels, but u changes sign from negative to positive in the lower troposphere) in severe weather outbreaks in the U.S. Great Plains region [Fig. 1d; e.g., Maddox (1976)]. Hodographs oc- casionally span more than two quadrants, for example, in “northwest flow” events [Fig. 1c; e.g., Johns (1982), (1984)]. Ground-relative veering is smaller when hodo- graphs are confined to a single quadrant compared to when hodographs span multiple quadrants, yet the magnitude of storm-relative wind speeds and veering is largely independent of hodograph orientation and po- sition with respect to the origin (storm motions tend to be faster when hodographs are confined to a single quadrant). In the specific examples of Fig. 1, the cases with the smallest ground-relative wind veering (Figs. 1a and 1b) actually are associated with the largest storm- FIG.1.(a)–(d) Hodographs observed in relative proximity to relative wind veering. outbreaks of supercell thunderstorms having a wide variety of The arguments presented above are further clarified mean wind velocities and deep-layer shear (thermal wind) orien- tations. Labels along the hodographs indicate heights above by the idealized hodographs depicted in Fig. 2. Hodo- ground level in km. Although wind data in only the lowest 6 km Ј graphs A and A are identical in length and shape (both are plotted [the winds are missing above 5 km in (b)], this does not are straight), but hodograph AЈ has been shifted by imply that the winds above 6 km are unimportant. The ࠘ symbols adding Ϫ5msϪ1 (10 m sϪ1) to the zonal (meridional) indicate the approximate average storm motions observed on wind speeds of the points composing hodograph A. each day. Profiles of ground-relative (g-r) and storm-relative (s-r) winds (half barb, 2.5 m sϪ1; full barb, 5 m sϪ1; flag, 25 m sϪ1) are Hodographs A and AЈ both have unidirectional shear displayed to the right of each hodograph. as defined by the variation of the wind shear vector with height (the shear is westerly at all levels), but have in the case of hodograph A; ϳ90° of veering in the case very different degrees of directional wind shear if di- of hodograph AЈ). Likewise, hodographs B and BЈ are rectional shear is defined as the angular turning of the identical in length and shape (both are half-circles), but ground-relative wind vector with height (0° of veering hodograph BЈ has been shifted by adding 20 m sϪ1

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FIG. 2. Idealized (top left) straight and (bottom left) curved hodographs and their corresponding (top right) ground-relative (g-r) and (bottom right) storm-relative (s-r) wind profiles (half barb, 2.5 m sϪ1; full barb, 5 m sϪ1; flag, 25 m sϪ1). Labels along the hodographs indicate heights above ground level in km. The ࠘ symbols indicate the storm motions predicted by the Bunkers et al. (2000) technique. Hodographs A and AЈ are identical, but hodograph AЈ has been shifted by adding Ϫ5msϪ1 (10 m sϪ1) to the zonal (meridional) wind components of the points composing hodograph A. Hodographs B and BЈ are iden- tical, but hodograph BЈ has been shifted by adding 20 m sϪ1 (8 m sϪ1) to the zonal (meridional) wind components of the points composing hodograph B. The storm-relative wind profiles are identical for the A and AЈ hodographs and the B and BЈ hodographs.

(8 m sϪ1) to the zonal (meridional) wind speeds of the relative wind profiles (and thus the implied dynamics) points composing hodograph B. Hodographs B and BЈ are identical within each pair of hodographs, assuming have identical amounts of directional shear if direc- that the storm motion is the same function of the envi- tional shear is defined as the veering of the shear vector ronmental wind profile (see the storm-relative wind with height or veering of the storm-relative winds with profiles in Fig. 2). height. But, if directional shear is defined as the veering of the ground-relative wind vector with height, then 4. Summary hodographs B and BЈ have very different degrees of Vertical wind shear routinely has been categorized as directional shear (ϳ180° of veering in the case of directional shear or speed shear, but the criteria used in hodograph B; ϳ45° of veering in the case of hodograph making such distinctions have varied throughout the BЈ). Furthermore, hodograph B has no speed shear, yet literature. We have attempted to summarize the range hodograph BЈ has 25 m sϪ1 of speed shear, if speed of interpretations permitted by these shear classifica- shear is defined as the variation of ground-relative wind tions, as well as provide some clarification regarding speed with height. It also is easily shown that the storm- the dynamical implications of these classifications.

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Wind shear has been described as directional most especially given the computational capabilities of the often, and almost exclusively outside of the severe local present day. storms context, when the ground-relative wind velocity vector turns with height. With regard to severe local Acknowledgments. This paper was motivated by storms, this terminology also has been applied to the many difficult questions asked by inquisitive students in storm-relative winds, and in a few cases, to describe the mesoscale meteorology class at Penn State Univer- environments in which the wind shear vector turns with sity. We thank the three anonymous reviewers for their height, as in the case of a curved hodograph. To avoid constructive reviews. potential confusion with the traditional terminology, curved hodographs have been described in most studies REFERENCES as having directionally varying wind shear, whereas Atkins, N. T., R. M. Wakimoto, and C. L. 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