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. © 2006 American Meteorological Society Unauthenticated | Downloaded 09/28/21 05:27 PM UTC WAF897 APRIL 2006 NOTES AND CORRESPONDENCE 243 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.