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

Transcription

1 242 W E A T H E R A N D F O R E C A S T I N G 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 classifications 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 Corresponding author address: Dr. Paul Markowski, Dept. of Meteorology, The Pennsylvania State University, 503 Walker Bldg., University Park, PA pmarkowski@psu.edu The Glossary of Meteorology defines vertical wind shear as the local variation of the wind vector or any of its components in a given direction (Glickman 2000). Vertical shear is a required presence in the geostrophic wind profile in a hydrostatic, baroclinic atmosphere. The relationship between the vertical shear of the geostrophic wind and the temperature gradient is given by the thermal wind relation: v g p p 1 f p k R fp k pt, 1 where p is the pressure (used here as the vertical coordinate), v g (1/f ) k p is the geostrophic wind, is the geopotential height, R is the gas constant for dry air, p T is the temperature gradient on a pressure surface, k is the unit vector in the vertical, and f is the Coriolis parameter. Vertical wind shear also can be present in the absence of large-scale baroclinity. For example, friction plays a role in creating vertical wind shear within the boundary layer, owing to the fact that the effects of friction decrease with height, becoming negligible at the top of the boundary layer. An analytical wind profile containing vertical wind shear the Ekman spiral can be derived by assuming the presence of boundary layer friction and no ambient baroclinity (e.g., Holton 2004, ). Large accelerations of the horizontal wind also can contribute to vertical wind shear in ways not predicted by the thermal wind relation given in (1). For example, near jet streaks or rapidly moving and/or intensifying cyclones, the observed vertical wind shear can differ substantially from the geostrophic vertical wind shear. A more lengthy discussion of the processes contributing to vertical wind shear is provided by Doswell (1991). Although the definition of vertical wind shear makes no distinction regarding whether the shear is associated with variations in wind direction and/or speed with height, the literature abounds with classifications of vertical wind shear as being either directional or speed shear. However, a survey of the literature indicates that the classifications have not always shared the same meaning from one study to the next. As classroom instructors, we have found the possible ambiguity in the wind shear classifications to be a source of confusion on occasion. The purpose of this note is to provide some clarification on wind shear classifications. Although vertical wind shear exerts important controls on many atmospheric phenomena (e.g., boundary layer rolls, lake-effect snowbands, gravity waves), our forthcoming discussion primarily will focus on the relevance of wind shear classifications to the structure and evolution of convective storms American Meteorological Society

2 APRIL 2006 N O T E S A N D C O R R E S P O N D E N C E Popular definitions of directional shear and speed shear Probably the most popular usage of the term directional wind shear has referred to the changing of the angle of the wind velocity vector with height, expressed in degrees per vertical distance. Speed shear correspondingly has been defined as the variation of wind speed with height. To the best of our knowledge, these are the only definitions that have been used outside of the severe storms community. For example, these definitions have been used by investigators of lake-effect snow (e.g., Cooper et al. 2000; Steenburgh et al. 2000), boundary layer convection (e.g., Balaji and Clark 1988; Redelsperger and Clark 1990; Weckwerth et al. 1997; Atkins et al. 1998; Kristovich et al. 1999), gravity waves (e.g., Kim and Mahrt 1992; Hauf 1993; Shutts 2003), and tropical convection (e.g., Halverson et al. 1999; Rickenbach 1999). Even within the severe storms community, these definitions frequently have been employed in the past (e.g., Schlesinger 1975, 1978; Johns 1984; Giordano and Fritsch 1991; Hagemeyer and Schmocker 1991). On the other hand, an alternative meaning of directional shear also has been used or implied within the context of severe local storms, whereby directional shear is the change in direction of the wind shear vector, rather than the horizontal wind vector, with height (e.g., Cotton and Anthes 1989, ; Houze 1993, ). Moreover, the terms unidirectional or one-directional shear commonly have been used to describe a shear vector that does not change direction with height, in contrast to a directionally varying shear vector. These classifications of the vertical wind shear, which describe whether a hodograph is curved (directional or directionally varying shear) or straight (unidirectional shear), have been used extensively within the severe storms community (e.g., Toutenhoofd and Klemp 1983; Peterson 1984; Klemp 1987; Wakimoto et al. 1998; Cai and Wakimoto 2001), especially in modeling studies of thunderstorms (e.g., Klemp and Wilhelmson 1978a,b; Wilhelmson and Klemp 1978; Weisman and Klemp 1982, 1984, 1986). 3. Importance of hodograph shape and length It probably is not coincidental that the severe storms community has had to develop terminology to describe the variation in the direction of the wind shear vector with height. The seminal three-dimensional numerical simulations of supercell thunderstorms in the late 1970s and early 1980s (Schlesinger 1975, 1978; Klemp and Wilhelmson 1978a,b; Wilhelmson and Klemp 1978; Weisman and Klemp 1982, 1984) demonstrated the dynamical importance of the shape and length of the hodograph characterizing the storm environment, rather than the orientation of the hodograph relative to the ground. Only the shear and its variation with height have dynamical importance the variation of the ground-relative wind direction (or speed) with height has no dynamical relevance to thunderstorm structure, at least for simulations in which a free-slip lower boundary is prescribed (almost universally the case throughout the 1970s and 1980s). 1 Indeed, some recently developed storm motion predictors have recognized the approximate invariance of gross storm dynamics to hodograph rotation and translation (Rasmussen and Blanchard 1998; Bunkers et al. 2000). A rotation or translation of a hodograph in the real atmosphere is complicated somewhat by surface drag, which tends to extend a hodograph toward the origin [(u, ) (0, 0) m s 1, where u and are the zonal and meridional wind components, respectively]; that is, the surface layer often contains strong vertical wind shear due to the requirement that wind speeds approach zero at the ground. Stated another way, because of surface drag, a hodograph generally cannot be rotated or translated without an attendant modification of the hodograph length and shape. It currently is not known what importance the vertical wind shear within this relatively shallow layer may have on storm dynamics, principally because this layer has not been well resolved in past numerical simulations. In spite of the complications arising from surface drag, the gross characteristics of convective storms are largely independent of the magnitude and degree of veering of the ground-relative winds as long as the hodograph length and shape outside this layer are held constant. The fact that it is the hodograph shape and length that dictate the structure and evolution of a convective storm is related to the fact that hodographs dictate the characteristics of the storm-relative wind profile. The importance of storm-relative winds has been stressed since the early days of severe storms research (e.g., Browning 1964), as well as in climatological (e.g., Maddox 1976; Darkow and McCann 1977) and theoretical (e.g., Davies-Jones 1984) studies of severe storms environments. Davies-Jones (1984) applied the traditional definitions of directional and speed shear to stormrelative wind profiles. This correctly implies that it is the hodograph shape and length that matter; a given 1 It is entirely possible that the profile of ground-relative winds could be relevant in considering the likelihood of thunderstorm initiation. A detailed discussion of this matter is beyond the scope of this paper.

3 244 W E A T H E R A N D F O R E C A S T I N G 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 rotation 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 variations 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 defined by ground-relative wind variations also depend on the orientation of the thermal wind, which largely controls 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, 0 at all levels) are commonly observed in eastern United States severe weather outbreaks [Figs. 1a and 1b; e.g., Kaplan et al. (1998)], whereas hodographs commonly span the first and second quadrants (i.e., 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 occasionally span more than two quadrants, for example, in northwest flow events [Fig. 1c; e.g., Johns (1982), (1984)]. Ground-relative veering is smaller when hodographs 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 position 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 stormrelative wind veering. The arguments presented above are further clarified by the idealized hodographs depicted in Fig. 2. Hodographs A and A are identical in length and shape (both are straight), but hodograph A has been shifted by adding 5 ms 1 (10 m s 1 ) to the zonal (meridional) wind speeds of the points composing hodograph A. Hodographs A and A both have unidirectional shear as defined by the variation of the wind shear vector with height (the shear is westerly at all levels), but have very different degrees of directional wind shear if directional shear is defined as the angular turning of the ground-relative wind vector with height (0 of veering FIG. 1.(a) (d) Hodographs observed in relative proximity to outbreaks of supercell thunderstorms having a wide variety of mean wind velocities and deep-layer shear (thermal wind) orientations. Labels along the hodographs indicate heights above ground level in km. Although wind data in only the lowest 6 km are plotted [the winds are missing above 5 km in (b)], this does not imply that the winds above 6 km are unimportant. The symbols indicate the approximate average storm motions observed on each day. Profiles of ground-relative (g-r) and storm-relative (s-r) winds (half barb, 2.5 m s 1 ; full barb, 5 m s 1 ; flag, 25 m s 1 ) are displayed to the right of each hodograph. in the case of hodograph A; 90 of veering in the case of hodograph A ). Likewise, hodographs B and B are identical in length and shape (both are half-circles), but hodograph B has been shifted by adding 20 m s 1

4 APRIL 2006 N O T E S A N D C O R R E S P O N D E N C E 245 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 s 1 ; full barb, 5 m s 1 ; flag, 25 m s 1 ). 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 A are identical, but hodograph A has been shifted by adding 5 ms 1 (10 m s 1 ) to the zonal (meridional) wind components of the points composing hodograph A. Hodographs B and B are identical, but hodograph B has been shifted by adding 20 m s 1 (8 m s 1 ) to the zonal (meridional) wind components of the points composing hodograph B. The storm-relative wind profiles are identical for the A and A hodographs and the B and B hodographs. (8 m s 1 ) to the zonal (meridional) wind speeds of the points composing hodograph B. Hodographs B and B have identical amounts of directional shear if directional shear is defined as the veering of the shear vector with height or veering of the storm-relative winds with height. But, if directional shear is defined as the veering of the ground-relative wind vector with height, then hodographs B and B have very different degrees of directional shear ( 180 of veering in the case of hodograph B; 45 of veering in the case of hodograph B ). Furthermore, hodograph B has no speed shear, yet hodograph B has 25 m s 1 of speed shear, if speed shear is defined as the variation of ground-relative wind speed with height. It also is easily shown that the stormrelative wind profiles (and thus the implied dynamics) are identical within each pair of hodographs, assuming that the storm motion is the same function of the environmental wind profile (see the storm-relative wind profiles in Fig. 2). 4. Summary Vertical wind shear routinely has been categorized as directional shear or speed shear, but the criteria used in making such distinctions have varied throughout the literature. We have attempted to summarize the range of interpretations permitted by these shear classifications, as well as provide some clarification regarding the dynamical implications of these classifications.

5 246 W E A T H E R A N D F O R E C A S T I N G VOLUME 21 Wind shear has been described as directional most often, and almost exclusively outside of the severe local storms context, when the ground-relative wind velocity vector turns with height. With regard to severe local storms, this terminology also has been applied to the storm-relative winds, and in a few cases, to describe environments in which the wind shear vector turns with height, as in the case of a curved hodograph. To avoid potential confusion with the traditional terminology, curved hodographs have been described in most studies as having directionally varying wind shear, whereas straight hodographs often have been described as having unidirectional or one-directional shear. Correspondingly, the term speed shear traditionally has been used to denote ground-relative winds that increase in speed with height. As is the case with the directional shear terminology, speed shear also has been used in reference to storm-relative winds. In this review it has been shown that vertical variations in ground-relative wind speed and direction change as a given hodograph is rotated or translated with respect to the origin; that is, the magnitude of ground-relative wind direction and the speed variations with height depend on the orientation of the thermal wind (which largely governs hodograph orientation) and mean wind (which governs hodograph position with respect to the origin). Thus, definitions of directional and speed shear that depend on vertical variations of the ground-relative winds are not the most dynamically relevant. Conversely, the traditional definitions of directional and speed shear applied to the storm-relative winds (or hodographs described as containing directionally varying or unidirectional shear) are insensitive to hodograph rotation and translation and are directly relevant to storm dynamics. Finally, when the effects of surface drag are considered, a hodograph generally cannot be rotated or translated while retaining its original shape and length. In other words, changes in the mean wind or mean shear orientation unavoidably cannot be considered independently of a hodograph that includes winds within the surface layer, all the way to the ground. No systematic study of the effects of near-surface wind shear changes has been undertaken yet. 2 We believe that further research into the influence of near-surface wind shear and surface drag on convective storms is well warranted, 2 The finding in a recent study (Markowski et al. 2003) of ground-relative wind speeds being a relatively skillful discriminator between tornadic and nontornadic supercell thunderstorms (speeds tended to be larger in tornadic supercell environments) might be an indication of the importance of surface drag and near-ground wind shear. especially given the computational capabilities of the present day. Acknowledgments. This paper was motivated by many difficult questions asked by inquisitive students in the mesoscale meteorology class at Penn State University. We thank the three anonymous reviewers for their constructive reviews. REFERENCES Atkins, N. T., R. M. Wakimoto, and C. L. 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