A REVIEW FOR FORECASTERS ON THE APPLICATION OF HODOGRAPHS TO FORECASTING SEVERE THUNDERSTORMS Charles A. Doswell III National Severe Storms Laboratory Norman, Oklahoma Abstract 2. Basics of the Hodograph Basics of the hodograph are reviewed in order to acquaint A verticC\l wind profile consists of a set of wind speeds and (or re-acquaint) forecasters with this useful toolfor diagnosis directions at various heights. Forecasters are probably most of vertical wind shear. This review makes use of existing familiar with the sort of vertical wind plot shown in Figure operational programs for hodograph analysis, as well as I, produ~ed by the plotting programs in the Automation of presenting the principles underlying their use. A brief sum­ Field Operations and Services (AFOS) system. The data used mary is given of the physical processes acting to create in this plot are shown in Table I. vertical wind shear. These processes provide the basis for Operational forecasters should recognize that wind data as interpretation of the hodograph and an understanding of provided by operational soundings include wind speed and them allows one to make subjective hodograph prognoses. direction at each mandatory pressure level and at a set of Finally, an explanationfor the concepts ofstreamwise vortic­ pre-specified heights. The plot shown in Figure I is especially ity and helicity is given, emphasizing the importance ofview­ effective at showing the veering and backing of the wind with ing them in a storm-relative framework. A representative set height, but it is difficult to use this plot to visualize the effect of references is provided, as well, to guide the forecaster in of changing wind speeds with height. In the next section, I developing enough understanding of hodographs to apply will discuss some of the processes which influence the change them to severe thunderstorm forecasting. of wind (speed and direction, both) with height, but for now I want to concentrate on the hodograph. The AFOS applications program developed by Stone 1. Introduction (1988) called CONVECT allows the forecaster to get a hodo­ With the development of automated procedures for plot­ graph plotted. Using the same data shown in Figure 1 and ting and analysis of upper-air data, many forecasters may Table 1, the resulting plot is shown in Figure 2. What does have forgotten (or never learned) the diagnostic skills neces­ this plot really represent? It is well-known that specification sary for interpreting the information contained in the vertical of a vector requires two quantities; for wind vectors, this wind profile. This is especially unfortunate because recent often takes the form of speed and direction. When the wind research has shown that the character of the wind profile can vector is given in this way, it implies a polar representation have a strong control on thunderstorm behavior in a given of the wind: the direction determines an angle and the speed thermodynamic environment. Although the research is not gives the length of the vector along that angle. Figure 3 shows yet complete, the results so far indicate that the revival of such a polar representation. Everyone should recognize this the hodograph as a thunderstorm forecasting tool is quite sort of plotting diagram; radar is done similarly. worthwhile, especially in recognizing the potential for super­ It also is well-known that there is at least one other way cell thunderstorms, which can be devastatingly destructive, to represent a vector. That is, one specifies an orthogonal even when non-tornadic. Cartesian representation of the wind by giving special sig­ The threat of supercells is quite variable across the nation. nificance to two mutually perpendicular wind directions. For those in regions where supercells (tornadic or not) are These are the Cartesian coordinates in this representation of rare, it is possible to conclude that it is a waste of time to the vector; by convention, these coordinates are usually study the tools of the severe thunderstorm forecasting trade. taken to be east-west (the so-called u-component) and I contend that this is an erroneous conclusion. The threat of north-south (the so-called v-component). The (horizontal) a supercell-related disaster looms quite large in those regions wind vector is specified completely by giving the u and v precisely because such storms are relatively rare but not components of the wind. Thus, the horizontal vector wind impossible (see, e.g., Braun and Monteverdi 1991). When a V H is described as the sum ui + vj, where i and j are unit supercell (especially one with a tornado) occurs in an area of vectors in the east-west and north-south directions: i gener­ low supercell frequency, forecasters may not recognize the ally is taken to point e:tstward and j northward, so positive seriousness of the impending event, at least in part because u is a westerly wind and positive v is a southerly wind. they are not accustomed to dealing with such events and may At this point, it is important to remember that these are not be familiar with (or using) the relevant forecasting tools vector representation systems, distinct from what we ordi­ (see discussions by Gonski et al. 1989, and Korotky 1990). narily think of as coordinate systems. To see this, consider These notes are intended to acquaint (or re-acquaint) fore­ where the vertical wind profile was taken; its location can be casters with the hodograph, an especially useful tool for given by latitude and longitude, or by saying it is so many revealing the key features in the wind profile. While the miles in some direction from point with a known position, or primary emphasis will be recognition of supercell potential, by giving its position as some number of kilometers east and I am including some discussion of the hodograph' s value in another number of kilometers north of some known point. other forecasting and analysis issues. I cannot overempha­ All these are different ways of representing the location of size the importance of pursuing the topics I have reviewed via the wind profile as a vector from some origin, and location the references, since this review is necessarily incomplete. is what one usually thinks of when talking about coordinate 2 Volume 16 Number I February, 1991 3 --53 --50 --40 --35 --30 --25 400~--:'-'- ... ,' , " ~-~:.:...::::.:. - ( .... --28 50e!-" " ......... -" :')--"" :..... ...I --18 ,I .. " , .. --16 - -14 - - 12 --18 --9 --8 - -7 --6 ::1 ::~ ::~ TOP 12Z/AP/ 27/ 87 Fig. 1. Conventional AFOS skew-T, log p plot of data from Table 1. Table 1. Mandatory and significant level data for Topeka, Kansas, 1200 UTe 27 April 1987. TOPMANTOP WOUSI3I3 KTOP 27121313 72456 TTAA 77121 72456 99988 15658 3213135 1313158 ///// ///// 85557 17269 1321327 713179 135662 325213 513582 159813 311322 48746 28380 33028 3£1945 45V/ 32538 25064 543// 331333 28284 645// 32026 15379 631// 313835 18631 6131// 313529 88172 673// 38527 ((999 51515 18164 1388133 18194 01527 34521 - TOPSGLTOP WOUS00 KTOP 27121313 72456 TT88 7712/ 72456 813988 15658 11984 17459 22958 1866El 33938 21665 44894 198813 55764 113658 666131 85363 77589 136567 88560 09562 9951313 15988 11438 23759 2241313 283813 33356 35359 44327 39961a 55226 61aV/ 66172 673// 77145 637// 88126 577// 991113 613// 111813 61aV/- PPBB 77120 72456 98812 328135 32588 132828 913345 031334 83832 82026 913678 1311322 35819 32528 9139// 321322 91246 331321 321316 31514 921356 311322 33829 33527 929// 32527 93858 32529 331333 33537 939// 32523 9427/ 313525 313542 95132/ 311332 385313 - 4 National Weather Digest TOP 122 27 APR 87 BAH- )(XX UNITS KNOTS, LVLS ' THSO FT CMSL) B+ • )(XX CM/SEC)**Z B- )(XX CM/SEC)**Z SHR • CM/SEC)**Z 180 WMAX • )(XX M/SEC EL 938 HB EL 23 HNO FT MPL )(Xx HNO FT .-------------,090 '------:-15~----:-'10'------!:5:----+---~5:-----:1-70----:-1=-5-----'270 PARCEL ~OM PMAX ENTRAINMENT - 60 PERCENT P0 988 MB PHAX 938 MB LCL - 7Z7 MB LFC )(Xx M8 EI -ez J/KG x 10 EI+ e C+ PART) EI- -6Z C- PART> ENERGY ~E IN LAYERS P1 P2 938 lee -62Z J/KG X 10 LI 3 K1 SIoII l'Z CCL 836 HB 360 C TMP • 35 C C TMP • 95 F WAVG . &se G/KG )( 10-Z L _ 17 Fig. 2. Output from the CONVECT applications program in AFOS for the data from Table 1. Now the vector connecting two points is not changed when the coordinate system is changed, but the components of the vector representation do, indeed, change when changing coordinates. Thus, no matter how the wind vectors are repre­ sented, the points corresponding to the wind vectors them­ selves do not change. It certainly would be disturbing if we could change the winds simply by changing the way we represent them on a diagram! The CONVECT program uses u and v components to display the wind vectors, I but the plot would look identical if the program used speed and direction. However, if the winds were shown in a moving coordinate system (e.g., one moving with constant speed), the vectors indeed would change; additional discussion of this issue is deferred to sec­ tion 6. When plotting the wind vectors, if the tails of the vectors are all put at the origin, one needs to label the tips of the vectors with the heights at which each wind vector applies, to distinguish them from each other. Since the winds generally change with height, the vector tips should trace out some Fig. 3. Hodograph plotted in polar representation form, using speed line in going from level to level. and (meteorological) wind direction. Circles are wind speed every 10 m S-l, hodograph heights (AGL) labelled in km, every 0.5 km .