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Using Hodographs: Plotting a Hodograph, Wind Barbs vs. Wind Vectors (page 1) Meteorologists are all familiar with the traditional vertical wind profile from a radiosonde that uses barbed lines to indicate wind direction and speed at various levels. The hodograph is simply another tool for communicating the same information.The hodograph, however, since its primary purpose is to reveal vertical wind shear, is based on wind vectors. Unlike the wind barb, a vector indicates speed by its length rather than a combination of barbs. Using Hodographs: Plotting a Hodograph, The Polar Coordinate Chart (page 2) For a hodograph, wind vectors are plotted on a polar coordinate chart. The axes of the chart represent the four compass directions. All the wind vectors extend from the origin and point in the direction of the wind’s movement. Since the vector length indicates speed, concentric circles drawn around the origin represent constant wind speeds. For example, this hodograph shows that both the 4 and 5 km winds are 25 m/s, although their wind directions are from the westerly and west- northwesterly, respectively. Using Hodographs: Plotting a Hodograph, The Hodograph (page 3) Typically, the actual wind vectors are not drawn on the hodograph, but are indicated only by their endpoints on the polar coordinate chart. Actually, the term "hodograph" refers to the group of line segments created by connecting the endpoints of each of the wind vectors. Using Hodographs: Vertical Wind Shear, The Vertical Wind Shear Vector (page 1) Vertical wind shear is a description of how the velocity of the horizontal wind changes with height. Since velocity is a vector quantity (i.e., it includes both speed and direction), vertical wind shear can be calculated as the vector difference between the horizontal wind at two levels. The resulting vector is called the vertical wind shear vector. Here we depict the shear vector in units of meters per second (m/s) or knots over the depth of the layer it represents (i.e., 25 m/s over 6 km). More accurately, wind shear is presented in terms of a unit distance, in which the shear vector magnitude is divided by the layer depth. For example, 25 m/s divided by 6 km (6000 m) results in .0042/s. Using Hodographs: Vertical Wind Shear, Displaying Vertical Wind Shear (page 2) The hodograph is ideally suited for displaying vertical wind shear. Using a polar stereographic grid, shear is revealed by drawing shear vectors from the ends of each wind vector in sequence of increasing height. You can see that the line segments of the typical hodograph actually represent the vertical wind shear for each layer. If the wind vectors on a hodograph represent the winds at even intervals (usually each kilometer or 500 m), the shear vectors are equivalent in terms of the depth they represent. Their relative lengths then indicate the relative strength of the wind shear from layer to layer. Using Hodographs: Vertical Wind Shear, Estimating Layer Shear Magnitude (page 3) The total magnitude of vertical wind shear over a particular depth is an important factor in anticipating possible storm structure and evolution. Therefore, it is important to measure the total vertical wind shear in some way. You can begin by estimating the length of any single shear vector. To do this, just visually compare it to the scale on one of the axes. Alternatively, you can measure the length of the vector and manually compare it with the scale units indicated on an axis. Using Hodographs: Vertical Wind Shear, Estimating Total Shear Magnitude (page 4) Estimating total vertical wind shear is done by combining the lengths of all the shear vectors over a particular depth (the net length of the hodograph). In this example, the total shear would be 60 m/s over 6 km. Using Hodographs: Vertical Wind Shear, Difficulties in Estimating the Shear Magnitude (page 5) Sometimes it can be difficult to visually estimate the length of the hodograph because the hodograph shape can mislead you. This is where shear strength calculations generated by computers can provide a big advantage. Using Hodographs: Vertical Wind Shear, Shear Distribution (page 6) It is also important to study how the wind shear is distributed over the depth of the hodograph. As demonstrated in this module, a hodograph with strong low-level shear has very different implications for storm structure than does a hodograph with equal total shear, but little shear at low levels. Using Hodographs: Vertical Wind Shear, Mean Wind Shear Vector (page 7) Another important quality of the storm environment that is easier to perceive on a hodograph than through other data is the mean wind shear vector. In later sections of this module we show how the direction of the mean shear vector provides information to help you anticipate how supercell motion will evolve. You can determine the direction of the mean wind shear vector simply by drawing a line from the point that plots the surface wind to the point plotting the 6 km wind. Again, the 0-6 km layer is used as the layer most effecting the storm. If you want to see why this works, use the In Depth button. In-depth: Calculating the mean wind shear vector is simply a matter of averaging the x and y components of each of the single layer wind shear vectors. If we are only concerned with the direction of the resulting vector, and not its magnitude, we can add the x and y components and plot the resulting line, using the surface winds as the origin of the re-oriented x/y reference frame ( x' ). The x/y ratio (direction) would not be changed by averaging. Without averaging, the process is the same as performing a vector addition of all the shear vectors. For this reason we can always get the direction of the mean wind shear by drawing a line from the first to the last wind plot of the layer. The re-oriented reference frame ( x' ) shows that the direction of the mean wind shear vector is toward the southeast. Using Hodographs: Hodograph Shape, Curved vs. Straight Hodographs (page 1) In addition to the magnitude of the shear, the hodograph shape is also important in anticipating storm structure and evolution. In this module, we are most concerned with whether the hodograph is relatively straight or curved, and when it does curve, the level through which it curves, and whether it curves clockwise or counterclockwise with height. These variations all have implications for storm structure. Using Hodographs: Hodograph Shape, The Irrelevance of Speed vs. Directional Shear (page 2) We know that vertical wind shear is created both by changes in wind speed with height (speed shear) and changes in wind direction with height (directional shear). The type of shear, however, tells us little about the shape of the hodograph since it refers to the speed and direction of the wind and not the wind shear vector. It is true that speed shear alone results in a straight hodograph (unidirectional shear), and that directional shear alone results in a curved hodograph (the shear vector turns with height), but combinations of the two can create any kind of pattern. Using Hodographs: Hodograph Shape, Large Scale Implications of Hodographs (page 3) While similarly shaped hodographs will have equal implications for our purposes in this module, they may have very different implications for larger scale processes and for the potential for convection. For example, both of the straight hodographs illustrated on this page should lead you to anticipate splitting supercells if convection occurs. However, the directional shear of hodograph A reveals backing with height through mid-levels, which is indicative of large-scale cold air advection in this layer. Hodograph B reveals veering winds with height through mid-levels, indicative of warm air advection in that layer. These two profiles would have very different implications for convective potential depending on other environmental factors. Thus, it is very important to consider the large scale environment as you analyze a hodograph. Using Hodographs: Hodograph Shape, Exercise: Plotting Hodographs (page 4) The examples on the previous pages should convince you that it is difficult to a visualize the hodograph shape by looking at the sounding. For this reason, it is important to use a tool (such as a computer program like SHARP) to create the hodograph for you. However, it may be useful to be able to quickly produce or modify a hodograph by hand. These exercises will give you practice doing this. Click the left mouse button on the hodograph location of each wind shown on the sounding, in sequence from the surface to the higher levels. Click Done to compare your answer to ours. Select each of the hodographs in turn to complete each part of the exercise. One full wind barb = 5 m/s, half barb = 2.5 m/s. Using Hodographs: Storm Motion and Storm-Relative Winds, Ground-Relative vs. Storm-Relative Winds (page 1) In anticipating the evolution of a convective storm, it is important to consider both the environment that the storm is experiencing and the one it might move into. For instance, the nature of the air making up the storm's inflow has implications for its evolution. To better understand this element of the storm’s environment, you must first determine or estimate anticipated storm motion on the hodograph and then study the potential storm- relative winds. Because the storm moves through its environment, the wind it experiences is often very different from the ground-relative winds measured with the stationary sounding. This difference is apparent for the hodograph and storm motion shown on this page. To determine storm-relative winds, the storm motion becomes zero in the new reference frame, and all environment winds are recalculated from this point. This is the same as performing a vector subtraction of the ground- relative wind minus the storm motion at each level. Using Hodographs: Storm Motion and Storm-Relative Winds, Determining Storm Motion (page 2) In order to study the storm- relative winds, you must first have a strategy for deter- mining storm motion. For existing storms, this can be done using loops of radar or satellite imagery. But to anticipate storm motion before storms exist or before the motion is apparent in the data, you must estimate it. We can assume (at least in the early stages of most convective storms) that the storm will move with a velocity close to that of the mean wind through the depth of the storm. Since both modelling and observations suggest that storm motion is most sensitive to winds in the lower levels, we use 6 km AGL as an approximate depth over which to calculate the mean wind. (Supercells will diverge from the mean wind, but this motion is discussed in other sections of this module.) There are several software packages (like SHARP) that can assist you by performing this calculation automatically. But it is useful to have a strategy for doing this on your own. Using Hodographs: Storm Motion and Storm-Relative Winds, Estimating Storm Motion: Straight Hodograph (page 3) When the hodograph is relatively straight, the rule-of-thumb for estimating mean wind and storm motion is simple. It would fall approximately at the midpoint on the 0-6 km AGL hodograph. Finding the storm-relative winds for each level is then just a matter of re- orienting the axes (xs,ys) such that storm motion becomes zero. The storm-relative wind at a given level is determined by the vector drawn from this new origin to the winds at that level. To be more accurate, we would pressure-weight the lower level winds since (because of their density) they will contribute more momentum to the storm motion. But this makes only a slight modification to the true average. Also, the fact that we suggest using only the 0-6 km winds takes this into account . Using Hodographs: Storm Motion and Storm-Relative Winds, Formula for Estimating Storm Motion: Curved Hodograph (page 4) When the hodograph curves, the estimation is a little more complicated. We have to look more closely at how the mean wind is actually calculated before we can use a rule-of-thumb. Each wind vector can be described in terms of separate u and v components. This illustration shows a component breakdown of the 3 km wind. As shown in the expression below, to calculate the mean wind, we take the average of the u components of the winds at all levels, and then separately average the v components of each wind. While this is not a quick calculation for you to make in practice, the hodograph allows you to do a visual approximation. Using Hodographs: Storm Motion and Storm-Relative Winds, Procedure for Estimating Storm Motion: Curved Hodograph (page 5) Illustrated here for a curving hodograph, to estimate the mean wind we find the average of the u components of the surface and 6 km winds. This assumes fairly equal spacing of the winds along the hodograph, but as a rough estimate it is adequate. Then estimate the average v components of the winds at all levels. By adding these vectors, we arrive at a good estimate of the mean wind. This will work for hodographs in any orientation if you re-orient the x-y reference frame ( x',y' ) to originate at the surface wind such that the x' axis also passes through the 6 km wind. View Hodograph 2 for an example of how to do this. Using Hodographs: Storm Motion and Storm-Relative Winds, Estimating Storm Motion: Multiple Curves Hodograph (page 6) When the hodograph is a more complex combination of multiple curves, this strategy can still help you estimate the mean wind, as the examples on this page show you. You will just have to work a little harder to make a good estimate of the mean v component when the curves are not symmetrical. Using Hodographs: Storm Motion and Storm-Relative Winds, Exercise: Determining Storm-Relative Surface Winds (page 7) For the hodographs on this page, click on the vector at the bottom right that best represents the direction (not magnitude) of the surface storm-relative winds. To do this, assume the storm moves with the mean wind. Select each of the hodographs in turn to complete each part of the exercise. That's correct. That's not correct. Review the diagram to see how we first re-orient the x-y reference frame ( x',y' ) to determine the mean wind (unnecessary for straight hodographs), and then re-orient it again ( xs,ys ) to plot the storm- relative wind. That's not correct. Review the diagram to see how we determine the mean wind as the mid-point on the 0-6 km straight hodograph, and then re-orient the x- y reference frame ( xs,ys ) to plot the storm-relative wind. Using Hodographs: Vorticity Vectors, Representing the Vorticity Vector (page 1) As we explain in other sections of this module, vertical wind shear in the environment always has horizontal vorticity associated with it. Here we are concerned with how this vorticity is represented by vectors on the hodograph. In another section of the module, we will show that it is the low-level storm-relative wind and its relationship to the horizontal vorticity vector over that same level that define the quantities of streamwise or crosswise vorticity, which are in turn used to define storm-relative helicity. We can represent the horizontal vorticity for each layer by drawing a vector perpendicular and to the left of the shear vector. This is in keeping with the "Right Hand Rule," which in this case states that the vorticity vector points in the same direction as the thumb of your right hand when your fingers are curled, palm-down in the direction of the shear vector. The length of the horizontal vorticity vector is proportional to the length of the shear vector (i.e., the magnitude of the vorticity is proportional to the magnitude of the wind shear). However, as with the mean shear vector, in this module we are mainly concerned with the direction of the horizontal vorticity vector, rather than its magnitude. We will not discuss how to calculate the magnitude of the vorticity vector or present vorticity vectors with calculated magnitudes. Using Hodographs: Vorticity Vectors, Mean Vorticity Vector (page 2) A final quantity represented on the hodograph that we will use in this module is the mean horizontal vorticity vector. This is simply the vorticity vector that can be drawn from the mean wind shear vector, just as we drew the vorticity vectors from the shear vector for each layer. Again, here we are only concerned with its direction, so we do not need to calculate its length. We can draw it at any point along the line representing the direction of the mean shear vector. For instance, if we want to show the orientation of the mean horizontal vorticity vector in relation to the mean wind, we can draw it such that it passes through the point indicating the mean wind.

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