## Principles of Convection II: Using Hodographs

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Contents

1. Introduction
2. Plotting a Hodograph
3. Vertical Wind Shear
4. Hodograph Shape
5. In-Depth: Storm Motion and Storm-Relative Winds
6. Summary

### 1. Introduction

1.1 The Importance of Shear

The hodograph is a graphical tool that helps forecasters evaluate vertical wind shear. In a convective environment, an understanding of the vertical wind shear is tremendously important for anticipating convective storm type, where new storms may form, the likelihood of supercell storms, and even storm and storm system motion. For example, these figures show the simulated radar returns for a series of modeled storms that evolved under different vertical wind shear conditions, which are depicted by the idealized hodographs in the lower left.

1.2 The Hodograph

The ability to anticipate possible storm structures is critical in managing your activities before and during a convective event. Having the right set of expectations for a given storm environment will make you a more efficient and accurate forecaster. The hodograph depicts the environmental wind shear, which profoundly influences storm evolution. Thus, a representative hodograph combined with a representative buoyancy profile can greatly enhance forecast skill. This figure shows an AFWA MM5 model sounding, along with the associated hodograph, downloaded from the Joint Army-Air Force Weather Information Network (JAAWIN) Website. Similar sounding/hodograph plots are available from many sources.

After completing this module you should understand how hodographs are constructed and how they can help you estimate the total shear, mean shear, and mean wind. To learn how shear impacts the development of convective storms, see the companion module Principles of Convection IIII: Shear and Convective Storms.

### 2. Plotting a Hodograph

2.1 Wind Barbs vs. Wind Vectors

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 communicates the same information. However, since its primary purpose is to reveal vertical wind shear, the hodograph is based on wind vectors. Unlike the wind barb, a vector indicates speed by its length rather than a combination of barbs.

2.2 The Polar Coordinate Chart

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 west and west-northwest, respectively.

2.3 The Hodograph

Typically, the actual wind vectors are not drawn on the hodograph, but are indicated only by their endpoints on the polar coordinate chart. The hodograph is plotted by connecting the endpoints of each of the wind vectors.

### 3. Vertical Wind Shear

3.1 The Vertical Wind Shear Vector

Vertical wind shear is a description of how the velocity of the horizontal wind changes with height. Velocity is a vector quantity; in other words, it possesses both speed and direction. Therefore, we determine the vertical wind shear by taking 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 (for example, 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. Thus, 25 m/s divided by 6000 m (6 km) results in a shear magnitude of 0.004 per second.

3.2 Displaying Vertical Wind Shear

The hodograph is ideally suited for displaying vertical wind shear. Using a polar coordinate chart, 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.

3.3 Estimating Layer Shear Magnitude

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.

3.4 Estimating Total Shear Magnitude

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 (20 kft).

3.5 Difficulties in Estimating the Shear Magnitude

Sometimes it can be difficult to visually estimate the length of the hodograph due to a complicated shape. Under these circumstances, shear magnitude calculated by computer may be more accurate than a visual estimate.

3.6 Shear Distribution

It is also important to study how the wind shear is distributed over the depth of the hodograph. 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.

3.7 Mean Wind Shear Vector

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. For example, the direction of the mean shear vector provides information to help you anticipate supercell motion.

You can determine the direction of the mean wind shear vector (but not the magnitude) simply by drawing a line from the point that plots the surface wind to the point plotting the 6-km (20-kft) wind. Again, we use the 0-6 km layer as the layer most effecting the storm. If you want to see why this works, use the In Depth button.

3.7 In-depth: Calculating the mean wind shear vector

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.

### 4. Hodograph Shape

4.1 Curved vs. Straight Hodographs

In addition to the magnitude of the shear, the hodograph shape is also important in anticipating the structure and evolution of convective storms. 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.

4.2 The Irrelevance of Speed vs. Directional Shear

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.

Select each of the hodographs for a comparison of shear types and hodograph shape.

4.3 Large Scale Implications of Hodographs

While similarly shaped hodographs may affect convective storm evolution in similar ways, their implications for larger-scale processes and for convective potential may differ substantially.

For example, both of the straight hodographs illustrated on this page would 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.

4.4 Exercise: Plotting Hodographs

### 5. In-Depth: Storm Motion and Storm-Relative Winds

5.1 Ground-Relative vs. Storm-Relative Winds

[Buttons for Ground-Relative Winds and Storm-Relative Winds]

In anticipating the evolution of a convective storm, it is important to consider both the environment that the storm is currently experiencing and the one into which it might move. 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, we first reposition the reference frame so that the storm motion becomes zero. Then, we recalculate the environment winds from this point. This is the same as subtracting the ground-relative storm motion vector from the ground-relative wind vector at each level.

5.2 Determining Storm Motion

In order to study the storm-relative winds, you must first determine 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 imagery, 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 modeling and observations suggest that storm motion is most sensitive to winds in the lower levels, we calculate the mean wind through a depth of 6 km (20 kft) AGL. Supercell motion will diverge from the mean wind, but that topic is discussed in another module.

There are several software packages (like SHARP) that calculate mean wind automatically, but it is useful to understand how this is done.

5.3 Estimating Storm Motion: Straight Hodograph

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 drawing a vector from this new origin to the winds at that level.

To be more accurate, we would pressure-weight the lower-level winds. 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, we account for much of the discrepancy by using only the 0-6 km winds.

5.4 Formula for Estimating Storm Motion: Curved Hodograph

When the hodograph curves, the estimation becomes 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 (10-kft) wind.

To calculate the mean wind, we separately average the u and v components of the wind at all levels. Then we add the mean u and v vectors. In practice, this is not a quick calculation. Luckily, the hodograph allows you to do a visual approximation.

5.5 Procedure for Estimating Storm Motion: Curved Hodograph

To illustrate how we estimate mean wind using a hodograph, let's return to our curved hodograph example. First, you can see that each point on the hodograph has u and v components. To estimate the mean u component, we average just the surface and 6-km (20-kft) winds. This assumes a fairly equal spacing of the winds along the hodograph, but it is adequate as a rough estimate. Then we estimate the average v components of the winds at all levels. By adding the mean u and v vectors, we arrive at a good estimate of the mean wind.

This technique will work for hodographs in any orientation, but first you must re-orient the x-y reference frame. Start by moving the origin to the point representing the surface wind. Then rotate the x'-y' axes so that the x' axis passes through the 6-km (20-kft) wind. Now estimate the mean wind as before.

5.6 Estimating Storm Motion: Multiple Curves Hodograph

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 will just have to work a little harder to make a good estimate of the mean v component when the curves are not symmetrical.

5.7 Exercise: Determining Storm-Relative Surface Winds

6. Summary

• The primary purpose of a hodograph is to reveal vertical wind shear
• Vertical wind shear is a description of how the velocity of the horizontal wind changes with height. We determine the vertical wind shear by taking the vector difference between the horizontal wind at two levels
• The hodograph is based on wind vectors, rather than wind barbs. To create a hodograph, wind vectors are plotted on a polar coordinate chart. Then their endpoints are connected
• The total magnitude of vertical wind shear over a particular depth is an important factor in anticipating possible storm structure and evolution. 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)
• You can determine the direction of the mean wind shear vector (but not the magnitude) by drawing a line from the point that plots the surface wind to the point plotting the 6-km (20-kft)wind
• 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
• In addition to the magnitude of the shear, we are also concerned with whether the hodograph is relatively straight or curved. While similarly shaped hodographs may affect convective storm evolution in similar ways, their implications for larger-scale processes and for convective potential may differ substantially
• Because the storm moves through its environment, the wind it experiences is often very different from the ground-relative winds. Storm-relative winds can also be calculated on a hodograph

In this module, we have learned how to calculate several different shear parameters and we have started to see a little of how these parameters are applied. To learn more about how shear affects convective storms, see the module Principles of Convection III: Shear and Convective Storms (http://www.meted.ucar.edu/mesoprim/shear/index.htm).