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Several months ago, we created a discussion to help people unfamiliar with Skew-T diagrams that can be viewed here. Understanding atmospheric dynamics such as wind shear is equally as important to forecasting as an understanding of thermodynamic diagrams. More useful and more common than perhaps any other tool for this purpose is the hodograph.

Before we can use hodographs for our forecasting and analysis, we first must have at least a basic understanding of vectors. A vector is a quantity that, unlike a scalar which has just a magnitude, consists of both a magnitude and a direction. Let’s relate these terms to meteorology! When you check your local forecast, the first thing you may see that your forecast high is 52°F. This quantity is a scalar, because it has only a magnitude. What do you look for next, most likely, the chance of rain! A 70% chance of rain has no direction, just a magnitude, so this value too is a scalar. But what are you likely to look for next? The wind, of course. For the sake of this example, let’s say that the wind today will be 20 miles per hour out of the north-northwest. This value, unlike the other two examples, is a vector. With a magnitude of 20 mph and a direction of south-southeast, or 158°. Important: When people refer to a “north wind,” they usually are talking about wind that is blowing from north to south. When talking direction, north is 0°/360°, east is 90°, south is 180°, and west is 270°. The NNW wind in this is example is blowing to the SSE, and because the direction of a vector is given as the direction it points, we assigned it a direction of 158°. However, to stay consistent with the way things are done in meteorology, from here on out all winds will refer to the direction they are coming from, so a NNW wind will be about 338°.

What does this have to do with hodographs? We’ll get to that! First, let’s show you a blank hodograph just to get that image in your head.

The above image is the most common of several ways a hodograph may be presented. It is the same concept as a polar coordinate chart. The lines directed outward from the center indicate direction, and the different sized rings encircling the center represent wind speed. This is the fundamental part of hodographs that must be understood. Two things: speed, direction. Does that sound familiar? Speed and direction? It should! Remember that wind is a vector, so it has both a magnitude (speed) and a direction.

Let’s start by plotting the wind speed at the surface on this hodograph. Let’s say the wind outside is blowing at 20 knots out of the east, toward the west.

The red dot on the hodograph indicates where the surface wind in this situation would be plotted! This represents the wind vector. In case this is difficult to visualize, here’s what the hodograph would look like with the vector drawn in as an arrow.

Technically, this first image we posted could be used as a real hodograph! It has the chart, with the wind at at least one level plotted. But we will almost never encounter a hodograph with only one level plotted, as it defeats the purpose of such a useful graphical display. Let’s plot the wind speeds in a hypothetical atmosphere all the way up to six kilometers above the ground! We will use the same easterly surface wind, and add in a few more points to show other levels of the atmosphere at the same time.

We can now see the wind direction at five different heights above one location on a single plot! The wind at the surface is blowing at 20 knots from the east. One kilometer above the ground, the wind is blowing 30 knots from the ESE. At 3 km, the wind is 35 knots from the SE. At 4.5 kilometers above the ground, the wind is blowing at 40 knots from the SSW, and at 6 km the wind is blowing 60 knots from the WSW! As before, to help us visualize all of these directions, let’s take a look at the same diagram, but with the vectors plotted.

Like before, the longer the arrow and the farther the plotted point from the center, the higher the wind speed! Without knowing what the atmosphere looks like before hand, we would have no idea which point was which, so points on a hodograph will usually be labeled with either a height or a pressure for reference.

Now that we’ve plotted several points from 0-6 kilometers, there is one more step before we are done. While digitally generated hodographs will usually have more than five data points, this illustrate the same point just as effectively. When a hodograph is created, it is helpful to “connect the dots” of all of the plotted points. This helps visualize how the atmospheric wind profile actually looks more effectively than to just look at several dots. To do this, we will draw a line from the lowest point (the surface), to the second-lowest point (1 km), and continue this all the way to the highest point (6 km). Let’s take a look!

There we have it! This is what a hodograph would look like in the environment we used. The line used to connect the dots shows perfectly that the wind speed increases with height, and the wind direction veers with height. A veering wind profile is one that rotates clockwise with height, like this one. When the wind turns counter-clockwise with height, it is said to be backing. A wind profile that veers and increases with height like this one is extremely favorable for supercells and tornadoes! Here are a couple more examples of hodographs that can be useful for forecasting.

Straight-line hodograph:

This is often called a straight-line hodograph. These do not have to be, and almost never will be, perfectly straight, but hodographs that generally exhibit a straight line fit into this category. Even though significant speed shear can be present, the lack of directional wind shear tends to favor splitting supercells that are more likely to produce large hail than tornadoes.

Weak wind shear environments

In environments like this, winds are weak and sporadic throughout all levels. Coming from several different directions, this hodograph has no winds that exceed 10 knots. Environments with weak wind shear can still have severe weather if instability is high, but it will likely be in the form of multicellular storms with hail and wind as the main threads. Supercells and tornadoes are rare in these environments, but they can happen, especially with extreme instability and local boundaries. For example, the environment near Jarrell, TX, on 5/27/97 looked much like this, but the presence of incredible instability along with a gravity wave moving through the region helped a southward-moving supercell produce a violent F5 tornado.

Values that can be drawn from hodographs

In addition to the assumptions that can be made simply by glancing at a hodograph, a slightly more in-depth look at an environment’s hodograph can reveal a bit extra at times. Here we’ll discuss a couple of these!

Bulk shear and bulk wind difference

Bulk wind difference is the difference between the wind vectors at two levels of the atmosphere. We usually see 0-6 km bulk wind difference, which means the difference between the winds at 6 km and at the surface. We can see this easily on a hodograph by drawing a vector from the surface wind to the 6 kilometer wind! Once we’ve drawn this vector, we can redraw an identical vector that originates at the center of the hodograph.

From the vector we’ve added at the origin of the plot, we can see that this hodograph has an 80 knot 0-6 km bulk wind difference in the ENE direction. When taken into consideration with other factors, this is very favorable for severe thunderstorms! Bulk shear is very similar to bulk wind difference, except that “shear” is normalized over the depth over which it is taken. A wind difference of 100 m/s over 6 km, or 6000 meters, results in a bulk shear value of .0167 s^-1. ((100 m/s)/(6000 m) = .0167 s^-1)

Storm Motion and Storm Relative Helicity

When forecasting for severe weather and possibly supercells, storm motion and storm relative helicity (SRH) are two very important factors that must be considered. The two are related, and both can be estimated using hodographs, although exact values are difficult to ascertain with out help from a computer! Storm motion tends to be near the “mean wind” of the environment, so without going into too much detail, we can estimate that the storm motion in this environment will be somewhere near this area:

The actual mean wind in an environment like this would likely be a bit more northerly and possibly a bit faster, but because tornadic supercells often move right of the mean wind, we have placed our estimated storm motion a bit farther to the east. Once we’ve plotted our storm motion, we can begin finding our storm relative helicity. SRH is typically measured either from 0-1 km or from 0-3 km, and represents the amount of “spin” in the atmosphere between those levels. For supercells in general, many meteorologists use 0-3 km SRH, while 0-1 km SRH can be very helpful when forecasting tornado potential. To calculate 0-3 SRH using this hodograph, we will draw two lines from the storm motion data point to the 0 km (surface) and 3 km data points. The area between these lines and the plotted hodograph represents the SRH in meters-squared per second-squared (m²/s²). It would be difficult to calculate an exact SRH by hand for a hodograph like this, but this would be an environment with a significantly high value! Over time, after observing many hodographs, it becomes easier to estimate SRH by looking at the hodograph. 0-3 km SRH values over 250 m²/s² and 0-1 km SRH values over 100 m²/s² are considered by many to be guidelines for the minimum needed for tornado formation with supercells, but there is no exact threshold. It all depends on the environment!

We hope this has been educational and you have learned something about hodographs. We plan to add more educational postings here with time. If you have any questions or special requests, let us know through Facebook, Twitter, or our contact page. Thanks!