Monday, July 29, 2013

Hodo you di'int!

Just when you thought I was finished with diagrams, I strike again.

Today we’ll be looking at the Hodograph, the Skew-T’s cousin, and seeing how it’s used.

But first, remember what it means for something to be a vector quantity. That means that it has magnitude and direction. One can easily see why wind is a vector quantity. It blows (for instance) at 10 knots, from the west.

The Hodograph is a diagram on which to plot wind vectors. The concentric circles are all lines of wind speed, and the numbers at the ends of the axes are the direction that the wind is blowing from (such that 0 degrees is north, and 270 degrees is west). So if you drew a vector from the origin to any point, it would represent the speed and direction of the wind at that particular level.

Consider the hypothetical wind vectors plotted below:

The red vector would be wind blowing from the southeast at 20 knots. The blue vector would be wind blowing from the south at 40 knots. The green, west-northwest at 50 knots. The yellow, east-northeast at 100 knots.

If we now switch to plotting more “real” data, as in from an actual sounding, we see that it is not very different. Although wind is blowing at every level of the atmosphere, each vector, regardless of the level it represents, starts from the origin. Each consecutive vector is essentially piled on top of the previous one.

Let’s say we had the following wind vectors and levels:
Surface: ESE at 20 kts
925 mb: SSE at 30 kts
850 mb: S at 50 kts
700 mb: SSW at 40 kts
500 mb: WSW 60 kts
300 mb: W at 110 kts

The vectors would be plotted like this:

We would then connect all of the tips of the vectors, and erase the actual vectors themselves, and have a sounding plotted on a Hodograph that looks like this:

The numbers are the height above ground level, in kilometers. So where you see “1,” that is the speed and direction of the wind 1 kilometer above the ground. (I forgot to include them in future images; don't be frightened that they disappered.)

Now in the real world, we’re dealing with more than six data points. A typical sounding might have hundreds. In that case, the curve is much smoother, like this:

If we want, we can draw another vector that connects the surface wind vector and any other height, and get the shear vector for that height range.

Below, I’ve drawn the 0-6 km shear vector.

If we then move that vector so that it starts at the origin, but do not actually change its magnitude or direction, we then know how much wind shear there is over a given region by noticing its magnitude and direction.

If we shade in that region and add up all of the pieces (in other words, integrate the polar curve, for those who have taken Calculus), we get a parameter known as Surface-Relative Helicity. The SRH is shaded in yellow below:

What I’ve drawn is 0-6 km SRH, but 0-1 km and 0-3 km are much more common. SRH is an excellent predictor of the potential for tornadoes (assuming adequate instability, no capping, and a source of lift, of course). 0-1 km SRH greater than 150 m2/s2, or 0-3 km SRH greater than 200 m2/s2 is generally considered adequate for tornadoes.

In addition to SRH, it is also important to look at Storm-Relative Helicity. (Yes, they both can be SRH, but if you’re looking at a model-produced image, you’re likely looking at Surface Relative Helicity.)

Storm Relative Helicity is calculated by drawing the storm motion vector from the origin, and then shading in all of the area between the tip of that vector, the surface, and whatever height you want to calculate for (again, in this case, 6 km).

Notice that in the same environment as above, a deviant storm motion toward the southeast (vector shown in blue) significantly increases the Helicity that that storm is able to ingest, in turn increasing the likelihood that it will produce a tornado.

Lest you believe that every Hodograph you look at will clearly depict a tornadic environment, I’ve drawn below what the majority of Hodographs you will see looks like: