Saddle-points and today’s weather

I've been following the weather with interest this week. First of all, I was very glad when the wind and rain disappeared late last weekend. We were at a wedding in Whakatane on Saturday afternoon/evening, and boy, did it rain. With the wedding in a garden in something that was a bit more substantial than a marquee (think marquee with hard walls and floor), with a portaloo outside,  and a four minute walk up a long, dark, mud and puddle infested driveway in a storm separating you from the car, it was certainly a memorable wedding reception. 

Now, with beautiful clear skies, light winds, and frosty mornings, you'd be forgiven for thinking there's a big fat high pressure system sitting over us.  But there isn't.  For the last few days, we (by which I mean at this end of the country) have been in or around a saddle-point, in terms of pressure. There have been lows to the north and south, highs to the east and west, and somewhere in the middle over us. I note today that things have rotated a bit, so the lows now lie east and west, with a high to the north and another approximately south. Here's a picture I've stolen from the metservice website this morning (www.metservice.com, 18 July 2014, 11am); it's the forecaset for noon today. Note how NZ is sandwiched between two lows, but isn't really covered by either. 

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You can see the strength of the wind on this plot by the feathers on the arrow symbols. The more feathers, the stronger the winds. (The arrows point in the direction of the wind). Note how the wind blows clockwise around the low pressures (and anticlockwise, less strongly, around the highs). Have a look just around Cape Reinga (for non-NZ dwellers, and I know there's a few of you out there, that's the northern-most tip of the North Island.) There's a point where the wind (anthropromorphising) doesn't know what to do. It's in what's mathematically termed a saddle point. It's a point where locally there is no gradient in pressure, but is neither a high or a low. Winds are light.  In two dimensions (this is what we have on the earth's surface) with a single variable such as pressure, there are those three possibilities where the gradient of pressure is zero – a the maximum of a high, the minimum of a low, or a saddle. 
 
In terms of terrain, a mountain pass is a saddle point. It's where one goes from valley to valley (low to low), between two mountains. On top of the pass, you are at a point where the gradient is zero. But it's neither a peak or a trough. It's called a 'saddle', because the shape looks rather like a saddle for a horse – which is low on both flanks, but high at the front and back. A marble placed on top of a saddle should, if it were placed exactly at the equilibrium point with no vibrations, stay there. 
 
Saddle-points crop up in all kinds of dynamical systems (e.g. brain dynamics) where there's more than one variable involved.  Such a point is termed an unstable equilibrium – any deviation from the equilibrium point will cause the system to move away from it. However, the change may not be terribly rapid. When there are lots of variables involved, such local equilibria may have very complicated dynamics associated with them indeed – the range of possibilities gets very large and dynamics can become very rich indeed. 

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