The jet stream: chicken or egg?

Wednesday 15th Dec 2010 by Dr Liz Bentley

Simeone Reginald asks: "When I look at forecast maps on westwind.ch that show the height of the 500mb layer and then look at the forecasts of the position of the jet stream, I notice that the jet stream almost always follows the dividing lines between the colder and warmer upper air masses. Does the position of the warm and cold upper air masses determine the route of the jet stream, or does the jet stream determine the position of the cold and warm upper air masses? Which is the chicken and which the egg?"


The simple answer

The sun shines on the planetary sphere directly overhead during the daytime in the tropics and more obliquely nearer the poles. Consequently, it heats the ground, or sea, more in the tropics than nearer the poles. In turn, the hotter surface warms the air more over the tropics than does the cooler surface nearer the poles. This leads to convection over the tropics and warming of the atmosphere in depth. Given more or less uniform pressure at the surface, pressure falls off more slowly with height in warm air than in cold, denser, air. This means that at some height, say 18,000 feet (say 5km) pressure will be higher over the equator than nearer the poles. This causes winds to become more westerly with height in both hemispheres. As vectors, the upper wind is the sum of the lower wind and the, so-called, thermal wind.

But, temperature gradients, mountains and the distribution of land and sea disturb the idealized flow, distort the horizontal temperature patterns , concentrate the gradients (and so the thermal winds) and strengthen the winds aloft. In extreme cases, this results in jet streams. (Above the jet stream, the temperature gradient is reversed and so the wind falls off with height.)

Now the atmosphere is three-dimensional and varying in time. Some areas near jet streams encourage air to ascend from below and so help develop low-level depressions beneath them. Other areas of the jet favour sinking air aloft and so the development of anticyclones. The winds around these new features distort the average temperature in-depth patterns and so on.

Nearer the truth

The way I've told the story suggests that the height of the 500mb (or hPa) surface ― and the thickness of the 1000-500mb layer ― are the chicken and the jet stream the egg. However, we never have a fresh start. The race just goes on for ever. The jet stream and the distributions of temperature and pressure are always closely related, but small changes in one or both grow to make other changes in both. Feedback.

Think of a simple internal combustion engine, with a cylinder, mixture of air and petrol, piston connected to a crankshaft which turns a flywheel driving a dynamo to provide a spark in the cylinder. When the engine is running, you might say the flywheel keeps the engine turning so that air and petrol enter the cylinder and drives the dynamo that generates the electricity to make the spark to cause the explosion which drives down the piston and keeps the flywheel turning. But you can take different parts of the engine and see them as either chicken or egg. From the flywheel's point of view, for example, the spark could be the chicken – or so could the petrol and air. Or, alternatively, I the flywheel am the chicken. From the piston's point of view, unless I come up, cause the petrol and air to come into the cylinder and let the spark explode them, nothing happens: I'm the chicken. And so on. We have a continuous internally consistent process. There is no chicken and no egg ― it's a wrong analogy.

By the way, it's an interesting fact that for any pattern of winds at any moment, it is only the differences between the corresponding theoretically consistent distribution of pressure at that moment and the real pressure distribution at that moment (the so-called ageostrophic component) that cause our cloud, rain and snow.

Comments

Sorry, but I have a problem understanding some key parts of the argument. Why does pressure fall off more slowly in warm air than cold air? And is the fact that this makes higher winds more westerly due to the exaggeration of the effect of the earth's rotation on pressure flow, in which case, can you explain this phenomenon?
Posted by Richard C on Mon, 17 Jan 2011 08:46:26 +0000
Quote Richard C:
"Why does pressure fall off more slowly in warm air than cold air"

Response:
Air density is the mass of all the gases contained within a unit volume of atmosphere. In standard units density is reported in units of kg / m^3. In warmer climates the air contained within a vertical column is on average less dense than for a column of the same thickness in cooler climates. This is because the gas molecules, such as nitrogen, oxygen and water vapour "jiggle about" more vigorously when then get warmer and its this increase in molecular kinetic energy that causes them to spread apart. If you were to imagine a vertical column 1 metre by 1 metre in the horizontal plane and extending from 0 km at the surface to an altitude of 10km aloft, the mass of this volume would therefore be lower in warmer climates.

Often in Meteorology we refer to the column temperature using pressure as a vertical dimension. Pressure always decreases with altitude, as this is governed by the mass of atmosphere that sits above. The average global air pressure, data which can be obtained from the 1976 US Standard Atmosphere, is close to 1013 mb (i.e. one atmosphere). The other level that meteorologists like to use is 500 mb, which usually sits at about the half way point in terms of atmospheric mass. The 500 mb pressure level is not placed at a fixed height, it varies substantially. In fact, in the tropical atmosphere the NASA Jet Propulsion Laboratory (JPL) science team use an expression z = 16 x (3 - log (p)), where z is the height in kilometres and p is the pressure in mb. That places the p = 500 mb level at 4.8 km above the surface.

To estimate the "thickness", or depth of the column 1000mb - 500mb, we can use a relationship.
The thickness of a column of atmosphere exhibits both a temperature and pressure dependency. The ideal gas law demonstrates that the pressure of a given volume of gas (P) in a standard mixed atmosphere with an universal gas constant (R = 287 J·kg-1·K-1) is: P = rho x RT. Here rho is the density of the air in SI units of kg.m-3.

The hydrostatic equation for air demonstrates that on a fixed level within an atmospheric column the upward pressure gradient force dP/dz is equal to the force exerted by a mass of air (per unit volume) acting downward. In this case dP/dz = -rho . g.

By combining the ideal gas law and the hydrostatic equation, we can then produce an equation that states the "thickness" of a vertical column of atmospheric air, with a depth of Dz. In the following equations Dz = z2 - z1.

The thickness equation is given by the following equation, where p2 and p1 are the pressures in Pascals (N.m-2) exerted at two fixed levels by overlying air. In this case level z2 is situated at a lower altitude than level z1. T here represents the average atmospheric temperature within the column of air, between levels z1 and z2.

Dz = -RT/g x ln(p2/p1)

The thickness of the atmosphere is related to the temperature of an allocated column of air. The "thicker" the column of air between pressure levels p1 and p2, the less dense the air column and the higher the average atmospheric temperature (T).

Point #2

Thermal wind balance explains why winds tend to blow at a particular strength and with a westerly direction in the northern hemisphere mid-latitudes. Without going into too much detail, the stronger the S-N temperature gradient, the greater the magnitude of the westerly flow. Thermal wind can explain why, away from the affects of surface friction, the jet stream is usually positioned where the S-N temperature gradient is the strongest in both pressure (altitude) and latitude co-ordinates.

I hope that adds some clarity.
Posted by Chris Nankervis on Sat, 17 Sep 2011 18:27:07 +0000