Lecture 2 Air Motions on Earth

Ito’s show

Three key factors at work in global atmospheric circulation

1. Pressure-gradient force:     While the equator and the poles represent major areas of air pressure differences, the planet is covered with areas of high and low pressure. These natural gradients generate additional wind, as high-pressure air flows into low-pressure areas. Meteorologists log these differences by drawing lines called isobars to connect areas of equal air pressure. These typically appear as swirling layers and concentric circles around key high- and low-pressure areas. We call these low pressure centers cyclones. These rotate in the familiar vortex pattern seen in hurricanes, where high-pressure winds spiral into the low-pressure center and then ascend in an updraft. We call the high-pressure centers anticyclones. High-pressure air descends in a downdraft and then spirals out along the surface into lower-pressure areas.

Three key factors at work in global atmospheric circulation

2. The Coriolis force:      All free-moving objects and fluids on Earth are subject to Coriolis force. In the N.H., winds are deflected to the right. In the S.H., they're deflected to the left. Coriolis force is strongest at the poles and weakest near the equator. Wind doesn't merely blow north and south from high to low pressure. Instead, the Coriolis effect forces these airflows to take an easterly or westerly direction. This breaks the hemispheric convection cell into three distinct types: Hadley, Ferrel and Polar cells.

Three key factors at work in global atmospheric circulation

3. Friction with Earth's surface:    Wherever surface winds meet the Earth, there's the potential for friction, which slows and redirects the flow of air. Upper air winds, however, don't encounter this resistance and travel at much higher speeds as a result. This is especially evident in the jet streams, great snaking rivers of fast-moving air that exist at between 6 and 14 km, and theoretically its travelling speed can reach 322 km/hr.

Global mean SLP in January. A stands for the Aleutian Low, P for the Pacific High, I for the Icelandic Low, Z for the Azores High, S for the Siberian High, H is a high. (a color Figure can be seen in the textbook)

Global mean SLP in July. The P for the Pacific High, B for the Bermuda High, H is a high. (a color Figure can be seen in the textbook) In the S.H. the pressure field is largely consistent with the Palmen-Newton model of the general circulation; whereas in the N.H. the land-sea contrast dominates in the extreme seasons. ( Lewis, J.M., 1998. Clarifying the dynamics of the General Circulation. Bull Amer. Meteor. Soc., 79, 39-60)

Dialogue between students and professor

[Q]

There is something I don’t understand concerning winds. I’m talking about winds beyond the influence of the surface’s roughness, wetness, friction and irregularities, at a height of 1000 metres, say. Why doesn’t

the wind flow straight from where pressures are high to where they

are low, just like rivers carving a valley down towards lower elevations? Why instead does the wind (aloft) go from a place at one pressure towards other places at the same pressure. If water flows along the same contour (on level ground), it stops flowing. Yet the winds aloft continuously blow along the same isobar, not across it. To say that air flows along an isobar seems like claiming that water flows along contour lines around a hill, instead of down. How do you explain this?

Dialogue between students and professor

[A]

This is because our EARTH KEEPS ROTATING, and the observer

rotates with it. As a result, the initial motion of winds towards places of lower pressure appears to be deflected, to the right(left) in the N.H.(S.H.). It looks as if there is a sideways force on the winds, in addition to the driving force due to the pressure gradient. This is

called the Coriolis effect.

It is true that wind blowing along the isobars would slow down eventually, because it is retarded by friction. But there is potential energy in a situation where cold air is next to warmer air. And this potential energy is continuously converted to kinetic energy, i.e. the airflow aloft.

Dialogue between students and professor

[Q]

Please explain the Coriolis effect.

[A]

1. There is a distinction between what we see and what is really happening, applied to the difference between the turning of an observer (O) and turning by what is observed (W). The difference could be due either to O turning or to W turning. However, in practice, O is unaware of her own twisting, so any difference is automatically attributed to rotation by W, even if this is untrue. The classic example is our Earth’s daily rotation, which makes us interpret what we see in the sky as the circling of the Sun. Actually the Sun is still; its apparent westward movement is the result of our own turning eastward. Similarly, we (on the rotating Earth) see all large-scale winds as apparently rotating, i.e. constantly pushed sideways.

Dialogue between students and professor

[Q]

Please explain the Coriolis effect.

[A]

2. The spherical shape of the rotating Earth means that places at 30 ° S spin eastwards at about 410 m/s, whilst those at 40 ° S turn at only 360 m/s. (We are unconscious of these enormous speeds because our whole environment moves at the same speed.) This means that a northerly wind at 30 ° S (simultaneously moving sideways at 410 m/s) is moving eastwards 50 m/s faster than the ground beneath, when it reaches 40 ° S. So the wind will now appear to be a westerly of 50 m/s. In moving to a higher latitude, the wind will seem to have turned to the left. You can work out likewise that a southerly wind from 40 ° S appears to turn, again leftwards, becoming an easterly of 50 m/s at 30 ° S.

Dialogue between students and professor

[Q]

Please explain the Coriolis effect.

[A]

3. In addition, there are several other ways of explaining the Coriolis effect by means of diagrams/ movies or mathematically. Also, it can be shown that it applies whatever the direction of the wind’s motion, and increases with the wind’s speed.

T 0 T +3hr

Dialogue between students and professor

[Q]

But how does the Coriolis effect explain why winds flow ALONG isobars on the usual weather map?

[A]

Well, this is a balance problem. As the wind moves as if always pushed to the right (in N.H.) or left (in S.H.), it is also constantly pulled towards the low pressure region, which is in a direction at right angles to the isobar. So the wind gradually accelerates and turns, until an equilibrium is reached, with a balance (in N.H.) between the pressure gradient force (PGF) across the isobars towards the left, opposite the Coriolis force to the right. Then the equality and exactly opposite directions of the two forces prevents further turning. The wind, called

geostrophic wind

, is now flowing along the isobars, in order that the

geostrophic balance

is maintained.

Dialogue between students and professor

[Q]

Is the explanation realistic? It is not easy to grasp.

[A]

Well, it is fairly realistic. There are complications due to friction of the winds on the ground, and to an outwards centrifugal force on spinning objects, but for large-scale flow, they are less important than the Coriolis effect, except near the equator, where the effect is small. The complications mean that the winds do not flow exactly along isobars. Usually they tend slightly to flow towards lower pressure, especially near the ground. So they SPIRAL out from a high and into a low.

Dialogue between students and professor

[Q]

Why did you say the Coriolis effect is small near the equator?

[A]

Because places at the equator do not rotate in the same way that places at higher latitudes do. A man standing at the N.P. with arms outstretched finds his right hand advances towards the Sun during the day, and it is the left hand which advances for someone at the S.P., but a person at the equator does not turn about his own axis at all. Without such turning there is no Coriolis effect. ALSO, the opposite directions of turning in the two hemispheres explain the different directions of the Coriolis effect. One may thus consider the Corilolis effect as positive in N.H. and negative in S.H., from which it follows that it must be zero at the equator between.

Dialogue between students and professor

[remark]

It may be an exaggeration to say that the Coriolis force is negligibly small near the equator. The upwelling of colder ocean water at the equator is an example of a situation where the Coriolis force, although small, is important!

 Imagine a steady easterly wind along the equator (see Figure to the right). Since the

Ekman transport

is to the left of the wind in the S.H., and to the right in the N.H., this wind induces a perpendicular flow of water away from the equator, in both hemispheres.

[remark]

    Dialogue between students and professor This divergence of near-surface water creates a “parting” along the equator, and the consequent upwelling (called Ekman pumping) produces a line of cooler SST at the equator, called cold tongue by oceanographer. The lower SST induces thermally direct atmospheric circulation cell, with subsidence and suppressed convection at the equator, and uplift and enhanced convection a few degrees poleward, namely the I.T.C.Z.

Importantly, these small-scale cells are opposite to the large-scale Hadley cell

.

This idealized picture is best established in the central and eastern equatorial Pacific, especially in summer and during La Niña years when a strong easterly Trade wind blows, and low SSTs prevail along the equator. The ITCZ is best established at 5-10N. The southern ITCZ is much weaker and ONLY present west of the dateline because of the widespread low SST off South America, due to the Humboldt (Peru) current.

Dialogue between students and professor

[Q]

I’m confused now concerning the importance of Coriolis effect.

[A]

Allow me tell you two things before doing the

scale analysis

judging the importance of Coriolis effect. Developments of ballistics make the Coriolis effect more significant.

German gun of 21-cm bore called “ Big Bertha

” was used in 1918 to shell Paris from a distance of 122 km. Over such a distance the inclusion of the Coriolis effect is as important as the wind deflection.

The Coriolis effect is of negligible importance in ball sports, relative to the effects of the wind and the spin of the ball itself. In 42N, a soccer ball kicked off 100 metres in 4 seconds will deviate 1.5 cm to the right. However, when the same ball is kicked with sufficient spin, it will easily deflect 100 times as much. The spin-induced deflection can be explained by the Bernouilli effect applied to air trajectories deflected to both sides of the ball.

Measurement of Coriolis effect

Measurement of Coriolis force

1. In a rotating disk, an object travels from the point O towards P. It takes time ∆t when travelling at speed v, so the distance OP equals v ∆t . 2. However, after a time ∆t, P will have moved from its original position (P') to a new position (P). The angle POP' equals Ω∆t . So for a short displacement the distance d = PP' is: 3. d = v∆t x tan(Ω ∆t) ~ v∆t x Ω ∆t = v Ω ∆t 2 (i) 4. The distance d is traveled in time t, which means the acceleration a, called Coriolis acceleration, is related to d by 5. d = ½ a ∆t 2 (ii) 6. (i)=(ii), therefore, a = 2 Ω v 7. Since the Earth' rotation rate around the local zenith is where Φ is the latitude and Ω e Ω e sin Φ the Earth's rotation rate (i.e., , 360 0 /24 hr), therefore,

a = 2 Ω

e parameter, f = 2 Ω e sin Φ .

sin Φ v = f v

, f is the Coriolis

Measure the importance of Coriolis force through scale analysis

1. Characteristic scale for the acceleration = V 2 /L 2. Characteristic scale for the Coriolis force = fV 3. Define Rossby number, R o = (V 2 /L)/(fV) = V/fL 4. Coriolis force becomes important when R o ≤ 1

[remark] There are Various force balances and types of horizontal flow in air/water

friction centrifugal force  pressure gradient force     Coriolis force   

balance geostrophic cyclostrophic antitriptic inertial

Various force balances and types of horizontal flow

1. For large-scale motion the pressure gradient force and the Coriolis force are an order of magnitude larger than the other terms, hence the

geostrophic balance

.

2. The balance of centrifugal and pressure-gradient forces is known as

cyclostrophic balance

. Smaller vortices, such as tornadoes and dust devils, can be cyclostrophically balanced at any latitude. centrifugal force is proportional to the flow's curvature and the square of the wind speed (= V 2 /R). Because the Coriolis force is not involved in cyclostrophic balance, there is no preference for winds to rotate counterclockwise around a small, short-lived low such as a tornado.

Various force balances and types of horizontal flow

3. A sea breeze reaches its strength around noon and may continue for several hours. Under a steady onshore pressure gradient force, sea breeze should continue to gain strength. The main force opposing this pressure gradient force is surface friction. This balance is known as

antitriptic balance

. Another example is the density currents , such as shallow outflows of cooler air from a mature thunderstorm, are also antitriptically balanced.

4. When pressure gradient is absent, Coriolis force may initiate rotation, then balanced by the centrifugal force. This is called

inertial balance

. The inertial period (i.e. complete one circle) equals 2  /f . Inertial motions frequently occur in the oceans .