SOEE1401 Lecture 7 - Atmospheric Motion Notes

Atmospheric Motion

Forces on the Air

• The air is subject to Newton's second law of motion: it accelerates when there is an unbalanced force.
• When the forces are balanced, the airflow is steady.
• There are three forces which influence horizontal airflow:
  • Pressure gradient force ($F_p$)
  • Coriolis force ($F_c$)
  • Frictional drag ($F_d$)

Pressure Gradient Force (PGF)

• Horizontal pressure gradients are the main driving force for winds.
• The pressure gradient force is inversely proportional to the spacing of isobars
  • Closer spacing implies a stronger force.
• The force is directed perpendicular to isobars, from high pressure to low pressure.
• The pressure gradient force acts to accelerate the air towards the low pressure.
• $F_p = - \frac{1}{\rho} \frac{dP}{dx}$, where:
  • $P$ is pressure
  • $\rho$ is air density
  • $x$ is distance
• Example calculation: $F_p \sim -\frac{(1004 - 1000) hPa}{\rho (2-1)}$

Coriolis Force

• The Coriolis force is an apparent force.
• It is introduced to account for the apparent deflection of a moving object observed from within a rotating frame of reference, such as the Earth.
• An object moving in a circle is accelerating because its velocity is continually changing with time.
• If we view motion from an accelerating frame of reference, we must introduce apparent forces.
• The Coriolis force acts at right angles to both the direction of motion and the spin axis of the rotating reference frame.
• In the atmosphere, we are concerned mostly with the horizontal component of the Coriolis force.
• It has a magnitude (per unit mass) of: $fV = 2\Omega V \sin\phi$, where:
  • $\Omega$ = angular velocity of the earth
  • $V$ = wind speed
  • $\phi$ = latitude
  • $f = 2\Omega \sin\phi$ = “Coriolis parameter”
  • $\sin(90^\circ) = 1.0$
  • $\sin(0^\circ) = 0$
• Therefore, $f$ is a maximum at the poles and zero at the equator.
• Results in a deflection to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

Geostrophic Balance

• Steady flow tends to lie parallel to the isobars, such that the pressure gradient and Coriolis forces balance.
• This is termed geostrophic balance, and $V_g$ is the geostrophic wind speed.
• Pressure gradient force = Coriolis force
• $\frac{1}{\rho} \frac{dP}{dx} = 2\Omega V_g \sin\phi$
• Geostrophic flow is a close approximation to observed winds throughout most of the free atmosphere, except near the equator where the Coriolis force approaches zero.
• Departures from geostrophic balance arise due to:
  • Constant changes in the pressure field
  • Curvature in the isobars
• Significant departure from geostrophic flow occurs near the surface due to the effects of friction.

Centrifugal Force

• Motion around a curve involves another apparent force: the centrifugal force.
• The required centripetal acceleration is provided by an imbalance between the pressure and Coriolis force.
• $V$ is here called the gradient wind.
• For a Low, the Coriolis force is weaker than the pressure force: LOW: $V$ < geostrophic (subgeostrophic).
• For a high, the Coriolis force is stronger than the pressure force: HIGH: $V$ > geostrophic (supergeostrophic).

Effect of Friction

• Friction at the surface slows the wind.
• The direction of the drag force ($F_d$) is approximately opposite to the wind direction.
• Near the surface, the wind speed is lower than the geostrophic wind.
• Lower wind speed results in a smaller Coriolis force, hence reduced turning to the right.
• Turbulent mixing extends the effects of friction up to ~100 m to ~1.5 km above the surface.
• Wind vector describes a spiral: the Ekman Spiral.
• Surface wind lies to the left of the geostrophic wind.
  • 10-20° over the ocean
  • 25-35° over land
• The wind speed a few meters above the surface is ~70% of the geostrophic wind speed over the ocean, even less over land (depending on surface conditions).

Estimating Surface Winds

• Angle backed:
  • Land, clear night: 40-50°
  • Land, average: 30°
  • Land, unstable: 10-20°
  • Stable Sea: 15-20°
  • Unstable Sea: 5-10°

Global Circulation

• Earth receives energy in the form of solar radiation.
• More solar radiation in the tropics than the poles.
• Earth also emits radiation – infrared.
• The tropics emit less energy than they receive, while the polar regions emit more.
• The atmospheric circulation – including weather systems – transport energy from the tropics to the high latitudes.
• Without weather, the tropics would be much hotter and the poles much colder.

Summary

• Balance of pressure and Coriolis forces results in geostrophic flow parallel to isobars.
• Curvature of isobars around centers of high and low pressure requires additional acceleration to turn the flow, so the resulting gradient wind is:
  • supergeostrophic around HIGH
  • subgeostrophic around LOW
• Friction reduces wind speed near the surface.
• Lower wind speed implies reduced Coriolis turning, and the wind vector describes an Ekman Spiral between the surface and the level of geostrophic flow.
• Surface wind lies 10-35° to the left of the geostrophic wind, crossing isobars from high to low pressure.