1. Atmospheric Motion
ENVI 1400: Lecture 3

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Isobars at 4mb intervals
ENVI1400 : Meteorology and Forecasting : lecture 3
ENVI1400 : Meteorology and Forecasting : lecture 3

3. The Pressure­Gradient Force
Horizontal pressure gradients are the main driving force for winds.
where P is pressure,  is air density, and x is distance. The force is thus inversely proportional to the spacing of isobars (closer spacing  stronger force), and is directed perpendicular to them, from high pressure to low.
The pressure force acts to accelerate the air towards the low pressure.
Pressure gradient force = -
1 dP  dx
1000 mb
1004 mb
pressure force
ENVI1400 : Meteorology and Forecasting : lecture 3

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The Coriolis Force
ENVI1400 : Meteorology and Forecasting : lecture 3
ENVI1400 : Meteorology and Forecasting : lecture 3

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The coriolis force is an apparent force, introduced to account for the apparent deflection of a moving object observed from within a rotating frame of reference – such as the Earth.
The coriolis force acts at right angles to both the direction of motion and the spin axis of the rotating reference frame.
Axis of spin V
Coriolis direction given by left-hand: thumb=spin, index finger=V, 2nd finger = coriolis.
Coriolis Force
ENVI1400 : Meteorology and Forecasting : lecture 3
ENVI1400 : Meteorology and Forecasting : lecture 3

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7. Coriolis Force on a Flat Disk2 3 V Fc 1 4 5 6
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Earth is a sphere – more complex than disk: horizontal and vertical components to the coriolis force.
In the atmosphere, we are concerned only with the horizontal component of the coriolis force. It has a magnitude (per unit mass) of:
2 V sin
 = angular velocity of the earth
V = wind speed
 = latitude
This is a maximum at the poles and zero at the equator, and results in a deflection to the right in the northern hemisphere, and to the left in the southern hemisphere.
ENVI1400 : Meteorology and Forecasting : lecture 3

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Geostrophic Balance
A pressure gradient imposed on a stationary air mass will start to accelerate it towards the region of low pressure
The pressure force continues to accelerate the flow, and the coriolis force continues to turn it FP
1000 mb FP FP FP Vg
1004 mb V V V Fc Fc Fc Fc
Eventually the flow becomes parallel to the isobars, and the pressure and coriolis forces balance. This is termed geostrophic balance, and Vg the geostrophic wind speed.
NB this is a simplification of real atmosphere, where there is a constant adjustment of pressure and flow.
The coriolis force acts to turn the flow to the right (in the northern hemisphere)
ENVI1400 : Meteorology and Forecasting : lecture 3
ENVI1400 : Meteorology and Forecasting : lecture 3

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Since the coriolis force balances the pressure force we have:
N.B. air density  changes very little at a fixed altitude, and is usually assumed constant, but decreases significantly with increasing altitude
 pressure gradient force for a given pressure gradient increases with altitude
 geostrophic wind speed increases with altitude.
Pressure gradient force = coriolis force
1 dP  dx
= 2 Vg sin
Geostrophic wind speed is directly proportional to the pressure gradient, and inversely dependent on latitude.
 For a fixed pressure gradient, the geostrophic wind speed decreases towards the poles.
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Geostrophic wind scale (knots)
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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
vertical wind shear
Significant departure from geostrophic flow occurs near the surface due to the effects of friction.
Geostrophic flow/balance is / results from an APPROXIMATION to the full equations of motion that works well for conditions of low friction & low curvature.
ENVI1400 : Meteorology and Forecasting : lecture 3
ENVI1400 : Meteorology and Forecasting : lecture 3

14. Centripetal Acceleration
Motion around a curved path requires an acceleration towards the centre of curvature: the centripetal acceleration.
HIGH Fc V
Centripetal acceleration
LOW FP FP
For a low, the coriolis force is less than the pressure force; for a high it is greater than pressure force. This results in:
LOW: V < geostrophic (subgeostrophic)
HIGH: V > geostrophic (supergeostrophic) V
Centripetal acceleration Fc
The required centripetal acceleration is provided by an imbalance between the pressure and coriolis forces.
V is here called the gradient wind
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Effect of Friction
Geostrophic flow away from surface
Friction at the surface slows the wind. Turbulent mixing extends effects of friction up to ~100 m to ~1.5 km above surface.
Lower wind speed results in a smaller coriolis force, hence reduced turning to right.
Wind vector describes a spiral: the Ekman Spiral. Surface wind lies to left of geostrophic wind
10-20 over ocean
25-35 over land
The wind speed a few metres above the surface is ~70% of geostrophic wind over the ocean, even less over land (depending on surface conditions)
A similar effect occurs in wind-driven ocean currents.
Discovered in oceans, and theory developed by the Swedish oceanographer V. Walfrid Ekman in 1902.
Ekman Spiral Vg
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Surface winds cross isobars at 10-35
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Global Circulation
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For a non-rotating Earth, convection could form simple symmetric cells in each hemisphere.
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Coriolis force turns the air flow. Stable mean circulation has 6 counter-rotating cells – 3 in each hemisphere.
Within each cell, coriolis forces turn winds to east or west. Exact boundaries between cells varies with season.
N.B. This is a simplified model, circulations are not continuous in space or time.
Polar Cell
Ferrel Cell
6 cell model does not account for all meridional heat transport – horizontal circulations are equally / more important.
ENVI1400 : Meteorology and Forecasting : lecture 3
ENVI1400 : Meteorology and Forecasting : lecture 3

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Summary
Balance of pressure and coriolis forces results in geostrophic flow parallel to isobars
Curvature of isobars around centres of high and low pressure requires centripetal acceleration to turn flow, resulting gradient wind is:
supergeostrophic around HIGH
subgeostrophic around LOW
Friction reduces wind speed near surface
Lower wind speed  reduced coriolis turning, wind vector describes an Ekman Spiral between surface and level of geostrophic flow
Surface wind lies 10-35 to left of geostrophic wind, crossing isobars from high to low pressure.
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Difference in solar heating between tropics and poles requires a compensating flow of heat
Coriolis turning interacts with large scale convective circulation to form 3 cells in each hemisphere
6 cell model is an over-simplification of reality, but accounts for major features of mean surface winds
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