Atmospheric Motion SOEE1400: Lecture 7

Plan of lecture 1.Forces on the air 2.Pressure gradient force 3.Coriolis force 4.Geostrophic wind 5.Effects of curvature 6.Effects of friction 7.Upper level charts. SOEE1400 : Meteorology and Forecasting2

3 Isobars at 4mb intervals

Steady flow 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 3 forces which influence horizontal airflow: –Pressure gradient force (p.g.f.) –Coriolis force –Frictional drag SOEE1400 : Meteorology and Forecasting4

5 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

SOEE1400 : Meteorology and Forecasting6 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. V Coriolis Force Axis of spin

SOEE1400 : Meteorology and Forecasting7 Movies … see web page.

SOEE1400 : Meteorology and Forecasting8 V FcFc Coriolis Force on a Flat Disk

SOEE1400 : Meteorology and Forecasting9 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: 2Ω V sin  = f V Ω = angular velocity of the earth V = wind speed  = latitude f = 2Ω V sin  = “Coriolis parameter” 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.

SOEE1400 : Meteorology and Forecasting10

SOEE1400 : Meteorology and Forecasting11 Geostrophic Balance 1000 mb 1004 mb VgVg FPFP FcFc Steady flow tends to lie parallel to the isobars, so that the pressure and coriolis forces balance. This is termed geostrophic balance, and V g is the geostrophic wind speed.

SOEE1400 : Meteorology and Forecasting12 Steady flow in the absence of friction 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 = 2Ω V g 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.

SOEE1400 : Meteorology and Forecasting13 Geostrophic wind scale (knots)

SOEE1400 : Meteorology and Forecasting14 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.

SOEE1400 : Meteorology and Forecasting15 Centripetal Acceleration Motion around a curved path requires an acceleration towards the centre of curvature: the centripetal acceleration. LOW V FPFP FcFc Centripetal acceleration The required centripetal acceleration is provided by an imbalance between the pressure and coriolis forces. V is here called the gradient wind 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) HIGH V FPFP FcFc Centripetal acceleration

SOEE1400 : Meteorology and Forecasting16 Effect of friction 1000 mb 1004 mb V FPFP FcFc The direction of the drag force (Fd) is approximately opposite to the wind direction. The drag force exactly balances the coriolis and pressure gradient forces. The wind speed is lower than the geostrophic wind. FPFP VgVg Fd

SOEE1400 : Meteorology and Forecasting17 Effect of Friction 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  over ocean  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) Geostrophic flow away from surface VgVg Ekman Spiral

SOEE1400 : Meteorology and Forecasting18 Surface winds cross isobars at 

Upper-level charts SOEE1400 : Meteorology and Forecasting19 Ground level 1000m 2000m 3000m 4000m 700 hPa surface 850 hPa surface On a 2000 m chart, the pressure here is lower than to each side. The height of the 850 hPa surface is also low. Higher pressure Lower pressure “Height of a pressure surface  Pressure on a height surface”

Example 500 hPa height is shaded (with black contour). 500hPa winds circulate around the low. Surface pressure is the white lines. SOEE1400 : Meteorology and Forecasting hPa geostrophic wind

SOEE1400 : Meteorology and Forecasting21

SOEE1400 : Meteorology and Forecasting22

SOEE1400 : Meteorology and Forecasting23

SOEE1400 : Meteorology and Forecasting24

SOEE1400 : Meteorology and Forecasting25

SOEE1400 : Meteorology and Forecasting26

SOEE1400 : Meteorology and Forecasting27 Global Circulation

SOEE1400 : Meteorology and Forecasting28 For a non-rotating Earth, convection could form simple symmetric cells in each hemisphere.

SOEE1400 : Meteorology and Forecasting29 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. This is a grossly simplified model, circulations are not continuous in space or time. Notably the Ferrel cell is highly irregular in reality. Ferrel Cell Polar Cell

SOEE1400 : Meteorology and Forecasting30 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 additional acceleration to turn the flow, so the 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  to left of geostrophic wind, crossing isobars from high to low pressure.

SOEE1400 : Meteorology and Forecasting31 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 This 6-cell model is a crude over-simplification of reality, but accounts for major features of mean surface winds, and the Hadley circulation is a robust feature which is well observed.