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Atmospheric Motion SOEE1400: Lecture 7 Plan of lecture 1. 2. 3. 4. 5. 6. 7. Forces on the air Pressure gradient force Coriolis force Geostrophic wind Effects of curvature Effects of friction Upper level charts. SOEE1400 : Meteorology and Forecasting 2 Isobars at 4mb intervals SOEE1400 : Meteorology and Forecasting 3 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 Forecasting 4 The PressureGradient Force Horizontal pressure gradients are the main driving force for winds. Pressure gradient force = - 1 dP dx 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. 1000 mb 1004 mb pressure force The pressure force acts to accelerate the air towards the low pressure. SOEE1400 : Meteorology and Forecasting 5 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. Axis of spin 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 SOEE1400 : Meteorology and Forecasting 6 Movies … see web page. SOEE1400 : Meteorology and Forecasting 7 Coriolis Force on a Flat Disk Fc V 1 2 3 4 5 6 SOEE1400 : Meteorology and Forecasting 8 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 Forecasting 9 SOEE1400 : Meteorology and Forecasting 10 Geostrophic Balance FP 1000 mb Vg 1004 mb Fc Steady flow tends to lie parallel to the isobars, so that the pressure and coriolis forces balance. This is termed geostrophic balance, and Vg is the geostrophic wind speed. SOEE1400 : Meteorology and Forecasting 11 Steady flow in the absence of friction Since the coriolis force balances the pressure force we have: Pressure gradient force = coriolis force 1 dP = 2Ω Vg sin dx 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. 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. SOEE1400 : Meteorology and Forecasting 12 Geostrophic wind scale (knots) SOEE1400 : Meteorology and Forecasting 13 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 Forecasting 14 Centripetal Acceleration Motion around a curved path requires an acceleration towards the centre of curvature: the centripetal acceleration. HIGH Fc V LOW FP FP V Centripetal acceleration 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 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) SOEE1400 : Meteorology and Forecasting 15 Effect of friction FP FP 1000 mb V Fd Vg 1004 mb Fc 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. SOEE1400 : Meteorology and Forecasting 16 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 Ekman Spiral • 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 Vg on surface conditions) SOEE1400 : Meteorology and Forecasting 17 Surface winds cross isobars at 10-35 SOEE1400 : Meteorology and Forecasting 18 Upper-level charts “Height of a pressure surface Pressure on a height surface” 4000m 700 hPa surface 3000m 2000m 1000m Ground level Lower pressure 850 hPa surface Higher pressure On a 2000 m chart, the pressure here is lower than to each side. The height of the 850 hPa surface is also low. SOEE1400 : Meteorology and Forecasting 19 Example 500 hPa height is shaded (with black contour). 500hPa winds circulate around the low. Surface pressure is the white lines. 500 hPa geostrophic wind SOEE1400 : Meteorology and Forecasting 20 SOEE1400 : Meteorology and Forecasting 21 SOEE1400 : Meteorology and Forecasting 22 SOEE1400 : Meteorology and Forecasting 23 SOEE1400 : Meteorology and Forecasting 24 SOEE1400 : Meteorology and Forecasting 25 SOEE1400 : Meteorology and Forecasting 26 Global Circulation SOEE1400 : Meteorology and Forecasting 27 For a non-rotating Earth, convection could form simple symmetric cells in each hemisphere. SOEE1400 : Meteorology and Forecasting 28 Coriolis force turns the air flow. Stable mean circulation has 6 counterrotating 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. Polar Cell Ferrel Cell SOEE1400 : Meteorology and Forecasting 29 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 10-35 to left of geostrophic wind, crossing isobars from high to low pressure. SOEE1400 : Meteorology and Forecasting 30 • 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. SOEE1400 : Meteorology and Forecasting 31