Pressure, Forces and Motion Readings A&B: Ch. 4 (p. 93-114) CD Tutorials: Pressure Gradients, Coriolis, Forces & Winds Topics 1. Review: What is Pressure? 2. Horizontal Pressure Gradients 3. Depicting Pressure Gradients a. Constant Height Charts b. Constant Pressure Charts 4. Newton s 2 nd Law 5. Forces & Winds a. Pressure Gradient Force b. Coriolis Force Geostrophic Wind Gradient Wind c. Friction Force 6. Anticyclones & Cyclones G109: Weather and Climate Review: What is Pressure? Pressure = Force / Area Atmospheric Pressure: weight of air above an area Weight above decreases steadily with height Pressure decreases steadily with height Can be used to measure height in the atmosphere
Review: The Ideal Gas Law The Ideal Gas Law: P = ρ T R d P: pressure [Pa = kg m -1 s -2 ] ρ: density [kg m -3 ] T: abs. temperature [K] R d : spec. gas constant 287 [J kg -1 K -1 ] for dry air If Pressure (P) is constant Increased T Decreased Density Increased Volume Decreased T Increased Density Decreased Volume Horizontal Pressure Gradients When surface under one air column is heated the air column expands, following: P = ρ R d T Example: Two columns of air with equal ρ, P, and T
Horizontal Pressure Gradients After heating and expansion of right-hand column: Height at which 500 mb pressure is reached is now At 5640 m the pressure in the warm column is now OR: The height of 500 mb level cool column Horizontal Pressure Gradients Gradual poleward decrease in mean temperature Denser air at higher latitude More rapid decrease of pressure with height Horizontal changes in pressure
Horizontal Pressure Gradients As a result of horizontal temperature differences: A given pressure (e.g. 500 mb) occurs at different At a given height (e.g. 5640 m) in the atmosphere, (If no air is flowing away or into the air column, the surface pressure does not vary horizontally yet) Horizontal Pressure Gradients With a horizontal pressure gradient aloft (created by T differences), air can start to flow from to The weight of the entire air column (surface pressure) changes as well, because of the air flow There are now at the surface and at height These give rise to Pressure differences cause Pressure differences occur because of
Depicting Horizontal Pressure Variation Pressure varies Spatial & temporal patterns Need a way to depict variations Two types of charts or maps At sea-level, show horizontal variation of pressure as isobars = pressure variation at For a given level of pressure (e.g. 500 mb), show at what height this occurs, as contours of geopotential = height variation of Depicting Horizontal Pressure Variation 1. Shows variations of pressure at the surface Altitude corrections: all pressures are corrected to same level (usually sea level) Prevents mountainous areas from appearing with lower pressure because of height
Depicting Horizontal Pressure Variation 2. Shows variation of height along an Isobaric Surface, i.e., the height at which a certain pressure occurs Isobaric Surface: a surface of constant pressure Newton s 2 nd Law of Motion Acceleration of an air parcel is equal to the Acceleration: change of velocity over (unit) time i.e., a change in and/or Net force: vector sum of all component forces
Newton s 2 nd Law of Motion Forces in the atmosphere (the most important ones): Pressure Gradient Force: F PG Driving force affects speed and direction Accelerates air from High to Low pressure Coriolis Force: F C Deflecting force affects direction only Friction Force: F f Retarding force affects speed only Friction Increases with increasing wind speed Pressure Gradient Force (F PG ) Force resulting from the horizontal difference in pressure Proportional to i.e., depends on H F PG L F PG goes from 1008 1004 1000 (mb) At right angles to the isobars
Pressure Gradient Force (F PG ) The closer the isobars, the stronger the pressure gradient and thus the F PG F PG P = = d change in PRESSURE DISTANCE H F PG L H F PG L 1008 1004 1000 1008 1004 1000 Pressure Gradient Force (F PG ) Can set a stationary air parcel in motion Mostly responsible for the If F PG were the only force, winds Air would move at But the earth rotates
Coriolis effect: Coriolis Effect An unaccelerating object moves in a straight line (due to balanced forces) Because of Earth s rotation, a straight line motion on Earth as viewed from (e.g.) another planet, leaves a curved trace on Earth: the motion appears to be accelerated (curved!) Coriolis Force (F C ) Apparent acceleration accounted for by apparent force: Coriolis force F C Northern Hemisphere: (counter-clockwise rotation) Southern Hemisphere: (clockwise rotation)
Latitude Strongest twisting motion at poles. No twisting motion at the equator. F C increases Coriolis Force (F C ) F C (on Earth) dependent on: Velocity: proportional to velocity. F C increases with the greater the distance traveled per unit time the greater the deflection Coriolis Force (F C ) Always at right angles to the direction of air flow Affects only the not Affected by Stronger the wind speed the greater the force Strongest at the and weakest at the F C = 2 ν Ωsin φ ν - wind speed Ω - earth's angular rate of spin (constant ) φ - latitude
Geostrophic Wind Wind aloft (above a few km) above the effects of friction Assume evenly spaced, and straight isobars Idealized model (an approximation of winds aloft) balances the and directs the airflow F PG = F C Net force = 0 F PG = F C Wind flows in a Geostrophic Wind Proportional to the pressure gradient force steep gradient strong winds; weak gradient light winds With back to wind, Low is (in northern hemisphere)
Gradient Wind A second idealized model of winds aloft Above the level of frictional influence wind, with isobars that are curved Wind blows at constant but with constantly changing therefore has acceleration Gradient Wind Above the level of frictional influence wind, when isobars are NOT parallel Wind blows
Troughs and Ridges In upper atmosphere pressure height variations are distributed as a series of ridges and troughs: Ridge: elongated zone of pressure, extending toward the pole: associated with weather Trough: elongated zone of pressure, extending toward the equator: associated with weather Greatest surface instability (T-storms) is usually ahead of (to the right of) the 500 mb trough Friction Force (F f ) As we move toward the surface (away from aloft) friction slows down the movement of air Roughness of the surface retards the airflow Wind speed reduced Impacts Coriolis force (F C ) Pressure gradient force (F PG ) is not affected Wind crosses isobars. Angle depends on friction Smooth ocean: Slight angle: 10-20 o Rough terrain: Greatest angle: 45 o
Anticyclones and Cyclones Anticyclone: enclosed area of with circular isobars or height contours Northern Hemisphere Winds rotate as F PG is outward and F C deflects to right NH surface Southern Hemisphere Winds rotate as F PG is outward and F C deflects to left SH surface Near surface: wind is not parallel to isobars but spirals Upper atmosphere: flow is parallel to isobars NH upper atm SH upper atm Anticyclones and Cyclones Cyclone: enclosed area of Low pressure, with circular isobars or height contours Northern Hemisphere Winds rotate as F PG is inward and F C deflects to right NH surface Southern Hemisphere Winds rotate as F PG is inward and F C deflects to left SH surface Near surface: wind is not parallel to isobars but spirals Upper atmosphere: flow is parallel to isobars NH upper atm SH upper atm