GEU 0047: MeteorologyLecture 8Air Pressure and Winds

How can you know this wind direction?

PressureThe steady drumbeat of countless numbers of atoms and molecules, exchanging momentum with the walls of a container and providing the Pressure.

Gas LawThe pressure is related to the density and temperature of the gas through its internal energy.Kinetic Energy = 1/2 m v2Exchange of Momentum, the drumbeat of atoms and molecules.Equation of StatePV = NkT N = number k = Boltzman's constant = 1.38 x 10-23 J/K

PV = nRT n = grams per mole / molar mass R = Gas constant = 8.31 Joules/mole/K

Partial PressuresPressure = PN2 + PO2 + + PAr + PH20 + PCO2 + ...

Pressure = Force / Area

(Snow shoes on thin ice, high heels on asphalt)

Force = Weight of overlying air = mass x gravity

WeightPressure = Force / Area Force = Weight of overlying column of air = mass x gravity

Pressure UnitsUnits of PressureForce / Area = Newton/m2 = Pascal

Weather RelatedSea Level5,000 feet10,000 feetPascals101,325Millibars1013.25500250Atmospheres1.00.50.2Inches of Mercury 30.015.07.5PSI14.77.43.0

Pressure Records

Fluid Pressure at Height (or Depth)Since pressure (P) = Force / Area and the force is the weight (W = mg) of the overlying column...P = mg/A

Multiply the top and bottom by the volume (V)P = Vmg/VA

m/V is the density and V/A is just the height for aTherefore, P = r g h

Pressure and ColumnsAt what depth do we encounter a pressure = 1 atm.In a) water, b) gasoline, c) mercury?

Pressure and ColumnsAt what depth do we encounter a pressure = 1 atm.In a) water, b) gasoline, c) mercury?

1 atm = 101325 Pascals

P = rghha = P/raghb = P/rbghc = P/rcg

Pressure and ColumnsAt what depth do we encounter a pressure = 1 atm.In a) water, b) gasoline, c) mercury?

1 atm = 101325 Pascals

P = rghha = P/rag= 101325/1000*9.8hb = P/rbg = 101325/680*9.8hc = P/rcg = 101325/13600*9.8

Inches of MercuryAt what depth do we encounter a pressure = 1 atm.In a) water, b) gasoline, c) mercury?

1 atm = 101325 Pascals

P = rghha = P/rag= 10.3 metershb = P/rbg = 15.2 metershc = P/rcg = 0.76 meters

1 atm ~ 30 inches mercury (0.76 meters)

Pressure and AltitudeThere is a large difference in pressure with altitude.

Pressure ChangesHorizontal: Changes ~ 1 mb over 10,000s of meters Vertical: 1 mb over 10s of meters

Barometric Pressure must be corrected for Altitude(and Temperature).

Vertical atmospheric motions are more important than horizontal ones because of temperature and pressure changes in this direction are much largerthan similar distances in the horizontal direction.

Pressure and AltitudeStation pressure:Local Reading

Local Valuesmust be correctedfor elevation andreduced to sea level forcomparison.

Pressure Lapse RateIn an average standard atmosphere with a lapse rateof ~ 6.5 oC/1000 m, atmospheric pressure decreases are approximated by ~ 100 mb/1000 m.

Station pressure at its elevation is then corrected to sea levelwith this standard gradient.

Example:Station Pressure 894 mb, Elevation +1100 m

Equivalent Sea Level Pressure = 894 + 1100*(100/1000) = 1004 mb

Pressure GradientsDP/Dd = Pressure Gradient (Change in Pressure/Distance)

Example:DP/Dz = - rg DP = change in pressure Dz = change in altitude r = density (air) g = gravity (9.8 m/s2)

Pressure Gradient Force (PGF): Force due to pressuredifferences, and the cause of air movement (winds).

Pressure Gradient ForceF = m a, acceleration a = F/m = Dv/Dt

P = F/Apressurer = m/Vdensityacceleration a = F/m = -(1/r)*DP/Dd

Wind is accelerated perpendicular to isobars from High toLow pressure.

Wind velocity ~ (1/r)*DP/Dd

IsobarsContours of Constant PressureTopographical Analogy: Just as close topographic linesindicate steep terrain, close isobars mean steep pressuregradient, large pressure force and therefore strong winds.SURFACE MAP

Pressure Gradient Force (PGF)Air moves from Highpressure to Low pressure.

The force provided bythe pressure differenceis the pressure gradientforce. Force is directed perpendicular to theisobars from Highs toLows.

Isobar LevelsStandard isobaric levels

Each isobaric level picksout a general altitude tostudy. These are constantaltitude charts, similar tothe surface map.

Fig. 8-12, p. 199

Isobar Levels

Bernoullis EquationRecall that WORK = change in both Potential Energyand Kinetic Energy.

W = Force * Distance = P A x = P V

Initially, P1, v1, x1, h1, A1Finally, P2, v2, x2, h2, A2h2

Bernoullis EquationD KE = 1/2 m (v2-v1)2D PE = mg (h2-h1)

Initially, P1, v1, x1, h1, A1Finally, P2, v2, x2, h2, A2h2

Bernoullis EquationD KE = 1/2 m (v2-v1)2D PE = mg (h2-h1)

DW = DKE + DPELeads to the equation of continuity...

P + 1/2 r v2 + r g h = constantThe sum of pressure, kinetic energy per volume andpotential energy per volume have the same valuealong all points in a streamline.

Bernoullis PrinciplePressure is lower for faster steady flow than for slower

Airplane WingsHigher v, Lower PLower v, Higher P

Wind Speed VectorsVectors are arrows representing wind direction andspeed.

Bernoulli Winds

Ridge and TroughWavelike patterns of constant pressure surfaces reflectpressure changes due to air temperature differences.

Constant Pressure SurfacesAt what height do you experience a Pressure of 500 mb?

Density and PressureThe warmer air column is less dense.At the same height, the pressure is higher in the warmer air column.

Latitude Pressure Gradient

At the same altitude, the pressure is higher on average in the warmer (i.e. lower) latitudes.

Temperature PGF versus Altitude

Air ForcesForce = Pressure Gradient Force + Coriolis + Friction

For any fixed height, the pressure decreases toward cooler latitudes.

Isobars for a fixed altitude show this decrease to the North (South) in the Northern (Southern) Hemisphere.

In the absence of rotation, air (in the upper level) would tend to flow from the equator toward the poles.

Global CirculationIn the absence of rotation, air would tend to flow from the equator toward the poles.

Hot, less dense airrising at the equator,becomes denser asit cools and descendsat the poles, travelingback to tropical areasto heat up again.

Coriolis

Outsiders viewInsiders viewFrom http://www.windpower.dk/tour/wres/coriolis.htmOutsiders viewInsiders view

A. Force: due to a rotating frame of reference.B. Objects moving in a straight line with respect to the stars, will experience an apparent deflection to the RIGHT in the N.Hemisphere and an apparent deflection to the LEFT in the S. Hemisphere.

C. The Coriolis force is strongest at the poles and zero at the equator.D. The Coriolis force is proportional to the speed.

E. The "force" affects the direction NOT the speed. But since velocity is a vector, with both direction and speed, the velocity change is the same as acceleration and the Coriolis force is the culprit.Coriolis FORCE

Relative to a carousel, someone walking on a carousel moves in a straight line with respect to the fixtures.

Relative to others and equipment on the ground,the person moves in an arc as if affected by a force.

The (horizontal) Coriolis Force Fc = 2W v sin f

v = wind speedW = angular velocity (earth rotation, 360 degrees/24 hours)f = latitude (sin 0 = 0.0 equator, sin 90 = 1.0 poles)Coriolis Force Equation

Coriolis DeflectionFc = 2W v sin f

Increase of theCoriolis Force withwind speed.

Pressure Gradient ForceAir flows from high pressure to low pressure, so on average, from the equators to the poles.

Geostrophic flowRemember that the coriolis force depends upon velocity.

As air is accelerated bythe PGF its speed increases and the coriolis deflection grows. Equilibrium is reached when the PGF andcoriolis effect are equal.

PGF = Coriolis 1/r*DP/Dd = 2 W v sin f

The wind velocityv = DP/Dd * (1/r 2 W sin f)

Utilizing the coriolis parameter fc = 2 W sin f

The wind velocity v = (1/rfc)*DP/Dd = vg

This is known as the geostrophic wind equation.

Geostrophic flowWith the inclusion of the Coriolis Force, air flows parallel to isobars of constant pressure.

WesterliesAt mid latitudes, air moving from S. to N. in the northern hemisphere flows from west to east.

Friction EffectFriction retardswind speed nearthe surface dueto topography, lowering thecoriolis force.Therefore, winddirection isaltered from parallel to isobars.

Cyclonic Flow

Low Pressure Cyclonic Winds

High Pressure Cyclonic Winds

Isobar Surface Map

Cyclone Anticyclone Circulations

SummaryPressure = Force / AreaForces on AirPressure Gradient ForceCoriolis ForceFriction

Isobar Charts

Global Circulation Pattern (3 cell model)

Cyclone and Anticyclone Circulations

Asphalt: *PSI: pounds per square inch**Figure 8.12The area shaded gray in the above diagram represents a surface of constant pressure, or isobaric surface. Because of the changes in air density, the isobaric surface rises in warm, less-dense air and lowers in cold, more-dense air. Where the horizontal temperature changes most quickly, the isobaric surface changes elevation most rapidly.*large mechanical apparatus with seats for children*