Chapter 6

Atmospheric Forces and Winds

Courtesy of RMS, Inc Figure CO: Chapter 6, Atmospheric Forces and Wind

Figure UN01: Winds over France on Feb. 27-28, 2010 Data from Météo-France

Figure UN02: Flooding in La Faute, France © Regis Duvignau/Reuters/Landov

Basics about Wind

• Wind direction is the direction from which the wind is blowing – A north wind blows from the north to the south – It is reported according to compass directions – Prevailing wind direction is the most frequent direction • Wind speed – Reported on U.S. weather maps in knots – 1 knot = 1.15 miles/hour = 0.5 meter/second – If wind > 15 knots and highly variable, the weather report will include the wind gust, the

Figure 01: Wind directions in angles, compass headings.

Forces

• Have magnitude (or strength) and direction • Multiple forces can act on the same point – The resultant force is the net force – If two forces act in opposite directions, the net force will have the direction of the stronger force and a strength equal to the difference of the two forces – If two forces act at an angle to each other, the resultant force is along a diagonal and away from where the two forces are applied

Figure 02: Force diagram.

Figure 03: Graphical addition of force vectors.

Forces and Movement

• A force applied to an object often results in movement • An object’s velocity is the magnitude and direction of its motion • The speed of the object, the distance traveled in a given amount of time, is the magnitude of the motion • Acceleration is a change in an object’s velocity —magnitude, direction or both

Forces cause the wind to blow

• Forces that act on air create horizontal wind • A force acting through a distance does work • Work is equivalent to energy • Ultimately, the sun provides the energy that allows the winds to blow • Radiation causes temperature imbalances, which lead to pressure imbalances and a force

Newton’s second law of motion

• Says that – the sum of the forces = mass x acceleration – Or that acceleration = sum of forces/mass • Helps scientist forecast changes in the wind direction and speed, or its acceleration • Requires that we specify which forces are acting and how strong they are • Is also called the Law of momentum • Momentum of an object is its mass x its velocity

Gravity, the strongest force

• Does not act horizontally, so does not influence the horizontal winds.

• Does influence vertical air motions • Is directed downward toward the center of Earth • Is a very strong force • Keeps our atmosphere from escaping • Equals the mass x 9.8 m/s 2

The Pressure Gradient Force (PGF)

• The force that results from pressure differences over distances in a fluid • A pressure gradient is a change in pressure over a distance • PGF always directed from high to low pressure • Is stronger when isobars more closely spaced • Is stronger when the difference in pressure is greater over a particular distance • Determines the way air moves

only if no other forces are acting

Figure B01A: Fan blowing on paper

Figure B01B: Air over plane wing, with lift and drag

Figure 04: Pressure gradient force in highs and lows.

The horizontal pressure gradient force

• Is always directed from high to low pressure • Is stronger where the density is less— higher in the troposphere • When stronger, causes stronger winds • Is always important in horizontal winds • Is not generally in the same direction the wind blows, because other forces can act

Figure 05: Surface weather map From Plymouth State University Weather Center, [http://vortex.plymouth.edu/make.html.].

Isobaric Charts

• Plot the altitude of a given pressure surface – Units of altitude are called geopotential meters • Also called a constant-pressure chart – Common levels are 850, 700, 500, 250, and 200 mb • Are useful for portraying horizontal pressure gradients above the ground • The spacing between the lines of constant height is proportional to the PGF • The winds in general blow parallel to the height contours, at right angles to the PGF

Figure 06: 500-mb isobaric chart From Plymouth State University Weather Center, [http://vortex.plymouth.edu/make.html.].

Figure 07A: Isolines of constant height are proportional to the PGF

Figure 07B: Isolines of constant height are proportional to the PGF

Figure 07C: Isolines of constant height are proportional to the PGF

Centrifugal Force/Centripetal Acceleration

• Centripetal acceleration is a change in direction even if the speed does not change • From the point of view of an observer experiencing the centripetal acceleration, there is an apparent force called the centrifugal force • The faster the speed and the tighter the curve, the larger is the centripetal acceleration • The sign of the centripetal acceleration is positive for cyclones, negative for anticyclones, and always directed inward to the center

Figure 08: Centrifugal force schematic

The Coriolis Force

• Deflects the wind to the right in the NH • Deflects the wind to the left in the SH • Is strongest at the poles • Is zero at the equator • Is stronger for stronger winds • Is weaker for weaker winds • Is zero for calm. It cannot start a wind

Figure 09A: Curving path of ocean buoy Adapted from Joseph et al., Current Science, 92 (2007).

Figure 6.10: The centrifugal (CENTF) and Coriolis forces acting on an air parcel moving with respect to the rotating Earth Modified from A. Persson,

Bull. Amer. Meteor. Soc., 79 [1998]: 1378.)

.

Figure 11A: Coriolis force at different latitudes.

Figure 11B: variation of Coriolis force with latitude and wind speed

Figure B02B: Carl-Gustaf Rossby Courtesy of University of Chicago News Office

The Friction Force

• Acts in the direction

opposite

direction the wind is blowing to the • Acts to slow down the wind • Is most important at Earth’s surface • Gets stronger when the winds are stronger • Is not important above the boundary layer (the lowest 1 km in the atmosphere) • The rougher the surface and the stronger the wind the greater is the friction force

Figure 12: Frictional force diagram

Why force-balances are important

• Force-balances simplify Newton’s second law of motion by limiting the number of forces • Force-balances describe winds that come close to describing the observed winds • Even though the forces are balanced, the wind need not be calm • The PGF is important in every force balance • Only the PGF can set calm air into motion

Figure T01: Some Atmospheric Force-Balances

Hydrostatic Balance

• Gravity (downward) balances the Vertical Pressure Gradient Force (upward) • Does not apply inside cumulus clouds, because buoyancy is important there • Does apply generally in the atmosphere • Limits vertical motions to be much weaker than horizontal winds

Figure 6.13: Air parcel in hydrostatic balance Reproduced from Lester, P.,

Aviation Weather, Second edition. With permission of Jeppsen Sanderson, Inc.

Not for Navigation Use. Copyright © 2010 Jeppesen Sanderson, Inc.

More on Hydrostatic Balance

• The pressure gradient force is stronger when the air is less dense • The density of air is less when the air Temperature is higher • Pressure decreases upward less rapidly when the air has a higher temperature • Hydrostatic balance helps explain the sea breeze and other

thermal circulations

Pressure levels on weather maps

• The atmosphere is very close to hydrostatic balance • This means that the height of a particular pressure level is roughly equivalent to the pressure at a related height level • An altimeter is a barometer with a height scale • Upper-level weather maps are labeled in m • Winds on a weather map are strong when the height contours are close together, weak where they are farther apart

Geostrophic Balance

• Is a balance between the horizontal pressure gradient force and the Coriolis force • Ignores the friction force • Has isobars that are straight lines • Does

not

mean that the wind is calm • Has a wind called the

geostrophic wind

• Winds on weather maps above the surface are close to the geostrophic wind • Blows with lower pressure (height) on the left (NH)

Figure 14: Geostrophic balance

The Geostrophic Wind

• Is a wind in geostrophic balance • Is parallel to the isobars • In the NH has low pressure on the left • In the SH has low pressure on the right • In the NH the wind blows clockwise around high pressure centers and counterclockwise around low pressure centers • In the SH CW flow around lows and CCW flow around highs

Figure 15: Geostrophic wind in highs and lows

Gradient Balance and the Gradient Wind

• Gradient balance is between the PGF, the Coriolis force and the centrifugal force • Gradient balance allows curving wind patterns called the gradient wind • The centrifugal force is always outward – Around a low the centrifugal force opposes the PGF and the resulting flow is subgeostrophic – Around a high the centrifugal force adds to the PGF and the resulting flow is supergeostrophic

Figure 16: As in Figure 6-15, except now we also include the centrifugal force, leading to gradient balance.

Adjustment to Geostrophic Balance

• Initially there is an imbalance of forces • Air parcels move toward lower pressure (PGF) • As soon as there is a wind, the Coriolis force acts • Parcels oscillate towards a balance between the PGF and the Coriolis force • Adjustment takes minutes to hours • Adjustment is temporary and incomplete

Figure 17: Wavy path of parcel adjusting to balance

Guldberg-Mohn Balance

• Is a balance between the PGF, the Coriolis force, and friction • Friction slows the wind and the Coriolis force weakens • The winds blow across the isobars at an angle toward low pressure (away from high pressure) – Between 15° and 30° over water – Between 25° and 50° over land • Friction damps oscillations during adjustment to balance

Figure 18: Guldberg-Mohn balance

Figure 19: A numerical simulation of how varying amounts of friction affect the adjustment to Guldberg – Modified from Knox, J., and Borenstein, S., Mohn balance.

[1998]: 190 –192.

Figure B03A: Chart of wind speeds and max wave heights

Figure 21: The isobars at the surface drawn over a satellite image of a cyclone Image created by Prof. Joshua Durkee, Western Kentucky University, using GREarth software.

The Thermal Wind

• The thermal wind relates temperature and winds to each other • The winds are more westerly as you go up wherever it’s colder toward the poles

Putting horizontal and vertical winds together

• At the surface, the wind blows across the isobars into low-pressure areas – At the center of the low-pressure area the air must rise – Low-pressure areas are usually cloudy and wet • At the surface, the wind blows across the isobars out of high-pressure areas – At the center of the high-pressure area the air must sink – High-pressure areas are usually clear and dry • These patterns are the result of Guldberg-Mohn balance

Figure 22: Schematic of pressure levels when air is heated

Figure 23: Cross-section of winds at various pressure levels

Figure 24A: How surface wind patterns induce vertical wind motions Figure 24B: How surface wind patterns induce vertical wind motions

Figure 24A: How surface wind patterns induce vertical wind motions

Figure 24B: How surface wind patterns induce vertical wind motions

The thermal circulation

• The sea breeze is a thermal circulation • A thermal circulation has both horizontal and vertical air motions • The horizontal pressure gradient force is most important in a thermal circulation • Upward air motions occur in the warmer air column of the circulation; downward air motions occur in the cooler air column

The sea breeze

• Is a daytime circulation • Depends on differential heating at the surface between land and water • Has the warmer, rising air column over the land, which absorbs more incoming solar radiation • Has the cooler, sinking air column over the water, which absorbs less radiation • Air flows from warmer to cooler column aloft • Air flows from cooler to warmer column at the surface

Figure 25: Sea breeze schematic

Figure 26A: Satellite image of sea breeze Courtesy of SSEC, University of Wisconsin-Madison

Figure 26B: Satellite image of sea breeze Courtesy of SSEC, University of Wisconsin-Madison

Figure 26C: Satellite image of sea breeze Courtesy of SSEC, University of Wisconsin-Madison

Figure 26D: Satellite image of sea breeze Courtesy of SSEC, University of Wisconsin-Madison

The sea breeze and the land breeze

• As solar heating diminishes in the late afternoon, the sea breeze weakens • At night, differential cooling occurs • The cooler, sinking air column is over land, where radiational cooling is more rapid than over the water • The warmer, rising air column is over the water • The land breeze develops at night – Air flows towards the land aloft – Air flows towards the water at the surface

Figure 27: Schematic of land breeze

Scales of motion in the atmosphere

• Describe the size and lifetime of wind patterns in the atmosphere • Determine which forces are most important to forming the wind patterns • Are largest when the lifetimes are longest • Are smaller when the lifetime is shorter • Have a variety of names and definitions

More on scales of motion

• Microscale: <1 km in diameter – PGF, centrifugal, friction forces are important • Mesoscale: Between 1 and 1000 km in size – PGF, centrifugal, friction, and Coriolis Force for largest sizes • Synoptic scale: At least 1000 km in size – Balance between PGF and Coriolis Force dominates • Planetary scale: Roughly 10,000 km in size