Atmospheric Pressure & Wind: Part 1

Speed, Velocity, Acceleration, Force, Pressure

Atmospheric Pressure & Its Measurement

Ideal Gas Law (Equation of State)

Pressure Gradient Force (Horizontal & Vertical)

Isobars (horizontal)

Hydrostatic Equilibrium (vertical)

Isobaric Surface

Isobars vs. Height Contours

Coriolis Effect & Coriolis Force

Frictional Force

Lecture 10

March 15, 2010, Monday

Speed: distance traveled per unit time, a scalar (magnitude

only), positive value only, in units of m s-1, mph, kmph, etc.

Velocity (v) : speed & direction, a vector (magnitude &

direction), both positive and negative (direction, coordinate),

same speed with opposite directions having different velocity,

also in units of m s-1, mph, etc.

Acceleration (a) : change of velocity (either in speed or in

direction) with time, in unit of m s-2, also a vector and can be

both positive (acceleration) or negative (deceleration).

Gravity (g): a particular acceleration in meteorology, related to

the downward gravitational force (G) due to attraction by the

solid Earth, 9.8 m s-2 with small changes with latitude & altitude

Newton’s Second Law: F = ma

F is force (a vector, in unit of N, newton), N = kg m s-2

a = F / m, g = G / m, m is the mass of a body (kg)

Pressure = Force / Area, Pa (pascal) = N m-2

Atmospheric

Pressure

Atmospheric

pressure units in

meteorology:

1 mb (millibar)

= 100 Pa

= hPa (hectoPascal)

1 kPa (kilopascal)

= 1000 Pa

= 10 mb = 10 hPa

Other units:

inch Hg or mm Hg

g x air mass (m) = weight (G)

surface area on Earth

The weight of the column

of mercury balances the

weight of the column of

atmosphere on the same

area which is the cross

section of the tube.

Atmospheric pressure

= g x density of mercury

x height of mercury

weight=g x density x volume

volume = height x area

pressure = weight / area

Measurement of

Atmospheric

Pressure

Mercury

Barometer:

an inverted

tube filled

with mercury.

inch Hg= inches of mercury

mm Hg= millimeters of

mercury

Conversion:

1 mm Hg = 1.3332 mb

1 inch Hg = 33.864 mb

Shown in this picture is a

Fortin Mercury Barometer

located in the Atmospheric

Science Laboratory (Brewster C-203) of the

Department of Geography at

ECU. It is very accurate as it

meets the National Weather

Service Standard.

Measurement of

Atmospheric

Pressure

~ 14.7 pounds per square inch (psi)

Range of Atmospheric Pressure

at the Mean Sea Level

Aneroid Barometers:

a collapsible chamber which compresses proportionally to atmospheric pressure.

Relationships between pressure (p),

temperature (T), and density (): p = R T

R=287 J kg-1 K-1, gas constant of dry atmosphere

(excluding water vapor) of the Earth.

At constant temperatures, an increase in air

density will trigger a pressure increase.

Under constant density, an increase in

temperature will be accompanied by an

increase in pressure.

Pressure is exerted in all directions equally,

not just downward.

Dalton’s Law: total pressure = sum of partial

pressures exerted by different gas molecules.

Vapor pressure is the partial pressure by water

vapor molecules and is a humidity index.

The Equation of State: Ideal Gas Law

Compressibility of atmospheric gases causes a non-linear

decrease in pressure with increasing altitude.

Pressure at P2 < P1 can be simply due to pressure decreasing

with elevation, thus difficult to evaluate horizontal pressure

difference, for example, at the surface.

Recorded surface pressure is reduced to sea level pressure

equivalents to facilitate horizontal pressure comparisons.

Vertical and Horizontal Changes in Pressure

Horizontal pressure differences across space are useful.

By analyzing isobaric maps, pressure gradients are apparent: strong or weak pressure gradients indicated by closely or widely spaced isobars, respectively.

In this weather

map, green lines

are isobars of

sea level

atmospheric

pressure

distribution.

Isobars:

lines of equal

atmospheric

pressure

Mapping Atmospheric Pressure

Forces that drive wind

Pressure Gradient Force (PGF) PGF drives air move from high pressure to low pressure.

PGF is perpendicular to isobars.

Magnitude of PGF increases with pressure gradient.

PGF is great in severe weather events (tornadoes, hurricanes).

weak pressure gradient: low wind speeds

strong pressure gradient: high wind speeds

Vertical Pressure Gradients Average vertical pressure gradients are usually

greater than extreme examples of horizontal

pressure gradients such as hurricane, tornado.

However, vertical wind speed is usually much smaller than horizontal wind speed because…

Hydrostatic Equilibrium The downward force of gravity balances strong

vertical pressure gradients to create hydrostatic equilibrium.

Forces balance and the atmosphere is held static relative in the vertical direction to Earth’s surface.

Local imbalances initiate various updrafts and downdrafts.

The Role of Density in Hydrostatic Equilibrium

Gravitational force is proportional to mass: G = g m

Denser atmosphere experiences greater gravitational force.

A vertical pressure gradient must increase to offset increased gravitational force to maintain hydrostatic equilibrium.

Higher temperature columns of air are less dense than cooler ones due to expansion in volume or increase in depth (height).

For warm or cold air, greater depth for the same pressure decrease in the vertical translates into smaller or larger vertical pressure gradients, which leads to or maintains hydrostatic equilibrium.

Heating

causes a

density

decrease in a

column of air.

The heated

column

contains the

same amount of

air as the cool

one, but has a

lower density

due to greater

depth or height

and thus

smaller vertical

pressure

gradient.

Upper air heights decrease with increasing latitude

Constant pressure surfaces of cooler air will be at a lower

altitude (height) than those of warmer air.

Height contours indicative of horizontal pressure gradient.

Horizontal Pressure Gradient in Upper Atmosphere Upper air horizontal pressure gradients may be determined

using height contour distribution for given constant pressure.

Isobaric Surface

Isobars Height Contours

Coriolis

Effect

Free moving

objects in the

atmosphere

are influenced

by Earth’s

rotation

Path of

missile

Deflected to

the right in

Northern

Hemisphere

South Pole

South Pole

Coriolis

Force

A resulting

apparent

deflective

force

Path of

missile

Deflected to

the left in

Southern

Hemisphere

The Coriolis force is a sine function of the latitude,

maximum at the poles and zero at the equator.

Taking place regardless of the direction of motion.

Coriolis force increases with speed of moving objects.

Overall deflection effect noticeable only on objects with long

periods of motion.

Only changes direction, DOES NOT change speed

Frictional Force

A force of opposition which slows air in motion (wind).

Initiated at the surface and extend, decreasingly, aloft

by atmospheric turbulence.

Important for air within 1.5 km (1 mi) above the ground

surface which is called the planetary or atmospheric

boundary layer (PBL or ABL).

Because friction reduces wind speed it also reduces

Coriolis deflection.

Friction above 1.5 km is negligible, thus atmosphere

above 1.5 km is called the free atmosphere (flow aloft).

Effects of

Frictional

Force on

Winds

near the

Surface

Balance

between PGF,

Coriolis force,

and frictional

force.

“Northern

Hemisphere”

Effects of Frictional Force on Winds near the Surface

Rougher surface

(Urban)

Strong Friction

Low Wind Speed

Smoother Surface

(Lakes & Oceans)

Weak Friction

Medium Wind Speed

Upper Free

Atmosphere

No Friction

Highest Wind Speed

L

H

L

H

L

H

1000 mb 1000 mb1000 mb

1012 mb

1008 mb 1008 mb1008 mb

1012 mb 1012 mb

For the same PGF,

lower wind speed

means smaller

Coriolis force and

greater angle

between the wind and

the isobar.

For the same PGF,

higher wind speed

means greater

Coriolis force and

smaller angle

between the wind and

the isobar.

Wind parallel

to the isobar

“Northern

Hemisphere”