G304 – Physical Meteorology and Climatology

Chapter 4

Atmospheric pressure

and wind

By Vu Thanh Hang, Department of Meteorology, HUS

4.1 The concept of pressure

• The atmosphere contains a tremendous number of gas

molecules being pulled toward Earth by the force of

gravity.

• These molecules exert a force on all surfaces with

which they are in contact, and the amount of that force

exerted per unit of surface area is pressure.

• The standard unit of pressure is the pascal (Pa).

• Air pressure at sea level is roughly 1000 mb (100 kPa)

or more precisely, 1013.2 mb.

Fig. 4-1

• The enclosed air molecules move about

continually and exert a pressure on the interior

walls of the container (a).

• Pressure can increase by increasing the

density of the molecules (b)

• Increasing the temperature (c).

• If the air in the container is a mixture of

gases, each gas exerts its own specific

amount of pressure Æ partial pressure.

• The total pressure exerted is equal to the

sum of the partial pressures Æ Dalton’s law.

4.1 The concept of pressure (cont.)

• In fact, atmospheric pressure is the mass of the air

above being pulled downward by gravity

• The pressure at any point reflects the mass of

atmosphere above that point

• The mass of atmosphere above necessarily decreases

Æ pressure must also decrease

• Air pressure is exerted equally in all directions: up,

down, and sideways

4.1 The concept of pressure (cont.)

• Surface pressure is the pressure actually observed at a

particular location, whereas sea level pressure is the pressure

that would exist if the observation point were at sea level.

• Sea level pressure allows us to compare pressure at different

locations taking into account differences in elevation.

• To correct for elevation, add 1 mb per 10 meters.

• For high-elevation sites, this method is unreliable because we

must account for compressibility of the atmosphere.

4.1 The concept of pressure (cont.)

Pressure will be less at P2 than at P1 due

to pressure decreasing with height

4.1 The concept of pressure (cont.)

• Pressure

does

not

decrease at a constant

rate.

• Surface pressure also

varies from place to place

• Horizontal

pressure

differences are very small

compared

to

vertical

differences

Fig. 4-3 Pressure decreases with altitude by

about half for each 5.5km

4.2 The equation of state

• Temperature, density and pressure are ralated to one

another

• The Equation of State (Ideal Gas Law)

p = ρRT

where p is pressure (Pa), ρ is density (kg m-3), R = 287 (J

kg-1 K-1), T is temperature (K).

• If the air density increases while temperature is held

constant, the pressure will increase, and at constant

density, an increase in temperature leads to an increase in

pressure.

Standard atmosphere: p0 = 101325 Pa, T0 = 288.15 K, ρ0 = 1.225 kg/m³

4.3 Measuring pressure

• The

standard

instrument

for

the

measurement of pressure is the mercury

barometer

• Barometric pressure is often expressed as

the height of the column of mercury in a

barometer, which at sea level averages 76

cm (29.92 in).

• To convert barometric heights to millibars:

1 cm = 13.32 mb

1 inch = 33.865 mb

4.3 Measuring pressure (cont.)

• An alternative instrument for the

observation of pressure is the aneroid

barometer (“without liquid”) which

contains a collapsible chamber from

which some of the air has been

removed.

• The weight of the atmosphere

presses on the chamber and

compresses it by an amount

proportional to the air pressure.

• Aneroid

devices

that

plot

continuous values of pressure over

extended

periods

are

called

barographs.

4.4 The distribution of pressure

• An isobar is a line that connects points having exactly

the same sea level pressure drawn at intervals of 4 mb

on surface weather maps.

• The spacing of the isobars indicates the strength of the

pressure gradient, or rate of change in pressure.

• A dense clustering of isobars indicates a steep pressure

gradient (a rapid change in pressure with distance),

while widely spaced isobars indicate a weak gradient.

A weather map showing the distribution of sea level air pressure.

The pressure is relatively low over the northeastern U.S. and

eastern Canada, and the highest and lowest pressure on the map

are only within about 4 percent of each other.

4.4 The distribution of pressure (cont.)

• If the air over one region exerts a greater pressure than

the air over an adjacent area, the higher-pressure air

will spread out toward the zone of lower pressure as

wind.

• The pressure gradient gives rise to the pressure

gradient force, which sets the air in motion.

• For pressure gradients measured at constant altitude,

we use the term horizontal pressure gradient force.

• Everything else being equal, the greater the horizontal

pressure gradient force, the greater the wind speed.

4.4 The distribution of pressure (cont.)

• The vertical pressure gradient force and the force of

gravity are normally of nearly equal value and

operate in opposite directions, a situation called

hydrostatic equilibrium.

• The Hydrostatic Equation

dp/dz = -ρg

where dp refers to a change in pressure, dz refers

to a change in altitude, and -ρg refers to density and

the acceleration of gravity

4.4 The distribution of pressure (cont.)

• Two columns of air with equal

temperatures, pressures, and

densities (a).

• Heating the column on the right

(b) causes it to expand upward.

It still contains the same amount

of mass, but it has a lower

density to compensate for its

greater height.

• Because

the

pressure

difference between the base and

top is still 500 mb, the vertical

pressure gradient is smaller.

Fig. 4-7

4.4 The distribution of pressure (cont.)

Fig. 4-8

The gradual poleward decrease in mean temperature results in denser air

occurring at high latitudes. As indicated by the hydrostatic equation, pressure

drops more rapidly with height at high latitudes and lowers the height of the

500 mb level. The dashed lines depict the height of the 500 mb level as

they would be drawn on a 500 mb weather map.

4.4 The distribution of pressure (cont.)

A 500 mb map with height contours

labeled in decameters ranging from

5880 m in the south to 5220 m in

the extreme northwest. Contours

for 500 mb maps are drawn at

60 m intervals. These maps depict

the varying heights of pressure levels.

Where height contours are close,

the pressure gradient force is large.

Fig. 4-9

4.5 Forces affecting the speed and direction

of the wind

• The unequal distribution of air across the globe establishes

the horizontal pressure gradients Æ movement of air as wind

• If no other force Æ the wind always flow in the direction of

pressure gradient force

• The pressure gradient force sets air in motion from higher

pressure to lower pressure

• Two other forces:

- due to planetary rotation Æ coriolis force Æ alters the

direction of the wind

- friction force Æ slows the wind

4.5 Forces affecting the speed and direction

of the wind (cont.)

• The pressure gradient force (PGF):

•

Horizontal pressure gradient force per unit

mass:

1 dP

PGF =

ρ dn

•

ρ = air density (1.2 kgm-3 at sea level)

•

dP/dn = horizontal gradient of pressure (SI

units)

– mb/km Æ Pa/m

– 1mb = 100Pa; 1km = 1000m

4.5 Forces affecting the speed and direction

of the wind (cont.)

• The coriolis force (CF):

• Deflective force (per unit mass):

CF = 2ωVsinφ

• ω = angular velocity of spin (Earth: 2π/24 rad/hr = 7.29*10-5

rad/s)

• V = velocity of mass (wind speed)

• φ = latitude

• Coriolis parameter f = 2ωsinφ

4.5 Forces affecting the speed and direction

of the wind (cont.)

• The coriolis force (CF):

•

Æ magnitude

proportional to:

of

deflection

directly

– Horizontal velocity

– Sine of latitude

•

Æ effect is maximum at poles and zero at

equator

•

deflection (turning) of the wind to the right

in the NH and to the left in the SH

•

acting on any moving object, increases

with the object’s speed

•

changes only the direction of a moving

object, never its speed

4.5 Forces affecting the speed and direction

of the wind (cont.)

• Geostrophic balance:

• In absence of friction (from surface)

OR centripetal forces (arises from

curve-isobars)

• ONLY two equal & opposite forces

acting on an air parcel

• For steady flow:

1 dP

−

= 2ωV sin φ

ρ dn

• PGF = CF Æ Geostrophic wind

VG = −

1

dP

2ω sin φρ dn

In geostrophic balance air flows parallel to isobars with high

pressure to the right in NH

4.5 Forces affecting the speed and direction

of the wind (cont.)

• The friction force (FrF):

•

Winds are slowed down by roughness of the surface over which it flows

Æ friction

• Friction: V ↓, CF ↓ Æ Imbalance & cross-isobaric flow

• Friction is important within the lowest 1.5 km of the atmosphere

(planetary boundary layer - PBL)

Chapter 4

Atmospheric pressure

and wind

By Vu Thanh Hang, Department of Meteorology, HUS

4.1 The concept of pressure

• The atmosphere contains a tremendous number of gas

molecules being pulled toward Earth by the force of

gravity.

• These molecules exert a force on all surfaces with

which they are in contact, and the amount of that force

exerted per unit of surface area is pressure.

• The standard unit of pressure is the pascal (Pa).

• Air pressure at sea level is roughly 1000 mb (100 kPa)

or more precisely, 1013.2 mb.

Fig. 4-1

• The enclosed air molecules move about

continually and exert a pressure on the interior

walls of the container (a).

• Pressure can increase by increasing the

density of the molecules (b)

• Increasing the temperature (c).

• If the air in the container is a mixture of

gases, each gas exerts its own specific

amount of pressure Æ partial pressure.

• The total pressure exerted is equal to the

sum of the partial pressures Æ Dalton’s law.

4.1 The concept of pressure (cont.)

• In fact, atmospheric pressure is the mass of the air

above being pulled downward by gravity

• The pressure at any point reflects the mass of

atmosphere above that point

• The mass of atmosphere above necessarily decreases

Æ pressure must also decrease

• Air pressure is exerted equally in all directions: up,

down, and sideways

4.1 The concept of pressure (cont.)

• Surface pressure is the pressure actually observed at a

particular location, whereas sea level pressure is the pressure

that would exist if the observation point were at sea level.

• Sea level pressure allows us to compare pressure at different

locations taking into account differences in elevation.

• To correct for elevation, add 1 mb per 10 meters.

• For high-elevation sites, this method is unreliable because we

must account for compressibility of the atmosphere.

4.1 The concept of pressure (cont.)

Pressure will be less at P2 than at P1 due

to pressure decreasing with height

4.1 The concept of pressure (cont.)

• Pressure

does

not

decrease at a constant

rate.

• Surface pressure also

varies from place to place

• Horizontal

pressure

differences are very small

compared

to

vertical

differences

Fig. 4-3 Pressure decreases with altitude by

about half for each 5.5km

4.2 The equation of state

• Temperature, density and pressure are ralated to one

another

• The Equation of State (Ideal Gas Law)

p = ρRT

where p is pressure (Pa), ρ is density (kg m-3), R = 287 (J

kg-1 K-1), T is temperature (K).

• If the air density increases while temperature is held

constant, the pressure will increase, and at constant

density, an increase in temperature leads to an increase in

pressure.

Standard atmosphere: p0 = 101325 Pa, T0 = 288.15 K, ρ0 = 1.225 kg/m³

4.3 Measuring pressure

• The

standard

instrument

for

the

measurement of pressure is the mercury

barometer

• Barometric pressure is often expressed as

the height of the column of mercury in a

barometer, which at sea level averages 76

cm (29.92 in).

• To convert barometric heights to millibars:

1 cm = 13.32 mb

1 inch = 33.865 mb

4.3 Measuring pressure (cont.)

• An alternative instrument for the

observation of pressure is the aneroid

barometer (“without liquid”) which

contains a collapsible chamber from

which some of the air has been

removed.

• The weight of the atmosphere

presses on the chamber and

compresses it by an amount

proportional to the air pressure.

• Aneroid

devices

that

plot

continuous values of pressure over

extended

periods

are

called

barographs.

4.4 The distribution of pressure

• An isobar is a line that connects points having exactly

the same sea level pressure drawn at intervals of 4 mb

on surface weather maps.

• The spacing of the isobars indicates the strength of the

pressure gradient, or rate of change in pressure.

• A dense clustering of isobars indicates a steep pressure

gradient (a rapid change in pressure with distance),

while widely spaced isobars indicate a weak gradient.

A weather map showing the distribution of sea level air pressure.

The pressure is relatively low over the northeastern U.S. and

eastern Canada, and the highest and lowest pressure on the map

are only within about 4 percent of each other.

4.4 The distribution of pressure (cont.)

• If the air over one region exerts a greater pressure than

the air over an adjacent area, the higher-pressure air

will spread out toward the zone of lower pressure as

wind.

• The pressure gradient gives rise to the pressure

gradient force, which sets the air in motion.

• For pressure gradients measured at constant altitude,

we use the term horizontal pressure gradient force.

• Everything else being equal, the greater the horizontal

pressure gradient force, the greater the wind speed.

4.4 The distribution of pressure (cont.)

• The vertical pressure gradient force and the force of

gravity are normally of nearly equal value and

operate in opposite directions, a situation called

hydrostatic equilibrium.

• The Hydrostatic Equation

dp/dz = -ρg

where dp refers to a change in pressure, dz refers

to a change in altitude, and -ρg refers to density and

the acceleration of gravity

4.4 The distribution of pressure (cont.)

• Two columns of air with equal

temperatures, pressures, and

densities (a).

• Heating the column on the right

(b) causes it to expand upward.

It still contains the same amount

of mass, but it has a lower

density to compensate for its

greater height.

• Because

the

pressure

difference between the base and

top is still 500 mb, the vertical

pressure gradient is smaller.

Fig. 4-7

4.4 The distribution of pressure (cont.)

Fig. 4-8

The gradual poleward decrease in mean temperature results in denser air

occurring at high latitudes. As indicated by the hydrostatic equation, pressure

drops more rapidly with height at high latitudes and lowers the height of the

500 mb level. The dashed lines depict the height of the 500 mb level as

they would be drawn on a 500 mb weather map.

4.4 The distribution of pressure (cont.)

A 500 mb map with height contours

labeled in decameters ranging from

5880 m in the south to 5220 m in

the extreme northwest. Contours

for 500 mb maps are drawn at

60 m intervals. These maps depict

the varying heights of pressure levels.

Where height contours are close,

the pressure gradient force is large.

Fig. 4-9

4.5 Forces affecting the speed and direction

of the wind

• The unequal distribution of air across the globe establishes

the horizontal pressure gradients Æ movement of air as wind

• If no other force Æ the wind always flow in the direction of

pressure gradient force

• The pressure gradient force sets air in motion from higher

pressure to lower pressure

• Two other forces:

- due to planetary rotation Æ coriolis force Æ alters the

direction of the wind

- friction force Æ slows the wind

4.5 Forces affecting the speed and direction

of the wind (cont.)

• The pressure gradient force (PGF):

•

Horizontal pressure gradient force per unit

mass:

1 dP

PGF =

ρ dn

•

ρ = air density (1.2 kgm-3 at sea level)

•

dP/dn = horizontal gradient of pressure (SI

units)

– mb/km Æ Pa/m

– 1mb = 100Pa; 1km = 1000m

4.5 Forces affecting the speed and direction

of the wind (cont.)

• The coriolis force (CF):

• Deflective force (per unit mass):

CF = 2ωVsinφ

• ω = angular velocity of spin (Earth: 2π/24 rad/hr = 7.29*10-5

rad/s)

• V = velocity of mass (wind speed)

• φ = latitude

• Coriolis parameter f = 2ωsinφ

4.5 Forces affecting the speed and direction

of the wind (cont.)

• The coriolis force (CF):

•

Æ magnitude

proportional to:

of

deflection

directly

– Horizontal velocity

– Sine of latitude

•

Æ effect is maximum at poles and zero at

equator

•

deflection (turning) of the wind to the right

in the NH and to the left in the SH

•

acting on any moving object, increases

with the object’s speed

•

changes only the direction of a moving

object, never its speed

4.5 Forces affecting the speed and direction

of the wind (cont.)

• Geostrophic balance:

• In absence of friction (from surface)

OR centripetal forces (arises from

curve-isobars)

• ONLY two equal & opposite forces

acting on an air parcel

• For steady flow:

1 dP

−

= 2ωV sin φ

ρ dn

• PGF = CF Æ Geostrophic wind

VG = −

1

dP

2ω sin φρ dn

In geostrophic balance air flows parallel to isobars with high

pressure to the right in NH

4.5 Forces affecting the speed and direction

of the wind (cont.)

• The friction force (FrF):

•

Winds are slowed down by roughness of the surface over which it flows

Æ friction

• Friction: V ↓, CF ↓ Æ Imbalance & cross-isobaric flow

• Friction is important within the lowest 1.5 km of the atmosphere

(planetary boundary layer - PBL)

## Bài giảng Khí cụ điện - chương 5

## Bài giảng Khí cụ điện - chương 6

## Bài giảng Khí cụ điện - chương 7

## Bài giảng Khí cụ điện - chương 8

## Bài giảng Khí cụ điện - chương 9

## Bài giảng Khí cụ điện - chương 10

## Bài giảng động lực học - Chương 1

## Bài giảng động lực học - Chương 2

## Bài giảng động lực học - Chương 3

## Bài giảng động lực học - Chương 4

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