Bài giảng khí hậu học chương 4

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

Chapter 4

Atmospheric pressure

and wind

G304 – Physical Meteorology and Climatology

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.

• 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

Fig 4-1

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

• 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

• 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

4.1 The concept of pressure (cont.)

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: p 0 = 101325 Pa, T 0 = 288.15 K, ρ0 = 1.225 kg/m³

cm (29.92 in).

• To convert barometric heights to millibars:

1 cm = 13.32 mb

1 inch = 33.865 mb

• 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

4.3 Measuring pressure (cont.)

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 andeastern 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

• 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

4.4 The distribution of pressure (cont.)

Fig 4-7

The gradual poleward decrease in mean temperature results in denser airoccurring at high latitudes As indicated by the hydrostatic equation, pressuredrops 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

Fig 4-8

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

4.4 The distribution of pressure (cont.)

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:

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

• dP/dn = horizontal gradient of pressure (SI

ρ 1

=

4.5 Forces affecting the speed and direction

of the wind (cont.)

• The coriolis force (CF):

• Deflective force (per unit mass):

4.5 Forces affecting the speed and direction

of the wind (cont.)

• The coriolis force (CF):

• Æ magnitude of deflection directly

• 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:

• PGF = CF Æ Geostrophic wind

In geostrophic balance air flows parallel to isobars with high

pressure to the right in NH

dP =

−

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 )

4.5 Forces affecting the speed and direction

of the wind (cont.)

• The Equation of Motion:

dV / dt = PGF + CF + FrF where PGF stands for pressure gradient, CF stands for the Coriolis effect, and FrF stands for friction (acting on

a unit mass of air).

• The equation of motion says the acceleration of a mass

of air is the sum of these three forces.

• The equation of motion is an expression of the conservation of momentum

- A stationary parcel of air in the

upper atmosphere subjected to a

south-to-north PGF (a)

- The horizontal pressure gradient

accelerates the parcel northward (b)

Initially, when the wind speed is low,

the CF is small

- As the parcel speeds up, the

strength of the CF increases and

causes greater displacement to the

right (c).

- The wind speed increases the CF

sufficiently to cause the air to flow

perpendicular to the PGF (d).

- The air flow becomes

unaccelerated, with unchanging

speed and direction known as

wind) Æ occurs only in upper atmos.

4.6 Winds in the upper atmosphere

In common pressure distributions the height contours curve and assumevarying distances from one another In the absence of friction, the air flowsparallel to the contours constantly changing direction and thereforeundergoing an acceleration In order for the air to follow the contours,there must be a continual mismatch between the pressure gradient andCoriolis forces This movement is known as gradient flow (or gradient wind).

4.6 Winds in the upper atmosphere (cont.)

Fig.4-13

Supergeostropic flow (a) occurs in the

upper atmosphere around high-pressure

systems As the air flows, it is constantly

turning to its right This turning motion

occurs because the Coriolis force has a

greater magnitude than the pressure

gradient force (as represented by the

length of the dashed arrows)

Observe the changing direction of the

four solid arrows 1 through 4

the upper atmosphere around

low-pressure systems The low-pressure gradient

force is greater than theCoriolis force and the air turns to its

left in the Northern Hemisphere

4.6 Winds in the upper atmosphere (cont.)

Fig 4-14

• Geostrophic flow cannot exist near the surface

• Friction slows the wind, so that the Coriolis force is less than the pressure gradient force Æ the wind

in BL do not flow parallel to the isobars.

• The air flows at an angle to the right of the pressure gradient force

in the NH (a) and to the left in the

SH (b).

4.7 Near-surface wind

• Enclosed areas of high pressure

marked by roughly circular isobars

or height contours are called

anticyclones

• The wind rotates clockwise around

anticyclones in the NH, as the

Coriolis force deflects the air to the

right and the PGF directs it outward.

• In the boundary layer, the air

spirals out of anticyclones (a), while

in the upper atmosphere it flows

parallel to the height contours (b)

• In the SH, the flow is

counterclockwise (c) and (d).

4.8 Cyclones, anti-cyclones, troughs, and

ridges

Fig 4-16

• Closed low-pressure systems are

called cyclones

• Air spirals counterclockwise into

surface cyclones in the NH (a) and

rotates counterclockwise around an

Elongated zones of high and low pressure are called ridges (a) and troughs (b), respectively.

4.8 Cyclones, anti-cyclones, troughs, and

ridges (cont.)

Maps depicting troughs, ridges, cyclones, and anticyclones

4.8 Cyclones, anti-cyclones, troughs, and

ridges (cont.)

• Direction is always given as that from which the wind blows, so that a “westerly” wind is one from the west.

• It is often expressed by its azimuth, the degree of angle from due north (0o or 360o), moving clockwise

• A simple device for observing wind direction is the wind vane

• Wind speeds are measured with anemometers that have

rotating cups mounted on a moving shaft

• Looking like an airplane without wings (right), an aerovane

indicates both wind direction and speed.

• Upper-level wind measurements are obtained by

rawinsondes , radiosondes whose movement is tracked by radar.

4.9 Measuring wind

An aerovane

A wind vane

4.9 Measuring wind (cont.)

Wind direction